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* feat(run_eval): add checkpoint resume functionality and update example documentation; - update new bootcamp benchmark dataset * refactor(data_pipeline): optimize data generation pipeline; add multiple preset configurations for data generation * docs: update bootcamp list and add new scripts - Update Fulllist_InternBootcamp.md with new bootcamps and categories - Add new scripts to .gitignore: - examples/pipelines/filter_autogen_configs.py - examples/pipelines/quickgen_data_configs_from_eval_meta.py - Update dependencies in setup.py: - Add scipy and scikit-learn * refactor(internbootcamp): update bootcamp modules and improve error handling - Update import statements in __init__.py files - Add timestamp to target directory name in verl_data_preprocess.py - Improve error handling and scoring logic in bootcamp_judger.py - Remove unnecessary comments and update puzzle descriptions in multiple files
100 lines
944 KiB
JSON
100 lines
944 KiB
JSON
{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=4.71379, x1=7.11460, y=0.10690\nx0=8.59885, x1=6.52206, y=0.06752\nx0=1.95430, x1=2.36132, y=0.70206\nx0=-8.14847, x1=-0.93523, y=0.11549\nx0=-4.84361, x1=-0.54685, y=0.31056\nx0=-4.13021, x1=-2.74673, y=0.30072\nx0=-3.70515, x1=8.66992, y=0.08801\nx0=-8.63488, x1=8.32965, y=0.05482\nx0=-8.34765, x1=8.31596, y=0.05680\nx0=-6.37411, x1=-3.97097, y=0.13699\nx0=-0.36169, x1=7.01542, y=0.15580\nx0=-4.44089, x1=8.33527, y=0.08772\nx0=1.93746, x1=-1.11139, y=1.14466\nx0=-5.16639, x1=2.12049, y=0.24105\nx0=2.95004, x1=4.82474, y=0.23543\nx0=-2.84435, x1=7.64286, y=0.11678\nx0=5.30873, x1=2.82247, y=0.20970\nx0=8.08481, x1=2.60242, y=0.10791\nx0=-2.82601, x1=-8.34417, y=0.10049\nx0=8.07073, x1=-6.02014, y=0.07739\nx0=-9.43866, x1=1.99621, y=0.08415\nx0=2.78038, x1=-3.88838, y=0.32193\nx0=-5.68680, x1=-0.99107, y=0.22649\nx0=-1.07374, x1=2.41219, y=0.89170\nx0=1.56048, x1=8.48923, y=0.10457\nx0=1.07137, x1=4.38708, y=0.35723\nx0=0.62484, x1=-5.07572, y=0.28416\nx0=9.80861, x1=-0.00327, y=0.08146\nx0=-1.69578, x1=6.81710, y=0.15580\nx0=-4.53101, x1=3.88397, y=0.21268\nx0=8.62420, x1=-9.31809, y=0.04902\nx0=-5.78148, x1=-1.98833, y=0.20315\nx0=7.19281, x1=2.54419, y=0.13287\nx0=9.55658, x1=-4.75831, y=0.06898\nx0=5.20213, x1=9.35881, y=0.06858\nx0=-4.69253, x1=8.43630, y=0.08404\nx0=1.72508, x1=5.24826, y=0.24600\nx0=5.73717, x1=-3.81320, y=0.16176\nx0=-2.56175, x1=-7.05496, y=0.13714\nx0=-0.39039, x1=2.39351, y=1.01506\nx0=0.26226, x1=-5.17588, y=0.27721\nx0=-5.47945, x1=0.08273, y=0.24976\nx0=-0.16788, x1=9.60482, y=0.08485\nx0=6.91849, x1=-1.92621, y=0.14932\nx0=-3.08491, x1=-2.74649, y=0.41973\nx0=-3.47329, x1=5.70079, y=0.17181\nx0=-4.88880, x1=-5.63190, y=0.13884\nx0=-9.67627, x1=8.37229, y=0.04827\nx0=-8.80483, x1=-9.44564, y=0.04741\nx0=-7.10499, x1=2.50627, y=0.13614\nx0=-4.96786, x1=-9.47858, y=0.06866\nx0=-9.96546, x1=-1.38490, y=0.07750\nx0=1.32279, x1=-4.56181, y=0.32573\nx0=5.41544, x1=-5.65378, y=0.12640\nx0=0.10702, x1=-6.11556, y=0.20299\nx0=-0.61748, x1=-5.28175, y=0.26422\nx0=-6.77427, x1=-1.04481, y=0.16332\nx0=5.82396, x1=-3.42314, y=0.16794\nx0=-5.54485, x1=-0.43531, y=0.24290\nx0=-5.33255, x1=-0.37186, y=0.26166\nx0=-5.17943, x1=-1.80358, y=0.24938\nx0=-1.60127, x1=-8.24790, y=0.11021\nx0=5.48282, x1=0.25728, y=0.24901\nx0=5.59269, x1=-2.75249, y=0.19582\nx0=6.36634, x1=-7.12471, y=0.08575\nx0=-2.74400, x1=8.77679, y=0.09242\nx0=5.46791, x1=5.62857, y=0.12583\nx0=7.83007, x1=3.10625, y=0.10965\nx0=1.55646, x1=-9.85993, y=0.07871\nx0=3.62696, x1=6.77266, y=0.13110\nx0=4.14360, x1=9.31425, y=0.07553\nx0=8.01067, x1=-9.24478, y=0.05276\nx0=5.80657, x1=-8.53507, y=0.07369\nx0=0.60607, x1=7.93791, y=0.12237\nx0=-8.64648, x1=8.96026, y=0.05094\nx0=-8.61165, x1=-1.72519, y=0.10109\nx0=-2.65491, x1=1.25970, y=0.75221\nx0=-8.77398, x1=1.14220, y=0.09964\nx0=-5.87760, x1=-6.23497, y=0.10607\nx0=-6.92289, x1=9.64569, y=0.05596\nx0=3.06235, x1=7.44397, y=0.11978\nx0=-5.07655, x1=-6.03435, y=0.12464\nx0=-0.30349, x1=-6.90508, y=0.16073\nx0=0.60020, x1=1.67820, y=1.54542\nx0=-3.71175, x1=-4.14445, y=0.24277\nx0=0.94401, x1=-0.47596, y=2.56600\nx0=7.19463, x1=2.89667, y=0.12871\nx0=-4.58182, x1=3.26158, y=0.23788\nx0=4.64935, x1=-5.76016, y=0.14086\nx0=0.99394, x1=-1.14526, y=1.86066\nx0=-2.35662, x1=-1.27152, y=0.87237\nx0=-9.13864, x1=4.98021, y=0.07252\nx0=0.86828, x1=-1.32997, y=1.76884\nx0=-3.50438, x1=0.17907, y=0.55894\nx0=4.67379, x1=5.83676, y=0.13814\nx0=4.97482, x1=0.12736, y=0.29890\nx0=-2.47755, x1=-7.44200, y=0.12594\nx0=-0.89554, x1=9.40593, y=0.08765\nx0=-8.72708, x1=-4.09314, y=0.08429\nx0=-6.20689, x1=0.97601, y=0.19287\nx0=9.42995, x1=-9.05556, y=0.04626\nx0=6.70144, x1=-7.62827, y=0.07612\nx0=4.43756, x1=-1.49709, y=0.33426\nx0=7.94060, x1=-0.13852, y=0.12294\nx0=-9.69256, x1=-5.58607, y=0.06292\nx0=-9.97948, x1=2.13677, y=0.07536\nx0=-9.00294, x1=6.50271, y=0.06383\nx0=9.81489, x1=3.14534, y=0.07392\nx0=7.26654, x1=-8.46185, y=0.06329\nx0=2.18365, x1=6.85226, y=0.14892\nx0=-6.07298, x1=-2.93694, y=0.16840\nx0=3.59026, x1=-9.91517, y=0.07067\nx0=7.22082, x1=-7.21053, y=0.07538\nx0=9.78590, x1=1.07273, y=0.08088\nx0=-1.20151, x1=-8.51428, y=0.10535\nx0=-0.75919, x1=9.41420, y=0.08772\nx0=0.26975, x1=7.33185, y=0.14330\nx0=5.23509, x1=-6.30975, y=0.11558\nx0=2.56599, x1=1.27686, y=0.78319\nx0=0.23475, x1=-5.26348, y=0.26882\nx0=3.93718, x1=-6.51394, y=0.13348\nx0=6.48922, x1=-3.09406, y=0.14902\nx0=-2.04097, x1=-3.58632, y=0.42045\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.67301, x1=-1.86158, y=1.35171\nx0=-8.72949, x1=6.95443, y=0.06321\nx0=7.24497, x1=2.06639, y=0.13615\nx0=6.18915, x1=-7.34193, y=0.08492\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 8 / (2 + x0**2 + x1**2)", "data": [[4.713789195428539, 7.114598304582742, 0.10689854012684244], [8.59884546754149, 6.5220587383817445, 0.06752343007818806], [1.9542966329699567, 2.36131743608556, 0.7020564325907512], [-8.148469601401382, -0.9352314333906016, 0.11548641886325231], [-4.843606032068011, -0.5468540788086678, 0.31056420505844073], [-4.130206218108947, -2.7467252222641525, 0.30071680152832686], [-3.705154610045911, 8.66991753694489, 0.08801302164981892], [-8.634879072607486, 8.32965115901709, 0.054815461169392746], [-8.34765328751563, 8.315959888010344, 0.05680264812243005], [-6.37411151251059, -3.970965735193161, 0.13699130614081184], [-0.3616878447037948, 7.015418459198436, 0.15580293608924345], [-4.4408870402527505, 8.335272474144965, 0.08772098637201088], [1.937462861081027, -1.1113887335139374, 1.1446645264377195], [-5.166390047941958, 2.1204918315107335, 0.24105046125860544], [2.9500425923933644, 4.824737770130341, 0.23542674705369732], [-2.8443511069223355, 7.642864112313866, 0.11678200461040142], [5.308726858119568, 2.822470334719485, 0.20970449686522485], [8.0848084732139, 2.60242442181635, 0.10790870897133711], [-2.8260088629071873, -8.344172670862871, 0.10048793972301491], [8.070732416692511, -6.020137342130121, 0.07738532374894472], [-9.438656215405256, 1.9962129611787027, 0.08414578070887654], [2.7803798391339445, -3.8883773720165316, 0.32193171083393196], [-5.686798707630734, -0.9910680566652488, 0.22648841183894766], [-1.07373969347673, 2.412190461425265, 0.891704718851558], [1.5604800122554003, 8.489234980989217, 0.10457214457024548], [1.0713701840453442, 4.387081082092044, 0.3572335291985886], [0.6248381192321482, -5.0757220408997945, 0.2841577415414502], [9.808609154392045, -0.003271367753461263, 0.08145907520493482], [-1.69577509722129, 6.817100618545609, 0.15579808203023726], [-4.531014025029236, 3.883969153404971, 0.21267938969724146], [8.62420143631105, -9.318086190672387, 0.04901853235765407], [-5.781478315134853, -1.9883347320516247, 0.20315413805847438], [7.192808452313379, 2.5441855457462843, 0.13286967679481418], [9.556575446403034, -4.7583139385125195, 0.06898354466339106], [5.202131780922478, 9.358807098622915, 0.06858155196760762], [-4.692534375832869, 8.436296806198264, 0.0840415738503255], [1.7250826311245948, 5.248263834978905, 0.24600107293442405], [5.737171447229164, -3.813203901683102, 0.1617610596221923], [-2.5617459634784723, -7.0549585433203195, 0.13713898019403006], [-0.3903905054612711, 2.3935088999278253, 1.0150623064530093], [0.26225981457235825, -5.17588160188202, 0.27721439182135277], [-5.4794514094659625, 0.0827302532091867, 0.24975623757265897], [-0.16787745539289567, 9.604815553353152, 0.08485302929675155], [6.918493409460304, -1.9262109997684078, 0.1493210375993578], [-3.0849074085114037, -2.7464906797263744, 0.4197301552406336], [-3.4732928005581787, 5.7007872934034864, 0.17181119996677469], [-4.8887971811357716, -5.631901700801323, 0.13884392214956592], [-9.676272596912398, 8.372291000851686, 0.04827259302362703], [-8.804825945635937, -9.445643893083005, 0.047408770395402464], [-7.1049914569453065, 2.506271213838394, 0.13614171222131613], [-4.967858393130726, -9.478576914527924, 0.06865595149856861], [-9.965456803682713, -1.3848991616962696, 0.07749814670888062], [1.3227922764053464, -4.561809066840857, 0.3257344724047992], [5.41543784251629, -5.653780334800742, 0.12639788336817945], [0.10701734767343751, -6.115561112603485, 0.2029862297125082], [-0.617478612948064, -5.281747289134073, 0.2642170726346536], [-6.774274507588878, -1.0448116603844344, 0.1633238810329715], [5.823959314096921, -3.4231374409776905, 0.16793890169915943], [-5.54485346242455, -0.4353074996976751, 0.24290347966107714], [-5.3325520624114, -0.37185760530297074, 0.2616569001276565], [-5.179427460453669, -1.8035772748376537, 0.24938153531666296], [-1.6012722602329212, -8.247897762371707, 0.11020514772981074], [5.482818404847672, 0.2572787676283834, 0.24900793662444293], [5.592690987417463, -2.752492320068516, 0.19581731065526908], [6.366341903277291, -7.124709767031463, 0.08575244693698025], [-2.7439997745247773, 8.776792929297791, 0.09241970262022484], [5.46790574307402, 5.628567362149875, 0.12582817793562656], [7.830069202958477, 3.106249455977343, 0.10965097225660492], [1.5564628501330091, -9.85993299923292, 0.07870850724543442], [3.6269556993270022, 6.77265546677393, 0.13109667178597187], [4.143604159213666, 9.314246914033554, 0.07552538454632489], [8.010669126741789, -9.244781621645116, 0.052757639477660795], [5.80657349685049, -8.535071449294518, 0.07368942861707152], [0.6060698394689581, 7.937907612833378, 0.12236588706084106], [-8.646477344564925, 8.960256579779887, 0.050939915155642605], [-8.611653233635774, -1.7251911441399397, 0.10109069799396639], [-2.654908228839547, 1.2596969130801483, 0.7522067383503532], [-8.773979641690365, 1.1422029251326862, 0.09964210266211251], [-5.877595755798424, -6.234968682523617, 0.10607130070263142], [-6.922893889447632, 9.645687693878742, 0.055957457993007664], [3.0623506617405756, 7.4439736773851415, 0.11977709060912131], [-5.076551536068616, -6.034354288736448, 0.12464008776283829], [-0.3034859562355585, -6.9050841887330705, 0.16073200124669157], [0.6001973976932273, 1.6782001317213346, 1.5454181197523718], [-3.7117538028861734, -4.14445194165082, 0.24276559888545277], [0.9440086099715721, -0.4759643936970086, 2.5659988045126307], [7.194631833071977, 2.896674748229774, 0.1287136879282782], [-4.58181543925993, 3.261577899330362, 0.2378763132120345], [4.6493451857533135, -5.760164797682439, 0.1408552150910151], [0.9939444180144186, -1.1452640298303844, 1.8606575843762003], [-2.3566241502894014, -1.271519201335245, 0.8723683202774983], [-9.138636957961603, 4.980210565202967, 0.0725181680905903], [0.8682753682769491, -1.329971273004693, 1.7688448353509887], [-3.504378269346673, 0.17906906356479624, 0.5589428741961846], [4.6737867010748, 5.836758306030788, 0.13814055643234524], [4.974817086789507, 0.12736106412609516, 0.2988975252097908], [-2.4775484224946798, -7.442004331352072, 0.12594126404282285], [-0.8955359681207753, 9.405925182122857, 0.0876487436960916], [-8.72708105926381, -4.093144972979195, 0.08428524777435759], [-6.206885907726065, 0.9760071265696446, 0.19287322543065666], [9.42994926862901, -9.055559821913516, 0.046262267053117916], [6.701436497392322, -7.628270761114737, 0.07611815239498164], [4.437564795483217, -1.4970870803571508, 0.33426298777940566], [7.94060259939026, -0.13852360261732422, 0.12294006538298394], [-9.692562407378393, -5.586071184794732, 0.06291783473403903], [-9.979483498218524, 2.136770549270505, 0.07536087548710911], [-9.002937820779014, 6.502707912531719, 0.0638273599607623], [9.814893534996749, 3.1453392198536534, 0.07391987317270644], [7.26654415251144, -8.461847489451355, 0.06328837194886609], [2.183648091123393, 6.852258360020777, 0.14891543875653168], [-6.072984939110702, -2.9369445110418235, 0.16839698380453086], [3.5902604980566935, -9.915168037093565, 0.07067104868006299], [7.220824412966014, -7.210527488790062, 0.07537782294976261], [9.785900429088844, 1.0727329011336977, 0.08087784564133486], [-1.2015097353855815, -8.51428340475836, 0.10535097688773849], [-0.7591859515237491, 9.414196766105047, 0.08771596652011873], [0.26974766937089, 7.331852363416193, 0.14329515806939477], [5.2350900562351015, -6.309746073869677, 0.11557509745830438], [2.565993992614505, 1.2768611392578002, 0.7831850530103965], [0.23475413483605756, -5.263480973237018, 0.26882315292159886], [3.9371780984701754, -6.51393618910938, 0.1334829765268325], [6.489224575411715, -3.0940556759871622, 0.1490223682328994], [-2.0409701066114057, -3.586317164582347, 0.4204500650937427], [-0.6730123849764365, -1.8615770777328713, 1.3517132801918739], [-8.729485532246741, 6.954432592491788, 0.0632071046242132], [7.244973804570915, 2.0663863417432395, 0.13614797037687262], [6.18914798370805, -7.341929832315548, 0.08491713842648886]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.52822, y=-7.28011\nx0=-1.51647, y=1.04323\nx0=-7.19163, y=-343.70760\nx0=-8.38017, y=-555.45290\nx0=-2.48322, y=-6.62609\nx0=-2.68051, y=-9.72547\nx0=0.63962, y=0.22854\nx0=-7.79479, y=-442.91098\nx0=-4.91454, y=-99.78328\nx0=8.13956, y=507.20734\nx0=-6.18829, y=-212.83124\nx0=-3.49982, y=-29.85041\nx0=-5.30390, y=-128.68387\nx0=-0.86850, y=1.40864\nx0=4.24793, y=60.60662\nx0=-9.41079, y=-796.21446\nx0=6.44832, y=242.96237\nx0=-8.15809, y=-510.79268\nx0=-8.61766, y=-605.95563\nx0=3.45324, y=28.51252\nx0=8.50524, y=581.71861\nx0=-9.07215, y=-710.80861\nx0=-9.31892, y=-772.41364\nx0=2.46990, y=6.72000\nx0=-8.66840, y=-617.12129\nx0=3.51284, y=30.42563\nx0=-6.03192, y=-195.95688\nx0=-0.15004, y=0.98782\nx0=-1.87633, y=-0.53956\nx0=-4.50488, y=-74.20159\nx0=1.17530, y=-0.68360\nx0=3.70806, y=37.22588\nx0=2.20972, y=3.62338\nx0=-1.47444, y=1.14926\nx0=-6.76051, y=-282.50088\nx0=-5.92082, y=-184.50715\nx0=8.21879, y=522.78513\nx0=-3.74772, y=-38.57741\nx0=9.02635, y=699.76616\nx0=-0.85828, y=1.39983\nx0=-1.84014, y=-0.32051\nx0=-1.06201, y=1.52380\nx0=8.40899, y=561.45590\nx0=3.32561, y=24.66366\nx0=-2.31981, y=-4.50222\nx0=0.37608, y=0.74289\nx0=5.53679, y=148.31992\nx0=3.43489, y=27.93866\nx0=-3.33974, y=-24.90889\nx0=-3.15831, y=-19.93073\nx0=1.31077, y=-0.69418\nx0=6.38318, y=235.18514\nx0=8.45304, y=570.67180\nx0=0.36993, y=0.75213\nx0=5.93668, y=186.16959\nx0=-7.29074, y=-358.89503\nx0=-4.75472, y=-89.23587\nx0=-6.02025, y=-194.73281\nx0=-4.66166, y=-83.43242\nx0=6.28437, y=223.69872\nx0=-0.06857, y=0.99628\nx0=2.39284, y=5.70112\nx0=2.33124, y=4.94920\nx0=-9.54622, y=-832.16857\nx0=3.57555, y=32.51963\nx0=5.90053, y=182.51911\nx0=5.06490, y=110.46895\nx0=0.26351, y=0.88493\nx0=-1.98811, y=-1.30956\nx0=1.28789, y=-0.70161\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.52831, y=827.37695\nx0=3.82191, y=41.58254\nx0=-6.63890, y=-266.62113\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x0**5 - 3 * x0**3 + 1) / (x0**2 + 1)", "data": [[-2.5282234446149214, -7.28011178385541], [-1.5164655818803539, 1.043230848748557], [-7.1916275317364065, -343.70760094498473], [-8.380173485922178, -555.4529038540657], [-2.483219121802689, -6.626087532849777], [-2.6805051325663793, -9.7254671126082], [0.6396167219171325, 0.22853661053132496], [-7.794788695160467, -442.9109753684611], [-4.914543137551483, -99.78327681728754], [8.139564661698039, 507.2073428740961], [-6.188287887622086, -212.83124170104395], [-3.4998241894172377, -29.850412658371624], [-5.30389541865897, -128.68387354637724], [-0.868501039634042, 1.4086427357374653], [4.2479324911313086, 60.60661555963798], [-9.410793765884478, -796.2144558842773], [6.448319290870906, 242.96237083283805], [-8.158088694528047, -510.79268440364086], [-8.617655916802196, -605.9556289696635], [3.4532390401361095, 28.5125180197472], [8.505242717614763, 581.7186100054944], [-9.072150914657994, -710.8086123253134], [-9.318920730651836, -772.4136376635892], [2.4698967308729465, 6.719998102088463], [-8.668395571537673, -617.1212907769795], [3.512842994729022, 30.425625271938088], [-6.031921635963295, -195.95687520682154], [-0.1500382662799069, 0.9878194376417698], [-1.8763310989699349, -0.539555565464074], [-4.5048811922160015, -74.20159499808827], [1.1752957794404821, -0.6835962667484814], [3.7080594217211633, 37.22587781727773], [2.2097231398827937, 3.6233752299552062], [-1.4744419506881208, 1.149261645538502], [-6.760507229571324, -282.5008817525927], [-5.920823982416657, -184.50714718166066], [8.218785468065644, 522.7851287609616], [-3.7477234967587325, -38.57740911514588], [9.026349345029129, 699.7661563524524], [-0.8582819632379639, 1.3998277930915408], [-1.840138148260479, -0.3205132039997432], [-1.0620052953263208, 1.5238033610721498], [8.408989172801064, 561.4559013960967], [3.3256079228598896, 24.66366027441444], [-2.319808164390336, -4.502216316727743], [0.3760761873856353, 0.7428850269443306], [5.536787674127368, 148.31991905606432], [3.434893576597558, 27.938661298120586], [-3.3397391045065428, -24.9088921562508], [-3.158313507841224, -19.93072999527936], [1.3107688989379245, -0.6941837146111624], [6.383177354583751, 235.18514360903032], [8.453044448814286, 570.671799046655], [0.3699284537357741, 0.7521300431339354], [5.936681713496277, 186.16958780908317], [-7.290736556738309, -358.8950304383102], [-4.7547167856114925, -89.23586661997396], [-6.020246963031037, -194.73280544761633], [-4.6616576453353105, -83.43241677877984], [6.284371532816216, 223.69872117281164], [-0.06856762728806842, 0.9962815632652636], [2.3928433767018547, 5.701116419242585], [2.331243271783796, 4.949201940551858], [-9.54621922484357, -832.1685709394195], [3.5755472508702653, 32.51962926467438], [5.900529823482186, 182.5191133446715], [5.064899385778611, 110.46894623778208], [0.2635146861900104, 0.8849260194836185], [-1.9881144799757084, -1.3095615894075678], [1.287891115459887, -0.7016057030007483], [9.528314732648305, 827.376949203678], [3.8219085451764627, 41.58253816880335], [-6.638902372507227, -266.6211338297848]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.42522, y=143.36137\nx0=-5.06294, y=14064.12683\nx0=1.52919, y=34.06077\nx0=-6.10352, y=44420.36890\nx0=4.59528, y=12033.85149\nx0=5.98427, y=55140.20144\nx0=-4.60225, y=7805.18067\nx0=-2.09393, y=56.36902\nx0=0.87903, y=3.91418\nx0=9.59929, y=873394.18130\nx0=4.79252, y=15310.22278\nx0=6.31854, y=75599.47725\nx0=-0.34874, y=-0.25810\nx0=9.48847, y=815726.23941\nx0=-5.90316, y=36185.58976\nx0=-7.80241, y=199985.98129\nx0=3.62196, y=3117.36980\nx0=-6.95619, y=99057.99528\nx0=4.24578, y=7661.44175\nx0=-7.98627, y=230582.22886\nx0=-9.33276, y=596835.52738\nx0=-0.11300, y=-0.10153\nx0=-2.07988, y=53.99229\nx0=1.52429, y=33.55958\nx0=-1.18694, y=0.97489\nx0=-2.42153, y=141.98578\nx0=-1.41221, y=4.05850\nx0=-5.56512, y=25180.42927\nx0=9.35248, y=749325.07071\nx0=0.51778, y=1.05307\nx0=2.56585, y=465.95160\nx0=2.52290, y=425.54117\nx0=4.14038, y=6640.71974\nx0=-0.71713, y=-0.36083\nx0=4.24107, y=7613.14429\nx0=0.53041, y=1.10437\nx0=-1.48882, y=5.91671\nx0=4.34995, y=8796.09507\nx0=-6.42163, y=60675.50029\nx0=-2.20241, y=77.80223\nx0=-2.94007, y=481.20163\nx0=-9.13795, y=524796.53962\nx0=-6.52206, y=66734.77602\nx0=-7.78354, y=197046.78010\nx0=2.23283, y=222.61977\nx0=-2.25845, y=91.28007\nx0=-8.49579, y=336429.25165\nx0=6.62055, y=99191.93626\nx0=5.78038, y=45104.36171\nx0=4.56637, y=11607.06105\nx0=-2.06522, y=51.60151\nx0=7.57591, y=217813.37245\nx0=-1.22492, y=1.30909\nx0=-1.31456, y=2.36288\nx0=1.59010, y=40.86089\nx0=0.95942, y=5.20318\nx0=-1.06435, y=0.23396\nx0=4.03366, y=5725.65937\nx0=3.08273, y=1268.85479\nx0=-9.49871, y=664531.43875\nx0=5.55675, y=35898.35694\nx0=2.56934, y=469.37255\nx0=-5.56191, y=25091.24127\nx0=-2.28176, y=97.42981\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=4.49728, y=10638.21429\nx0=6.08166, y=60553.93536\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**6 + x0**5 + x0**4 + x0**3 + x0**2 + x0", "data": [[-2.4252220329990877, 143.36137157014014], [-5.062944473309534, 14064.126830732439], [1.5291909675879989, 34.06076569781613], [-6.103523581588785, 44420.36890197853], [4.595279331068072, 12033.85148741103], [5.984272626338438, 55140.201435124494], [-4.60224949963788, 7805.180671169195], [-2.0939292884675247, 56.36901651409532], [0.8790304254029664, 3.9141771995107426], [9.599288720672043, 873394.1812959389], [4.792515569223777, 15310.222781991286], [6.318542185169992, 75599.47725450085], [-0.34874139223805223, -0.2581028677437301], [9.488474174882235, 815726.2394132469], [-5.903164370918505, 36185.589759611816], [-7.802414986422184, 199985.9812948567], [3.6219618442204844, 3117.3697979263397], [-6.956185982508096, 99057.99528485877], [4.245782265393167, 7661.441747345854], [-7.986267137548262, 230582.22886128968], [-9.33276346306561, 596835.5273797505], [-0.11300414204718834, -0.10153053565318879], [-2.0798768726647427, 53.992290541974725], [1.5242878811947662, 33.55957715547683], [-1.1869407401359684, 0.9748909443953524], [-2.4215260959853424, 141.98577656640106], [-1.4122135972405268, 4.058500833570344], [-5.56511725961008, 25180.429265210158], [9.352475750696676, 749325.0707112859], [0.5177849770961629, 1.0530715402179296], [2.565846406663992, 465.95159911026127], [2.522900161479429, 425.54116964495825], [4.140383616573889, 6640.719736529332], [-0.7171279472730809, -0.36082887388704454], [4.2410683308488455, 7613.144294265006], [0.530411403414659, 1.104371608464011], [-1.4888238186261908, 5.9167149503668615], [4.34995437766659, 8796.095072241898], [-6.42163459417665, 60675.50028569941], [-2.202413131394896, 77.80223333362872], [-2.9400702960647163, 481.20163381517636], [-9.137951420805951, 524796.53962395], [-6.522062728940727, 66734.77602369992], [-7.783542191865227, 197046.7801006502], [2.2328262963282377, 222.61976988892587], [-2.25844907485353, 91.2800691734679], [-8.49578879403669, 336429.2516502109], [6.62055484961072, 99191.93625808597], [5.7803751199058, 45104.361710340054], [4.566367948827999, 11607.061049320333], [-2.0652152573614675, 51.601512659873535], [7.575907166568918, 217813.37244754127], [-1.2249152071119003, 1.309094650141228], [-1.3145584249604454, 2.362881052927669], [1.5900981061900854, 40.8608883809778], [0.9594201040691885, 5.203175002270035], [-1.0643459773486441, 0.2339591732202857], [4.033657110497625, 5725.659374879146], [3.0827335870412647, 1268.8547878014156], [-9.498708788321492, 664531.4387501571], [5.556746722147732, 35898.3569425056], [2.5693354849622967, 469.3725512598905], [-5.561908724396048, 25091.24126561425], [-2.2817576248534106, 97.42980526824428], [4.4972838777056054, 10638.214288419957], [6.081663865873342, 60553.93536076591]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=4.56071, x1=-6.31997, y=-43.23525\nx0=-4.16538, x1=6.76596, y=-42.27420\nx0=4.51317, x1=-8.25927, y=-55.91327\nx0=-6.83333, x1=-7.10135, y=72.78877\nx0=-7.96850, x1=-0.59052, y=7.05830\nx0=9.31348, x1=-0.48159, y=-6.72788\nx0=7.27386, x1=-4.73858, y=-51.70169\nx0=1.07373, x1=0.60309, y=0.97133\nx0=-1.26949, x1=-8.11719, y=15.45702\nx0=-1.77940, x1=-0.06299, y=0.16814\nx0=0.90448, x1=-6.03150, y=-8.18304\nx0=1.22190, x1=-0.59108, y=-1.08335\nx0=9.51396, x1=6.68540, y=95.40685\nx0=-6.65476, x1=4.60571, y=-45.97478\nx0=-4.98174, x1=-2.39889, y=17.92594\nx0=-4.60881, x1=-7.47133, y=51.65092\nx0=-8.39311, x1=3.97499, y=-50.04381\nx0=-0.87224, x1=-9.44313, y=12.35498\nx0=7.73966, x1=4.35514, y=50.56090\nx0=4.34959, x1=-0.61967, y=-4.04300\nx0=8.99657, x1=-3.74560, y=-50.54624\nx0=-7.51756, x1=-9.91560, y=111.81174\nx0=9.09484, x1=8.37777, y=114.29162\nx0=-8.17111, x1=4.85476, y=-59.50317\nx0=9.02674, x1=-1.03896, y=-14.06768\nx0=2.96998, x1=6.84434, y=30.49131\nx0=3.55520, x1=-7.15402, y=-38.15098\nx0=3.67429, x1=5.34487, y=29.45790\nx0=8.76840, x1=-5.15765, y=-67.83653\nx0=2.56734, x1=-8.59272, y=-33.09062\nx0=8.01703, x1=8.98173, y=108.01020\nx0=-8.34126, x1=-4.11710, y=51.51272\nx0=-3.42223, x1=-4.75150, y=24.39111\nx0=1.59627, x1=4.22701, y=10.12116\nx0=-0.87955, x1=3.92893, y=-5.18356\nx0=-3.79596, x1=4.31619, y=-24.57613\nx0=1.81371, x1=-7.14737, y=-19.44490\nx0=7.28411, x1=5.26066, y=57.47883\nx0=2.22569, x1=-9.77847, y=-32.64574\nx0=5.33619, x1=-9.56760, y=-76.58185\nx0=3.82309, x1=7.93159, y=45.48476\nx0=-3.96554, x1=1.64425, y=-9.78049\nx0=-3.69279, x1=2.71596, y=-15.04422\nx0=-4.24480, x1=-0.00395, y=0.02518\nx0=4.95065, x1=-3.94154, y=-29.26977\nx0=-6.22808, x1=9.47557, y=-88.52200\nx0=7.32435, x1=-4.50866, y=-49.53450\nx0=-0.79499, x1=0.84515, y=-1.00782\nx0=1.12102, x1=0.93416, y=1.57081\nx0=9.82666, x1=-4.21457, y=-62.12267\nx0=9.22196, x1=-0.96285, y=-13.31909\nx0=-0.22876, x1=-9.10709, y=3.12496\nx0=7.07104, x1=-2.40103, y=-25.46669\nx0=6.61413, x1=-9.20521, y=-91.32661\nx0=9.03109, x1=-3.92944, y=-53.23073\nx0=-3.37103, x1=1.20892, y=-6.11299\nx0=-3.96654, x1=4.65218, y=-27.67962\nx0=-1.03044, x1=-2.29382, y=3.54547\nx0=7.79806, x1=-1.60277, y=-18.74775\nx0=9.00523, x1=-4.74132, y=-64.04511\nx0=-6.49960, x1=-7.26402, y=70.81983\nx0=-9.76683, x1=-9.84024, y=144.16191\nx0=5.48229, x1=-9.80645, y=-80.64275\nx0=0.58012, x1=-6.47002, y=-5.63007\nx0=-8.03718, x1=6.17194, y=-74.40757\nx0=-9.54410, x1=-0.80695, y=11.55243\nx0=9.95187, x1=-2.65599, y=-39.64804\nx0=1.80345, x1=5.16120, y=13.96194\nx0=1.44519, x1=0.45822, y=0.99332\nx0=8.58382, x1=-8.66076, y=-111.51356\nx0=-5.87802, x1=-9.15393, y=80.71044\nx0=6.90492, x1=-6.40588, y=-66.34808\nx0=7.52856, x1=-5.35071, y=-60.42470\nx0=-5.35709, x1=-7.79171, y=62.61136\nx0=-5.19643, x1=-1.46071, y=11.38568\nx0=-6.66284, x1=2.25082, y=-22.49527\nx0=-8.84089, x1=-0.30776, y=4.08124\nx0=9.40585, x1=-8.81261, y=-124.33512\nx0=-4.04869, x1=-0.35279, y=2.14248\nx0=-6.69153, x1=-9.83088, y=98.67546\nx0=7.76948, x1=1.35811, y=15.82771\nx0=1.52629, x1=-5.34010, y=-12.22581\nx0=0.79320, x1=4.89920, y=5.82904\nx0=2.54675, x1=6.54538, y=25.00421\nx0=5.01860, x1=-2.49499, y=-18.78207\nx0=-8.43464, x1=-3.27154, y=41.39142\nx0=-4.22027, x1=-8.43303, y=53.38451\nx0=2.79569, x1=4.05670, y=17.01196\nx0=-5.46180, x1=-3.79025, y=31.05240\nx0=4.58102, x1=3.68465, y=25.31916\nx0=9.60993, x1=0.93305, y=13.44980\nx0=9.98876, x1=5.21436, y=78.12745\nx0=7.89697, x1=-1.77115, y=-20.98010\nx0=-1.37759, x1=7.76209, y=-16.03948\nx0=-8.37607, x1=7.87440, y=-98.93485\nx0=-4.19377, x1=4.24344, y=-26.69402\nx0=1.31615, x1=5.40165, y=10.66409\nx0=3.75265, x1=-0.73061, y=-4.11260\nx0=9.04850, x1=3.52285, y=47.81479\nx0=-1.36460, x1=9.71787, y=-19.89154\nx0=4.66885, x1=7.38696, y=51.73292\nx0=1.72218, x1=2.35231, y=6.07664\nx0=-3.35661, x1=-8.01565, y=40.35812\nx0=-6.98861, x1=1.44661, y=-15.16474\nx0=-0.16410, x1=-5.02059, y=1.23580\nx0=-2.75948, x1=-4.50790, y=18.65918\nx0=2.57897, x1=-3.04469, y=-11.77825\nx0=2.87395, x1=0.96616, y=4.16505\nx0=-3.40773, x1=-8.74575, y=44.70470\nx0=-3.53410, x1=2.02358, y=-10.72730\nx0=-2.59590, x1=-9.00328, y=35.05745\nx0=-1.32256, x1=4.26997, y=-8.47095\nx0=-2.26423, x1=1.50236, y=-5.10254\nx0=8.10611, x1=0.56200, y=6.83343\nx0=-5.28497, x1=-3.62513, y=28.73811\nx0=1.13434, x1=2.48751, y=4.23252\nx0=-5.01622, x1=2.05849, y=-15.48873\nx0=-1.21812, x1=8.02255, y=-14.65864\nx0=7.11223, x1=6.47277, y=69.05373\nx0=-3.37667, x1=0.17789, y=-0.90101\nx0=-1.32675, x1=4.85754, y=-9.66712\nx0=8.62710, x1=5.44610, y=70.47602\nx0=-1.14572, x1=5.07669, y=-8.72468\nx0=-9.50777, x1=-5.99580, y=85.51009\nx0=6.30014, x1=7.97187, y=75.33586\nx0=3.34375, x1=3.79951, y=19.05692\nx0=-3.31943, x1=-1.80974, y=9.01096\nx0=4.17225, x1=-3.54833, y=-22.20682\nx0=4.94951, x1=9.41437, y=69.89475\nx0=8.30660, x1=7.31504, y=91.14474\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-8.94611, x1=-8.19660, y=109.99145\nx0=-6.93163, x1=6.96524, y=-72.42073\nx0=0.17967, x1=0.01019, y=0.00275\nx0=8.59348, x1=0.65929, y=8.49837\nx0=-6.78033, x1=-7.30712, y=74.31701\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (3/2) * x0 * x1", "data": [[4.560705232090607, -6.319966082958395, -43.235253571775296], [-4.165382300617626, 6.765957858725791, -42.27420166719171], [4.513170257539855, -8.259274563845718, -55.91326846560593], [-6.833327441770589, -7.101349760755012, 72.78877229066734], [-7.968500591670429, -0.5905168017644478, 7.058300226376997], [9.313481280099186, -0.48158714874568176, -6.727879341868874], [7.273860763822299, -4.738582931672745, -51.70168869421863], [1.073727926776609, 0.6030860555154955, 0.9713255100848041], [-1.269489431446873, -8.11718591123774, 15.45702259110865], [-1.7794016578751481, -0.06299385753032638, 0.16813706178812046], [0.9044784039620861, -6.031495227228538, -8.183035764942911], [1.2218953248087683, -0.5910751673444175, -1.083347975383056], [9.513956427302922, 6.685396155143724, 95.40685157894382], [-6.654757181033684, 4.605706141721557, -45.97478403052871], [-4.981740338933349, -2.3988862253193215, 17.92594241577723], [-4.608808690594266, -7.4713329564764, 51.65091639019767], [-8.393108291808769, 3.9749920897486675, -50.04380860251571], [-0.872237819884278, -9.443126447194603, 12.35497803778888], [7.739657289795975, 4.35513693231824, 50.56090095941482], [4.349590985792117, -0.6196747917783867, -4.042997832662817], [8.996565706007644, -3.7455950433479472, -50.54623787336453], [-7.517562662860769, -9.915602098865756, 111.81174017732562], [9.094837355658267, 8.377765543704442, 114.29162253574478], [-8.17110528881897, 4.854763240958119, -59.50317239123521], [9.026736200648074, -1.0389640597125833, -14.067681733469794], [2.9699789226745636, 6.844339155963542, 30.4913145492719], [3.5552005036966676, -7.154023030733498, -38.15097942348194], [3.674292326773047, 5.344866304380641, 29.457901874720406], [8.768397818616652, -5.15765270582582, -67.83652610241809], [2.5673385145637084, -8.592718121560225, -33.09062426740663], [8.017031131551903, 8.981729279232901, 108.0102048701721], [-8.341256166320187, -4.11710325077963, 51.512719316913724], [-3.4222315569796162, -4.751501904279833, 24.39110963981278], [1.5962659579777512, 4.227014152767133, 10.12115819392851], [-0.8795528822543979, 3.928932563833577, -5.183555941054475], [-3.7959630528695376, 4.316186977495438, -24.576129443773983], [1.8137128870124108, -7.147365705015172, -19.444903931064847], [7.284106986115496, 5.260661543778971, 57.478832253944304], [2.225688824334128, -9.778466468117825, -32.645735305823784], [5.33619466028361, -9.567598427361483, -76.58185145973631], [3.823088480897212, 7.931590762394556, 45.48475991835205], [-3.9655433862260807, 1.6442461773818646, -9.780494331066253], [-3.6927948635401897, 2.7159597714830834, -15.044223440571777], [-4.24480456331052, -0.003953952770718416, 0.025175635146389715], [4.950650572408167, -3.9415382495123126, -29.26976788667522], [-6.228084725490186, 9.475571974167043, -88.52199761638897], [7.324347661674246, -4.508660606988517, -49.534496661118695], [-0.7949877940175121, 0.8451490886101389, -1.0078248143551278], [1.1210167639589699, 0.934155987814485, 1.5708067837390332], [9.826659763983695, -4.214566494330645, -62.12266648870915], [9.221957922150224, -0.9628536522077944, -13.31909379877342], [-0.22875652890084552, -9.10709442690326, 3.124960964205937], [7.07104402611267, -2.401030551633365, -25.466689107961674], [6.614127355814713, -9.205206477457812, -91.32661196771475], [9.031089423822095, -3.92944336622687, -53.23073163935907], [-3.371033571022588, 1.2089248760305704, -6.11298951291506], [-3.966543664730356, 4.652180512892414, -27.679615710893135], [-1.0304398135012818, -2.2938235545841295, 3.5454706736857764], [7.7980629817892755, -1.6027699598155731, -18.747751637942557], [9.005233874779766, -4.741324888674927, -64.04510924824778], [-6.4995952810232005, -7.26402436674654, 70.81982774301503], [-9.766827486739523, -9.84024168059911, 144.16191438335295], [5.482291093393162, -9.806453154389928, -80.64274617913377], [0.5801187529427914, -6.470023240789395, -5.630072720936432], [-8.037182492495681, 6.171944983994813, -74.40757225501447], [-9.544101834463019, -0.8069505664063943, 11.55242757174036], [9.951867649621981, -2.6559866349352497, -39.648041205060686], [1.8034478644678291, 5.161203548026311, 13.96194227515775], [1.4451945884458084, 0.4582165763534931, 0.9933181747233507], [8.58381763943975, -8.660758395625123, -111.51355603093927], [-5.87802058298567, -9.153925523078946, 80.71044395966386], [6.904916654744643, -6.405877480409137, -66.34807515409604], [7.5285579336613075, -5.350710054056751, -60.42469594228542], [-5.35709085170649, -7.791711307315426, 62.611358045336225], [-5.196427808712865, -1.4607064419586262, 11.385683363039742], [-6.66283675780976, 2.250820514209561, -22.495274485961595], [-8.84088785275872, -0.3077551226736155, 4.081242788504155], [9.405847708192258, -8.812610987955278, -124.3351152963736], [-4.048686188380359, -0.352785938020606, 2.1424793320782554], [-6.6915300924534264, -9.830881634905765, 98.6754604429795], [7.7694759760629175, 1.358110884586921, 15.82771483594146], [1.5262883074449203, -5.340104459544987, -12.225808495706984], [0.7931956591915359, 4.899200459396692, 5.829036806853952], [2.546752035001653, 6.545384462121191, 25.004206798163015], [5.018601715588105, -2.4949940385265723, -18.782072043197324], [-8.434640157544965, -3.271542431225516, 41.391424751290536], [-4.220272760915442, -8.433026062769924, 53.384505277196865], [2.7956940456673163, 4.056704765196331, 17.011958035634418], [-5.461801354184431, -3.7902513849915875, 31.0524002208697], [4.581015950962168, 3.684649316877964, 25.319155941479718], [9.6099308435955, 0.9330489007758658, 13.449803115223304], [9.988758181629567, 5.214358272230413, 78.12744578053403], [7.896965133827585, -1.7711530512234788, -20.980100838276233], [-1.3775907201094988, 7.7620905113732555, -16.039475785676686], [-8.376074478811804, 7.874401068234523, -98.9348547353514], [-4.1937721502017595, 4.243438991969395, -26.694024398402213], [1.3161515131228008, 5.401652072858338, 10.664088823583123], [3.7526501254534033, -0.7306133987949153, -4.112604693968514], [9.048498168761846, 3.52285305798803, 47.814794166032634], [-1.364601534893172, 9.717874951845669, -19.891540612782762], [4.668847539434498, 7.386964901531925, 51.7329193566095], [1.722178458923242, 2.3523083142052386, 6.076642061205461], [-3.3566113426777626, -8.01564739569535, 40.35811945094472], [-6.988614870901369, 1.446613978643505, -15.164741945402692], [-0.1640978687585566, -5.020588260994678, 1.235801750315182], [-2.7594771265062352, -4.507902295669936, 18.659179910139205], [2.5789692112001106, -3.0446916770341703, -11.778249139002535], [2.873950221668027, 0.9661614695801539, 4.165049954500485], [-3.4077261865537034, -8.745753757429952, 44.70470115051675], [-3.534099836864275, 2.0235793958311383, -10.727297419033102], [-2.5959014569749623, -9.003281639260443, 35.05744788736817], [-1.32256112665746, 4.269971183702312, -8.470946849268326], [-2.26422655247344, 1.502364829326691, -5.102541507095583], [8.106108055570328, 0.5619984798116135, 6.833430606628799], [-5.2849747750155185, -3.6251332317178075, 28.73810652854865], [1.134340144594134, 2.487509449341232, 4.232522742667511], [-5.016221424579827, 2.0584858839523648, -15.488731489915494], [-1.2181197856774517, 8.02254953504788, -14.658639480328894], [7.112226179566406, 6.472772017385495, 69.05372789462096], [-3.3766718048151585, 0.17788898335154713, -0.9010090717056035], [-1.3267522455891179, 4.857536245915522, -9.66712068344843], [8.627099587405493, 5.446095814772288, 70.47601643488919], [-1.1457168076069024, 5.076693864849505, -8.724680232049382], [-9.507771668748987, -5.995802937083738, 85.5100879449101], [6.300143147528669, 7.9718672944005, 75.33585766173783], [3.3437488438958436, 3.79951086279792, 19.056915082275367], [-3.319431316677452, -1.8097389166509146, 9.010956052411457], [4.172252469203642, -3.5483341387717093, -22.20681880807476], [4.949509732294414, 9.414366201125503, 69.89474570378141], [8.306603759601991, 7.315042628446633, 91.14474089865546], [-8.946106010787647, -8.196598120372137, 109.99145356900786], [-6.93163217186626, 6.9652404547418385, -72.42072723130936], [0.17967226022188498, 0.01018789262039732, 0.0027457225410069735], [8.59347905206262, 0.6592883481620007, 8.498370913798679], [-6.7803253702976685, -7.307123193931013, 74.31700916355148]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=5.06395, y=10.33291\nx0=-4.80065, y=-1.90316\nx0=4.46427, y=9.90885\nx0=1.87626, y=8.99928\nx0=-6.51845, y=-3.36052\nx0=3.35102, y=9.27775\nx0=9.02755, y=13.72397\nx0=-1.73569, y=-0.06927\nx0=-1.32414, y=-0.00835\nx0=5.66426, y=10.79431\nx0=-3.23480, y=-0.75934\nx0=-0.72914, y=0.00879\nx0=7.98671, y=12.77755\nx0=4.03114, y=9.63390\nx0=4.05647, y=9.64910\nx0=-4.48902, y=-1.65648\nx0=-6.99168, y=-3.78201\nx0=-1.76252, y=-0.07554\nx0=-0.44065, y=0.10705\nx0=-8.30617, y=-4.98098\nx0=-4.70958, y=-1.83033\nx0=-3.15828, y=-0.71136\nx0=4.62482, y=10.01802\nx0=-0.68477, y=0.01454\nx0=4.90359, y=10.21538\nx0=9.78197, y=14.42280\nx0=2.73138, y=9.06829\nx0=-0.15265, y=0.51737\nx0=8.75815, y=13.47680\nx0=8.42506, y=13.17322\nx0=-4.01485, y=-1.29664\nx0=2.15245, y=9.00102\nx0=-5.48211, y=-2.46451\nx0=-0.54315, y=0.05187\nx0=2.27723, y=9.00545\nx0=-3.94449, y=-1.24510\nx0=8.89318, y=13.60052\nx0=-8.65785, y=-5.30722\nx0=7.32429, y=12.18957\nx0=-7.62125, y=-4.35175\nx0=-8.98752, y=-5.61470\nx0=-4.75124, y=-1.86357\nx0=4.90768, y=10.21834\nx0=-8.67896, y=-5.32686\nx0=-0.06530, y=0.76349\nx0=-7.44633, y=-4.19254\nx0=1.92260, y=8.99983\nx0=9.73756, y=14.38142\nx0=-1.58730, y=-0.03967\nx0=-5.43693, y=-2.42650\nx0=6.50058, y=11.48008\nx0=-4.24243, y=-1.46677\nx0=8.46328, y=13.20793\nx0=9.11504, y=13.80453\nx0=3.14186, y=9.19262\nx0=-1.68970, y=-0.05917\nx0=-4.32059, y=-1.52633\nx0=5.49866, y=10.66400\nx0=4.25129, y=9.76981\nx0=-7.82384, y=-4.53694\nx0=-6.81000, y=-3.61943\nx0=5.51707, y=10.67839\nx0=-3.46095, y=-0.90663\nx0=-4.58970, y=-1.73538\nx0=-8.53632, y=-5.19426\nx0=0.94222, y=7.74829\nx0=-3.47090, y=-0.91329\nx0=7.12411, y=12.01467\nx0=4.76042, y=10.11285\nx0=6.91782, y=11.83599\nx0=-6.25007, y=-3.12456\nx0=5.30410, y=10.51372\nx0=5.45659, y=10.63124\nx0=9.59711, y=14.25074\nx0=4.54945, y=9.96633\nx0=7.93693, y=12.73292\nx0=6.05407, y=11.10872\nx0=6.75190, y=11.69354\nx0=6.60431, y=11.56783\nx0=-5.00224, y=-2.06634\nx0=7.26152, y=12.13457\nx0=4.86802, y=10.18969\nx0=0.72186, y=6.38741\nx0=-1.14878, y=-0.00095\nx0=8.27942, y=13.04124\nx0=1.96631, y=8.99999\nx0=0.59185, y=5.31849\nx0=7.02441, y=11.92811\nx0=-9.26272, y=-5.87250\nx0=-1.08887, y=-0.00021\nx0=3.08796, y=9.17291\nx0=-6.59717, y=-3.43018\nx0=4.91492, y=10.22359\nx0=5.35756, y=10.55470\nx0=-6.70204, y=-3.52326\nx0=8.93989, y=13.64339\nx0=8.60421, y=13.33621\nx0=-2.53367, y=-0.36244\nx0=-0.25901, y=0.30680\nx0=-7.88760, y=-4.59539\nx0=1.16568, y=8.51324\nx0=-4.02472, y=-1.30391\nx0=0.24773, y=2.38740\nx0=-4.28117, y=-1.49623\nx0=3.74253, y=9.46973\nx0=5.37285, y=10.56646\nx0=2.39834, y=9.01452\nx0=-4.17409, y=-1.41515\nx0=1.89956, y=8.99963\nx0=-5.64695, y=-2.60404\nx0=7.46207, y=12.31075\nx0=-8.24478, y=-4.92424\nx0=-9.75026, y=-6.33146\nx0=-7.31864, y=-4.07674\nx0=-6.54844, y=-3.38704\nx0=-4.27684, y=-1.49293\nx0=-0.12621, y=0.58412\nx0=-3.82876, y=-1.16149\nx0=5.46267, y=10.63597\nx0=0.08905, y=1.40568\nx0=4.09529, y=9.67262\nx0=8.75903, y=13.47761\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-8.64655, y=-5.29671\nx0=-8.14514, y=-4.83227\nx0=7.01663, y=11.92137\nx0=-5.70159, y=-2.65057\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x0 + 1)**3 / (x0**2 - x0 + 1)", "data": [[5.0639526474868095, 10.332911987107785], [-4.800650187595625, -1.9031571984777484], [4.4642732937653395, 9.908850960795728], [1.8762551661138431, 8.999283350302285], [-6.518451231481448, -3.3605195719483825], [3.3510187220814522, 9.277749897337106], [9.027550122370648, 13.723969338221291], [-1.7356906067674451, -0.0692700121729263], [-1.324135205253281, -0.008351950591845498], [5.6642585600184425, 10.794311122617279], [-3.2348006344979208, -0.7593401692736123], [-0.7291414706106387, 0.008789568683575487], [7.986712847009258, 12.777550692844327], [4.031138394566858, 9.633901777515414], [4.056465565338181, 9.649097374567269], [-4.489018004153634, -1.6564812269322327], [-6.991678294210408, -3.782005805259983], [-1.762517554391776, -0.07554165385733985], [-0.4406460657007969, 0.10705118323062761], [-8.306166943364454, -4.9809812784553875], [-4.709577136838769, -1.8303303040495773], [-3.1582793886635985, -0.7113582660802721], [4.624822348125468, 10.01801712455513], [-0.6847697298303341, 0.014544630952220517], [4.903591392063332, 10.215380220035868], [9.78196877323284, 14.422804724320818], [2.731378221997403, 9.068287867978503], [-0.152647641139529, 0.5173728826833641], [8.758148819846337, 13.476800496620127], [8.42506016041498, 13.17321813320339], [-4.014848704478835, -1.2966350763874877], [2.1524528312756868, 9.00101801065155], [-5.482109634960124, -2.4645109846869726], [-0.5431496881337345, 0.05187261777566203], [2.277234969877979, 9.005451635217257], [-3.9444915201051423, -1.2450959429458015], [8.89318109000498, 13.600516447652348], [-8.657854215649643, -5.3072223550884114], [7.32429065963105, 12.189568089787484], [-7.621252952216137, -4.351748427701853], [-8.987518121877077, -5.614702201958439], [-4.751240647194632, -1.8635744935686538], [4.907682328623631, 10.218344187889706], [-8.67895907802259, -5.326860525439683], [-0.06530426301190495, 0.7634876483284373], [-7.4463343471566645, -4.192536412877708], [1.9226006642672466, 8.999832837942767], [9.737559670064353, 14.381422853008843], [-1.5873044229444702, -0.0396677515080056], [-5.43693344811982, -2.4264999060605446], [6.500582126686869, 11.480082809852766], [-4.242428026303246, -1.4667741826857703], [8.463275349415028, 13.207927102180204], [9.115036479883887, 13.80452573351126], [3.1418632392293127, 9.192616801714813], [-1.6896977976942829, -0.05916876121251918], [-4.3205876435749, -1.526334150634424], [5.498661481291013, 10.664003816244726], [4.2512903072708355, 9.769808056250593], [-7.823840404871709, -4.536942450798253], [-6.809998635347703, -3.6194314596560453], [5.517071194558305, 10.678385312541803], [-3.460951655767433, -0.9066302495394605], [-4.589702109916911, -1.7353834173061067], [-8.53631991404604, -5.194263830496201], [0.9422159735322726, 7.748288526795342], [-3.4709000831980834, -0.9132860880445427], [7.124113022859511, 12.014672769566712], [4.760416897959443, 10.112847754683987], [6.917815583331269, 11.83599398567111], [-6.250074137254769, -3.1245587707383056], [5.304096262652783, 10.513721727992756], [5.4565947249824465, 10.631243850154867], [9.597113748526553, 14.250740027711892], [4.549449168542834, 9.966328126100676], [7.936926280756914, 12.732917203891446], [6.0540743024148505, 11.10872075445866], [6.751898523771423, 11.693538490498621], [6.604313408915452, 11.567831815931592], [-5.002237007665009, -2.0663412727496864], [7.261518698551384, 12.134570997605817], [4.868023696702323, 10.189689347487809], [0.7218573475894363, 6.387409946996528], [-1.14877749062199, -0.0009494543627640013], [8.279415612083014, 13.041240671899955], [1.966311329811873, 8.999986816118643], [0.5918519204349089, 5.3184932708632084], [7.024407674835384, 11.928109149489872], [-9.262719805882927, -5.872504244783322], [-1.0888687685534926, -0.00021433937807140512], [3.0879583153340775, 9.172911790855089], [-6.597172243051432, -3.430176061593414], [4.914915135195365, 10.223589031700211], [5.35756495493507, 10.55470061583607], [-6.702035585408909, -3.5232589749619954], [8.939890748102357, 13.64339323838951], [8.60420834644669, 13.336205529259184], [-2.5336696881456877, -0.3624389601414394], [-0.25901189550303627, 0.30680168591086954], [-7.887598671307394, -4.595394872089547], [1.1656792117313053, 8.51324338678078], [-4.024718751743423, -1.3039069180623224], [0.24772624388139874, 2.3873964583405094], [-4.281167334975152, -1.496226094709411], [3.7425343977319407, 9.469732173311906], [5.372850176279789, 10.566460967595052], [2.3983420362498897, 9.014518096183572], [-4.174086352406084, -1.415154406601512], [1.8995554376700579, 8.999625881229507], [-5.646948340265419, -2.6040448765007858], [7.462065419407196, 12.310746673287365], [-8.244779031323176, -4.924238831973275], [-9.750262537149975, -6.331464636584482], [-7.31864083696528, -4.076736786425176], [-6.548444376150004, -3.3870362824157136], [-4.27683634147118, -1.4929266701843837], [-0.1262106874250808, 0.5841184315151863], [-3.8287572326791057, -1.1614931679516471], [5.462670083174784, 10.63596623706199], [0.08905159026823739, 1.4056824590574173], [4.095294674984853, 9.67262293106457], [8.75903137295915, 13.477607925686858], [-8.64655005759129, -5.2967064936941535], [-8.14513669799737, -4.832273106656956], [7.016625291395865, 11.92136856140796], [-5.7015858090303535, -2.650574110417745]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.85962, x1=-2.74072, y=-7.83740\nx0=-6.16854, x1=0.02233, y=-0.13775\nx0=7.42938, x1=-8.42610, y=-62.60065\nx0=-2.09175, x1=-0.51378, y=1.07470\nx0=-6.53018, x1=7.60374, y=-49.65377\nx0=9.25199, x1=0.16227, y=1.50127\nx0=-3.52076, x1=-4.54690, y=16.00857\nx0=1.14625, x1=-0.50410, y=-0.57783\nx0=4.28642, x1=-1.94915, y=-8.35486\nx0=-5.15411, x1=-2.08791, y=10.76129\nx0=4.51139, x1=-1.66896, y=-7.52933\nx0=-2.06639, x1=-2.73862, y=5.65907\nx0=8.32526, x1=-6.20152, y=-51.62925\nx0=5.98537, x1=3.95186, y=23.65334\nx0=1.81659, x1=-9.24807, y=-16.79993\nx0=3.72163, x1=-2.29329, y=-8.53476\nx0=-3.58169, x1=-1.21139, y=4.33881\nx0=6.58216, x1=-5.16326, y=-33.98539\nx0=7.27995, x1=5.63841, y=41.04731\nx0=0.11050, x1=-4.95673, y=-0.54770\nx0=5.67445, x1=2.57752, y=14.62602\nx0=-3.74296, x1=-2.00877, y=7.51873\nx0=1.05004, x1=4.10626, y=4.31176\nx0=-5.11747, x1=-1.35094, y=6.91341\nx0=5.82747, x1=-8.99377, y=-52.41091\nx0=-0.70978, x1=9.09293, y=-6.45398\nx0=-2.60126, x1=8.52299, y=-22.17047\nx0=4.62600, x1=1.02476, y=4.74052\nx0=0.21995, x1=-0.85915, y=-0.18897\nx0=-5.06916, x1=-0.38873, y=1.97055\nx0=4.59377, x1=-3.94566, y=-18.12544\nx0=-9.30872, x1=-2.90341, y=27.02702\nx0=-2.46041, x1=-0.05274, y=0.12976\nx0=8.77732, x1=3.86189, y=33.89704\nx0=-8.73529, x1=-3.70757, y=32.38669\nx0=2.00118, x1=7.51621, y=15.04130\nx0=-0.80983, x1=-3.86161, y=3.12724\nx0=-4.29995, x1=-5.75119, y=24.72983\nx0=9.57064, x1=-5.83207, y=-55.81659\nx0=1.76680, x1=-3.75985, y=-6.64290\nx0=8.38532, x1=-3.36692, y=-28.23267\nx0=7.92859, x1=-9.43938, y=-74.84095\nx0=-5.28754, x1=-8.08656, y=42.75804\nx0=6.29241, x1=-6.12251, y=-38.52534\nx0=2.14636, x1=2.83383, y=6.08240\nx0=6.23175, x1=6.78236, y=42.26602\nx0=-7.54673, x1=9.33172, y=-70.42403\nx0=0.23185, x1=9.50041, y=2.20270\nx0=-2.92475, x1=1.84352, y=-5.39183\nx0=-1.48158, x1=9.95246, y=-14.74539\nx0=0.85396, x1=-2.76643, y=-2.36243\nx0=0.61190, x1=6.44440, y=3.94334\nx0=5.19053, x1=-9.34997, y=-48.53125\nx0=-4.47746, x1=1.49507, y=-6.69411\nx0=-3.73002, x1=3.56144, y=-13.28422\nx0=-4.33983, x1=4.93417, y=-21.41347\nx0=-6.07199, x1=-8.98754, y=54.57224\nx0=-1.58081, x1=9.00705, y=-14.23842\nx0=-8.87399, x1=-5.32975, y=47.29618\nx0=5.13993, x1=3.06258, y=15.74146\nx0=0.01242, x1=4.66298, y=0.05791\nx0=9.37308, x1=-3.61301, y=-33.86507\nx0=-4.77403, x1=-7.79467, y=37.21200\nx0=3.05584, x1=-0.21673, y=-0.66229\nx0=7.84566, x1=9.61547, y=75.43970\nx0=-4.52041, x1=-5.97301, y=27.00045\nx0=-5.17747, x1=-0.58589, y=3.03341\nx0=-7.99790, x1=-8.48158, y=67.83480\nx0=3.24625, x1=7.98879, y=25.93365\nx0=-2.66161, x1=6.07472, y=-16.16852\nx0=-6.37708, x1=3.97449, y=-25.34563\nx0=2.05393, x1=1.71412, y=3.52067\nx0=8.53863, x1=3.68524, y=31.46692\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-4.90880, x1=-7.45286, y=36.58455\nx0=8.76889, x1=-3.80898, y=-33.40051\nx0=-1.02554, x1=6.98471, y=-7.16309\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1", "data": [[2.8596151601786097, -2.7407196742025564, -7.83740353014941], [-6.168538046781611, 0.022331398345340148, -0.13775208033106662], [7.429376645531988, -8.426096568163697, -62.600645056512604], [-2.0917548695727417, -0.5137786378018419, 1.0746989675044527], [-6.530181041830849, 7.603736249095917, -49.65377430092816], [9.251987585600922, 0.16226511032448343, 1.5012747862982847], [-3.5207649322482997, -4.546900825438247, 16.008568976613827], [1.1462543047657725, -0.5040986087007138, -0.5778252002496299], [4.28641754012312, -1.9491465179324496, -8.354855822735555], [-5.15410689306202, -2.087906225824656, 10.761291870589968], [4.511387870200094, -1.668961301413292, -7.529331771029289], [-2.0663927923668135, -2.7386212276874122, 5.6590671659160225], [8.325262474755142, -6.201515745343142, -51.62924632130843], [5.985370162913187, 3.9518589538412137, 23.65333867036252], [1.816588059129744, -9.248070471748255, -16.79993438896826], [3.721629197512426, -2.2932863347157344, -8.53476138153433], [-3.581686685362957, -1.2113878447525757, 4.338811714360829], [6.5821565789054155, -5.163261114319426, -33.985393112224116], [7.279946568154802, 5.638407880797711, 41.04730810167029], [0.1104970834897312, -4.956731352476296, -0.5477043580907415], [5.674454214689291, 2.5775207607106054, 14.626023544063443], [-3.7429575141480598, -2.0087679261227027, 7.518733003260585], [1.0500440470088073, 4.106261478884644, 4.311755421364402], [-5.117474655932077, -1.3509413278060904, 6.913408006698896], [5.827467062437847, -8.993771474442475, -52.4109070344066], [-0.7097796628991944, 9.092929206991297, -6.453976227304522], [-2.601255772349189, 8.52298591898084, -22.170466319399768], [4.625996933567686, 1.024755866092983, 4.7405174942016375], [0.2199469479699694, -0.8591522751349085, -0.18896792075737856], [-5.069164407929955, -0.3887318224510814, 1.9705455185987686], [4.5937666377222826, -3.945660748571944, -18.125444710560124], [-9.308718397277884, -2.9034088220583936, 27.02701511671388], [-2.4604099085688613, -0.05273772571672808, 0.1297564229088246], [8.777324674360742, 3.861887384921758, 33.89703943327623], [-8.735288337645436, -3.7075698089158156, 32.38669131282864], [2.0011808760496557, 7.516212600691091, 15.041300916826458], [-0.8098270671810397, -3.8616139372881664, 3.127239489419503], [-4.299954321904147, -5.751185409578423, 24.729834557988816], [9.57063822556755, -5.832065125698767, -55.81658542601203], [1.7667986479342872, -3.759851132800918, -6.64289989786686], [8.38531503673022, -3.366918684931772, -28.23267387620632], [7.928588469189069, -9.439378338117683, -74.84094624791294], [-5.287541113029728, -8.086563427944524, 42.758036588379284], [6.292407953689537, -6.1225108643850845, -38.525336059607305], [2.146356514439196, 2.833825789360313, 6.0824004437793056], [6.231754819853556, 6.782361902774884, 42.26601647760852], [-7.5467342247459275, 9.331722050762274, -70.4240261763039], [0.2318530572862585, 9.500413567952101, 2.202699931213546], [-2.9247475402312944, 1.8435205771169656, -5.391832273288621], [-1.4815821254326664, 9.952464361523766, -14.745393302039247], [0.853964760065562, -2.766427404606673, -2.362431514813733], [0.6119008202392351, 6.444404131355132, 3.9433361739293202], [5.190525233896853, -9.349969416721846, -48.53125219365858], [-4.477463910874895, 1.4950666072512337, -6.6941067783215695], [-3.730015179514627, 3.5614391612033245, -13.28422213220624], [-4.339834759804528, 4.9341671341750075, -21.413470039577792], [-6.071991046419269, -8.98753590967226, 54.57223757290163], [-1.5808090371749284, 9.007046474083474, -14.23842046448573], [-8.873988505446519, -5.329754979698742, 47.29618442669298], [5.139934939851269, 3.062580418799998, 15.741464100694442], [0.01241960247977758, 4.662975904044568, 0.057912307101015026], [9.373076518248435, -3.613014930950264, -33.865065409370914], [-4.774029845424286, -7.794672327300207, 37.21199832583397], [3.0558418787226103, -0.2167280185242575, -0.6622865552989957], [7.845661494602648, 9.615467405247049, 75.43970237395361], [-4.520405512722538, -5.973014957996298, 27.00044974370065], [-5.177474570662874, -0.5858852645106687, 3.033406058330079], [-7.997896788311869, -8.481580067272947, 67.83480197985227], [3.2462545947037924, 7.988790492622073, 25.933647842800376], [-2.661608104105704, 6.07471810343014, -16.16851893424729], [-6.377082348871157, 3.9744875813214335, -25.345634600652534], [2.0539253653429324, 1.7141193427176518, 3.52067319723274], [8.538625715362727, 3.685243578223412, 31.466915584393778], [-4.908795994120747, -7.452855624978898, 36.5845478366567], [8.768892146421404, -3.808976814463221, -33.40050687424775], [-1.0255391900516475, 6.984707188549372, -7.163090952892843]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-9.82902, x1=5.77254, y=-56.73840\nx0=0.32108, x1=5.61880, y=1.80410\nx0=0.02025, x1=-2.20364, y=-0.04461\nx0=-8.12603, x1=-2.13862, y=17.37851\nx0=-1.40459, x1=4.13762, y=-5.81166\nx0=-4.09592, x1=-0.64326, y=2.63475\nx0=0.61801, x1=4.55180, y=2.81308\nx0=2.60651, x1=-0.84770, y=-2.20953\nx0=1.92768, x1=-7.85954, y=-15.15072\nx0=6.99536, x1=5.39575, y=37.74526\nx0=6.02678, x1=-6.82792, y=-41.15034\nx0=-9.83372, x1=-4.66622, y=45.88630\nx0=-9.19967, x1=7.93626, y=-73.01091\nx0=-8.13095, x1=0.12233, y=-0.99468\nx0=5.92175, x1=-0.91208, y=-5.40113\nx0=-4.07825, x1=-3.09825, y=12.63542\nx0=6.83299, x1=3.15575, y=21.56318\nx0=5.30587, x1=-6.17951, y=-32.78768\nx0=3.54948, x1=1.15000, y=4.08189\nx0=-5.45776, x1=-9.54715, y=52.10609\nx0=9.44283, x1=3.91378, y=36.95720\nx0=3.45096, x1=7.14741, y=24.66543\nx0=-4.74315, x1=-4.19736, y=19.90869\nx0=0.19922, x1=-1.52990, y=-0.30479\nx0=-6.51105, x1=-9.67393, y=62.98742\nx0=-8.78376, x1=5.32834, y=-46.80286\nx0=-1.63966, x1=6.11006, y=-10.01843\nx0=-4.84091, x1=7.20068, y=-34.85785\nx0=-9.38751, x1=2.81894, y=-26.46285\nx0=5.03026, x1=1.96812, y=9.90016\nx0=-6.52705, x1=3.00391, y=-19.60669\nx0=1.45664, x1=-3.93618, y=-5.73358\nx0=-8.58806, x1=-8.69104, y=74.63916\nx0=-4.84956, x1=-0.45031, y=2.18380\nx0=4.23042, x1=-8.83482, y=-37.37498\nx0=-6.24482, x1=-5.33796, y=33.33463\nx0=-0.50198, x1=1.92100, y=-0.96430\nx0=4.41742, x1=3.85089, y=17.01098\nx0=6.54937, x1=-3.19095, y=-20.89871\nx0=6.03087, x1=-6.85406, y=-41.33599\nx0=-7.31878, x1=0.76148, y=-5.57312\nx0=-0.55109, x1=1.50662, y=-0.83029\nx0=-6.39221, x1=8.54398, y=-54.61486\nx0=-7.78806, x1=-6.08561, y=47.39507\nx0=2.72357, x1=6.80950, y=18.54616\nx0=-5.61086, x1=-2.38924, y=13.40570\nx0=-2.23129, x1=9.10456, y=-20.31494\nx0=-0.36056, x1=6.61044, y=-2.38343\nx0=-4.59246, x1=0.03443, y=-0.15813\nx0=2.58473, x1=6.62757, y=17.13046\nx0=9.03243, x1=3.66956, y=33.14503\nx0=4.52101, x1=2.70606, y=12.23414\nx0=8.86868, x1=4.23760, y=37.58195\nx0=-3.77783, x1=-2.13576, y=8.06853\nx0=1.58406, x1=2.66157, y=4.21608\nx0=-3.90241, x1=-1.09860, y=4.28717\nx0=2.78603, x1=-7.94426, y=-22.13293\nx0=-9.04477, x1=-1.39208, y=12.59107\nx0=-6.45690, x1=-3.55388, y=22.94702\nx0=-2.80702, x1=-6.41637, y=18.01085\nx0=5.98051, x1=4.37136, y=26.14298\nx0=6.06764, x1=9.91010, y=60.13087\nx0=-1.65860, x1=4.32658, y=-7.17609\nx0=-9.32324, x1=4.47208, y=-41.69431\nx0=-2.31024, x1=9.84446, y=-22.74302\nx0=2.99894, x1=-5.58465, y=-16.74802\nx0=-8.12411, x1=8.56407, y=-69.57552\nx0=8.11973, x1=-3.21013, y=-26.06536\nx0=-3.30891, x1=3.18217, y=-10.52953\nx0=3.38234, x1=8.81677, y=29.82135\nx0=-7.36789, x1=-6.20800, y=45.73986\nx0=-2.05636, x1=-4.71237, y=9.69034\nx0=8.62701, x1=9.56561, y=82.52268\nx0=9.28236, x1=9.53174, y=88.47704\nx0=3.96596, x1=8.52384, y=33.80520\nx0=1.76794, x1=-3.07403, y=-5.43472\nx0=6.64313, x1=3.37206, y=22.40104\nx0=-1.98179, x1=-6.96189, y=13.79702\nx0=1.29169, x1=4.44368, y=5.73986\nx0=-3.61265, x1=-4.46845, y=16.14294\nx0=5.18102, x1=6.80311, y=35.24706\nx0=7.23462, x1=-0.74308, y=-5.37588\nx0=-8.71561, x1=4.65166, y=-40.54202\nx0=-3.59901, x1=-1.80013, y=6.47870\nx0=-7.52239, x1=-6.86489, y=51.64036\nx0=-0.45852, x1=-4.17441, y=1.91407\nx0=-0.38550, x1=-9.75087, y=3.75901\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-2.02611, x1=0.21065, y=-0.42681\nx0=5.96743, x1=5.56615, y=33.21563\nx0=-7.60964, x1=-1.94040, y=14.76571\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1", "data": [[-9.829018450211542, 5.772539522589666, -56.738397472109156], [0.3210836040190106, 5.618795437180177, 1.8041030892153835], [0.020245809890088395, -2.2036443783664446, -0.04461456514976906], [-8.12603316349374, -2.1386216512218548, 17.378510461994537], [-1.40459137043832, 4.1376166089467645, -5.81166058310889], [-4.0959170475699285, -0.643262594939781, 2.6347502286779187], [0.6180148030821968, 4.551795749975646, 2.8130771540915793], [2.6065135466998335, -0.8476950706085731, -2.2095286850119176], [1.9276847137433109, -7.859543680359444, -15.150722209626743], [6.99536294871886, 5.395753864780124, 37.745256666089475], [6.026775286277271, -6.8279204599296595, -41.15034228457101], [-9.833720917184044, -4.666219624252541, 45.88630152318688], [-9.19966783454969, 7.936255478162025, -73.01091424921594], [-8.130954996024295, 0.12233228884672442, -0.9946783351733611], [5.92174657292669, -0.9120842713721977, -5.401131908218649], [-4.078245670933391, -3.0982478463027014, 12.635415866662695], [6.832987363523447, 3.1557469738410955, 21.563179194733564], [5.305872654364274, -6.179506856621318, -32.78767644800358], [3.5494797786435957, 1.1499954040580374, 4.081885432237074], [-5.457763465765673, -9.547149811108223, 52.10608544125811], [9.442834234035558, 3.9137823995914154, 36.957198427427656], [3.450961615073851, 7.14740686430104, 24.665426736018244], [-4.7431473578433225, -4.197357613159738, 19.908685672782166], [0.1992244083066268, -1.5298981446635764, -0.30479305264000717], [-6.511050119560229, -9.67392678772656, 62.98742216784392], [-8.783762055595336, 5.328338996877811, -46.80286190012423], [-1.639662185872524, 6.110057743766557, -10.018430635951615], [-4.840910012670676, 7.200681741708145, -34.85785234148988], [-9.387509085025222, 2.8189425265385424, -26.462848578044518], [5.030257738133699, 1.96812172317596, 9.900159527594901], [-6.527046770650811, 3.003914800552618, -19.60669239825714], [1.4566351408122369, -3.9361831981004425, -5.733582767027799], [-8.588059239084929, -8.691039324157417, 74.63916056508054], [-4.849559829604315, -0.45030983894783283, 2.183804505836999], [4.23041740031568, -8.834820299770476, -37.374977524811214], [-6.244821443225739, -5.337964283035279, 33.33463381787182], [-0.5019761403906955, 1.921000972802105, -0.964296654013972], [4.417416047996154, 3.850889910355132, 17.010982889069233], [6.54936589402309, -3.190951320096551, -20.89870774532831], [6.030873604911481, -6.8540628685530125, -41.33598684036023], [-7.3187796395612175, 0.7614814759288215, -5.5731151219308845], [-0.551093378095981, 1.5066156989786634, -0.8302859350425893], [-6.392207342179377, 8.543975817847066, -54.614864954245064], [-7.788059160165901, -6.085606707735172, 47.39506506534396], [2.7235690356679125, 6.809504664855478, 18.546156053436587], [-5.610859920645144, -2.3892422327592744, 13.405703484501728], [-2.231293760339355, 9.104557392446857, -20.31494210041822], [-0.3605559864853909, 6.6104385708400315, -2.383433200010305], [-4.592455609140849, 0.03443148768754689, -0.1581250787617388], [2.5847279164150923, 6.627569090072942, 17.130462845081304], [9.032426612665954, 3.6695600688783756, 33.145032022913355], [4.521013729814275, 2.706062201069713, 12.234144364767609], [8.868684314750869, 4.23760115964993, 37.58194693675743], [-3.777829535275994, -2.1357592394308655, 8.068534334960518], [1.5840551181645068, 2.6615713174310347, 4.2160756677364795], [-3.90241245201302, -1.0985954755165146, 4.287172663380812], [2.7860297383120187, -7.944256462527104, -22.132934753377953], [-9.044770411215994, -1.392083042036834, 12.591071508570307], [-6.456898705920937, -3.5538757990723795, 22.947016048034182], [-2.807015452627666, -6.416371430004002, 18.01085375381991], [5.980509082982996, 4.371363500109471, 26.142979117425032], [6.067635054714348, 9.910099333211843, 60.13086610989746], [-1.6586045690733968, 4.32658390222424, -7.176091828708531], [-9.323244071489388, 4.472082253315753, -41.69431435543899], [-2.310236794235667, 9.844456009548022, -22.74302449249227], [2.9989372795167135, -5.584650941287956, -16.748017900916555], [-8.124114723053992, 8.564074456259434, -69.57552337942788], [8.119731101434695, -3.2101255409274065, -26.065356194178136], [-3.308912131052553, 3.182173539897363, -10.52953262928083], [3.3823442286302203, 8.816769824712814, 29.821350531778467], [-7.367885543498682, -6.208003454961181, 45.73985890979836], [-2.0563639551374058, -4.712366966526506, 9.690341573345306], [8.62701467925978, 9.56561277914026, 82.52268186175796], [9.282362860978772, 9.531737092244185, 88.47704238566122], [3.965959616529048, 8.523837875050024, 33.805196790289166], [1.7679442248093444, -3.0740329712769476, -5.434718838442589], [6.643126507081966, 3.372062864498375, 22.4010401986959], [-1.9817923601407195, -6.961889346938985, 13.797019119908743], [1.2916902555827487, 4.44367841672589, 5.739856109828208], [-3.612646629024086, -4.4684513382847735, 16.14293566421265], [5.181020338051612, 6.80311187559343, 35.24706098949001], [7.2346225341936155, -0.7430761337389455, -5.375875341769244], [-8.715611553051549, 4.651655163241591, -40.542019481560295], [-3.5990148934214456, -1.8001323788328278, 6.478703241549523], [-7.52238549243764, -6.864890872036078, 51.64035550297177], [-0.4585249362515338, -4.174412898611992, 1.914072408223644], [-0.38550467247287834, -9.750868074872805, 3.7590052035300867], [-2.0261095457891525, 0.21065410114387362, -0.42680828518723596], [5.967433127515543, 5.566149719295302, 33.215626227634125], [-7.609638867993982, -1.9403959573905265, 14.765712496657345]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.85437, x1=-6.59549, y=-0.89756\nx0=-0.34755, x1=-6.44410, y=0.49641\nx0=8.41775, x1=7.50561, y=-0.04932\nx0=4.52058, x1=-2.77551, y=0.08690\nx0=-2.06653, x1=9.10359, y=0.00668\nx0=6.43635, x1=-0.32237, y=-0.22478\nx0=-3.13192, x1=8.43592, y=-0.47448\nx0=7.70374, x1=-2.02022, y=-0.45053\nx0=-3.80602, x1=7.04095, y=-0.50461\nx0=-2.03765, x1=-2.36413, y=-0.03222\nx0=-1.53261, x1=0.47164, y=-0.72577\nx0=2.45564, x1=-0.99337, y=-0.45342\nx0=8.53250, x1=-3.07556, y=0.00760\nx0=-4.37368, x1=-8.13503, y=0.16457\nx0=2.71931, x1=-3.55860, y=0.16684\nx0=-5.46451, x1=-2.85816, y=-0.13303\nx0=-6.13540, x1=-3.96874, y=0.08836\nx0=-0.67445, x1=7.78846, y=0.61874\nx0=-8.73421, x1=-7.55931, y=0.40949\nx0=-7.81970, x1=2.56906, y=0.20967\nx0=8.72882, x1=6.24985, y=-0.50274\nx0=4.72551, x1=-5.30665, y=-0.63665\nx0=-8.91211, x1=-8.59376, y=0.29007\nx0=6.70850, x1=-4.18745, y=0.29744\nx0=-6.32826, x1=-8.32520, y=-0.03530\nx0=2.75016, x1=-6.81222, y=0.80357\nx0=6.63462, x1=-4.54768, y=0.32526\nx0=-3.39550, x1=-9.44058, y=0.00734\nx0=3.45153, x1=4.11519, y=0.41815\nx0=8.33029, x1=-0.65816, y=-0.06708\nx0=-1.42166, x1=4.71815, y=0.60019\nx0=8.69072, x1=-9.90272, y=0.10714\nx0=-7.02153, x1=-6.20150, y=-0.89385\nx0=5.25479, x1=3.76618, y=-0.30712\nx0=-7.03910, x1=2.88904, y=0.11411\nx0=8.77628, x1=6.17955, y=-0.56227\nx0=-0.84596, x1=5.73453, y=0.91909\nx0=5.54696, x1=-0.06269, y=0.89273\nx0=8.56726, x1=7.89848, y=-0.19402\nx0=-4.18946, x1=4.42162, y=0.00060\nx0=9.31911, x1=5.03609, y=-0.80164\nx0=7.40519, x1=-5.50927, y=0.92024\nx0=1.85908, x1=-9.16101, y=-0.04546\nx0=0.95332, x1=-4.99253, y=-0.79100\nx0=8.01977, x1=-7.70164, y=0.38802\nx0=7.42979, x1=8.75216, y=0.32635\nx0=1.00820, x1=3.12253, y=0.00951\nx0=8.28781, x1=3.40764, y=0.01781\nx0=9.44140, x1=0.09248, y=0.99862\nx0=-6.47807, x1=-8.44586, y=-0.13548\nx0=1.52493, x1=-9.02405, y=-0.15007\nx0=5.18272, x1=-0.93685, y=0.88943\nx0=2.51477, x1=1.39444, y=-0.45200\nx0=1.61367, x1=-7.52081, y=-0.53778\nx0=-8.15023, x1=3.09713, y=0.00743\nx0=5.17452, x1=7.07706, y=-0.91833\nx0=-1.21381, x1=7.61933, y=0.76063\nx0=-7.11262, x1=0.05145, y=0.94681\nx0=-7.71713, x1=-1.25037, y=0.67820\nx0=-8.08965, x1=-6.64442, y=-0.41178\nx0=-2.09370, x1=-6.23593, y=0.00104\nx0=8.30146, x1=4.45361, y=0.06949\nx0=-7.20385, x1=9.35002, y=-0.03670\nx0=-1.20129, x1=-7.48435, y=0.80307\nx0=-2.24914, x1=3.88831, y=-0.08390\nx0=3.37133, x1=-1.65729, y=-0.63614\nx0=0.37626, x1=-7.50105, y=-0.43875\nx0=-0.12066, x1=7.67274, y=0.13828\nx0=-9.05989, x1=-1.57836, y=-0.60152\nx0=1.67178, x1=4.68932, y=-0.41397\nx0=-1.59630, x1=8.88865, y=0.17999\nx0=8.21423, x1=6.81058, y=0.23419\nx0=8.88004, x1=-0.79605, y=0.63083\nx0=9.75655, x1=5.18761, y=-0.75013\nx0=2.36041, x1=5.46391, y=0.35637\nx0=-3.72355, x1=8.67058, y=-0.23662\nx0=8.02975, x1=8.82071, y=0.14826\nx0=3.61490, x1=-0.23111, y=-0.75333\nx0=8.01240, x1=-9.99663, y=-0.14688\nx0=3.16069, x1=-0.12691, y=-0.99758\nx0=6.32681, x1=-4.24093, y=0.03416\nx0=5.12212, x1=-0.02190, y=0.98539\nx0=8.33056, x1=3.93356, y=0.02718\nx0=-1.37925, x1=1.39287, y=-0.67393\nx0=1.00610, x1=6.49030, y=-0.99275\nx0=-8.42245, x1=5.63813, y=0.06378\nx0=3.24579, x1=-7.65659, y=0.76392\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-5.27094, x1=8.44114, y=0.47158\nx0=1.69409, x1=5.39827, y=-0.51062\nx0=-5.65777, x1=-7.32802, y=0.69888\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(1.5 * x0) * cos(0.5 * x1)", "data": [[-2.8543706596340845, -6.595494571389329, -0.8975626820322198], [-0.3475461810577958, -6.444100610185986, 0.4964134990922484], [8.417752398168762, 7.505611417560683, -0.04931856663924285], [4.520577520215724, -2.77550896634531, 0.08689505354824845], [-2.0665279487644757, 9.103594327053607, 0.006682092307753952], [6.436353517964651, -0.32236513532700073, -0.22478447943666108], [-3.1319182369127097, 8.435920229822276, -0.4744790293059412], [7.7037442614573415, -2.0202187735607673, -0.4505313351213016], [-3.8060156695838536, 7.040948500770906, -0.5046117259513452], [-2.0376475834396413, -2.3641325355277854, -0.03222317033548938], [-1.5326104810255892, 0.4716437693993054, -0.7257680701236124], [2.455641142038976, -0.9933748286100279, -0.45341943066400353], [8.532495058859435, -3.075562637546634, 0.007601525949715561], [-4.373678015752955, -8.135034671450537, 0.16457421680303558], [2.719312563341191, -3.558603033926282, 0.16684176510691553], [-5.464508278986704, -2.858158062400136, -0.13302637829684316], [-6.135404960604037, -3.968735605555514, 0.08835766107641241], [-0.6744533330351103, 7.7884582599438374, 0.6187447228038252], [-8.734210522332775, -7.5593111312436605, 0.4094924722981005], [-7.819696742074256, 2.5690607274614194, 0.20966709239085865], [8.728815107556088, 6.249853867267834, -0.5027449389120794], [4.725507599786402, -5.306653172058455, -0.6366464032323206], [-8.912109526591498, -8.593763176908581, 0.2900677665446968], [6.708497997099702, -4.187450859188235, 0.2974371242058047], [-6.3282557158620945, -8.325202891337318, -0.0352974419213824], [2.7501623845187098, -6.8122220708840135, 0.8035690169780713], [6.634624049046071, -4.5476755886201214, 0.3252613686123761], [-3.395499188685516, -9.440584258164503, 0.007336775156952817], [3.4515290397667027, 4.115192855944416, 0.418149839340215], [8.330286636286928, -0.6581641007799082, -0.06707764626774079], [-1.4216572800204048, 4.71814813107172, 0.6001851988955244], [8.69072226633427, -9.902722348258443, 0.10713944730366408], [-7.021528742570286, -6.201502078491057, -0.8938450038408831], [5.254785012370755, 3.7661820798387335, -0.30712104141139607], [-7.039097870804946, 2.8890413992353547, 0.11410898209691515], [8.776278667341234, 6.179550665212481, -0.562274128451012], [-0.8459623853631548, 5.734534004028312, 0.9190860090978079], [5.546960867677967, -0.06268636825613783, 0.8927273803209536], [8.567260097793454, 7.898484428005641, -0.1940170018584289], [-4.189464705484092, 4.421623683636302, 0.0006042256004068698], [9.31911151246641, 5.036094326096077, -0.8016373749993606], [7.405185051973092, -5.509273560354964, 0.9202388617266835], [1.859075437178765, -9.16100996797928, -0.045459605956611124], [0.953320872274583, -4.992533288051089, -0.7909961287240781], [8.019773450932163, -7.701635299447092, 0.38801750680639463], [7.429789720307319, 8.752155728654998, 0.326345241575156], [1.0082029976487341, 3.122533774495471, 0.009512998705017902], [8.287807522278502, 3.4076421733985605, 0.017806313529821628], [9.441403212372407, 0.09248125085066405, 0.9986204923696269], [-6.4780650521265715, -8.445862621246668, -0.13548432909097144], [1.5249273173416373, -9.024050554587932, -0.15007474601365542], [5.182721824055491, -0.9368456604506665, 0.8894348841074246], [2.514766211686794, 1.3944362628669005, -0.4520016043532112], [1.613669721539054, -7.520807261603181, -0.5377801588704609], [-8.150231388852498, 3.09713025081016, 0.007434654130125124], [5.1745212010884245, 7.077062470425204, -0.9183316937928144], [-1.2138128032195201, 7.619331421031816, 0.7606275189762391], [-7.112624575076472, 0.05145388706504228, 0.9468131893536756], [-7.7171251651615975, -1.2503695033149036, 0.6781995062346717], [-8.089653357344629, -6.644420316364603, -0.4117793283759497], [-2.0936984788311186, -6.235934809544236, 0.0010446435499977557], [8.301463523653663, 4.453611247761366, 0.06949109883408629], [-7.203851493176394, 9.350023875187745, -0.03669730018514829], [-1.201292100139007, -7.484345973311077, 0.8030670844142933], [-2.2491352945056553, 3.8883098541075984, -0.08390285505603146], [3.371329810024651, -1.6572888259211371, -0.636139885006258], [0.37625578216369604, -7.501048231328406, -0.4387529426753838], [-0.1206583264204486, 7.672742939886067, 0.13827594329516618], [-9.059894879243034, -1.5783641568514675, -0.601523427636053], [1.6717802416995848, 4.689324158000051, -0.41396827170013223], [-1.5962973760400718, 8.888653366001272, 0.17998746549421116], [8.214234278839754, 6.810579814932975, 0.23418983102996915], [8.88003650718138, -0.7960531274767213, 0.6308341390211054], [9.75654623294404, 5.1876093425704095, -0.7501322241980751], [2.3604093813315288, 5.463909061680043, 0.35637288738214956], [-3.723545477642771, 8.670580353798453, -0.23661560919716126], [8.029745725047167, 8.820706615986701, 0.14825617514438882], [3.614902953768686, -0.23110716336002746, -0.7533268144363413], [8.012402509682747, -9.996626203910798, -0.14688356119041712], [3.160689162440587, -0.12691354344172368, -0.9975778870864183], [6.326807805927459, -4.240928349962861, 0.034158466359946446], [5.122122245390857, -0.021895119866879753, 0.9853903483978957], [8.330560998412487, 3.933560378382083, 0.027181667827931147], [-1.3792503519582429, 1.3928699108060183, -0.6739286054742817], [1.006103732328178, 6.490295406965657, -0.9927539514159233], [-8.422447072951815, 5.638127191283402, 0.063781620699713], [3.2457859853683324, -7.65658789846295, 0.763915734855806], [-5.2709395897476385, 8.441142943177027, 0.471579906062988], [1.6940852123579386, 5.398270960411512, -0.5106153621500267], [-5.6577699060140425, -7.328023598836286, 0.6988811027358094]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-7.54017, y=-379.37663\nx0=-2.84875, y=-17.85214\nx0=-2.52432, y=-12.23761\nx0=-2.55260, y=-12.66900\nx0=-5.01737, y=-106.15083\nx0=-8.51066, y=-552.51689\nx0=6.20537, y=283.66018\nx0=4.72286, y=132.37332\nx0=9.47981, y=951.26732\nx0=-4.16984, y=-59.28562\nx0=-5.76712, y=-164.31964\nx0=-3.12960, y=-23.98781\nx0=4.91100, y=147.47216\nx0=-8.64368, y=-579.72756\nx0=5.44979, y=197.01040\nx0=5.87079, y=242.68046\nx0=-3.50497, y=-34.27815\nx0=-3.60123, y=-37.33616\nx0=-3.27259, y=-27.61158\nx0=2.11296, y=16.01113\nx0=4.68619, y=129.55727\nx0=0.25394, y=0.33481\nx0=1.37274, y=5.84397\nx0=4.63535, y=125.71920\nx0=8.37624, y=666.22622\nx0=-1.86263, y=-4.85547\nx0=4.44806, y=112.23957\nx0=4.34067, y=104.96652\nx0=-3.95729, y=-50.26891\nx0=-7.76708, y=-416.00900\nx0=-2.88408, y=-18.55579\nx0=-2.51829, y=-12.14702\nx0=-1.07844, y=-1.16966\nx0=-0.72597, y=-0.58154\nx0=5.37766, y=189.81499\nx0=1.11744, y=3.76139\nx0=0.23574, y=0.30441\nx0=-0.15772, y=-0.13677\nx0=-8.91752, y=-638.53481\nx0=3.70761, y=68.42010\nx0=1.80078, y=10.88320\nx0=-2.93080, y=-19.51555\nx0=3.44891, y=56.36844\nx0=5.78000, y=232.28897\nx0=-6.31748, y=-218.54054\nx0=-9.43650, y=-760.68597\nx0=6.86733, y=377.89243\nx0=-5.59031, y=-149.04466\nx0=-3.89986, y=-48.00370\nx0=-3.15003, y=-24.48412\nx0=7.89564, y=562.45994\nx0=0.25097, y=0.32977\nx0=-9.04769, y=-667.83781\nx0=-2.37541, y=-10.13626\nx0=-1.53216, y=-2.78142\nx0=-1.25268, y=-1.64918\nx0=8.99389, y=817.39981\nx0=7.11943, y=418.66344\nx0=-4.12615, y=-57.34938\nx0=6.17900, y=280.27376\nx0=8.47775, y=689.66532\nx0=4.49414, y=115.46063\nx0=1.48302, y=6.94399\nx0=4.07112, y=88.11999\nx0=6.33604, y=300.84429\nx0=9.89831, y=1077.67614\nx0=-9.02367, y=-662.36454\nx0=8.72310, y=748.57713\nx0=2.62335, y=27.55913\nx0=4.81777, y=139.85325\nx0=0.36227, y=0.54105\nx0=-5.82021, y=-169.10389\nx0=-4.74613, y=-89.13062\nx0=-2.14040, y=-7.36492\nx0=-3.03980, y=-21.88831\nx0=-3.47431, y=-33.34127\nx0=-2.78733, y=-16.67349\nx0=-1.84330, y=-4.70864\nx0=1.17151, y=4.15179\nx0=0.32122, y=0.45755\nx0=1.71644, y=9.71949\nx0=-8.39958, y=-530.46134\nx0=9.78302, y=1041.79856\nx0=8.49708, y=694.19002\nx0=1.32384, y=5.39652\nx0=-9.12146, y=-684.83591\nx0=9.89599, y=1076.94806\nx0=-8.02603, y=-460.62327\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.38425, y=-0.29333\nx0=7.19992, y=432.27348\nx0=1.86536, y=11.83553\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 + x0**2 + x0", "data": [[-7.540173637661145, -379.3766345701491], [-2.848754306653534, -17.852137039902324], [-2.5243218167025443, -12.237606263941998], [-2.5526012885721405, -12.668999369847267], [-5.017372781769492, -106.15083422977709], [-8.51065557310001, -552.5168892700071], [6.2053730448976125, 283.66018433872324], [4.722856600747676, 132.37331612555147], [9.479811871894846, 951.2673165607761], [-4.169839628292995, -59.28562436162414], [-5.767116323027979, -164.3196446514401], [-3.129602509772589, -23.98780660811386], [4.911001532749733, 147.4721585186655], [-8.643680277576218, -579.7275604052878], [5.449794786783752, 197.01039765670242], [5.87078841168389, 242.6804576008401], [-3.5049728707370553, -34.27815082785277], [-3.6012282844946286, -37.336155124229], [-3.27258643149748, -27.611582482506154], [2.1129628602037354, 16.01113435271474], [4.686192663508482, 129.55726758129856], [0.25394456681843636, 0.3348087471949463], [1.3727405515864213, 5.843972286617647], [4.6353509722971165, 125.71919924703883], [8.376239491028436, 666.2262165057386], [-1.8626347552880134, -4.855466876154397], [4.448064950149142, 112.23956525761325], [4.340671038639787, 104.96652421365185], [-3.9572908047138577, -50.268909917459204], [-7.767084098589931, -416.0089955993421], [-2.8840843879215905, -18.55579047535709], [-2.5182941647028922, -12.147020448998129], [-1.078437870645356, -1.1696633293574237], [-0.7259655414154604, -0.5815422658002067], [5.377663375208941, 189.81499025312888], [1.1174350600910863, 3.76139388003234], [0.23573525224065683, 0.3044064308221475], [-0.1577192455006493, -0.13676720817340404], [-8.917515383938504, -638.5348120775963], [3.7076085404508454, 68.42009540420317], [1.8007815213333984, 10.883195294935405], [-2.930798692285112, -19.51555040551319], [3.4489062482731008, 56.36844279818453], [5.780000131989366, 232.28896688644738], [-6.317475271087112, -218.54053911370158], [-9.436499861051594, -760.6859711915124], [6.8673305137297085, 377.8924343199534], [-5.59030969292065, -149.04465978465484], [-3.899863516236608, -48.003700534782595], [-3.1500304872228613, -24.48412095397941], [7.89564022028156, 562.4599435508535], [0.2509721335190189, 0.32976713005831587], [-9.047692746829757, -667.8378088159607], [-2.3754101185120557, -10.136262435052778], [-1.5321620517909462, -2.7814234058692993], [-1.252676794768849, -1.6491770068887024], [8.993888402774747, 817.3998071440836], [7.119431658519787, 418.6634385072035], [-4.126153930955736, -57.349381842820435], [6.179001911739622, 280.27375884698074], [8.4777517150102, 689.665321219953], [4.494136205410509, 115.46063490043363], [1.48301500107981, 6.943993057638174], [4.071120632815877, 88.11999168629414], [6.3360397600732625, 300.84428917936987], [9.89830717664113, 1077.676136392559], [-9.02367236406568, -662.3645374457144], [8.72309717086598, 748.5771321434192], [2.6233502760270166, 27.559126112029006], [4.817766991124001, 139.85325139683337], [0.3622681114595103, 0.5410497053192812], [-5.820207988276875, -169.1038909031171], [-4.746131681382302, -89.13061710545819], [-2.140399352385711, -7.364921611189583], [-3.039799029068975, -21.88831338141425], [-3.4743096361601484, -33.3412743069633], [-2.7873309877268664, -16.673487983019413], [-1.8433017200694302, -4.708639610734823], [1.1715128715697265, 4.151789226580457], [0.3212205857333128, 0.45754764642425483], [1.7164376176671325, 9.719492295450923], [-8.399577983478393, -530.4613397136427], [9.783019563829384, 1041.7985602398112], [8.497081106465345, 694.1900154962667], [1.3238433003369376, 5.39652063346602], [-9.121462566995946, -684.8359141318958], [9.895993288621305, 1076.9480598420205], [-8.026031988397662, -460.62326586899707], [-0.38424558312709856, -0.29333272658434956], [7.199915069721332, 432.2734838797866], [1.8653571871949044, 11.835532094178312]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=3.26917, x1=2.11916, y=0.39795\nx0=8.24614, x1=6.82425, y=4.75254\nx0=-0.10550, x1=9.11592, y=0.60192\nx0=2.47811, x1=7.32870, y=1.85300\nx0=-1.61392, x1=8.34305, y=2.81618\nx0=1.64758, x1=7.69776, y=0.93080\nx0=-5.83483, x1=2.57321, y=-2.19195\nx0=2.01424, x1=9.68118, y=-5.24250\nx0=-1.09195, x1=-7.80919, y=-0.23844\nx0=5.06240, x1=8.63487, y=3.96738\nx0=-1.56251, x1=-4.81361, y=-0.60628\nx0=5.17259, x1=3.04771, y=5.35210\nx0=2.22611, x1=-1.59156, y=-0.09879\nx0=-1.54579, x1=3.86105, y=4.51156\nx0=5.08347, x1=3.54940, y=5.13307\nx0=6.78329, x1=3.25596, y=-2.85831\nx0=-7.66538, x1=-9.52038, y=5.86669\nx0=-8.16243, x1=-4.69440, y=0.10283\nx0=0.00909, x1=-9.32521, y=-0.05427\nx0=0.42525, x1=-9.23767, y=-2.43207\nx0=4.97814, x1=-5.96207, y=-5.49344\nx0=0.04895, x1=-7.82006, y=0.00996\nx0=-9.26049, x1=-6.24366, y=-0.98055\nx0=7.61672, x1=-7.45783, y=2.25037\nx0=-0.42035, x1=4.58020, y=0.32273\nx0=1.02108, x1=9.66040, y=-4.97467\nx0=3.65731, x1=9.07490, y=2.77967\nx0=-8.25903, x1=-9.23371, y=5.41415\nx0=-7.77660, x1=8.72389, y=4.57190\nx0=-6.55205, x1=4.86981, y=-0.24986\nx0=-2.23397, x1=-6.53456, y=-4.57966\nx0=-8.21971, x1=9.44913, y=5.60151\nx0=7.34748, x1=5.62660, y=4.15581\nx0=-4.67912, x1=-7.12798, y=3.98112\nx0=7.28483, x1=9.49187, y=-5.04277\nx0=3.66512, x1=-1.07945, y=-1.41525\nx0=-8.45602, x1=1.99441, y=2.03272\nx0=5.11894, x1=3.10467, y=5.50718\nx0=4.26869, x1=4.46053, y=1.35043\nx0=9.45990, x1=-2.39310, y=0.15437\nx0=-6.44899, x1=8.93771, y=0.87510\nx0=6.56268, x1=4.65714, y=-0.09140\nx0=0.87946, x1=-2.21207, y=-2.76515\nx0=-2.84481, x1=-5.95557, y=-1.66134\nx0=-9.24301, x1=-2.44761, y=0.83374\nx0=-1.04231, x1=7.21474, y=-3.09117\nx0=-9.40822, x1=-6.08922, y=-0.09745\nx0=-3.65236, x1=-1.14423, y=1.21355\nx0=-8.99264, x1=-8.66384, y=1.81982\nx0=5.49270, x1=2.27010, y=2.74479\nx0=-3.16952, x1=3.25078, y=-0.16656\nx0=-7.42074, x1=1.54776, y=-0.12543\nx0=-6.07149, x1=-1.88160, y=-0.38556\nx0=-9.18126, x1=7.87247, y=0.02675\nx0=-5.67810, x1=5.49863, y=2.41540\nx0=0.00300, x1=1.37792, y=0.00345\nx0=1.08106, x1=9.28913, y=-5.24610\nx0=4.23929, x1=-0.98883, y=-2.93574\nx0=-4.07028, x1=-4.57715, y=-0.64786\nx0=0.88426, x1=-1.09142, y=2.14040\nx0=-3.73178, x1=0.69937, y=2.55526\nx0=4.02270, x1=-7.69777, y=-0.72009\nx0=9.66755, x1=-5.33686, y=-0.84332\nx0=-6.32756, x1=-8.12885, y=0.07224\nx0=0.96705, x1=-6.95712, y=3.85943\nx0=3.66060, x1=8.22696, y=1.08447\nx0=3.80678, x1=-9.06706, y=3.46881\nx0=9.71061, x1=0.93323, y=-1.00700\nx0=-6.07054, x1=9.96900, y=-1.08334\nx0=7.09046, x1=-1.34034, y=0.99008\nx0=0.66544, x1=-5.32008, y=2.11515\nx0=9.70340, x1=0.13562, y=-1.63502\nx0=-6.25011, x1=9.64376, y=-0.19367\nx0=8.75190, x1=-3.95620, y=-2.56581\nx0=7.31090, x1=0.08634, y=5.11759\nx0=2.66027, x1=-6.40038, y=2.75866\nx0=9.61930, x1=3.71193, y=0.97622\nx0=-7.04591, x1=3.77190, y=3.34883\nx0=0.64220, x1=9.31609, y=-3.57254\nx0=-6.13818, x1=2.31908, y=-0.58990\nx0=8.78441, x1=1.29807, y=0.96562\nx0=2.10608, x1=-6.61141, y=4.88526\nx0=5.90448, x1=-4.11589, y=1.24614\nx0=0.37644, x1=-1.07034, y=1.05835\nx0=-3.99485, x1=-1.93480, y=-1.60938\nx0=3.82376, x1=5.42007, y=-2.45913\nx0=4.36141, x1=3.23571, y=5.60929\nx0=7.02011, x1=8.25606, y=-1.57789\nx0=-1.25226, x1=8.18535, y=1.85382\nx0=-4.80430, x1=-5.54616, y=4.42408\nx0=7.38942, x1=-6.97546, y=4.12927\nx0=0.03400, x1=-7.13509, y=0.13433\nx0=4.00958, x1=5.71395, y=-3.85626\nx0=-6.04410, x1=4.56470, y=-0.20909\nx0=-8.39455, x1=4.33125, y=1.91366\nx0=-8.82020, x1=-4.45485, y=0.86865\nx0=3.81390, x1=-4.69659, y=0.05905\nx0=8.05465, x1=-7.27832, y=3.20079\nx0=3.53412, x1=3.55365, y=2.10306\nx0=-5.72396, x1=0.59658, y=2.63330\nx0=-0.77623, x1=-2.81066, y=3.97547\nx0=-3.80540, x1=8.54851, y=-2.36599\nx0=8.16846, x1=8.08174, y=-1.28834\nx0=-9.82315, x1=-7.25141, y=1.31913\nx0=-8.82740, x1=-0.02487, y=-3.37381\nx0=5.36547, x1=-7.60535, y=-1.17263\nx0=-4.42441, x1=2.13853, y=-3.09346\nx0=-1.14716, x1=1.08577, y=-2.55010\nx0=0.22867, x1=2.50070, y=-1.09021\nx0=7.80047, x1=-0.76273, y=4.33149\nx0=-3.54024, x1=-4.67215, y=-0.09369\nx0=5.61536, x1=-5.81961, y=-3.32354\nx0=-5.03434, x1=0.83743, y=3.80991\nx0=0.86520, x1=8.28029, y=-1.88865\nx0=-9.05296, x1=-0.10299, y=-2.16829\nx0=-3.60767, x1=-7.54179, y=0.82817\nx0=-1.70445, x1=-4.32529, y=2.24480\nx0=0.60321, x1=6.20759, y=3.39401\nx0=6.75512, x1=-2.71100, y=-2.47869\nx0=-8.09642, x1=-0.24188, y=-5.65497\nx0=5.81807, x1=-6.15249, y=-2.66818\nx0=1.32103, x1=-4.76720, y=0.31852\nx0=-9.63066, x1=7.43562, y=0.49832\nx0=2.04209, x1=9.10650, y=-5.07741\nx0=-3.76985, x1=-0.94573, y=2.06347\nx0=6.02282, x1=2.00952, y=0.65612\nx0=-3.12381, x1=-2.00337, y=0.04472\nx0=-8.22277, x1=-0.08733, y=-5.57527\nx0=0.64342, x1=6.90501, y=2.92585\nx0=-8.96599, x1=0.11065, y=-2.64092\nx0=3.33338, x1=5.33957, y=-0.67119\nx0=-1.88943, x1=-3.11752, y=5.69634\nx0=-2.52511, x1=2.67100, y=3.09193\nx0=-1.89931, x1=4.28366, y=2.36089\nx0=-9.32467, x1=-3.96394, y=0.40807\nx0=-1.16215, x1=-8.02025, y=0.91125\nx0=-1.19416, x1=6.45678, y=-5.49560\nx0=1.04092, x1=8.88114, y=-4.43082\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-4.31855, x1=2.23113, y=-3.39851\nx0=-0.46671, x1=-7.57903, y=-0.73298\nx0=7.03069, x1=9.66837, y=-3.95846\nx0=6.95547, x1=-2.29966, y=-2.48871\nx0=4.33733, x1=-8.01373, y=0.88810\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 6 * sin(x0) * cos(x1)", "data": [[3.2691716131756507, 2.119155619904525, 0.39795053160822874], [8.246138465916331, 6.824252224597721, 4.752540071668419], [-0.1054982084686813, 9.115916718403692, 0.60191841745228], [2.4781069933560502, 7.32869544190012, 1.8529976307541791], [-1.61391702572522, 8.343046081374926, 2.8161810551868802], [1.647579889544593, 7.697755000519781, 0.9308008399343095], [-5.8348349112416535, 2.57321244696713, -2.191951728257223], [2.0142427913035394, 9.68117891562223, -5.2424952109600635], [-1.0919487845159779, -7.809191273675071, -0.23843605139344004], [5.062400853149448, 8.63486812298802, 3.9673822750052867], [-1.562505194372104, -4.813611459975959, -0.606277444960079], [5.172593485075627, 3.0477114827869762, 5.352097387205894], [2.2261105881211645, -1.5915638427019978, -0.09878685277581604], [-1.5457933443110665, 3.86105137543783, 4.5115646092712725], [5.083468561929648, 3.5493968700381657, 5.133071469796843], [6.783290812720612, 3.2559633657280234, -2.858312017031433], [-7.665378968935624, -9.520384488959785, 5.866688005526734], [-8.162431912814565, -4.69440029467539, 0.10283273156262333], [0.009090041360975576, -9.325206177642347, -0.05426935336334108], [0.42524674679868646, -9.237665720111785, -2.432068777765735], [4.978135779290287, -5.962067229143598, -5.493444765663098], [0.0489501916490358, -7.820064686545816, 0.009955559796961963], [-9.26048792326898, -6.243660251194704, -0.9805454000552638], [7.616723674868435, -7.457830287307942, 2.2503653184895644], [-0.4203538952632009, 4.580197848685941, 0.32272833114360255], [1.021077596483977, 9.660399369388916, -4.974670396820293], [3.657307333120709, 9.074895144824854, 2.7796665805870227], [-8.259032966120788, -9.233714657244425, 5.414145050620026], [-7.776599874321743, 8.723892057891103, 4.571904664700664], [-6.552045134184636, 4.869806504159177, -0.2498562569769501], [-2.233967757280821, -6.534560067953148, -4.57966007433331], [-8.219712894454439, 9.449125361272454, 5.601514243553197], [7.347481859270182, 5.626603212835617, 4.155812829605909], [-4.679116459680368, -7.12797618986454, 3.9811214017552516], [7.284828284261053, 9.491874327346657, -5.042772900361622], [3.6651181362756073, -1.079452672597741, -1.4152533508351355], [-8.456019584586311, 1.9944096207338298, 2.032717824599849], [5.118942806534397, 3.1046710310976167, 5.507178464145102], [4.268691368436812, 4.460532804071287, 1.350431427268081], [9.459898791203436, -2.393102157572309, 0.15437003125799842], [-6.448986614730612, 8.937707104159443, 0.8750969461112605], [6.562683847918567, 4.657144532300936, -0.09139643027729905], [0.8794568837861796, -2.2120657705281976, -2.765154444989284], [-2.844810914028983, -5.95557132261169, -1.6613392813717678], [-9.243011215717248, -2.44760501234137, 0.8337375801753283], [-1.0423083801048634, 7.214738695107194, -3.0911748834440282], [-9.408224712555617, -6.089222676992372, -0.09745261439656024], [-3.6523591687605395, -1.1442316742237306, 1.213547873994618], [-8.99263572528251, -8.663843294457882, 1.8198232528679792], [5.492695848777547, 2.270098235904621, 2.744786690918355], [-3.1695221580063526, 3.2507816571061916, -0.16655741591755496], [-7.420739566859487, 1.547761777446068, -0.1254271558209254], [-6.071485762219955, -1.8815956614261573, -0.3855564160279087], [-9.181259839581344, 7.872474929965854, 0.026752922321408825], [-5.67809986264505, 5.498634656943134, 2.4153957628304865], [0.0029957454746032397, 1.3779186906760899, 0.003445412980551168], [1.0810572038800697, 9.289134815976372, -5.24609919416345], [4.239294371818591, -0.988834899485111, -2.9357392888712677], [-4.070277665290916, -4.577147705227715, -0.6478550182927305], [0.8842602498998975, -1.0914196529694298, 2.140402179628273], [-3.731782490825042, 0.6993660556881416, 2.5552573113784742], [4.022698797702155, -7.6977742335953785, -0.7200939792628428], [9.667554747656357, -5.336857238457197, -0.8433183501291744], [-6.327558350266207, -8.128848555720701, 0.0722383724591544], [0.9670543715658617, -6.95712185126335, 3.8594275223245917], [3.6606031766295093, 8.226957760127686, 1.084466692349228], [3.8067787633764603, -9.067060356655784, 3.4688129010514115], [9.710613585152814, 0.9332310148842495, -1.0070020019938706], [-6.070540494530654, 9.969000259164616, -1.0833367329344032], [7.090458708540503, -1.3403393611847765, 0.9900803542027836], [0.6654446968790229, -5.320081425340928, 2.115149007361315], [9.703397217278887, 0.13561534477717352, -1.6350191566066743], [-6.250110525273933, 9.643758650083079, -0.1936742989658071], [8.751902770282602, -3.956204334640274, -2.5658081094881817], [7.310900875398257, 0.08633753837472291, 5.117590989131089], [2.660268960519751, -6.400382551311797, 2.7586628598225844], [9.619300304575432, 3.7119282496907005, 0.9762160997755704], [-7.0459113115147165, 3.7718962004345773, 3.3488304862484184], [0.6421986556458883, 9.316086638868093, -3.5725381638858704], [-6.13817569882293, 2.319082730570347, -0.5899007848314113], [8.784410836110006, 1.2980730572730437, 0.9656214914409027], [2.106075186615877, -6.611406913973674, 4.88526239272339], [5.904478979607816, -4.115889249939261, 1.2461373927479047], [0.37644056507428303, -1.0703350329036105, 1.0583500246516775], [-3.9948453670101642, -1.934796263932828, -1.609379384472542], [3.823759622367204, 5.4200664429176975, -2.4591258493719557], [4.361412233987336, 3.235705717915515, 5.6092905367207315], [7.020109456539888, 8.256061168914059, -1.5778854055626157], [-1.2522550996783988, 8.18534923230824, 1.853819520506662], [-4.80430352000726, -5.546160996493008, 4.424076610616769], [7.389423357857485, -6.975461164391739, 4.129272595112007], [0.03400385023775776, -7.135090736298904, 0.13433361165981247], [4.009580823338911, 5.713947474985295, -3.8562566008916725], [-6.044095710002308, 4.564702683983983, -0.20908682182998084], [-8.394550617017698, 4.331245882046735, 1.9136588063742248], [-8.82019640631764, -4.454851952964532, 0.8686547408890671], [3.81390444487616, -4.6965858247431935, 0.059050428738132085], [8.054648469759314, -7.278321445374154, 3.2007895707786327], [3.5341230022601593, 3.5536457194608566, 2.1030610899310913], [-5.723964750465258, 0.5965823293416506, 2.6332976522945355], [-0.7762300727748261, -2.810655868205421, 3.9754736687428887], [-3.8054042081456307, 8.548505066471026, -2.3659856850430905], [8.168458537242202, 8.081742135635302, -1.2883379491818725], [-9.823146484645743, -7.251411905363991, 1.319132174124592], [-8.82740090288907, -0.024870324203691396, -3.37381068042094], [5.365471339831391, -7.605351383384349, -1.1726256078679969], [-4.424413173774422, 2.138526748397746, -3.09346193879333], [-1.1471600343331652, 1.085770261687058, -2.5500998435511], [0.2286718657948139, 2.500696395526962, -1.0902060117791676], [7.800470730035762, -0.7627348904632409, 4.331486233102561], [-3.540238503665214, -4.6721494133585555, -0.09369364295529611], [5.615355054789621, -5.819605857831527, -3.32353904079962], [-5.034338999450087, 0.837425107944556, 3.8099128894962084], [0.8651981064204417, 8.280288722561743, -1.8886474455206743], [-9.052962780215912, -0.10298666562587755, -2.1682932964549693], [-3.6076693321420406, -7.54178539003515, 0.828169964800078], [-1.7044486296242738, -4.325294624145293, 2.2447964991798885], [0.6032092925880388, 6.207587776537306, 3.394008323164211], [6.755121901586104, -2.710999719521368, -2.4786859957193683], [-8.096418588468035, -0.24188402793147112, -5.654973467831161], [5.818074227370431, -6.152486539247366, -2.6681800176595485], [1.3210271624602683, -4.767202809006694, 0.3185180137182905], [-9.63066404897293, 7.435621670976303, 0.4983245891992669], [2.0420868837778556, 9.10650064871746, -5.077405534953934], [-3.769845028669561, -0.9457294961757725, 2.063472510320435], [6.022821934752422, 2.00952379529204, 0.656123051715918], [-3.123813790208607, -2.0033737553757653, 0.044716343796328065], [-8.222765348727537, -0.08733423313308997, -5.575269082260874], [0.6434246893037265, 6.905008091077029, 2.9258466519120456], [-8.965990507414945, 0.110645956522335, -2.6409190154170283], [3.3333807480453626, 5.339573649290264, -0.6711928301943643], [-1.8894256282446076, -3.1175247644010273, 5.696343973170653], [-2.525112704829242, 2.671004588341191, 3.0919260028288527], [-1.8993100007625578, 4.283662472955061, 2.360890778074261], [-9.324667964064288, -3.9639418029679057, 0.40806776334142353], [-1.16214739250524, -8.020249079395532, 0.9112483035827385], [-1.1941648842747945, 6.456777596367957, -5.49559747518899], [1.0409158966616303, 8.8811401665127, -4.430821334047614], [-4.318551764131433, 2.231125455703541, -3.3985126609014946], [-0.4667132981190836, -7.579029552120353, -0.7329765039122093], [7.030693764660793, 9.668373336789454, -3.958461128302302], [6.955474603541187, -2.2996622183761417, -2.488713963602483], [4.337333429222328, -8.013733810879604, 0.8880954495824901]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.49042, x1=-1.87163, y=-1.33062\nx0=-5.49128, x1=-7.10926, y=0.77241\nx0=1.23183, x1=-7.98907, y=-0.15419\nx0=-9.77666, x1=7.16787, y=-1.36396\nx0=9.50895, x1=-2.30768, y=-4.12056\nx0=-9.50848, x1=0.82330, y=-11.54917\nx0=2.48000, x1=-4.78141, y=-0.51868\nx0=0.26067, x1=4.41518, y=0.05904\nx0=-7.97892, x1=1.57113, y=-5.07847\nx0=8.15628, x1=4.92583, y=1.65582\nx0=-8.38820, x1=-0.73845, y=11.35917\nx0=-3.56147, x1=-0.18432, y=19.32202\nx0=6.03014, x1=1.87502, y=3.21604\nx0=5.40809, x1=-5.86790, y=-0.92164\nx0=-9.67735, x1=-1.78655, y=5.41680\nx0=6.50299, x1=0.75499, y=8.61336\nx0=7.39594, x1=7.72117, y=0.95788\nx0=-4.19404, x1=-7.10785, y=0.59006\nx0=-5.70012, x1=2.73237, y=-2.08614\nx0=-2.08466, x1=-7.40302, y=0.28160\nx0=6.00272, x1=-2.88708, y=-2.07917\nx0=-9.04609, x1=7.24103, y=-1.24928\nx0=-6.14962, x1=-2.63533, y=2.33353\nx0=-9.19564, x1=9.28509, y=-0.99037\nx0=2.86651, x1=2.17608, y=1.31728\nx0=-4.74586, x1=1.74207, y=-2.72426\nx0=1.25892, x1=7.36162, y=0.17101\nx0=-1.54448, x1=-0.77645, y=1.98914\nx0=-8.81638, x1=-8.99300, y=0.98036\nx0=-6.86132, x1=-4.32351, y=1.58698\nx0=-3.59552, x1=0.40493, y=-8.87933\nx0=0.43918, x1=6.65714, y=0.06597\nx0=8.44081, x1=4.33937, y=1.94517\nx0=2.45404, x1=-1.32963, y=-1.84566\nx0=7.53546, x1=6.85542, y=1.09920\nx0=6.53740, x1=-9.68363, y=-0.67510\nx0=1.14685, x1=-9.16664, y=-0.12511\nx0=7.06434, x1=-4.51874, y=-1.56334\nx0=-2.08293, x1=9.86854, y=-0.21107\nx0=-5.81310, x1=-7.85584, y=0.73997\nx0=-2.46322, x1=-7.02307, y=0.35073\nx0=0.03665, x1=-7.32336, y=-0.00500\nx0=0.73392, x1=-2.58785, y=-0.28360\nx0=4.86729, x1=-7.90026, y=-0.61609\nx0=4.51090, x1=2.43992, y=1.84879\nx0=6.21789, x1=9.68424, y=0.64206\nx0=-6.19579, x1=2.02489, y=-3.05981\nx0=5.33654, x1=-2.43936, y=-2.18768\nx0=6.78648, x1=-0.08517, y=-79.68116\nx0=-0.78501, x1=2.33146, y=-0.33670\nx0=5.06702, x1=-4.24731, y=-1.19300\nx0=0.56221, x1=-3.80217, y=-0.14787\nx0=-5.49377, x1=-9.29709, y=0.59091\nx0=-5.11957, x1=5.30833, y=-0.96444\nx0=4.77268, x1=5.08357, y=0.93884\nx0=-3.08796, x1=-3.41037, y=0.90546\nx0=4.98025, x1=-3.38393, y=-1.47173\nx0=-1.22408, x1=-4.59515, y=0.26638\nx0=0.19998, x1=-6.04913, y=-0.03306\nx0=2.29995, x1=-4.73926, y=-0.48530\nx0=-3.56356, x1=5.17808, y=-0.68820\nx0=-3.17044, x1=-9.33990, y=0.33945\nx0=-4.02541, x1=4.68847, y=-0.85858\nx0=6.73446, x1=3.44739, y=1.95350\nx0=-8.29566, x1=-9.07702, y=0.91392\nx0=-3.42806, x1=-0.67683, y=5.06485\nx0=-2.27693, x1=-2.15284, y=1.05764\nx0=-7.64792, x1=-1.37752, y=5.55194\nx0=-4.89503, x1=2.41553, y=-2.02648\nx0=5.82362, x1=-6.04164, y=-0.96391\nx0=-4.92309, x1=-3.03898, y=1.61998\nx0=6.54853, x1=0.57591, y=11.37084\nx0=7.29087, x1=6.73856, y=1.08196\nx0=-9.47294, x1=6.00872, y=-1.57653\nx0=-9.75735, x1=-0.06614, y=147.53605\nx0=2.03948, x1=-5.14864, y=-0.39612\nx0=6.79548, x1=8.71421, y=0.77982\nx0=-0.10584, x1=1.57461, y=-0.06722\nx0=-0.10606, x1=-0.04057, y=2.61445\nx0=-7.33804, x1=4.11691, y=-1.78241\nx0=0.47591, x1=-2.27436, y=-0.20925\nx0=-8.60825, x1=-8.39252, y=1.02571\nx0=9.92806, x1=-6.41314, y=-1.54808\nx0=7.34489, x1=6.91508, y=1.06216\nx0=7.43317, x1=-0.92322, y=-8.05135\nx0=-8.18332, x1=-4.83331, y=1.69311\nx0=-3.25568, x1=-7.96632, y=0.40868\nx0=4.28173, x1=5.60877, y=0.76340\nx0=-1.19948, x1=8.76340, y=-0.13687\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=8.42254, x1=0.05617, y=149.94365\nx0=8.44083, x1=-5.39205, y=-1.56542\nx0=-2.05007, x1=7.19275, y=-0.28502\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 / x1", "data": [[2.490415806142604, -1.8716261495092148, -1.3306160564147123], [-5.491284837461974, -7.109257813615306, 0.7724132365751782], [1.2318347684982953, -7.989065575563378, -0.15419009355314098], [-9.77666457728535, 7.167865675079977, -1.363957560097032], [9.508953099137884, -2.3076830638147916, -4.120562848617], [-9.50847701758413, 0.8233041838291122, -11.549166400881235], [2.480001288420514, -4.781405454550893, -0.5186762160193032], [0.26066886333632766, 4.4151803743336835, 0.05903923310849253], [-7.978917517804584, 1.5711271848540385, -5.078466972453185], [8.156282238633654, 4.925831436361978, 1.6558183819334178], [-8.388199840182637, -0.7384521172342655, 11.35916553614752], [-3.5614722821343836, -0.18432191572548362, 19.322022929918955], [6.030136130658395, 1.8750180191556467, 3.2160416961613363], [5.408091621809394, -5.8678971496947785, -0.9216404929814931], [-9.677353443990405, -1.7865456819887662, 5.416795966402418], [6.5029930109402905, 0.75498885153673, 8.61336296251776], [7.39594133044158, 7.721166770680309, 0.9578787183468551], [-4.194043238398462, -7.107845680172911, 0.5900582858878886], [-5.7001234988141185, 2.7323742384144865, -2.086143039513404], [-2.0846591936778243, -7.403017349973586, 0.2815958811288295], [6.002722329255175, -2.8870753382617114, -2.0791706574825213], [-9.046088070390999, 7.241030229710937, -1.2492819092611522], [-6.149616574919725, -2.6353334614092923, 2.3335250225340007], [-9.195635173486245, 9.28509420989976, -0.9903653065449638], [2.8665068421418844, 2.1760789176873114, 1.3172807377722975], [-4.745864909096847, 1.7420748965603607, -2.7242599720983973], [1.2589235252956854, 7.361623526106623, 0.17101166893840036], [-1.5444756616053574, -0.7764540188416902, 1.9891398899697856], [-8.816378359384947, -8.993003335679862, 0.9803597341508644], [-6.8613189940423736, -4.323507117464351, 1.5869799233883064], [-3.5955199540946854, 0.40493155879292075, -8.879327570349759], [0.4391831195405853, 6.657143724173707, 0.0659717046435102], [8.440814288134344, 4.339369664562081, 1.9451705986395078], [2.454043768921041, -1.3296295508832117, -1.8456597683850609], [7.535456280707912, 6.85542286211475, 1.0991964219087407], [6.537401333236549, -9.683631518763525, -0.6750981096884292], [1.1468524956896893, -9.166637011952151, -0.12511158609142445], [7.064337473068477, -4.5187412860992975, -1.5633418746056622], [-2.082928607587302, 9.86854023137067, -0.21106754988604817], [-5.813097280665474, -7.855843663362019, 0.7399711004658254], [-2.463221065245113, -7.0230731807349684, 0.3507326496329255], [0.03665159789531458, -7.3233571994241515, -0.005004753543661172], [0.7339209590820381, -2.587851091166251, -0.2836024690861507], [4.867293724095541, -7.9002624926556475, -0.6160926587718247], [4.51089930660644, 2.4399176457595306, 1.848791623949351], [6.217888631969288, 9.68423937081717, 0.6420626746078265], [-6.1957857087593515, 2.0248939718120376, -3.0598074738771954], [5.336537677558708, -2.439360728266653, -2.1876787699827873], [6.786478634165519, -0.0851704309305461, -79.6811588249411], [-0.7850142161765667, 2.331463270520956, -0.33670451776028126], [5.067021485645606, -4.247305819291114, -1.1929966197939814], [0.5622120724260391, -3.8021708957132017, -0.14786607121208337], [-5.493765820382652, -9.29708871961047, 0.5909124873461281], [-5.1195670672810945, 5.308334872184595, -0.9644393563238381], [4.772682761210181, 5.083573417472717, 0.9388440707487422], [-3.087955637111275, -3.410374243450784, 0.9054594647614773], [4.980245617025478, -3.383932803384244, -1.4717330119690244], [-1.2240751784350383, -4.595152724293166, 0.26638400329193146], [0.19997725444712167, -6.049133184035924, -0.03305882815985525], [2.299953594938067, -4.7392588552368276, -0.48529815846556773], [-3.563555680389296, 5.178083199416442, -0.6881997726090807], [-3.170437789750629, -9.33990336683398, 0.33945081284340284], [-4.025414466359248, 4.688472913498863, -0.8585768843346488], [6.734455275564667, 3.4473872766845055, 1.9534954256840764], [-8.295664391847842, -9.077019997458946, 0.9139193693712431], [-3.428063980564282, -0.6768342318409104, 5.064850179401161], [-2.2769273408823043, -2.1528429915407017, 1.0576374356277605], [-7.647915482472387, -1.3775217828096125, 5.551937964184924], [-4.8950294610292815, 2.415532081719803, -2.0264808313140406], [5.823618263091717, -6.041636124730269, -0.9639141025481263], [-4.923093529071512, -3.038977155359783, 1.619983723927885], [6.5485262610989, 0.5759050484914425, 11.370843645584408], [7.290872802585241, 6.738563111064998, 1.0819625315393022], [-9.47294104445221, 6.008718284050989, -1.5765327307150259], [-9.757350557464665, -0.06613536311161994, 147.53605481830803], [2.0394827310788095, -5.148635021050996, -0.39612105397645525], [6.795476264417147, 8.714207771898032, 0.7798157264888156], [-0.10584454739208127, 1.5746092123094897, -0.06721956569582009], [-0.1060559224912403, -0.040565364948754734, 2.614445170780991], [-7.338036388309314, 4.1169114163009475, -1.7824129902951746], [0.47591268424621447, -2.2743645671268986, -0.2092508347715834], [-8.608248687615315, -8.39251744025848, 1.025705189043991], [9.928058834907905, -6.413136231154796, -1.548081699352921], [7.344885440444354, 6.915077366641231, 1.0621552082521224], [7.433174476414116, -0.923220709897695, -8.051351531355714], [-8.183323666279321, -4.83331283994543, 1.6931086269954159], [-3.2556828265211895, -7.9663202949565814, 0.40868088477214987], [4.281728073435801, 5.608774467374403, 0.7633981537931542], [-1.1994780421099644, 8.763404260570184, -0.1368735261371956], [8.42254157219148, 0.056171379427139456, 149.9436484930276], [8.440829318038823, -5.392052157751841, -1.5654205617992643], [-2.050065382410457, 7.1927490172984285, -0.28501833964734313]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.65979, y=-2.19165\nx0=7.41299, y=1.15611\nx0=-7.09458, y=1.19164\nx0=-8.11070, y=1.55919\nx0=-8.40674, y=1.39467\nx0=-0.52582, y=-0.02548\nx0=5.15124, y=1.25725\nx0=-8.91945, y=-1.29720\nx0=8.15889, y=2.05744\nx0=-1.60538, y=-0.29608\nx0=-6.92965, y=-0.88924\nx0=7.95548, y=-0.65893\nx0=4.44190, y=0.47572\nx0=-5.42854, y=0.70693\nx0=-7.17256, y=1.90207\nx0=5.38901, y=1.03826\nx0=-2.04450, y=0.16926\nx0=8.34310, y=2.08674\nx0=9.88920, y=-1.90257\nx0=4.93090, y=-0.62229\nx0=-9.84897, y=-2.40156\nx0=-1.72458, y=-0.51079\nx0=7.21756, y=2.12044\nx0=2.44445, y=0.25079\nx0=-5.67329, y=-1.50810\nx0=-3.22642, y=0.95733\nx0=-3.89541, y=-0.71389\nx0=-2.34345, y=0.58529\nx0=2.58442, y=-0.39224\nx0=9.74011, y=-2.91639\nx0=3.61137, y=-0.69774\nx0=0.65760, y=-0.16496\nx0=-5.41719, y=0.80791\nx0=-8.15777, y=2.04780\nx0=-4.42362, y=0.61275\nx0=6.67530, y=-1.78602\nx0=9.87732, y=-2.06453\nx0=-8.48125, y=0.29912\nx0=-7.78046, y=-2.29153\nx0=-9.11150, y=1.76207\nx0=-7.80442, y=-2.20580\nx0=-1.10266, y=0.19889\nx0=0.10122, y=0.01804\nx0=-8.12144, y=1.68386\nx0=6.20230, y=1.77776\nx0=-5.47827, y=0.22370\nx0=-2.60122, y=-0.46351\nx0=-2.49970, y=0.00139\nx0=-1.06309, y=0.12314\nx0=-9.46196, y=0.67201\nx0=-5.10217, y=0.91648\nx0=1.15296, y=0.28356\nx0=-4.79521, y=-1.38091\nx0=-4.24276, y=1.27151\nx0=1.84035, y=-0.46550\nx0=-5.99092, y=-0.10248\nx0=6.36411, y=1.43920\nx0=-6.46356, y=0.44016\nx0=3.27177, y=0.97236\nx0=0.50791, y=-0.00757\nx0=1.45478, y=0.12233\nx0=-1.31681, y=0.36074\nx0=4.69351, y=-1.32030\nx0=8.31672, y=2.27895\nx0=-8.73929, y=-2.61585\nx0=-9.52533, y=-0.45281\nx0=7.68530, y=-2.11766\nx0=4.83697, y=-1.23976\nx0=8.29867, y=2.37411\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.40424, y=1.25728\nx0=7.11141, y=1.37442\nx0=-0.12640, y=0.02705\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 0.3 * x0 * sin(2 * pi * x0)", "data": [[8.659787773946789, -2.191652015586414], [7.412992557235196, 1.1561094702882444], [-7.094577074555957, 1.1916411612751892], [-8.11069743049261, 1.55918663728524], [-8.406742145316686, 1.3946696372578218], [-0.5258239591846419, -0.025483379159376075], [5.151235648101126, 1.2572456267743237], [-8.919449145581762, -1.297201296185321], [8.15889004254307, 2.057436758456267], [-1.6053760237489243, -0.29608215668823357], [-6.929653780665957, -0.8892407684697777], [7.955480204398132, -0.6589343577800336], [4.441900610667071, 0.47572126621562205], [-5.42853669168593, 0.7069263691105857], [-7.172564492780385, 1.902067644154925], [5.389009055411835, 1.0382611014096674], [-2.04449810766254, 0.16926080143050728], [8.343104327581841, 2.086735485452187], [9.889198727469683, -1.9025683400874722], [4.9308962446604525, -0.6222947482506244], [-9.848972480431362, -2.4015583972896963], [-1.7245760024814416, -0.5107856548270222], [7.217558077607322, 2.1204393397079486], [2.4444503447893524, 0.250789829678457], [-5.673292309857684, -1.508104286716826], [-3.2264249203711604, 0.9573279936235455], [-3.8954069418244615, -0.7138933645701954], [-2.3434500796919666, 0.5852872608381731], [2.584421067521829, -0.3922430680059192], [9.740110164755492, -2.916393385467936], [3.611366972498903, -0.6977359150390559], [0.6576003599363069, -0.16495643265091292], [-5.417194359857982, 0.8079082348831761], [-8.157772661357761, 2.047796831291636], [-4.423615031850421, 0.6127504332598367], [6.675298513820163, -1.7860224486747305], [9.87732001076959, -2.064531207871022], [-8.481245851922147, 0.2991249240020319], [-7.780457273954502, -2.2915270993024346], [-9.111495084863968, 1.7620735270172683], [-7.804415919855088, -2.20580318288734], [-1.102660834958808, 0.19888518530330868], [0.10121893760025813, 0.01803612336633314], [-8.121440269177395, 1.6838566381941007], [6.202303558922743, 1.7777588759857392], [-5.478269452943387, 0.22369946900513796], [-2.601219513408566, -0.4635115429873067], [-2.4997048595143445, 0.00139065178068539], [-1.0630913264989879, 0.12314213497630659], [-9.461960301258102, 0.6720111714715642], [-5.102168100934814, 0.9164788919927098], [1.15295634261485, 0.28355637286810487], [-4.795211446159151, -1.3809089520300812], [-4.242755041866788, 1.271507965248464], [1.8403506273346775, -0.465504961225408], [-5.9909198250496924, -0.10248332754669574], [6.364106397677709, 1.4392024545485214], [-6.463555054888939, 0.44015712225194853], [3.2717672922548466, 0.9723644981981572], [0.507910476382964, -0.007570282823396451], [1.4547849693382098, 0.1223277540056666], [-1.3168145703766942, 0.36074151493870565], [4.693514587482872, -1.3203021099291756], [8.316723941764636, 2.278946264757416], [-8.739289985073249, -2.615853052038626], [-9.5253260483455, -0.4528079074057049], [7.685295082889045, -2.1176585840988866], [4.836974605223595, -1.23975581375208], [8.29866638108307, 2.374113515384641], [-7.404241973504259, 1.2572763258487656], [7.111411005750384, 1.3744151237190712], [-0.1263998771591801, 0.02704826569458444]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.18554, y=3.17305\nx0=9.69585, y=3.45339\nx0=5.12302, y=2.51024\nx0=0.27535, y=0.58196\nx0=3.25215, y=2.00003\nx0=6.34029, y=2.79259\nx0=6.77462, y=2.88665\nx0=4.31147, y=2.30285\nx0=9.48367, y=3.41539\nx0=8.17231, y=3.17048\nx0=5.32277, y=2.55871\nx0=0.75611, y=0.96438\nx0=5.43901, y=2.58650\nx0=8.27961, y=3.19122\nx0=7.23050, y=2.98220\nx0=8.89922, y=3.30848\nx0=6.28557, y=2.78051\nx0=6.28017, y=2.77932\nx0=9.52327, y=3.42252\nx0=6.18865, y=2.75899\nx0=2.04766, y=1.58702\nx0=1.68372, y=1.43909\nx0=9.80968, y=3.47360\nx0=8.25967, y=3.18738\nx0=8.96746, y=3.32114\nx0=5.97785, y=2.71160\nx0=6.02408, y=2.72206\nx0=0.71601, y=0.93845\nx0=4.56999, y=2.37088\nx0=0.19327, y=0.48757\nx0=0.28248, y=0.58945\nx0=7.14040, y=2.96356\nx0=2.55712, y=1.77349\nx0=8.70377, y=3.27195\nx0=5.82794, y=2.67738\nx0=4.34836, y=2.31268\nx0=3.20703, y=1.98611\nx0=5.91743, y=2.69786\nx0=5.13288, y=2.51266\nx0=4.30807, y=2.30194\nx0=3.05005, y=1.93689\nx0=5.08460, y=2.50081\nx0=0.31675, y=0.62418\nx0=9.31201, y=3.38434\nx0=3.72408, y=2.14024\nx0=5.10668, y=2.50624\nx0=4.39369, y=2.32470\nx0=5.20443, y=2.53011\nx0=1.07626, y=1.15057\nx0=8.45970, y=3.22574\nx0=5.78208, y=2.66683\nx0=9.20488, y=3.36482\nx0=8.39566, y=3.21351\nx0=0.69187, y=0.92250\nx0=6.13690, y=2.74743\nx0=1.55996, y=1.38519\nx0=0.26762, y=0.57373\nx0=1.80599, y=1.49043\nx0=8.62542, y=3.25719\nx0=1.52379, y=1.36904\nx0=2.59381, y=1.78617\nx0=2.89272, y=1.88628\nx0=6.68404, y=2.86729\nx0=5.23758, y=2.53815\nx0=0.77472, y=0.97617\nx0=0.90243, y=1.05356\nx0=7.54188, y=3.04574\nx0=1.60847, y=1.40656\nx0=1.74196, y=1.46376\nx0=9.46212, y=3.41151\nx0=3.08472, y=1.94787\nx0=8.25328, y=3.18615\nx0=9.33127, y=3.38784\nx0=4.73709, y=2.41384\nx0=9.35901, y=3.39287\nx0=9.61718, y=3.43935\nx0=4.26818, y=2.29126\nx0=3.70904, y=2.13591\nx0=1.31627, y=1.27241\nx0=5.50003, y=2.60097\nx0=9.20850, y=3.36548\nx0=7.31254, y=2.99907\nx0=5.73906, y=2.65689\nx0=1.83654, y=1.50298\nx0=7.45079, y=3.02729\nx0=2.83456, y=1.86722\nx0=6.86251, y=2.90532\nx0=6.60273, y=2.84980\nx0=5.91124, y=2.69645\nx0=5.92744, y=2.70014\nx0=9.61470, y=3.43891\nx0=7.07469, y=2.94989\nx0=1.64345, y=1.42178\nx0=0.58408, y=0.84759\nx0=8.10609, y=3.15761\nx0=5.87593, y=2.68838\nx0=3.28689, y=2.01069\nx0=7.25729, y=2.98772\nx0=8.81502, y=3.29279\nx0=5.27786, y=2.54789\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=2.03522, y=1.58219\nx0=5.58907, y=2.62194\nx0=6.51638, y=2.83110\nx0=9.42881, y=3.40550\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sqrt(1.23 * x0)", "data": [[8.185542686719568, 3.1730454621175914], [9.695852749379831, 3.4533894772726055], [5.123018281303074, 2.510241519456397], [0.27534554052458754, 0.5819579150121095], [3.2521457564498406, 2.0000348198052182], [6.340293643286191, 2.7925904069952674], [6.774615510555704, 2.886654998087491], [4.311472057575439, 2.302848373388438], [9.48367399438294, 3.415394415450576], [8.172310801584917, 3.1704798195146138], [5.322771750862558, 2.558712421035417], [0.756114924070957, 0.96437614892078], [5.43901183156256, 2.5865004451617493], [8.279605725742554, 3.1912246932272432], [7.230500273112575, 2.9821997478251587], [8.899215969080775, 3.3084793549256615], [6.285568223398962, 2.780512347532501], [6.280172944818714, 2.779318751443777], [9.523270186123511, 3.422516958165713], [6.1886466132186415, 2.758991724209934], [2.0476641038513144, 1.5870182253953826], [1.6837194627362533, 1.4390882318904514], [9.809676410415143, 3.4736007232856503], [8.259670777859474, 3.1873805949034586], [8.9674643135728, 3.321141536534465], [5.977845374261739, 2.7115954363329937], [6.024078530719357, 2.722061092772311], [0.7160128267898813, 0.9384539290511557], [4.569985826580127, 2.370882233830592], [0.1932704129395804, 0.4875680546505105], [0.28247962859205733, 0.5894488469479174], [7.140399466544459, 2.9635605854865963], [2.5571249600269943, 1.7734891318621588], [8.703768439470476, 3.2719466958599206], [5.827936590478439, 2.677379690348095], [4.348363216237714, 2.312679561887546], [3.2070309353707653, 1.9861138060307697], [5.917428011252447, 2.6978577527068563], [5.132883031891467, 2.5126571849789787], [4.3080708911093675, 2.301939876726694], [3.0500468027997627, 1.936893793537399], [5.084603142359175, 2.500812241073241], [0.3167450960859207, 0.624176632200919], [9.31201492663296, 3.384343120866811], [3.7240753565847418, 2.1402365964068597], [5.1066837234981675, 2.5062364174001477], [4.393690360464868, 2.3247019472121093], [5.2044344786132894, 2.530109564563228], [1.0762602406833044, 1.1505651202954401], [8.4596974544016, 3.2257445448940834], [5.782083911020981, 2.6668264305267013], [9.204875698448959, 3.364817544695728], [8.395659210094857, 3.213512226274648], [0.6918719794616994, 0.9224979863056004], [6.136899407988484, 2.7474326692069844], [1.5599620666091105, 1.3851907240265509], [0.26761520018185536, 0.5737305083605727], [1.8059935789474428, 1.4904268187688212], [8.625420480214178, 3.257187005786344], [1.5237890707915882, 1.3690363607565899], [2.5938138129668364, 1.7861665627676495], [2.8927183574624653, 1.8862777048141193], [6.684038041343654, 2.8672925889857614], [5.237582812242625, 2.5381542228671625], [0.7747245030723714, 0.9761716748497746], [0.9024314398221837, 1.0535609479196173], [7.541877201569295, 3.0457361930952267], [1.60846790310978, 1.4065615951052495], [1.7419570038003789, 1.4637647060489125], [9.462119691439725, 3.4115109878865737], [3.0847154438578595, 1.9478706312137763], [8.253281204391229, 3.1861474983749862], [9.331271026286666, 3.387840516071051], [4.737085282420365, 2.413838208616524], [9.359013351206592, 3.3928728862107516], [9.617179669964125, 3.4393503738432694], [4.268182904135504, 2.2912583817820837], [3.7090376532756144, 2.1359111202315963], [1.316273933644899, 1.2724059644560066], [5.500033533078381, 2.600969289646917], [9.208501816414834, 3.3654802382706412], [7.31254363245729, 2.999071300906739], [5.7390560749259185, 2.6568852011629818], [1.8365382732886628, 1.5029777364103065], [7.450794861371179, 3.027288833178381], [2.8345638643731372, 1.8672208099683734], [6.86251301631753, 2.9053211543770057], [6.602730364817738, 2.849799703264388], [5.911240101159329, 2.696446796142278], [5.9274417153546395, 2.7001394982271165], [9.614704592809032, 3.4389077697948043], [7.0746887397093845, 2.949892735311323], [1.6434537099327606, 1.421776375952734], [0.5840788030786872, 0.8475947898534908], [8.106094738195395, 3.157609305785044], [5.8759340645847296, 2.6883822085855273], [3.2868861426826017, 2.0106889255923175], [7.257292761266974, 2.987719882512139], [8.815018926310236, 3.292791107762768], [5.27785948555901, 2.5478946538735783], [2.03521904592253, 1.582188176698557], [5.589066893645168, 2.6219367420255466], [6.516379094135334, 2.831103368968791], [9.428805457957635, 3.405500068020533]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=9.41139, x1=1.12798, y=5.98726\nx0=8.02538, x1=3.84189, y=59.22774\nx0=4.98317, x1=0.17131, y=0.07312\nx0=5.00028, x1=-5.39439, y=72.75281\nx0=-4.24878, x1=7.99253, y=-135.70717\nx0=1.29463, x1=-8.46301, y=46.36222\nx0=-2.35570, x1=-1.08997, y=-1.39932\nx0=1.51094, x1=-2.45721, y=4.56142\nx0=-0.72662, x1=4.67481, y=-7.93972\nx0=-0.29581, x1=-9.94687, y=-14.63397\nx0=-3.66147, x1=-5.69641, y=-59.40570\nx0=-5.17759, x1=-9.70771, y=-243.96727\nx0=6.65642, x1=-9.07307, y=273.98032\nx0=4.04934, x1=4.84971, y=47.61968\nx0=-5.84515, x1=-6.29151, y=-115.68449\nx0=-1.52681, x1=-4.46075, y=-15.19050\nx0=-8.82468, x1=-7.51791, y=-249.38073\nx0=3.09307, x1=-8.89378, y=122.33011\nx0=-9.78604, x1=-1.74544, y=-14.90686\nx0=-9.26237, x1=1.22562, y=-6.95667\nx0=6.00852, x1=4.99790, y=75.04344\nx0=-8.04057, x1=8.21317, y=-271.19300\nx0=-5.44529, x1=-2.67737, y=-19.51679\nx0=-9.15215, x1=-9.41482, y=-405.61743\nx0=-5.38451, x1=-2.86949, y=-22.16789\nx0=-0.45422, x1=-4.67806, y=-4.97014\nx0=-3.03494, x1=9.12222, y=-126.27632\nx0=0.18616, x1=3.60378, y=1.20882\nx0=2.50786, x1=9.39114, y=110.58846\nx0=-5.30638, x1=-2.89661, y=-22.26122\nx0=-5.44760, x1=5.72519, y=-89.28024\nx0=1.72944, x1=7.10292, y=43.62644\nx0=9.91796, x1=8.89829, y=392.64993\nx0=2.05903, x1=6.07317, y=37.97201\nx0=2.94329, x1=-3.21189, y=15.18183\nx0=9.26185, x1=-9.63961, y=430.31498\nx0=9.81810, x1=8.45202, y=350.68624\nx0=-3.62705, x1=-9.44337, y=-161.72513\nx0=-4.36402, x1=-8.84778, y=-170.81489\nx0=-6.52718, x1=-9.77665, y=-311.94358\nx0=1.67593, x1=-1.20719, y=1.22117\nx0=-5.31859, x1=6.54793, y=-114.01840\nx0=0.75135, x1=7.19892, y=19.46914\nx0=-9.46886, x1=-1.77698, y=-14.94980\nx0=-2.17420, x1=-7.63533, y=-63.37593\nx0=4.42784, x1=5.13570, y=58.39308\nx0=1.06010, x1=-7.77888, y=32.07376\nx0=4.02073, x1=-3.51197, y=24.79570\nx0=1.27329, x1=-3.24409, y=6.70011\nx0=6.31897, x1=0.52189, y=0.86055\nx0=3.52042, x1=9.86398, y=171.26512\nx0=5.76543, x1=3.92298, y=44.36420\nx0=2.47905, x1=6.16718, y=47.14410\nx0=5.48431, x1=-8.35564, y=191.44835\nx0=-7.91700, x1=2.32599, y=-21.41635\nx0=-9.24469, x1=-2.50123, y=-28.91800\nx0=2.80625, x1=-0.81335, y=0.92822\nx0=9.62092, x1=-4.08217, y=80.16208\nx0=5.91308, x1=-3.88054, y=44.52131\nx0=9.73991, x1=0.24542, y=0.29332\nx0=9.23062, x1=-6.82488, y=214.97650\nx0=6.66971, x1=5.20545, y=90.36351\nx0=6.74277, x1=-7.12380, y=171.09273\nx0=-6.04994, x1=-1.83362, y=-10.17050\nx0=4.18017, x1=-2.28318, y=10.89541\nx0=5.78242, x1=9.92718, y=284.92577\nx0=3.91969, x1=1.86202, y=6.79499\nx0=6.13699, x1=-1.97083, y=11.91853\nx0=-7.57098, x1=3.20889, y=-38.97906\nx0=0.40880, x1=-7.22302, y=10.66398\nx0=-4.90283, x1=3.28161, y=-26.39919\nx0=9.96708, x1=6.16698, y=189.53189\nx0=4.38781, x1=-5.81857, y=74.27637\nx0=-8.63672, x1=1.21308, y=-6.35470\nx0=2.85026, x1=6.61294, y=62.32241\nx0=8.60091, x1=-2.92775, y=36.86217\nx0=-9.38162, x1=-6.88308, y=-222.23579\nx0=-7.33672, x1=-0.73919, y=-2.00441\nx0=4.71710, x1=3.26894, y=25.20344\nx0=-3.95119, x1=-7.77946, y=-119.56307\nx0=-6.64957, x1=5.60122, y=-104.31080\nx0=5.03180, x1=-6.02975, y=91.47283\nx0=8.01417, x1=-4.97252, y=99.07916\nx0=4.61271, x1=3.79643, y=33.24125\nx0=-2.79337, x1=-1.71048, y=-4.08633\nx0=-2.30057, x1=-8.96604, y=-92.47118\nx0=3.20954, x1=-8.66199, y=120.40578\nx0=-8.38210, x1=0.65998, y=-1.82549\nx0=-8.14070, x1=2.60043, y=-27.52460\nx0=5.00166, x1=5.57465, y=77.71760\nx0=-8.23166, x1=-9.77359, y=-393.15679\nx0=5.07469, x1=6.40706, y=104.15909\nx0=4.16939, x1=-8.03312, y=134.52746\nx0=0.51097, x1=-5.59951, y=8.01067\nx0=8.12462, x1=-2.96490, y=35.71029\nx0=-3.13721, x1=-4.58925, y=-33.03673\nx0=-2.33335, x1=5.81335, y=-39.42792\nx0=6.55363, x1=-6.57062, y=141.47018\nx0=9.52635, x1=-5.47308, y=142.67922\nx0=-9.66502, x1=8.57377, y=-355.23604\nx0=4.73034, x1=9.73164, y=223.99317\nx0=4.36159, x1=-7.34253, y=117.57256\nx0=-2.31319, x1=3.93820, y=-17.93809\nx0=8.38362, x1=-0.24585, y=0.25335\nx0=-8.39807, x1=7.57064, y=-240.66620\nx0=8.41028, x1=-7.17584, y=216.53413\nx0=-6.42598, x1=1.00905, y=-3.27143\nx0=-2.14394, x1=-6.66744, y=-47.65432\nx0=-2.51822, x1=-5.41950, y=-36.98120\nx0=2.15496, x1=-7.77560, y=65.14454\nx0=5.76281, x1=4.55050, y=59.66529\nx0=4.64750, x1=-3.03953, y=21.46846\nx0=3.97283, x1=3.90379, y=30.27215\nx0=-8.75102, x1=-8.71175, y=-332.07717\nx0=9.23388, x1=-0.80711, y=3.00759\nx0=-6.50092, x1=9.24096, y=-277.57445\nx0=-5.29594, x1=3.87594, y=-39.78028\nx0=6.54559, x1=-9.43407, y=291.28405\nx0=1.66627, x1=-1.67882, y=2.34815\nx0=-6.76181, x1=-8.77911, y=-260.57589\nx0=3.66284, x1=1.51770, y=4.21850\nx0=9.07476, x1=2.46401, y=27.54792\nx0=-7.44163, x1=9.33102, y=-323.96358\nx0=4.53850, x1=3.44709, y=26.96424\nx0=0.42893, x1=6.08609, y=7.94398\nx0=-2.83767, x1=-7.04297, y=-70.37908\nx0=-4.97309, x1=-2.96766, y=-21.89901\nx0=9.72226, x1=0.61596, y=1.84437\nx0=-1.86276, x1=-4.67934, y=-20.39368\nx0=-6.21064, x1=-1.46827, y=-6.69453\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.78799, x1=2.86128, y=3.22561\nx0=2.87358, x1=-8.24777, y=97.73861\nx0=8.18502, x1=5.91203, y=143.04161\nx0=-1.38690, x1=4.00054, y=-11.09818\nx0=-2.41613, x1=7.72393, y=-72.07216\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1**2 / 2", "data": [[9.411386050364396, 1.1279822108616386, 5.987259665376513], [8.025380538926676, 3.841888440011566, 59.227736874393585], [4.983165288459501, 0.17130759618561342, 0.07311871309263099], [5.000283846384017, -5.3943927885791165, 72.75281378385898], [-4.248780869887357, 7.992529198477179, -135.70717201599095], [1.294627201585996, -8.463007771558678, 46.36221872329259], [-2.3556984023263006, -1.0899681810114856, -1.3993209351194065], [1.510938699817581, -2.457205358119559, 4.561416788020765], [-0.7266193731548665, 4.674811249365526, -7.939719106015958], [-0.29581460608926413, -9.946867278067234, -14.63397350743052], [-3.66146643576835, -5.696413639492322, -59.40569716574903], [-5.177592399291053, -9.707711196650493, -243.96726506280106], [6.656417769542845, -9.073072865143917, 273.98032277796233], [4.049340936710861, 4.849713016548396, 47.61967510352358], [-5.84514641594061, -6.291509551554022, -115.68448544585178], [-1.526812495262071, -4.460752850945287, -15.19049874961166], [-8.82467896613932, -7.5179077076073515, -249.3807341780392], [3.0930743999564463, -8.893782494186873, 122.33011364359575], [-9.78604289651682, -1.745438557240231, -14.90686266280964], [-9.262372250045605, 1.2256160895956274, -6.956665839393191], [6.008515083227895, 4.997902561795087, 75.04343931136793], [-8.04057049508048, 8.213169865448936, -271.1930018431453], [-5.44529103150889, -2.677371879583559, -19.51679479788394], [-9.152145866230443, -9.414815993882575, -405.6174313700115], [-5.38450544659915, -2.869487004437337, -22.167889572409912], [-0.4542205016576233, -4.678062377085985, -4.970141504728241], [-3.0349435870361035, 9.122222274707937, -126.27632307959588], [0.18615626076877234, 3.6037754525883425, 1.2088240634128478], [2.5078600271607634, 9.391138570582932, 110.58845615331614], [-5.306379676384029, -2.8966117253220602, -22.26121653041133], [-5.447602954375162, 5.725190582419437, -89.28023968401467], [1.7294430016112443, 7.102917133244663, 43.62643782539361], [9.91795611772763, 8.898292296946806, 392.6499278811224], [2.059027257035426, 6.073174049451943, 37.972007271123864], [2.9432935412972974, -3.2118868320085365, 15.181827465192162], [9.261853392240734, -9.639605937982093, 430.31498268059653], [9.818104072835801, 8.452020545347263, 350.6862385340952], [-3.627052203777044, -9.44336671204084, -161.7251342978068], [-4.364020257585981, -8.847783304430287, -170.8148867505333], [-6.527183791006639, -9.776650786709855, -311.9435797640729], [1.6759328302536662, -1.2071879137931987, 1.2211706850916433], [-5.3185917992845955, 6.547931654781916, -114.01839923136647], [0.7513496122782488, 7.198920444319729, 19.46914229713784], [-9.468864142762804, -1.776984875233392, -14.949798959496087], [-2.17419854044336, -7.635325585171504, -63.375927187360595], [4.4278418236621775, 5.135699768745772, 58.39307643888712], [1.0600978856863446, -7.778877525840679, 32.0737574251049], [4.020728447807944, -3.5119704579260613, 24.795704674166636], [1.2732884642316158, -3.244086359275733, 6.700105211725591], [6.318972658849489, 0.5218920050386444, 0.8605532880531543], [3.5204217079126643, 9.863978438215874, 171.26511999121004], [5.765427370396479, 3.922975134749594, 44.364196547757764], [2.479047152243826, 6.167175122935067, 47.14410042709448], [5.484309565679567, -8.355642080436551, 191.44834748392256], [-7.9170032559345955, 2.3259873489029914, -21.416353385072497], [-9.24468514230628, -2.501226737740483, -28.91800003621073], [2.8062485842945524, -0.8133514355372888, 0.9282236267362933], [9.620919232199512, -4.082171081807234, 80.1620798630799], [5.913079015374436, -3.880539657654385, 44.52131045436491], [9.739906212156392, 0.24541936840707024, 0.29332052086385413], [9.230624310465359, -6.824879035940128, 214.9765042122392], [6.669711296972686, 5.205447042026831, 90.36351270938317], [6.742773400831219, -7.123796256350059, 171.09272728243863], [-6.049943310187514, -1.833624795024523, -10.170498863335666], [4.180174690942977, -2.2831768666039354, 10.895409225680025], [5.7824201562210416, 9.92718329371235, 284.925769893888], [3.9196886483573543, 1.8620171371231393, 6.794991580265566], [6.136993614735335, -1.970826939747285, 11.918528958220598], [-7.570980284273576, 3.208888256408116, -38.979055118261186], [0.4088009983189913, -7.2230162847651025, 10.663975534827655], [-4.9028292293030535, 3.2816094597520458, -26.399187513030597], [9.967077932915018, 6.1669754235429295, 189.53189016215686], [4.387809774143662, -5.818572397304795, 74.27637160261159], [-8.636717732448467, 1.2130761190958026, -6.354696841080834], [2.8502645084105733, 6.612939035531674, 62.322405433630166], [8.60090687269161, -2.9277456604129437, 36.862173721787734], [-9.381622764857624, -6.883083163166088, -222.23579139817693], [-7.336723449888504, -0.7391915247498915, -2.004407924437594], [4.717096638025009, 3.2689443516490364, 25.20344067213022], [-3.951191914208321, -7.779460092198418, -119.56306599260513], [-6.649565897642877, 5.601224607681697, -104.31079967417547], [5.031797895883582, -6.029752214096893, 91.47283195491458], [8.014171412834568, -4.972523564001334, 99.07916348842362], [4.612714279664232, 3.7964300783360034, 33.24125178335705], [-2.793369775070582, -1.710478994959903, -4.0863345972662], [-2.3005701900691244, -8.966035524019013, -92.47118070148542], [3.2095362601618955, -8.661986847398966, 120.40577870817292], [-8.382100527233309, 0.6599762580963748, -1.8254901525587075], [-8.140701439809037, 2.6004266949651687, -27.524602958062573], [5.00165648693066, 5.5746519382088895, 77.71759969077435], [-8.23166192560381, -9.773590164676486, -393.15678738305127], [5.0746866958883174, 6.407062761398766, 104.15909442943435], [4.169386345098843, -8.03312281902575, 134.52746483897062], [0.5109738156692707, -5.599512393628496, 8.010674227544849], [8.124622282426085, -2.9649004035746156, 35.71029207411252], [-3.137206957415877, -4.589252245921498, -33.03672833265407], [-2.333354270122186, 5.813351274098423, -39.427915655350226], [6.553629368569318, -6.570622362578343, 141.4701767151251], [9.526354877009467, -5.473082307743717, 142.67921754391523], [-9.665023436692078, 8.573774450300913, -355.23604363981514], [4.730341927909365, 9.731641891631028, 223.99317060628343], [4.361589598219762, -7.342527418222231, 117.57255514744752], [-2.313186183302342, 3.938200777563214, -17.93809423194391], [8.383624710864126, -0.24584564662977648, 0.25335348235181304], [-8.398070233831936, 7.57064358357178, -240.66620400107863], [8.410282206893609, -7.175842349032562, 216.53412572274993], [-6.425984515112278, 1.0090531599158226, -3.271431058883916], [-2.143944227528733, -6.667444208641209, -47.65431908179775], [-2.5182161404796233, -5.419497215100897, -36.98120025680531], [2.1549648517235713, -7.775600173364863, 65.14454227371483], [5.762810929342619, 4.5504954424561035, 59.665288232100934], [4.647498676042069, -3.0395253830347757, 21.468456829284687], [3.972828445268359, 3.9037926430643406, 30.272152228099124], [-8.751018464594658, -8.711746061070393, -332.0771704580032], [9.233878715281257, -0.8071087942854671, 3.0075879011132973], [-6.500923033591805, 9.240962895562902, -277.57444592999815], [-5.2959367552836145, 3.875944433813846, -39.780283971669256], [6.545591163501278, -9.434066008610282, 291.28404801005286], [1.6662717321175151, -1.67882231752386, 2.348147094317779], [-6.761808904558102, -8.779113603111641, -260.575893220291], [3.662844577382643, 1.517695626034838, 4.218498124102545], [9.074762561150354, 2.4640061440401677, 27.547922201461052], [-7.441627568894997, 9.331020074978756, -323.96357511142173], [4.538500776373358, 3.447091958054397, 26.96423831611369], [0.42893488577194283, 6.086091420635238, 7.943983201312715], [-2.837667043647752, -7.04297363916387, -70.37907693420331], [-4.973089528953329, -2.9676595345872343, -21.899007481923086], [9.722256963770327, 0.6159641744530653, 1.8443698194746574], [-1.8627559739758297, -4.679342093328424, -20.393678193695376], [-6.210644195929902, -1.4682725267757686, -6.694528567598136], [0.7879919827361643, 2.8612774770043448, 3.2256092490585395], [2.8735770158528844, -8.247771996119688, 97.7386056418445], [8.185015508129403, 5.91202737954565, 143.0416082322103], [-1.3868999472048653, 4.000537840443386, -11.098183501764966], [-2.416133275822217, 7.723929896537928, -72.0721599576712]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.65370, x1=-4.17543, y=-5.08620\nx0=5.36972, x1=-7.30047, y=-6.23912\nx0=4.62771, x1=9.11915, y=6.71647\nx0=-2.00080, x1=7.39578, y=-2.35509\nx0=2.65094, x1=-1.57578, y=-0.66484\nx0=0.64530, x1=5.43909, y=0.55861\nx0=1.35404, x1=2.37213, y=0.51120\nx0=0.23986, x1=8.38218, y=0.31999\nx0=1.06193, x1=-7.87978, y=-1.33177\nx0=4.12907, x1=-2.41321, y=-1.58587\nx0=3.66593, x1=3.84578, y=2.24382\nx0=5.55063, x1=-9.70366, y=-8.57232\nx0=8.79585, x1=2.06816, y=2.89522\nx0=2.08238, x1=6.40542, y=2.12289\nx0=2.75101, x1=-7.74521, y=-3.39113\nx0=3.42889, x1=-6.35708, y=-3.46922\nx0=1.35338, x1=7.35507, y=1.58426\nx0=-0.45439, x1=2.28378, y=-0.16516\nx0=2.11227, x1=6.20298, y=2.08530\nx0=-9.38632, x1=-2.33849, y=3.49342\nx0=6.87433, x1=-1.95720, y=-2.14135\nx0=-9.51758, x1=2.39872, y=-3.63351\nx0=-6.06732, x1=-8.57507, y=8.28046\nx0=7.61531, x1=-7.84763, y=-9.51144\nx0=6.54339, x1=-7.61190, y=-7.92713\nx0=-2.72861, x1=-3.03346, y=1.31735\nx0=8.77795, x1=-2.59163, y=-3.62064\nx0=-4.53338, x1=4.65854, y=-3.36118\nx0=6.58815, x1=5.21480, y=5.46791\nx0=-9.05889, x1=-8.97342, y=12.93759\nx0=1.34165, x1=-4.23464, y=-0.90422\nx0=0.08558, x1=-6.57614, y=-0.08957\nx0=7.70536, x1=-5.69934, y=-6.98936\nx0=3.55478, x1=2.46473, y=1.39445\nx0=5.69666, x1=8.01583, y=7.26756\nx0=-6.56384, x1=-2.01509, y=2.10510\nx0=1.27432, x1=3.82681, y=0.77613\nx0=8.93978, x1=8.90291, y=12.66715\nx0=9.21583, x1=3.35054, y=4.91439\nx0=6.27420, x1=1.73845, y=1.73596\nx0=8.78896, x1=-6.37762, y=-8.92105\nx0=1.73281, x1=8.74045, y=2.41049\nx0=7.42785, x1=0.03033, y=0.03586\nx0=-3.94434, x1=7.66010, y=-4.80872\nx0=7.64783, x1=3.37622, y=4.10950\nx0=9.25387, x1=7.82441, y=11.52378\nx0=8.98697, x1=7.01203, y=10.02946\nx0=5.88094, x1=-1.05400, y=-0.98652\nx0=-5.39665, x1=8.47992, y=-7.28343\nx0=2.75669, x1=-4.99544, y=-2.19171\nx0=6.39461, x1=6.32600, y=6.43818\nx0=-4.44194, x1=-6.37582, y=4.50743\nx0=9.55484, x1=-7.88779, y=-11.99496\nx0=-8.52251, x1=-6.56015, y=8.89819\nx0=-4.51028, x1=-3.51489, y=2.52311\nx0=5.73153, x1=3.40957, y=3.11021\nx0=7.03134, x1=7.45465, y=8.34229\nx0=-1.59311, x1=-3.65022, y=0.92552\nx0=9.82323, x1=5.56071, y=8.69370\nx0=6.33535, x1=-1.54577, y=-1.55861\nx0=6.57085, x1=9.33626, y=9.76371\nx0=4.37867, x1=-1.90599, y=-1.32826\nx0=2.99323, x1=9.58847, y=4.56783\nx0=4.26807, x1=4.51560, y=3.06737\nx0=2.56231, x1=4.92688, y=2.00920\nx0=-6.12240, x1=-2.65020, y=2.58238\nx0=3.71512, x1=5.19613, y=3.07237\nx0=-8.58973, x1=-3.20825, y=4.38599\nx0=-8.60468, x1=-0.12565, y=0.17208\nx0=0.84813, x1=3.89114, y=0.52524\nx0=9.51319, x1=9.01330, y=13.64677\nx0=1.78144, x1=8.45537, y=2.39731\nx0=-3.34222, x1=-6.69968, y=3.56377\nx0=-8.05642, x1=0.65161, y=-0.83551\nx0=3.24615, x1=-5.38493, y=-2.78207\nx0=-7.24072, x1=0.11518, y=-0.13273\nx0=2.54325, x1=3.23822, y=1.31073\nx0=0.76969, x1=-0.69353, y=-0.08496\nx0=9.13268, x1=-1.52476, y=-2.21625\nx0=2.15175, x1=3.93023, y=1.34596\nx0=0.71426, x1=-9.78736, y=-1.11261\nx0=-3.21039, x1=7.53534, y=-3.85018\nx0=-5.67333, x1=-1.85932, y=1.67885\nx0=-4.99124, x1=-2.20291, y=1.74995\nx0=4.03114, x1=-3.76674, y=-2.41665\nx0=3.25090, x1=9.81042, y=5.07588\nx0=-8.55762, x1=-8.89461, y=12.11434\nx0=3.40193, x1=4.61069, y=2.49638\nx0=-2.85282, x1=3.68267, y=-1.67208\nx0=-3.46677, x1=-6.74844, y=3.72348\nx0=9.68994, x1=0.70821, y=1.09220\nx0=1.61637, x1=6.69498, y=1.72231\nx0=5.79523, x1=2.14937, y=1.98245\nx0=8.80294, x1=1.80008, y=2.52197\nx0=-7.13802, x1=6.52083, y=-7.40800\nx0=-8.03151, x1=-3.91837, y=5.00867\nx0=7.94946, x1=0.84103, y=1.06406\nx0=1.46167, x1=9.35846, y=2.17707\nx0=4.22589, x1=-8.03770, y=-5.40593\nx0=-9.30582, x1=-9.66279, y=14.31124\nx0=3.46790, x1=-1.00013, y=-0.55201\nx0=6.42782, x1=6.18916, y=6.33163\nx0=-6.61328, x1=4.44324, y=-4.67667\nx0=8.65097, x1=-1.34238, y=-1.84825\nx0=-4.41962, x1=2.22287, y=-1.56358\nx0=-7.21652, x1=-4.96181, y=5.69886\nx0=8.65954, x1=3.23092, y=4.45288\nx0=6.89807, x1=-6.00257, y=-6.58999\nx0=6.27272, x1=-5.39141, y=-5.38243\nx0=-4.80645, x1=-3.51414, y=2.68821\nx0=-2.11517, x1=5.74271, y=-1.93322\nx0=0.09518, x1=-6.11242, y=-0.09259\nx0=-1.84080, x1=-7.78594, y=2.28107\nx0=-1.02297, x1=-8.01004, y=1.30412\nx0=-4.03520, x1=-3.25045, y=2.08752\nx0=7.82948, x1=8.18923, y=10.20461\nx0=3.80036, x1=8.04196, y=4.86415\nx0=-4.18603, x1=3.75311, y=-2.50042\nx0=-3.01065, x1=8.23024, y=-3.94360\nx0=0.84745, x1=6.06183, y=0.81759\nx0=8.80814, x1=2.26679, y=3.17772\nx0=-4.04138, x1=1.50345, y=-0.96703\nx0=7.19393, x1=2.97856, y=3.41030\nx0=2.06204, x1=8.31496, y=2.72883\nx0=1.44851, x1=9.71283, y=2.23917\nx0=-7.18466, x1=2.91030, y=-3.32785\nx0=1.04821, x1=-7.63803, y=-1.27424\nx0=3.98930, x1=3.77910, y=2.39941\nx0=1.38200, x1=-7.62655, y=-1.67747\nx0=4.82308, x1=7.76102, y=5.95750\nx0=-0.91569, x1=-3.27564, y=0.47738\nx0=8.23485, x1=-4.24851, y=-5.56817\nx0=-6.85426, x1=-2.16370, y=2.36036\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-4.39932, x1=-4.87719, y=3.41487\nx0=3.52247, x1=2.05781, y=1.15365\nx0=-7.69096, x1=9.49852, y=-11.62670\nx0=-6.23948, x1=1.23728, y=-1.22868\nx0=2.74777, x1=3.31203, y=1.44842\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x1 / (2 * pi)) * x0", "data": [[7.653699174293614, -4.175433631180345, -5.086196152573442], [5.369724938823293, -7.300472915263077, -6.239117511542728], [4.627713960523005, 9.119148837366918, 6.716467893211514], [-2.000802418575356, 7.395780387478553, -2.355094520228564], [2.6509398458553513, -1.575784559932627, -0.6648395478063917], [0.6453033732187752, 5.439088634156615, 0.5586119255223241], [1.3540437121617082, 2.3721338601852118, 0.5112013701266223], [0.23985974524836529, 8.38218287387074, 0.31998869211360986], [1.0619256773763013, -7.879781904818568, -1.3317676190912975], [4.1290693518984725, -2.413206877932563, -1.5858673701818202], [3.665928019310904, 3.845776798531187, 2.2438206470914617], [5.550633519785009, -9.703659125925686, -8.572316902286031], [8.795845702164431, 2.0681597963546885, 2.895221701541917], [2.082380423243116, 6.4054191618566065, 2.1228913064325896], [2.7510057704735296, -7.745213949072102, -3.3911347868576285], [3.4288938781952467, -6.357075342961782, -3.4692175482712653], [1.353382894350709, 7.355073371353246, 1.5842649867591068], [-0.45439079514342673, 2.283776813652514, -0.16515940745849259], [2.1122682323676667, 6.202976984608249, 2.0853039644914126], [-9.386323358807367, -2.338490158406101, 3.493423116632736], [6.8743310060304275, -1.9572044320080124, -2.1413455841766877], [-9.517580077793335, 2.398718418643579, -3.6335064966858432], [-6.067316441998409, -8.575069385298502, 8.280459182581886], [7.615313557992316, -7.847625659415154, -9.511438412281812], [6.543393437110311, -7.611895490710559, -7.927130040390743], [-2.7286149859040965, -3.033462927026531, 1.317349719482421], [8.777950597787761, -2.5916278738006016, -3.6206446781183876], [-4.5333755950224734, 4.6585414991782965, -3.361180246688318], [6.588152361175904, 5.214799388363446, 5.467910179928636], [-9.058893919199061, -8.973424905944125, 12.937594602209177], [1.3416489298278744, -4.234640456793435, -0.9042230269049658], [0.08557886355994349, -6.576140233251966, -0.08956899729337228], [7.705359178127544, -5.699340331084947, -6.989363226199479], [3.554777525543802, 2.4647299572040193, 1.3944466429140385], [5.696660246949818, 8.015828540045785, 7.267564071087721], [-6.563838385273439, -2.0150914645877833, 2.1051002092814954], [1.274321144835648, 3.8268060337849477, 0.7761317878790707], [8.939784408572134, 8.902905844217337, 12.667151288085513], [9.215829489665104, 3.350539724369737, 4.914386778129518], [6.274197766159048, 1.7384499689194364, 1.7359632699532348], [8.788955859710395, -6.377615616229432, -8.921045520842872], [1.732808375605659, 8.740449567527786, 2.4104850448807746], [7.427845299718918, 0.03033313992805553, 0.035859179671633976], [-3.944340328046647, 7.660104173521699, -4.80871665111253], [7.647826270729702, 3.3762178088874624, 4.109496376783687], [9.253868477351933, 7.824409016163738, 11.523781077386001], [8.986974578983894, 7.012031314689327, 10.029458641008826], [5.880937353897565, -1.0539969278399948, -0.9865203078993537], [-5.396647976505006, 8.479923324987467, -7.283433293049495], [2.7566943658654246, -4.995438576311042, -2.191706388574582], [6.394610076870308, 6.32599851110184, 6.438182521711544], [-4.441941642832575, -6.375818067663744, 4.507429018449993], [9.554835294786326, -7.887793444986208, -11.99496171472447], [-8.522511881203584, -6.560154190503296, 8.898192445033649], [-4.510279742034047, -3.5148918685575836, 2.5231064842350914], [5.731528378180752, 3.4095675051315038, 3.1102111361659395], [7.031339413389574, 7.454647104462097, 8.342290006729646], [-1.593107845454579, -3.6502219674088376, 0.9255173880173224], [9.823234683098207, 5.5607092668588525, 8.693703824144146], [6.335352650660724, -1.545774290593748, -1.5586083762396976], [6.570852730198318, 9.336258723377135, 9.7637071203743], [4.378669294414394, -1.905992341392329, -1.3282610224955842], [2.9932336055957762, 9.588473905763287, 4.567833179822614], [4.268070532818678, 4.515595733177394, 3.067374292601829], [2.562307940291703, 4.926879206838953, 2.009200922041294], [-6.122396475953346, -2.6501970779469897, 2.5823776408542503], [3.715122224773255, 5.196125678987951, 3.0723655357840305], [-8.589727016767188, -3.2082515756668446, 4.3859927550762805], [-8.60468390867448, -0.12565462137114736, 0.1720812367776936], [0.8481321017676979, 3.8911369439601238, 0.5252428494788798], [9.513188705191244, 9.01329880588857, 13.646774399398135], [1.7814429765362618, 8.45536926555927, 2.3973124228787936], [-3.3422203574501452, -6.699682715664917, 3.5637681949577034], [-8.056422075278158, 0.6516112902651354, -0.8355086356268873], [3.246151488216505, -5.384925114474768, -2.782073394256344], [-7.240720214962792, 0.1151767118610394, -0.1327292296969551], [2.5432457481884096, 3.238217761835024, 1.3107338319442188], [0.7696878737961086, -0.6935344957104874, -0.08495771894515035], [9.132679851822033, -1.5247565814180035, -2.2162506800710586], [2.151754605860077, 3.930227379746782, 1.345955029654166], [0.7142616803702158, -9.787360706552624, -1.1126103023992653], [-3.210394714880838, 7.535335478429758, -3.8501810804723937], [-5.6733267794809095, -1.859320234378119, 1.6788508951462324], [-4.9912359921468985, -2.2029071344231106, 1.7499451057294035], [4.031135739577449, -3.7667399128921897, -2.416646834719649], [3.2508967938371782, 9.81042301152813, 5.07587651090293], [-8.557615537487116, -8.894605503733564, 12.114335410670261], [3.401927582844639, 4.6106917614930545, 2.4963833967294833], [-2.852824576948745, 3.68266503731385, -1.6720814067212], [-3.4667725576592616, -6.748436214879141, 3.7234766019273575], [9.689940024540157, 0.7082054910263729, 1.0921958206857358], [1.6163735519225941, 6.69498079067608, 1.7223095216232385], [5.795229538322161, 2.149371851036989, 1.9824504023038383], [8.802937159829114, 1.8000844040671993, 2.521973985596965], [-7.138017984544083, 6.520834816588955, -7.407999910788372], [-8.031514925542, -3.9183668336104933, 5.008673175997407], [7.949462123891962, 0.8410251760621108, 1.06406185007878], [1.4616658747074762, 9.358462230494954, 2.177071694260364], [4.2258919550134255, -8.037696402758723, -5.405926278578179], [-9.305817069651287, -9.662791456482356, 14.311239487631433], [3.4679034572994265, -1.0001327966290763, -0.5520072723663481], [6.427816886587774, 6.189162962956839, 6.331630257932884], [-6.613281330229947, 4.443241883976764, -4.6766738780444195], [8.65097280744611, -1.3423776793983162, -1.8482461099034917], [-4.419622290618202, 2.222870805283863, -1.5635778478427418], [-7.216517208529536, -4.961811954343142, 5.6988612627880615], [8.659536722772792, 3.230919856694479, 4.452879833961258], [6.898067467102365, -6.002567553888552, -6.589988029678109], [6.272719745028034, -5.391405582319426, -5.38242540945368], [-4.806450263749471, -3.514136191175008, 2.6882098803650503], [-2.1151704523572086, 5.742708195353119, -1.9332243277053685], [0.09517514724201703, -6.112422437078742, -0.09258850042026147], [-1.8408033537498838, -7.785935828694457, 2.2810686116745607], [-1.0229719797777932, -8.010040872080229, 1.3041231427075513], [-4.035204786063947, -3.250454709007866, 2.0875160857797925], [7.829484669502399, 8.189231114668239, 10.204610612716154], [3.800358051502, 8.04196154291433, 4.864146417034901], [-4.186025457429632, 3.7531122587458015, -2.500423382666933], [-3.0106484522857286, 8.230238738687436, -3.9435977627872885], [0.8474461483478244, 6.06182544274192, 0.8175901827276248], [8.808138271255615, 2.2667908458704353, 3.177720571065849], [-4.041378949028765, 1.5034528078072498, -0.9670290197215002], [7.193927969596892, 2.978557777202518, 3.4102973340596874], [2.0620371669225612, 8.314962093126898, 2.7288325967384712], [1.4485097800343496, 9.712828195222702, 2.239171048559899], [-7.184664275761459, 2.91029845573207, -3.327853043393346], [1.0482125064484897, -7.6380299216575365, -1.274238797216549], [3.9893020286163594, 3.7790953157709044, 2.3994123796273623], [1.3819954955277325, -7.626552251599454, -1.6774709550701592], [4.823081490529006, 7.761022858019164, 5.957495102255286], [-0.9156932179444421, -3.2756350063750928, 0.47738155301128393], [8.234845608636835, -4.248511501910992, -5.568168782922519], [-6.854263616807921, -2.1637047534079645, 2.3603637396866413], [-4.399315405856871, -4.87718533909548, 3.4148724811577083], [3.5224721641956087, 2.0578088335732367, 1.1536464358634873], [-7.690958384971123, 9.49851749907804, -11.626698757532157], [-6.239480792948957, 1.2372842728310278, -1.2286779839081963], [2.7477662399148794, 3.3120335775333825, 1.448420443594377]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-3.90421, x1=-6.54133, y=319.79160\nx0=-9.14718, x1=3.18343, y=7768.05711\nx0=6.21427, x1=-8.32567, y=1294.29033\nx0=-9.89721, x1=4.17899, y=10569.14963\nx0=0.49830, x1=5.05128, y=7.64434\nx0=8.54691, x1=-6.51014, y=4739.61289\nx0=-0.16995, x1=-5.66371, y=21.70825\nx0=-4.19860, x1=-8.48355, y=429.23918\nx0=4.95806, x1=0.13169, y=482.29003\nx0=-1.99278, x1=-1.10300, y=25.39508\nx0=-4.76412, x1=9.71298, y=660.73345\nx0=-8.52815, x1=-2.97967, y=5917.23485\nx0=5.28507, x1=3.53428, y=635.28468\nx0=-7.03387, x1=-7.91137, y=2835.01290\nx0=4.86178, x1=9.32153, y=477.91136\nx0=-1.97842, x1=9.02306, y=54.74924\nx0=-8.68255, x1=2.55153, y=6338.40353\nx0=8.85768, x1=-9.86045, y=5519.24394\nx0=-6.05287, x1=5.22607, y=1572.47717\nx0=6.81147, x1=3.22699, y=1838.55097\nx0=-3.41452, x1=9.72576, y=213.30955\nx0=4.82613, x1=7.83020, y=452.91215\nx0=9.06607, x1=0.44129, y=6010.27436\nx0=3.39217, x1=6.45614, y=107.75857\nx0=0.49236, x1=3.11796, y=1.68230\nx0=5.64636, x1=-8.08112, y=877.14104\nx0=-7.40967, x1=4.63458, y=3427.27509\nx0=0.68318, x1=4.85961, y=6.84727\nx0=8.77828, x1=-3.40456, y=5270.73135\nx0=-5.16464, x1=-3.85742, y=860.53249\nx0=5.12047, x1=5.89290, y=564.66292\nx0=-0.48808, x1=-6.05124, y=24.53302\nx0=-6.47986, x1=-1.29406, y=2037.25448\nx0=-0.67252, x1=-1.41455, y=2.92374\nx0=-0.90608, x1=4.09555, y=5.70911\nx0=-1.72361, x1=-4.23565, y=27.15252\nx0=-6.96589, x1=-3.59587, y=2702.60699\nx0=-5.29214, x1=5.68055, y=943.04734\nx0=-8.47173, x1=0.72838, y=5758.50592\nx0=-3.59472, x1=6.20470, y=226.47404\nx0=3.87458, x1=-0.21850, y=167.44686\nx0=3.92857, x1=-2.48279, y=183.13123\nx0=8.57891, x1=-8.96447, y=4834.38950\nx0=0.87188, x1=7.32071, y=19.39077\nx0=9.56704, x1=6.74934, y=7517.78210\nx0=6.49388, x1=-5.58276, y=1525.66536\nx0=-1.75346, x1=-6.12188, y=39.70512\nx0=-6.94103, x1=-6.14122, y=2680.51208\nx0=5.10924, x1=4.47667, y=553.60482\nx0=0.88657, x1=-6.83812, y=30.13899\nx0=-0.13104, x1=-4.59701, y=15.16579\nx0=-2.52722, x1=6.72257, y=72.80649\nx0=-6.08111, x1=-3.36422, y=1601.41749\nx0=-3.06817, x1=0.45238, y=117.15041\nx0=-3.61210, x1=8.63696, y=246.02191\nx0=-8.00274, x1=-4.31852, y=4627.77294\nx0=-4.56732, x1=7.68931, y=552.30782\nx0=0.45465, x1=3.15245, y=1.76527\nx0=3.19317, x1=-0.63428, y=72.24156\nx0=-9.67446, x1=-5.15746, y=9683.99137\nx0=-1.48197, x1=-9.84729, y=66.41005\nx0=8.55797, x1=-2.07350, y=4741.38673\nx0=6.37253, x1=-7.66443, y=1427.35147\nx0=-1.55143, x1=-8.27637, y=52.05303\nx0=9.42812, x1=-2.24542, y=7068.03554\nx0=-8.97274, x1=-9.49417, y=7258.82918\nx0=2.11476, x1=-6.60403, y=38.95369\nx0=-6.78197, x1=2.92605, y=2428.83825\nx0=1.28371, x1=-9.84094, y=58.86310\nx0=-3.38280, x1=-1.58242, y=172.49471\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=1.22784, x1=-4.48479, y=14.96320\nx0=7.03725, x1=1.55222, y=2103.65944\nx0=2.45430, x1=-1.40560, y=23.89345\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**4 - x0**3 + x1**2 / 2 - x1", "data": [[-3.904209394299172, -6.541327193947608, 319.79159641341187], [-9.147180239326937, 3.183429896067002, 7768.057110256909], [6.214269176784523, -8.325667426277413, 1294.2903349917685], [-9.897205590056986, 4.1789926584889, 10569.149627145918], [0.49830497515253924, 5.051275994561422, 7.644342343404949], [8.546912812209925, -6.510137090565964, 4739.612893952837], [-0.16994940045181828, -5.663709444037983, 21.708254607666856], [-4.198604154332335, -8.48355235003738, 429.2391834982417], [4.958063594468117, 0.13168727288102033, 482.2900323352061], [-1.9927775349947812, -1.103002759003342, 25.395083373927807], [-4.764116910107887, 9.712980494614563, 660.7334517006282], [-8.528154439087995, -2.979666872565394, 5917.234846882414], [5.285072217732532, 3.5342780667586737, 635.284680060222], [-7.033867166834355, -7.91136853904765, 2835.0128991368083], [4.861784046136542, 9.32153260803982, 477.91136161294986], [-1.978422879762828, 9.02306161689651, 54.74924253276265], [-8.682550227569672, 2.5515298088996534, 6338.40353291032], [8.857677663306095, -9.860450322331566, 5519.243938034938], [-6.052869918002681, 5.226066499847018, 1572.4771651353826], [6.811467101436058, 3.226992785591831, 1838.5509655250376], [-3.414516485362289, 9.725764764854354, 213.30955109449476], [4.826126957831027, 7.8302049878147955, 452.91214530624353], [9.06606978509544, 0.44129137592666723, 6010.274360965275], [3.3921707704810995, 6.4561366295891, 107.75857126972352], [0.49236347946490966, 3.1179643222796383, 1.6822951234245673], [5.646358342539703, -8.081118389496883, 877.1410352161209], [-7.409666058729516, 4.6345766568635085, 3427.2750898910353], [0.6831789862039841, 4.859609217878889, 6.847269304838166], [8.778281453375008, -3.4045557693182094, 5270.731348485337], [-5.164640320127544, -3.8574248840644065, 860.5324879161462], [5.120470499885624, 5.892904354900168, 564.6629233794824], [-0.4880788710068842, -6.051240741563307, 24.533017864191805], [-6.4798613526618905, -1.294062086613014, 2037.2544816955292], [-0.6725182931309917, -1.4145470915199194, 2.9237439483661873], [-0.9060798002083548, 4.095554741698988, 5.709112674099638], [-1.723613401552191, -4.235652917557693, 27.152524887118098], [-6.96588580032987, -3.595870822515394, 2702.606985289195], [-5.292140239035326, 5.68054525696512, 943.0473425233349], [-8.47172556807757, 0.7283822389367955, 5758.505917039903], [-3.5947208026513593, 6.204701355812709, 226.47404387817997], [3.8745792279387246, -0.21850160186838963, 167.4468572907141], [3.928573074933503, -2.4827905484578006, 183.13122619493635], [8.578914850809216, -8.964473799238718, 4834.389504564438], [0.8718807282759649, 7.320710363474369, 19.39077449875797], [9.567036217150122, 6.749336865350212, 7517.782101912541], [6.493879830328936, -5.58276187910506, 1525.665361186618], [-1.7534591895753735, -6.121884547370828, 39.70512171164303], [-6.941029704515427, -6.141215404388385, 2680.5120761393464], [5.109236235445046, 4.476670842609874, 553.6048233477011], [0.8865658574552562, -6.838116928167639, 30.13899305385923], [-0.13104333274342572, -4.597007873307333, 15.165793779347979], [-2.5272190690077956, 6.722566179921742, 72.8064930708885], [-6.081112498392232, -3.3642210321811543, 1601.4174873425768], [-3.0681741831622205, 0.4523762529957782, 117.15040763309965], [-3.6121049841028956, 8.636959978802182, 246.0219052847802], [-8.002735074937604, -4.318517991572759, 4627.7729374478595], [-4.56732324374665, 7.689307792361916, 552.3078235076434], [0.454647298129105, 3.152447953123275, 1.7652652171226464], [3.193165127807573, -0.634280616260888, 72.24156143697158], [-9.674458571240333, -5.157455429254356, 9683.991366920356], [-1.4819722831014186, -9.847285845939993, 66.41005291169489], [8.557974451343316, -2.0735017526324206, 4741.386728495097], [6.372525718523875, -7.664433058210767, 1427.351473721952], [-1.551427690011577, -8.276373505467202, 52.053029069915425], [9.428118633927262, -2.2454243702836845, 7068.035544757412], [-8.972739759862778, -9.49417032218043, 7258.829178716384], [2.1147631540971545, -6.604025235378526, 38.95368738633819], [-6.781966474039159, 2.9260491564879647, 2428.8382461064944], [1.2837068657070727, -9.840935329843443, 58.86309995317684], [-3.382798960841768, -1.582421713965111, 172.4947060013275], [1.227843025724864, -4.484785991613325, 14.963197612813854], [7.03724639878773, 1.5522218004162411, 2103.6594413570406], [2.4543016230085613, -1.4056026274538702, 23.89345371377143]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=3.82376, x1=5.42007, y=-2.45913\nx0=-4.95978, x1=-8.47779, y=-3.39806\nx0=2.25722, x1=-5.38128, y=2.87803\nx0=5.05397, x1=7.07525, y=-3.97077\nx0=4.79868, x1=9.56394, y=5.91988\nx0=-7.74629, x1=-8.10797, y=1.49886\nx0=-3.40704, x1=3.80968, y=-1.23565\nx0=-1.32749, x1=-4.19752, y=2.86749\nx0=0.65645, x1=-6.03006, y=3.54516\nx0=-1.91046, x1=0.41062, y=-5.18693\nx0=-5.42628, x1=-5.91743, y=4.23497\nx0=6.85641, x1=-1.82970, y=-0.83311\nx0=1.94630, x1=6.47207, y=5.48266\nx0=-4.43027, x1=-0.82506, y=3.91014\nx0=9.40884, x1=-9.68304, y=-0.09243\nx0=7.04653, x1=2.25290, y=-2.61506\nx0=-3.54232, x1=-2.72769, y=-2.14289\nx0=7.50281, x1=-3.01330, y=-5.58751\nx0=2.90157, x1=-4.69434, y=-0.02574\nx0=-4.95874, x1=7.70091, y=0.88725\nx0=0.35740, x1=-3.17588, y=-2.09782\nx0=-1.67345, x1=-2.42263, y=4.49118\nx0=2.24741, x1=0.31618, y=4.44628\nx0=-1.54579, x1=3.86105, y=4.51156\nx0=-1.03341, x1=-5.89716, y=-4.77503\nx0=3.43713, x1=-3.09759, y=1.74583\nx0=-3.45195, x1=3.96633, y=-1.24372\nx0=-4.29535, x1=-8.80913, y=-4.47858\nx0=-8.19084, x1=0.00421, y=-5.66274\nx0=6.00431, x1=4.68134, y=0.05127\nx0=-1.05792, x1=4.89195, y=-0.93373\nx0=7.62057, x1=-6.57441, y=5.59150\nx0=-6.01482, x1=-7.14949, y=1.03036\nx0=-3.70008, x1=-5.18980, y=1.46087\nx0=-7.23253, x1=-4.71727, y=-0.02379\nx0=-5.45722, x1=3.34552, y=-4.31983\nx0=-3.69433, x1=-3.86987, y=-2.35098\nx0=2.10608, x1=-6.61141, y=4.88526\nx0=2.87471, x1=-3.96240, y=-1.07857\nx0=6.28958, x1=-2.05842, y=-0.01798\nx0=6.17836, x1=-9.78359, y=0.58780\nx0=-8.39994, x1=-0.23337, y=-4.98879\nx0=-7.10248, x1=1.13830, y=-1.83748\nx0=4.37282, x1=-1.24117, y=-1.83125\nx0=9.80224, x1=-4.85840, y=-0.32175\nx0=1.61969, x1=-3.03788, y=-5.96062\nx0=7.43146, x1=2.81679, y=-5.18621\nx0=0.94798, x1=-4.39111, y=-1.53895\nx0=-5.22532, x1=-7.70644, y=0.76852\nx0=-2.17438, x1=8.04780, y=0.95144\nx0=-1.70928, x1=-8.22911, y=2.17729\nx0=0.15679, x1=0.57779, y=0.78480\nx0=-0.16682, x1=8.42536, y=0.53878\nx0=-3.99014, x1=-1.90619, y=-1.48178\nx0=-0.71438, x1=5.83401, y=-3.54097\nx0=7.38144, x1=-6.42218, y=5.29097\nx0=4.56963, x1=-8.15487, y=1.76013\nx0=6.83921, x1=9.75850, y=-2.99216\nx0=7.04203, x1=-1.12802, y=1.76887\nx0=-2.41468, x1=-8.15051, y=1.16512\nx0=3.92392, x1=-2.40268, y=3.12652\nx0=-0.28764, x1=-8.69538, y=1.26906\nx0=9.82658, x1=6.98166, y=-1.79700\nx0=-1.80811, x1=1.54478, y=-0.15171\nx0=7.14411, x1=-0.45149, y=4.09467\nx0=-7.13684, x1=4.49538, y=0.97367\nx0=3.98456, x1=2.64571, y=3.94013\nx0=-2.40249, x1=-5.41453, y=-2.61038\nx0=-0.00526, x1=3.19407, y=0.03150\nx0=2.22186, x1=6.90065, y=3.89135\nx0=0.06563, x1=8.57355, y=-0.25932\nx0=-1.61969, x1=-0.96293, y=-3.42260\nx0=2.49774, x1=-7.12045, y=2.41132\nx0=-2.66254, x1=-3.35765, y=2.70135\nx0=-8.86229, x1=7.89154, y=0.12013\nx0=4.78061, x1=7.42305, y=-2.50046\nx0=-7.83175, x1=-7.24417, y=-3.43542\nx0=-5.50906, x1=0.10788, y=4.17014\nx0=7.00532, x1=-7.43228, y=1.62332\nx0=-6.13818, x1=2.31908, y=-0.58990\nx0=-7.17159, x1=2.02498, y=2.04289\nx0=0.06986, x1=2.80800, y=-0.39575\nx0=8.77111, x1=-0.46234, y=3.26555\nx0=7.21584, x1=-9.73236, y=-4.59307\nx0=8.34756, x1=5.59210, y=4.07152\nx0=-2.81823, x1=-1.91036, y=0.63502\nx0=-7.93178, x1=-2.86768, y=5.75884\nx0=9.70362, x1=8.38695, y=0.83909\nx0=-4.09671, x1=5.28137, y=2.63907\nx0=-3.56866, x1=-4.01503, y=-1.59600\nx0=1.98477, x1=1.65758, y=-0.47612\nx0=2.00694, x1=-6.57407, y=5.20987\nx0=4.42554, x1=3.28048, y=5.69943\nx0=-9.93956, x1=3.00914, y=-2.92820\nx0=3.95510, x1=-9.76196, y=4.11470\nx0=-9.05880, x1=-4.48800, y=0.47776\nx0=-7.77787, x1=-8.56902, y=3.92250\nx0=-2.34650, x1=-3.26998, y=4.24832\nx0=2.03945, x1=8.80511, y=-4.35778\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.69062, x1=-3.54693, y=1.44860\nx0=9.75469, x1=-9.80499, y=1.80493\nx0=8.81050, x1=1.06181, y=1.68518\nx0=0.02737, x1=-7.02267, y=0.12130\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 6 * sin(x0) * cos(x1)", "data": [[3.823759622367204, 5.4200664429176975, -2.4591258493719557], [-4.9597798465547775, -8.477786613959843, -3.3980625293572206], [2.2572234611116997, -5.38128240902088, 2.878025920063538], [5.053974983521748, 7.07525190414249, -3.9707744091284813], [4.798678469858862, 9.563943168367494, 5.919884896130647], [-7.746288085590902, -8.10796872360176, 1.4988567419148693], [-3.4070421498613435, 3.809677232056723, -1.2356509846282102], [-1.3274890740372527, -4.19752362503411, 2.8674855070937326], [0.6564489006210632, -6.030063231360733, 3.545162237626777], [-1.910458013726032, 0.41062410237358726, -5.18693177438526], [-5.426275222493118, -5.9174281971717075, 4.234966402739087], [6.85641335798222, -1.8296987114409635, -0.8331089036778492], [1.9463030658848464, 6.47206662335201, 5.482656145641248], [-4.430265508197692, -0.8250588527566869, 3.9101380188804824], [9.408843866683501, -9.68304033285113, -0.09242994968541463], [7.046529614029481, 2.2529036569683143, -2.6150560942416896], [-3.5423205802674573, -2.727691112864754, -2.142894537104924], [7.502806893021404, -3.0132951337744434, -5.587512042351603], [2.9015717044995064, -4.694342176317607, -0.02573944249414024], [-4.958741453398909, 7.70090640693078, 0.8872473379130199], [0.3574027105588655, -3.175877336513178, -2.097819982835461], [-1.67345490475061, -2.422633952411002, 4.491181465010243], [2.2474105744780015, 0.31618454385905537, 4.446279647654121], [-1.5457933443110665, 3.86105137543783, 4.5115646092712725], [-1.0334132008213963, -5.897164927508475, -4.7750259960883], [3.4371291382589693, -3.0975913614245147, 1.7458272830997967], [-3.451946095776199, 3.9663301760368057, -1.2437215337768512], [-4.2953521782879855, -8.809132497730971, -4.478578614386284], [-8.19083599193366, 0.004209693423566918, -5.662744006480299], [6.004313779572929, 4.681344375593948, 0.05126583115275195], [-1.0579187214630572, 4.891952637094796, -0.9337251544584196], [7.620566043933959, -6.5744081202245, 5.591504249516694], [-6.014818597377703, -7.149494148251653, 1.030362958590908], [-3.7000772225858896, -5.189796007234067, 1.460867808111333], [-7.232530926581284, -4.717265461555629, -0.02378839581775872], [-5.457216366689012, 3.345517845487196, -4.3198253718239314], [-3.6943255415051297, -3.8698721426427163, -2.350977806915826], [2.106075186615877, -6.611406913973674, 4.88526239272339], [2.8747108277064743, -3.9624031782751112, -1.0785744057475684], [6.289582514732611, -2.0584229214105765, -0.01798359581252507], [6.178362923126567, -9.783592137371077, 0.5878021148352355], [-8.399936930287069, -0.2333706243372582, -4.9887880674227265], [-7.102477685809956, 1.138302707423195, -1.8374832523882247], [4.372815470431789, -1.2411673175921738, -1.8312491100869077], [9.802240465862102, -4.858403249092951, -0.32174643138101794], [1.6196949205146627, -3.0378765898975635, -5.960624603170978], [7.431462035154375, 2.8167850945332145, -5.186214424606233], [0.9479770983619922, -4.39110553037128, -1.538951895326894], [-5.225315711191216, -7.70644275793013, 0.768519117983013], [-2.174380004733889, 8.04779734046916, 0.9514358453444602], [-1.7092826614787526, -8.229107136222428, 2.177289157815457], [0.15678846284154702, 0.5777942024832168, 0.7847967873953391], [-0.16682029297836287, 8.425357360967137, 0.5387811458766847], [-3.9901419157722557, -1.9061916180515688, -1.4817772800874622], [-0.7143790762292479, 5.834011192249481, -3.5409699520226243], [7.381444469402862, -6.422181964481906, 5.290972551647839], [4.569625884092083, -8.154870795954054, 1.7601267976521147], [6.839208390370516, 9.758500454759233, -2.992157304950409], [7.042030749884379, -1.1280168578627112, 1.7688683608083315], [-2.414680802495841, -8.150508062445887, 1.165115798563009], [3.9239230869930353, -2.402675170147848, 3.126516129839094], [-0.2876364653067043, -8.695381087002179, 1.2690602653589795], [9.826583485848744, 6.981655967452699, -1.7969998542902013], [-1.8081060087235539, 1.5447800032064585, -0.15170601849867846], [7.14410670694981, -0.45149359012246926, 4.094668001473428], [-7.136842442263836, 4.495377501547273, 0.9736704816194317], [3.9845588842425315, 2.645709098256015, 3.9401300402740413], [-2.4024867426889074, -5.414528747159874, -2.6103847786767567], [-0.00525797585063259, 3.1940696188922857, 0.03150428116346023], [2.2218609509696847, 6.900654916366797, 3.8913487490260006], [0.06562559526989098, 8.573552917373995, -0.25932190314312614], [-1.6196869031671053, -0.9629324858952728, -3.422596959962613], [2.4977358580925113, -7.120453666390942, 2.411322822870033], [-2.6625363960839827, -3.357654814287743, 2.7013477409551823], [-8.862293570017934, 7.891535018016178, 0.12013270448855], [4.780612376977976, 7.423052111231385, -2.500462735947421], [-7.831747603833696, -7.24417111886797, -3.435423504049228], [-5.509064358617033, 0.10787553656141924, 4.170144282926699], [7.005324273779824, -7.432277992713454, 1.6233235315743046], [-6.13817569882293, 2.319082730570347, -0.5899007848314113], [-7.171585279531176, 2.024981319806818, 2.042894868550319], [0.06986331122202927, 2.808001704659077, -0.39574946354668283], [8.771109465236329, -0.4623442604915802, 3.265545759162117], [7.2158433009319225, -9.732356665726147, -4.593067269617736], [8.347558782374737, 5.592103632041994, 4.071517288469881], [-2.8182306622332343, -1.9103607887166003, 0.6350224482105057], [-7.931776927178009, -2.8676754505495, 5.758841364315394], [9.703621324185683, 8.386946750587214, 0.8390910268711378], [-4.096706790166178, 5.281371605191815, 2.639070890218885], [-3.5686602434633237, -4.015028752870331, -1.596000274272831], [1.9847659587653865, 1.6575807405425067, -0.4761248824507662], [2.0069379354143138, -6.574069010000643, 5.209870318455364], [4.425540004230541, 3.2804765031234506, 5.699428342167064], [-9.93956127949425, 3.0091359922844383, -2.9282011327453756], [3.955102361713866, -9.761956408715228, 4.1147002463493765], [-9.058804592435418, -4.488001393793672, 0.4777609878297157], [-7.777874525474329, -8.569022882035924, 3.9225037482315064], [-2.346498692737571, -3.2699772773349567, 4.2483226065305315], [2.039448073080072, 8.805111311268682, -4.35778371393548], [9.690620138706706, -3.5469298902895785, 1.448600729042166], [9.754685541026006, -9.804987292350322, 1.804925660527808], [8.81049506379403, 1.0618067532037596, 1.685181633349164], [0.027366098021552432, -7.022666293894304, 0.12129632321527785]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=5.50094, x1=6.77684, y=126.31682\nx0=-6.36590, x1=-1.98178, y=-12.50094\nx0=0.83389, x1=-9.05365, y=34.17658\nx0=-4.45475, x1=5.25639, y=-61.54166\nx0=9.48949, x1=6.57840, y=205.33038\nx0=-9.61195, x1=3.84499, y=-71.05110\nx0=2.29793, x1=-4.82353, y=26.73232\nx0=-5.33830, x1=-6.03153, y=-97.10181\nx0=6.33850, x1=-3.79873, y=45.73328\nx0=-9.46526, x1=0.42355, y=-0.84900\nx0=7.57342, x1=-2.06585, y=16.16061\nx0=-7.91700, x1=2.32599, y=-21.41635\nx0=4.70279, x1=5.56170, y=72.73469\nx0=-4.36323, x1=6.97715, y=-106.20247\nx0=3.59755, x1=-2.20573, y=8.75149\nx0=4.65079, x1=5.96138, y=82.63991\nx0=-3.82923, x1=-4.39999, y=-37.06669\nx0=-8.70058, x1=-8.28697, y=-298.75120\nx0=3.66724, x1=-1.86906, y=6.40556\nx0=-2.97762, x1=-5.64842, y=-47.49997\nx0=2.27964, x1=-5.92689, y=40.03965\nx0=-7.73550, x1=-5.19388, y=-104.33780\nx0=5.96696, x1=6.47505, y=125.08595\nx0=7.98625, x1=-0.26192, y=0.27393\nx0=2.93327, x1=-7.94036, y=92.47050\nx0=-0.17494, x1=5.39105, y=-2.54214\nx0=0.72853, x1=-4.34514, y=6.87738\nx0=-0.54836, x1=2.35399, y=-1.51932\nx0=-2.54205, x1=3.70421, y=-17.43997\nx0=8.62921, x1=6.45610, y=179.83784\nx0=-7.40622, x1=-4.79610, y=-85.18103\nx0=-0.41460, x1=2.68825, y=-1.49808\nx0=7.55197, x1=7.18356, y=194.85432\nx0=7.82822, x1=4.95956, y=96.27621\nx0=5.34205, x1=-1.60278, y=6.86164\nx0=-8.24498, x1=-8.40088, y=-290.94366\nx0=7.64577, x1=9.56844, y=350.00460\nx0=5.29993, x1=3.89466, y=40.19562\nx0=-3.45296, x1=6.23538, y=-67.12547\nx0=-5.72499, x1=-6.67753, y=-127.63687\nx0=0.63504, x1=6.22260, y=12.29452\nx0=0.80325, x1=-5.31994, y=11.36675\nx0=-7.22826, x1=-1.60877, y=-9.35384\nx0=-2.83767, x1=-7.04297, y=-70.37908\nx0=9.04890, x1=-6.07274, y=166.85371\nx0=8.56526, x1=8.20443, y=288.27526\nx0=-6.95063, x1=-5.43655, y=-102.71678\nx0=-7.04142, x1=-5.92765, y=-123.70738\nx0=3.86833, x1=8.35395, y=134.98220\nx0=9.65333, x1=1.93826, y=18.13304\nx0=-8.05887, x1=-1.60726, y=-10.40914\nx0=0.35386, x1=2.34847, y=0.97583\nx0=9.53841, x1=-2.79888, y=37.36077\nx0=4.00754, x1=6.86957, y=94.55995\nx0=9.22564, x1=-8.38325, y=324.18346\nx0=7.24135, x1=-7.21832, y=188.65191\nx0=4.79335, x1=3.50747, y=29.48476\nx0=6.94392, x1=-9.40247, y=306.94383\nx0=1.17560, x1=-4.19384, y=10.33837\nx0=1.05088, x1=-5.51300, y=15.96977\nx0=9.67468, x1=-0.73327, y=2.60098\nx0=6.46500, x1=1.29976, y=5.46092\nx0=9.80147, x1=-6.15111, y=185.42523\nx0=0.69942, x1=-4.02395, y=5.66252\nx0=8.93196, x1=1.85563, y=15.37795\nx0=6.26405, x1=3.43022, y=36.85271\nx0=5.71927, x1=-2.00193, y=11.46068\nx0=5.88968, x1=1.46068, y=6.28306\nx0=2.88517, x1=-1.17238, y=1.98280\nx0=-4.20816, x1=0.12572, y=-0.03326\nx0=2.87477, x1=3.11416, y=13.93974\nx0=-1.06364, x1=9.84910, y=-51.58900\nx0=8.60091, x1=-2.92775, y=36.86217\nx0=8.48861, x1=-7.46833, y=236.73029\nx0=7.81216, x1=6.40925, y=160.45575\nx0=8.61689, x1=5.10219, y=112.15885\nx0=-7.54993, x1=9.35864, y=-330.62699\nx0=-6.51709, x1=-7.23315, y=-170.48209\nx0=-2.75043, x1=7.98501, y=-87.68408\nx0=2.46505, x1=-7.58492, y=70.90850\nx0=5.60045, x1=-8.58849, y=206.55058\nx0=1.99790, x1=0.34111, y=0.11623\nx0=9.92515, x1=-4.63381, y=106.55725\nx0=8.27817, x1=8.10579, y=271.95347\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=6.74277, x1=-7.12380, y=171.09273\nx0=9.75876, x1=0.92018, y=4.13152\nx0=6.09187, x1=9.40914, y=269.66214\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1**2 / 2", "data": [[5.500938493318429, 6.776839551615716, 126.31682476087528], [-6.3659016475831764, -1.9817839553793881, -12.500936378611286], [0.8338944893010449, -9.053651205919316, 34.17658198392372], [-4.454753959492203, 5.256391807492866, -61.54165713531073], [9.489490065695875, 6.578398333682937, 205.33038161440146], [-9.61194742006622, 3.844985380118695, -71.05109515883514], [2.297926041733792, -4.823533904131669, 26.73232436939376], [-5.338300672113457, -6.031525299079885, -97.1018139699759], [6.338501578347568, -3.7987250905429937, 45.733278687650206], [-9.465263181056107, 0.4235490627620351, -0.8490048055674254], [7.5734165556651405, -2.0658459108582994, 16.16060810456933], [-7.9170032559345955, 2.3259873489029914, -21.416353385072497], [4.70279154423249, 5.561704803062135, 72.73469154872409], [-4.363229644761699, 6.977153493674027, -106.20247314278971], [3.5975510093236718, -2.205731220420031, 8.751492913914754], [4.650791895239513, 5.961375211317781, 82.63990818781294], [-3.829225738514028, -4.399987365503295, -37.06669227562552], [-8.700578938817028, -8.286969744991895, -298.75120284550934], [3.667235109836046, -1.8690633871445002, 6.4055557985673905], [-2.9776220570858802, -5.648418772993513, -47.4999719063782], [2.2796438832221337, -5.926886925763291, 40.03965220603151], [-7.7354967962094, -5.193877829656575, -104.33779990050913], [5.966955412509911, 6.475046248373584, 125.08595436852724], [7.98625021409293, -0.2619168898963924, 0.2739302080520928], [2.933273064464437, -7.940362774768062, 92.47049616905022], [-0.17493756652743286, 5.391045224790066, -2.542137490362941], [0.7285268818835728, -4.345138954969496, 6.877378470070554], [-0.5483645556462609, 2.3539940075196633, -1.5193229076333783], [-2.542051409359938, 3.704211239439669, -17.43997363058717], [8.629214220299687, 6.4560950179267245, 179.83784172351156], [-7.406222997980074, -4.796098041322714, -85.18103119239969], [-0.4145958990548735, 2.688250688256728, -1.4980783843186347], [7.5519742037481485, 7.183560764466062, 194.8543213005621], [7.828215714371623, 4.959559389262964, 96.27620860757672], [5.34205402446559, -1.602783180513157, 6.861638482399449], [-8.244983754044632, -8.400875468640658, -290.94366309000225], [7.645773195365678, 9.568440640769204, 350.0045976637848], [5.2999268908603465, 3.8946586556113676, 40.19561554278494], [-3.4529555569024524, 6.23538353366088, -67.1254695131678], [-5.72499475869261, -6.67752508277413, -127.63687242073793], [0.6350359046520087, 6.222595730700952, 12.294516623393655], [0.8032537003855822, -5.319941023893566, 11.366751743126514], [-7.22825715098563, -1.6087673078530855, -9.353842724831768], [-2.837667043647752, -7.04297363916387, -70.37907693420331], [9.048901741582434, -6.072744292177237, 166.85370924317664], [8.565255291839819, 8.20443217742, 288.2752614354629], [-6.950630914492672, -5.436552491404756, -102.71678158336464], [-7.041423331645127, -5.927650210551105, -123.70737613398823], [3.868327662948964, 8.3539452223173, 134.98220064024366], [9.653327558107915, 1.9382586624915916, 18.133035613894915], [-8.058866766899058, -1.607257768220606, -10.409144732222153], [0.35386314825911747, 2.348468825777786, 0.9758317415381967], [9.538412153239296, -2.7988837935869455, 37.36077043964756], [4.007544302755846, 6.869568392779463, 94.55995128829466], [9.225636201625683, -8.383246981233569, 324.1834588897507], [7.241345315912369, -7.218317418680722, 188.65191325341365], [4.793345484440572, 3.5074736431464437, 29.484758096873037], [6.943917210957181, -9.402474946266786, 306.9438303736756], [1.1755979071378562, -4.193838634042628, 10.338374041749482], [1.0508770618968537, -5.513004391912649, 15.969767514718518], [9.674681630253414, -0.7332727436962632, 2.6009845423418856], [6.465004520569384, 1.2997614704263842, 5.460924280595503], [9.801474738915587, -6.1511128237035155, 185.42522520280193], [0.6994150653030253, -4.023948662509151, 5.662521314546561], [8.931961633710447, 1.8556276843111768, 15.37795336866441], [6.26404569371676, 3.430222046632691, 36.85270656759649], [5.719269542507439, -2.0019345203899537, 11.460677873915037], [5.889678589646037, 1.4606786225337203, 6.283056225193961], [2.8851661413914975, -1.1723821122435822, 1.9828013151740336], [-4.208159344652813, 0.1257182817311353, -0.033255160932446313], [2.874774947850888, 3.1141562504829707, 13.93973938220696], [-1.0636386250964875, 9.84909937037919, -51.589003930240295], [8.60090687269161, -2.9277456604129437, 36.862173721787734], [8.488610574529837, -7.468331847139602, 236.7302892738335], [7.812157335199846, 6.409249107800726, 160.45575148051617], [8.616889142708754, 5.102188643215911, 112.15884634848109], [-7.549925604248495, 9.35864150892029, -330.62698717402725], [-6.517093550743873, -7.23314884615732, -170.4820912232228], [-2.7504265849370473, 7.985007753465446, -87.68407923368639], [2.465051424224878, -7.5849225015783865, 70.90849757478578], [5.600453166470407, -8.588486199622709, 206.5505798172733], [1.9978961917345721, 0.34111092630077167, 0.11623426798599613], [9.925149004508803, -4.633807449664191, 106.55725069747787], [8.278168027942453, 8.105786871724426, 271.95346880739567], [6.742773400831219, -7.123796256350059, 171.09272728243863], [9.758755760829892, 0.9201798350652535, 4.131520164946185], [6.091867577172174, 9.409136221130378, 269.66213630844527]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.99181, x1=7.09286, y=0.45408\nx0=-4.39762, x1=-4.79324, y=0.08666\nx0=6.85921, x1=-1.96064, y=-0.36960\nx0=-9.86572, x1=-7.29421, y=-0.27205\nx0=8.98342, x1=-4.62268, y=0.13900\nx0=7.02423, x1=-6.37527, y=0.57574\nx0=-5.81749, x1=-0.42143, y=-1.74815\nx0=5.83551, x1=1.19338, y=0.71077\nx0=0.33489, x1=-5.50059, y=0.59809\nx0=9.20626, x1=3.00304, y=1.11557\nx0=-1.85438, x1=-0.34328, y=-1.25719\nx0=-3.47684, x1=-9.89503, y=-1.74998\nx0=-9.46907, x1=0.21872, y=0.49546\nx0=3.39613, x1=8.71442, y=1.44969\nx0=-6.44256, x1=-8.66575, y=1.25825\nx0=-7.93788, x1=-5.06972, y=0.54557\nx0=9.21369, x1=-7.14323, y=-0.72440\nx0=2.99548, x1=-3.57655, y=1.23970\nx0=7.86179, x1=-1.14827, y=-0.58578\nx0=-7.48891, x1=-9.17014, y=-0.59193\nx0=7.69377, x1=3.03395, y=1.08491\nx0=-1.25439, x1=5.57884, y=-1.52134\nx0=-9.88058, x1=0.05879, y=-0.54864\nx0=1.02387, x1=6.69924, y=1.77705\nx0=5.09827, x1=5.82922, y=0.60714\nx0=-8.89598, x1=0.22755, y=1.64123\nx0=-8.88298, x1=6.77020, y=1.50467\nx0=2.33927, x1=3.28441, y=-0.19870\nx0=-3.46264, x1=-9.97320, y=-1.66886\nx0=-5.18787, x1=2.55957, y=0.74327\nx0=4.88417, x1=-1.00491, y=0.07097\nx0=8.18435, x1=6.11949, y=-1.84960\nx0=-5.94215, x1=-6.45902, y=-1.95275\nx0=-5.52888, x1=5.92901, y=-1.47448\nx0=-7.76154, x1=-0.26566, y=1.19117\nx0=-1.47525, x1=-2.24796, y=1.17847\nx0=7.69642, x1=3.05030, y=1.09242\nx0=9.59467, x1=5.19656, y=-0.08674\nx0=-9.43366, x1=-2.54191, y=-0.49204\nx0=1.44985, x1=8.23784, y=-0.71238\nx0=5.32737, x1=4.71762, y=0.00626\nx0=-4.95453, x1=-4.92122, y=-0.06512\nx0=-7.04852, x1=-7.19624, y=-0.31633\nx0=1.33610, x1=8.87567, y=-1.68250\nx0=-4.43667, x1=-2.41995, y=-0.74018\nx0=-9.74058, x1=5.41872, y=-0.12493\nx0=8.77794, x1=-8.78777, y=1.47079\nx0=-4.84417, x1=-4.58095, y=0.00373\nx0=4.39239, x1=8.27537, y=0.44356\nx0=-8.90909, x1=-0.83359, y=1.11996\nx0=-5.31551, x1=8.97705, y=1.05774\nx0=-3.09650, x1=-1.88873, y=-0.48340\nx0=8.29208, x1=-7.24921, y=-1.11075\nx0=-8.73410, x1=-4.32853, y=-0.70132\nx0=4.16513, x1=4.64146, y=0.10820\nx0=-6.69101, x1=-7.53024, y=-0.42261\nx0=4.05792, x1=-5.53932, y=-1.24464\nx0=8.76828, x1=-1.47664, y=-0.17296\nx0=7.75422, x1=6.89667, y=-0.99707\nx0=-1.52714, x1=6.91066, y=-1.48193\nx0=-3.98257, x1=7.96113, y=-0.19119\nx0=-1.95555, x1=2.70506, y=1.02246\nx0=-1.14448, x1=-0.19252, y=-1.95630\nx0=-0.30785, x1=-0.17022, y=-0.76795\nx0=-3.65648, x1=-1.68551, y=-0.22873\nx0=4.77317, x1=9.98504, y=0.13213\nx0=8.98373, x1=0.03983, y=-1.54979\nx0=-2.12699, x1=-1.51297, y=-0.04250\nx0=-5.41201, x1=6.36577, y=-1.36217\nx0=9.64022, x1=1.67349, y=0.00699\nx0=-2.54982, x1=-5.12749, y=0.13898\nx0=4.98241, x1=-1.66701, y=-0.03703\nx0=4.00200, x1=-7.46979, y=-0.66134\nx0=-1.91577, x1=9.04224, y=1.12451\nx0=9.10079, x1=8.64966, y=0.95842\nx0=-6.88331, x1=6.16294, y=-0.91067\nx0=-9.21299, x1=-1.96352, y=-0.42552\nx0=-0.62738, x1=3.06176, y=1.45163\nx0=4.96228, x1=2.95859, y=-0.32842\nx0=3.61219, x1=3.63607, y=1.76019\nx0=-9.32565, x1=0.01607, y=0.85723\nx0=1.61517, x1=-7.25220, y=0.97750\nx0=5.62330, x1=-7.45581, y=0.66365\nx0=-2.42964, x1=1.15994, y=0.01353\nx0=2.56602, x1=2.75036, y=0.35687\nx0=5.40016, x1=-1.93219, y=-0.47527\nx0=4.67471, x1=3.50536, y=0.38245\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-2.24857, x1=-4.04455, y=0.26842\nx0=8.19602, x1=-7.74157, y=-0.21145\nx0=-5.11685, x1=-6.89377, y=-0.59059\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 2 * sin(1.3 * x0) * cos(x1)", "data": [[6.991809689521233, 7.092864130545447, 0.45407870515126536], [-4.397624935124682, -4.793241290770118, 0.08665849715078867], [6.859209494248283, -1.960644338626917, -0.36960483427955576], [-9.865717379778278, -7.294208214298353, -0.27205376478951915], [8.9834248072396, -4.622681206229995, 0.1389967761562089], [7.024230118955373, -6.375274273278862, 0.57573527439915], [-5.8174851378913335, -0.42142901922709264, -1.7481510519405763], [5.835508917938768, 1.193379138446529, 0.710765865670035], [0.334892045670788, -5.500589437769987, 0.5980945480500864], [9.206258773213381, 3.003038989881741, 1.1155742185536197], [-1.8543758711554936, -0.3432847402954131, -1.2571893196953743], [-3.4768417971832966, -9.895033079902227, -1.7499752539172015], [-9.469067244581202, 0.21872070092007867, 0.49546212945251006], [3.3961349619112102, 8.714419395068735, 1.4496889888178897], [-6.442555631557234, -8.665749918755326, 1.258247040503065], [-7.937884925594134, -5.069723265631508, 0.5455692515016834], [9.213688272939788, -7.143234359725977, -0.7243953833651733], [2.9954846524347385, -3.576547448824609, 1.2397049578944357], [7.8617900429704015, -1.148265566289437, -0.5857833059125016], [-7.4889092793480145, -9.17013775808491, -0.591925395420799], [7.693766377926959, 3.0339512006694065, 1.084906789100764], [-1.2543943183901956, 5.578841492554732, -1.5213383723991818], [-9.880575517603118, 0.05879033259385125, -0.5486425537664419], [1.0238744143403533, 6.699242022883453, 1.7770502749782762], [5.098266534812421, 5.829224195283352, 0.6071439528133648], [-8.89598319112411, 0.22755381750074832, 1.6412320565203518], [-8.882983120258515, 6.770203585103566, 1.5046744698131695], [2.3392721845816915, 3.284409719823616, -0.19869531669158544], [-3.4626427176918506, -9.973197984323996, -1.6688640011166274], [-5.187868024917348, 2.5595688435084867, 0.7432669316863889], [4.88416628703601, -1.0049128337379223, 0.07096900882732175], [8.184352519193485, 6.119493917991235, -1.8495958526384098], [-5.94215349991633, -6.459022365171845, -1.9527530582639778], [-5.5288790174063, 5.929012393655155, -1.4744843757251629], [-7.761540694877267, -0.2656557315239194, 1.1911676501399444], [-1.4752461036353246, -2.247961291874079, 1.1784694523000425], [7.696416777198756, 3.050302050520612, 1.092423004058379], [9.594666976069398, 5.196562541879944, -0.08673534765459204], [-9.433658666802984, -2.5419143907246466, -0.49203597112713954], [1.4498518392999404, 8.237842095193113, -0.7123808943980623], [5.327372256867886, 4.717616007790326, 0.006263180230153629], [-4.954531379555451, -4.9212162157540495, -0.06511800770028581], [-7.048520939063079, -7.1962399795503185, -0.3163318176536773], [1.3361012117451878, 8.875674462942996, -1.6824962552115517], [-4.436671892485046, -2.4199533756797553, -0.7401840046488979], [-9.740583067090874, 5.418723860916124, -0.12492678268192435], [8.777943707541667, -8.787767501324723, 1.4707946288263885], [-4.844172107368245, -4.580954222033853, 0.0037319566980179406], [4.3923944844939165, 8.27536960839987, 0.44356258510170854], [-8.909085118494096, -0.8335904946145973, 1.1199602703661775], [-5.315508911343092, 8.97704984856848, 1.0577393158187167], [-3.0965025277522056, -1.8887277871678414, -0.4834038695511502], [8.292078910565419, -7.24921442278422, -1.110748190027676], [-8.734100799382631, -4.328528349279717, -0.7013196974021292], [4.16513172656577, 4.641458547159532, 0.10820153596484401], [-6.691012694138905, -7.530236970210186, -0.4226073843041047], [4.057919938394633, -5.539321563489903, -1.2446407461283995], [8.768282521742865, -1.4766390857332752, -0.1729582610606519], [7.754215191776723, 6.896668395338928, -0.9970651924703923], [-1.5271432849058506, 6.9106613009435875, -1.4819279310256204], [-3.9825738517867704, 7.9611326418683745, -0.19118555771955975], [-1.9555459568974456, 2.7050605506250047, 1.0224610836215597], [-1.144476786138064, -0.1925169286352375, -1.9562975346077907], [-0.30784788439077815, -0.17022057461126394, -0.7679476578466886], [-3.6564769027548145, -1.68550913672075, -0.22873010751655037], [4.773166351774387, 9.985036870710601, 0.1321330093285973], [8.983728409630103, 0.03982858392087785, -1.5497914416993799], [-2.1269898759869355, -1.5129684934631378, -0.04249980272931856], [-5.412013035444088, 6.365767075741324, -1.3621738156039334], [9.640215685500479, 1.673489008112588, 0.006987979366343352], [-2.5498177453580144, -5.127494556949559, 0.13897754883520994], [4.9824094958542435, -1.6670058644964385, -0.03702840079214901], [4.001998785570516, -7.46979052070027, -0.6613392879184304], [-1.9157659332020458, 9.042239558941453, 1.1245067843794418], [9.100786466429295, 8.649655061430195, 0.9584167809508566], [-6.8833109592478365, 6.162935256508302, -0.9106729220734666], [-9.212990077783463, -1.9635245096582938, -0.425521655945305], [-0.6273804031421122, 3.0617622004528737, 1.4516286131197298], [4.962284904392156, 2.9585866748730396, -0.3284204658180569], [3.6121896056352334, 3.636074611477003, 1.7601884874538243], [-9.32565415212231, 0.016069989747222735, 0.857229429181181], [1.6151730195103315, -7.252203043729645, 0.9774992637241597], [5.623297112153615, -7.455805994509854, 0.6636534913415053], [-2.4296355497403743, 1.1599439369144413, 0.013525574907215855], [2.5660237672621715, 2.7503568062339383, 0.35686868451019443], [5.400159621636627, -1.932190019064958, -0.4752699133457642], [4.6747058978597416, 3.5053558888046155, 0.3824468402860516], [-2.2485735001463603, -4.044553777051072, 0.26841650450232907], [8.196018731088813, -7.741567825188933, -0.21145498556196804], [-5.116846390852237, -6.893767437992489, -0.5905898267159324]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=3.99573, x1=-7.53140, y=-1.72804\nx0=3.61068, x1=-6.10624, y=-1.64068\nx0=-1.68943, x1=0.52144, y=0.31903\nx0=1.08003, x1=0.07173, y=1.07953\nx0=0.44398, x1=-4.21590, y=-0.15262\nx0=2.59369, x1=1.24189, y=-42.71057\nx0=-1.95643, x1=3.71848, y=-1.12408\nx0=-0.18299, x1=7.14885, y=0.08905\nx0=3.46824, x1=-9.25689, y=-1.74363\nx0=4.19181, x1=-6.58412, y=-1.70588\nx0=7.47436, x1=-3.26800, y=-1.67185\nx0=-6.61651, x1=4.02702, y=-1.69641\nx0=3.57019, x1=-7.81266, y=-1.70867\nx0=-9.49072, x1=8.06927, y=-1.88691\nx0=-7.51246, x1=-4.42679, y=-2.29746\nx0=4.47320, x1=-9.17149, y=-1.79557\nx0=-1.02261, x1=4.93382, y=-0.88134\nx0=-4.66642, x1=6.14151, y=-1.71572\nx0=8.61090, x1=5.89896, y=-2.18830\nx0=-5.79324, x1=2.47330, y=-1.48062\nx0=6.38301, x1=7.70000, y=-2.19502\nx0=2.04698, x1=-9.78160, y=-1.60908\nx0=-4.62639, x1=-8.32317, y=-2.25348\nx0=-2.05894, x1=8.80818, y=-1.57418\nx0=-0.33900, x1=-7.09969, y=13.17122\nx0=4.35133, x1=7.20100, y=-2.31764\nx0=4.20287, x1=7.83019, y=-2.30091\nx0=-8.62376, x1=2.61441, y=-1.64770\nx0=-2.42699, x1=-8.45466, y=-2.51372\nx0=6.93124, x1=2.98108, y=-2.50955\nx0=3.67265, x1=5.40919, y=-2.53362\nx0=3.35092, x1=6.60356, y=-2.47051\nx0=2.68765, x1=-9.32683, y=-1.67934\nx0=-7.25059, x1=-8.90885, y=-2.14612\nx0=5.22786, x1=1.91532, y=-3.28333\nx0=-4.10561, x1=-7.72931, y=-2.31322\nx0=-1.49986, x1=-8.51965, y=-2.92041\nx0=2.35789, x1=-6.47467, y=-1.50730\nx0=-7.39157, x1=5.94518, y=-1.80828\nx0=7.82909, x1=7.58811, y=-2.15955\nx0=-8.72592, x1=0.64749, y=-0.95953\nx0=-4.99414, x1=-0.57775, y=76.49524\nx0=-3.17785, x1=9.21275, y=-1.72116\nx0=9.33117, x1=-9.24987, y=-1.89923\nx0=3.90182, x1=0.29203, y=2.83730\nx0=-6.41175, x1=-7.36638, y=-2.20348\nx0=-1.06353, x1=2.96393, y=-0.53711\nx0=3.39291, x1=-4.93168, y=-1.54391\nx0=-6.61450, x1=5.97738, y=-1.78842\nx0=-9.03638, x1=4.73914, y=-1.80360\nx0=-1.54860, x1=7.68073, y=-1.39575\nx0=5.11321, x1=-6.16371, y=-1.73925\nx0=1.42375, x1=8.84112, y=-2.93871\nx0=-3.43416, x1=7.16329, y=-1.67391\nx0=6.06821, x1=2.89843, y=-2.61693\nx0=-2.30327, x1=-2.89695, y=-4.45067\nx0=-2.28338, x1=-1.59584, y=-15.97730\nx0=5.56905, x1=-4.81496, y=-1.69814\nx0=9.06894, x1=4.72083, y=-2.22606\nx0=-8.46162, x1=5.94451, y=-1.83114\nx0=5.87410, x1=-3.37434, y=-1.60563\nx0=-9.04915, x1=-6.62160, y=-2.15812\nx0=8.27715, x1=6.36090, y=-2.18127\nx0=5.96034, x1=-1.49457, y=-1.24422\nx0=3.41599, x1=-0.29784, y=0.24025\nx0=-3.06508, x1=6.98840, y=-1.63145\nx0=-8.27563, x1=-5.61447, y=-2.20707\nx0=7.94372, x1=0.05569, y=1.51891\nx0=-5.42319, x1=0.27418, y=0.00583\nx0=5.73784, x1=6.71468, y=-2.25332\nx0=6.28270, x1=-1.56030, y=-1.29704\nx0=-2.01980, x1=5.57997, y=-1.36932\nx0=6.44339, x1=-1.54198, y=-1.30425\nx0=-2.60610, x1=-6.98422, y=-2.59204\nx0=-3.39247, x1=0.44160, y=0.00084\nx0=-7.07889, x1=-4.93026, y=-2.28212\nx0=-9.26153, x1=-3.37738, y=-2.31825\nx0=-8.47644, x1=-3.15979, y=-2.37841\nx0=8.13245, x1=-8.50611, y=-1.87530\nx0=4.69884, x1=6.82872, y=-2.30942\nx0=3.28287, x1=-2.48156, y=-1.19258\nx0=7.63431, x1=4.90466, y=-2.26130\nx0=-1.27455, x1=-0.93037, y=2.96086\nx0=-3.97024, x1=7.32623, y=-1.71951\nx0=7.22595, x1=8.23141, y=-2.15935\nx0=-0.38437, x1=-9.24964, y=-18.20723\nx0=-6.61026, x1=-3.32568, y=-2.47409\nx0=0.02549, x1=5.54806, y=1.14844\nx0=-8.47420, x1=2.32835, y=-1.60406\nx0=9.46852, x1=1.80937, y=-2.63685\nx0=1.40470, x1=-3.06058, y=-0.76699\nx0=-0.02453, x1=-9.14102, y=1.24238\nx0=-6.45318, x1=9.25084, y=-1.85645\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.40579, x1=4.69581, y=-2.69268\nx0=-8.39975, x1=-9.31557, y=-2.11960\nx0=-3.84012, x1=9.06580, y=-1.76199\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1 + x0 * x1 / (1 - (x0 * x1 / 3))", "data": [[3.9957337949736633, -7.531395166993853, -1.7280428620235044], [3.6106764371526694, -6.106235351004483, -1.640684712671511], [-1.689433348465716, 0.5214415170216427, 0.3190253918398459], [1.0800286387397229, 0.07173384544778116, 1.0795284184507439], [0.44397564816723545, -4.215903903576532, -0.1526178505629614], [2.593690409991879, 1.241887931513947, -42.71056799812277], [-1.9564313402037943, 3.718481405273458, -1.1240836322900223], [-0.18299030151041684, 7.148845265971826, 0.08905436797585486], [3.4682445643508775, -9.25689209787085, -1.7436274741843363], [4.191809091344128, -6.5841214920527396, -1.705876396735409], [7.474357894833865, -3.267996471704702, -1.6718463320170538], [-6.616512786945767, 4.02702446943306, -1.6964060435648585], [3.570190529336209, -7.812662805190325, -1.7086689888632791], [-9.490721685461876, 8.069273173842976, -1.8869108420955616], [-7.512456305676418, -4.426790058936048, -2.297461002848727], [4.47319925903167, -9.171493018800456, -1.7955749507674272], [-1.02260684426302, 4.933820303337701, -0.8813425653989071], [-4.666424577404316, 6.1415149068202695, -1.7157198948149226], [8.610904038292098, 5.898964897922038, -2.1883025586025404], [-5.793237948417795, 2.473296897371016, -1.4806213310078458], [6.383014741011966, 7.700002047755071, -2.195019519667424], [2.0469818972430964, -9.78159958846193, -1.6090824444217735], [-4.626394266219577, -8.323174821180011, -2.253476227413599], [-2.0589375033897506, 8.808177973230361, -1.5741759066721461], [-0.3389966948682872, -7.099689864018184, 13.17121726282662], [4.351326016770759, 7.201003138353357, -2.317640568087796], [4.202872319974391, 7.830189549408761, -2.3009098821000427], [-8.623756354879127, 2.614412224686955, -1.6476951005038325], [-2.426987722564606, -8.45466393548355, -2.513717232746128], [6.931236165690738, 2.981075603851613, -2.5095530139012836], [3.672650269867411, 5.409194981840841, -2.5336153538757493], [3.3509219311603733, 6.603559101989845, -2.4705141580722567], [2.687652168114532, -9.326833675779042, -1.6793419783904322], [-7.250589570573311, -8.908850961178166, -2.146117127614883], [5.227859323193611, 1.9153190528811734, -3.2833275590790976], [-4.105613891653834, -7.729307579602205, -2.3132226680828336], [-1.499858672050463, -8.519648900050639, -2.920408278516633], [2.3578862828193685, -6.474673002040962, -1.5072959251855864], [-7.391565963063997, 5.945178096015322, -1.808282927605004], [7.829086545136665, 7.588108575904993, -2.1595519532827883], [-8.725921023920815, 0.6474873766919202, -0.9595283960164258], [-4.994143565187672, -0.5777453776236143, 76.495235845982], [-3.1778499350861855, 9.212746424641239, -1.7211613066373537], [9.331169997178957, -9.249869378476376, -1.899229783702502], [3.901821431634101, 0.2920319421923061, 2.837296174661054], [-6.4117526210071425, -7.366381344655297, -2.20347529061827], [-1.0635301693994812, 2.9639254069254033, -0.5371144047790921], [3.392912567996362, -4.93168335268293, -1.5439059085737008], [-6.6145028210621515, 5.97738216813292, -1.7884215389885965], [-9.036375164203212, 4.739144109520643, -1.8035993008855113], [-1.5485991541836448, 7.6807327003789965, -1.3957450851707685], [5.1132143295789305, -6.163706078399582, -1.7392540075489382], [1.4237549463953503, 8.841121773315969, -2.938713398888167], [-3.434160610043979, 7.1632850636549925, -1.6739115241436817], [6.068213008379871, 2.898430490802575, -2.6169330177833676], [-2.303273896503928, -2.8969481249082047, -4.450670056955373], [-2.2833817128583123, -1.5958352231922053, -15.977304716101841], [5.569047935552046, -4.814961653922946, -1.6981360126035754], [9.068936723012232, 4.7208295124701785, -2.2260573599680575], [-8.461615078519532, 5.944506489648877, -1.831144863659579], [5.874104290968891, -3.374340408525822, -1.6056303276989379], [-9.049153679701208, -6.6216039083985905, -2.1581169011488677], [8.277145366332906, 6.3609040872490255, -2.1812684156182134], [5.960344733596898, -1.4945713926137856, -1.2442157773265587], [3.415986357316898, -0.2978373632107214, 0.24025022412235475], [-3.0650841588578874, 6.988395189746669, -1.6314499241153846], [-8.275630260639197, -5.614467020426632, -2.2070714763219823], [7.943724424392126, 0.055690809422937804, 1.518913593863598], [-5.423190354570968, 0.2741794460341431, 0.005827004492321763], [5.7378418218121645, 6.714684061551278, -2.2533227855190217], [6.282698487878861, -1.5603047515690438, -1.2970356000877818], [-2.01979634002819, 5.57996551818567, -1.3693236470244488], [6.443389051660645, -1.5419828867201275, -1.3042454137083195], [-2.6060993089876057, -6.984221813846698, -2.592043891464247], [-3.3924736249614877, 0.44159698397491276, 0.0008420783999413262], [-7.078891481165803, -4.930257914052825, -2.2821249333572067], [-9.261532225829468, -3.3773784030586063, -2.318249498548711], [-8.47644388990963, -3.159790237128739, -2.378409077144666], [8.132450644089104, -8.506114410007175, -1.8753040427102867], [4.6988366794700465, 6.828719730327208, -2.3094161657231], [3.2828735915753455, -2.481558601156088, -1.1925820320622078], [7.634311427146443, 4.9046601433403065, -2.2612959473491827], [-1.274548443347749, -0.930366506418439, 2.9608565884572515], [-3.970235174748879, 7.326230800064426, -1.7195113445637138], [7.2259546323811605, 8.231410272460082, -2.1593490141232836], [-0.3843727087322364, -9.249636515861708, -18.20722653809234], [-6.610263038361559, -3.3256825649547794, -2.4740925155579205], [0.025493724918545624, 5.548059234358373, 1.1484391410934818], [-8.474197945467466, 2.3283545720977816, -1.604063845248335], [9.468516432686577, 1.80937324381585, -2.636848914956771], [1.4047011831151153, -3.0605764683620933, -0.76698738369011], [-0.024533168345211465, -9.141017608120439, 1.2423764173659948], [-6.453179367194711, 9.250835504525522, -1.8564531505480946], [3.4057875210932274, 4.695810187510499, -2.692684313398364], [-8.399746606364804, -9.31557042352168, -2.119603822621377], [-3.840119805185558, 9.065795147533656, -1.761991273013349]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.10568, y=-206.18612\nx0=-3.24872, y=-99.64307\nx0=4.39706, y=337.00949\nx0=5.42930, y=614.69634\nx0=-4.54595, y=-282.75502\nx0=-1.74189, y=-14.58495\nx0=-5.33090, y=-462.81483\nx0=-8.12520, y=-1692.95533\nx0=-4.00702, y=-191.19797\nx0=-6.58448, y=-887.56113\nx0=-9.87605, y=-3076.29718\nx0=-0.85156, y=-2.07181\nx0=-9.99729, y=-3193.15907\nx0=-8.55137, y=-1980.05346\nx0=3.88271, y=237.29983\nx0=6.34462, y=962.43113\nx0=1.11015, y=9.22696\nx0=1.28640, y=13.01460\nx0=-6.38136, y=-805.95383\nx0=5.13588, y=524.30609\nx0=8.17076, y=2005.28807\nx0=0.59350, y=2.51190\nx0=-4.08386, y=-202.80548\nx0=4.19516, y=295.06860\nx0=1.19981, y=11.04259\nx0=-0.64611, y=-1.17943\nx0=2.90952, y=106.62080\nx0=2.21806, y=51.37120\nx0=5.44977, y=621.36324\nx0=3.48867, y=175.95176\nx0=6.17383, y=889.53819\nx0=-7.95266, y=-1585.12844\nx0=-2.74787, y=-59.22136\nx0=5.98193, y=812.15384\nx0=-4.97764, y=-374.42408\nx0=9.26051, y=2890.46959\nx0=-5.61180, y=-542.33373\nx0=4.76575, y=423.57070\nx0=-7.49229, y=-1320.08184\nx0=3.12178, y=129.35186\nx0=3.57347, y=188.12538\nx0=-9.82771, y=-3030.51554\nx0=-3.67368, y=-146.00340\nx0=-4.63955, y=-301.17876\nx0=-7.45996, y=-1302.67227\nx0=9.87805, y=3491.92392\nx0=-6.88644, y=-1018.81537\nx0=-4.71513, y=-316.62980\nx0=-4.13386, y=-210.60926\nx0=-9.74937, y=-2957.29447\nx0=-0.31205, y=-0.45202\nx0=2.25769, y=53.83621\nx0=1.01029, y=7.45790\nx0=0.21502, y=0.51444\nx0=3.26597, y=146.52261\nx0=-5.25476, y=-442.69343\nx0=7.51429, y=1571.42655\nx0=8.20524, y=2030.06195\nx0=-8.28121, y=-1794.57506\nx0=-3.67163, y=-145.74969\nx0=-2.57861, y=-48.61752\nx0=8.83444, y=2518.60268\nx0=7.85766, y=1789.55071\nx0=-2.89383, y=-69.54947\nx0=0.87919, y=5.50748\nx0=9.31997, y=2945.10774\nx0=-6.09311, y=-699.00054\nx0=1.71211, y=26.27551\nx0=8.10219, y=1956.63675\nx0=5.28445, y=568.87317\nx0=-5.37921, y=-475.89295\nx0=0.10327, y=0.21017\nx0=-3.29910, y=-104.52539\nx0=-3.23732, y=-98.55956\nx0=7.74982, y=1719.00370\nx0=-0.34146, y=-0.49559\nx0=9.78069, y=3392.03374\nx0=-5.62515, y=-546.32630\nx0=7.15645, y=1363.80408\nx0=-4.46294, y=-267.06261\nx0=7.18039, y=1377.08510\nx0=-9.66409, y=-2878.93250\nx0=-9.16281, y=-2446.18823\nx0=6.20960, y=904.49016\nx0=-4.63677, y=-300.62029\nx0=4.21746, y=299.51963\nx0=-5.33250, y=-463.24185\nx0=-9.19278, y=-2470.75006\nx0=0.93990, y=6.36071\nx0=-5.44270, y=-493.45234\nx0=-9.57952, y=-2802.60841\nx0=-0.03559, y=-0.06081\nx0=6.56663, y=1063.00853\nx0=-1.56038, y=-10.49507\nx0=-4.90369, y=-357.48142\nx0=-8.13356, y=-1698.29763\nx0=1.46335, y=17.76745\nx0=9.69877, y=3309.47048\nx0=4.45715, y=350.22289\nx0=-6.35832, y=-797.02952\nx0=1.51154, y=19.24172\nx0=3.70231, y=207.68529\nx0=-3.87178, y=-171.86965\nx0=3.35751, y=158.18263\nx0=-5.57898, y=-532.60631\nx0=-0.42198, y=-0.62834\nx0=0.18522, y=0.42397\nx0=6.50648, y=1035.09672\nx0=1.39533, y=15.82050\nx0=-9.76816, y=-2974.74749\nx0=-7.51675, y=-1333.35718\nx0=-0.35312, y=-0.51347\nx0=0.66490, y=3.11724\nx0=3.39369, y=162.95729\nx0=-1.58445, y=-10.98253\nx0=-8.35617, y=-1844.82100\nx0=-6.57385, y=-883.15826\nx0=-7.05908, y=-1099.38640\nx0=7.41590, y=1512.37365\nx0=4.08329, y=273.41271\nx0=-8.46457, y=-1919.12701\nx0=4.16519, y=289.15817\nx0=-1.38442, y=-7.39615\nx0=2.18503, y=49.37570\nx0=-1.86131, y=-17.82869\nx0=2.90837, y=106.50533\nx0=2.19407, y=49.91646\nx0=8.15005, y=1990.51455\nx0=-0.03283, y=-0.05628\nx0=5.60367, y=673.05267\nx0=-9.35616, y=-2607.54481\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=8.05080, y=1920.69462\nx0=-3.32725, y=-107.32204\nx0=-8.12343, y=-1691.82570\nx0=4.21132, y=298.29027\nx0=-9.52050, y=-2750.14454\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 3.39 * x0**3 + 2.12 * x0**2 + 1.78 * x0", "data": [[-4.105676420782636, -206.18611883169933], [-3.248723245265994, -99.64306543140431], [4.397055681876203, 337.00948579884243], [5.429303082077148, 614.6963449784321], [-4.545953457406955, -282.7550200875698], [-1.7418894906471767, -14.584947102906064], [-5.330903999301904, -462.81482758982577], [-8.125200535166677, -1692.955332928458], [-4.007022274215362, -191.19796899528333], [-6.584484834046373, -887.5611348570886], [-9.876045823731536, -3076.297175716183], [-0.8515581139627404, -2.0718063513368667], [-9.997294439696482, -3193.1590738949444], [-8.551371252446705, -1980.0534619164403], [3.8827096808812556, 237.2998291183193], [6.344621976115398, 962.4311349906975], [1.1101490942993841, 9.226956693045606], [1.2864024887319125, 13.014600352668735], [-6.381357715930145, -805.9538258526285], [5.135878502770641, 524.3060852744817], [8.170755238730443, 2005.2880655473475], [0.5935015983475918, 2.511895241513077], [-4.083857394879676, -202.80547542798215], [4.195157635985126, 295.0686043848909], [1.199807910020425, 11.04258813519835], [-0.6461091321525494, -1.1794256401160168], [2.9095177880155703, 106.6208026281719], [2.2180616539747593, 51.37120452254722], [5.449768787376444, 621.3632439862638], [3.4886735321314646, 175.9517579098175], [6.173825668224779, 889.5381913323367], [-7.952663871051846, -1585.1284377985855], [-2.747871626128835, -59.221357075035], [5.981932288995944, 812.1538381185348], [-4.977642374357647, -374.42407922925133], [9.260508870019667, 2890.469594496676], [-5.611796101077758, -542.3337304355088], [4.765745150936516, 423.5706968359191], [-7.492290611830117, -1320.0818397872652], [3.121775559486661, 129.35186401709436], [3.5734703644443897, 188.12537514877476], [-9.827707314969924, -3030.5155394701223], [-3.673683209933385, -146.00339909367463], [-4.639553925011142, -301.1787642055052], [-7.45996136867916, -1302.6722698801725], [9.878047079758613, 3491.9239159791573], [-6.886443616602238, -1018.8153677848413], [-4.715128584504599, -316.6297996154826], [-4.133863067449049, -210.60925769502265], [-9.7493730229625, -2957.2944702191694], [-0.31204643839920365, -0.45201672559253175], [2.2576905348273417, 53.83620789437113], [1.0102902798302456, 7.457904710685588], [0.2150167952715769, 0.5144411942135183], [3.2659682600712223, 146.52261262819871], [-5.254757600959472, -442.6934250869451], [7.514289418547719, 1571.4265463415443], [8.205243456862537, 2030.0619467594202], [-8.281206347284503, -1794.575060856105], [-3.671626979066451, -145.7496911969478], [-2.5786065846209443, -48.61751899638347], [8.834436321179783, 2518.6026812761256], [7.857655352230179, 1789.5507059955544], [-2.893826748034556, -69.54947389026677], [0.8791895911091068, 5.507476527654399], [9.31996723003278, 2945.1077416480143], [-6.093112051384583, -699.0005441626095], [1.712110277777004, 26.275506505984744], [8.102189655288111, 1956.6367498644292], [5.284453814472078, 568.8731693298041], [-5.379213006154169, -475.8929489905664], [0.10327095683466325, 0.21016552707234343], [-3.299104270012629, -104.52539061774618], [-3.2373167062088566, -98.55956499847173], [7.749820538060188, 1719.0036955489375], [-0.34146492359873193, -0.49558941208208296], [9.780693413077742, 3392.0337418672975], [-5.62514932489643, -546.3262991317359], [7.156451944416336, 1363.8040819938108], [-4.462940970035216, -267.06261021095895], [7.180391507186041, 1377.0851040954885], [-9.664090700688401, -2878.9325044007064], [-9.162808324403981, -2446.188226733403], [6.209602388571241, 904.490160124661], [-4.6367740337837375, -300.6202924578019], [4.217462582959614, 299.51963331568425], [-5.332495741822529, -463.2418545808541], [-9.1927798566628, -2470.750058719821], [0.9399046731759082, 6.360705622746222], [-5.442695394437664, -493.45233981998325], [-9.57952291870329, -2802.6084133725344], [-0.03558781052609561, -0.06081413216667814], [6.566632595188256, 1063.0085256945424], [-1.5603838775702812, -10.495065307293732], [-4.903685253707191, -357.4814246001804], [-8.133555528615936, -1698.2976337289715], [1.4633501736224837, 17.76745214672519], [9.698771814817459, 3309.470478399078], [4.457149852391595, 350.2228860080405], [-6.358322405167263, -797.0295161997494], [1.5115449385576323, 19.24172391025792], [3.7023140916951096, 207.68529019110645], [-3.871783124738151, -171.86964638787262], [3.3575129659050127, 158.18262866138315], [-5.578984505313933, -532.606312530688], [-0.42197605174601804, -0.6283421791805166], [0.18522166315891653, 0.42396699230892987], [6.506481395620156, 1035.0967233732356], [1.3953266832246527, 15.820503440731088], [-9.768161361970682, -2974.74748813155], [-7.5167516462498725, -1333.3571793501246], [-0.35311923973238457, -0.5134696805244818], [0.6649008305855304, 3.1172448691427297], [3.3936907801922462, 162.9572911459954], [-1.5844458473176921, -10.982528564327726], [-8.356168589782381, -1844.8209952542463], [-6.573852372028764, -883.1582584476417], [-7.059083363708442, -1099.3863985654682], [7.4158991233078275, 1512.3736527739484], [4.083290191867075, 273.4127115358877], [-8.464565778158178, -1919.127006633865], [4.16518791524156, 289.1581651186361], [-1.3844248420988343, -7.396154461915017], [2.185027633432515, 49.37570463206107], [-1.8613085012879989, -17.82868685541315], [2.908365049771744, 106.5053307122256], [2.194067349214052, 49.91645982338822], [8.150053111896423, 1990.5145493432997], [-0.032833462442154016, -0.056278117581741796], [5.603665018557891, 673.052668343682], [-9.356163727972868, -2607.544810036144], [8.050800683256096, 1920.6946151674003], [-3.3272479645998825, -107.32203735875909], [-8.123431611173288, -1691.8257002136634], [4.211324341223058, 298.2902688889123], [-9.520496632816755, -2750.1445380129126]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-0.15335, y=-0.13344\nx0=0.42213, y=0.67555\nx0=-6.28043, y=-214.56046\nx0=8.47775, y=689.66532\nx0=-6.20136, y=-206.22960\nx0=2.55943, y=25.87604\nx0=-2.90363, y=-18.95325\nx0=9.56396, y=975.84273\nx0=0.01338, y=0.01356\nx0=-6.58866, y=-249.19512\nx0=0.73676, y=1.67950\nx0=-5.21385, y=-119.76400\nx0=4.72043, y=132.18602\nx0=-8.69788, y=-591.06574\nx0=5.56362, y=208.73305\nx0=-4.61503, y=-81.60983\nx0=-0.34273, y=-0.26552\nx0=-6.30564, y=-217.26395\nx0=-3.55880, y=-35.96630\nx0=-1.33195, y=-1.92086\nx0=6.91788, y=385.84387\nx0=8.73464, y=751.42904\nx0=-6.23992, y=-210.26509\nx0=-1.65989, y=-3.47807\nx0=-6.61779, y=-252.64923\nx0=-2.88726, y=-18.62003\nx0=2.58694, y=26.59157\nx0=5.62127, y=214.84435\nx0=9.47061, y=948.60391\nx0=-0.22720, y=-0.18731\nx0=-7.50663, y=-374.15117\nx0=4.65114, y=126.90313\nx0=9.74791, y=1031.03370\nx0=8.52950, y=701.82379\nx0=-5.35802, y=-130.46988\nx0=8.72990, y=750.25629\nx0=5.05235, y=159.54584\nx0=1.58107, y=8.03315\nx0=7.11943, y=418.66344\nx0=-2.50931, y=-12.01286\nx0=-5.22643, y=-120.67413\nx0=-4.60389, y=-80.99105\nx0=2.45927, y=23.38103\nx0=-9.63082, y=-810.16179\nx0=-2.24490, y=-8.51868\nx0=8.56335, y=709.85190\nx0=-1.29129, y=-1.77700\nx0=0.08301, y=0.09047\nx0=-3.52494, y=-34.89790\nx0=6.31478, y=298.00235\nx0=-1.15002, y=-1.34844\nx0=6.26840, y=291.86409\nx0=5.46676, y=198.72932\nx0=-9.43748, y=-760.93116\nx0=-8.61837, y=-574.48200\nx0=-8.59034, y=-568.71075\nx0=1.05116, y=3.31757\nx0=-8.86794, y=-627.60551\nx0=-9.39408, y=-750.16185\nx0=-8.93886, y=-643.27946\nx0=-7.66129, y=-398.64811\nx0=4.82271, y=140.25003\nx0=2.28383, y=19.41186\nx0=9.03396, y=827.92996\nx0=-4.69072, y=-85.89686\nx0=-5.83163, y=-170.14504\nx0=-1.23201, y=-1.58415\nx0=3.50459, y=58.83064\nx0=8.52829, y=701.53706\nx0=-2.73237, y=-15.66593\nx0=-2.50666, y=-11.97352\nx0=-0.27558, y=-0.22057\nx0=3.85124, y=75.80499\nx0=8.13335, y=612.31622\nx0=-0.81433, y=-0.69121\nx0=-7.52977, y=-377.75145\nx0=-5.22822, y=-120.80339\nx0=-5.00437, y=-105.28847\nx0=4.25756, y=99.56019\nx0=-7.70860, y=-406.34975\nx0=6.39980, y=309.47734\nx0=-3.31669, y=-28.80121\nx0=-5.74368, y=-162.23707\nx0=-2.37541, y=-10.13626\nx0=-0.57877, y=-0.43767\nx0=-6.35003, y=-222.07831\nx0=3.93267, y=80.22055\nx0=-3.19107, y=-25.50263\nx0=1.40366, y=6.13950\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=6.83304, y=372.56115\nx0=1.98483, y=13.74373\nx0=3.01571, y=39.53653\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 + x0**2 + x0", "data": [[-0.15334619752847622, -0.1334370856997613], [0.42213142111762636, 0.675548039675349], [-6.280428141190509, -214.5604615686585], [8.4777517150102, 689.665321219953], [-6.201362287716794, -206.2296016046271], [2.5594268916047476, 25.8760436578695], [-2.903629530995211, -18.95325280195916], [9.56396140586586, 975.8427267380303], [0.013377975106589446, 0.013559339583662563], [-6.588662297538084, -249.19512417267003], [0.7367610576929451, 1.6795042348837532], [-5.2138482032443045, -119.7639956742925], [4.720434369500472, 132.1860168504461], [-8.697876413123726, -591.0657371346915], [5.563620023401439, 208.73304628611996], [-4.615031328233452, -81.6098272635403], [-0.3427262658382908, -0.26552204297452087], [-6.305642288945612, -217.26394682670897], [-3.5588045866417772, -35.966295188680526], [-1.3319501184893845, -1.920859875368212], [6.917876853627504, 385.8438690775572], [8.734641622788637, 751.4290418563276], [-6.23992471778106, -210.26509441351496], [-1.659894926784462, -3.4780711945413936], [-6.617785925160757, -252.6492292151466], [-2.8872632021913347, -18.6200342948708], [2.58693602927538, 26.59156569813267], [5.621267307302551, 214.8443499500896], [9.470605157552193, 948.6039138339822], [-0.22720297216948993, -0.18731026952960161], [-7.506625070919249, -374.1511736841792], [4.651143867785583, 126.90312624435049], [9.747911906453059, 1031.0337027888386], [8.529502449972128, 701.8237912654193], [-5.358022269315645, -130.46988028430187], [8.729897896569653, 750.2562876585536], [5.05234708332476, 159.54583608242564], [1.5810672380637154, 8.03315100871068], [7.119431658519787, 418.6634385072035], [-2.509307978377433, -12.012856637495648], [-5.226434924976317, -120.6741338489402], [-4.603886746492448, -80.991052771837], [2.4592726673348935, 23.381030044296637], [-9.630816784811236, -810.1617893904379], [-2.244900848391014, -8.518678040731169], [8.563345322567503, 709.8519033461725], [-1.2912920919517639, -1.7770027989937793], [0.0830095534226789, 0.09047212384542457], [-3.524942353127212, -34.8979030251284], [6.3147810247080365, 298.0023495033134], [-1.1500246573516115, -1.348440774975002], [6.2683971160179155, 291.8640887902527], [5.466764233655786, 198.72931907824577], [-9.437483377887174, -760.9311584466269], [-8.618366507079775, -574.4819951205574], [-8.590336610560101, -568.7107490087914], [1.051160534405014, 3.317566715149617], [-8.86793971637241, -627.6055106608865], [-9.394083232180911, -750.1618536680074], [-8.938860622143238, -643.2794606755816], [-7.661289827213658, -398.6481064005395], [4.822705445533691, 140.25002909720496], [2.2838285786712405, 19.41186132245998], [9.033960414011794, 827.9299603101215], [-4.690715890223531, -85.89685691749062], [-5.831627530345518, -170.14503510892956], [-1.232005891805441, -1.584153370661527], [3.5045898134926503, 58.83063651394772], [8.528288946889546, 701.5370599306385], [-2.7323673068471654, -15.66592902211097], [-2.5066598731465994, -11.973521724720896], [-0.2755847289078428, -0.2205676037455378], [3.851238484413793, 75.80499137170771], [8.133346048409106, 612.3162243817335], [-0.8143343155184795, -0.6912119034354282], [-7.529772946228926, -377.7514480295429], [-5.228217227825045, -120.8033867409196], [-5.004366763726709, -105.28847344998717], [4.257556896010289, 99.56019046301752], [-7.708595587035509, -406.3497540867463], [6.399804914882388, 309.4773365348931], [-3.3166872555634352, -28.80120698894477], [-5.743680551371579, -162.23706759815022], [-2.3754101185120557, -10.136262435052778], [-0.5787744341315282, -0.437672359112336], [-6.350026829465618, -222.07830660162716], [3.9326651611913235, 80.22055063978421], [-3.1910719476365994, -25.50262650952601], [1.4036596551298235, 6.13949515466421], [6.833040364413144, 372.56114638641895], [1.9848305676740843, 13.743726941535554], [3.0157076212225515, 39.53653029074287]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.96605, y=1.94105\nx0=8.20105, y=2.10426\nx0=6.30342, y=1.84109\nx0=9.84351, y=2.28681\nx0=7.15107, y=1.96726\nx0=4.91183, y=1.59165\nx0=2.97066, y=1.08879\nx0=8.30361, y=2.11669\nx0=5.37357, y=1.68149\nx0=7.77484, y=2.05089\nx0=0.46804, y=-0.75919\nx0=0.31354, y=-1.15983\nx0=4.53769, y=1.51242\nx0=1.51023, y=0.41226\nx0=3.50600, y=1.25448\nx0=5.70381, y=1.74113\nx0=5.71334, y=1.74280\nx0=5.50889, y=1.70636\nx0=6.64477, y=1.89383\nx0=1.92259, y=0.65367\nx0=0.12812, y=-2.05478\nx0=9.63922, y=2.26584\nx0=3.33909, y=1.20570\nx0=0.25034, y=-1.38494\nx0=4.97593, y=1.60461\nx0=2.02553, y=0.70583\nx0=0.74846, y=-0.28974\nx0=5.15016, y=1.63903\nx0=5.00413, y=1.61026\nx0=0.27457, y=-1.29255\nx0=4.48595, y=1.50095\nx0=7.90237, y=2.06716\nx0=0.39403, y=-0.93132\nx0=8.01770, y=2.08165\nx0=3.90748, y=1.36289\nx0=1.91804, y=0.65130\nx0=5.66550, y=1.73440\nx0=8.84998, y=2.18042\nx0=6.46237, y=1.86600\nx0=8.39656, y=2.12782\nx0=5.65671, y=1.73284\nx0=0.45125, y=-0.79574\nx0=9.23766, y=2.22329\nx0=2.89818, y=1.06408\nx0=2.83951, y=1.04363\nx0=3.64385, y=1.29304\nx0=7.10497, y=1.96079\nx0=6.35107, y=1.84862\nx0=1.88171, y=0.63218\nx0=0.19124, y=-1.65424\nx0=1.88282, y=0.63277\nx0=6.15720, y=1.81762\nx0=7.39238, y=2.00045\nx0=7.05212, y=1.95333\nx0=9.28964, y=2.22890\nx0=3.04122, y=1.11226\nx0=1.17064, y=0.15755\nx0=7.96127, y=2.07459\nx0=8.98820, y=2.19591\nx0=9.99978, y=2.30256\nx0=0.66165, y=-0.41302\nx0=6.95301, y=1.93917\nx0=9.60531, y=2.26232\nx0=3.43423, y=1.23379\nx0=8.81966, y=2.17698\nx0=5.73406, y=1.74642\nx0=1.08216, y=0.07896\nx0=2.84814, y=1.04667\nx0=2.67387, y=0.98353\nx0=3.24665, y=1.17762\nx0=3.52303, y=1.25932\nx0=1.73254, y=0.54959\nx0=3.17138, y=1.15417\nx0=1.65785, y=0.50552\nx0=8.12555, y=2.09501\nx0=2.05137, y=0.71851\nx0=0.86321, y=-0.14709\nx0=0.71730, y=-0.33227\nx0=4.93094, y=1.59553\nx0=6.31933, y=1.84361\nx0=5.54333, y=1.71260\nx0=0.74669, y=-0.29211\nx0=4.07966, y=1.40601\nx0=6.65960, y=1.89606\nx0=1.01367, y=0.01358\nx0=3.63838, y=1.29154\nx0=4.85598, y=1.58021\nx0=3.58903, y=1.27788\nx0=3.21090, y=1.16655\nx0=4.10746, y=1.41280\nx0=5.65581, y=1.73268\nx0=0.07859, y=-2.54356\nx0=8.95749, y=2.19249\nx0=4.41082, y=1.48406\nx0=0.04863, y=-3.02360\nx0=1.77479, y=0.57368\nx0=9.78051, y=2.28039\nx0=8.33199, y=2.12010\nx0=6.11183, y=1.81023\nx0=7.08984, y=1.95866\nx0=6.66781, y=1.89729\nx0=5.32756, y=1.67289\nx0=3.76308, y=1.32524\nx0=8.70833, y=2.16428\nx0=4.32493, y=1.46440\nx0=6.31232, y=1.84250\nx0=4.82609, y=1.57404\nx0=5.77724, y=1.75393\nx0=5.49782, y=1.70435\nx0=0.86315, y=-0.14717\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.07107, y=1.12203\nx0=5.64838, y=1.73137\nx0=7.81091, y=2.05552\nx0=2.73347, y=1.00557\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = log(x0)", "data": [[6.966054744337565, 1.9410490307038517], [8.201049323240289, 2.1042621123320413], [6.303418723417541, 1.841092140724493], [9.843506850446737, 2.286812034813836], [7.151066279032507, 1.9672614755217692], [4.911831866485692, 1.5916469611233621], [2.970664010587192, 1.0887855004142617], [8.303608456125442, 2.116690174074576], [5.3735681866012035, 1.6814921546390882], [7.774842320143644, 2.0508931774922714], [0.46804440319356627, -0.7591921089464504], [0.3135401148108999, -1.159827969165574], [4.537691871482807, 1.5124184844231916], [1.5102287847097755, 0.4122611524027211], [3.505999324141159, 1.2544755937269645], [5.703807395093539, 1.7411339159033088], [5.713344744492818, 1.7428046217853201], [5.508887095213933, 1.7063626236742695], [6.644765617133905, 1.8938294194790122], [1.9225905875327096, 0.6536735409404709], [0.12812138067585163, -2.0547771778720545], [9.639223373395648, 2.2658405424513246], [3.3390854509623975, 1.205696952416742], [0.250338883291182, -1.3849397458608357], [4.975933694773257, 1.6046130303427253], [2.025530494884338, 0.705831639032014], [0.7484552359555706, -0.28974388191342215], [5.1501564194867555, 1.639027086930278], [5.004128124090349, 1.6102631966114815], [0.2745710883243967, -1.2925450777011245], [4.485954068944221, 1.500951197290411], [7.902370907045503, 2.0671628292634194], [0.394033355675169, -0.9313197141935474], [8.01770278887308, 2.081651945545388], [3.9074832295617408, 1.362893491445485], [1.9180366474100343, 0.6513020833746594], [5.665499331568406, 1.7343950338556702], [8.849981075867406, 2.180415320697485], [6.462371184348098, 1.8659963068464243], [8.396560205628994, 2.127822122651639], [5.6567108079251325, 1.7328425939521397], [0.45124619410921285, -0.7957422034776211], [9.23765808522249, 2.2232883995484545], [2.8981818030686624, 1.0640835759089413], [2.839513147630563, 1.043632610587199], [3.6438513509324557, 1.2930411857370272], [7.104969309694569, 1.960794442003432], [6.351068370072839, 1.8486230460081832], [1.881707633014355, 0.6321796800061902], [0.19123737600487295, -1.6542398162717615], [1.8828216400675333, 0.6327715240349572], [6.1571990889897, 1.8176219807952352], [7.392380831461308, 2.0004498524199485], [7.052122484819329, 1.9533286331907052], [9.289643252999518, 2.228900150904282], [3.0412165710584085, 1.112257623212491], [1.1706373335921507, 0.1575483300643128], [7.961266416487311, 2.074588084750276], [8.98819569950285, 2.195912127506478], [9.999776983812431, 2.3025627911266042], [0.6616504589420255, -0.4130178701306955], [6.953008890692138, 1.9391744998003921], [9.605312056467161, 2.2623162846534273], [3.4342250326423867, 1.2337912910918907], [8.819662443189422, 2.176983597539087], [5.7340559436196425, 1.7464231238871875], [1.0821561303984095, 0.07895546797959814], [2.848141103369683, 1.0466665370449313], [2.6738666695382007, 0.9835256156333945], [3.2466480062923937, 1.1776230814212727], [3.523027221799311, 1.2593206262095524], [1.7325369444673104, 0.5495867762224161], [3.171377472555088, 1.154166027435712], [1.6578528771301724, 0.5055233176312586], [8.125554728092302, 2.0950140001119673], [2.051369528906218, 0.7185076329767298], [0.8632145293883653, -0.1470920331729581], [0.717295732471675, -0.3322670653004938], [4.930944739251841, 1.595530600375672], [6.319333476260307, 1.843613739980153], [5.543333441254165, 1.712596024005307], [0.7466885555688577, -0.29210710773684606], [4.079657172579113, 1.4060129585570118], [6.6595984293662385, 1.8960591868434722], [1.0136693421003937, 0.013576759386075162], [3.638379971985243, 1.2915385199374592], [4.855983111873213, 1.5802115759655675], [3.589026238139814, 1.2778809228491996], [3.2108965553477984, 1.1665501988761378], [4.107457337943954, 1.4128041844952994], [5.655811970975308, 1.7326836838718185], [0.07858602226828597, -2.54356142909809], [8.95749194490869, 2.192490270939932], [4.410819263165177, 1.4840604461652669], [0.048625883144448864, -3.023599314854756], [1.7747947307784926, 0.573684771608188], [9.780512576018712, 2.2803918933091967], [8.331988582276496, 2.120102153051711], [6.111833514588155, 1.810226812387887], [7.089841887437048, 1.9586630395107505], [6.667807823842205, 1.897291143813687], [5.327560448980829, 1.672893431520506], [3.7630765983493015, 1.3252368670643182], [8.708328567474071, 2.1642798743410108], [4.324932355307776, 1.4643964998702648], [6.312319334294176, 1.8425031738820759], [4.826086411883975, 1.574035872530308], [5.777238816655637, 1.7539258551615184], [5.497816722184417, 1.704351053826272], [0.8631512021626244, -0.14716539795842842], [3.0710685501555823, 1.1220255629795297], [5.64838167963796, 1.7313690757472437], [7.810911683438742, 2.0555216898735136], [2.7334747466021, 1.0055736008255518]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.40481, y=560.58594\nx0=3.62221, y=34.13283\nx0=-2.69332, y=-9.94814\nx0=6.86331, y=296.43429\nx0=-6.14134, y=-207.67094\nx0=-6.12300, y=-205.67602\nx0=4.72995, y=87.75322\nx0=2.90387, y=14.20877\nx0=-6.54104, y=-254.27052\nx0=0.51416, y=0.49681\nx0=-4.20181, y=-58.22399\nx0=4.46355, y=71.97538\nx0=9.50562, y=821.30202\nx0=-0.46316, y=1.05124\nx0=9.17756, y=736.73550\nx0=-4.29462, y=-62.86269\nx0=5.78402, y=171.06784\nx0=-1.43138, y=1.24291\nx0=-3.90314, y=-44.74977\nx0=2.66022, y=9.62619\nx0=9.97319, y=952.49325\nx0=-3.62566, y=-34.11267\nx0=3.77716, y=39.83503\nx0=-4.16233, y=-56.31686\nx0=-7.87533, y=-457.41688\nx0=-9.30363, y=-768.49847\nx0=-5.23307, y=-123.07777\nx0=5.50727, y=145.74164\nx0=4.14625, y=55.66126\nx0=-7.08436, y=-327.74738\nx0=8.44809, y=569.62945\nx0=8.48446, y=577.30297\nx0=-3.74772, y=-38.57741\nx0=0.02552, y=0.99930\nx0=5.75058, y=167.86909\nx0=8.55539, y=592.46209\nx0=6.82185, y=290.78065\nx0=5.95170, y=187.70011\nx0=5.11667, y=114.27890\nx0=-0.71408, y=1.26278\nx0=-6.54436, y=-254.68303\nx0=0.10375, y=0.98605\nx0=-4.67888, y=-84.48801\nx0=5.40712, y=137.20739\nx0=-8.43086, y=-565.99118\nx0=8.37023, y=553.42923\nx0=-6.91835, y=-304.00906\nx0=5.83373, y=175.89541\nx0=-7.28038, y=-357.28821\nx0=-3.38525, y=-26.26032\nx0=-5.16458, y=-117.80619\nx0=7.18490, y=342.73022\nx0=-5.48948, y=-144.13710\nx0=0.03631, y=0.99854\nx0=-2.80547, y=-12.01144\nx0=-1.44294, y=1.21922\nx0=-7.92552, y=-466.61199\nx0=-0.29822, y=0.98923\nx0=5.41819, y=138.13482\nx0=-4.95621, y=-102.65619\nx0=-5.13293, y=-115.41975\nx0=-8.09058, y=-497.69889\nx0=6.49823, y=249.03182\nx0=-6.59733, y=-261.32810\nx0=-6.08327, y=-201.39949\nx0=6.37891, y=234.68101\nx0=-2.32973, y=-4.62020\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-2.14307, y=-2.62424\nx0=1.69864, y=0.11279\nx0=-7.44661, y=-383.65225\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x0**5 - 3 * x0**3 + 1) / (x0**2 + 1)", "data": [[8.404806073899731, 560.5859412091633], [3.6222070012255525, 34.13282988032117], [-2.6933245152604286, -9.948138277130054], [6.863307523970079, 296.43428522623054], [-6.141344597007876, -207.670942299465], [-6.122995527618926, -205.67602058268326], [4.729954431118976, 87.75321778223369], [2.903871030089448, 14.20876570139821], [-6.541041810566579, -254.2705159646012], [0.5141641253814377, 0.4968136493596966], [-4.201811281573555, -58.22398562853021], [4.4635484977855455, 71.97537788538172], [9.505619416906065, 821.3020232606905], [-0.46316019070718184, 1.051244042123664], [9.177557404213744, 736.7355016555974], [-4.294623213830102, -62.86269443963685], [5.7840165340222, 171.0678365263633], [-1.431376182298914, 1.242910708872476], [-3.903136330320476, -44.74977414271887], [2.660221561012788, 9.626191515210284], [9.97319146874706, 952.4932531795956], [-3.625659044166758, -34.11267491520141], [3.7771607790725685, 39.83502866104862], [-4.162327130583536, -56.316860603008635], [-7.875328709691329, -457.416878043953], [-9.303630531922176, -768.4984680402898], [-5.2330712834329525, -123.07776646655554], [5.507270535546523, 145.74163977312395], [4.146245659617149, 55.661257517194535], [-7.08435861726342, -327.7473845063819], [8.448085096330338, 569.629446288787], [8.484456507325945, 577.3029711284298], [-3.7477234967587325, -38.57740911514588], [0.025515783325495534, 0.9992995750818692], [5.750579840412911, 167.86909168139934], [8.555388801222279, 592.4620874151235], [6.8218515947321166, 290.7806506893512], [5.9517034274902585, 187.70010961794387], [5.116666993902321, 114.27890065358744], [-0.714076755687401, 1.262776029267955], [-6.5443593953848955, -254.68302603334286], [0.10375235712036357, 0.9860471243971025], [-4.678879927863193, -84.48800972010083], [5.407117833866126, 137.20739003336595], [-8.430860738575984, -565.9911792162595], [8.370231578853364, 553.4292306076221], [-6.918347707557437, -304.0090620082961], [5.833728172666579, 175.8954074141174], [-7.280381482649849, -357.2882140225238], [-3.3852542712293427, -26.260322184500843], [-5.164578354777245, -117.80619366708989], [7.18490069089761, 342.7302205487767], [-5.489477040693802, -144.1371032605736], [0.036309754852304366, 0.9985399775494204], [-2.8054746275588416, -12.011439748988913], [-1.4429387841707868, 1.2192227694828441], [-7.9255221013516834, -466.61198803688154], [-0.2982191762506581, 0.9892304591443394], [5.418190968213603, 138.13482492381118], [-4.956213227348913, -102.65619433769689], [-5.132931268979761, -115.41974855496854], [-8.09058143847105, -497.69888904523856], [6.498226559914471, 249.03181781236603], [-6.597329739338662, -261.32810175946474], [-6.083270835028438, -201.39948542028725], [6.378907008431206, 234.68101009878416], [-2.3297252532164254, -4.620204662160901], [-2.143069171885033, -2.624240791660038], [1.6986400869611487, 0.1127852096196901], [-7.446605938185553, -383.65224990528566]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-5.80222, y=8223.88786\nx0=8.68822, y=0.05855\nx0=0.90756, y=-0.08024\nx0=7.17441, y=-0.05707\nx0=-5.13939, y=5265.98416\nx0=0.83826, y=-0.07192\nx0=2.73668, y=0.89366\nx0=0.39278, y=-0.01241\nx0=5.85801, y=0.16884\nx0=1.75316, y=0.16852\nx0=-8.63459, y=859727.72470\nx0=-3.90656, y=-1942.72115\nx0=-3.42398, y=-93.33017\nx0=-0.68678, y=-0.20474\nx0=6.58703, y=-0.17244\nx0=2.40932, y=0.41102\nx0=-7.31361, y=-269850.68705\nx0=7.55325, y=-0.05480\nx0=5.54288, y=0.48849\nx0=6.65548, y=-0.09166\nx0=8.27663, y=0.04123\nx0=7.26798, y=-0.08579\nx0=-3.02738, y=81.40011\nx0=-6.91860, y=-246998.90712\nx0=5.68674, y=0.09858\nx0=2.26616, y=0.24688\nx0=2.35154, y=0.32099\nx0=-6.16081, y=10043.47744\nx0=3.95655, y=-0.61313\nx0=1.29613, y=-0.11359\nx0=-0.49841, y=-0.06709\nx0=-2.06580, y=16.61155\nx0=5.87410, y=0.19795\nx0=0.94988, y=-0.08525\nx0=4.02636, y=-0.39627\nx0=-5.96425, y=44421.77719\nx0=8.27371, y=0.04033\nx0=-9.44487, y=-416435.58228\nx0=8.98172, y=0.00828\nx0=7.08893, y=-0.14977\nx0=-3.08771, y=30.93477\nx0=-9.57016, y=-975080.76521\nx0=-6.73758, y=-11464.92198\nx0=0.12158, y=-0.00019\nx0=-7.69835, y=-144172.34728\nx0=2.96941, y=0.35443\nx0=0.08022, y=-0.00004\nx0=3.56374, y=-0.53764\nx0=5.19505, y=0.17722\nx0=-4.71318, y=9.28051\nx0=-0.23579, y=-0.00357\nx0=6.48594, y=-0.15772\nx0=-7.56565, y=-186653.59132\nx0=9.24556, y=0.00534\nx0=-4.15813, y=-974.73257\nx0=1.01645, y=-0.09319\nx0=6.31858, y=-0.00333\nx0=2.56654, y=0.74142\nx0=-9.21669, y=1399258.02804\nx0=8.97330, y=0.00628\nx0=6.04371, y=0.22877\nx0=2.60352, y=0.80931\nx0=1.64783, y=0.06818\nx0=-7.86022, y=7808.72356\nx0=7.26225, y=-0.08148\nx0=-9.01625, y=1435344.23598\nx0=7.81972, y=-0.00680\nx0=8.87516, y=0.03512\nx0=4.55072, y=-0.18249\nx0=-3.18760, y=-11.87572\nx0=3.35168, y=-0.01334\nx0=9.79773, y=-0.03400\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.17269, y=-98159.99784\nx0=-2.04905, y=16.34565\nx0=0.19562, y=-0.00113\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 * exp(-x0) * cos(x0) * sin(x0) * (sin(x0**2) * cos(x0) - 1)", "data": [[-5.802216673646507, 8223.887864684386], [8.688215247923779, 0.05854533225268897], [0.9075645560548189, -0.08023989389970296], [7.174414731894505, -0.05706721010135198], [-5.139386145126297, 5265.984163016606], [0.8382562283550055, -0.07191501716630581], [2.7366774444059487, 0.8936608231430704], [0.39278232987576267, -0.012413811220401982], [5.858013218744205, 0.16884166629627353], [1.7531552591183779, 0.1685206290926473], [-8.63459370287728, 859727.7246975425], [-3.9065641280202463, -1942.7211463152107], [-3.4239760464713287, -93.33017048763686], [-0.6867849832058237, -0.20473760688887022], [6.5870314430587555, -0.17243614996008036], [2.4093220803647615, 0.4110158375855779], [-7.313607397138357, -269850.6870464365], [7.553254181754745, -0.0548049701130214], [5.542884130176484, 0.4884937138437759], [6.655483244230467, -0.0916648879863752], [8.276634263846624, 0.04123436209407756], [7.26798130377658, -0.08579197300765089], [-3.0273762142984406, 81.40011178256702], [-6.91859969300223, -246998.907122725], [5.686742717572944, 0.09858383778505232], [2.266159465080225, 0.24688433718284683], [2.3515440865825283, 0.3209901186670509], [-6.1608120814553295, 10043.477444970318], [3.9565479425388705, -0.6131292730426038], [1.2961337262782013, -0.11358878073424557], [-0.49841065387993666, -0.06709337287099716], [-2.065799700275428, 16.611546919964432], [5.87409987173638, 0.19794714663876462], [0.949884008159005, -0.08524700215836284], [4.026358116673634, -0.39627453499555426], [-5.964253125431906, 44421.77719020752], [8.273712975333545, 0.0403269384896845], [-9.444873196742133, -416435.58227606135], [8.98171514525308, 0.00828325657101697], [7.088928482545896, -0.14977372240765888], [-3.0877120790445733, 30.93477249842088], [-9.570158489290353, -975080.7652084419], [-6.737579752196532, -11464.92197657638], [0.12157664570205284, -0.00018875295103398335], [-7.6983471599545865, -144172.3472787933], [2.9694140306125156, 0.35442776131677595], [0.08021613689628104, -3.780510426389202e-05], [3.5637415214881827, -0.5376395258181719], [5.195051902072214, 0.17722390576249183], [-4.71318448425353, 9.280509719290412], [-0.23579106071277778, -0.003565913257652689], [6.48593593983631, -0.15771706140883376], [-7.565654457562864, -186653.59132016957], [9.245563116076983, 0.005335584956770222], [-4.1581341204274525, -974.7325667587613], [1.0164496983622477, -0.09318533364860124], [6.318577059471451, -0.0033308672644827664], [2.5665351432090517, 0.741416120993064], [-9.2166923964375, 1399258.0280392854], [8.973300463849505, 0.006277153727813397], [6.043713715247804, 0.22876998543547739], [2.6035234637304434, 0.8093111526759929], [1.647830063792835, 0.06818025939682859], [-7.8602188694302715, 7808.723556547095], [7.262248860518202, -0.08147959181777471], [-9.016247940485052, 1435344.2359821023], [7.819722613817561, -0.006799570839231896], [8.875161608709949, 0.03512239780319088], [4.550718187882307, -0.18249317415630542], [-3.187603210329872, -11.87571745157566], [3.3516768346994468, -0.01333925885364996], [9.797733265472967, -0.03399700141684558], [-7.172694518548372, -98159.99784284279], [-2.049048519429433, 16.345653720104927], [0.19562382985139415, -0.0011297414100318952]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.43508, x1=4.80912, y=148.82856\nx0=-5.51714, x1=-8.43544, y=-392.58115\nx0=9.34985, x1=-8.68694, y=705.56655\nx0=-6.99306, x1=2.43399, y=-41.42897\nx0=2.76882, x1=-4.84565, y=65.01278\nx0=0.53140, x1=-6.69328, y=23.80688\nx0=-3.75747, x1=4.34490, y=-70.93411\nx0=-5.37165, x1=-0.17947, y=-0.17302\nx0=-9.59151, x1=3.03449, y=-88.32009\nx0=6.70150, x1=3.87565, y=100.66108\nx0=-0.99403, x1=-3.57076, y=-12.67419\nx0=4.36503, x1=1.57242, y=10.79248\nx0=-0.67516, x1=-4.41790, y=-13.17776\nx0=5.30677, x1=4.92476, y=128.70633\nx0=3.14940, x1=-0.47047, y=0.69708\nx0=0.74756, x1=9.69562, y=70.27454\nx0=-9.29921, x1=-3.92737, y=-143.43327\nx0=7.45161, x1=4.36306, y=141.85141\nx0=0.13472, x1=-3.25938, y=1.43116\nx0=-6.74503, x1=8.21801, y=-455.53040\nx0=-5.93961, x1=-3.26138, y=-63.17728\nx0=6.64025, x1=-3.45147, y=79.10297\nx0=-5.43552, x1=6.31097, y=-216.48802\nx0=0.53066, x1=5.59990, y=16.64090\nx0=-6.69351, x1=3.28910, y=-72.41151\nx0=-4.45066, x1=0.21377, y=-0.20338\nx0=-8.80539, x1=7.55561, y=-502.67558\nx0=5.96162, x1=-1.72188, y=17.67552\nx0=0.61045, x1=-1.50614, y=1.38479\nx0=-5.42328, x1=5.52003, y=-165.25107\nx0=3.02078, x1=3.53952, y=37.84498\nx0=9.59348, x1=7.44446, y=531.67047\nx0=7.57904, x1=-6.57307, y=327.45427\nx0=-6.63644, x1=3.51541, y=-82.01372\nx0=0.04136, x1=1.81088, y=0.13563\nx0=-3.80921, x1=-6.94996, y=-183.99235\nx0=3.58929, x1=9.62121, y=332.25191\nx0=3.76884, x1=-7.95228, y=238.33678\nx0=-0.12199, x1=9.44456, y=-10.88118\nx0=3.22461, x1=-5.95719, y=114.43519\nx0=-6.68008, x1=-6.63013, y=-293.64687\nx0=-3.93134, x1=-6.56653, y=-169.51708\nx0=0.45301, x1=3.01657, y=4.12220\nx0=-0.99742, x1=-7.13788, y=-50.81776\nx0=2.83583, x1=-9.71585, y=267.69633\nx0=-7.74351, x1=5.13305, y=-204.02724\nx0=6.32916, x1=0.26230, y=0.43546\nx0=9.21031, x1=-1.46911, y=19.87856\nx0=-6.17437, x1=5.77690, y=-206.05451\nx0=8.37545, x1=-1.10237, y=10.17799\nx0=-2.33330, x1=-5.23101, y=-63.84710\nx0=8.37802, x1=1.37751, y=15.89758\nx0=3.98125, x1=5.81592, y=134.66554\nx0=-5.86634, x1=0.21940, y=-0.28239\nx0=-6.85518, x1=1.01258, y=-7.02873\nx0=-8.61031, x1=-3.19938, y=-88.13525\nx0=-7.85570, x1=-8.79816, y=-608.09096\nx0=2.69206, x1=3.81628, y=39.20718\nx0=2.80751, x1=2.22935, y=13.95332\nx0=5.44930, x1=1.94841, y=20.68708\nx0=-4.76696, x1=6.68574, y=-213.07934\nx0=9.61620, x1=-2.60499, y=65.25531\nx0=-0.64270, x1=-9.19925, y=-54.38893\nx0=-1.44805, x1=7.40355, y=-79.37124\nx0=8.59474, x1=9.06623, y=706.45774\nx0=5.64988, x1=-1.69415, y=16.21588\nx0=5.75010, x1=-0.28505, y=0.46720\nx0=-2.57735, x1=5.49851, y=-77.92244\nx0=-2.35858, x1=-0.98012, y=-2.26571\nx0=3.14396, x1=5.42023, y=92.36579\nx0=3.40883, x1=-5.01867, y=85.85848\nx0=5.98285, x1=7.71367, y=355.98395\nx0=9.92346, x1=-8.66486, y=745.05157\nx0=9.30583, x1=5.27891, y=259.32508\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-6.91878, x1=3.77710, y=-98.70681\nx0=-3.32022, x1=7.89394, y=-206.89715\nx0=5.52648, x1=-3.61553, y=72.24264\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1**2", "data": [[6.435084266939466, 4.809124489529683, 148.82855911820727], [-5.517144990242953, -8.435435799100306, -392.5811529845437], [9.349854045209117, -8.686935097449355, 705.566552807997], [-6.993056025419788, 2.433988778469768, -41.428971417872674], [2.768823816110693, -4.845646262479352, 65.01277979588161], [0.5314042891619195, -6.693275093539612, 23.80687574146179], [-3.757470397537757, 4.344900078057787, -70.93411491639132], [-5.3716549614669145, -0.1794692741751973, -0.17301681842145702], [-9.591512528312245, 3.03449343723479, -88.32009012197008], [6.70150350074827, 3.875651096831259, 100.66108213400065], [-0.9940264828452356, -3.570764109192681, -12.674191851270825], [4.365026540929396, 1.572415216866256, 10.792482788297386], [-0.6751646476190523, -4.417900368648004, -13.17775804191647], [5.306770622806752, 4.924756793710408, 128.70632569777885], [3.149398831818921, -0.47046548006862743, 0.6970809077756885], [0.7475620769223124, 9.695615471135504, 70.27454266324072], [-9.299213277064444, -3.9273702879071397, -143.43327301721402], [7.4516136387947824, 4.363064823428104, 141.8514109362033], [0.13471508200597526, -3.259381936007742, 1.4311551852183404], [-6.7450263900335266, 8.21801363482567, -455.5304032198649], [-5.9396122740902975, -3.261380124198306, -63.17728178269051], [6.640246037407302, -3.4514715755810403, 79.10296704497672], [-5.435518139630824, 6.310974935410375, -216.48801586815344], [0.5306605262706761, 5.599896911582835, 16.64090141400635], [-6.6935055731088156, 3.2890993758252876, -72.41151267245225], [-4.450660057870836, 0.21376842378980676, -0.20338154121689037], [-8.805392839003108, 7.555609915787365, -502.675584856911], [5.961624483775122, -1.7218833971149916, 17.675515705639146], [0.61045379767525, -1.5061426500278259, 1.3847934906150154], [-5.423279666028473, 5.5200262191201475, -165.25107055705973], [3.0207814770538555, 3.539521087567188, 37.84498328685815], [9.593481753514684, 7.444458978298851, 531.6704659826374], [7.5790406124357865, -6.5730693153670146, 327.45427033243465], [-6.636439221858277, 3.5154076405365373, -82.01371901763142], [0.041360905072910015, 1.8108792652215868, 0.13563414236919694], [-3.809208882233537, -6.949962882461338, -183.99234673976778], [3.589289002353082, 9.621206306056557, 332.25190736004384], [3.768843846049066, -7.952276263035147, 238.3367768986222], [-0.12198661819858891, 9.444564824742802, -10.881182522837033], [3.22460781575254, -5.957188637877044, 114.43519323447882], [-6.6800819323080285, -6.630126136422099, -293.64686649422396], [-3.9313431233732103, -6.566534985009103, -169.5170847671518], [0.4530059282483645, 3.0165657536283454, 4.122203977618943], [-0.9974183637422911, -7.137877558676822, -50.8177634926937], [2.8358325127173387, -9.715852631498132, 267.6963286946902], [-7.743511371537329, 5.133045405123415, -204.02723887638192], [6.329157864423937, 0.26230066916249584, 0.4354564474931654], [9.210309548111294, -1.4691133483959007, 19.878556116147227], [-6.1743679544040875, 5.776899397698481, -206.05450608694585], [8.375452945236358, -1.1023684248431938, 10.177985633127948], [-2.3333010887643617, -5.23100553543771, -63.847095139171515], [8.378016164356676, 1.377510275476304, 15.897575208086021], [3.9812457602348807, 5.815924276531279, 134.66553906661454], [-5.86633684386292, 0.2194014551129797, -0.2823878478869203], [-6.8551770817390505, 1.0125793259422817, -7.028728854936043], [-8.610314247062316, -3.199376297199108, -88.13525146585529], [-7.8556962737612395, -8.798161520278562, -608.0909573183554], [2.6920626991562244, 3.8162796437153705, 39.20717508875003], [2.807505191323136, 2.2293513474252595, 13.953321661388657], [5.4492972563087925, 1.9484056157421232, 20.687082401889494], [-4.766963404479632, 6.685744372043882, -213.07934482257252], [9.616196000114229, -2.6049913734429264, 65.25531426859328], [-0.6426956350933377, -9.199253694411649, -54.38893340113254], [-1.4480484252371184, 7.403550449009465, -79.37124010666771], [8.594739240443921, 9.066230189044969, 706.4577404506169], [5.649877793600883, -1.6941456147884786, 16.215880159030142], [5.750103443057522, -0.2850464267527606, 0.4672043309759819], [-2.5773484825352355, 5.498506126746523, -77.922444796857], [-2.358578862824996, -0.9801156914020197, -2.265713991324538], [3.143956286095648, 5.420225271139724, 92.36579495236221], [3.408829304180019, -5.018673703978931, 85.85847598130121], [5.982848171595252, 7.713672892221901, 355.9839502840184], [9.923464620410169, -8.664859079654308, 745.051569021179], [9.305832782994834, 5.27891461934175, 259.32507970336417], [-6.918779119775227, 3.7771029192037098, -98.70680702320337], [-3.32022157282311, 7.893938137587469, -206.89714808894982], [5.5264799533259605, -3.6155344110538135, 72.24263823497373]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.50312, x1=-8.16781, y=-83.49555\nx0=1.84892, x1=-3.66035, y=12.38610\nx0=0.82304, x1=-7.86312, y=25.44384\nx0=2.44399, x1=4.95510, y=30.00373\nx0=3.83410, x1=5.37396, y=55.36336\nx0=1.06674, x1=3.22027, y=5.53113\nx0=-6.90436, x1=8.63218, y=-257.23776\nx0=3.14771, x1=7.89174, y=98.01902\nx0=4.22586, x1=-6.94023, y=101.77317\nx0=-7.16756, x1=-7.97868, y=-228.14084\nx0=-3.93644, x1=7.33828, y=-105.98915\nx0=8.58795, x1=-4.92302, y=104.06916\nx0=-0.41487, x1=-9.08015, y=-17.10303\nx0=-9.35284, x1=-1.12094, y=-5.87597\nx0=5.89112, x1=0.55269, y=0.89978\nx0=4.73052, x1=9.80618, y=227.44606\nx0=7.79483, x1=8.36215, y=272.52923\nx0=-8.95753, x1=-1.11156, y=-5.53384\nx0=0.39447, x1=1.67614, y=0.55412\nx0=-9.94190, x1=0.18227, y=-0.16515\nx0=-6.39578, x1=-9.03049, y=-260.78726\nx0=4.84066, x1=1.13122, y=3.09717\nx0=7.11354, x1=-0.72319, y=1.86019\nx0=-6.53710, x1=0.40543, y=-0.53726\nx0=-6.85926, x1=-2.09527, y=-15.05664\nx0=4.07656, x1=-9.70284, y=191.89412\nx0=4.50403, x1=1.26552, y=3.60667\nx0=9.41653, x1=-7.30334, y=251.13331\nx0=-6.46234, x1=6.19674, y=-124.07571\nx0=3.06585, x1=-7.81529, y=93.62907\nx0=8.80033, x1=-7.56334, y=251.70742\nx0=-8.08087, x1=6.67658, y=-180.10928\nx0=-4.11844, x1=-2.34322, y=-11.30652\nx0=-2.59573, x1=-0.68724, y=-0.61297\nx0=-5.76206, x1=1.81416, y=-9.48193\nx0=-4.40506, x1=-6.56709, y=-94.98794\nx0=-4.23360, x1=-0.89723, y=-1.70407\nx0=-4.02346, x1=-9.71954, y=-190.04719\nx0=7.72503, x1=3.86936, y=57.82947\nx0=1.36730, x1=7.63336, y=39.83509\nx0=-3.39473, x1=7.74431, y=-101.79814\nx0=6.42827, x1=-1.59557, y=8.18271\nx0=-7.95104, x1=7.54901, y=-226.55525\nx0=1.18526, x1=-4.53435, y=12.18469\nx0=-4.53887, x1=4.80987, y=-52.50302\nx0=-6.46470, x1=4.14673, y=-55.58156\nx0=-1.11193, x1=4.20466, y=-9.82898\nx0=-3.92760, x1=6.22174, y=-76.01875\nx0=5.79702, x1=1.86159, y=10.04483\nx0=3.38378, x1=-0.86495, y=1.26576\nx0=-1.38052, x1=4.05476, y=-11.34866\nx0=5.74024, x1=-0.64765, y=1.20386\nx0=8.37627, x1=5.37036, y=120.78898\nx0=-2.90406, x1=8.03543, y=-93.75494\nx0=-8.57970, x1=2.03031, y=-17.68345\nx0=-2.55686, x1=-7.03661, y=-63.29996\nx0=9.89655, x1=2.23615, y=24.74318\nx0=4.22338, x1=-5.62554, y=66.82794\nx0=6.63844, x1=-9.43972, y=295.76966\nx0=0.79082, x1=-6.34572, y=15.92244\nx0=-6.69410, x1=-3.84202, y=-49.40615\nx0=-6.52589, x1=6.17667, y=-124.48565\nx0=-1.70915, x1=6.45212, y=-35.57571\nx0=6.35066, x1=8.86462, y=249.52246\nx0=-9.07226, x1=3.31243, y=-49.77131\nx0=9.41365, x1=-4.74696, y=106.06169\nx0=-4.64671, x1=5.18780, y=-62.52909\nx0=0.03957, x1=2.20553, y=0.09625\nx0=-7.74340, x1=-5.79992, y=-130.24062\nx0=-9.60775, x1=-7.35079, y=-259.57297\nx0=-0.96486, x1=8.91952, y=-38.38101\nx0=3.30117, x1=1.31848, y=2.86934\nx0=-5.63805, x1=4.23890, y=-50.65308\nx0=-4.84629, x1=6.40421, y=-99.38269\nx0=-6.96366, x1=4.29812, y=-64.32261\nx0=-8.73943, x1=0.66272, y=-1.91918\nx0=-0.67601, x1=7.13674, y=-17.21566\nx0=-1.32444, x1=1.52160, y=-1.53321\nx0=0.72787, x1=3.00012, y=3.27567\nx0=-4.94043, x1=-9.67562, y=-231.25572\nx0=9.22794, x1=3.88667, y=69.69941\nx0=-7.68952, x1=-5.64764, y=-122.63182\nx0=7.18243, x1=9.77284, y=342.99084\nx0=6.03205, x1=8.78343, y=232.68264\nx0=-3.71412, x1=-2.14871, y=-8.57393\nx0=5.49293, x1=-7.59192, y=158.29870\nx0=6.23335, x1=-7.80798, y=190.00682\nx0=4.41614, x1=-3.82796, y=32.35544\nx0=-9.96437, x1=-4.16480, y=-86.41863\nx0=4.71313, x1=3.15489, y=23.45572\nx0=-5.85338, x1=0.92946, y=-2.52834\nx0=0.85444, x1=-3.96485, y=6.71594\nx0=6.05514, x1=7.52411, y=171.39745\nx0=4.76013, x1=-5.43407, y=70.28122\nx0=-7.39944, x1=-0.95749, y=-3.39184\nx0=2.37997, x1=-6.49512, y=50.20149\nx0=-2.05278, x1=6.90960, y=-49.00262\nx0=-5.19415, x1=-7.53414, y=-147.41839\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.12772, x1=4.06576, y=-75.44243\nx0=6.49170, x1=-3.31592, y=35.68923\nx0=5.35743, x1=7.39687, y=146.56212\nx0=2.09363, x1=-4.58632, y=22.01898\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1/2 * x0 * x1**2", "data": [[-2.5031202065274645, -8.167813438373052, -83.4955498992638], [1.8489229073287472, -3.660351796840633, 12.386096592687554], [0.8230441416213612, -7.863118086191485, 25.443844222286575], [2.443994581296147, 4.955100553785936, 30.00372574793839], [3.834104423119255, 5.373957878012989, 55.363362257249456], [1.0667415027660336, 3.2202698932759546, 5.531128395966933], [-6.9043610478070505, 8.632182472614652, -257.23776194007127], [3.147707524152901, 7.891744044543717, 98.01902063476395], [4.225863337272266, -6.940230866353305, 101.77316655916917], [-7.1675617014477, -7.978675430167296, -228.14084276481552], [-3.936435487284826, 7.338277496854552, -105.989148673903], [8.587948900574641, -4.92301648046058, 104.0691566748422], [-0.41487467344211737, -9.08015118178511, -17.103031154143316], [-9.352844002443, -1.1209412000994217, -5.875967146405918], [5.891124061458363, 0.5526933287584086, 0.8997805850806164], [4.7305161467937324, 9.806181912648306, 227.44606340833025], [7.79483188867761, 8.362154122738652, 272.5292324342098], [-8.957533679280088, -1.1115626914972143, -5.53383718679569], [0.39447330673334235, 1.6761365333802694, 0.5541232966092733], [-9.941902929851029, 0.18227124812648476, -0.16514896556756312], [-6.395782603544928, -9.030490347057016, -260.78725508078804], [4.840657266626522, 1.1312154281961906, 3.0971695299490225], [7.1135372418873715, -0.7231870298504539, 1.8601881397457594], [-6.537100477676738, 0.40542872088283133, -0.5372596032428303], [-6.859259204217267, -2.0952718218572786, -15.056636438127958], [4.076557634016693, -9.702843847891442, 191.89412354220462], [4.504026467254963, 1.2655154842371985, 3.606665494824959], [9.416528865667281, -7.30334363167263, 251.13330771388078], [-6.462337024306231, 6.196744403076725, -124.0757115139266], [3.0658496926613648, -7.815286915470958, 93.62907148340322], [8.800330272932545, -7.563338208240619, 251.7074198302515], [-8.08086714862636, 6.676580092867205, -180.10928313685216], [-4.118438124371653, -2.3432202993468483, -11.306515744110131], [-2.59572687037422, -0.6872351141478461, -0.6129706500663532], [-5.76205597548096, 1.814155906208935, -9.481928831684582], [-4.4050627948151755, -6.567093220754909, -94.98794026461], [-4.233600411799401, -0.8972304926946446, -1.7040719144561143], [-4.023460381530715, -9.719543249093533, -190.0471874445011], [7.725026291997981, 3.8693642736818123, 57.82946911757693], [1.3673007543933107, 7.633361772751549, 39.83508508072485], [-3.394726658201492, 7.744306127471383, -101.79813914127057], [6.428270540887457, -1.5955719515614923, 8.182705804526963], [-7.95104233194301, 7.549010585640968, -226.55525424542412], [1.1852617687850397, -4.534350396087927, 12.184688634104923], [-4.538865267530343, 4.809871590450925, -52.50301696565554], [-6.464699107688108, 4.146734145152472, -55.58155667568616], [-1.1119309430321973, 4.204655564898346, -9.828984967702407], [-3.927603664687509, 6.221735130847204, -76.01874543985062], [5.797024853145739, 1.8615886864179352, 10.04483086424457], [3.3837817016021727, -0.8649482532611312, 1.2657635751581533], [-1.380524874458974, 4.054760168328876, -11.34865996713075], [5.740239159117008, -0.6476460554083943, 1.2038584926542852], [8.376268196593816, 5.370359629303696, 120.78898104839327], [-2.9040634191548893, 8.035428227394078, -93.75493849750039], [-8.579701666660046, 2.0303100081540038, -17.68344605962148], [-2.556856025006411, -7.036611452028958, -63.299957697476], [9.896547470517472, 2.2361496147231836, 24.743175288197293], [4.223378423151292, -5.62553786438545, 66.82794484814386], [6.638435587758718, -9.439716223787538, 295.76966370772345], [0.7908191565414526, -6.345724133235957, 15.922437821950464], [-6.694104214980716, -3.8420168180331027, -49.40614820449785], [-6.5258940422094724, 6.176673294269502, -124.48564779390038], [-1.7091463270753664, 6.452115698526612, -35.575707308760414], [6.350660507408342, 8.864624985957345, 249.52245610636854], [-9.072261642907947, 3.3124304579187562, -49.77131436142673], [9.413647846381128, -4.746957037440187, 106.06169280514135], [-4.646709719649169, 5.187800869050818, -62.52909490269474], [0.03957433380682929, 2.2055313570876507, 0.09625207271687018], [-7.7434043853368735, -5.799923403801596, -130.2406217151174], [-9.60775183913811, -7.350787128597913, -259.5729744825852], [-0.9648583748403734, 8.919518476769358, -38.38100956244966], [3.301166922554259, 1.3184758228430322, 2.869338793982731], [-5.638048267934601, 4.238903678554875, -50.653083738980946], [-4.846285636462562, 6.404214417327651, -99.38268820198306], [-6.963659753319407, 4.298115265734285, -64.32261080062197], [-8.739427661683354, 0.6627220598516779, -1.919180624397794], [-0.6760116196119874, 7.136738598629002, -17.215662695972867], [-1.3244381823616287, 1.521595990110109, -1.5332056362238728], [0.7278693440445583, 3.0001181719120584, 3.2756700944190578], [-4.940432281660931, -9.675619207370543, -231.25572399104644], [9.227936315800903, 3.886666309345344, 69.69941043859538], [-7.6895180512269, -5.647640294718039, -122.63182217412638], [7.182425544203969, 9.772837816202816, 342.99083861795526], [6.0320543287394734, 8.783434584856199, 232.68264458548632], [-3.7141200592073904, -2.148705960825561, -8.57392973032088], [5.492926610390963, -7.591922638720671, 158.29870021707958], [6.233351665073169, -7.8079814516424655, 190.0068155150089], [4.4161443576441854, -3.8279566766100492, 32.355438772643765], [-9.964367293972627, -4.164796892679547, -86.41863164442547], [4.713134041312108, 3.154892166382391, 23.455723585990828], [-5.853381964854285, 0.9294569746303001, -2.528339856251704], [0.8544433035533636, -3.9648489519387553, 6.715935991352522], [6.055137919120387, 7.524110331317765, 171.39744928608414], [4.760127569186881, -5.43407165979086, 70.28122433676452], [-7.399441587926113, -0.9574878698723932, -3.3918412061712426], [2.3799744062744743, -6.495119866755301, 50.20149282348674], [-2.052782951395682, 6.90960386674228, -49.00262393844935], [-5.194147055058997, -7.53414043566665, -147.41839131815394], [-9.127716197339389, 4.065760173667773, -75.44242633799753], [6.491701004716873, -3.3159224282158135, 35.68923489349046], [5.357426393245273, 7.39686623191449, 146.562122857663], [2.0936266027983486, -4.586315747714198, 22.01897679529314]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-8.21210, y=-0.65144\nx0=-7.59028, y=-0.77215\nx0=-7.34880, y=-1.27240\nx0=4.74597, y=-1.01706\nx0=-6.90788, y=-1.45455\nx0=-6.66040, y=-0.65634\nx0=-3.97520, y=-0.93674\nx0=-1.77204, y=-1.00029\nx0=1.98250, y=-0.71609\nx0=-0.53006, y=-0.76076\nx0=1.23597, y=-0.67170\nx0=-5.40104, y=-1.49659\nx0=2.19717, y=-0.41767\nx0=-0.26249, y=-0.93351\nx0=6.13604, y=-1.04756\nx0=1.49014, y=-0.93585\nx0=0.81845, y=-0.57572\nx0=-1.97864, y=-0.72291\nx0=6.34341, y=-0.43484\nx0=0.06912, y=-0.99523\nx0=5.51180, y=-1.61685\nx0=-7.06841, y=-1.21109\nx0=7.24195, y=-0.52896\nx0=7.00282, y=-1.70780\nx0=2.61026, y=-1.43603\nx0=-1.74281, y=-1.01781\nx0=-0.04231, y=-0.99821\nx0=-2.52142, y=-1.06047\nx0=-2.75385, y=-1.89215\nx0=-5.28053, y=-0.79527\nx0=-0.81662, y=-0.57650\nx0=-5.21250, y=-0.57174\nx0=4.68252, y=-1.00194\nx0=7.09553, y=-0.94431\nx0=3.98137, y=-0.90461\nx0=-0.10026, y=-0.99000\nx0=-5.57722, y=-1.23250\nx0=7.03678, y=-1.49664\nx0=2.20112, y=-0.41576\nx0=-0.45616, y=-0.81454\nx0=-7.61924, y=-0.76793\nx0=1.07874, y=-0.56617\nx0=-1.09641, y=-0.57390\nx0=6.70859, y=-0.22247\nx0=1.48663, y=-0.93254\nx0=-6.98919, y=-1.75194\nx0=0.81386, y=-0.57769\nx0=-7.04781, y=-1.40376\nx0=5.67302, y=-0.43109\nx0=-1.95235, y=-0.76875\nx0=3.84914, y=-1.59154\nx0=-5.28754, y=-0.83080\nx0=3.19379, y=-0.30089\nx0=-2.08069, y=-0.54731\nx0=-2.10899, y=-0.50525\nx0=-0.86562, y=-0.55852\nx0=6.52151, y=-1.96490\nx0=-5.32253, y=-1.03152\nx0=-5.97718, y=-1.87766\nx0=-6.08649, y=-1.59647\nx0=-1.76648, y=-1.00411\nx0=-0.22594, y=-0.95027\nx0=5.62027, y=-0.86550\nx0=3.99406, y=-0.84068\nx0=-6.08376, y=-1.62162\nx0=-8.88067, y=-0.72561\nx0=-1.67346, y=-1.03429\nx0=-6.69666, y=-0.30428\nx0=6.86247, y=-0.97456\nx0=-1.28957, y=-0.72364\nx0=-2.97039, y=-1.55766\nx0=-6.67082, y=-0.54199\nx0=5.74510, y=-0.14147\nx0=-3.17297, y=-0.40074\nx0=-2.41247, y=-0.66680\nx0=6.63892, y=-0.91297\nx0=-5.59367, y=-1.09755\nx0=6.38709, y=-0.95452\nx0=1.96293, y=-0.75046\nx0=1.81279, y=-0.96547\nx0=-3.48264, y=-0.60065\nx0=1.23700, y=-0.67264\nx0=-3.85493, y=-1.56685\nx0=-1.54344, y=-0.98117\nx0=4.14972, y=-0.46747\nx0=6.47425, y=-1.86366\nx0=5.38810, y=-1.42968\nx0=5.50750, y=-1.63081\nx0=-1.98235, y=-0.71637\nx0=7.83425, y=-1.01960\nx0=7.75091, y=-1.03877\nx0=3.30020, y=-0.01792\nx0=-3.95416, y=-1.04989\nx0=-8.75631, y=-1.75063\nx0=-3.05092, y=-1.11590\nx0=7.89769, y=-0.98067\nx0=2.50664, y=-1.00004\nx0=-8.83204, y=-1.42282\nx0=5.99798, y=-1.94846\nx0=7.80628, y=-1.04522\nx0=3.96680, y=-0.98133\nx0=-1.18822, y=-0.63139\nx0=2.41624, y=-0.67791\nx0=6.56832, y=-1.71420\nx0=9.20073, y=-1.16462\nx0=3.15219, y=-0.51050\nx0=2.27812, y=-0.42286\nx0=3.53286, y=-0.92124\nx0=-4.28425, y=-0.80285\nx0=-3.35502, y=-0.05568\nx0=6.76020, y=-0.12124\nx0=5.14069, y=-0.60050\nx0=-4.99292, y=-1.05594\nx0=-5.22142, y=-0.58702\nx0=2.23929, y=-0.40825\nx0=7.72841, y=-1.00477\nx0=5.49433, y=-1.66372\nx0=-5.75087, y=-0.14153\nx0=-9.20149, y=-1.15110\nx0=2.32536, y=-0.47387\nx0=-1.22135, y=-0.65869\nx0=-1.99515, y=-0.69367\nx0=-3.92387, y=-1.21722\nx0=7.16212, y=-0.45292\nx0=-7.86899, y=-0.98814\nx0=7.28052, y=-0.78820\nx0=0.92217, y=-0.54600\nx0=-6.97482, y=-1.76937\nx0=2.70223, y=-1.77063\nx0=4.26054, y=-0.71961\nx0=9.43723, y=-1.88967\nx0=5.08211, y=-0.76856\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=7.81896, y=-1.03474\nx0=3.61265, y=-1.41532\nx0=0.30030, y=-0.91397\nx0=3.33007, y=-0.02203\nx0=-1.17036, y=-0.61803\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0**2) * cos(x0) - 1", "data": [[-8.21209898043288, -0.6514435600390162], [-7.590281540141075, -0.7721459098974188], [-7.34880305130436, -1.2723995330596471], [4.745968510988586, -1.0170611890260088], [-6.907875262446749, -1.4545533814808536], [-6.6604003012883055, -0.6563362535264123], [-3.97519876438386, -0.9367433234084948], [-1.772043715817297, -1.0002905870242114], [1.9825036069104502, -0.7160932456270035], [-0.5300646576853492, -0.7607644487326135], [1.2359708446414164, -0.671701839608059], [-5.401043486452459, -1.496591015922476], [2.1971666723587404, -0.4176742658844148], [-0.26248844099102087, -0.9335124730366912], [6.136042534071645, -1.04755582394208], [1.4901421913753943, -0.9358488515445945], [0.8184471207755166, -0.5757229468163423], [-1.9786434625809513, -0.7229119872574072], [6.343408683126178, -0.4348409240016198], [0.0691193278429445, -0.9952339442708513], [5.511795889134136, -1.6168497118606717], [-7.068408034436509, -1.2110879492259992], [7.241952932521222, -0.5289578959157291], [7.002815688902878, -1.7078009661030795], [2.61025811141414, -1.4360312417087426], [-1.7428076386664149, -1.0178054804846828], [-0.042306851274773294, -0.9982117328678424], [-2.5214213155185554, -1.0604731940577232], [-2.753845778366422, -1.8921459051716725], [-5.28053010206601, -0.7952664270196508], [-0.8166172575700728, -0.5765019847872925], [-5.212500411213665, -0.5717412632807776], [4.682518828276368, -1.0019448516429412], [7.095529418424572, -0.9443113134804545], [3.9813735993258277, -0.9046084138440653], [-0.10026186268768988, -0.9899982108164881], [-5.577224932380571, -1.2325002800358624], [7.036781991356584, -1.4966363313402427], [2.201122733871454, -0.4157619377269225], [-0.4561608875924037, -0.8145388078516436], [-7.6192439839557435, -0.7679275706407689], [1.0787358605866952, -0.5661731958244183], [-1.0964116767346237, -0.5739030956253934], [6.708589637446714, -0.22247003445125557], [1.486634564681001, -0.932538045552892], [-6.989190389151658, -1.7519429691876411], [0.8138646337517752, -0.5776886658889224], [-7.047814735377711, -1.4037614717890952], [5.67302282400723, -0.4310923609036945], [-1.952345943730684, -0.768752114090929], [3.849140020890424, -1.5915378514978997], [-5.287535046617274, -0.8307972159550123], [3.1937862640633075, -0.30088532270008417], [-2.0806857523288125, -0.5473066034109733], [-2.1089886808071174, -0.5052487363181144], [-0.8656202627397658, -0.5585164572022945], [6.521513646540523, -1.964903264022688], [-5.322533516344454, -1.0315150171736829], [-5.977178148067821, -1.877655749435609], [-6.086487168604231, -1.5964681558901717], [-1.7664790684551335, -1.0041109235067538], [-0.22593673902193423, -0.950271579801159], [5.620268090673054, -0.8654955118815071], [3.9940552705280723, -0.8406763241113491], [-6.083761388958129, -1.6216199639445552], [-8.880669540722948, -0.7256071085583797], [-1.6734615638729284, -1.0342855172326884], [-6.696656996898831, -0.3042794350567666], [6.86246945064125, -0.9745611561937487], [-1.289567173349715, -0.7236417602309199], [-2.9703890504251884, -1.5576612280357005], [-6.6708177147962395, -0.5419855860692342], [5.745097537100728, -0.14147170524937747], [-3.1729667563620367, -0.40074397562053343], [-2.412468251312778, -0.6667973188034878], [6.63892103525037, -0.9129712906013172], [-5.593671047199573, -1.0975488494786174], [6.387093000405205, -0.9545151098049267], [1.9629304813948139, -0.7504588281898714], [1.812786421750829, -0.9654689131795187], [-3.482639819971629, -0.6006481535646739], [1.2369990287745516, -0.6726372988272633], [-3.8549291983046245, -1.5668479304766558], [-1.5434431665181059, -0.9811705480241346], [4.149715455999797, -0.4674668692967745], [6.474246259910341, -1.8636593081303745], [5.388104726200522, -1.4296819612494462], [5.507495183996339, -1.630811426956607], [-1.9823455041399551, -0.716372822010993], [7.8342535972775025, -1.0195976484629972], [7.750908311216492, -1.0387673881083528], [3.3001963036877804, -0.017915128607332464], [-3.9541558905351355, -1.0498887130846009], [-8.75631062758831, -1.750633358086921], [-3.0509229832454103, -1.1159045026576762], [7.897689349988092, -0.9806666115913556], [2.5066393902198314, -1.0000448645048858], [-8.832037487523332, -1.4228188848363792], [5.997980707468024, -1.9484610580692059], [7.806275599464282, -1.045220089416036], [3.9667982154225783, -0.981329360019039], [-1.1882156313598387, -0.631389584118039], [2.416236991181526, -0.6779148025428825], [6.568324894368459, -1.7141951335451946], [9.200725238407124, -1.1646237675573607], [3.1521938410560892, -0.51049979332407], [2.278115803700153, -0.42286046067693706], [3.532855309418343, -0.9212381946342375], [-4.284246248128605, -0.8028521851331089], [-3.355019563162209, -0.055683018739786205], [6.760201003697752, -0.12124123794834962], [5.140685441087427, -0.6004978449138549], [-4.992922830405194, -1.055944621687886], [-5.221419535686227, -0.5870246966552086], [2.2392941703268754, -0.4082515544590969], [7.7284131608062125, -1.0047716392330328], [5.49433214726905, -1.6637183383676546], [-5.750867021522312, -0.14153299629740002], [-9.201490287645495, -1.1511045652760725], [2.325363413651502, -0.4738712538423834], [-1.2213494502746673, -0.6586924232593254], [-1.9951529253596227, -0.693667979592713], [-3.9238653622196544, -1.2172222464018247], [7.162117804629414, -0.45291851177633136], [-7.868990008263587, -0.9881434583968286], [7.280524011658283, -0.788202856164354], [0.9221697849231365, -0.5459988920789811], [-6.9748240171491656, -1.7693687705311687], [2.7022257163469927, -1.7706250975916227], [4.260544202007468, -0.7196141821136304], [9.437232826353764, -1.8896681869673544], [5.082112121214566, -0.7685580850744069], [7.8189615695818375, -1.0347401750144967], [3.6126477134954023, -1.4153176160061856], [0.30030349157151015, -0.9139704795307786], [3.3300704636824925, -0.022027108951817698], [-1.1703587169185266, -0.6180311613725189]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.48663, y=-0.93254\nx0=-7.19679, y=-0.38966\nx0=-0.67898, y=-0.65381\nx0=2.85479, y=-1.91749\nx0=-7.23060, y=-0.47312\nx0=-1.38661, y=-0.82808\nx0=4.85027, y=-1.13735\nx0=-3.88883, y=-1.40506\nx0=8.35629, y=-1.31474\nx0=-9.18843, y=-1.37480\nx0=-7.70041, y=-0.94127\nx0=9.53551, y=-1.17813\nx0=-3.91488, y=-1.26654\nx0=1.07874, y=-0.56617\nx0=-3.62559, y=-1.48400\nx0=-3.23661, y=-0.13607\nx0=-4.03179, y=-0.67252\nx0=2.81408, y=-1.94484\nx0=-9.70231, y=-0.89166\nx0=-2.77760, y=-1.92548\nx0=-4.97269, y=-1.10142\nx0=8.35837, y=-1.32848\nx0=-0.95960, y=-0.54316\nx0=-6.13081, y=-1.11075\nx0=-1.34177, y=-0.77893\nx0=9.11052, y=-1.92132\nx0=8.63615, y=-0.48703\nx0=7.27031, y=-0.71212\nx0=-5.91238, y=-1.36185\nx0=-6.81967, y=-0.50340\nx0=-1.84212, y=-0.93323\nx0=7.50117, y=-1.09588\nx0=2.05425, y=-0.59039\nx0=5.83941, y=-0.60001\nx0=5.58509, y=-1.16917\nx0=-3.90951, y=-1.29573\nx0=-6.06734, y=-1.75686\nx0=-9.71106, y=-1.05462\nx0=5.34102, y=-1.14674\nx0=-4.70375, y=-0.99884\nx0=-9.07143, y=-1.53710\nx0=5.08194, y=-0.76915\nx0=0.70836, y=-0.63473\nx0=0.21436, y=-0.95512\nx0=8.46281, y=-1.34040\nx0=6.06101, y=-1.80085\nx0=-7.85996, y=-0.99481\nx0=8.15076, y=-0.86978\nx0=1.60512, y=-1.01838\nx0=-9.65480, y=-0.16399\nx0=5.63896, y=-0.70196\nx0=6.21471, y=-0.20417\nx0=5.03972, y=-0.91547\nx0=-6.83249, y=-0.63596\nx0=1.19420, y=-0.63608\nx0=5.09058, y=-0.73998\nx0=-6.76846, y=-0.14496\nx0=-0.60760, y=-0.70374\nx0=9.73033, y=-1.39892\nx0=-6.16809, y=-0.66293\nx0=2.61555, y=-1.45783\nx0=-4.74032, y=-1.01289\nx0=9.93802, y=-0.14552\nx0=-3.28157, y=-0.03515\nx0=-6.08376, y=-1.62162\nx0=5.23218, y=-0.61134\nx0=-6.07521, y=-1.69572\nx0=-4.82908, y=-1.11304\nx0=6.54084, y=-1.90117\nx0=4.67230, y=-1.00641\nx0=-3.04134, y=-1.17325\nx0=2.21202, y=-0.41156\nx0=-4.30497, y=-0.87656\nx0=-0.61682, y=-0.69708\nx0=-9.27680, y=-0.06587\nx0=8.71081, y=-1.34904\nx0=-2.14888, y=-0.45603\nx0=6.71529, y=-0.18549\nx0=-8.35231, y=-1.28776\nx0=6.68465, y=-0.40540\nx0=3.84438, y=-1.61109\nx0=-5.26184, y=-0.71060\nx0=-8.62593, y=-0.41625\nx0=-2.44786, y=-0.77927\nx0=-5.69906, y=-0.27093\nx0=-9.70219, y=-0.88934\nx0=-3.12839, y=-0.64583\nx0=-2.53360, y=-1.11123\nx0=1.48414, y=-0.93016\nx0=4.87892, y=-1.16093\nx0=-1.29288, y=-0.72704\nx0=1.03498, y=-0.55186\nx0=-6.97482, y=-1.76937\nx0=3.91559, y=-1.26266\nx0=-7.63288, y=-0.78289\nx0=9.48244, y=-1.92663\nx0=-6.45624, y=-1.73504\nx0=3.24041, y=-0.12447\nx0=4.51355, y=-1.19730\nx0=0.33179, y=-0.89613\nx0=6.33420, y=-0.34249\nx0=4.94649, y=-1.14313\nx0=4.10340, y=-0.48265\nx0=0.67751, y=-0.65479\nx0=-6.62600, y=-1.07381\nx0=3.05392, y=-1.09781\nx0=9.10395, y=-1.88468\nx0=-0.96287, y=-0.54313\nx0=-5.93569, y=-1.58746\nx0=-0.82579, y=-0.57268\nx0=2.92560, y=-1.74383\nx0=0.42556, y=-0.83595\nx0=-2.14904, y=-0.45586\nx0=-6.22904, y=-0.10928\nx0=2.78823, y=-1.93523\nx0=4.39999, y=-1.15014\nx0=-6.41202, y=-1.26772\nx0=-8.18144, y=-0.73604\nx0=-5.07942, y=-0.77781\nx0=9.34932, y=-0.47476\nx0=-3.92067, y=-1.23481\nx0=1.17832, y=-0.62386\nx0=-4.36143, y=-1.05903\nx0=1.64555, y=-1.03139\nx0=8.87854, y=-0.75669\nx0=-2.13745, y=-0.46872\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.78098, y=-1.92656\nx0=5.44525, y=-1.65639\nx0=9.25743, y=-0.24194\nx0=1.68155, y=-1.03414\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0**2) * cos(x0) - 1", "data": [[1.486634564681001, -0.932538045552892], [-7.196794697076266, -0.38965754968112454], [-0.6789768391307387, -0.6538088233580454], [2.8547872902647846, -1.9174877162192943], [-7.230595274501175, -0.47312442799877874], [-1.3866140447579909, -0.8280805047903377], [4.850265318457982, -1.1373465041374589], [-3.888828302248082, -1.4050634633149797], [8.356287283367397, -1.3147351978070436], [-9.188429139750163, -1.3748025529132601], [-7.700405352397855, -0.9412733292882737], [9.535511964783272, -1.1781271788944652], [-3.9148814792306252, -1.2665440962061996], [1.0787358605866952, -0.5661731958244183], [-3.625591298532907, -1.483998384747803], [-3.2366071388762947, -0.1360696377967675], [-4.031788074881366, -0.6725155490183969], [2.814084737111422, -1.9448418198398933], [-9.702313830657944, -0.8916642449797871], [-2.7776026079075073, -1.9254829783243217], [-4.9726945179495186, -1.1014228333392009], [8.358372016608683, -1.3284779728338327], [-0.959603200784775, -0.5431567190030513], [-6.130809774015262, -1.110749307862297], [-1.3417714840356236, -0.778927484890862], [9.11052094784418, -1.9213167074903041], [8.63615147991116, -0.4870303977759236], [7.270311688102314, -0.7121199996495167], [-5.912380330738709, -1.3618544726007342], [-6.819669603922243, -0.5033986659528316], [-1.8421165341537655, -0.9332273765901451], [7.5011667599785845, -1.0958789274168745], [2.054249261308687, -0.5903941175631682], [5.839408791865633, -0.6000060366613236], [5.585093195392595, -1.1691675800447126], [-3.909514478706968, -1.295726774347659], [-6.067343547285051, -1.7568561335435666], [-9.711063223168379, -1.054621080279165], [5.341024019884928, -1.146738968024398], [-4.70374835198686, -0.9988447759304637], [-9.071434372905316, -1.5371013670506584], [5.081937753678744, -0.7691541944378049], [0.708355756960275, -0.6347309462284187], [0.21436181928527276, -0.9551165197113357], [8.462807528719502, -1.3404000983374729], [6.061014866389428, -1.800849048039268], [-7.8599585464790245, -0.9948069016223506], [8.150762797054885, -0.8697803172733942], [1.6051150014842293, -1.0183769061934642], [-9.654802123634479, -0.16399325335226778], [5.638962914597013, -0.7019574059465549], [6.214706746176994, -0.20417172205593614], [5.039720150794405, -0.9154696743213795], [-6.83248837028146, -0.6359554223487998], [1.194196832546515, -0.6360824686419022], [5.090583437457445, -0.7399782732586344], [-6.768462880027915, -0.1449562711708977], [-0.6076004692504728, -0.7037354556328868], [9.730331565567177, -1.3989244636451927], [-6.168087207408364, -0.6629306721658461], [2.615547334278629, -1.4578317576400486], [-4.740323315672182, -1.0128858383568795], [9.938016391110402, -0.14552051222421558], [-3.281571028006132, -0.03515423781556315], [-6.083761388958129, -1.6216199639445552], [5.232178639005124, -0.6113434987077946], [-6.075205810717681, -1.6957240749923457], [-4.829084351250419, -1.1130410678260723], [6.540840633545397, -1.9011677368149593], [4.672302473041336, -1.0064140035108604], [-3.0413428006421395, -1.1732456623591252], [2.212021397388977, -0.4115564240568764], [-4.304968046710487, -0.8765572708485768], [-0.6168198156871938, -0.6970784660723495], [-9.27679542957071, -0.06586753100460196], [8.710813758377999, -1.3490350277544025], [-2.1488805059821647, -0.4560280038479727], [6.71529007210286, -0.18549137361132184], [-8.352311845277105, -1.2877588343787505], [6.684652625563441, -0.40539880789656524], [3.8443765465095616, -1.611093910293269], [-5.26183978344692, -0.7105973824971223], [-8.625930402265904, -0.4162524150671225], [-2.4478571180753494, -0.7792721248332843], [-5.699057435375137, -0.2709332269439084], [-9.70218894207074, -0.8893447978286849], [-3.128391325099975, -0.6458347411335372], [-2.533597858546912, -1.1112296904319325], [1.4841367990837036, -0.9301595855848116], [4.878915467796084, -1.160932926575255], [-1.292876860595399, -0.7270352759659247], [1.0349765530151167, -0.5518606374438204], [-6.9748240171491656, -1.7693687705311687], [3.915591729090167, -1.2626641132817755], [-7.632882139257548, -0.7828870202446138], [9.482442196584547, -1.9266317021907193], [-6.456238408721013, -1.735037646169992], [3.2404107752730145, -0.12447192059931333], [4.513547667600292, -1.1973038145009354], [0.3317944201290306, -0.8961268166090242], [6.334197543675661, -0.3424903266869608], [4.946494648519552, -1.1431287180500584], [4.10340456314173, -0.48265316613216624], [0.6775131754605219, -0.6547864131251191], [-6.6259979079169185, -1.073808407668072], [3.053920558517584, -1.0978116042055015], [9.103954983223236, -1.8846847409330465], [-0.9628679746380264, -0.5431272906127824], [-5.935689047643149, -1.5874619258446359], [-0.8257945668546345, -0.5726750826113449], [2.9255953158652463, -1.7438341200239988], [0.4255641412880742, -0.8359488581113552], [-2.14903715450699, -0.4558627313181165], [-6.22903857715632, -0.10928053617744693], [2.7882305162114367, -1.9352323994729932], [4.399992968248402, -1.1501386868304055], [-6.412023968923128, -1.2677181109295592], [-8.181443904846763, -0.7360394508668804], [-5.079415804056335, -0.7778050631061851], [9.349322839958635, -0.4747622360429382], [-3.9206715885250576, -1.23481109236686], [1.178315999030863, -0.6238613510884239], [-4.361434438842564, -1.059029283604361], [1.645545612750773, -1.0313876304416383], [8.878544961169538, -0.7566857963796544], [-2.137447846055485, -0.46872344600116544], [-9.780980756399737, -1.9265643680730875], [5.445247644936746, -1.6563946440740234], [9.257427456772344, -0.2419411472808265], [1.6815540399386855, -1.0341360449883756]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.58776, x1=-6.65960, y=5.53664\nx0=-3.70447, x1=-5.40222, y=2.03761\nx0=-7.29935, x1=8.82345, y=4.20583\nx0=3.05855, x1=3.84059, y=-0.38096\nx0=-9.74554, x1=6.42531, y=1.87267\nx0=2.77986, x1=6.81178, y=1.83358\nx0=-0.48282, x1=-2.71377, y=2.53461\nx0=-1.39126, x1=-1.99007, y=2.40334\nx0=-1.37263, x1=-7.84984, y=-0.02434\nx0=-6.75309, x1=-0.23187, y=-2.64408\nx0=-2.52814, x1=-3.70879, y=2.91326\nx0=9.81237, x1=-9.81137, y=2.10038\nx0=-1.74665, x1=-8.07122, y=1.27328\nx0=-6.67303, x1=0.55699, y=-1.93559\nx0=9.75536, x1=-8.31281, y=0.86257\nx0=7.23969, x1=2.93230, y=-4.79609\nx0=5.49576, x1=-0.44179, y=-3.84305\nx0=2.24113, x1=3.21788, y=-4.68802\nx0=-1.32101, x1=7.51756, y=-1.91920\nx0=7.43025, x1=5.05989, y=1.86257\nx0=-3.59796, x1=-5.94501, y=2.49440\nx0=-0.23319, x1=-3.80955, y=1.08854\nx0=5.31288, x1=8.48631, y=2.92578\nx0=9.70362, x1=8.38695, y=0.83909\nx0=2.75032, x1=9.26360, y=-2.25851\nx0=-6.81017, x1=8.02638, y=0.51766\nx0=8.51188, x1=6.23627, y=4.74245\nx0=-0.46433, x1=-0.85011, y=-1.77311\nx0=-7.77507, x1=7.56114, y=-1.72665\nx0=-6.76382, x1=6.00718, y=-2.66905\nx0=-4.42441, x1=2.13853, y=-3.09346\nx0=-3.73819, x1=-2.85227, y=-3.23086\nx0=2.52552, x1=-3.13323, y=-3.46687\nx0=-4.76975, x1=1.36926, y=1.19909\nx0=5.85849, x1=3.44057, y=2.36257\nx0=7.24099, x1=5.73306, y=4.18349\nx0=-4.51487, x1=-8.40194, y=-3.06488\nx0=-1.01663, x1=5.23715, y=-2.55614\nx0=-6.83608, x1=-6.38843, y=-3.13347\nx0=0.17844, x1=-8.41632, y=-0.56781\nx0=0.33378, x1=0.78078, y=1.39636\nx0=7.27816, x1=-8.59684, y=-3.40392\nx0=-9.88098, x1=-6.85988, y=2.21577\nx0=1.56166, x1=-2.66169, y=-5.32203\nx0=0.49247, x1=-3.37879, y=-2.75740\nx0=-6.52660, x1=8.83467, y=1.20156\nx0=9.59551, x1=0.18110, y=-1.00276\nx0=6.75031, x1=6.78866, y=2.36406\nx0=-5.53548, x1=2.99411, y=-4.03544\nx0=-9.00181, x1=-9.23984, y=2.42081\nx0=5.29059, x1=6.09751, y=-4.93832\nx0=-5.37052, x1=-0.12236, y=4.71132\nx0=0.49219, x1=4.67812, y=-0.09715\nx0=-9.88224, x1=5.62426, y=2.09528\nx0=-1.69516, x1=3.18416, y=5.94826\nx0=6.15482, x1=-8.85712, y=0.64761\nx0=0.81498, x1=-7.51633, y=1.44643\nx0=-1.88172, x1=-9.21774, y=5.59032\nx0=3.38438, x1=8.67904, y=1.05960\nx0=1.18885, x1=4.99206, y=1.53687\nx0=-3.26020, x1=7.50108, y=0.24539\nx0=-9.93418, x1=-2.25029, y=-1.83867\nx0=-4.74104, x1=5.83433, y=5.40345\nx0=2.78338, x1=5.55776, y=1.57396\nx0=-1.14392, x1=-9.49704, y=5.44734\nx0=6.45061, x1=-8.15147, y=-0.29307\nx0=8.29325, x1=-9.08090, y=-5.11246\nx0=1.89469, x1=9.45363, y=-5.68566\nx0=7.04203, x1=-1.12802, y=1.76887\nx0=3.88517, x1=-6.06339, y=-3.96385\nx0=-8.30983, x1=4.45961, y=1.34735\nx0=-3.06306, x1=2.26803, y=0.30223\nx0=2.04906, x1=3.94589, y=-3.69474\nx0=-9.28649, x1=4.03909, y=0.51576\nx0=-4.96500, x1=-5.19001, y=2.67045\nx0=0.40295, x1=-8.03217, y=-0.41702\nx0=5.86116, x1=-5.08872, y=-0.90322\nx0=9.30534, x1=8.88824, y=-0.61446\nx0=-8.28068, x1=8.17707, y=1.73416\nx0=-4.03902, x1=9.17971, y=-4.55019\nx0=-7.18931, x1=-0.24380, y=-4.58304\nx0=3.43996, x1=1.20640, y=-0.62858\nx0=7.91344, x1=-1.18712, y=2.24200\nx0=-1.00251, x1=0.51393, y=-4.40368\nx0=2.60016, x1=-0.40961, y=2.83640\nx0=2.85779, x1=-4.20392, y=-0.81792\nx0=-8.78839, x1=-5.20376, y=-1.68244\nx0=-1.34726, x1=3.04873, y=5.82551\nx0=1.45645, x1=-3.50248, y=-5.57684\nx0=9.79229, x1=8.57667, y=1.42584\nx0=-4.16455, x1=-4.08980, y=-2.98679\nx0=5.28722, x1=6.69607, y=-4.61256\nx0=2.22186, x1=6.90065, y=3.89135\nx0=-6.58432, x1=5.57394, y=-1.35050\nx0=3.09922, x1=7.40593, y=0.11011\nx0=7.32578, x1=-5.84849, y=4.70033\nx0=-9.01126, x1=4.42535, y=0.68258\nx0=6.37382, x1=9.36514, y=-0.54211\nx0=9.20795, x1=-6.69439, y=1.18318\nx0=7.26320, x1=0.71025, y=3.77813\nx0=6.26515, x1=1.82945, y=0.02767\nx0=-3.21606, x1=-8.79947, y=-0.36195\nx0=1.11266, x1=3.92057, y=-3.82947\nx0=2.22611, x1=-1.59156, y=-0.09879\nx0=-5.60370, x1=-8.78185, y=-3.01757\nx0=-7.83175, x1=-7.24417, y=-3.43542\nx0=-4.95874, x1=7.70091, y=0.88725\nx0=3.32529, x1=3.23697, y=1.09099\nx0=-0.58976, x1=-1.49150, y=-0.26435\nx0=-6.37816, x1=-5.16486, y=-0.24874\nx0=-5.70225, x1=-0.81189, y=2.26589\nx0=-6.19047, x1=7.02943, y=0.40788\nx0=5.87224, x1=-3.47288, y=2.26652\nx0=4.82732, x1=3.78517, y=4.76805\nx0=-8.30383, x1=-0.74689, y=-3.96481\nx0=-4.07389, x1=-0.46499, y=4.30642\nx0=3.78026, x1=4.79458, y=-0.29363\nx0=5.11785, x1=-4.63346, y=0.43473\nx0=-5.89138, x1=1.92294, y=-0.79024\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.72856, x1=8.03060, y=0.31534\nx0=8.11196, x1=2.20820, y=-3.45248\nx0=-2.51308, x1=-7.53234, y=-1.11517\nx0=-4.13610, x1=1.81878, y=-1.23485\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 6 * sin(x0) * cos(x1)", "data": [[-4.587756878165559, -6.659604678668263, 5.536640011342584], [-3.7044720435821565, -5.402220203795036, 2.0376106691838185], [-7.299346268436773, 8.823447167527807, 4.205833425459889], [3.0585528335525307, 3.8405928739423363, -0.3809566845837372], [-9.745540000713465, 6.42530638039295, 1.87266603361476], [2.7798563694287175, 6.81177958417133, 1.8335848787250535], [-0.48282104763219813, -2.7137681985674362, 2.5346058674376475], [-1.3912583334594544, -1.9900738949767511, 2.403342527464056], [-1.3726346736540602, -7.849844294452366, -0.024338164882827817], [-6.75308721955147, -0.23187495238145672, -2.644084100935441], [-2.5281439880067254, -3.708787474813249, 2.913264883399841], [9.812367359364139, -9.811372801525135, 2.100382811103355], [-1.746654151530917, -8.071223228463253, 1.2732756710371145], [-6.6730283501509025, 0.5569937481820801, -1.9355940261567253], [9.75535823773366, -8.312809062007162, 0.862565005585083], [7.239687559077282, 2.932296562980941, -4.796085219337967], [5.495764916521084, -0.4417873813638291, -3.843048098023827], [2.2411269480084357, 3.217875790275663, -4.6880246389940385], [-1.3210126444401062, 7.517560118071714, -1.9191997741328974], [7.430249246592638, 5.059886894470045, 1.8625719158132252], [-3.5979631193732686, -5.945009037609412, 2.494395938312128], [-0.23319419461774693, -3.8095501404157783, 1.0885396808600234], [5.31288093547316, 8.486312038236427, 2.9257843688063945], [9.703621324185683, 8.386946750587214, 0.8390910268711378], [2.750323427705082, 9.263597108373052, -2.2585139363479034], [-6.810172405144279, 8.026381356974643, 0.5176583076804296], [8.511881300440145, 6.23626922214147, 4.742445293273103], [-0.46432993082528995, -0.8501125272309284, -1.7731097129603692], [-7.7750713701763585, 7.561140971048562, -1.7266489360283253], [-6.763819580702728, 6.007176378308465, -2.6690543270287495], [-4.424413173774422, 2.138526748397746, -3.09346193879333], [-3.7381867946833918, -2.852270337747891, -3.2308632498158123], [2.5255234142835477, -3.1332322009168845, -3.4668679458377123], [-4.769747194100036, 1.369257383027227, 1.1990889860139888], [5.8584939966227285, 3.4405652957243795, 2.3625677481798903], [7.240986815230983, 5.73305578964151, 4.183493434273897], [-4.514867711152246, -8.401936277957907, -3.064879342109336], [-1.01662757714141, 5.237148564059746, -2.556141800389537], [-6.836077428962484, -6.388431796279019, -3.1334689651538015], [0.1784425532925873, -8.4163223397621, -0.5678144662750131], [0.33377923561207545, 0.7807835624466932, 1.396356342920281], [7.278155475027198, -8.596836834283652, -3.403921436669813], [-9.880983549750258, -6.8598832316422715, 2.2157675075016687], [1.561655248553242, -2.6616938921747035, -5.32202764839916], [0.4924715730356244, -3.378791890065904, -2.7573996717579687], [-6.5266046165164955, 8.834665317981138, 1.2015619384239375], [9.595510874760738, 0.18110419113070364, -1.00275558918831], [6.750314002892946, 6.7886561237293215, 2.364059102187135], [-5.535484340579934, 2.9941101289408323, -4.035439779323157], [-9.001810757453253, -9.239835199404979, 2.42080903827931], [5.290590086214234, 6.097508000993955, -4.93831572171681], [-5.370522343032369, -0.12236287534409485, 4.711320013333049], [0.4921939413407088, 4.678119849533697, -0.09714641701942713], [-9.882243814339427, 5.624264212479982, 2.095275222749038], [-1.6951637984935015, 3.1841646485676165, 5.948263659290789], [6.154821672057274, -8.857118633949847, 0.6476059760030565], [0.8149807647415841, -7.516329491819214, 1.4464276125948694], [-1.881715051314746, -9.21773930890549, 5.590324869432288], [3.3843774386478813, 8.679040233515039, 1.0595984661568338], [1.1888470563079174, 4.992057354250694, 1.5368739572045074], [-3.260203527465193, 7.501075091789865, 0.24539416107984222], [-9.93418258262662, -2.2502916613159947, -1.8386655669883045], [-4.741043888091488, 5.834332829681108, 5.4034546950939095], [2.78337643675407, 5.557755563104092, 1.5739627776703946], [-1.1439239332218811, -9.497041370530972, 5.447336648043307], [6.450608228649205, -8.151467330669306, -0.29307364312554884], [8.293248246412372, -9.080903166346278, -5.112463189942727], [1.8946858496000516, 9.453629240560794, -5.685661180185246], [7.042030749884379, -1.1280168578627112, 1.7688683608083315], [3.8851721571758784, -6.063393820182698, -3.963852357582333], [-8.30983459993214, 4.459609653672217, 1.3473455576153357], [-3.0630635939613082, 2.2680262695994067, 0.30222858026903743], [2.0490643138483637, 3.94588944224477, -3.6947366792183947], [-9.28648684737097, 4.039086252595425, 0.5157586463695093], [-4.964997834699769, -5.1900053140732165, 2.670453226213769], [0.4029501573530787, -8.032165362476798, -0.4170164278453655], [5.861158706166043, -5.088723524083452, -0.9032246505940258], [9.305340369204597, 8.888241256947143, -0.6144649333327932], [-8.280684173561365, 8.177067183293584, 1.734156046768759], [-4.039015017344871, 9.17970733708707, -4.550185925861079], [-7.189305474981995, -0.24380065114976546, -4.583037582211461], [3.4399604384038707, 1.2063979095472348, -0.6285826909684314], [7.913440786367442, -1.1871246525453216, 2.2419972786034683], [-1.0025059999986023, 0.5139277319588835, -4.403681070412842], [2.600157281750084, -0.4096084791023493, 2.836402963398644], [2.857788241552031, -4.203920926296489, -0.8179195487844311], [-8.788393192263808, -5.203759223309272, -1.6824440425678364], [-1.347262933608743, 3.048728048634805, 5.825511903801962], [1.4564516602492734, -3.5024843987695053, -5.576836461082548], [9.792294233448814, 8.576665919200106, 1.4258416155141214], [-4.16455112982812, -4.089802078657074, -2.9867870821251548], [5.28721613559491, 6.69606826721844, -4.6125554867315035], [2.2218609509696847, 6.900654916366797, 3.8913487490260006], [-6.584324520312894, 5.573944193659733, -1.350498719626418], [3.099216228703664, 7.405934786249258, 0.11011336478525997], [7.3257814522700855, -5.848488261603945, 4.700327891744994], [-9.01126284481943, 4.425350040028015, 0.6825822222491258], [6.373821198752417, 9.365135372968645, -0.5421054632594616], [9.207952643354549, -6.694393878073159, 1.1831805225782035], [7.263203480999604, 0.7102523175104007, 3.77813164806849], [6.265154665054869, 1.829454570134562, 0.027670162545124725], [-3.2160642048380828, -8.79947485484192, -0.3619480508831737], [1.1126597747478613, 3.9205732241158486, -3.829473271018429], [2.2261105881211645, -1.5915638427019978, -0.09878685277581604], [-5.603702673446273, -8.781851423611265, -3.0175744215814158], [-7.831747603833696, -7.24417111886797, -3.435423504049228], [-4.958741453398909, 7.70090640693078, 0.8872473379130199], [3.3252860753322366, 3.2369716208363677, 1.090991228563728], [-0.5897611617485126, -1.4914954643405203, -0.2643477502077627], [-6.378155629042011, -5.164855071419298, -0.24874317216442732], [-5.702252014876366, -0.8118888106872255, 2.265889716584208], [-6.19046683916398, 7.02943356461191, 0.4078812368754814], [5.872240290024207, -3.472884747289946, 2.266520944974739], [4.827319973169946, 3.7851732528383852, 4.768048668648635], [-8.303834853371637, -0.7468853519077516, -3.964814838492758], [-4.073890178699935, -0.46498622522796573, 4.306415740675906], [3.780262744991523, 4.794575924962935, -0.29363290435308564], [5.117845406621701, -4.633458799092982, 0.4347325748997964], [-5.891379612606813, 1.922939004548521, -0.790239167901208], [9.728559865180301, 8.030597688302365, 0.3153426900533573], [8.11196433509394, 2.2081960790989204, -3.4524818951581264], [-2.5130848149512524, -7.5323392748323315, -1.1151725781961987], [-4.136104937065985, 1.8187795694789877, -1.2348460503259406]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.51844, x1=-9.86912, y=0.04376\nx0=0.25140, x1=-0.35405, y=4.40214\nx0=3.70083, x1=-0.25229, y=1.94083\nx0=9.35426, x1=-0.26120, y=1.50570\nx0=5.91888, x1=7.60917, y=2029855.68314\nx0=9.32102, x1=-7.27410, y=0.00000\nx0=5.72536, x1=0.07582, y=3.08193\nx0=5.59112, x1=4.35081, y=4826.03418\nx0=6.57008, x1=6.37302, y=438288.86312\nx0=3.85034, x1=0.31319, y=4.11847\nx0=9.03891, x1=9.62215, y=4278128539.19272\nx0=8.05154, x1=4.69972, y=48836.09131\nx0=9.29833, x1=-3.23278, y=0.00200\nx0=9.48163, x1=-8.11926, y=0.00000\nx0=9.17718, x1=-5.87916, y=0.00001\nx0=4.32238, x1=-0.80314, y=0.83328\nx0=7.56631, x1=-6.80545, y=0.00000\nx0=4.66133, x1=-6.11917, y=0.00022\nx0=6.16098, x1=-6.84249, y=0.00001\nx0=7.09773, x1=5.25324, y=79890.89957\nx0=1.11266, x1=-5.37642, y=1.52089\nx0=3.90289, x1=3.25628, y=227.55176\nx0=1.39741, x1=2.93437, y=7.20768\nx0=0.22030, x1=-9.62924, y=5722054.38019\nx0=4.63698, x1=7.32748, y=205677.11069\nx0=7.11857, x1=7.18681, y=3608678.05074\nx0=5.75272, x1=-0.66636, y=0.84143\nx0=4.10998, x1=-7.97539, y=0.00003\nx0=9.26955, x1=-0.84942, y=0.40731\nx0=6.83045, x1=-6.81065, y=0.00001\nx0=1.69781, x1=5.50323, y=49.71675\nx0=2.20248, x1=8.44384, y=2122.55400\nx0=2.48282, x1=8.96762, y=9399.13237\nx0=6.77422, x1=-8.12565, y=0.00000\nx0=0.08033, x1=-6.57632, y=42965655.97835\nx0=1.31951, x1=5.25038, y=11.57625\nx0=9.09680, x1=-5.72063, y=0.00001\nx0=4.47533, x1=-7.83709, y=0.00002\nx0=2.47088, x1=9.05673, y=9756.90898\nx0=8.38665, x1=6.07661, y=1105741.48677\nx0=5.44762, x1=-2.16218, y=0.06911\nx0=2.35703, x1=-8.31052, y=0.00217\nx0=6.22682, x1=3.04992, y=714.18308\nx0=1.90299, x1=-6.06284, y=0.05460\nx0=3.88036, x1=8.12050, y=163416.09166\nx0=9.46544, x1=-9.03379, y=0.00000\nx0=4.65682, x1=8.16885, y=774255.38156\nx0=8.73526, x1=6.01067, y=1227616.20350\nx0=6.56786, x1=0.90784, y=14.90920\nx0=3.87806, x1=6.75106, y=25417.79864\nx0=9.66084, x1=-8.00300, y=0.00000\nx0=6.69518, x1=-8.15610, y=0.00000\nx0=9.51313, x1=-5.15627, y=0.00002\nx0=5.16707, x1=0.57383, y=6.92857\nx0=9.29521, x1=4.96087, y=171700.36886\nx0=9.98765, x1=8.97342, y=2511692285.08089\nx0=8.68963, x1=-0.10426, y=2.15507\nx0=5.79365, x1=-1.29050, y=0.27975\nx0=2.46265, x1=1.81207, y=13.82327\nx0=1.78793, x1=-0.13345, y=2.49854\nx0=7.69716, x1=8.03777, y=35932068.52710\nx0=8.91929, x1=-8.13989, y=0.00000\nx0=6.06947, x1=5.59511, y=65040.40051\nx0=7.63346, x1=7.09816, y=4978017.49512\nx0=9.50162, x1=-8.01189, y=0.00000\nx0=9.66211, x1=0.99543, y=25.81879\nx0=8.99377, x1=-6.06824, y=0.00000\nx0=6.81476, x1=-4.33203, y=0.00066\nx0=6.72806, x1=2.67910, y=446.03236\nx0=2.22109, x1=-2.06960, y=0.51774\nx0=8.62458, x1=1.60578, y=85.89228\nx0=7.27561, x1=4.20898, y=11453.87420\nx0=0.92485, x1=7.25543, y=1.53182\nx0=3.70995, x1=3.53879, y=279.40849\nx0=7.41075, x1=3.47290, y=2833.38425\nx0=3.10309, x1=7.08310, y=8218.54502\nx0=1.35310, x1=2.50317, y=5.75574\nx0=9.47538, x1=-7.08011, y=0.00000\nx0=2.54828, x1=8.34765, y=6646.24437\nx0=4.90452, x1=2.33212, y=110.13265\nx0=0.06483, x1=7.22354, y=0.00000\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.64108, x1=4.14292, y=0.42797\nx0=2.03573, x1=-9.79746, y=0.00255\nx0=1.75370, x1=8.01860, y=244.08845\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 2.7 * x0 ** x1", "data": [[1.5184413772644678, -9.869116811003815, 0.04376484753336983], [0.2513995005451477, -0.3540489699663709, 4.402142805553501], [3.7008300236834994, -0.2522892958712841, 1.940832136176594], [9.354264079052307, -0.2611970491528446, 1.5057016110459993], [5.918882532509324, 7.609167514125758, 2029855.6831387198], [9.32102285978582, -7.274100076014555, 2.3954588428735137e-07], [5.725359772476647, 0.07582236843306767, 3.081925710703455], [5.591120036681492, 4.350811745211248, 4826.034182268654], [6.570083554341593, 6.373021248482363, 438288.8631154026], [3.8503359201079377, 0.3131893101826826, 4.118467786030441], [9.038910949918407, 9.622147341549535, 4278128539.1927238], [8.051540349577852, 4.699719561325894, 48836.09130762713], [9.298333549900075, -3.232782020970384, 0.0019985779864390915], [9.481628785297541, -8.119258685695723, 3.160810078425584e-08], [9.177177645945129, -5.879158090184971, 5.908055189482786e-06], [4.322382034667802, -0.8031354873854966, 0.833281888889619], [7.566308411199781, -6.805454530384603, 2.819411032734302e-06], [4.661327099452631, -6.119166220735877, 0.00021910007460444156], [6.160984311232561, -6.8424936956854765, 1.0670577230008044e-05], [7.097733888374847, 5.253236978645475, 79890.89956986124], [1.112660447172205, -5.376418892626409, 1.5208932646786764], [3.9028889974255883, 3.256275571855074, 227.55176033621004], [1.397407944902957, 2.934369767969452, 7.207684905333704], [0.220304433612025, -9.629241971249328, 5722054.380189337], [4.63697947196888, 7.32747593420526, 205677.11068785735], [7.118569906570038, 7.186809534695996, 3608678.0507361204], [5.7527208472026885, -0.6663562721507574, 0.8414289002703597], [4.109983937650419, -7.975387681506019, 3.433608662958566e-05], [9.269554447212517, -0.8494166910079031, 0.4073125836324078], [6.830454940393739, -6.810652503766812, 5.6003774414226495e-06], [1.6978144048838075, 5.503230914623112, 49.71674607971062], [2.202481362082933, 8.44383672725482, 2122.5539970523246], [2.4828239136039336, 8.967617653409398, 9399.132365946007], [6.774219942669216, -8.125654366582605, 4.787274403467684e-07], [0.08033323232305634, -6.576318501531513, 42965655.97834715], [1.3195050520612543, 5.25038362709177, 11.576252960500637], [9.096801572833762, -5.720631896109499, 8.82905776970613e-06], [4.475327195866338, -7.837092068327038, 2.1418543993489656e-05], [2.470877198864594, 9.05673403984818, 9756.90897745482], [8.386648033419025, 6.07661349579562, 1105741.4867719284], [5.4476248552512665, -2.1621792540894447, 0.06911174289284779], [2.3570324469325517, -8.310516402029426, 0.002171769158382498], [6.2268197984574805, 3.0499163801298224, 714.1830774897409], [1.9029910152811897, -6.062843556991455, 0.054598729718943806], [3.8803569418104047, 8.120497628972444, 163416.09166065953], [9.465444615518525, -9.03378931372103, 4.103093947272113e-09], [4.656818826875224, 8.168848273447981, 774255.381564819], [8.735256621029311, 6.010671517431042, 1227616.2035016017], [6.567863541819545, 0.9078404113772915, 14.909202534049294], [3.87805994229943, 6.751063815164333, 25417.798641520658], [9.66083914827842, -8.00300405308648, 3.534157642438534e-08], [6.6951820953914805, -8.156104563858664, 4.970033755300068e-07], [9.513133415680098, -5.156274149092797, 2.437020264681104e-05], [5.167072627427212, 0.573828327507762, 6.92857145976714], [9.295213565627481, 4.960868544460311, 171700.3688632492], [9.987654260363357, 8.973416904746433, 2511692285.080895], [8.689629926051463, -0.10426192781084964, 2.1550714841677245], [5.79364512748273, -1.2904997736927388, 0.27975285180925386], [2.462648229079578, 1.812065924247488, 13.823266490715474], [1.787926395005277, -0.1334521174212675, 2.4985449724902926], [7.697158684299321, 8.037768007512554, 35932068.52710217], [8.9192879509955, -8.139885061600843, 4.963468706622256e-08], [6.069473262837505, 5.595114388121258, 65040.400513976354], [7.633455968664563, 7.098155816470115, 4978017.495123036], [9.501624510871448, -8.011886585729847, 3.956928252689315e-08], [9.662114561028513, 0.9954317292737809, 25.818789112978525], [8.993769395630512, -6.06823788040195, 4.3915548768816095e-06], [6.814756697448171, -4.332034810204936, 0.0006619540035400373], [6.728055750486156, 2.6791043802146817, 446.03235998930813], [2.221089849999201, -2.0695951034485986, 0.5177405774229551], [8.624582405642972, 1.6057809352440806, 85.89227920452026], [7.2756123478700445, 4.208976450025588, 11453.874197822797], [0.9248536028756522, 7.255433598807002, 1.531823104870517], [3.709954194398211, 3.5387901866788507, 279.40848650310147], [7.4107537511745, 3.47289614051242, 2833.3842482326827], [3.103090331066179, 7.083104334203501, 8218.54502016837], [1.3530952348740914, 2.503172140460954, 5.755741326399802], [9.475376190909117, -7.080111633444841, 3.288151333031992e-07], [2.548282310222321, 8.347650661781156, 6646.244371783615], [4.9045158267167, 2.3321189074887734, 110.13264775757186], [0.06482782409662313, 7.223543005304215, 7.048090336022959e-09], [0.641077129651741, 4.142920426360202, 0.427965179143172], [2.03572923717733, -9.797460179851925, 0.0025508899337114807], [1.7537021214900133, 8.018596988260349, 244.08844836374956]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.07284, y=266.91484\nx0=8.82768, y=774.67762\nx0=3.45683, y=56.71442\nx0=-7.50663, y=-374.15117\nx0=-0.48759, y=-0.36577\nx0=7.74480, y=532.27398\nx0=-9.75780, y=-843.62985\nx0=3.62535, y=64.41715\nx0=-8.50526, y=-551.43226\nx0=-5.35071, y=-129.91180\nx0=8.52950, y=701.82379\nx0=6.75357, y=360.40014\nx0=5.27206, y=179.60115\nx0=2.34166, y=20.66525\nx0=2.32891, y=20.38432\nx0=4.82271, y=140.25003\nx0=7.47481, y=480.98526\nx0=2.23898, y=18.47610\nx0=4.41297, y=109.82647\nx0=-2.26552, y=-8.76091\nx0=-8.29651, y=-510.52972\nx0=-9.47131, y=-769.39692\nx0=-0.79945, y=-0.67128\nx0=8.75347, y=756.09510\nx0=-0.10910, y=-0.09850\nx0=5.83532, y=238.58398\nx0=-5.90520, y=-176.95653\nx0=7.38665, y=464.98470\nx0=-6.67629, y=-259.68492\nx0=-9.63082, y=-810.16179\nx0=8.95142, y=806.33676\nx0=-7.26068, y=-337.30773\nx0=6.33930, y=301.28202\nx0=-9.25967, y=-717.45707\nx0=3.11386, y=43.00237\nx0=3.38983, y=53.83319\nx0=9.82374, y=1054.37867\nx0=-9.41150, y=-754.47207\nx0=-1.07844, y=-1.16966\nx0=9.25528, y=887.72404\nx0=-9.78099, y=-849.83997\nx0=6.13001, y=274.05501\nx0=1.43727, y=6.47201\nx0=9.73840, y=1028.13043\nx0=8.13275, y=612.18683\nx0=-9.36074, y=-741.95746\nx0=-5.59372, y=-149.33011\nx0=-7.72395, y=-408.87072\nx0=-7.47016, y=-368.52582\nx0=-6.41574, y=-229.33745\nx0=-8.02101, y=-459.72955\nx0=-7.05632, y=-308.61054\nx0=-4.18559, y=-59.99463\nx0=3.03425, y=40.17639\nx0=-6.38257, y=-225.65304\nx0=7.78591, y=540.39173\nx0=-1.60766, y=-3.17821\nx0=-8.93989, y=-643.50976\nx0=4.92347, y=148.51163\nx0=3.80629, y=73.43896\nx0=9.35300, y=915.01897\nx0=2.37464, y=21.40390\nx0=9.50741, y=959.28130\nx0=5.03164, y=157.73733\nx0=3.72054, y=69.06432\nx0=5.15599, y=168.80841\nx0=-6.52519, y=-241.77750\nx0=-8.33527, y=-517.96525\nx0=9.89728, y=1077.35301\nx0=-3.24770, y=-26.95542\nx0=-0.11051, y=-0.09965\nx0=-8.63278, y=-577.46493\nx0=-8.84898, y=-623.45793\nx0=4.31290, y=103.13845\nx0=8.60622, y=720.11043\nx0=-0.42892, y=-0.32386\nx0=-8.59817, y=-570.32046\nx0=3.17765, y=45.36112\nx0=-9.89653, y=-881.23463\nx0=-9.36276, y=-742.45182\nx0=-9.67245, y=-821.03547\nx0=-4.64361, y=-83.21138\nx0=-6.93389, y=-292.22833\nx0=5.40756, y=192.77587\nx0=1.52071, y=7.34995\nx0=-8.04278, y=-463.61379\nx0=7.23151, y=437.69556\nx0=0.48551, y=0.83568\nx0=-8.64368, y=-579.72756\nx0=-7.47405, y=-369.12367\nx0=7.29479, y=448.69411\nx0=-2.69245, y=-14.96154\nx0=-0.06013, y=-0.05673\nx0=9.99146, y=1107.26022\nx0=-7.06531, y=-309.83779\nx0=-0.11196, y=-0.10083\nx0=-5.73819, y=-161.75196\nx0=9.45600, y=944.39000\nx0=3.01014, y=39.34591\nx0=-1.26220, y=-1.67994\nx0=7.19546, y=431.51300\nx0=-1.80575, y=-4.43305\nx0=1.53183, y=7.47276\nx0=-7.48420, y=-370.68475\nx0=5.17625, y=170.66024\nx0=-7.94165, y=-445.74991\nx0=9.85026, y=1062.62433\nx0=-6.18827, y=-204.87185\nx0=8.09796, y=604.71388\nx0=-2.68325, y=-14.80239\nx0=0.40922, y=0.64522\nx0=-5.89649, y=-176.14048\nx0=-4.41026, y=-70.74095\nx0=1.61312, y=8.41281\nx0=-4.65458, y=-83.83134\nx0=0.55144, y=1.02320\nx0=-6.05159, y=-191.04953\nx0=3.02627, y=39.90001\nx0=-7.01725, y=-303.31737\nx0=6.42513, y=312.95218\nx0=-5.89792, y=-176.27464\nx0=-3.70870, y=-40.96524\nx0=0.95174, y=2.71966\nx0=-9.49121, y=-774.40424\nx0=3.06651, y=41.30587\nx0=4.81053, y=139.27326\nx0=-8.11430, y=-476.53357\nx0=7.39999, y=467.38306\nx0=-7.85301, y=-430.47603\nx0=3.51873, y=59.46727\nx0=-7.63763, y=-394.83242\nx0=-2.55260, y=-12.66900\nx0=4.32115, y=103.67915\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.85347, y=75.92352\nx0=1.35374, y=5.66722\nx0=4.25846, y=99.61818\nx0=8.61469, y=722.14935\nx0=-7.61507, y=-391.21767\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 + x0**2 + x0", "data": [[6.072840057216723, 266.9148411935879], [8.827676576838947, 774.6776160661013], [3.4568283295552646, 56.71442090551872], [-7.506625070919249, -374.1511736841792], [-0.48758813863434725, -0.3657662190263944], [7.744796044401582, 532.2739785602885], [-9.75780409076144, -843.6298494635116], [3.6253515082895156, 64.41714915153486], [-8.505263165133234, -551.4322592185181], [-5.350707820237699, -129.91179543850237], [8.529502449972128, 701.8237912654193], [6.753574975897177, 360.4001382987633], [5.272055640267816, 179.60114940545174], [2.341661279192337, 20.665251705419447], [2.3289099761138026, 20.384324064816735], [4.822705445533691, 140.25002909720496], [7.474805723034802, 480.9852580009795], [2.238980732173655, 18.476103596877575], [4.412965308387566, 109.82647432175274], [-2.265520602546472, -8.760910893350502], [-8.296506130286742, -510.52971802153894], [-9.471312821884714, -769.3969233633042], [-0.7994548305628602, -0.6712807922745471], [8.753466721879896, 756.0950995731065], [-0.10910163049634392, -0.09849711951371785], [5.835315260452488, 238.58398029483897], [-5.905202141296277, -176.9565285703291], [7.386653537724676, 464.9846992669625], [-6.6762918131114475, -259.6849223554813], [-9.630816784811236, -810.1617893904379], [8.951415185305649, 806.3367574245204], [-7.260678702470451, -337.30772784994457], [6.339302164013976, 301.2820175441326], [-9.259674161594397, -717.4570679482772], [3.113860486858327, 43.00237476917484], [3.3898312375698243, 53.83318804224702], [9.823741651659049, 1054.3786715296583], [-9.411503029190387, -754.472069675587], [-1.078437870645356, -1.1696633293574237], [9.25527762367594, 887.7240396187085], [-9.780994786783445, -849.8399660961019], [6.130013595161753, 274.0550098675297], [1.4372660133788209, 6.472008292813845], [9.738401515435875, 1028.1304310660564], [8.132746188900974, 612.1868314406906], [-9.360739219914109, -741.957460104247], [-5.593722970650939, -149.3301050682186], [-7.723949554542527, -408.87072356177777], [-7.4701563445687675, -368.5258165829952], [-6.415744800334487, -229.33744808129472], [-8.021013465300417, -459.7295486486503], [-7.056320311547188, -308.61053994393933], [-4.1855937152739076, -59.99463040543243], [3.034253560865533, 40.176394323671104], [-6.382566746694216, -225.6530402379475], [7.785912490954637, 540.3917347761405], [-1.607662652917055, -3.178214909656668], [-8.939893999149167, -643.509757675674], [4.923469343937088, 148.5116264041067], [3.8062879289403106, 73.43895979101782], [9.352999739327174, 915.0189654302947], [2.374637664283739, 21.40389561159359], [9.50741077383158, 959.2813030258076], [5.0316428002250735, 157.7373327711392], [3.720541916478151, 69.06432311727787], [5.155991601877883, 168.80840764210367], [-6.525191642519617, -241.77749741499477], [-8.335267089647669, -517.9652527289759], [9.897280377444613, 1077.35300827862], [-3.2476991929835393, -26.95541892406473], [-0.11051401369305935, -0.0996504124927006], [-8.6327802571043, -577.4649272274268], [-8.848975021714306, -623.4579323932819], [4.312895918295897, 103.13845118361682], [8.606220401456937, 720.1104312054367], [-0.4289202991588432, -0.32385726863561576], [-8.598173768900473, -570.3204634923353], [3.177645192882707, 45.36112079760885], [-9.896531191756072, -881.2346252017838], [-9.36275535012652, -742.4518221741325], [-9.672452972148724, -821.0354682258225], [-4.64361344008659, -83.2113812181127], [-6.9338895856742795, -292.22832727669015], [5.407563268987616, 192.77586566998227], [1.5207053400916344, 7.349949193690074], [-8.042777522514701, -463.61378784234086], [7.231506548273821, 437.69556468073444], [0.4855129711056261, 0.835682315105146], [-8.643680277576218, -579.7275604052878], [-7.474049787301096, -369.1236655007111], [7.294793894568468, 448.69410520974833], [-2.6924519822822894, -14.961540205699034], [-0.06012895902068749, -0.056730863060821264], [9.991457829607214, 1107.2602247095303], [-7.06531482059656, -309.83778511043937], [-0.11195944236133215, -0.10082792791504044], [-5.738192489420375, -161.75196029052213], [9.456003379778895, 944.3900007327729], [3.0101434953498245, 39.34590879054244], [-1.2622046646661111, -1.679938809613826], [7.195462984975428, 431.51299850842855], [-1.8057453267101682, -4.433052154450246], [1.5318282478121343, 7.472757612657891], [-7.484196347331922, -370.6847505444763], [5.176252608435409, 170.66023932123474], [-7.941648549371898, -445.74990706963], [9.850257240639493, 1062.6243262926675], [-6.188273968725002, -204.8718492142217], [8.097957192905284, 604.713883567432], [-2.6832516422261925, -14.802393094817461], [0.409223726423793, 0.6452180506585223], [-5.8964891129269725, -176.14048144975436], [-4.410255859390859, -70.7409489172634], [1.6131153744781521, 8.412810580492655], [-4.654577669688784, -83.8313437940698], [0.5514366455752384, 1.0232011840015434], [-6.05158915513174, -191.04952984503018], [3.0262675122197535, 39.90001336156959], [-7.017249321740142, -303.3173650275366], [6.425134667986825, 312.9521836803074], [-5.897923355486392, -176.27463578319112], [-3.7086955105744135, -40.96523768933094], [0.9517435584942486, 2.7196637135423685], [-9.491205205212736, -774.4042420186779], [3.0665100267566476, 41.30587095898525], [4.810531232946646, 139.27325902425028], [-8.114302688105768, -476.53356657497545], [7.399994769171844, 467.38305803310044], [-7.853007015957565, -430.47602531551786], [3.5187314256652353, 59.46727283328114], [-7.637625729107002, -394.83241641461717], [-2.5526012885721405, -12.668999369847267], [4.3211452678272515, 103.67914703272679], [3.853465413031735, 75.92352310302911], [1.3537385080457671, 5.667218405794774], [4.258464290385838, 99.61818020827684], [8.614693260246757, 722.1493469950282], [-7.615066147969802, -391.2176745950425]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=9.09604, y=45.91696\nx0=6.31236, y=23.07910\nx0=6.18953, y=22.24988\nx0=0.20484, y=0.12340\nx0=2.25709, y=3.67576\nx0=5.93048, y=20.55055\nx0=-5.86993, y=14.29306\nx0=-9.65863, y=41.81524\nx0=1.06626, y=1.10159\nx0=-3.03618, y=3.09111\nx0=-0.28478, y=-0.10184\nx0=5.17433, y=15.97399\nx0=1.44331, y=1.76323\nx0=8.97112, y=44.72608\nx0=1.53158, y=1.93866\nx0=3.56484, y=8.13648\nx0=5.94544, y=20.64683\nx0=-8.99001, y=35.91517\nx0=-3.63021, y=4.77411\nx0=-1.92528, y=0.89071\nx0=1.38365, y=1.64907\nx0=8.97404, y=44.75369\nx0=-6.45677, y=17.61654\nx0=-9.47124, y=40.11654\nx0=-6.69386, y=19.05694\nx0=-4.83856, y=9.28657\nx0=-9.30479, y=38.63720\nx0=-8.28569, y=30.18350\nx0=-5.39752, y=11.86786\nx0=-5.92735, y=14.60305\nx0=3.60619, y=8.30539\nx0=6.79911, y=26.51353\nx0=-2.07292, y=1.11204\nx0=1.83735, y=2.60659\nx0=2.87425, y=5.56777\nx0=9.97930, y=54.78290\nx0=-8.34735, y=30.66542\nx0=2.57089, y=4.59018\nx0=-6.78554, y=19.62900\nx0=9.68448, y=51.73680\nx0=2.63709, y=4.79567\nx0=3.29689, y=7.08318\nx0=3.55986, y=8.11625\nx0=9.16461, y=46.57738\nx0=-9.01431, y=36.12170\nx0=7.33898, y=30.59983\nx0=0.23850, y=0.14769\nx0=-8.78735, y=34.21511\nx0=3.78739, y=9.06586\nx0=-1.82369, y=0.75108\nx0=2.76136, y=5.19322\nx0=-2.38719, y=1.65574\nx0=-2.40907, y=1.69727\nx0=-6.33490, y=16.89800\nx0=-3.44796, y=4.22023\nx0=-9.38695, y=39.36398\nx0=3.53311, y=8.00798\nx0=1.60870, y=2.09830\nx0=8.88369, y=43.90183\nx0=6.54012, y=24.65666\nx0=1.93493, y=2.83944\nx0=-0.53747, y=-0.12430\nx0=-0.60793, y=-0.11918\nx0=6.62392, y=25.25009\nx0=-4.57065, y=8.16009\nx0=7.07673, y=28.57845\nx0=7.73271, y=33.76374\nx0=-5.06063, y=10.27469\nx0=-7.35165, y=23.34752\nx0=-4.22514, y=6.81332\nx0=-0.86514, y=-0.05833\nx0=-7.48996, y=24.30477\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=4.92706, y=14.60147\nx0=6.26607, y=22.76485\nx0=9.07363, y=45.70224\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * (x0 + 1) / 2", "data": [[9.096036268204685, 45.916956030349844], [6.312356016542367, 23.079097248060492], [6.189525663979534, 22.249876804520415], [0.20484245144224467, 0.12340144067755651], [2.2570867225785634, 3.675763597909502], [5.930482599945808, 20.5505532341029], [-5.8699268409359355, 14.293057138502098], [-9.658628781057864, 41.815240574610726], [1.0662647875479223, 1.101592692356269], [-3.0361819083766317, 3.0911093361884667], [-0.28477717026588856, -0.10183956678062084], [5.174326685052179, 15.973991664347626], [1.4433109711913552, 1.763228765376344], [8.971122183112922, 44.72607770372684], [1.5315799582307044, 1.9386585633423352], [3.564844713130654, 8.136481270933114], [5.945437768077543, 20.64683401108021], [-8.990014295770782, 35.91517137119613], [-3.6302115096856564, 4.774112047684278], [-1.9252807039104436, 0.8907125424697248], [1.3836490419383836, 1.6490668565976951], [8.974037180786862, 44.75369025146593], [-6.456766939101519, 17.61653618338644], [-9.47123666688777, 40.11654366665579], [-6.693857537731834, 19.056935598858725], [-4.838564289435386, 9.286570046781987], [-9.304793993209973, 38.637198631433215], [-8.285691949196565, 30.183499563892102], [-5.397521277792778, 11.867857333216504], [-5.927347093156527, 14.603048234797303], [3.6061885608365944, 8.305392248572652], [6.799113640811761, 26.513529970742162], [-2.0729227591235144, 1.1120430030843647], [1.837345736675184, 2.606592546376829], [2.8742477350831663, 5.567773888856939], [9.979303843698016, 54.782904524272006], [-8.347346076215782, 30.665420219949617], [2.570889505497913, 4.590181177488608], [-6.785539250750203, 19.62900183636071], [9.684478197254787, 51.73679807517906], [2.6370916126044968, 4.795671892936741], [3.2968876478063276, 7.083177905032134], [3.5598637153990076, 8.116246693806717], [9.164613610733298, 46.57737812238565], [-9.014305859901233, 36.12170213797424], [7.338982792670951, 30.59982561189563], [0.23850107140393462, 0.14769191623237968], [-8.787353543345116, 34.21511437619743], [3.7873914353148113, 9.065862659805399], [-1.8236930743329296, 0.7510816775184813], [2.7613557646579032, 5.193220711833669], [-2.387188127731184, 1.6557395147247658], [-2.409066250012984, 1.6972669734693182], [-6.334895253407411, 16.898001309118168], [-3.4479599001061345, 4.220233786316886], [-9.386954034734298, 39.36397600774011], [3.5331075812708654, 8.007978381052265], [1.608698217687337, 2.098304086638876], [8.883690667853685, 43.901825274982166], [6.54012269618487, 24.656663788668663], [1.9349297069309639, 2.839441338847455], [-0.5374683370408722, -0.1242980618596958], [-0.6079348643103728, -0.1191750325331507], [6.623915929124479, 25.250089082616743], [-4.570649678722541, 8.160094403441962], [7.07673390470233, 28.578448331332908], [7.73270798664166, 33.763740396656694], [-5.060632730760533, 10.274685452442139], [-7.351645225387808, 23.347521147289775], [-4.225136304198777, 6.813320242429863], [-0.8651444307140537, -0.05833477235925483], [-7.489959386919891, 24.304766115394745], [4.927057019635637, 14.60147394718822], [6.266070213849993, 22.764853069374045], [9.073634338918321, 45.70223722765802]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-8.34803, y=4336.20816\nx0=-3.19162, y=78.24684\nx0=-8.79848, y=5380.31128\nx0=-8.65223, y=5022.66522\nx0=1.51470, y=12.54806\nx0=7.94476, y=4556.57559\nx0=7.62123, y=3882.01577\nx0=-2.55937, y=30.13333\nx0=4.25892, y=428.65046\nx0=9.48857, y=9059.75780\nx0=6.99126, y=2786.60947\nx0=1.84425, y=23.08687\nx0=-4.31672, y=281.10736\nx0=-6.93565, y=2021.46193\nx0=-6.37556, y=1427.36325\nx0=0.13053, y=0.15008\nx0=-3.22313, y=81.60437\nx0=-0.25903, y=-0.20481\nx0=8.14047, y=5005.21475\nx0=-2.94607, y=55.49381\nx0=4.04343, y=353.79949\nx0=3.46830, y=201.91770\nx0=1.05736, y=4.60748\nx0=6.18384, y=1743.18189\nx0=-5.33045, y=678.96386\nx0=-5.64552, y=862.10911\nx0=-3.09917, y=68.99157\nx0=2.12013, y=36.34956\nx0=3.40533, y=188.96427\nx0=4.33038, y=455.93205\nx0=9.89306, y=10655.08351\nx0=-5.23862, y=631.56472\nx0=2.34876, y=51.25619\nx0=-9.46779, y=7266.63742\nx0=9.63250, y=9605.24582\nx0=3.91610, y=314.49680\nx0=8.24578, y=5259.92284\nx0=-3.31322, y=91.79759\nx0=-1.46552, y=2.14751\nx0=-7.63999, y=3011.77307\nx0=4.98048, y=768.62449\nx0=-2.53812, y=29.05307\nx0=1.58437, y=14.37284\nx0=-5.05873, y=545.96261\nx0=9.42191, y=8815.13743\nx0=5.05651, y=813.64857\nx0=7.17743, y=3082.28862\nx0=0.99222, y=3.92278\nx0=-5.45984, y=750.21980\nx0=-7.22551, y=2393.43040\nx0=-8.38359, y=4412.58695\nx0=3.67518, y=249.25979\nx0=-5.39655, y=714.69611\nx0=1.08778, y=4.95834\nx0=-3.63816, y=136.64004\nx0=-6.09076, y=1181.26744\nx0=5.99792, y=1551.95613\nx0=7.12029, y=2989.14453\nx0=-0.89244, y=-0.17244\nx0=-7.22785, y=2396.61994\nx0=-4.57590, y=358.98312\nx0=-9.06747, y=6087.59768\nx0=-5.01270, y=525.53447\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=7.50603, y=3660.99201\nx0=3.08081, y=131.90027\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**4 + x0**3 + x0**2 + x0", "data": [[-8.348028347338241, 4336.208164801637], [-3.1916174947081233, 78.24683923132149], [-8.798481643431055, 5380.311282435161], [-8.65222571633701, 5022.665224815059], [1.5146982217329263, 12.548058868008251], [7.944764419349113, 4556.575589023491], [7.621227166743822, 3882.015772564943], [-2.559365100481692, 30.133329576385762], [4.258924321943576, 428.65046287582663], [9.488574914742628, 9059.757802525079], [6.991255099930225, 2786.609469460634], [1.844250808456934, 23.086866976825014], [-4.316718018828849, 281.1073632071613], [-6.9356498263349, 2021.4619263350824], [-6.375562681102586, 1427.3632475006718], [0.13053048009449242, 0.1500829920394868], [-3.2231328506403507, 81.60436778478878], [-0.25903110328421697, -0.2048122073838858], [8.14047496485173, 5005.214747063982], [-2.946066561914882, 55.493812603326255], [4.043426621060473, 353.79948818225995], [3.4683018227190914, 201.91769825744814], [1.057362316064939, 4.607482075606814], [6.183840641374779, 1743.1818919580355], [-5.3304504079886, 678.9638600011701], [-5.64551747502245, 862.1091066219013], [-3.099167135691328, 68.99156737375326], [2.1201301658759135, 36.34955801185408], [3.405329981197598, 188.96426674158008], [4.330381806699791, 455.9320547205057], [9.8930612040073, 10655.083509414095], [-5.238616970902936, 631.5647246669], [2.348756331674533, 51.25619085857076], [-9.467787138344653, 7266.637417627522], [9.632502463934646, 9605.245818264537], [3.9161007508439027, 314.49680496414885], [8.245778776505155, 5259.9228399687445], [-3.3132209872799256, 91.79759197990532], [-1.4655235042028387, 2.147513463465025], [-7.639985833914347, 3011.7730694313423], [4.980480200645701, 768.624491282488], [-2.538115886942447, 29.053071538142998], [1.5843651633291316, 14.372841276153189], [-5.058731859145842, 545.9626106605065], [9.421910219386621, 8815.137425249404], [5.056509678881113, 813.6485666452751], [7.1774299398118515, 3082.2886224076697], [0.9922181221628517, 3.9227844452623564], [-5.459839113814193, 750.2198049869941], [-7.225511895198862, 2393.43040177032], [-8.383590325939064, 4412.586949925817], [3.6751781729933057, 249.25978639051425], [-5.396545669232598, 714.696106925613], [1.087783980829549, 4.958341792814527], [-3.6381614495155112, 136.64004289337126], [-6.090757529006117, 1181.26743543645], [5.997923979295599, 1551.9561322000618], [7.120287866066647, 2989.1445273559943], [-0.892439702777386, -0.17244304292756407], [-7.227846112439198, 2396.619943375231], [-4.575895127041727, 358.98311843886796], [-9.067469490079493, 6087.597679348955], [-5.012701592686108, 525.5344711278395], [7.506030910287112, 3660.9920088346707], [3.080812673771657, 131.90026728387954]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-8.86622, x1=-2.63094, y=34.98972\nx0=-5.99512, x1=5.68375, y=-51.11214\nx0=9.02674, x1=-1.03896, y=-14.06768\nx0=-3.31499, x1=-5.88612, y=29.26863\nx0=-9.44602, x1=8.71040, y=-123.41792\nx0=-3.63380, x1=4.54823, y=-24.79106\nx0=9.40434, x1=1.35261, y=19.08063\nx0=-4.64916, x1=-3.27231, y=22.82021\nx0=-4.16572, x1=7.19454, y=-44.95567\nx0=-1.77968, x1=1.41087, y=-3.76634\nx0=0.48944, x1=-4.17554, y=-3.06554\nx0=0.85043, x1=-0.68017, y=-0.86765\nx0=5.15957, x1=-3.80051, y=-29.41353\nx0=-0.41351, x1=-5.51059, y=3.41803\nx0=-2.77406, x1=-8.62898, y=35.90594\nx0=8.51569, x1=-6.71653, y=-85.79378\nx0=7.34041, x1=6.99746, y=77.04628\nx0=-6.38215, x1=-0.74230, y=7.10621\nx0=-4.28667, x1=4.52433, y=-29.09144\nx0=3.56590, x1=1.08244, y=5.78981\nx0=2.81080, x1=0.66708, y=2.81255\nx0=4.00949, x1=3.19309, y=19.20399\nx0=-7.28793, x1=5.11903, y=-55.96076\nx0=-9.51414, x1=9.08251, y=-129.61835\nx0=3.56847, x1=-3.80307, y=-20.35670\nx0=-2.89648, x1=-8.94557, y=38.86598\nx0=2.72559, x1=2.64154, y=10.79961\nx0=1.32204, x1=8.02456, y=15.91317\nx0=-1.88909, x1=-8.09966, y=22.95150\nx0=7.96470, x1=4.82640, y=57.66123\nx0=3.76312, x1=0.73035, y=4.12257\nx0=5.64248, x1=9.89914, y=83.78345\nx0=-9.83591, x1=-8.21528, y=121.20712\nx0=2.46090, x1=-8.45689, y=-31.21733\nx0=-8.25964, x1=-3.92852, y=48.67229\nx0=-7.05026, x1=8.46326, y=-89.50227\nx0=4.72851, x1=-3.83750, y=-27.21847\nx0=-5.64345, x1=0.73292, y=-6.20426\nx0=-9.91617, x1=-6.17311, y=91.82040\nx0=-6.51914, x1=8.76884, y=-85.74799\nx0=-1.79918, x1=-6.63942, y=17.91828\nx0=-4.90206, x1=-2.67819, y=19.69295\nx0=2.53430, x1=-5.25320, y=-19.96979\nx0=-3.81083, x1=-3.13501, y=17.92050\nx0=0.76139, x1=-2.29252, y=-2.61824\nx0=1.90223, x1=2.58770, y=7.38357\nx0=3.92823, x1=2.84101, y=16.74022\nx0=-4.64174, x1=3.94059, y=-27.43678\nx0=-0.42536, x1=-9.39274, y=5.99288\nx0=3.63330, x1=5.93429, y=32.34154\nx0=-7.85329, x1=3.50360, y=-41.27217\nx0=9.97715, x1=-6.32889, y=-94.71644\nx0=3.33446, x1=-8.56388, y=-42.83394\nx0=-3.34233, x1=-2.85869, y=14.33202\nx0=-4.81604, x1=-6.38173, y=46.10203\nx0=-5.04862, x1=-1.94688, y=14.74355\nx0=-6.08925, x1=-6.83915, y=62.46789\nx0=-3.44812, x1=-0.80952, y=4.18700\nx0=-3.31189, x1=1.29436, y=-6.43017\nx0=8.32096, x1=-1.44379, y=-18.02058\nx0=-9.54125, x1=-7.11196, y=101.78547\nx0=-0.24411, x1=9.57066, y=-3.50437\nx0=2.16255, x1=-5.95523, y=-19.31768\nx0=3.39388, x1=-0.12352, y=-0.62883\nx0=-5.15966, x1=6.80751, y=-52.68666\nx0=9.73821, x1=7.67859, y=112.16358\nx0=0.96529, x1=3.85653, y=5.58398\nx0=-9.96617, x1=-4.66345, y=69.71514\nx0=-9.37610, x1=-3.31928, y=46.68290\nx0=-7.38870, x1=2.73330, y=-30.29330\nx0=8.72662, x1=4.67724, y=61.22473\nx0=7.59308, x1=5.25615, y=59.86551\nx0=0.16345, x1=-1.11799, y=-0.27410\nx0=-2.33847, x1=8.36700, y=-29.34896\nx0=4.44179, x1=1.21973, y=8.12669\nx0=-2.41350, x1=-7.10975, y=25.73914\nx0=9.30731, x1=-7.90704, y=-110.38991\nx0=5.06320, x1=6.52775, y=49.57701\nx0=-8.73975, x1=-2.93204, y=38.43797\nx0=-7.81198, x1=-1.49096, y=17.47104\nx0=9.29848, x1=-9.68680, y=-135.10864\nx0=1.07937, x1=-6.09205, y=-9.86338\nx0=4.48281, x1=3.80024, y=25.55363\nx0=-7.37371, x1=-3.88803, y=43.00379\nx0=6.68469, x1=-5.51768, y=-55.32599\nx0=-8.41647, x1=1.95527, y=-24.68476\nx0=-5.14058, x1=6.71673, y=-51.79185\nx0=-7.35298, x1=-8.39517, y=92.59435\nx0=-0.85947, x1=-8.01868, y=10.33776\nx0=6.99231, x1=9.64117, y=101.12106\nx0=9.70508, x1=-5.98336, y=-87.10339\nx0=2.01511, x1=9.72053, y=29.38187\nx0=7.88076, x1=-3.21829, y=-38.04382\nx0=1.84332, x1=0.68907, y=1.90526\nx0=-0.12332, x1=4.68005, y=-0.86573\nx0=6.08547, x1=7.16876, y=65.43793\nx0=7.27386, x1=-4.73858, y=-51.70169\nx0=7.00981, x1=-8.83591, y=-92.90701\nx0=-3.02309, x1=-6.95190, y=31.52436\nx0=7.03443, x1=-9.24602, y=-97.56072\nx0=2.87299, x1=1.50927, y=6.50417\nx0=4.35771, x1=1.72919, y=11.30294\nx0=-1.10807, x1=4.63621, y=-7.70584\nx0=-3.81862, x1=-8.60279, y=49.27614\nx0=8.06843, x1=-2.06237, y=-24.96014\nx0=-4.85653, x1=8.77319, y=-63.91088\nx0=4.45615, x1=1.06732, y=7.13420\nx0=-6.37285, x1=-9.82680, y=93.93713\nx0=4.30087, x1=3.24436, y=20.93035\nx0=8.87180, x1=9.07542, y=120.77296\nx0=2.75523, x1=-2.70180, y=-11.16612\nx0=2.82114, x1=2.74813, y=11.62930\nx0=-8.43464, x1=-3.27154, y=41.39142\nx0=1.75813, x1=-1.75483, y=-4.62783\nx0=-5.60395, x1=-7.33902, y=61.69130\nx0=-2.90501, x1=-0.61851, y=2.69517\nx0=-3.96624, x1=7.87017, y=-46.82246\nx0=-3.94583, x1=-5.26593, y=31.16770\nx0=5.11304, x1=7.06895, y=54.21579\nx0=7.05282, x1=-6.07352, y=-64.25316\nx0=-4.52975, x1=8.78467, y=-59.68855\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=4.70874, x1=1.29322, y=9.13419\nx0=8.90609, x1=-4.77640, y=-63.80859\nx0=-7.33685, x1=7.34352, y=-80.81743\nx0=0.44692, x1=1.83429, y=1.22969\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (3/2) * x0 * x1", "data": [[-8.866219999443192, -2.630938362626482, 34.989717492031865], [-5.995117416916946, 5.683751359417599, -51.11213515240472], [9.026736200648074, -1.0389640597125833, -14.067681733469794], [-3.3149867495149765, -5.8861236483691615, 29.268632850525783], [-9.44601730151117, 8.710402582143463, -123.41792024108207], [-3.6337988381591257, 4.548234826541327, -24.791055642541117], [9.404344237819412, 1.3526108167929696, 19.080626611378758], [-4.649155229214177, -3.2723087171660143, 22.820206776023266], [-4.165720145997462, 7.194541029628944, -44.95566676249593], [-1.779678807923963, 1.4108669995182215, -3.7663351497627704], [0.48944341933969504, -4.175539181727808, -3.0655352620375957], [0.8504338424144713, -0.6801651134490232, -0.8676531463600914], [5.159570613903682, -3.800514555249279, -29.413534825466105], [-0.4135095891677558, -5.510594667214079, 3.41802560536458], [-2.7740581071427206, -8.628980045269204, 35.90593807642769], [8.515685692030164, -6.71652976731213, -85.79378465939189], [7.3404088445024485, 6.997455947339898, 77.04628128730506], [-6.38215081520033, -0.7423000968209426, 7.106206752073593], [-4.28666775344007, 4.524328463817554, -29.09143939772663], [3.5658957418440025, 1.0824416370236545, 5.789811036385951], [2.810799131788661, 0.6670827990892843, 2.812553628766965], [4.009492247581122, 3.1930876266058803, 19.20399012708522], [-7.287933486518612, 5.119033348563931, -55.96076183940687], [-9.514138244794982, 9.082507537744661, -129.61834848524276], [3.5684680156955437, -3.8030699320087447, -20.356700120739948], [-2.8964773374207597, -8.945573836614022, 38.86597783196489], [2.72558571606689, 2.6415388869730485, 10.799610988153457], [1.3220397825849801, 8.0245553350647, 15.913172085765119], [-1.8890917982453477, -8.099660874380866, 22.951504389542453], [7.964696512521655, 4.826401510134815, 57.66123491370002], [3.7631176601549328, 0.7303469270903982, 4.1225721290606465], [5.6424758042448175, 9.899135670778719, 83.78345025795858], [-9.835907768193799, -8.215280768979753, 121.20711590025161], [2.4608987372612656, -8.456891844791596, -31.2173316930041], [-8.259643130996642, -3.9285220936325027, 48.672285788460364], [-7.050263060349982, 8.463255403274989, -89.50226541002556], [4.728510051832188, -3.8374983604895068, -27.218474357196264], [-5.6434476866287415, 0.73291605981494, -6.204260163383514], [-9.916165543769386, -6.1731122080311955, 91.82040386265164], [-6.519139808398546, 8.768844522521931, -85.7479851006454], [-1.7991808699863725, -6.6394211870666116, 17.91827938132869], [-4.902063309840621, -2.6781853533910667, 19.69295123671633], [2.5343000664179733, -5.253202349731357, -19.969786595746847], [-3.8108284887439403, -3.135013912867805, 17.92050049764787], [0.761386857359243, -2.292520238190763, -2.618242169382792], [1.902226067409016, 2.587695940097227, 7.383574007672136], [3.9282274781283526, 2.841013841238391, 16.740222955343445], [-4.641739153055151, 3.940589284690464, -27.436781353285976], [-0.4253556869567774, -9.392742000991689, 5.992884339359393], [3.633296394763315, 5.934287633795474, 32.34153879803643], [-7.853293139252838, 3.5035973601816988, -41.27216566712893], [9.977147888912445, -6.328892004746558, -94.71643725646796], [3.3344644422712832, -8.563881291680573, -42.83393648241171], [-3.3423295446764385, -2.85868829726752, 14.332017532467018], [-4.8160427789310045, -6.381730022408845, 46.10202718726397], [-5.0486158528080445, -1.9468769328725202, 14.743550620149763], [-6.089248975846577, -6.839145782157208, 62.467892174499326], [-3.4481248164191474, -0.809522878205577, 4.187003888699557], [-3.311888113220993, 1.2943609859659393, -6.430168145456399], [8.32096340671097, -1.4437895822123554, -18.020580420869294], [-9.541245399984666, -7.111962854726917, 101.7854743087875], [-0.24410504285215673, 9.570661371622553, -3.5043700563651066], [2.1625454166461786, -5.955230278052193, -19.317683914311477], [3.3938848191095516, -0.12352160050077643, -0.6288271271575498], [-5.159657994624887, 6.807513270243934, -52.68666040249368], [9.738211547975236, 7.678588815046741, 112.16358340626249], [0.9652867088437489, 3.856527537325805, 5.583982161105771], [-9.966167025947321, -4.663454036596654, 69.71514276982576], [-9.376101295514918, -3.3192829827850945, 46.68290021260792], [-7.388698610181478, 2.733300732289621, -30.293302982814506], [8.726618341210518, 4.677240152779682, 61.22473455524018], [7.593081275934541, 5.256145709261768, 59.865512352868805], [0.16344995735216195, -1.1179860687219705, -0.2741021628793759], [-2.338468247078347, 8.367002955108276, -29.3489561005971], [4.441785145976889, 1.2197340279900022, 8.126694731352826], [-2.4135046762965278, -7.109754796187553, 25.739139671880487], [9.307309416074112, -7.907040745578486, -110.38991217690648], [5.063203291257496, 6.527753317155451, 49.577013119907775], [-8.7397457872033, -2.9320429684068454, 38.43796527154918], [-7.811978941635466, -1.490961668950126, 17.47104174093608], [9.298475100566787, -9.68679518645634, -135.10863576833174], [1.079371596124636, -6.092048063074436, -9.863375462262976], [4.482809167759719, 3.8002403530123186, 25.553628441261075], [-7.373713712351764, -3.888026664254647, 43.00379329230566], [6.684692982285501, -5.517679326361953, -55.325988407150305], [-8.416474923454224, 1.955272907196747, -24.684758087896288], [-5.140579597478602, 6.7167330139693995, -51.79185103998309], [-7.3529838024424565, -8.395172239523852, 92.59434824390017], [-0.8594738815952301, -8.018675637751041, 10.337763413446492], [6.992310230948931, 9.641168007302284, 101.12105654363592], [9.705076186705728, -5.9833558146924615, -87.10338605063859], [2.015107427454801, 9.72053151476581, 29.381872881319573], [7.880756958009133, -3.2182878270253257, -38.04381627855889], [1.8433228805878148, 0.6890670965634698, 1.9052597180334856], [-0.12332187148197171, 4.6800548732812945, -0.8657296884170568], [6.085474628924246, 7.168756982555966, 65.43793310740179], [7.273860763822299, -4.738582931672745, -51.70168869421863], [7.009808402098066, -8.835906202349928, -92.90701430607442], [-3.023094464728082, -6.951896692717967, 31.52436061667572], [7.034432761140213, -9.24601618986273, -97.5607187940048], [2.872991793070982, 1.5092665186546572, 6.504165482477464], [4.357706166206768, 1.72918870261109, 11.302944407855142], [-1.1080661966758125, 4.636209005670951, -7.705839719861942], [-3.818615353776007, -8.602794353518629, 49.27614390558566], [8.06843383739226, -2.0623698364460115, -24.960141860397208], [-4.856527719214596, 8.773192577954141, -63.91087941126307], [4.456146065061974, 1.0673192649434462, 7.134195813963864], [-6.3728540107832155, -9.82679903116721, 93.93713342840186], [4.300873894015167, 3.24435549499829, 20.9303457770142], [8.871804092266363, 9.075415090492605, 120.7729571082723], [2.755232230294741, -2.7017972251271445, -11.166118191586808], [2.8211384445438163, 2.7481336573451003, 11.629298267221598], [-8.434640157544965, -3.271542431225516, 41.391424751290536], [1.7581257516093984, -1.7548333464011368, -4.627826544136101], [-5.603953231121959, -7.339021357918911, 61.69129867797412], [-2.905007397637716, -0.6185102819978567, 2.6951654170781456], [-3.966238817808434, 7.870169761603137, -46.822459216818764], [-3.945830220024897, -5.265929794875603, 31.167697381724494], [5.1130443665197145, 7.068950998292308, 54.2157901185336], [7.052819099456897, -6.073520289816234, -64.25315985143239], [-4.529753008305002, 8.784666189786655, -59.68855215021202], [4.708741283103759, 1.2932249452780447, 9.134192532255494], [8.906088647208506, -4.776401936176244, -63.80858858742596], [-7.336851365686701, 7.34351594712102, -80.81742750836537], [0.44692429808613277, 1.8342943083520762, 1.22968604436546]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-3.02004, y=-1.04726\nx0=2.46372, y=-0.58515\nx0=4.70637, y=-0.74905\nx0=1.35430, y=-0.54260\nx0=3.77790, y=-1.54694\nx0=-9.58682, y=-0.04134\nx0=-9.32095, y=0.12932\nx0=-6.39380, y=-0.78970\nx0=7.06374, y=-1.00632\nx0=1.68810, y=-0.78368\nx0=9.51042, y=-1.35933\nx0=-1.11005, y=-0.33063\nx0=7.45299, y=-1.07878\nx0=6.31114, y=0.09663\nx0=1.55580, y=-0.74010\nx0=-1.05367, y=-0.30713\nx0=0.81855, y=-0.32568\nx0=7.74433, y=-0.78070\nx0=-4.90399, y=-0.91828\nx0=-6.01419, y=-1.71318\nx0=1.60850, y=-0.76984\nx0=8.44940, y=-1.17659\nx0=-7.77462, y=-0.80430\nx0=8.72103, y=-1.21634\nx0=7.07810, y=-0.86569\nx0=4.48781, y=-0.96403\nx0=-2.78919, y=-1.68595\nx0=6.32564, y=-0.01481\nx0=-8.65580, y=-0.42116\nx0=-4.11776, y=-0.21873\nx0=-3.33361, y=0.22486\nx0=6.83072, y=-0.36703\nx0=6.25935, y=0.24563\nx0=2.00535, y=-0.42556\nx0=3.39978, y=0.06767\nx0=-1.84331, y=-0.68180\nx0=7.29747, y=-0.66900\nx0=-1.54297, y=-0.73082\nx0=-6.35554, y=-0.31816\nx0=6.11871, y=-1.00413\nx0=0.55199, y=-0.49456\nx0=-9.85697, y=-0.95659\nx0=2.40668, y=-0.40013\nx0=-7.69765, y=-0.68418\nx0=8.58322, y=-0.09177\nx0=-1.32152, y=-0.50709\nx0=3.07930, y=-0.69285\nx0=3.73161, y=-1.56228\nx0=-3.60713, y=-1.13468\nx0=-2.23915, y=-0.15824\nx0=4.05820, y=-0.33034\nx0=7.50979, y=-0.80101\nx0=6.55314, y=-1.58049\nx0=-9.57778, y=-0.16961\nx0=1.70549, y=-0.78099\nx0=2.35127, y=-0.26797\nx0=2.58530, y=-1.08118\nx0=-2.73196, y=-1.59825\nx0=-4.63385, y=-0.78888\nx0=6.57388, y=-1.41448\nx0=5.57374, y=-1.00968\nx0=-3.31894, y=0.23412\nx0=-2.14266, y=-0.21278\nx0=-9.33306, y=0.00377\nx0=-6.56274, y=-1.51047\nx0=-1.36512, y=-0.55446\nx0=3.16760, y=-0.17822\nx0=2.20300, y=-0.16493\nx0=3.56572, y=-0.88440\nx0=-4.87313, y=-0.90731\nx0=-2.15077, y=-0.20405\nx0=2.58181, y=-1.06633\nx0=0.50493, y=-0.52927\nx0=1.09387, y=-0.32272\nx0=5.40886, y=-1.28331\nx0=-7.30579, y=-0.73307\nx0=6.81407, y=-0.19947\nx0=-9.11358, y=-1.68394\nx0=-2.53005, y=-0.84636\nx0=3.51877, y=-0.57932\nx0=5.82937, y=-0.26048\nx0=7.54238, y=-0.64809\nx0=-0.12290, y=-0.73501\nx0=-1.58113, y=-0.75619\nx0=3.45307, y=-0.17949\nx0=2.94510, y=-1.41935\nx0=-4.88235, y=-0.91277\nx0=-5.85662, y=-0.51813\nx0=5.81007, y=-0.11110\nx0=-0.28015, y=-0.67465\nx0=-5.55377, y=-1.15334\nx0=-1.67518, y=-0.78429\nx0=-9.31741, y=0.15771\nx0=7.92758, y=-0.75108\nx0=-0.85648, y=-0.31140\nx0=0.87283, y=-0.30641\nx0=-8.93600, y=0.10356\nx0=-6.35013, y=-0.25723\nx0=8.96104, y=0.12836\nx0=-0.23678, y=-0.69553\nx0=9.69977, y=-0.59458\nx0=4.93037, y=-0.90873\nx0=9.60517, y=0.14920\nx0=-2.90151, y=-1.57049\nx0=6.86338, y=-0.73497\nx0=9.19762, y=-0.96903\nx0=3.47842, y=-0.32514\nx0=7.76649, y=-0.80135\nx0=-2.63710, y=-1.29437\nx0=-0.52532, y=-0.51426\nx0=-3.88489, y=-1.17513\nx0=5.52697, y=-1.30532\nx0=-8.14529, y=-0.64551\nx0=-7.01969, y=-1.36914\nx0=-8.96093, y=0.12865\nx0=5.36870, y=-1.06819\nx0=-8.52649, y=-0.48220\nx0=0.64968, y=-0.42380\nx0=3.82056, y=-1.44750\nx0=7.88667, y=-0.73069\nx0=4.56557, y=-0.88333\nx0=5.32773, y=-0.81359\nx0=1.88807, y=-0.62187\nx0=7.00841, y=-1.43233\nx0=0.96191, y=-0.29313\nx0=-4.14714, y=-0.21609\nx0=9.28561, y=0.22586\nx0=-2.75216, y=-1.63920\nx0=6.76439, y=0.11808\nx0=4.61757, y=-0.80874\nx0=-4.78590, y=-0.80815\nx0=-5.83671, y=-0.32520\nx0=-1.59111, y=-0.76164\nx0=-4.03503, y=-0.40995\nx0=-6.87583, y=-0.87649\nx0=-1.78448, y=-0.74093\nx0=-4.14127, y=-0.21389\nx0=3.13631, y=-0.34986\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.22542, y=-0.20191\nx0=9.25366, y=-0.03814\nx0=-5.84077, y=-0.36268\nx0=7.19799, y=-0.14025\nx0=6.95613, y=-1.49544\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0**2) * cos(x0) - 0.75", "data": [[-3.020040335630134, -1.0472577605679103], [2.4637231090461924, -0.5851505431674906], [4.706369590417882, -0.7490483402425923], [1.3543019606650226, -0.5425979832743343], [3.7778959709641935, -1.5469439965410061], [-9.586824349823795, -0.04134490393622803], [-9.32094806960938, 0.12931864501495993], [-6.393798570853075, -0.7897009170020175], [7.063739723150594, -1.0063158349766987], [1.688095468748159, -0.7836810504743305], [9.510423015173249, -1.3593265243541155], [-1.1100489356258532, -0.33062561192706075], [7.452993819979856, -1.0787763561082728], [6.31113742474399, 0.09663334607221585], [1.5558034102164022, -0.740102234314686], [-1.053669495186437, -0.3071320522142983], [0.8185548163593346, -0.32567734303899315], [7.744329280750954, -0.7807022521890489], [-4.9039944157455455, -0.918276061964566], [-6.0141913026370375, -1.7131812191549423], [1.608503375794088, -0.7698426419913512], [8.44940182872223, -1.1765886785237316], [-7.774624272541746, -0.8042980452231316], [8.721030746638057, -1.2163413686709907], [7.078102015191547, -0.8656923937546129], [4.487806570768571, -0.9640297718496916], [-2.789187507007007, -1.685947857592012], [6.3256445520506865, -0.014810213939077], [-8.6558034713065, -0.42116024548080455], [-4.1177647038365395, -0.21873141304685917], [-3.3336125018053764, 0.22486403744210304], [6.8307212063320115, -0.36702716843673083], [6.259350248268742, 0.2456299710115507], [2.0053484965840944, -0.42556129003460524], [3.3997780665419874, 0.06767134359562943], [-1.8433073189286464, -0.6817983127920084], [7.297474201701668, -0.6690031855685586], [-1.5429727223560459, -0.7308175087090801], [-6.355542242509122, -0.31816087187556663], [6.118706699599649, -1.0041258872171654], [0.5519898058289101, -0.4945550888143671], [-9.856969593888664, -0.9565929419793281], [2.4066771126830453, -0.4001349107609218], [-7.6976468429433265, -0.6841761204557357], [8.58321682832845, -0.09177256515161647], [-1.3215178003246653, -0.5070895613982882], [3.079296744445463, -0.692851924221296], [3.7316084296278405, -1.5622825874293855], [-3.607132908655357, -1.1346782051332194], [-2.2391475932859954, -0.15824049715928268], [4.058197449746917, -0.3303366679402042], [7.509788131502614, -0.8010098458893996], [6.5531429868848114, -1.5804928913947633], [-9.57777892709352, -0.1696060437870991], [1.7054944394651113, -0.7809919924760103], [2.351272211881593, -0.267970344284878], [2.5853040557856506, -1.0811805658902232], [-2.7319551666102715, -1.598246483146113], [-4.633854063892895, -0.7888832417294774], [6.573876056376793, -1.4144843256042212], [5.573742461232358, -1.009681479272873], [-3.318941893430871, 0.23412184153335325], [-2.1426649215011784, -0.21277737853872747], [-9.33305762112106, 0.003766117565868754], [-6.562739968072638, -1.5104682227336796], [-1.3651171971427534, -0.5544571765041678], [3.1675993220865006, -0.17822175805331186], [2.2029963846290066, -0.16492702932905923], [3.5657219007194474, -0.8843967859085808], [-4.873131196073752, -0.9073061891853615], [-2.1507680736087202, -0.20405261387281615], [2.5818131549988657, -1.066332091318536], [0.5049326966500907, -0.5292694373045653], [1.093867395056229, -0.3227217946193768], [5.40886413562461, -1.2833061331768545], [-7.305791381003068, -0.7330723757110899], [6.814065017657601, -0.19947473540068483], [-9.11357675284475, -1.6839384610202446], [-2.530048474764839, -0.8463573729686686], [3.518769394388311, -0.5793192020119846], [5.829369852190052, -0.26048302885630475], [7.542381977343169, -0.6480890797517496], [-0.1229036173411906, -0.7350092124306492], [-1.581133726393949, -0.7561866691750383], [3.453069304774278, -0.17949395260919554], [2.9451006708933143, -1.4193542897164344], [-4.882351543546692, -0.9127709216184721], [-5.8566194366811875, -0.5181315236400946], [5.810074986093635, -0.11110196799788874], [-0.28015399914107064, -0.6746511060449436], [-5.5537653749217135, -1.1533429229633871], [-1.675180671713214, -0.784291721731305], [-9.317408346674544, 0.15770904672739394], [7.9275830518202, -0.7510823937942561], [-0.8564807561850003, -0.311398653987739], [0.8728267220847297, -0.3064052968507228], [-8.935997969872103, 0.10355942270137053], [-6.350131013396223, -0.25723124831851407], [8.961036470573461, 0.12836396244165316], [-0.2367832036303934, -0.6955266483428026], [9.699772429852437, -0.5945832853375782], [4.930372156237253, -0.9087323997213878], [9.605170080118953, 0.14919646682406007], [-2.901506387262806, -1.5704896546003901], [6.863375335187747, -0.7349724399959621], [9.197622403860468, -0.969030777869219], [3.4784229974783365, -0.3251362329355358], [7.766489172087535, -0.801345293211281], [-2.637095450097659, -1.294367694512773], [-0.525323907672794, -0.51426445724203], [-3.8848911037722766, -1.1751315359406116], [5.526967286840296, -1.3053241811627325], [-8.14529300771094, -0.645511305044628], [-7.019685640139095, -1.3691429971571654], [-8.960925656639438, 0.12864822409818266], [5.368695579925614, -1.0681908037859058], [-8.526488766945663, -0.4821954736522187], [0.6496799541018952, -0.4237950049765165], [3.8205592585750594, -1.447498401979165], [7.886665960001327, -0.7306855481066722], [4.5655699106864525, -0.8833334894732799], [5.327732008623114, -0.8135946039208194], [1.8880736249377605, -0.6218672507943912], [7.008414281516469, -1.4323326455091652], [0.9619138185872007, -0.29313219155434556], [-4.147138453384787, -0.21608579827585028], [9.285613787165001, 0.22585894490997582], [-2.752160448384604, -1.6391997990524572], [6.764388695333867, 0.11808240916508683], [4.617565768299558, -0.8087388898409745], [-4.785895344572562, -0.8081452405166745], [-5.836706087564966, -0.32520481287234093], [-1.5911110453942392, -0.7616361464190801], [-4.0350278782746285, -0.40995389174558716], [-6.875825654265501, -0.8764868225565112], [-1.7844830869199502, -0.7409291260814875], [-4.14126634328702, -0.21389204375262583], [3.136311593692369, -0.3498629695816368], [-7.225423231511088, -0.20190913322023707], [9.253663143352433, -0.03814137945327467], [-5.840769771931917, -0.36267779525490546], [7.197994739002709, -0.14025129715896256], [6.956130835432393, -1.4954433679867813]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.61432, x1=-4.28385, y=-42.33941\nx0=7.08908, x1=3.61640, y=46.35671\nx0=6.00533, x1=0.06551, y=0.01288\nx0=-8.66399, x1=4.15094, y=-74.64162\nx0=7.10007, x1=2.76273, y=27.09625\nx0=-3.27606, x1=7.99504, y=-104.70390\nx0=3.16729, x1=-2.71032, y=11.63317\nx0=6.63844, x1=-9.43972, y=295.76966\nx0=-4.25390, x1=4.70704, y=-47.12508\nx0=-1.82611, x1=6.91954, y=-43.71709\nx0=-8.46946, x1=-5.08510, y=-109.50249\nx0=6.59994, x1=0.75193, y=1.86579\nx0=-8.68429, x1=8.81313, y=-337.25983\nx0=8.86299, x1=3.60145, y=57.47857\nx0=-9.13293, x1=-3.89495, y=-69.27610\nx0=-1.79967, x1=0.79307, y=-0.56596\nx0=-8.05804, x1=4.88075, y=-95.97841\nx0=-5.87598, x1=-5.64445, y=-93.60381\nx0=-0.56604, x1=-7.67125, y=-16.65514\nx0=-1.29105, x1=6.45553, y=-26.90149\nx0=8.30217, x1=9.33293, y=361.57469\nx0=-1.43868, x1=6.64205, y=-31.73495\nx0=-5.16535, x1=4.22043, y=-46.00268\nx0=7.58277, x1=-2.03534, y=15.70631\nx0=5.83943, x1=-0.19861, y=0.11517\nx0=-8.17994, x1=4.31978, y=-76.32095\nx0=-2.70679, x1=6.39948, y=-55.42608\nx0=-1.17209, x1=3.41675, y=-6.84161\nx0=7.92064, x1=4.55891, y=82.31001\nx0=-4.28314, x1=2.71139, y=-15.74400\nx0=-2.55686, x1=-7.03661, y=-63.29996\nx0=4.54727, x1=-3.16069, y=22.71351\nx0=-8.09807, x1=4.83659, y=-94.71729\nx0=5.79702, x1=1.86159, y=10.04483\nx0=-3.52393, x1=-0.75733, y=-1.01056\nx0=1.19922, x1=-1.83452, y=2.01797\nx0=4.02814, x1=-5.14977, y=53.41350\nx0=2.71564, x1=-6.29182, y=53.75209\nx0=-7.93965, x1=9.59353, y=-365.36580\nx0=6.43621, x1=8.88895, y=254.27359\nx0=9.37646, x1=3.56574, y=59.60865\nx0=-9.95605, x1=8.01104, y=-319.47374\nx0=2.43876, x1=6.79295, y=56.26719\nx0=4.02798, x1=9.34458, y=175.86398\nx0=1.38983, x1=9.80711, y=66.83661\nx0=1.77572, x1=-0.69742, y=0.43185\nx0=4.75320, x1=-6.88416, y=112.63082\nx0=8.94828, x1=9.97187, y=444.90034\nx0=5.16833, x1=7.65007, y=151.23458\nx0=0.72787, x1=3.00012, y=3.27567\nx0=6.73090, x1=-1.40995, y=6.69038\nx0=-2.35459, x1=-3.09067, y=-11.24584\nx0=-4.58995, x1=7.38592, y=-125.19520\nx0=3.75986, x1=-1.81540, y=6.19563\nx0=0.43843, x1=9.24084, y=18.71953\nx0=-2.52159, x1=1.53697, y=-2.97835\nx0=0.78860, x1=0.49296, y=0.09582\nx0=-0.56061, x1=3.17265, y=-2.82148\nx0=1.97286, x1=-5.89301, y=34.25632\nx0=-8.40533, x1=-3.16305, y=-42.04721\nx0=1.54147, x1=-6.45444, y=32.10870\nx0=6.29925, x1=-3.83823, y=46.40039\nx0=8.82564, x1=2.10019, y=19.46404\nx0=7.06771, x1=9.68531, y=331.49396\nx0=7.93301, x1=-2.55322, y=25.85728\nx0=-7.37822, x1=-9.06825, y=-303.36749\nx0=1.27162, x1=7.75328, y=38.22063\nx0=-0.21851, x1=-7.49283, y=-6.13376\nx0=-3.53229, x1=8.18536, y=-118.33194\nx0=0.73765, x1=5.77395, y=12.29608\nx0=-9.50094, x1=1.76503, y=-14.79937\nx0=-9.45055, x1=0.34489, y=-0.56207\nx0=2.60470, x1=-4.52401, y=26.65477\nx0=6.20442, x1=0.02348, y=0.00171\nx0=0.82841, x1=-5.33387, y=11.78428\nx0=1.35009, x1=3.09582, y=6.46972\nx0=-4.13485, x1=-1.24632, y=-3.21138\nx0=-0.95636, x1=5.41265, y=-14.00915\nx0=-5.61804, x1=-5.54082, y=-86.23896\nx0=-0.30652, x1=4.26901, y=-2.79306\nx0=4.59542, x1=7.66797, y=135.10007\nx0=3.09270, x1=9.36638, y=135.66011\nx0=9.17954, x1=7.95557, y=290.49175\nx0=9.87538, x1=-9.81311, y=475.48482\nx0=-6.60502, x1=-6.73591, y=-149.84327\nx0=-1.62916, x1=0.63184, y=-0.32520\nx0=8.97395, x1=4.45500, y=89.05327\nx0=6.05195, x1=-9.02372, y=246.39762\nx0=1.03132, x1=3.36876, y=5.85198\nx0=7.29078, x1=9.20369, y=308.79343\nx0=-0.20283, x1=-4.17544, y=-1.76813\nx0=-1.49629, x1=-3.04221, y=-6.92414\nx0=3.52547, x1=-3.35717, y=19.86711\nx0=-4.23888, x1=-5.17215, y=-56.69736\nx0=-8.84181, x1=6.06916, y=-162.84276\nx0=4.61956, x1=-3.84212, y=34.09668\nx0=5.36022, x1=-1.67849, y=7.55079\nx0=-1.19521, x1=-8.72004, y=-45.44145\nx0=-2.19801, x1=0.23917, y=-0.06287\nx0=8.09917, x1=5.38181, y=117.29182\nx0=-6.61124, x1=0.79037, y=-2.06495\nx0=9.42401, x1=0.09750, y=0.04479\nx0=8.07166, x1=4.49514, y=81.54925\nx0=-5.51985, x1=-6.05401, y=-101.15408\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-5.11499, x1=-1.25396, y=-4.02145\nx0=-4.31974, x1=-3.97382, y=-34.10697\nx0=9.55766, x1=-0.87443, y=3.65406\nx0=0.39825, x1=-9.89009, y=19.47741\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1/2 * x0 * x1**2", "data": [[-4.6143151286766955, -4.28384500791722, -42.33940533049705], [7.089076223282234, 3.6164001178933862, 46.35670934848712], [6.005326825701701, 0.06550527796651195, 0.012884252872987447], [-8.663992611900472, 4.150940369554776, -74.64162173272159], [7.1000661028293806, 2.762729515242171, 27.0962462997713], [-3.2760579942060915, 7.9950397805062146, -104.70389638249073], [3.1672943157472826, -2.7103155397021332, 11.633171643070558], [6.638435587758718, -9.439716223787538, 295.76966370772345], [-4.253898922864419, 4.707035515833244, -47.12508223796606], [-1.8261081807294808, 6.91954198749999, -43.717085832196275], [-8.469458305579131, -5.085096149956534, -109.50248546586229], [6.599942045308108, 0.7519274973285981, 1.8657869884428135], [-8.684292328024181, 8.813128238100049, -337.25983053797955], [8.862987160532509, 3.6014545029000473, 57.4785746413251], [-9.132926954897055, -3.8949484356573016, -69.27609730460327], [-1.7996726733688426, 0.7930678752493403, -0.5659580521457808], [-8.05804399613489, 4.8807544607594995, -95.97841161674897], [-5.8759798294008725, -5.644449747090143, -93.60380912377991], [-0.5660386385381972, -7.67124892789022, -16.655137913674157], [-1.2910481075826112, 6.455531203472358, -26.90149396820534], [8.302171923699312, 9.332933001279965, 361.5746906147553], [-1.4386785782091174, 6.6420480593617235, -31.734949292434184], [-5.16534791968311, 4.220430678198362, -46.00267924903205], [7.58277223463946, -2.0353449507896126, 15.706306340292432], [5.839425362118362, -0.19860793382502173, 0.11516839189685142], [-8.179938290412359, 4.319782458255601, -76.32095302389776], [-2.7067920541811645, 6.399479144625968, -55.42607861479152], [-1.172092095204091, 3.4167507764699003, -6.841610487210571], [7.920644197762105, 4.558910574549721, 82.31001027733795], [-4.283138998032454, 2.711386555224305, -15.74399884669196], [-2.556856025006411, -7.036611452028958, -63.299957697476], [4.547272138698084, -3.160688096168995, 22.7135089259048], [-8.098065911193919, 4.836586750882169, -94.71729250993226], [5.797024853145739, 1.8615886864179352, 10.04483086424457], [-3.523929580935617, -0.757325916359946, -1.0105617676416891], [1.199224242997614, -1.8345209858180915, 2.017974956052451], [4.0281424930795495, -5.149773014867678, 53.413495948568126], [2.715640234500027, -6.2918238155254125, 53.752088698117305], [-7.939648028610575, 9.5935273726407, -365.36579979646433], [6.436213931908171, 8.888948421438691, 254.27358594164218], [9.376461031893424, 3.5657441798362797, 59.608654836976825], [-9.956046977815898, 8.011043926511388, -319.47374126057], [2.4387564288828028, 6.792949544256711, 56.267187708712655], [4.027979662396216, 9.344580447862452, 175.86397611377996], [1.3898318654173671, 9.807110579501387, 66.83660991025998], [1.7757205042700939, -0.6974205550458397, 0.43185116965024767], [4.753198267410987, -6.884155103961458, 112.63081529288893], [8.948275433376224, 9.971871939684839, 444.9003352408189], [5.168331659520053, 7.650069281284427, 151.2345840097511], [0.7278693440445583, 3.0001181719120584, 3.2756700944190578], [6.730902889413642, -1.4099495542388158, 6.6903752666031515], [-2.35459457006554, -3.090671917480609, -11.245841406886196], [-4.589950827719589, 7.385923859494312, -125.19520331772245], [3.7598615034298533, -1.8153972610729436, 6.195626145858107], [0.43843121569830146, 9.240844873189666, 18.71952530670412], [-2.5215908024399747, 1.5369699409865145, -2.9783474730542596], [0.7885978494206665, 0.4929590403191, 0.09581803576031384], [-0.5606114037987258, 3.1726539250248376, -2.8214823335077033], [1.9728614607605426, -5.893007977584077, 34.25631562934796], [-8.405333510013095, -3.1630504604190772, -42.04721108939854], [1.5414695465170674, -6.454444255983029, 32.10869554748085], [6.299245508447086, -3.838234885045482, 46.40039055073565], [8.825642831467153, 2.1001888064937404, 19.464041911916684], [7.0677103138920465, 9.685308020297747, 331.4939595469788], [7.93300599441465, -2.553215676949046, 25.857277215783064], [-7.378219982234726, -9.068254908563, -303.36749342948275], [1.271617696177076, 7.753282726618153, 38.22062718274091], [-0.21850678448968708, -7.492833611890591, -6.133764641545423], [-3.5322879898253357, 8.185362762954188, -118.33193653170402], [0.7376515487648057, 5.773946379970738, 12.296082145523279], [-9.50093996911491, 1.7650347241837867, -14.79936515873161], [-9.450549216568596, 0.34489188987657293, -0.5620733789645188], [2.6046987735639977, -4.524011465370497, 26.654767807294572], [6.204423128993195, 0.02348162801550302, 0.001710518675791983], [0.8284139076749213, -5.333874782325061, 11.784279042364265], [1.350091934724734, 3.0958214461677063, 6.46971509419948], [-4.134847742712293, -1.2463249034843429, -3.2113827666471124], [-0.9563604214801344, 5.412652634794565, -14.009154084034899], [-5.618044333812233, -5.540821554177963, -86.23895665774997], [-0.30651734140870524, 4.269012187376784, -2.79305728877612], [4.595418038753046, 7.667967586637307, 135.10006743930217], [3.092702798654873, 9.366384746036097, 135.66011429281113], [9.179538266358673, 7.955573311867674, 290.49175162128097], [9.875377453149081, -9.81310567083428, 475.4848231641608], [-6.605022080524192, -6.735913214636923, -149.8432707975731], [-1.629155399555163, 0.6318441177385044, -0.32520140248710927], [8.973947039529449, 4.455004755271501, 89.05326573189572], [6.051954635826007, -9.023716060076142, 246.3976213939435], [1.0313216343321407, 3.368755785793864, 5.851984799205714], [7.2907773954525155, 9.20369256046635, 308.79342813512613], [-0.2028325965084754, -4.175443542963546, -1.7681250874631909], [-1.4962944536451133, -3.042211484381008, -6.924140527052847], [3.5254676582469173, -3.3571746018446813, 19.867105453566243], [-4.238875760190939, -5.172149520477694, -56.69735966080269], [-8.841807561874422, 6.069161470565568, -162.84275714325275], [4.619564414506858, -3.8421163264018565, 34.0966766439755], [5.3602227780293195, -1.6784944229964243, 7.5507944762402115], [-1.195213641840171, -8.720036387464795, -45.44144573236752], [-2.1980050536869378, 0.23916929559247535, -0.06286508973804544], [8.09916534015564, 5.381814506326707, 117.29181837750001], [-6.611242422384597, 0.790365866932845, -2.064949520031007], [9.424012446752442, 0.09749504844380574, 0.04478895958259621], [8.071658221106212, 4.4951438315598224, 81.54924666951392], [-5.519848321713834, -6.054009780441916, -101.15407542081074], [-5.114994599388806, -1.2539605211204474, -4.021452202155664], [-4.319740215355874, -3.9738159424491304, -34.10696923469627], [9.557663599426181, -0.8744335169493471, 3.654057157568217], [0.39825435180106616, -9.890090986404596, 19.477405614934387]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-6.23700, y=16.33161\nx0=-7.75028, y=26.15827\nx0=6.76200, y=26.24335\nx0=1.58587, y=2.05043\nx0=-1.89829, y=0.85261\nx0=7.23870, y=29.81874\nx0=-0.71364, y=-0.10218\nx0=-7.37947, y=23.53853\nx0=-8.53195, y=32.13110\nx0=5.01866, y=15.10280\nx0=-1.45523, y=0.33123\nx0=-3.27222, y=3.71761\nx0=-0.21393, y=-0.08408\nx0=0.49353, y=0.36855\nx0=-6.47888, y=17.74850\nx0=-9.01165, y=36.09908\nx0=-5.06063, y=10.27469\nx0=2.64700, y=4.82679\nx0=-7.06882, y=21.44967\nx0=-1.23701, y=0.14660\nx0=4.23043, y=11.06348\nx0=-4.38420, y=7.41852\nx0=7.95613, y=35.62805\nx0=-2.26859, y=1.43896\nx0=6.62392, y=25.25009\nx0=5.27314, y=16.53957\nx0=8.01783, y=36.15170\nx0=5.43921, y=17.51213\nx0=3.12348, y=6.43979\nx0=-1.59095, y=0.47009\nx0=3.93606, y=9.71430\nx0=7.85014, y=34.73745\nx0=-9.44625, y=39.89272\nx0=5.57455, y=18.32510\nx0=1.58753, y=2.05389\nx0=-7.88753, y=27.16281\nx0=-0.29032, y=-0.10302\nx0=-4.83319, y=9.26329\nx0=0.19639, y=0.11748\nx0=1.13158, y=1.20603\nx0=6.55749, y=24.77909\nx0=-7.59826, y=25.06764\nx0=9.72223, y=52.12198\nx0=4.41123, y=11.93508\nx0=6.54012, y=24.65666\nx0=4.34281, y=11.60139\nx0=-1.28411, y=0.18242\nx0=-1.92948, y=0.89670\nx0=-5.95838, y=14.77197\nx0=7.02212, y=28.16614\nx0=-0.91441, y=-0.03913\nx0=3.23643, y=6.85544\nx0=7.85538, y=34.78118\nx0=6.53193, y=24.59904\nx0=-0.02086, y=-0.01021\nx0=-9.64585, y=41.69832\nx0=2.80233, y=5.32768\nx0=1.18546, y=1.29539\nx0=7.12224, y=28.92424\nx0=9.60729, y=50.95367\nx0=-0.74234, y=-0.09564\nx0=1.64173, y=2.16850\nx0=-7.19101, y=22.25981\nx0=-9.97016, y=44.71698\nx0=0.78500, y=0.70061\nx0=6.04057, y=21.26456\nx0=1.28212, y=1.46297\nx0=-7.72489, y=25.97450\nx0=8.62723, y=41.52816\nx0=-8.33236, y=30.54792\nx0=-9.85688, y=43.65064\nx0=-8.28569, y=30.18350\nx0=2.06602, y=3.16723\nx0=4.72037, y=13.50114\nx0=-7.93564, y=27.51939\nx0=-2.58966, y=2.05834\nx0=-0.30065, y=-0.10513\nx0=7.05593, y=28.42105\nx0=-7.79452, y=26.48001\nx0=-3.50901, y=4.40206\nx0=0.62198, y=0.50442\nx0=5.49083, y=17.82000\nx0=1.07532, y=1.11581\nx0=-2.27682, y=1.45354\nx0=0.99938, y=0.99907\nx0=-7.56579, y=24.83768\nx0=1.09453, y=1.14626\nx0=7.61439, y=32.79665\nx0=-8.75309, y=33.93171\nx0=-0.15315, y=-0.06485\nx0=2.98971, y=5.96402\nx0=-9.30479, y=38.63720\nx0=-0.63542, y=-0.11583\nx0=7.82020, y=34.48784\nx0=-0.71280, y=-0.10236\nx0=-1.97452, y=0.96210\nx0=-3.24720, y=3.64856\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.99083, y=27.93127\nx0=5.87758, y=20.21178\nx0=5.44297, y=17.53444\nx0=5.94082, y=20.61709\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * (x0 + 1) / 2", "data": [[-6.237004071612285, 16.331607858847967], [-7.7502782585651975, 26.158267413311595], [6.762004462295533, 26.243354405200115], [1.58587098154322, 2.0504288758220377], [-1.8982931612797458, 0.8526118824408526], [7.238699959594324, 29.8187385323126], [-0.7136441417726935, -0.10217809034310461], [-7.379465827913824, 23.53852503871702], [-8.531949146277732, 32.131103544195796], [5.018658863107714, 15.10279782367866], [-1.4552265282683159, 0.33122886015376984], [-3.2722227435400235, 3.7176094699002875], [-0.21393350682235202, -0.08408298074052134], [0.4935300216891392, 0.36855095199881066], [-6.478880168970056, 17.748504037451703], [-9.011648198871109, 36.0990775306729], [-5.060632730760533, 10.274685452442139], [2.6469968632550653, 4.82679462866861], [-7.068815692312418, 21.449669799784935], [-1.2370144347756433, 0.1465951385338305], [4.230428842258192, 11.063478515834088], [-4.384203210379695, 7.418517289761966], [7.9561280491645014, 35.62805079193332], [-2.2685948108679366, 1.4389638025144962], [6.623915929124479, 25.250089082616743], [5.273139308923355, 16.539568740118018], [8.017828723944088, 36.15170308522349], [5.439213882989556, 17.512130773947938], [3.123476101106885, 6.439789527646376], [-1.5909516628828904, 0.47008776537347186], [3.9360560114105265, 9.714296468185735], [7.850143755132745, 34.73745036569119], [-9.446252852037249, 39.892720046292304], [5.5745526706530235, 18.32509507426889], [1.5875276164266179, 2.0538857746718984], [-7.887531517768078, 27.16281096300836], [-0.29032320226498953, -0.10301782024579575], [-4.833194646652618, 9.263287922889456], [0.19638534955075926, 0.11747627753446657], [1.1315847050147418, 1.206034324819021], [6.557491409909922, 24.779092500476168], [-7.5982588015704415, 25.06763900703612], [9.722228668443126, 52.12197947497026], [4.411228465043088, 11.935082517924743], [6.54012269618487, 24.656663788668663], [4.342808050159967, 11.601394905347089], [-1.2841124641796657, 0.1824161782409538], [-1.929477551785867, 0.8967030355298582], [-5.958381867262494, 14.771966304429995], [7.0221195940152406, 28.166141593334004], [-0.9144062394876045, -0.039133734336871104], [3.236426216096886, 6.855440434168046], [7.855378749603574, 34.78117702466349], [6.531932768023061, 24.599039226998237], [-0.020862866947620518, -0.010213803865173201], [-9.645853600972693, 41.698319045212585], [2.8023260571539055, 5.32767869387883], [1.185462536764339, 1.2953919814180404], [7.122236131801362, 28.924241824469092], [9.607291469590585, 50.953670425629305], [-0.7423423454417524, -0.09563509380289519], [1.6417293154509522, 2.1685022303310024], [-7.191010365380435, 22.259809854814208], [-9.970161704631643, 44.71698135593585], [0.784999024872457, 0.7006112469615826], [6.040574348601741, 21.26455640479354], [1.2821193980393915, 1.4629747744341415], [-7.724886949202963, 25.97449571438165], [8.62723009080488, 41.52816456524702], [-8.332358552114876, 30.547920244443517], [-9.856883704482469, 43.65063632960478], [-8.285691949196565, 30.183499563892102], [2.066021759256456, 3.167233834488799], [4.72037147312491, 13.501139158708172], [-7.9356420663529, 27.51938646945841], [-2.5896620738949387, 2.0583437915374483], [-0.30064582449751853, -0.10512895635486291], [7.055930906584788, 28.421045932541606], [-7.794520375687732, 26.480013755661744], [-3.5090071421677145, 4.402061990808158], [0.621983832204343, 0.5044238598639716], [5.490826728049585, 17.82000244275665], [1.0753156652373814, 1.1158097225711467], [-2.27681967406109, 1.4535440770652794], [0.9993825593894741, 0.9990740297006648], [-7.56578783968987, 24.837678897754618], [1.0945265193234626, 1.1462574104128984], [7.6143880903533265, 32.79664704043395], [-8.753085512984702, 33.931710242318985], [-0.15314904461531498, -0.06484720737436563], [2.9897059133325783, 5.964023680774182], [-9.304793993209973, 38.637198631433215], [-0.635418175139705, -0.11583095892091609], [7.820196744352998, 34.48783693237112], [-0.7128024691025416, -0.10235755457193091], [-1.97451795644451, 0.9621016019386468], [-3.2472040069941954, 3.648564928022482], [-7.990830535049733, 27.931271052416736], [5.877582468238094, 20.21177906958895], [5.442968388218949, 17.534436631684866], [5.940822148379377, 20.617094973527166]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=4.61150, y=20.31086\nx0=-1.13312, y=0.72180\nx0=-8.40902, y=69.72551\nx0=1.02424, y=0.53710\nx0=-0.20786, y=0.00179\nx0=-0.01940, y=0.00000\nx0=-7.10693, y=49.52791\nx0=8.39443, y=69.48036\nx0=0.40693, y=0.02352\nx0=-0.43639, y=0.03047\nx0=0.39593, y=0.02124\nx0=8.37055, y=69.08024\nx0=4.98553, y=23.89423\nx0=-9.34761, y=86.38912\nx0=-2.94225, y=7.76037\nx0=4.71990, y=21.32045\nx0=-4.51660, y=19.44638\nx0=-1.08714, y=0.64020\nx0=8.96010, y=79.29575\nx0=-4.44877, y=18.83962\nx0=-4.81736, y=22.24825\nx0=2.42654, y=5.03328\nx0=4.91444, y=23.19145\nx0=9.25311, y=84.63154\nx0=5.70069, y=31.52772\nx0=-5.56656, y=30.01786\nx0=-2.20086, y=4.01491\nx0=-8.12054, y=64.95816\nx0=-4.55785, y=19.81996\nx0=-5.01871, y=24.22560\nx0=-1.89755, y=2.81805\nx0=6.51250, y=41.43574\nx0=5.85743, y=33.33782\nx0=-0.56598, y=0.07772\nx0=-8.71940, y=75.04098\nx0=3.66678, y=12.51453\nx0=-7.28758, y=52.12730\nx0=7.71364, y=58.51678\nx0=-9.43122, y=87.95899\nx0=7.93993, y=62.05805\nx0=4.91836, y=23.22993\nx0=9.71491, y=93.38998\nx0=7.10499, y=49.50025\nx0=-0.67786, y=0.14466\nx0=7.49342, y=55.16888\nx0=9.45480, y=88.40422\nx0=-1.98887, y=3.15739\nx0=-0.97517, y=0.46353\nx0=6.40935, y=40.10356\nx0=-7.31013, y=52.45638\nx0=-9.05124, y=80.93695\nx0=-2.92146, y=7.63981\nx0=-3.72434, y=12.93794\nx0=1.81797, y=2.53729\nx0=0.55680, y=0.07337\nx0=8.90855, y=78.37476\nx0=-4.63650, y=20.54156\nx0=4.06101, y=15.54900\nx0=-8.42467, y=69.98898\nx0=-1.58506, y=1.79713\nx0=-8.36619, y=69.00715\nx0=9.30459, y=85.58677\nx0=6.86354, y=46.12900\nx0=-1.81942, y=2.54228\nx0=-9.82813, y=95.60236\nx0=3.47959, y=11.18385\nx0=2.78691, y=6.88096\nx0=2.22243, y=4.10755\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-1.11138, y=0.68256\nx0=-8.36857, y=69.04704\nx0=3.44614, y=10.95353\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x0**6 + x0**5) / (x0**4 + x0**3 + x0**2 + x0)", "data": [[4.611502169171949, 20.310863876876173], [-1.1331240577805097, 0.7218042275030843], [-8.409017159163191, 69.72551433435682], [1.0242429559187585, 0.5370990428748058], [-0.2078610440994666, 0.0017894610613817124], [-0.01939796150108819, 1.4153406696215283e-07], [-7.106932719122156, 49.52790694832119], [8.39442502932841, 69.48036416810568], [0.406927618138333, 0.023524631030277406], [-0.4363944322276314, 0.03046556635311226], [0.3959280526578155, 0.021243310636578146], [8.370553956716456, 69.08024493450057], [4.985534360494778, 23.89422927109825], [-9.347609454313554, 86.38911756880984], [-2.9422464564647743, 7.760368030524038], [4.719903237537185, 21.320446536352755], [-4.516596987592763, 19.446378088172725], [-1.0871403618814508, 0.6401957394101653], [8.96010302501185, 79.29574884680945], [-4.448766939596802, 18.83962379766517], [-4.8173581003242365, 22.248249535515708], [2.4265412440768266, 5.033280273963484], [4.914437119384356, 23.191450956653878], [9.253107184961568, 84.63153725528029], [5.700690412960423, 31.527723827725502], [-5.566560768833277, 30.017861885712847], [-2.2008615886679266, 4.0149135050797], [-8.12054300025803, 64.95815665190736], [-4.5578545750074095, 19.81996458023591], [-5.018706062375308, 24.225596828489273], [-1.8975476136503708, 2.8180457908953733], [6.512504104803405, 41.4357444440019], [5.857430697939343, 33.33781537577073], [-0.565983819676628, 0.07771968725154006], [-8.719403773185423, 75.04098445162965], [3.666783254567214, 12.51452610755945], [-7.287579879828026, 52.127301780028105], [7.713640897404964, 58.51678474982694], [-9.431217814764496, 87.95898702024026], [7.939926510903707, 62.05804764579676], [4.918356706007307, 23.229930613798885], [9.714911009367107, 93.38998035360846], [7.1049862480193084, 49.500254290945264], [-0.6778620970796148, 0.14466457317357717], [7.493422478147792, 55.16887782614135], [9.45479560550256, 88.40422272579166], [-1.9888672778089251, 3.1573852439748173], [-0.975174724082926, 0.4635324053592387], [6.409352172655332, 40.10355964729478], [-7.310130988046493, 52.45638457860523], [-9.051236982184072, 80.93695001305977], [-2.9214598907755507, 7.639805456322027], [-3.724338639613314, 12.937944640224423], [1.8179654217663312, 2.5372864049953807], [0.5567987782263195, 0.07336916067561196], [8.908553175172386, 78.37476331766636], [-4.636497662485151, 20.541560726915456], [4.061013931644688, 15.549003686593018], [-8.424671206786813, 69.98897863916072], [-1.5850647088564465, 1.7971333033194776], [-8.366185544292994, 69.00714644531345], [9.304587651702665, 85.58677010630299], [6.863542404992387, 46.129000816079895], [-1.8194163987139884, 2.5422797348269897], [-9.8281284890611, 95.60235632752337], [3.4795918235538092, 11.183851112752397], [2.786914397275959, 6.880957368785621], [2.2224252140808147, 4.107547418855335], [-1.11138279975059, 0.6825646449400015], [-8.368569875046568, 69.04703972488028], [3.446137627262285, 10.953529233823398]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-1.89874, y=-0.68248\nx0=-7.56569, y=-403.29657\nx0=-5.90188, y=-182.59903\nx0=-4.63833, y=-82.01586\nx0=-3.23954, y=-22.07990\nx0=-1.18634, y=1.51993\nx0=0.33317, y=0.80392\nx0=-2.82622, y=-12.41624\nx0=-3.71595, y=-37.38343\nx0=7.84742, y=452.38800\nx0=-1.98811, y=-1.30956\nx0=2.54312, y=7.77114\nx0=-2.16075, y=-2.79346\nx0=-8.81547, y=-650.24536\nx0=0.02552, y=0.99930\nx0=5.62113, y=155.84724\nx0=6.24659, y=219.40371\nx0=1.78985, y=0.51558\nx0=7.90736, y=463.30172\nx0=-0.14728, y=0.98808\nx0=2.03373, y=2.05528\nx0=-4.30979, y=-63.64175\nx0=4.35754, y=66.23333\nx0=6.61279, y=263.33301\nx0=5.45824, y=141.52220\nx0=6.26815, y=221.84836\nx0=-6.74189, y=-280.03120\nx0=4.82099, y=93.60223\nx0=-9.32758, y=-774.63671\nx0=6.69824, y=274.33859\nx0=-1.20902, y=1.51054\nx0=2.73264, y=10.88392\nx0=4.02181, y=49.96019\nx0=-6.97702, y=-312.26656\nx0=8.37181, y=553.75411\nx0=5.28706, y=127.40611\nx0=-6.09637, y=-202.80297\nx0=-1.84552, y=-0.35215\nx0=-7.79778, y=-443.44401\nx0=3.54120, y=31.36219\nx0=0.90941, y=-0.34718\nx0=-6.90043, y=-301.51582\nx0=2.73801, y=10.98061\nx0=-1.01974, y=1.50917\nx0=2.95849, y=15.37657\nx0=6.28437, y=223.69872\nx0=2.77472, y=11.65467\nx0=4.74036, y=88.40986\nx0=-0.25956, y=0.98493\nx0=-9.91878, y=-936.54593\nx0=-1.42603, y=1.25352\nx0=-2.15449, y=-2.73305\nx0=1.83220, y=0.73340\nx0=-4.08133, y=-52.52636\nx0=3.97079, y=47.73170\nx0=7.31029, y=361.97854\nx0=-9.00585, y=-694.82678\nx0=5.83120, y=175.64775\nx0=3.43489, y=27.93866\nx0=4.08221, y=52.67976\nx0=5.67543, y=160.82046\nx0=-9.55977, y=-835.82334\nx0=3.71127, y=37.34476\nx0=-6.14134, y=-207.67094\nx0=-2.17351, y=-2.91811\nx0=9.73541, y=884.17927\nx0=6.37421, y=234.12683\nx0=2.64837, y=9.42852\nx0=-1.73242, y=0.24825\nx0=0.56225, y=0.39735\nx0=1.44105, y=-0.57310\nx0=9.18387, y=738.30511\nx0=-4.22802, y=-59.51138\nx0=-7.41541, y=-378.61085\nx0=-0.92489, y=1.45343\nx0=5.00949, y=106.48162\nx0=6.73043, y=278.56152\nx0=-8.95125, y=-681.84138\nx0=5.17345, y=118.55283\nx0=0.05701, y=0.99621\nx0=0.82609, y=-0.18219\nx0=6.52637, y=252.49719\nx0=8.03250, y=486.64079\nx0=-6.81206, y=-289.41400\nx0=4.76627, y=90.05757\nx0=2.12585, y=2.82572\nx0=-3.53179, y=-30.90120\nx0=-6.54436, y=-254.68303\nx0=-1.72753, y=0.27120\nx0=9.13282, y=725.66734\nx0=5.21581, y=121.80619\nx0=-1.33461, y=1.40133\nx0=6.76012, y=282.49281\nx0=5.06490, y=110.46895\nx0=5.31873, y=129.94635\nx0=-0.13288, y=0.98953\nx0=2.74700, y=11.14361\nx0=5.02962, y=107.91925\nx0=7.81826, y=447.13833\nx0=-9.21539, y=-746.15875\nx0=-9.26258, y=-758.05169\nx0=2.67961, y=9.95451\nx0=-0.83600, y=1.38000\nx0=-1.84014, y=-0.32051\nx0=-1.81921, y=-0.20037\nx0=-5.30390, y=-128.68387\nx0=0.26351, y=0.88493\nx0=4.80831, y=92.77324\nx0=7.35039, y=368.27997\nx0=2.81196, y=12.36171\nx0=0.31522, y=0.82698\nx0=3.86910, y=43.47557\nx0=-6.91191, y=-303.11113\nx0=4.85458, y=95.82073\nx0=-8.84001, y=-655.88413\nx0=-0.74869, y=1.29684\nx0=7.88023, y=458.34151\nx0=-5.15514, y=-117.09117\nx0=-3.80279, y=-40.70102\nx0=-3.88019, y=-43.80333\nx0=3.02658, y=16.90757\nx0=4.30290, y=63.38974\nx0=-8.61832, y=-606.10191\nx0=3.33740, y=25.00532\nx0=4.09750, y=53.38239\nx0=4.73238, y=87.90603\nx0=6.65645, y=268.91949\nx0=9.17480, y=736.04990\nx0=0.88643, y=-0.30367\nx0=5.76493, y=169.23713\nx0=6.46063, y=244.45092\nx0=3.65620, y=35.33819\nx0=0.62196, y=0.26772\nx0=-7.45995, y=-385.82164\nx0=8.49176, y=578.85147\nx0=-4.93296, y=-101.04679\nx0=-0.86530, y=1.40590\nx0=0.01189, y=0.99985\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.71178, y=-428.27849\nx0=4.78006, y=90.94258\nx0=-2.84528, y=-12.79452\nx0=-5.81842, y=-174.34181\nx0=-2.32973, y=-4.62020\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x0**5 - 3 * x0**3 + 1) / (x0**2 + 1)", "data": [[-1.8987419329888748, -0.6824796898579557], [-7.5656859254782365, -403.2965734287967], [-5.901882262566385, -182.59902583737625], [-4.638330050436405, -82.01586135670311], [-3.2395397721187535, -22.079899905145954], [-1.1863405017147564, 1.5199337962544408], [0.3331717842252466, 0.8039179656476901], [-2.826223082883872, -12.416244671289673], [-3.715953198335839, -37.38343267204933], [7.847421662574519, 452.38799982657764], [-1.9881144799757084, -1.3095615894075678], [2.5431156668955968, 7.771135989745552], [-2.1607510881499454, -2.7934552629193132], [-8.815468460439268, -650.2453581798984], [0.025515783325495534, 0.9992995750818692], [5.621128823270567, 155.84724204046506], [6.246585541331463, 219.4037061475273], [1.789852091547763, 0.5155751467939838], [7.907355802957319, 463.3017231752992], [-0.14727551953564522, 0.9880823810761122], [2.0337285405377408, 2.0552792332724907], [-4.3097900630244235, -63.641748692049056], [4.357535987801224, 66.23332669176719], [6.612788500534915, 263.33300954503875], [5.4582360701491, 141.5221997171909], [6.268150658876294, 221.84836383747052], [-6.741890602428555, -280.0311966142717], [4.820994296656522, 93.60223398744594], [-9.327580007875191, -774.636707612799], [6.698236592815768, 274.3385928201704], [-1.2090163304654347, 1.5105350772174302], [2.7326382875298982, 10.883922608052229], [4.021808649680597, 49.960191494605795], [-6.977019837575023, -312.2665555088258], [8.371807391185179, 553.7541062114826], [5.287062135853821, 127.40610875746154], [-6.096367157078124, -202.80297392479292], [-1.8455167270428845, -0.3521544412465667], [-7.797778465665218, -443.4440142339331], [3.541200165963904, 31.362190526113515], [0.9094113686392546, -0.3471824079711101], [-6.900429576301892, -301.515823021822], [2.7380067080067345, 10.98060541420277], [-1.01973510341573, 1.5091706562793354], [2.958486193872945, 15.376567114413769], [6.284371532816216, 223.69872117281164], [2.7747179355521396, 11.654672323911647], [4.74036223566462, 88.4098642637713], [-0.2595628281298996, 0.9849269425869461], [-9.918781829815998, -936.5459329603071], [-1.4260258861580404, 1.2535161585904657], [-2.1544878161362435, -2.733053915874921], [1.8321956105550719, 0.733402182074792], [-4.081329907618507, -52.52636190266947], [3.970785516077708, 47.731698166233656], [7.3102888589646255, 361.9785357259492], [-9.005854763843237, -694.8267807406083], [5.831199357432901, 175.6477461610174], [3.434893576597558, 27.938661298120586], [4.08220702975135, 52.67976295009012], [5.67543026302066, 160.82045600499913], [-9.559768517986427, -835.8233430480168], [3.711270936101638, 37.34475697260805], [-6.141344597007876, -207.670942299465], [-2.173513662642133, -2.9181117319743466], [9.735407060883048, 884.1792710624968], [6.374205865471744, 234.12682682119652], [2.648370959579916, 9.428519976355124], [-1.7324219842631905, 0.24824864404013988], [0.5622524391814707, 0.39734652854423697], [1.441050686634462, -0.5731004723955525], [9.183865906399909, 738.3051079949613], [-4.22801500522916, -59.51137846807714], [-7.415408397269115, -378.6108542757751], [-0.9248948684800595, 1.4534349446762072], [5.009493806548253, 106.48161937136337], [6.730433907091971, 278.5615215537675], [-8.951248071091232, -681.8413754012073], [5.173450557929115, 118.55283214438427], [0.05700665642640956, 0.9962073945564579], [0.8260922318762773, -0.18219389305435152], [6.5263692877799215, 252.4971855355983], [8.032498790234136, 486.64079405646265], [-6.812064404356981, -289.4139989235674], [4.766265522646702, 90.05756986359471], [2.125853786443212, 2.8257245449102424], [-3.5317943504627696, -30.90120222549724], [-6.5443593953848955, -254.68302603334286], [-1.7275342489448455, 0.27119903815597324], [9.13282025651505, 725.6673365136738], [5.215808090304366, 121.80618624506052], [-1.3346116512198964, 1.401326458040947], [6.760124604229365, 282.492808376383], [5.064899385778611, 110.46894623778208], [5.31872726044444, 129.94634502446965], [-0.13287604907418427, 0.9895256649455132], [2.746998032354151, 11.143610952026094], [5.029619602536567, 107.91925091446387], [7.818255878019304, 447.1383283548934], [-9.215392288927218, -746.1587500285015], [-9.262580067848463, -758.0516928799626], [2.6796103181724877, 9.954513134820765], [-0.8359962996389587, 1.3800000532947687], [-1.840138148260479, -0.3205132039997432], [-1.8192067710760629, -0.20036674868786403], [-5.30389541865897, -128.68387354637724], [0.2635146861900104, 0.8849260194836185], [4.808313567784197, 92.77323753752518], [7.350393022759366, 368.27997434053094], [2.8119593172945656, 12.361711178795801], [0.315219026224554, 0.8269777825629494], [3.8691019836860523, 43.47556909751994], [-6.911905537933302, -303.11112558513577], [4.8545842971072695, 95.82072509150208], [-8.840012533013146, -655.8841280682351], [-0.7486884151377602, 1.2968376837129447], [7.880231689058018, 458.34150931936546], [-5.155139294477786, -117.09116920144112], [-3.8027919452712355, -40.70101696746744], [-3.880191231670967, -43.80333313674066], [3.0265750271387724, 16.90757079233035], [4.302902937432407, 63.38973513429863], [-8.618324585785784, -606.1019073844272], [3.3373994295264158, 25.00532283268678], [4.097496564131195, 53.38238590723942], [4.732380903369865, 87.90603242371819], [6.656445334996171, 268.91948858723003], [9.17479908997915, 736.0498995644173], [0.8864344451300443, -0.3036683077911402], [5.764929586048579, 169.237126559256], [6.460633152548219, 244.45092419801003], [3.656204500474587, 35.33819331708229], [0.6219617603699561, 0.26771683666208557], [-7.4599486133867465, -385.82164215604445], [8.49175772030408, 578.851466841713], [-4.932961859450467, -101.04679471160385], [-0.8652997641014011, 1.4059014903195837], [0.011894406930906598, 0.999853495696775], [-7.711782994477225, -428.2784908085735], [4.780055452770558, 90.94258426930672], [-2.845280588949377, -12.794524539467686], [-5.818415650196336, -174.34180888985927], [-2.3297252532164254, -4.620204662160901]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.16226, x1=4.37818, y=2868.31717\nx0=9.32922, x1=-1.96396, y=0.01245\nx0=2.36729, x1=-2.67094, y=0.10009\nx0=4.27528, x1=1.90902, y=16.01484\nx0=9.58359, x1=-3.26776, y=0.00062\nx0=8.00037, x1=-6.53078, y=0.00000\nx0=0.44497, x1=2.28185, y=0.15760\nx0=0.03399, x1=-5.98093, y=608374511.26232\nx0=7.90062, x1=-6.96775, y=0.00000\nx0=9.02984, x1=-0.56420, y=0.28894\nx0=7.88995, x1=-4.46112, y=0.00010\nx0=1.66649, x1=-8.20250, y=0.01516\nx0=8.73410, x1=6.57487, y=1543076.64295\nx0=2.04865, x1=2.51621, y=6.07744\nx0=8.61675, x1=-6.20926, y=0.00000\nx0=6.21788, x1=-1.62038, y=0.05176\nx0=3.77672, x1=-1.45170, y=0.14528\nx0=3.07456, x1=-7.95541, y=0.00013\nx0=2.82427, x1=-3.90478, y=0.01735\nx0=8.17110, x1=-2.98058, y=0.00191\nx0=7.39474, x1=7.17373, y=1711675.64398\nx0=5.37758, x1=8.96666, y=3555742.96935\nx0=1.51922, x1=9.88886, y=62.52125\nx0=2.25870, x1=-3.40025, y=0.06263\nx0=8.67250, x1=-1.93218, y=0.01539\nx0=9.09430, x1=7.20832, y=8149228.05400\nx0=9.44887, x1=-4.58658, y=0.00003\nx0=0.61601, x1=0.78237, y=0.68451\nx0=4.48722, x1=3.67771, y=249.90984\nx0=7.80395, x1=-5.75461, y=0.00001\nx0=5.93191, x1=-7.15890, y=0.00000\nx0=3.23385, x1=1.98015, y=10.21699\nx0=4.01378, x1=6.26451, y=6039.06494\nx0=3.17545, x1=-2.96032, y=0.03270\nx0=3.96310, x1=3.51805, y=127.03294\nx0=4.78570, x1=3.85881, y=420.51274\nx0=8.31351, x1=-5.36749, y=0.00001\nx0=2.58100, x1=-5.08579, y=0.00805\nx0=0.45715, x1=-8.68248, y=894.32968\nx0=7.96743, x1=-7.81377, y=0.00000\nx0=8.04597, x1=8.31356, y=33773985.18126\nx0=0.97540, x1=-3.76857, y=1.09841\nx0=6.18430, x1=-7.23239, y=0.00000\nx0=1.31139, x1=-4.71416, y=0.27861\nx0=9.70617, x1=-7.95683, y=0.00000\nx0=2.94810, x1=-9.96566, y=0.00002\nx0=6.69303, x1=-9.86326, y=0.00000\nx0=3.12259, x1=8.61248, y=18155.19190\nx0=7.67482, x1=8.98158, y=88984278.71489\nx0=7.66344, x1=8.98808, y=88976121.95153\nx0=1.84506, x1=-3.49632, y=0.11747\nx0=2.69824, x1=-4.94573, y=0.00738\nx0=7.66423, x1=-4.25240, y=0.00017\nx0=6.13415, x1=2.53360, y=99.05044\nx0=5.32106, x1=6.29449, y=37135.43754\nx0=9.75684, x1=-7.47427, y=0.00000\nx0=2.21127, x1=-2.72175, y=0.11534\nx0=9.28406, x1=2.30117, y=168.62845\nx0=3.27326, x1=1.14327, y=3.87935\nx0=2.38432, x1=-3.05807, y=0.07014\nx0=9.61876, x1=-2.69888, y=0.00222\nx0=8.82879, x1=9.42278, y=818497825.15721\nx0=5.07282, x1=5.28028, y=5295.61354\nx0=9.41626, x1=-6.44297, y=0.00000\nx0=9.85433, x1=2.11268, y=125.66467\nx0=2.89391, x1=-4.72413, y=0.00661\nx0=9.96654, x1=4.36508, y=22841.56796\nx0=5.07508, x1=4.65155, y=1911.62692\nx0=6.12886, x1=1.82715, y=27.45735\nx0=9.47843, x1=8.00117, y=65318463.16949\nx0=2.49249, x1=3.48892, y=24.20040\nx0=4.13196, x1=6.86082, y=16878.57851\nx0=6.74378, x1=3.17458, y=427.97484\nx0=1.63990, x1=-7.73853, y=0.02176\nx0=9.66875, x1=-9.83862, y=0.00000\nx0=7.85846, x1=2.83267, y=343.71570\nx0=7.99959, x1=6.85206, y=1541242.45227\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=7.48525, x1=-7.06527, y=0.00000\nx0=7.87478, x1=1.10191, y=9.71785\nx0=3.58154, x1=-8.98225, y=0.00001\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 ** x1", "data": [[6.16225773330504, 4.37818496300884, 2868.317173693974], [9.329223759485423, -1.9639604964042245, 0.01245264855544794], [2.367288265264042, -2.6709393145442277, 0.10009166242618577], [4.275279456219206, 1.9090179247855268, 16.01483820813419], [9.58359208671149, -3.2677587247794238, 0.0006203006951710833], [8.000370376769617, -6.530777604896447, 1.2647038167771572e-06], [0.4449744422038755, 2.281851920480733, 0.15759872440061293], [0.03398618464665759, -5.980925607640559, 608374511.2623158], [7.900621432947517, -6.967745484440462, 5.563202399941509e-07], [9.029840606297498, -0.5641983030955533, 0.28893950082189174], [7.889946491143792, -4.461117041886748, 9.955145974695376e-05], [1.6664921558692214, -8.202501862720728, 0.015158569999687949], [8.734095247821376, 6.574872132794962, 1543076.6429503416], [2.04865455716571, 2.5162106070816392, 6.077443535141041], [8.61675288214613, -6.209258286800454, 1.5567173442650594e-06], [6.21787685724825, -1.6203768127394298, 0.051760768578536655], [3.7767229825348743, -1.45169696783951, 0.14527929179908525], [3.07455607010332, -7.955406283893234, 0.00013167177492290886], [2.8242745619174663, -3.904778451817352, 0.017350356269459112], [8.1711003242139, -2.980582696463559, 0.0019092922068391373], [7.394744126193025, 7.1737316046998885, 1711675.6439846305], [5.377584680956925, 8.966663856546315, 3555742.9693471096], [1.5192222670579465, 9.888859234577886, 62.52124815676004], [2.25870077933552, -3.4002489689125266, 0.06263142809002223], [8.672499998714997, -1.9321813869019184, 0.015393416809655268], [9.094296691471936, 7.208321939417274, 8149228.053999103], [9.448868962824527, -4.586584685414032, 3.359988775574777e-05], [0.6160137963423331, 0.7823734191378726, 0.6845121357794234], [4.487224732368917, 3.677706935619602, 249.90983808823356], [7.803952875185189, -5.754611466239106, 7.3295270417745e-06], [5.93190825449464, -7.158897322247412, 2.9159528566522613e-06], [3.2338546141582114, 1.980149724007985, 10.216988158836612], [4.013782375429344, 6.264511240192537, 6039.064939442768], [3.175446531079565, -2.9603204302636037, 0.032696177739791325], [3.9630964444374754, 3.518050946820477, 127.03293610450235], [4.785696323450727, 3.8588101011910325, 420.5127448002941], [8.313511755468618, -5.367486499611598, 1.1562960231857144e-05], [2.5810014959821643, -5.085792290294668, 0.008048787491184966], [0.4571544547333257, -8.682483114905715, 894.3296798650626], [7.967429695137181, -7.813773669571669, 9.063652970727084e-08], [8.045971922993953, 8.313561113270453, 33773985.181263305], [0.9753994765213001, -3.7685696443988963, 1.0984149459040804], [6.184297153122277, -7.232386399643715, 1.8927028715685597e-06], [1.3113920954042655, -4.714163831474334, 0.2786053273108001], [9.706173215914596, -7.9568340831564965, 1.4003046595003986e-08], [2.9481039530581032, -9.965664696047295, 2.0926373064327283e-05], [6.693029082071753, -9.863260045112463, 7.189000133451265e-09], [3.122590727435412, 8.612479454746278, 18155.191897412427], [7.674823914937036, 8.981580523575943, 88984278.71488601], [7.66343641943352, 8.988084267845402, 88976121.9515317], [1.8450552463179015, -3.4963233745454563, 0.11747493280643781], [2.6982423105429767, -4.94572720875357, 0.007378893223185938], [7.664226854474126, -4.2524046741427775, 0.0001733335572992851], [6.134153377556821, 2.533601608186009, 99.05043781451054], [5.321057979960228, 6.29449199699955, 37135.43753601693], [9.756838833467047, -7.474267135478643, 4.0331026297256e-08], [2.211272529343331, -2.721748483561857, 0.11533747044346727], [9.284063029164077, 2.3011710569271777, 168.62845495820744], [3.2732554564319685, 1.1432659352776593, 3.879350121687813], [2.3843212671984855, -3.0580673127193414, 0.0701444192900295], [9.618757356462059, -2.6988829376364425, 0.0022216568907692347], [8.828793924117882, 9.422776749211245, 818497825.1572086], [5.0728214981301925, 5.280281457648957, 5295.613539638652], [9.41625869946865, -6.442966524033102, 5.312931155352792e-07], [9.854331604070051, 2.112676930389199, 125.66467276069407], [2.893910492735598, -4.7241294139051915, 0.006605180515807751], [9.966537602103202, 4.365080117986706, 22841.567964966896], [5.075080105412912, 4.65155029768159, 1911.6269247411385], [6.128855274588222, 1.8271479972910285, 27.457350773306512], [9.478433203516545, 8.001170763031489, 65318463.16949082], [2.492488436418853, 3.488922938919849, 24.200397686167456], [4.1319610344113435, 6.860818326853767, 16878.578509887415], [6.743781664600061, 3.1745773052534823, 427.9748448677137], [1.6399047217747764, -7.738532580874471, 0.021758008321401342], [9.668749031453363, -9.838616048750914, 2.0198544480960628e-10], [7.858463960135179, 2.8326736038779554, 343.71570192564724], [7.999587408783238, 6.852057414050783, 1541242.4522714037], [7.4852462489054865, -7.065265596766713, 6.660422383234825e-07], [7.87478131252092, 1.1019055206525579, 9.717849148849325], [3.5815383902038285, -8.982252618612527, 1.0548890603448607e-05]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.26639, x1=-6.39053, y=-2.30511\nx0=-1.50347, x1=6.41442, y=-1.53487\nx0=8.09280, x1=1.68958, y=2.17620\nx0=8.10572, x1=-8.64242, y=-11.14929\nx0=8.51532, x1=0.36761, y=0.49820\nx0=-0.79831, x1=-7.01088, y=0.89076\nx0=-5.77807, x1=2.18587, y=-2.01014\nx0=-6.22383, x1=8.45337, y=-8.37351\nx0=-0.34049, x1=5.82328, y=-0.31556\nx0=-3.39093, x1=6.89294, y=-3.72000\nx0=-3.46677, x1=-6.74844, y=3.72348\nx0=3.73354, x1=4.92230, y=2.92488\nx0=7.64500, x1=-4.10263, y=-4.99184\nx0=-2.33964, x1=-0.60393, y=0.22488\nx0=8.55778, x1=-6.57673, y=-8.95759\nx0=3.46790, x1=-1.00013, y=-0.55201\nx0=-1.15069, x1=-7.00020, y=1.28200\nx0=6.89807, x1=-6.00257, y=-6.58999\nx0=-5.99452, x1=-6.54636, y=6.24560\nx0=-9.59552, x1=-6.46021, y=9.86587\nx0=-9.74021, x1=-0.65566, y=1.01641\nx0=3.44393, x1=2.55971, y=1.40302\nx0=-8.33661, x1=5.86479, y=-7.78148\nx0=-8.58774, x1=-8.35579, y=11.42053\nx0=-9.13885, x1=-5.14119, y=7.47783\nx0=1.32243, x1=-8.92603, y=-1.87868\nx0=-0.24965, x1=2.95413, y=-0.11738\nx0=-4.58312, x1=2.11192, y=-1.54049\nx0=4.94670, x1=-8.58892, y=-6.76199\nx0=-0.26327, x1=2.21667, y=-0.09288\nx0=7.75027, x1=-6.48811, y=-8.00304\nx0=9.55484, x1=-7.88779, y=-11.99496\nx0=4.72027, x1=-4.40176, y=-3.30684\nx0=-8.31715, x1=-8.45680, y=11.19440\nx0=-0.02916, x1=7.37302, y=-0.03422\nx0=-3.32139, x1=5.57345, y=-2.94622\nx0=-6.65818, x1=-0.91311, y=0.96760\nx0=7.75647, x1=2.93217, y=3.61971\nx0=1.35279, x1=1.64574, y=0.35433\nx0=-5.52404, x1=8.24118, y=-7.24547\nx0=-5.10280, x1=7.33619, y=-5.95799\nx0=0.11986, x1=6.77309, y=0.12920\nx0=6.08200, x1=8.14027, y=7.87962\nx0=-3.87925, x1=-3.40195, y=2.10037\nx0=-4.74338, x1=-2.05595, y=1.55211\nx0=-5.64523, x1=3.97262, y=-3.56927\nx0=-8.60468, x1=-0.12565, y=0.17208\nx0=2.18975, x1=4.14792, y=1.44559\nx0=5.62217, x1=-9.27292, y=-8.29737\nx0=7.68417, x1=-1.15974, y=-1.41833\nx0=-4.59579, x1=8.02037, y=-5.86644\nx0=-8.45165, x1=-5.16040, y=6.94137\nx0=5.37877, x1=0.96351, y=0.82482\nx0=3.29350, x1=-8.46731, y=-4.43838\nx0=-9.23881, x1=-6.85023, y=10.07259\nx0=5.69683, x1=7.82512, y=7.09487\nx0=4.06844, x1=-9.07551, y=-5.87651\nx0=-2.91869, x1=0.95989, y=-0.44589\nx0=-5.57627, x1=-5.65892, y=5.02224\nx0=-4.30024, x1=-7.27047, y=4.97595\nx0=-2.59354, x1=3.18821, y=-1.31601\nx0=-7.41243, x1=-8.24615, y=9.72820\nx0=7.45743, x1=-4.87670, y=-5.78809\nx0=2.06204, x1=8.31496, y=2.72883\nx0=-1.21611, x1=-4.58952, y=0.88830\nx0=-8.53145, x1=-9.21971, y=12.51872\nx0=7.56856, x1=-2.10281, y=-2.53299\nx0=9.74503, x1=3.34105, y=5.18187\nx0=8.29936, x1=-1.06553, y=-1.40745\nx0=-5.94640, x1=-8.22561, y=7.78471\nx0=-3.44610, x1=8.82769, y=-4.84167\nx0=9.03802, x1=-1.23873, y=-1.78185\nx0=-8.03151, x1=-3.91837, y=5.00867\nx0=-2.59207, x1=9.75172, y=-4.02298\nx0=-3.55564, x1=-9.29067, y=5.25757\nx0=2.53329, x1=-8.24492, y=-3.32424\nx0=3.22443, x1=3.27226, y=1.67927\nx0=-1.53321, x1=-9.19124, y=2.24282\nx0=0.53791, x1=3.98956, y=0.34155\nx0=-7.47079, x1=-3.61934, y=4.30344\nx0=-9.10734, x1=6.61743, y=-9.59183\nx0=5.85579, x1=7.79362, y=7.26348\nx0=-8.40068, x1=0.51890, y=-0.69378\nx0=-4.05437, x1=-8.89337, y=5.73865\nx0=2.40289, x1=-5.43545, y=-2.07869\nx0=0.53431, x1=-9.61536, y=-0.81767\nx0=1.47278, x1=4.21238, y=0.98739\nx0=-3.45374, x1=-9.57543, y=5.26343\nx0=3.92094, x1=-3.92076, y=-2.44670\nx0=-4.13830, x1=3.71803, y=-2.44881\nx0=1.18057, x1=3.75896, y=0.70629\nx0=-7.74243, x1=-1.80092, y=2.21917\nx0=-5.81402, x1=2.71005, y=-2.50769\nx0=5.95627, x1=-8.24636, y=-7.81730\nx0=0.84689, x1=5.96215, y=0.80362\nx0=-0.71804, x1=8.14346, y=-0.93064\nx0=-9.13271, x1=-4.20967, y=6.11883\nx0=6.27994, x1=4.65683, y=4.65442\nx0=6.72849, x1=-5.89511, y=-6.31291\nx0=-2.70153, x1=-4.22043, y=1.81462\nx0=6.47620, x1=8.05164, y=8.29898\nx0=-7.81303, x1=-3.87016, y=4.81248\nx0=-6.28009, x1=1.31489, y=-1.31424\nx0=-9.80365, x1=-8.89454, y=13.87815\nx0=1.99044, x1=0.59700, y=0.18912\nx0=7.62115, x1=6.18711, y=7.50461\nx0=-0.08756, x1=5.69619, y=-0.07938\nx0=-6.20120, x1=2.97111, y=-2.93234\nx0=7.82902, x1=-2.89137, y=-3.60273\nx0=8.57779, x1=8.54358, y=11.66367\nx0=4.36317, x1=3.64448, y=2.53080\nx0=-7.81138, x1=4.11286, y=-5.11318\nx0=-3.48913, x1=-8.67504, y=4.81735\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-2.29011, x1=3.66965, y=-1.33752\nx0=2.56746, x1=8.19858, y=3.35014\nx0=3.98930, x1=3.77910, y=2.39941\nx0=6.75894, x1=0.89962, y=0.96774\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x1 / (2 * pi)) * x0", "data": [[2.2663948610325058, -6.390530152709976, -2.3051149996842195], [-1.5034680881373408, 6.414424832968731, -1.5348716564358582], [8.092804846750216, 1.6895812846919789, 2.1761974128169523], [8.10571788167902, -8.642422536967555, -11.149287419372529], [8.515320719596946, 0.36760739895905203, 0.4982019068347822], [-0.7983068421543926, -7.010878265646365, 0.8907634926160306], [-5.778066311241821, 2.185865178685253, -2.010138700739238], [-6.223826504999739, 8.453371399011282, -8.373510313257004], [-0.34048717333253364, 5.823281901296626, -0.3155649081088481], [-3.3909267491217143, 6.892939854587237, -3.7200007623997555], [-3.4667725576592616, -6.748436214879141, 3.7234766019273575], [3.7335352105573527, 4.9223015436776425, 2.924883674734507], [7.644997032961641, -4.102634195313084, -4.991835305996177], [-2.3396433208652017, -0.6039285567420638, 0.22488233992506448], [8.557779337189583, -6.5767268169651105, -8.957586655331154], [3.4679034572994265, -1.0001327966290763, -0.5520072723663481], [-1.150692055236238, -7.000195552525477, 1.2820041131345998], [6.898067467102365, -6.002567553888552, -6.589988029678109], [-5.994515877243806, -6.546358481278018, 6.245598042335297], [-9.595515053014626, -6.4602125994583055, 9.865866469502988], [-9.740206775259658, -0.6556614980146147, 1.0164078016195797], [3.44392953136175, 2.5597050809117388, 1.4030214753742087], [-8.336614570857854, 5.864787742199727, -7.781479067749758], [-8.58773914213345, -8.3557867383178, 11.420531677456127], [-9.1388543779399, -5.141190031630698, 7.477829274699483], [1.322432621319665, -8.926033111698462, -1.8786772614204772], [-0.2496524354480183, 2.954131651074194, -0.11737775113556244], [-4.583123005538479, 2.111917743691416, -1.5404891505996123], [4.946701718970033, -8.58891994578151, -6.761988224562646], [-0.2632746271979851, 2.2166663990848985, -0.09288155470673858], [7.750270024393959, -6.488105766724573, -8.003038137596315], [9.554835294786326, -7.887793444986208, -11.99496171472447], [4.72026953587806, -4.401755419186273, -3.3068373752767406], [-8.317150693113796, -8.456802679908193, 11.194402016180211], [-0.02916452904469935, 7.373019590172362, -0.03422318990640158], [-3.3213928170742406, 5.573451240360733, -2.946215973432304], [-6.658176857488423, -0.9131075429056583, 0.9676034070848712], [7.756473171508045, 2.932171440349274, 3.619710067335309], [1.3527923397886017, 1.6457403460349553, 0.3543338011777498], [-5.524043162739383, 8.241184148317274, -7.24547418573963], [-5.102802775420576, 7.3361907030196605, -5.957986666031873], [0.11985640363718275, 6.773092511747166, 0.129201745654761], [6.081996014827528, 8.14026946750801, 7.879615838233122], [-3.8792452001480253, -3.401953835460885, 2.1003698668980872], [-4.743379782748214, -2.0559547977697523, 1.5521067651532976], [-5.645229975930636, 3.972620005946405, -3.5692650215050232], [-8.60468390867448, -0.12565462137114736, 0.1720812367776936], [2.1897491846368577, 4.147916702595744, 1.44558798975289], [5.6221734013613265, -9.272916320060784, -8.2973748089402], [7.6841726241936605, -1.1597423124680066, -1.4183347606193708], [-4.595794298528113, 8.020367126500709, -5.866444440203859], [-8.451650846245114, -5.160398183168309, 6.9413651737917155], [5.37877043533307, 0.9635074913360526, 0.8248182021145295], [3.29350485489077, -8.4673132148831, -4.438375731053574], [-9.238812586732998, -6.8502273157427584, 10.072592682305478], [5.696830878931307, 7.825123992720929, 7.094873987284851], [4.068442569248186, -9.07550853247156, -5.8765074474075325], [-2.918686934818558, 0.9598909225678689, -0.44589184586812236], [-5.576274699188519, -5.658920477762566, 5.022244855457242], [-4.300243817351563, -7.270469268480797, 4.975945956154414], [-2.593540535407519, 3.1882092676259415, -1.3160124310676264], [-7.412434790713871, -8.246154579491014, 9.728199966469116], [7.45743031514138, -4.876698382843168, -5.7880894132566], [2.0620371669225612, 8.314962093126898, 2.7288325967384712], [-1.2161100092382267, -4.589522926292712, 0.8883017920727635], [-8.531446302468211, -9.219705714735964, 12.518717877053533], [7.5685647312535025, -2.102808876544991, -2.532989928118052], [9.745027367793636, 3.3410518221712096, 5.181868726213049], [8.299362937695022, -1.0655333528236195, -1.4074466349412578], [-5.946395921085676, -8.22561467418623, 7.784707780480787], [-3.4461021403386134, 8.827688857390001, -4.841671219044553], [9.038017062376266, -1.2387347680294258, -1.7818519464029967], [-8.031514925542, -3.9183668336104933, 5.008673175997407], [-2.5920706836956526, 9.751721773737877, -4.0229837080213375], [-3.5556434547046356, -9.290668886352568, 5.257573093991088], [2.5332928363822376, -8.244919123429037, -3.3242365982851174], [3.2244324771308523, 3.272257107361426, 1.6792711936160736], [-1.5332075251086899, -9.191235819600232, 2.2428229050569417], [0.5379129383281605, 3.989564738357604, 0.34155263391772817], [-7.470791293590546, -3.6193354219553875, 4.303438182545924], [-9.107344423370368, 6.617431774684228, -9.591827619876009], [5.855788935938984, 7.793619009292431, 7.263479546495245], [-8.400680827922457, 0.5189012018099639, -0.6937760330973942], [-4.0543722658653785, -8.893365365528236, 5.73865199344101], [2.402888201153445, -5.435452764679227, -2.078688543731229], [0.534308202075767, -9.615362239445238, -0.8176691692658944], [1.4727844256402793, 4.212380528652297, 0.9873858774116445], [-3.4537417232299994, -9.575433654208041, 5.263425016570782], [3.9209382193257127, -3.9207603831746107, -2.446698367727779], [-4.138302304169477, 3.7180270545387906, -2.448808872337554], [1.1805739141693135, 3.7589569859194114, 0.7062861184422051], [-7.7424251694528845, -1.800916560208993, 2.2191708539797306], [-5.814017861063214, 2.7100526224190897, -2.5076921307989433], [5.956273820728054, -8.246355832104712, -7.817301409692376], [0.8468890330242438, 5.962150627535847, 0.8036178678239965], [-0.7180442007416907, 8.143463789614596, -0.930637353859534], [-9.132706720847931, -4.209673878338823, 6.118825888733904], [6.279935044712676, 4.65683141604886, 4.654422458867696], [6.728490827348725, -5.895107339343166, -6.312908774739235], [-2.701530333163138, -4.220428663602536, 1.8146235541780327], [6.476195407142985, 8.051643816835647, 8.298978329822454], [-7.81302749085304, -3.870164840850361, 4.812480106411175], [-6.280086539735022, 1.3148896513262578, -1.314241168582948], [-9.803646078418398, -8.89454399033091, 13.878145724985734], [1.9904431334841064, 0.5969952110165089, 0.18912143449484], [7.621148433595902, 6.187109029420064, 7.504613342244063], [-0.0875596172489086, 5.696192378727291, -0.07937955035125249], [-6.201200995147023, 2.9711120677038387, -2.9323443779201215], [7.82902149487769, -2.891369446715819, -3.6027257579216516], [8.57779277533244, 8.543575808478685, 11.663673640459582], [4.36317208315449, 3.6444756608342193, 2.5307982629316683], [-7.811375544936294, 4.112856089150231, -5.113180959014517], [-3.4891273723932414, -8.675038502540417, 4.817351839232316], [-2.290109998063312, 3.669645668613379, -1.3375209904184076], [2.5674629909532953, 8.19858111980885, 3.3501405058649194], [3.9893020286163594, 3.7790953157709044, 2.3994123796273623], [6.758943550308757, 0.8996188554570814, 0.967737343967849]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.20389, y=1390.20309\nx0=7.00263, y=1280.50331\nx0=5.96344, y=804.94438\nx0=0.18985, y=0.43755\nx0=9.61391, y=3225.37100\nx0=-3.12147, y=-88.00426\nx0=8.81819, y=2505.09177\nx0=-5.53311, y=-519.20364\nx0=8.90144, y=2574.83205\nx0=9.67214, y=3282.92537\nx0=-3.27221, y=-101.89929\nx0=5.00874, y=488.07629\nx0=7.66426, y=1664.36965\nx0=8.06472, y=1930.38475\nx0=1.84452, y=31.77026\nx0=3.00013, y=115.96430\nx0=2.56451, y=75.68363\nx0=7.38438, y=1493.77356\nx0=3.26796, y=146.77033\nx0=2.34367, y=59.45657\nx0=4.08329, y=273.41271\nx0=-9.25293, y=-2520.53769\nx0=-2.97680, y=-75.93582\nx0=-2.26255, y=-32.43895\nx0=3.21202, y=139.92959\nx0=-7.20140, y=-1168.92511\nx0=-2.75725, y=-59.85135\nx0=-9.15874, y=-2442.86792\nx0=-0.45622, y=-0.69272\nx0=-4.01268, y=-192.03706\nx0=-0.39191, y=-0.57605\nx0=7.66945, y=1667.64775\nx0=-9.53701, y=-2764.75859\nx0=1.04421, y=8.03012\nx0=-1.90723, y=-19.20186\nx0=9.72704, y=3337.80819\nx0=-4.70880, y=-315.31624\nx0=-2.49157, y=-43.70895\nx0=8.61004, y=2336.27908\nx0=-5.50298, y=-510.52383\nx0=-5.27841, y=-448.88032\nx0=-2.82567, y=-64.58586\nx0=-3.25816, y=-100.54537\nx0=-2.52776, y=-45.70666\nx0=-9.52725, y=-2756.11219\nx0=6.83284, y=1192.58302\nx0=0.24780, y=0.62284\nx0=0.29104, y=0.78120\nx0=-0.37198, y=-0.54326\nx0=-7.34652, y=-1242.79903\nx0=-5.39241, y=-479.50696\nx0=5.14329, y=526.47200\nx0=-8.94185, y=-2270.12671\nx0=8.43784, y=2202.49943\nx0=-2.47729, y=-42.93778\nx0=6.12712, y=870.26993\nx0=1.45923, y=17.64499\nx0=4.36416, y=329.91908\nx0=5.23016, y=552.30511\nx0=5.45310, y=622.45383\nx0=4.99694, y=484.80294\nx0=6.54435, y=1052.60945\nx0=5.61079, y=675.51373\nx0=1.70636, y=26.05266\nx0=-5.66383, y=-558.00333\nx0=-4.71513, y=-316.62980\nx0=3.47451, y=173.97209\nx0=8.83444, y=2518.60268\nx0=-6.79488, y=-977.73147\nx0=3.42280, y=166.86801\nx0=2.27043, y=54.64520\nx0=-0.03559, y=-0.06081\nx0=7.25901, y=1421.30761\nx0=-9.11982, y=-2411.24282\nx0=8.59924, y=2327.73022\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.74423, y=-2952.52757\nx0=-3.79447, y=-161.43494\nx0=-1.83420, y=-17.05163\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 3.39 * x0**3 + 2.12 * x0**2 + 1.78 * x0", "data": [[7.203886241626453, 1390.203091133734], [7.0026289716428956, 1280.5033096297575], [5.963441692963865, 804.9443771028042], [0.18985138444858407, 0.43754527685288813], [9.613911127008588, 3225.3709964587874], [-3.1214702683639945, -88.00426000509273], [8.818187196940798, 2505.0917746207247], [-5.533111438534775, -519.2036394177717], [8.901443350051036, 2574.832051703583], [9.672143494797467, 3282.925366113616], [-3.272208506654546, -101.89928692670263], [5.008737319027727, 488.07629298443095], [7.664260537635236, 1664.3696537352055], [8.064718140514675, 1930.3847506149182], [1.8445246543655536, 31.770261673795737], [3.0001348592674866, 115.96429972158245], [2.5645136084634466, 75.68362739246339], [7.384378225369332, 1493.7735648193247], [3.2679631118556465, 146.77032735185503], [2.3436654480272257, 59.45657381423046], [4.083290191867075, 273.4127115358877], [-9.252928086513371, -2520.537689519726], [-2.976803422123564, -75.9358216021509], [-2.2625544684708494, -32.43894991322007], [3.212019989364503, 139.92958825214285], [-7.2014024099606955, -1168.9251118539812], [-2.757251690423768, -59.851352127014806], [-9.15874132592349, -2442.8679184047196], [-0.45621600744433266, -0.6927152324699362], [-4.012680302027869, -192.03705873764432], [-0.39191258586019195, -0.5760464351329193], [7.669446683873865, 1667.6477474573114], [-9.53701368653209, -2764.758588931194], [1.0442126265104346, 8.030119359110858], [-1.907232638749825, -19.20185607829366], [9.727041482424642, 3337.8081869005346], [-4.708801263882389, -315.31623595005703], [-2.491570481421503, -43.70895102703181], [8.61004153662413, 2336.2790794677935], [-5.502978329398842, -510.52383493944495], [-5.278413712891221, -448.8803185869973], [-2.825673921057912, -64.58586233374464], [-3.2581582835391583, -100.5453728976512], [-2.5277640773505468, -45.70666207558326], [-9.52724843873516, -2756.1121892259393], [6.832840179968265, 1192.5830225147824], [0.24779971984837346, 0.622843937435168], [0.2910412423475215, 0.781200504314375], [-0.3719759114628136, -0.5432604310859198], [-7.346521755025817, -1242.7990260586935], [-5.392405471275927, -479.50695763308937], [5.143290543995487, 526.4720006943389], [-8.941852286217419, -2270.1267143618334], [8.437839030981934, 2202.4994296193327], [-2.4772947091862463, -42.937780368815744], [6.127123108501156, 870.2699281064258], [1.459225763463884, 17.644988047348672], [4.3641556890076885, 329.91907682754396], [5.230161695529805, 552.3051143245048], [5.453102609837728, 622.4538296410358], [4.996942782910693, 484.80294269761225], [6.544346901350963, 1052.609445719871], [5.6107921341144085, 675.5137311011225], [1.7063576835126568, 26.052658828484688], [-5.663831954500809, -558.0033324787528], [-4.715128584504599, -316.6297996154826], [3.474514647722076, 173.97209444338682], [8.834436321179783, 2518.6026812761256], [-6.7948783370926735, -977.731471923602], [3.4227954013513813, 166.86800978799357], [2.2704283424406917, 54.6451964374492], [-0.03558781052609561, -0.06081413216667814], [7.25900949691037, 1421.30761439391], [-9.11981787195878, -2411.242824279223], [8.599237267513015, 2327.730215237084], [-9.744228547965744, -2952.527574664663], [-3.794465436576873, -161.43494242591285], [-1.8342035097915037, -17.051625397622598]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-1.07534, x1=-5.04966, y=-0.00336\nx0=-4.72564, x1=4.92881, y=-0.01548\nx0=1.10546, x1=-1.37635, y=0.04644\nx0=-0.57184, x1=5.86168, y=-0.00132\nx0=-5.04219, x1=-0.62669, y=-1.02165\nx0=-3.21569, x1=-0.48181, y=-1.10231\nx0=9.18253, x1=-4.74171, y=0.03250\nx0=-8.98092, x1=2.23274, y=-0.14336\nx0=0.48665, x1=6.21712, y=0.00100\nx0=2.33044, x1=1.81079, y=0.05656\nx0=5.31146, x1=-3.70535, y=0.03079\nx0=2.02989, x1=-6.38520, y=0.00396\nx0=-7.68473, x1=3.98094, y=-0.03859\nx0=-9.12183, x1=1.25700, y=-0.45941\nx0=-3.86192, x1=5.81358, y=-0.00909\nx0=0.04037, x1=7.71361, y=0.00005\nx0=-9.12305, x1=4.71914, y=-0.03260\nx0=5.44528, x1=6.30033, y=0.01092\nx0=-3.82806, x1=-7.39033, y=-0.00558\nx0=-2.86605, x1=-3.07628, y=-0.02410\nx0=2.52703, x1=-9.24190, y=0.00235\nx0=9.25451, x1=-9.30400, y=0.00851\nx0=2.58466, x1=-4.43833, y=0.01044\nx0=9.35732, x1=7.46668, y=0.01336\nx0=4.07278, x1=2.26155, y=0.06337\nx0=-6.38654, x1=-5.82543, y=-0.01498\nx0=-4.32556, x1=2.42660, y=-0.05846\nx0=8.24734, x1=-6.46808, y=0.01569\nx0=-3.09893, x1=-3.45341, y=-0.02068\nx0=8.24306, x1=9.26528, y=0.00764\nx0=-4.92040, x1=0.03064, y=-417.01806\nx0=0.69642, x1=-4.46668, y=0.00278\nx0=-3.82612, x1=6.04521, y=-0.00833\nx0=-1.34852, x1=-6.40982, y=-0.00261\nx0=3.11551, x1=-1.86394, y=0.07136\nx0=0.41840, x1=-4.63869, y=0.00155\nx0=6.14046, x1=-3.46003, y=0.04082\nx0=-8.50814, x1=1.63307, y=-0.25387\nx0=-4.32342, x1=1.81871, y=-0.10401\nx0=4.69859, x1=-6.15846, y=0.00986\nx0=4.69559, x1=6.94316, y=0.00775\nx0=-3.30953, x1=-8.89231, y=-0.00333\nx0=-6.54156, x1=2.80291, y=-0.06626\nx0=3.61616, x1=3.26594, y=0.02698\nx0=-7.34726, x1=3.69169, y=-0.04290\nx0=6.68634, x1=9.16402, y=0.00634\nx0=-0.55748, x1=0.42025, y=-0.25119\nx0=-0.57394, x1=-5.04043, y=-0.00180\nx0=0.00687, x1=4.32648, y=0.00003\nx0=-3.67291, x1=4.21539, y=-0.01645\nx0=-9.11502, x1=6.57015, y=-0.01680\nx0=1.75199, x1=-1.97163, y=0.03586\nx0=-3.70711, x1=0.74312, y=-0.53420\nx0=8.87098, x1=7.01968, y=0.01433\nx0=-8.38134, x1=-0.71197, y=-1.31575\nx0=7.25000, x1=9.81718, y=0.00599\nx0=-3.66803, x1=-3.53877, y=-0.02331\nx0=-5.78136, x1=1.74085, y=-0.15181\nx0=-0.38014, x1=1.99707, y=-0.00758\nx0=-3.57286, x1=6.58544, y=-0.00656\nx0=1.15183, x1=9.97030, y=0.00092\nx0=4.18296, x1=-7.33895, y=0.00618\nx0=7.48736, x1=2.58327, y=0.08929\nx0=-9.04030, x1=-6.20795, y=-0.01867\nx0=3.81495, x1=3.60011, y=0.02342\nx0=-8.33159, x1=-5.10118, y=-0.02548\nx0=6.00567, x1=-1.52650, y=0.20510\nx0=-8.38511, x1=6.12579, y=-0.01778\nx0=-4.00913, x1=-8.08400, y=-0.00488\nx0=-5.51982, x1=-6.15807, y=-0.01158\nx0=-8.61266, x1=4.79113, y=-0.02986\nx0=5.67180, x1=8.57062, y=0.00614\nx0=0.31250, x1=8.22008, y=0.00037\nx0=7.77510, x1=-7.63250, y=0.01062\nx0=-7.43650, x1=9.31161, y=-0.00683\nx0=1.05572, x1=-4.87347, y=0.00354\nx0=4.43045, x1=3.66481, y=0.02625\nx0=-0.53446, x1=-5.00380, y=-0.00170\nx0=-9.04006, x1=-6.48830, y=-0.01709\nx0=2.18009, x1=0.53570, y=0.60453\nx0=6.73071, x1=-5.84331, y=0.01569\nx0=9.98910, x1=-4.75030, y=0.03523\nx0=0.31994, x1=4.89141, y=0.00106\nx0=-5.79267, x1=-1.79794, y=-0.14260\nx0=7.78016, x1=3.91332, y=0.04043\nx0=-4.93015, x1=0.46899, y=-1.78372\nx0=8.52639, x1=3.35156, y=0.06040\nx0=6.35517, x1=-3.38053, y=0.04425\nx0=-6.29395, x1=-5.70874, y=-0.01537\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=1.10799, x1=-1.52080, y=0.03812\nx0=7.41161, x1=-8.39836, y=0.00836\nx0=-5.66818, x1=9.12786, y=-0.00541\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 / (4 * pi * x1**2)", "data": [[-1.07534305469202, -5.049657872731688, -0.0033559328427034954], [-4.725640262476894, 4.928814841272004, -0.015479815745904676], [1.1054639888465267, -1.3763522963096992, 0.04643821438643288], [-0.5718376015161812, 5.861682825318471, -0.0013243970812070905], [-5.042192030691803, -0.6266923056090192, -1.0216468316911316], [-3.2156949527075662, -0.4818145080807881, -1.1023137731728132], [9.182528860452038, -4.741713358285471, 0.03249988649707764], [-8.980918399845553, 2.232737457485918, -0.14336250129157724], [0.4866519642629452, 6.21711685985624, 0.0010019142541701743], [2.3304378996296204, 1.8107899650213923, 0.056557670366783615], [5.311464546863343, -3.70534529138469, 0.03078555965039401], [2.0298865992146347, -6.385198813236457, 0.003961987161876332], [-7.6847274154914995, 3.9809409979542725, -0.03858754255696471], [-9.121825100987506, 1.256998772501511, -0.45941182528740443], [-3.8619163324169197, 5.813578624374539, -0.0090929728825439], [0.04036717407844037, 7.713612171124808, 5.3988701802843946e-05], [-9.123053509637613, 4.719141638683144, -0.032599004171434215], [5.445277083147989, 6.300330072889814, 0.010916502396368622], [-3.828058855322423, -7.390333352787726, -0.005577514211296646], [-2.86604607262952, -3.0762763434565965, -0.024100309060689693], [2.527034976699296, -9.241903764304913, 0.0023543905459784747], [9.254507597204288, -9.304002495263315, 0.008507536398876539], [2.58465648611314, -4.438325423927307, 0.010441302619983996], [9.357321428484507, 7.466683892647655, 0.013356299616009884], [4.072783976205983, 2.2615540500320215, 0.06336764511765836], [-6.38654314173142, -5.825425087863067, -0.014976169355669401], [-4.325557512472722, 2.4265972248708536, -0.058457041707213296], [8.247335388514298, -6.468078684452367, 0.01568748064828747], [-3.098934466756404, -3.453408114529239, -0.020677913678265367], [8.243061449350403, 9.26528244017302, 0.007641196143627578], [-4.92040261613969, 0.030642059970812596, -417.01805683676207], [0.6964225611349768, -4.466679118604777, 0.002777751937921697], [-3.8261167057542966, 6.045207453189004, -0.00833155241076623], [-1.3485161598808197, -6.409819229161419, -0.0026118890691736087], [3.1155082699013157, -1.8639423044733974, 0.0713598804492909], [0.4183959341784398, -4.638688283960521, 0.001547345203444016], [6.140462320231112, -3.460031533123729, 0.04081606126882222], [-8.508139379019005, 1.633065395971622, -0.25387362197299485], [-4.3234234954253274, 1.8187063021984002, -0.10401423299367471], [4.698590771055722, -6.158463315990947, 0.00985854991498844], [4.695590892629394, 6.943164749548881, 0.007751137600532095], [-3.3095332439318925, -8.89231012730072, -0.0033306399154229764], [-6.5415607588427065, 2.8029099124428587, -0.0662602753990885], [3.616158328625703, 3.26594439086659, 0.026978636814012705], [-7.3472614671773995, 3.6916909809409972, -0.04290075647839738], [6.686335905450882, 9.16401988047312, 0.00633587034370454], [-0.5574751623991894, 0.4202500758367478, -0.25118867653664295], [-0.5739396137819348, -5.040426087669134, -0.0017977191129734023], [0.006868724916975211, 4.326476958408774, 2.9200982871547068e-05], [-3.6729093024316466, 4.215385540995209, -0.01644847871088693], [-9.115020903671631, 6.570149545156912, -0.01680340501526581], [1.7519912182299713, -1.9716334021023219, 0.03586490846742642], [-3.7071099916494283, 0.7431244977387141, -0.5341982378012551], [8.870977264968182, 7.019684905924297, 0.014326046800800208], [-8.381336695419105, -0.7119748504948458, -1.3157522378442148], [7.249995304307571, 9.8171800360523, 0.005986243109906409], [-3.668033733592326, -3.5387677190354694, -0.02330876928523614], [-5.781360123627362, 1.740845555094177, -0.15180975266964036], [-0.38013955578214365, 1.9970733624830075, -0.007584817942300948], [-3.572859361406766, 6.585437055803041, -0.006555968394154636], [1.1518331657328957, 9.970295186439714, 0.0009220695544387491], [4.182955313822285, -7.338951823128919, 0.006180239245155163], [7.487355179580646, 2.5832662749140773, 0.08928535361109281], [-9.040300756243196, -6.207946724434803, -0.018667108532876415], [3.814946725118773, 3.6001096965881914, 0.0234232495479595], [-8.331594354122007, -5.101176881061309, -0.02547871303832656], [6.005673698412526, -1.526499498020451, 0.20509663578307266], [-8.385108665880898, 6.125794470302942, -0.017781729042591288], [-4.009133607703063, -8.084004365639213, -0.004881885474191587], [-5.51981679823955, -6.158074069555262, -0.011583104732208261], [-8.61266453932759, 4.791126101777376, -0.029857432883479744], [5.671797032214156, 8.57062343807587, 0.006144492077494168], [0.3125016013129951, 8.220075639222326, 0.0003680363842854676], [7.775100678302962, -7.632496118830298, 0.010620940431126932], [-7.436502406671246, 9.311608909237304, -0.006825106058352113], [1.055720983458606, -4.873474066023331, 0.0035372191778606744], [4.430445823821202, 3.6648091448885083, 0.026250334468180696], [-0.5344568848230313, -5.003803786344509, -0.0016986436077451495], [-9.040064419388125, -6.488301807103605, -0.01708832813902277], [2.1800872289703026, 0.53570348647842, 0.6045261070733263], [6.730707694722721, -5.843312677427727, 0.015686736945145892], [9.989097548489298, -4.75029531177471, 0.035226960441818896], [0.31993533929114903, 4.891410085291071, 0.0010641043057702181], [-5.792674823181015, -1.7979350923647495, -0.1426005719522908], [7.780163231857266, 3.9133186784723133, 0.04042857307043602], [-4.930151273868568, 0.4689885905736819, -1.783716485603542], [8.526389920429985, 3.3515574582545486, 0.06040348373395119], [6.355168455895509, -3.380533761544438, 0.04425340044120644], [-6.293952973188375, -5.708742220449048, -0.015368545388071544], [1.1079878886382115, -1.5207969366850094, 0.03812261568734098], [7.411606754582348, -8.398357688903346, 0.008362069437001926], [-5.668180420633013, 9.127862355921987, -0.005413718085990001]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.40155, y=7.48606\nx0=-0.93273, y=-0.03137\nx0=2.08940, y=3.22748\nx0=-0.36628, y=-0.11606\nx0=5.58289, y=18.37577\nx0=5.31237, y=16.76681\nx0=1.72331, y=2.34655\nx0=-0.30065, y=-0.10513\nx0=-5.22693, y=11.04692\nx0=3.23643, y=6.85544\nx0=4.98066, y=14.89381\nx0=-1.05536, y=0.02921\nx0=4.14462, y=10.66124\nx0=-4.42271, y=7.56884\nx0=-7.21183, y=22.39933\nx0=-8.09942, y=28.75060\nx0=-8.23370, y=29.78002\nx0=3.42448, y=7.57577\nx0=-2.70470, y=2.30534\nx0=-3.61918, y=4.73963\nx0=-8.83324, y=34.59643\nx0=-4.63286, y=8.41528\nx0=5.15891, y=15.88661\nx0=1.13306, y=1.20844\nx0=-2.00003, y=1.00005\nx0=9.25211, y=47.42680\nx0=-0.32698, y=-0.11003\nx0=0.78500, y=0.70061\nx0=-2.17231, y=1.27331\nx0=-7.08208, y=21.53688\nx0=-8.48890, y=31.78624\nx0=-4.96746, y=9.85408\nx0=2.13725, y=3.35254\nx0=-8.79480, y=34.27688\nx0=8.97112, y=44.72608\nx0=4.73810, y=13.59387\nx0=-3.92634, y=5.74490\nx0=8.65747, y=41.80465\nx0=-5.83889, y=14.12686\nx0=2.36547, y=3.98046\nx0=-9.14916, y=37.27896\nx0=-2.33839, y=1.56484\nx0=2.81678, y=5.37552\nx0=-8.86228, y=34.83885\nx0=-2.07292, y=1.11204\nx0=7.85014, y=34.73745\nx0=2.18782, y=3.48718\nx0=6.38117, y=23.55028\nx0=8.05081, y=36.43316\nx0=-6.55333, y=18.19643\nx0=-1.82254, y=0.74956\nx0=-6.41905, y=17.39258\nx0=6.83611, y=26.78426\nx0=8.70430, y=42.23454\nx0=-7.82455, y=26.69951\nx0=-4.72444, y=8.79794\nx0=-1.51418, y=0.38928\nx0=5.22855, y=16.28316\nx0=7.33691, y=30.58358\nx0=7.99027, y=35.91732\nx0=2.63709, y=4.79567\nx0=-6.65262, y=18.80238\nx0=-3.99870, y=5.99544\nx0=9.45383, y=49.41436\nx0=8.16193, y=37.38952\nx0=-7.95347, y=27.65212\nx0=-7.99681, y=27.97605\nx0=-1.38035, y=0.26251\nx0=9.17626, y=46.68999\nx0=5.62188, y=18.61369\nx0=8.24429, y=38.10631\nx0=-1.75736, y=0.66548\nx0=8.01421, y=36.12089\nx0=-3.63021, y=4.77411\nx0=-6.30688, y=16.73492\nx0=-8.36375, y=30.79429\nx0=-7.22278, y=22.47287\nx0=1.62253, y=2.12757\nx0=-5.25635, y=11.18643\nx0=-1.53131, y=0.40680\nx0=-6.83649, y=19.95055\nx0=-5.33191, y=11.54869\nx0=-2.67375, y=2.23760\nx0=-3.89633, y=5.64254\nx0=2.38181, y=4.02742\nx0=8.64440, y=41.68503\nx0=-9.99577, y=44.95986\nx0=-2.81351, y=2.55118\nx0=8.44198, y=39.85448\nx0=6.34641, y=23.31170\nx0=6.46916, y=24.15962\nx0=5.68525, y=19.00364\nx0=-0.51520, y=-0.12488\nx0=1.33132, y=1.55186\nx0=5.75948, y=19.46557\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=2.11900, y=3.30458\nx0=4.33825, y=11.57935\nx0=1.16736, y=1.26505\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * (x0 + 1) / 2", "data": [[-4.401553403089453, 7.486059478579446], [-0.9327324361015279, -0.03137131937281854], [2.0893955405716707, 3.2274846327662274], [-0.3662838398853214, -0.11605999426209282], [5.582888503187322, 18.375766271104247], [5.312367779977038, 16.7668096048576], [1.7233094505093423, 2.3465524563620765], [-0.30064582449751853, -0.10512895635486291], [-5.2269273001474925, 11.04692085043983], [3.236426216096886, 6.855440434168046], [4.9806584255085475, 14.893808388548916], [-1.0553553215579896, 0.02920976659138902], [4.144617434004079, 10.661235554127318], [-4.422714364389233, 7.568843992292811], [-7.211829426199719, 22.399327123200223], [-8.099420537262707, 28.75059625108511], [-8.233695239473256, 29.780021028525653], [3.4244792831371207, 7.575768821886224], [-2.704696062692009, 2.3053423644248237], [-3.6191750094776998, 4.739626369875104], [-8.833238469677656, 34.5964316962578], [-4.63286227097365, 8.415275275418738], [5.1589066213510115, 15.88661207458516], [1.133055870500172, 1.2084357380875375], [-2.0000320872013244, 1.0000481313167808], [9.252107623079098, 47.426801546058726], [-0.32697812479866784, -0.11003171535090732], [0.784999024872457, 0.7006112469615826], [-2.172308303856491, 1.2733075315736873], [-7.0820789773047155, 21.536881831738345], [-8.488896753662727, 31.786235670341433], [-4.967456278731024, 9.854082801186626], [2.13724674502531, 3.3525351970732964], [-8.794803037724105, 34.27687871731852], [8.971122183112922, 44.72607770372684], [4.73810491432695, 13.593871546748073], [-3.9263402507608935, 5.7449037569921115], [8.657472424344562, 41.80465060131553], [-5.838886778294475, 14.126856015723778], [2.3654689641028153, 3.9804561921182304], [-9.14915766342693, 37.278964143408395], [-2.338390070663767, 1.5648390259575649], [2.816781450374286, 5.375519594773476], [-8.862278843820198, 34.83885373090143], [-2.0729227591235144, 1.1120430030843647], [7.850143755132745, 34.73745036569119], [2.1878151816626605, 3.4871752253881403], [6.381174613602326, 23.55028203144256], [8.05080800546169, 36.43315877313386], [-6.553334471596197, 18.196429112507406], [-1.8225446241874934, 0.7495621414836191], [-6.419050909731245, 17.39258183599514], [6.836110413167656, 26.78425799709346], [8.704297306074299, 42.2345444493033], [-7.8245491298995296, 26.699509978155977], [-4.7244394325222565, 8.797944259524483], [-1.514176606056223, 0.38927709413585965], [5.228552778814322, 16.283158469830646], [7.336910337689162, 30.583581820489623], [7.990266883491689, 35.917315876457835], [2.6370916126044968, 4.795671892936741], [-6.652622642680486, 18.8023826916123], [-3.998696311076422, 5.995437938569882], [9.45382897413386, 49.41435562315336], [8.161930105842814, 37.38951657925305], [-7.953471705910373, 27.652120235403245], [-7.996805460583092, 27.97604605691423], [-1.380347705333481, 0.2625060411429627], [9.176258715549295, 46.68999136512185], [5.6218765742395185, 18.61368639511129], [8.24429111678188, 38.10631356751526], [-1.7573612322573418, 0.6654786341918505], [8.014210424671866, 36.12088957779554], [-3.6302115096856564, 4.774112047684278], [-6.306878102962566, 16.734916651333062], [-8.363750753204782, 30.794287954264387], [-7.222777225123222, 22.472866809317743], [1.622533496708666, 2.1275742223251584], [-5.256348421692629, 11.186425154268983], [-1.5313109201117818, 0.406801106970905], [-6.836490180369208, 19.950553902957697], [-5.331912094164348, 11.54868724286585], [-2.673753913091172, 2.2376030373395914], [-3.8963327849648755, 5.642538193113634], [2.3818111023749715, 4.027417614885824], [8.64440044274826, 41.68502972866729], [-9.99577409227458, 44.95986280575656], [-2.813514842057616, 2.551175462210438], [8.441977799809813, 39.85448348614577], [6.346414580242179, 23.311696302276346], [6.4691633066904615, 24.159618597660362], [5.685246909676119, 19.003639666828988], [-0.5152034840477082, -0.12488442703640554], [1.3313173309051862, 1.5518615832368476], [5.7594835006336265, 19.4655668473523], [2.1189979293597183, 3.304575076995246], [4.338253938911002, 11.579350588693915], [1.1673645712697596, 1.2650523067627946]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=0.88575, x1=8.21788, y=0.11377\nx0=-2.43226, x1=-2.38562, y=0.58793\nx0=-4.17211, x1=2.09604, y=0.33614\nx0=-7.68002, x1=0.60114, y=0.13041\nx0=5.96786, x1=-9.30016, y=0.06446\nx0=-9.16314, x1=-9.24075, y=0.04669\nx0=-2.93667, x1=5.16635, y=0.21439\nx0=-2.47755, x1=-7.44200, y=0.12594\nx0=7.64387, x1=-7.89380, y=0.06518\nx0=-8.60987, x1=-9.52162, y=0.04796\nx0=7.53744, x1=8.20634, y=0.06341\nx0=9.33145, x1=-2.33287, y=0.08464\nx0=7.55918, x1=4.43698, y=0.10149\nx0=-0.63921, x1=-4.57830, y=0.34233\nx0=-4.51961, x1=-4.15254, y=0.20166\nx0=-2.79958, x1=7.56529, y=0.11928\nx0=2.53370, x1=2.21852, y=0.59963\nx0=5.70983, x1=7.64419, y=0.08599\nx0=4.89644, x1=0.54370, y=0.30452\nx0=-7.91047, x1=-4.88352, y=0.09047\nx0=7.57374, x1=-8.37157, y=0.06180\nx0=-7.33431, x1=-8.75252, y=0.06042\nx0=8.68991, x1=3.46214, y=0.08938\nx0=5.49358, x1=6.44741, y=0.10848\nx0=-0.68129, x1=5.17222, y=0.27382\nx0=-0.09670, x1=1.08208, y=2.51553\nx0=4.27329, x1=-5.14272, y=0.17127\nx0=5.48569, x1=-9.68137, y=0.06358\nx0=2.54525, x1=-4.56287, y=0.27306\nx0=4.89106, x1=5.69817, y=0.13701\nx0=4.06621, x1=-0.34677, y=0.42886\nx0=4.55056, x1=-2.41899, y=0.28012\nx0=6.06827, x1=-3.44360, y=0.15785\nx0=-0.01812, x1=-4.67935, y=0.33477\nx0=5.55015, x1=-0.87204, y=0.23835\nx0=-8.77788, x1=3.32967, y=0.08875\nx0=4.90526, x1=-4.92930, y=0.15886\nx0=8.75546, x1=-9.13287, y=0.04936\nx0=-1.73527, x1=9.95326, y=0.07687\nx0=-3.09981, x1=4.29487, y=0.26618\nx0=3.06042, x1=7.85840, y=0.10941\nx0=-2.15389, x1=-8.71597, y=0.09684\nx0=4.96135, x1=7.19916, y=0.10198\nx0=-5.16721, x1=-6.99749, y=0.10301\nx0=-2.73372, x1=5.61764, y=0.19497\nx0=-7.48831, x1=-4.52277, y=0.10187\nx0=3.40930, x1=2.34573, y=0.41828\nx0=-4.77014, x1=9.94326, y=0.06471\nx0=-7.68802, x1=5.76155, y=0.08483\nx0=4.14360, x1=9.31425, y=0.07553\nx0=1.90993, x1=-2.87650, y=0.57463\nx0=1.76770, x1=6.24277, y=0.18142\nx0=7.89181, x1=-0.25874, y=0.12432\nx0=6.48922, x1=-3.09406, y=0.14902\nx0=-9.65839, x1=-0.18566, y=0.08393\nx0=0.41141, x1=-8.84190, y=0.09957\nx0=4.20039, x1=6.87038, y=0.11968\nx0=5.66407, x1=-5.62707, y=0.12168\nx0=7.42208, x1=-6.12314, y=0.08458\nx0=-9.62020, x1=2.06297, y=0.08097\nx0=-1.70701, x1=5.94569, y=0.19868\nx0=-3.71175, x1=-4.14445, y=0.24277\nx0=-4.07753, x1=-7.36381, y=0.10981\nx0=0.03712, x1=-7.26082, y=0.14620\nx0=2.97566, x1=1.20253, y=0.65037\nx0=-2.28617, x1=-5.90280, y=0.19016\nx0=-0.95025, x1=-3.65242, y=0.49251\nx0=-7.52295, x1=-7.51920, y=0.06948\nx0=0.92902, x1=-1.25708, y=1.80045\nx0=-4.15368, x1=-5.93421, y=0.14688\nx0=8.79913, x1=1.95431, y=0.09610\nx0=8.22082, x1=7.89855, y=0.06062\nx0=-9.69419, x1=-8.49367, y=0.04759\nx0=-8.87768, x1=-5.76308, y=0.07016\nx0=-0.66458, x1=1.74085, y=1.46193\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.39242, x1=2.44220, y=0.98542\nx0=-9.71230, x1=9.19822, y=0.04421\nx0=-7.23881, x1=-0.64377, y=0.14595\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 8 / (2 + x0**2 + x1**2)", "data": [[0.8857486486767403, 8.217880173254773, 0.11376870830122003], [-2.432263997620283, -2.3856171844687513, 0.5879293328849146], [-4.17210566757295, 2.0960407455947365, 0.33613653685935113], [-7.680019865933618, 0.6011431928471396, 0.13041193582789679], [5.967855061554149, -9.300162601747306, 0.06445982106286309], [-9.163143185107627, -9.240749835583753, 0.0466867982520831], [-2.9366659413472496, 5.166346629322742, 0.21439016625403343], [-2.4775484224946798, -7.442004331352072, 0.12594126404282285], [7.64386808704284, -7.893799324096831, 0.06517800797058969], [-8.609869024964551, -9.521618007588843, 0.047964203132553375], [7.537435968309175, 8.206343053042744, 0.0634130451605223], [9.331449254500878, -2.3328730512525864, 0.08463974617334423], [7.559182265273179, 4.4369797132526685, 0.1014867485227466], [-0.6392051152896912, -4.578303001896307, 0.3423273928317594], [-4.519610019021396, -4.152544848656079, 0.20166116649527904], [-2.7995776332499833, 7.565286829615058, 0.11927623228953974], [2.533701345621907, 2.218517614067059, 0.5996343918450967], [5.709827971984797, 7.644186211984515, 0.08598847996284983], [4.896441153593898, 0.5437044371830346, 0.3045211823841452], [-7.910465407056568, -4.883520047787484, 0.09047293833733641], [7.573735120618522, -8.371569485936236, 0.061802482057885376], [-7.334314049213344, -8.752516291433194, 0.06042355218024399], [8.689914076610393, 3.462138013560798, 0.0893844698754718], [5.4935813961393585, 6.4474110854516695, 0.10847671453356932], [-0.6812901990143025, 5.172219359737902, 0.27382247449936054], [-0.09669512059098295, 1.0820773511647133, 2.515532358739715], [4.273288278490352, -5.142717895522391, 0.17127488868281512], [5.485693527641827, -9.681365340446408, 0.06358205312250054], [2.5452486678090267, -4.56287255909815, 0.2730552794052885], [4.891059823511537, 5.698173032832285, 0.13700590891124353], [4.0662089833845645, -0.34676527711307514, 0.4288555073461046], [4.550557270179995, -2.41899000907077, 0.28012102778561326], [6.068273283877787, -3.4435964835984727, 0.1578460411628755], [-0.01812267848728233, -4.679354616157028, 0.3347744248705875], [5.5501515012835, -0.8720376290092595, 0.23834613064129462], [-8.777877894543325, 3.329668659935102, 0.08875296498875766], [4.905261130608512, -4.929303593555221, 0.15885743165794702], [8.755462146842067, -9.132870284495695, 0.04936216766427874], [-1.7352710100773212, 9.953259671346537, 0.07686502641253956], [-3.099811505245569, 4.294867993971067, 0.2661811305137449], [3.0604158533516728, 7.858400050476245, 0.1094082977655142], [-2.1538921309908616, -8.715967017593428, 0.0968437034714537], [4.961346935915945, 7.199164035722422, 0.10198497664867562], [-5.167212461271786, -6.997488729889461, 0.1030065909550098], [-2.733716442393157, 5.61764201815382, 0.19497402095101402], [-7.488311437870612, -4.522768453117944, 0.10187158129014526], [3.4093028918098582, 2.345726319203422, 0.4182836341486143], [-4.7701431143263395, 9.94326021642399, 0.06471303982025586], [-7.688021102811787, 5.761553245346443, 0.08483458355365761], [4.143604159213666, 9.314246914033554, 0.07552538454632489], [1.9099258440786553, -2.876503606498593, 0.5746263783852132], [1.7677003460101375, 6.242766458985734, 0.18141865845423932], [7.891805525494259, -0.25874236427441843, 0.1243248730795533], [6.489224575411715, -3.0940556759871622, 0.1490223682328994], [-9.658394681240111, -0.18565609823759388, 0.08392865325423597], [0.4114132874156784, -8.841904724414732, 0.09956621483292849], [4.200390424105363, 6.870383787249693, 0.11967904515733396], [5.664071221105985, -5.62706582497195, 0.12168119744152592], [7.422082275627936, -6.123137772719264, 0.0845843700978434], [-9.62019761130377, 2.0629701400446994, 0.08096834261058679], [-1.7070088135934984, 5.94569098726434, 0.19868312622413212], [-3.7117538028861734, -4.14445194165082, 0.24276559888545277], [-4.077532319728341, -7.363807809064992, 0.10981177055420664], [0.03712122141224583, -7.260816120676572, 0.1461966162911097], [2.9756647643535317, 1.2025344251698158, 0.6503710861493638], [-2.2861670098808506, -5.902796495742999, 0.19016121980475673], [-0.950250689827099, -3.6524226452792607, 0.49251477421296624], [-7.522949596852961, -7.519199284211872, 0.06948477908452438], [0.9290212233354751, -1.2570764242002763, 1.8004548792001855], [-4.153675976579385, -5.934210900424397, 0.14687554464039276], [8.799129500029522, 1.9543093145410477, 0.09610301683486415], [8.220816742028237, 7.898548092889683, 0.06062034777417015], [-9.694185478127944, -8.493674885944207, 0.04758513042441792], [-8.877675280051445, -5.763078387407104, 0.07015931987589633], [-0.6645796143223563, 1.7408490010833866, 1.4619291781563948], [-0.39242410783124626, 2.442198554498791, 0.9854242863620646], [-9.712302037886353, 9.198221361096952, 0.044214507614149245], [-7.238811498833098, -0.6437699648635391, 0.1459459010331594]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.72739, x1=-1.63570, y=-14.27535\nx0=1.13574, x1=4.26893, y=4.84840\nx0=-4.76897, x1=-7.12907, y=33.99833\nx0=-1.79532, x1=4.01011, y=-7.19945\nx0=3.93974, x1=-6.36709, y=-25.08469\nx0=2.74673, x1=-7.59037, y=-20.84872\nx0=-3.74875, x1=1.15920, y=-4.34556\nx0=3.96796, x1=-5.22958, y=-20.75077\nx0=2.87611, x1=-1.82785, y=-5.25710\nx0=3.65138, x1=2.84298, y=10.38078\nx0=5.75881, x1=-3.34599, y=-19.26893\nx0=3.80770, x1=-1.48345, y=-5.64855\nx0=4.66233, x1=-4.18578, y=-19.51549\nx0=2.79891, x1=-7.18505, y=-20.11035\nx0=-4.59843, x1=7.35304, y=-33.81241\nx0=-7.12128, x1=7.61114, y=-54.20108\nx0=-7.18823, x1=0.60829, y=-4.37254\nx0=-5.25906, x1=2.38522, y=-12.54401\nx0=8.37752, x1=-7.05877, y=-59.13500\nx0=-9.22559, x1=-3.27789, y=30.24044\nx0=-2.09874, x1=0.98156, y=-2.06004\nx0=1.62885, x1=-6.95056, y=-11.32145\nx0=-3.50318, x1=1.14662, y=-4.01684\nx0=-9.11186, x1=-8.28432, y=75.48558\nx0=-7.65009, x1=1.02220, y=-7.81991\nx0=9.99751, x1=5.85534, y=58.53887\nx0=9.32095, x1=-4.51233, y=-42.05918\nx0=-9.65437, x1=8.18033, y=-78.97588\nx0=1.45668, x1=7.56752, y=11.02349\nx0=-7.66483, x1=2.82690, y=-21.66774\nx0=-2.79134, x1=2.58480, y=-7.21506\nx0=9.09821, x1=4.80789, y=43.74319\nx0=-2.58069, x1=-0.31896, y=0.82315\nx0=0.38609, x1=-5.46435, y=-2.10971\nx0=-4.55005, x1=2.41654, y=-10.99538\nx0=-9.01699, x1=-4.41321, y=39.79388\nx0=-0.65978, x1=0.47529, y=-0.31359\nx0=-0.90684, x1=-7.20618, y=6.53484\nx0=9.63585, x1=0.47641, y=4.59065\nx0=9.38166, x1=9.86072, y=92.50998\nx0=0.86699, x1=-8.12587, y=-7.04506\nx0=-4.37678, x1=-6.29500, y=27.55185\nx0=-3.20257, x1=-1.03389, y=3.31110\nx0=8.34127, x1=1.41562, y=11.80805\nx0=0.32160, x1=9.78747, y=3.14764\nx0=0.59947, x1=3.66742, y=2.19850\nx0=2.42188, x1=4.05054, y=9.80991\nx0=6.43019, x1=-4.20293, y=-27.02565\nx0=3.23917, x1=0.40068, y=1.29788\nx0=-5.70280, x1=-3.96239, y=22.59672\nx0=1.45614, x1=4.08954, y=5.95497\nx0=-1.35866, x1=5.41498, y=-7.35709\nx0=-0.57298, x1=3.94130, y=-2.25830\nx0=2.90282, x1=6.42823, y=18.66002\nx0=-3.87848, x1=-6.60191, y=25.60540\nx0=-5.22941, x1=-4.37418, y=22.87441\nx0=1.70774, x1=6.82052, y=11.64766\nx0=5.29710, x1=-6.84636, y=-36.26587\nx0=-4.54694, x1=2.90923, y=-13.22810\nx0=-8.75961, x1=9.62864, y=-84.34311\nx0=-1.41010, x1=-9.87788, y=13.92884\nx0=-6.51433, x1=7.40412, y=-48.23287\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.73977, x1=0.64900, y=0.48012\nx0=6.86590, x1=3.11417, y=21.38154\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1", "data": [[8.727393769673458, -1.6356950033928914, -14.275354381697127], [1.1357412034017003, 4.268927947769235, 4.8483973646345815], [-4.768973423315915, -7.129067306177806, 33.998332516192335], [-1.7953242761547656, 4.010112600786066, -7.199452502305348], [3.939741817196488, -6.367090395869985, -25.08469228647912], [2.746732595787119, -7.590372705947357, -20.84872412559848], [-3.748753129721731, 1.1592010108410165, -4.345558417366854], [3.9679611399817354, -5.229579269987159, -20.7507673217631], [2.8761147510522065, -1.8278472989855779, -5.257098579283353], [3.6513780120612367, 2.842976830069624, 10.38078308611578], [5.758812644880644, -3.3459902421702044, -19.26893091625702], [3.807699674167374, -1.4834542410497633, -5.648548230287393], [4.662327853833435, -4.185781847621581, -19.51548729823648], [2.7989138358855303, -7.185054853160784, -20.110349440108195], [-4.598426041578321, 7.353039993649087, -33.81241059156286], [-7.121280824212151, 7.611142750046863, -54.20108491625006], [-7.18823446071408, 0.6082906508753538, -4.372535818752415], [-5.259060732419791, 2.3852183715916695, -12.544008276284027], [8.37751684340273, -7.05877387373153, -59.13499702095704], [-9.225593611595635, -3.2778857197813593, 30.240441555955467], [-2.0987398354939195, 0.9815610079386587, -2.0600411883284266], [1.6288531598265799, -6.950562695623901, -11.321446009339741], [-3.5031845820640806, 1.1466240656459519, -4.016835748194531], [-9.111864548969816, -8.284318021675432, 75.48558369409614], [-7.65008601387831, 1.0221988933577109, -7.81990945747771], [9.997511067532685, 5.85534393072297, 58.53886575161323], [9.320946438512511, -4.5123295720087135, -42.0591822536093], [-9.654365939940382, 8.180327912295546, -78.97587917400973], [1.456684527362178, 7.567521519279957, 11.023491507615436], [-7.664834961781977, 2.826902936698888, -21.667744462773776], [-2.7913424162794147, 2.584799731374037, -7.215061127771987], [9.098206327226912, 4.807891557077141, 43.7431893852201], [-2.5806942534266923, -0.3189648302802457, 0.8231507045494503], [0.3860864198319387, -5.464345219682034, -2.1097094825928053], [-4.550054547228424, 2.416537663301092, -10.995378183451884], [-9.016991841007371, -4.413210487446488, 39.793882957953144], [-0.6597827766452156, 0.4752879986927496, -0.3135868354836499], [-0.9068388020528868, -7.206177367012208, 6.534841250881977], [9.6358510152556, 0.47641398890557696, 4.590654218677774], [9.38166129996613, 9.860724255401468, 92.50997513653728], [0.866990998835222, -8.125869422025477, -7.045055646606457], [-4.376780087523448, -6.295003408211233, 27.551845567951165], [-3.2025735854703052, -1.0338864944728527, 3.311097577573249], [8.341273534406518, 1.4156176902618451, 11.808054374618813], [0.32159901965676596, 9.787468273470694, 3.147640201669875], [0.5994661721036199, 3.6674241946708452, 2.198496743459532], [2.421877541040443, 4.05053764766371, 9.809906158015526], [6.430188587363553, -4.202932433905547, -27.025648169959567], [3.239166804854051, 0.4006844232559885, 1.2978836830328886], [-5.7028034553074125, -3.962387726542782, 22.59671841819586], [1.4561439747547293, 4.089544385110116, 5.95496541587013], [-1.3586566490647005, 5.4149767353961735, -7.357094146076677], [-0.572983267850864, 3.9413021242448654, -2.2583001707373747], [2.9028245155357784, 6.428228760599463, 18.660020037740296], [-3.878484164169567, -6.601909084045589, 25.60539983575803], [-5.229414112612972, -4.374182630359229, 22.87441237834708], [1.7077387425848443, 6.820518867764569, 11.647664315012472], [5.297102639273863, -6.846360601252339, -36.26587481031436], [-4.546941471757151, 2.9092296830449023, -13.228097096703777], [-8.759609457806905, 9.628637903053644, -84.34310764138674], [-1.41010393750161, -9.8778823052426, 13.928840732800072], [-6.514329302788253, 7.404119279918849, -48.232871186514814], [0.7397734083741447, 0.6490044379403237, 0.48011622510505936], [6.865897101167558, 3.1141661240526517, 21.381544163687312]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-5.32255, x1=-1.04332, y=-0.85969\nx0=5.40030, x1=4.35927, y=-0.55463\nx0=0.54535, x1=-3.43664, y=-0.10727\nx0=4.13975, x1=-0.56971, y=-0.07054\nx0=9.18103, x1=-4.80710, y=-0.69089\nx0=-3.64814, x1=-9.27995, y=-0.05245\nx0=6.20816, x1=-1.58697, y=0.07876\nx0=-0.22475, x1=8.57296, y=0.13666\nx0=5.98929, x1=-7.93444, y=-0.28934\nx0=-8.54607, x1=-5.08827, y=0.20674\nx0=-0.37090, x1=0.41514, y=-0.51675\nx0=7.70315, x1=-2.89528, y=-0.10414\nx0=-9.87096, x1=-1.92704, y=-0.44753\nx0=-9.86182, x1=-3.26063, y=0.04715\nx0=-1.86548, x1=3.97329, y=0.13600\nx0=-6.08829, x1=-9.32416, y=0.01449\nx0=-7.96600, x1=9.92246, y=0.14257\nx0=-6.83105, x1=7.23108, y=-0.65165\nx0=9.95537, x1=-1.99805, y=0.37860\nx0=1.78852, x1=-4.71772, y=-0.31400\nx0=-3.85737, x1=-3.43835, y=-0.07050\nx0=-0.89134, x1=-2.27913, y=-0.40662\nx0=-3.55280, x1=-2.60368, y=0.21676\nx0=-1.46097, x1=3.56776, y=0.17204\nx0=-6.70397, x1=-7.83942, y=-0.42028\nx0=-1.43592, x1=0.05256, y=-0.83448\nx0=5.56915, x1=5.75473, y=-0.84725\nx0=-4.49815, x1=7.71823, y=0.33721\nx0=-1.03122, x1=6.54528, y=0.99114\nx0=-1.37051, x1=2.58302, y=-0.24388\nx0=-2.52706, x1=6.53085, y=-0.59976\nx0=-4.10575, x1=-2.35836, y=0.04742\nx0=8.28232, x1=-8.02840, y=0.09155\nx0=1.80783, x1=5.72637, y=-0.40068\nx0=9.81441, x1=-8.25849, y=-0.45925\nx0=-0.46124, x1=-0.40833, y=-0.62472\nx0=0.94523, x1=8.45877, y=-0.45902\nx0=-9.26688, x1=5.70977, y=0.93240\nx0=1.26405, x1=2.56630, y=0.26882\nx0=6.40420, x1=-1.77754, y=-0.11380\nx0=-1.49874, x1=-4.94019, y=0.61008\nx0=7.09927, x1=6.72643, y=0.91750\nx0=4.29170, x1=-7.17844, y=-0.13860\nx0=-8.02717, x1=7.06163, y=-0.46422\nx0=-2.30375, x1=1.94198, y=0.17437\nx0=-3.15632, x1=7.64442, y=-0.77699\nx0=2.53121, x1=8.31440, y=0.32118\nx0=1.89465, x1=7.20578, y=-0.26430\nx0=-4.61580, x1=-3.85481, y=0.20862\nx0=6.43635, x1=-0.32237, y=-0.22478\nx0=0.75113, x1=1.78457, y=0.56675\nx0=-7.04450, x1=8.92465, y=-0.22506\nx0=-3.29535, x1=-3.82950, y=-0.32828\nx0=5.61933, x1=3.38293, y=-0.10102\nx0=-9.97261, x1=-9.81602, y=-0.13236\nx0=-2.40378, x1=9.34886, y=-0.01699\nx0=8.23825, x1=-9.14084, y=0.02936\nx0=1.80753, x1=5.57904, y=-0.39156\nx0=-7.63186, x1=4.00815, y=-0.37765\nx0=4.67484, x1=4.22726, y=-0.34412\nx0=-2.19689, x1=0.36491, y=0.15060\nx0=5.49001, x1=-0.88587, y=0.83870\nx0=1.16809, x1=9.64991, y=0.11049\nx0=-0.84736, x1=3.09266, y=-0.02337\nx0=-6.52131, x1=-5.64583, y=-0.33204\nx0=-8.47308, x1=-2.81637, y=-0.02311\nx0=-0.34757, x1=-8.60292, y=0.19895\nx0=3.61490, x1=-0.23111, y=-0.75333\nx0=6.19491, x1=-8.52209, y=-0.05759\nx0=5.63577, x1=-0.79490, y=0.76117\nx0=-7.94705, x1=8.45235, y=-0.28122\nx0=7.54351, x1=0.34374, y=-0.93535\nx0=5.15887, x1=8.46197, y=-0.45993\nx0=3.99530, x1=6.16477, y=0.28568\nx0=0.21022, x1=-7.98794, y=-0.20412\nx0=-4.30111, x1=1.24956, y=-0.13600\nx0=3.91622, x1=8.31261, y=0.20986\nx0=-6.86897, x1=-7.75088, y=-0.57173\nx0=-9.32716, x1=-2.56847, y=-0.27963\nx0=-7.71713, x1=-1.25037, y=0.67820\nx0=-0.78008, x1=-9.79957, y=-0.17155\nx0=-8.90879, x1=2.91135, y=-0.08215\nx0=1.16730, x1=-5.52175, y=-0.91337\nx0=4.32854, x1=5.65267, y=-0.19783\nx0=-5.17730, x1=-4.42164, y=0.59490\nx0=5.32272, x1=-0.87204, y=0.89878\nx0=-4.12956, x1=9.62133, y=0.00871\nx0=4.98816, x1=2.62787, y=0.23669\nx0=9.06921, x1=2.62332, y=0.22065\nx0=2.01086, x1=-4.47169, y=-0.07712\nx0=-2.82921, x1=-0.45375, y=0.86935\nx0=4.97445, x1=-2.45805, y=0.30970\nx0=0.93461, x1=-0.47608, y=0.95798\nx0=-8.68853, x1=-2.34617, y=-0.17417\nx0=8.69072, x1=-9.90272, y=0.10714\nx0=-5.74470, x1=-1.75029, y=-0.46318\nx0=-3.47928, x1=-3.87424, y=-0.31321\nx0=-4.65875, x1=5.74191, y=0.62441\nx0=8.75308, x1=-3.76606, y=-0.16402\nx0=-0.17138, x1=-3.76080, y=0.07746\nx0=-4.03171, x1=-1.58851, y=0.16360\nx0=2.17671, x1=-4.67024, y=0.08524\nx0=4.04856, x1=-6.86483, y=0.20003\nx0=3.95064, x1=-9.57727, y=-0.02664\nx0=9.82946, x1=-3.31325, y=-0.07041\nx0=-9.99241, x1=4.02838, y=0.28267\nx0=4.22257, x1=7.36075, y=-0.04348\nx0=-8.31959, x1=4.49239, y=-0.05432\nx0=6.47902, x1=-6.89751, y=0.27600\nx0=-7.11007, x1=6.70436, y=-0.92499\nx0=-3.10670, x1=7.44260, y=-0.83548\nx0=-1.42166, x1=4.71815, y=0.60019\nx0=8.62053, x1=-9.90992, y=0.08561\nx0=6.67221, x1=-2.99798, y=-0.03953\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.01255, x1=4.37646, y=-0.51439\nx0=-9.47510, x1=4.97294, y=0.79072\nx0=9.71771, x1=2.84317, y=0.13454\nx0=-4.13042, x1=-7.46473, y=-0.07262\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(1.5 * x0) * cos(0.5 * x1)", "data": [[-5.322552246126085, -1.043321785547061, -0.8596941573694404], [5.400298586733472, 4.359267035655625, -0.5546311016720518], [0.5453516113414558, -3.4366415180411813, -0.10727303883791438], [4.139745187302871, -0.5697072025210304, -0.07053929239469496], [9.181025235538502, -4.80709731357363, -0.6908854742013841], [-3.6481369010343894, -9.279950945390237, -0.052451209949698666], [6.208164743051565, -1.5869702664034087, 0.07875876982261612], [-0.22475444320061655, 8.572955202692246, 0.13666271458832144], [5.989292989725282, -7.934441956128864, -0.2893418583500253], [-8.546073150208507, -5.088267000417592, 0.2067390193470706], [-0.37089771861032794, 0.41514208320535495, -0.5167515528871441], [7.70315197346109, -2.895278061180684, -0.10413725685684025], [-9.870963271155704, -1.9270378099481569, -0.4475308634052028], [-9.861822759905907, -3.2606287838271513, 0.04715225608884037], [-1.8654764206486956, 3.973289841663462, 0.13600328147652496], [-6.088293984529372, -9.324158733726923, 0.01449265449215494], [-7.965998854694629, 9.92246177178005, 0.1425711359603936], [-6.831050810517738, 7.231078032416757, -0.651645149540145], [9.955365312892155, -1.9980536264103073, 0.37859828733612316], [1.788520390409552, -4.717719915190175, -0.3139994359891417], [-3.857368903029257, -3.4383489329961225, -0.07050315092868069], [-0.8913425424975863, -2.279133107569262, -0.4066178158970422], [-3.552797940475429, -2.603678121304071, 0.21676068091930809], [-1.4609677208664742, 3.567762111503505, 0.17203509815557438], [-6.703966733208877, -7.839424712019136, -0.42028359717702424], [-1.4359233293682134, 0.05255707299152235, -0.834477787113431], [5.569147658505962, 5.754732489386525, -0.8472462671587766], [-4.498146677080199, 7.718231747439262, 0.3372079172345023], [-1.0312233746035186, 6.545282590249787, 0.9911408128351502], [-1.3705086695310147, 2.5830211003754666, -0.24388189126452686], [-2.527061987902326, 6.530847246667864, -0.5997623061162731], [-4.105753414280944, -2.358364604518295, 0.04741748806725122], [8.282316390436751, -8.028398089362181, 0.0915458773700457], [1.8078328524445642, 5.726365694195801, -0.4006817530079974], [9.814407043175642, -8.258494201573598, -0.45925207556246794], [-0.4612374252811584, -0.40833154195903987, -0.6247173332554888], [0.9452301229198241, 8.45876917533338, -0.4590199613532905], [-9.266881211749254, 5.709767782202652, 0.9324024570113417], [1.264049229352004, 2.566300525062042, 0.26881937222047564], [6.404201105012078, -1.7775359292998072, -0.11379952209747232], [-1.4987366492908034, -4.940189369720985, 0.6100770308456863], [7.0992652015786675, 6.726428209182341, 0.9175045238732649], [4.291699114490154, -7.17843716862072, -0.13860307980206152], [-8.027168616107122, 7.061634172847995, -0.4642185328088843], [-2.303753095082315, 1.9419753847856995, 0.17436966425935413], [-3.1563152088210717, 7.644424676763105, -0.77699340933344], [2.5312065016375236, 8.314400321983289, 0.3211808765581644], [1.8946535814940546, 7.205780529768788, -0.26429944976034], [-4.615800020584853, -3.8548093487688178, 0.20862382030798923], [6.436353517964651, -0.32236513532700073, -0.22478447943666108], [0.7511333444898742, 1.7845682312461122, 0.5667543833831246], [-7.044502563392152, 8.924653818958522, -0.2250579185196501], [-3.295345179313191, -3.829498219365288, -0.32828259689016254], [5.619332955387854, 3.3829256923527478, -0.10101569082999595], [-9.972610998420905, -9.816023783789023, -0.13235967618656727], [-2.403779800045484, 9.34886041996991, -0.016986176784040446], [8.238254719717936, -9.140839332706802, 0.029355607389326396], [1.8075289335931455, 5.579042790457878, -0.3915554510327307], [-7.631858782626637, 4.008153974539113, -0.37764799451992254], [4.674835003245866, 4.227257539512198, -0.3441211907564135], [-2.1968922824888004, 0.36490889716539066, 0.15059884834886253], [5.490012782584998, -0.8858663177822894, 0.8386988772989953], [1.1680947887279949, 9.649908313088385, 0.1104856447835288], [-0.8473617133296951, 3.092660474476572, -0.023372795836420934], [-6.521313624475069, -5.645830340565128, -0.3320408672640806], [-8.47307963446324, -2.816368821494539, -0.023112210283118193], [-0.34757280791901835, -8.602924238168256, 0.19895434124473071], [3.614902953768686, -0.23110716336002746, -0.7533268144363413], [6.19491089678904, -8.522086710702375, -0.05758625540818417], [5.635772700088266, -0.794901016201786, 0.7611692861311712], [-7.947053616133721, 8.452348373633555, -0.28122461079433264], [7.5435109336538915, 0.34374145239011433, -0.9353452839401017], [5.158868003948356, 8.4619736660173, -0.4599278408015405], [3.995300496773824, 6.164771137824832, 0.28567553767676546], [0.21021544924584745, -7.987936801350621, -0.20412233122543308], [-4.301106447738611, 1.249559107738623, -0.1360027114800539], [3.916221741891931, 8.312612943982572, 0.20985555665255676], [-6.868969141826151, -7.750878984334044, -0.5717263610721793], [-9.327156350015585, -2.568470941160548, -0.2796300049066198], [-7.7171251651615975, -1.2503695033149036, 0.6781995062346717], [-0.7800827706809432, -9.799573035887994, -0.1715472802862205], [-8.908788546746504, 2.9113489232331737, -0.08214554386331058], [1.167299106600142, -5.52174650391779, -0.913372748416345], [4.328537269722814, 5.652669612428774, -0.1978334642335118], [-5.177297165575274, -4.421641399366907, 0.5949021821110232], [5.322715938094493, -0.8720447507355527, 0.8987792560496601], [-4.129563978567099, 9.621330616046961, 0.008705295237004581], [4.988160812883386, 2.627868219065011, 0.23669469089994827], [9.069209500651205, 2.6233247092463348, 0.22065318567576897], [2.01086007771368, -4.47169322425689, -0.0771218512043591], [-2.8292076496244896, -0.4537495560168132, 0.8693479056189931], [4.974453477411009, -2.4580485578604394, 0.30969583280772506], [0.9346068289030267, -0.4760780786839618, 0.9579760235299537], [-8.688532351927913, -2.346166562468948, -0.17417318701138912], [8.69072226633427, -9.902722348258443, 0.10713944730366408], [-5.744697014918603, -1.7502939121297345, -0.4631809000329043], [-3.4792773389765337, -3.8742419359351583, -0.3132105701336083], [-4.65875369668014, 5.7419066289542755, 0.6244053164443326], [8.753084604903275, -3.7660578260899875, -0.16401854973250193], [-0.17137872115525, -3.760795451853798, 0.07746344260995039], [-4.031713826471465, -1.588505856656555, 0.16359935793829766], [2.176713958594936, -4.670240230321996, 0.08523604397457264], [4.0485587545314505, -6.864830879115857, 0.2000315867860418], [3.950636504776961, -9.57727435914532, -0.02663671640938128], [9.82946417573385, -3.313251049360102, -0.07040896507052456], [-9.992409042486232, 4.028377841657772, 0.2826704865356891], [4.222573538526884, 7.360748179759533, -0.043477490318869334], [-8.319589245297411, 4.492385824555001, -0.054316153258043634], [6.4790228727397405, -6.897513656187913, 0.2759972749500162], [-7.110065032656077, 6.704361462787009, -0.9249913465773404], [-3.1067046516560843, 7.4425987707684556, -0.8354779889198071], [-1.4216572800204048, 4.71814813107172, 0.6001851988955244], [8.620526263158311, -9.909918439252303, 0.08560822715804711], [6.672214648571174, -2.9979818994903322, -0.03952969042010547], [-7.0125512518788895, 4.376457339842602, -0.5143867761936497], [-9.475096148616355, 4.972944968660869, 0.7907170751013519], [9.717707625811673, 2.8431731444894695, 0.1345357242904742], [-4.13042098180973, -7.464733065462217, -0.07262145892576534]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-6.24091, x1=-6.97060, y=0.19601\nx0=-7.88129, x1=1.52051, y=-0.30145\nx0=-1.69827, x1=7.44141, y=-2.38627\nx0=-8.97686, x1=-5.17691, y=-1.16413\nx0=2.55911, x1=6.74493, y=2.95496\nx0=-9.16890, x1=8.01034, y=0.23647\nx0=-2.99703, x1=2.43448, y=0.65714\nx0=3.09829, x1=-0.20709, y=0.25417\nx0=-2.76508, x1=1.56358, y=-0.01592\nx0=-4.45137, x1=2.41581, y=-4.33588\nx0=-5.27331, x1=3.23641, y=-5.05778\nx0=-8.36706, x1=5.14919, y=-2.21142\nx0=0.17844, x1=-8.41632, y=-0.56781\nx0=-2.69624, x1=-7.29043, y=-1.38068\nx0=1.44847, x1=-6.33810, y=5.94619\nx0=1.98618, x1=3.49744, y=-5.14585\nx0=5.32114, x1=-6.17899, y=-4.89548\nx0=9.58608, x1=-9.29107, y=0.95499\nx0=7.03583, x1=6.08018, y=4.01720\nx0=-3.83161, x1=1.80776, y=-0.89658\nx0=9.20947, x1=-1.51226, y=0.07499\nx0=9.23792, x1=-6.22620, y=1.11282\nx0=1.98948, x1=9.48338, y=-5.47233\nx0=-7.57602, x1=8.42861, y=3.13598\nx0=0.22280, x1=-3.34228, y=-1.29914\nx0=4.55257, x1=-0.55492, y=-5.03468\nx0=-2.36239, x1=4.00659, y=2.73484\nx0=-0.30277, x1=4.64167, y=0.12641\nx0=1.83189, x1=8.85067, y=-4.86732\nx0=6.94957, x1=8.71895, y=-2.82273\nx0=2.74949, x1=-9.10101, y=-2.17364\nx0=2.49498, x1=4.52624, y=-0.66901\nx0=3.15459, x1=-6.37099, y=-0.07768\nx0=-6.80949, x1=0.97663, y=-1.68734\nx0=-1.16215, x1=-8.02025, y=0.91125\nx0=-4.81436, x1=8.90237, y=-5.17271\nx0=-5.60434, x1=-8.43962, y=-2.08234\nx0=6.97443, x1=-8.94100, y=-3.38605\nx0=3.38438, x1=8.67904, y=1.05960\nx0=0.57078, x1=-3.98935, y=-2.14495\nx0=-0.25890, x1=9.88782, y=1.37434\nx0=6.03367, x1=7.02137, y=-1.09593\nx0=1.84877, x1=1.33498, y=1.34802\nx0=4.17832, x1=4.79284, y=-0.41506\nx0=5.28722, x1=6.69607, y=-4.61256\nx0=3.44801, x1=4.35954, y=0.62544\nx0=6.49411, x1=-9.37021, y=-1.25431\nx0=-8.17252, x1=5.37288, y=-3.49584\nx0=2.33197, x1=0.67387, y=3.39458\nx0=2.73711, x1=-8.93632, y=-2.08513\nx0=-0.24328, x1=-4.20400, y=0.70356\nx0=8.59655, x1=-2.65886, y=-3.91529\nx0=-2.53800, x1=9.77275, y=3.20152\nx0=9.12396, x1=0.12828, y=1.76322\nx0=-4.12867, x1=6.53740, y=4.84559\nx0=0.95663, x1=-2.13262, y=-2.61225\nx0=-9.61404, x1=-7.15368, y=0.72744\nx0=-7.12230, x1=7.59048, y=-1.16279\nx0=-7.77787, x1=-8.56902, y=3.92250\nx0=9.23649, x1=-0.95000, y=0.65327\nx0=-6.07149, x1=-1.88160, y=-0.38556\nx0=8.26477, x1=-8.94487, y=-4.87946\nx0=-1.48966, x1=-9.15342, y=5.76143\nx0=-2.35639, x1=2.22432, y=2.57899\nx0=6.95221, x1=9.03391, y=-3.44067\nx0=5.83772, x1=2.92229, y=2.52337\nx0=8.51429, x1=1.05840, y=2.32328\nx0=-0.14225, x1=-9.37134, y=0.84942\nx0=2.75267, x1=9.39997, y=-2.27444\nx0=-8.47791, x1=-1.58986, y=0.09281\nx0=-9.27937, x1=3.13103, y=0.86934\nx0=6.51660, x1=6.08879, y=1.36168\nx0=-8.79363, x1=5.53537, y=-2.59577\nx0=-3.25192, x1=1.76960, y=-0.13047\nx0=9.40715, x1=6.78056, y=0.09296\nx0=-8.67124, x1=3.88535, y=3.02125\nx0=2.37699, x1=0.41221, y=3.80562\nx0=-9.13983, x1=-9.22466, y=1.65300\nx0=-7.08762, x1=-4.84118, y=-0.55516\nx0=8.03698, x1=3.19660, y=-5.89088\nx0=-0.61645, x1=5.29803, y=-1.91736\nx0=-1.61393, x1=-5.33551, y=-3.49817\nx0=9.86420, x1=-2.68136, y=2.28690\nx0=-0.21322, x1=9.05806, y=1.18524\nx0=-2.92504, x1=6.08435, y=-1.26381\nx0=2.87471, x1=-3.96240, y=-1.07857\nx0=7.28515, x1=7.59011, y=1.31847\nx0=3.55012, x1=-0.48821, y=-2.10507\nx0=7.17009, x1=4.58179, y=-0.60567\nx0=-4.67442, x1=5.47474, y=4.14077\nx0=-2.59687, x1=5.39252, y=-1.95530\nx0=-3.99014, x1=-1.90619, y=-1.48178\nx0=-0.06018, x1=-1.77484, y=0.07313\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-4.88938, x1=-4.17659, y=-3.01533\nx0=8.00965, x1=-9.70154, y=-5.70188\nx0=-8.84353, x1=-9.34607, y=3.28418\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 6 * sin(x0) * cos(x1)", "data": [[-6.240905907241768, -6.970596865243643, 0.19600581655306298], [-7.881294760965705, 1.520514259089321, -0.30145281693507164], [-1.6982672847129514, 7.441411922446893, -2.386269281222456], [-8.9768633299654, -5.176911542081443, -1.1641270064433684], [2.5591080298065716, 6.744928049474183, 2.9549556419984726], [-9.168897297968915, 8.010335227760418, 0.23646998809803962], [-2.997026373552396, 2.43448013181351, 0.6571366105248265], [3.0982918540379405, -0.2070891970372717, 0.25417424761894164], [-2.765077400442033, 1.5635798641159422, -0.015920045118130416], [-4.45136574530504, 2.41581403714428, -4.3358760498864815], [-5.273307397483049, 3.236405583616291, -5.057782509358738], [-8.36705668884342, 5.149188796284731, -2.2114242384668223], [0.1784425532925873, -8.4163223397621, -0.5678144662750131], [-2.6962447925192468, -7.290433149454712, -1.3806822866211454], [1.4484656426215974, -6.338096639922048, 5.9461856614666], [1.9861823493182094, 3.497435194437797, -5.145848077079623], [5.321141113180488, -6.17899470207078, -4.895480837032376], [9.586075251471332, -9.291072715344626, 0.9549924631126879], [7.035826980444696, 6.080184984045609, 4.017197497349331], [-3.831611957343952, 1.807756351410827, -0.8965785838647415], [9.209469520091023, -1.5122598324097432, 0.07499465014412524], [9.237920418912108, -6.226195344320291, 1.1128227693647668], [1.9894823224751477, 9.483376185366986, -5.472334924036081], [-7.576021534773694, 8.42861314870828, 3.1359808770093793], [0.22279613592675496, -3.3422816639050534, -1.2991366310037655], [4.55257021059548, -0.5549150007749564, -5.034681866168555], [-2.3623885831492686, 4.006593933234209, 2.7348443420289668], [-0.30277419682503925, 4.641668379180883, 0.1264148605459495], [1.8318863345904859, 8.850671327342528, -4.867322672048727], [6.949566391547311, 8.718950596048366, -2.8227302838441894], [2.7494945084386213, -9.101010273400924, -2.173644756828416], [2.4949838393916206, 4.52624447106305, -0.6690144986485965], [3.1545891036985996, -6.37099408474135, -0.07767608427591907], [-6.809494992696809, 0.9766279339618595, -1.6873392099757345], [-1.16214739250524, -8.020249079395532, 0.9112483035827385], [-4.814364257786339, 8.902370051100949, -5.172708915941196], [-5.604338214649934, -8.439616076394111, -2.082335460059443], [6.9744349810769855, -8.940996540720942, -3.3860548040442944], [3.3843774386478813, 8.679040233515039, 1.0595984661568338], [0.570783618403448, -3.989351405285042, -2.144953246228986], [-0.258897318767346, 9.887815991429385, 1.3743379607080854], [6.033670999656351, 7.021369653537683, -1.0959271100925376], [1.8487748090374936, 1.334976985231899, 1.3480247858637824], [4.178320751361797, 4.792844484845158, -0.4150610974654956], [5.28721613559491, 6.69606826721844, -4.6125554867315035], [3.448005945670447, 4.359536611546437, 0.625438937183757], [6.494109043808958, -9.370214803681002, -1.2543100764626895], [-8.172520734571936, 5.3728783684389505, -3.495842772812758], [2.331967098529974, 0.6738736205126816, 3.394582166294272], [2.7371081195331115, -8.936316148990102, -2.0851326864739868], [-0.2432832967282259, -4.203995098725328, 0.7035567637265098], [8.596549365809409, -2.6588604730702787, -3.915288121884256], [-2.537996669560229, 9.772754571979615, 3.2015218656458515], [9.123957204565276, 0.12828176241977296, 1.7632171484325057], [-4.128665381599843, 6.537404571781188, 4.845588268378112], [0.9566303140834442, -2.1326177222972387, -2.6122480812216127], [-9.614036390750368, -7.153682614544142, 0.7274405539298049], [-7.122300083392437, 7.5904783690861635, -1.1627946969414602], [-7.777874525474329, -8.569022882035924, 3.9225037482315064], [9.236489470821958, -0.9500007933868666, 0.6532686217810254], [-6.071485762219955, -1.8815956614261573, -0.3855564160279087], [8.264770096329737, -8.944873346216667, -4.879457203206761], [-1.4896637875872294, -9.153419145053569, 5.761430981897477], [-2.356386818763861, 2.2243224176726155, 2.5789856891950294], [6.952212929768699, 9.03391038369891, -3.4406733813108903], [5.83771566516929, 2.922291707532633, 2.5233721074808284], [8.514286541645419, 1.0584039601354274, 2.323277411732039], [-0.14225212925316555, -9.371337302985598, 0.8494227398214023], [2.7526709863131416, 9.399969111308419, -2.2744448913255235], [-8.477907755618386, -1.5898562999900907, 0.09280779390171418], [-9.279367468959771, 3.131031354527643, 0.8693431236012398], [6.516601750469189, 6.088792276094058, 1.3616765992221846], [-8.7936256737863, 5.535368983054159, -2.595773520448638], [-3.2519207969183617, 1.7696035348627674, -0.13047389426070352], [9.407148204140327, 6.780562865047699, 0.09295725881629367], [-8.671237795321836, 3.8853508582805993, 3.021246136797103], [2.3769862911509687, 0.4122060767732769, 3.8056160296568082], [-9.13982636646088, -9.224657876480913, 1.6530047112957982], [-7.087617970043989, -4.841176442810906, -0.5551621021989543], [8.036984963620181, 3.1966033228797848, -5.89088475667258], [-0.6164521809867765, 5.298031833100797, -1.9173633684087603], [-1.613925679040051, -5.335508411358932, -3.4981709334061204], [9.864198282586813, -2.6813606749755685, 2.286901722829189], [-0.21322089435359892, 9.05806493439319, 1.18523558805361], [-2.9250350476746974, 6.084346684655518, -1.2638116501827044], [2.8747108277064743, -3.9624031782751112, -1.0785744057475684], [7.285152450472349, 7.590114681184282, 1.3184732849840608], [3.5501168865895067, -0.48821360348930476, -2.105069693427934], [7.17008733949589, 4.581786003713189, -0.6056711366774431], [-4.674416654783244, 5.474743265884083, 4.14076895448728], [-2.596865186227637, 5.392519796800064, -1.9553029984342214], [-3.9901419157722557, -1.9061916180515688, -1.4817772800874622], [-0.06018404177090986, -1.774840463106873, 0.07312682986305434], [-4.889376815377662, -4.176587810658048, -3.01532909166899], [8.009654013555448, -9.701537237583754, -5.701881934122641], [-8.84353463975499, -9.346072913237695, 3.2841827971151147]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.84834, x1=8.09844, y=17632094.72298\nx0=3.63286, x1=-0.88439, y=0.31954\nx0=7.56379, x1=4.96111, y=22883.48257\nx0=5.99307, x1=2.55337, y=96.74379\nx0=8.24020, x1=-9.06087, y=0.00000\nx0=6.25377, x1=3.08995, y=288.42679\nx0=0.83861, x1=6.64369, y=0.31056\nx0=2.88295, x1=-3.22725, y=0.03281\nx0=9.67186, x1=6.99589, y=7843610.30019\nx0=5.32106, x1=6.29449, y=37135.43754\nx0=7.76601, x1=1.93101, y=52.35786\nx0=7.55047, x1=0.53688, y=2.96050\nx0=8.29887, x1=1.95032, y=61.99823\nx0=1.43926, x1=-2.30450, y=0.43208\nx0=5.37154, x1=7.31309, y=218411.87271\nx0=2.04865, x1=2.51621, y=6.07744\nx0=2.29474, x1=-8.43719, y=0.00090\nx0=0.58543, x1=-7.72985, y=62.71314\nx0=1.97308, x1=-8.42061, y=0.00327\nx0=4.76294, x1=-1.28989, y=0.13354\nx0=8.22454, x1=9.40037, y=400297663.50538\nx0=3.34325, x1=4.12559, y=145.37926\nx0=9.08878, x1=-6.38258, y=0.00000\nx0=9.18580, x1=0.69348, y=4.65482\nx0=2.83613, x1=6.52829, y=902.66085\nx0=7.86591, x1=9.91418, y=759656376.27593\nx0=8.30340, x1=-1.77052, y=0.02357\nx0=0.44497, x1=2.28185, y=0.15760\nx0=8.94364, x1=-3.79231, y=0.00025\nx0=6.86223, x1=-0.93826, y=0.16413\nx0=9.91758, x1=-0.08862, y=0.81601\nx0=1.73819, x1=-7.16737, y=0.01902\nx0=2.86318, x1=2.93968, y=22.02877\nx0=5.84343, x1=-0.78053, y=0.25211\nx0=2.26633, x1=-3.85230, y=0.04278\nx0=6.69303, x1=-9.86326, y=0.00000\nx0=8.96093, x1=-1.14466, y=0.08126\nx0=4.02859, x1=-1.75191, y=0.08706\nx0=6.69271, x1=4.31130, y=3625.89928\nx0=0.95764, x1=7.29698, y=0.72918\nx0=2.39834, x1=-4.90176, y=0.01373\nx0=6.51875, x1=1.26402, y=10.69360\nx0=4.12456, x1=-2.89161, y=0.01662\nx0=1.51922, x1=9.88886, y=62.52125\nx0=8.84660, x1=-7.54938, y=0.00000\nx0=9.10266, x1=-4.65615, y=0.00003\nx0=2.99437, x1=-8.44795, y=0.00009\nx0=4.01993, x1=-4.14848, y=0.00311\nx0=3.41194, x1=1.59694, y=7.09859\nx0=4.29573, x1=1.49272, y=8.80938\nx0=8.83634, x1=-4.96871, y=0.00002\nx0=9.72232, x1=0.08839, y=1.22268\nx0=0.52618, x1=-6.16504, y=52.38425\nx0=8.79860, x1=-3.56745, y=0.00043\nx0=1.50087, x1=-2.66995, y=0.33820\nx0=2.95029, x1=6.50024, y=1133.01363\nx0=9.56791, x1=-8.41741, y=0.00000\nx0=9.81684, x1=4.49684, y=28889.24717\nx0=0.40085, x1=-6.19135, y=287.14666\nx0=7.78497, x1=8.81454, y=71783281.72799\nx0=6.37106, x1=5.35928, y=20417.08522\nx0=2.75199, x1=-5.68187, y=0.00318\nx0=0.61601, x1=0.78237, y=0.68451\nx0=6.26346, x1=-9.74065, y=0.00000\nx0=6.04394, x1=-5.83797, y=0.00003\nx0=4.54755, x1=-9.10546, y=0.00000\nx0=9.73934, x1=3.58612, y=3507.38864\nx0=1.43668, x1=7.71998, y=16.39913\nx0=4.22297, x1=2.53804, y=38.71198\nx0=4.76417, x1=-4.51694, y=0.00087\nx0=6.61580, x1=-4.69306, y=0.00014\nx0=9.39326, x1=6.70931, y=3364524.76533\nx0=5.99386, x1=2.90128, y=180.44569\nx0=3.08013, x1=-6.64264, y=0.00057\nx0=0.41941, x1=-3.46483, y=20.29982\nx0=3.16114, x1=9.01056, y=31906.14873\nx0=8.58072, x1=-9.01170, y=0.00000\nx0=1.62698, x1=8.50026, y=62.63301\nx0=8.98622, x1=2.35009, y=174.17892\nx0=1.03451, x1=7.35906, y=1.28360\nx0=4.52055, x1=-0.49071, y=0.47697\nx0=1.16821, x1=9.75848, y=4.55922\nx0=6.83626, x1=1.29133, y=11.96823\nx0=1.77576, x1=-9.41575, y=0.00449\nx0=4.69580, x1=0.85156, y=3.73251\nx0=6.97534, x1=1.93820, y=43.15189\nx0=7.41207, x1=6.85597, y=921041.18854\nx0=2.84055, x1=9.88062, y=30192.71584\nx0=2.71191, x1=-4.38525, y=0.01259\nx0=9.87767, x1=8.00621, y=91921078.04001\nx0=4.03375, x1=-6.73830, y=0.00008\nx0=5.85296, x1=-6.70147, y=0.00001\nx0=0.38847, x1=-2.20176, y=8.01926\nx0=5.24723, x1=5.04203, y=4264.90193\nx0=6.94069, x1=-6.47694, y=0.00000\nx0=6.94144, x1=3.07554, y=387.18328\nx0=1.80200, x1=5.02649, y=19.29977\nx0=7.16989, x1=1.60602, y=23.65776\nx0=2.01556, x1=2.92341, y=7.76026\nx0=2.65261, x1=2.38325, y=10.22637\nx0=4.07123, x1=-5.93884, y=0.00024\nx0=6.92697, x1=4.95492, y=14615.95416\nx0=3.80969, x1=7.75115, y=31810.02027\nx0=8.46453, x1=7.84720, y=19014481.95091\nx0=2.64741, x1=1.27160, y=3.44874\nx0=6.67090, x1=0.93151, y=5.85779\nx0=4.29490, x1=-1.59392, y=0.09798\nx0=6.90970, x1=0.00411, y=1.00797\nx0=3.31661, x1=-4.55465, y=0.00425\nx0=5.27762, x1=-1.84835, y=0.04620\nx0=1.20203, x1=-5.36546, y=0.37258\nx0=6.24265, x1=-1.98947, y=0.02616\nx0=6.70814, x1=0.05195, y=1.10393\nx0=1.41116, x1=-6.38493, y=0.11091\nx0=5.80832, x1=-4.98606, y=0.00016\nx0=2.44170, x1=3.83852, y=30.77282\nx0=2.89340, x1=0.96240, y=2.78011\nx0=1.90516, x1=3.87097, y=12.12288\nx0=0.93617, x1=-9.93209, y=1.92539\nx0=2.87463, x1=7.11093, y=1823.65264\nx0=7.41860, x1=-0.65420, y=0.26955\nx0=5.45568, x1=5.93309, y=23539.25244\nx0=2.43226, x1=-9.74340, y=0.00017\nx0=0.41543, x1=-2.09190, y=6.28160\nx0=1.48990, x1=3.31693, y=3.75273\nx0=0.12329, x1=5.98673, y=0.00000\nx0=0.54909, x1=-5.63611, y=29.33682\nx0=7.35786, x1=-7.51570, y=0.00000\nx0=7.13635, x1=-2.93159, y=0.00315\nx0=4.83627, x1=-4.11589, y=0.00152\nx0=3.53041, x1=-7.24039, y=0.00011\nx0=0.01511, x1=-4.24492, y=53558748.59105\nx0=3.85738, x1=7.55536, y=26893.96787\nx0=5.49770, x1=9.76835, y=16995878.06841\nx0=9.96278, x1=2.42648, y=264.57342\nx0=5.85427, x1=-4.55223, y=0.00032\nx0=8.66308, x1=3.69171, y=2894.75850\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.93984, x1=-2.75213, y=0.02297\nx0=7.56089, x1=-0.48060, y=0.37823\nx0=2.21897, x1=0.04759, y=1.03866\nx0=8.18542, x1=5.65265, y=144911.72449\nx0=5.15012, x1=-3.66418, y=0.00246\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 ** x1", "data": [[7.8483374210025545, 8.098440745206524, 17632094.722975425], [3.6328552194218933, -0.8843863394704794, 0.31953927264706955], [7.563790199280362, 4.961108778800172, 22883.48257223753], [5.993066229092978, 2.5533664892655654, 96.74378926526819], [8.240202823157006, -9.060867790122852, 5.021202896023172e-09], [6.253766949107323, 3.0899469432763595, 288.42678594965446], [0.8386076125557711, 6.643694713331417, 0.3105617795639787], [2.8829483373781493, -3.2272498693525193, 0.03280889125379888], [9.671855789498693, 6.995887733643727, 7843610.300186615], [5.321057979960228, 6.29449199699955, 37135.43753601693], [7.7660074617619195, 1.9310111578705431, 52.35786045085969], [7.550472222884551, 0.5368777606680339, 2.960498029508584], [8.298869395994693, 1.9503181769430782, 61.9982347152937], [1.4392600040685615, -2.3045028994668426, 0.4320834421688517], [5.371535973548443, 7.313090392794745, 218411.87271249876], [2.04865455716571, 2.5162106070816392, 6.077443535141041], [2.2947414260617123, -8.437186862141111, 0.0009045277483599277], [0.5854342016273648, -7.729846092383403, 62.713143693160525], [1.9730772557939211, -8.420607432517818, 0.0032712028725984848], [4.762943891411096, -1.289892667182615, 0.1335406260311687], [8.224538231259828, 9.400365782818987, 400297663.50537914], [3.343247267839125, 4.125586470425615, 145.37926373929102], [9.088784550499359, -6.382578499116731, 7.625379012137766e-07], [9.185804092976959, 0.6934799977236334, 4.654815791985392], [2.8361260378315922, 6.528292379607532, 902.6608531674975], [7.865914263805795, 9.914178102609633, 759656376.2759273], [8.303396544458057, -1.7705164586406514, 0.023574501260602367], [0.4449744422038755, 2.281851920480733, 0.15759872440061293], [8.94364236932702, -3.792308133374947, 0.00024635654696101336], [6.862234377943853, -0.9382563512324982, 0.16412732366707064], [9.91757777890659, -0.0886244735779389, 0.8160073618547475], [1.7381925064852606, -7.167371083330534, 0.01901644999254538], [2.8631843919887263, 2.9396789695678294, 22.028774242856286], [5.843425308694336, -0.7805267093718253, 0.25211317469143046], [2.266325587979301, -3.8523049690105937, 0.04277501096670454], [6.693029082071753, -9.863260045112463, 7.189000133451265e-09], [8.96093266157138, -1.1446619777431106, 0.08126012514545072], [4.028588986664218, -1.7519149803729999, 0.08706096206041296], [6.69271397623157, 4.3112959908093345, 3625.8992763092697], [0.9576400237740916, 7.296976015219357, 0.7291779913013547], [2.3983385229807936, -4.9017629011761805, 0.013733109635699183], [6.518750921347806, 1.2640246560525537, 10.693598138445697], [4.124557880602227, -2.891613320939057, 0.016617531301410002], [1.5192222670579465, 9.888859234577886, 62.52124815676004], [8.846596031673585, -7.549379084645215, 7.11914086531955e-08], [9.102664975395271, -4.656149896346291, 3.419537844654584e-05], [2.9943709458810055, -8.447945217498066, 9.466651350430965e-05], [4.0199326655717655, -4.148479472763902, 0.0031146611060420873], [3.411940005639929, 1.5969419464588164, 7.0985929096321465], [4.295732652767388, 1.4927170788476296, 8.809383308048064], [8.83634386101626, -4.968713475789992, 1.9872044071862156e-05], [9.722320266104177, 0.08839271741413413, 1.2226767888565038], [0.5261832771210528, -6.165038082065031, 52.38425346842554], [8.798601690760645, -3.567445343812947, 0.0004274210371738829], [1.5008668572862618, -2.669952110931508, 0.3382009769247809], [2.9502911652539954, 6.500241393979493, 1133.0136303427223], [9.567913630050803, -8.417409358346877, 5.5470200087988514e-09], [9.816836275406917, 4.49683888013209, 28889.247171908093], [0.40084599470301185, -6.191347008322303, 287.1466591081911], [7.784971059643592, 8.814543153905, 71783281.72799179], [6.371058683035184, 5.359278220954128, 20417.085219567543], [2.751990852550467, -5.6818693020461986, 0.0031767518135390224], [0.6160137963423331, 0.7823734191378726, 0.6845121357794234], [6.263461757604404, -9.740647759193397, 1.7318541184012958e-08], [6.04394191255377, -5.837969626581733, 2.7458444208485364e-05], [4.547545647199572, -9.105455107165081, 1.0248031342070376e-06], [9.739341847223152, 3.5861180652752935, 3507.3886423533972], [1.4366816863003589, 7.719982782303646, 16.39912895618073], [4.222968093461596, 2.538043844288202, 38.711981941604385], [4.7641729362517005, -4.516936533291691, 0.0008661107165070925], [6.6158018250773125, -4.693056888236622, 0.0001409158045219899], [9.393258924742977, 6.709307575243521, 3364524.7653267947], [5.993859495631128, 2.9012826034556998, 180.4456878489216], [3.0801335274641595, -6.642644375813513, 0.0005683374387097475], [0.4194104037798603, -3.4648331294130896, 20.29982080210937], [3.161143750719706, 9.010555639416225, 31906.148725387142], [8.580723887968304, -9.011697325314135, 3.86691762306034e-09], [1.626979984672463, 8.500257881033942, 62.633012152887495], [8.98621717541435, 2.3500942309134043, 174.1789208527681], [1.034508902142452, 7.359061816163642, 1.283601232994187], [4.520550787302572, -0.4907054554579702, 0.47697325608809127], [1.1682068558092968, 9.758482587871033, 4.559217499818766], [6.8362568124559395, 1.2913347661584638, 11.968231566845896], [1.7757582055812033, -9.415745548618862, 0.004486062409441068], [4.695799137023435, 0.8515598987374204, 3.73250917320599], [6.975335015833565, 1.9382023471365866, 43.151887871269516], [7.412065873486309, 6.855971738642918, 921041.1885406193], [2.8405533888854535, 9.880619693456946, 30192.715842283826], [2.7119131026961174, -4.385250718912386, 0.012588590915107653], [9.877674945367591, 8.006210463322208, 91921078.0400092], [4.033752850024065, -6.7383012251231245, 8.289882616759655e-05], [5.852963757917845, -6.701473066562354, 7.201973354783389e-06], [0.3884715199689115, -2.2017649639242336, 8.019264896454896], [5.247231379228239, 5.0420290376456816, 4264.90193184219], [6.940687989598796, -6.47693863773368, 3.550483491350466e-06], [6.941443825454602, 3.0755447944492964, 387.1832789857968], [1.8020026764501544, 5.026489980965545, 19.299769177796392], [7.169891582434612, 1.6060238415574286, 23.657759587023488], [2.015561736030051, 2.923414927645556, 7.760257233036001], [2.6526125628367865, 2.383252533229177, 10.226374897034338], [4.0712314997364825, -5.938840045470942, 0.00023929631652955745], [6.9269677481514975, 4.954923605307018, 14615.954163718754], [3.8096892970106317, 7.751153184563371, 31810.02026946003], [8.464525326226763, 7.847201408080927, 19014481.950909827], [2.6474110499732006, 1.271600961000205, 3.4487369458810515], [6.670900002037797, 0.9315069939316523, 5.857786803989917], [4.294900875755996, -1.5939156516931252, 0.09797743720579437], [6.909695457436321, 0.004108117205593231, 1.0079722956194144], [3.316613903876311, -4.554650303248405, 0.004250272138490894], [5.277618791304148, -1.8483472789263171, 0.04620443418974263], [1.202026036969336, -5.36546319496863, 0.3725847241808423], [6.242647747610558, -1.9894716905543284, 0.026159909039989597], [6.708139772031128, 0.05194745578566895, 1.1039257816585073], [1.4111633588994934, -6.3849267526689175, 0.1109072534858159], [5.808320681802348, -4.9860566846525085, 0.0001550245458894684], [2.441704697474325, 3.8385184996124426, 30.772819194279787], [2.893400199121565, 0.9624037799044487, 2.780105591580456], [1.9051591882941192, 3.8709703822201273, 12.1228757433308], [0.9361673941646949, -9.932089472727977, 1.9253934585673893], [2.87462634366722, 7.110934092891053, 1823.6526427083847], [7.418597685407875, -0.6541987693570306, 0.269548262430215], [5.455678268035168, 5.933093676587799, 23539.252441499404], [2.432258922328943, -9.743396764475508, 0.0001733617622183093], [0.41542703625131416, -2.0918979605753973, 6.281596547241805], [1.4898962671834166, 3.316934005545491, 3.75272837496413], [0.12328824964533425, 5.986731954746682, 3.6107033858196538e-06], [0.5490865367524318, -5.6361095971578905, 29.336818418494623], [7.357861317869418, -7.51569571308173, 3.0602628569618354e-07], [7.136347488121562, -2.9315925454567733, 0.0031474305313265523], [4.836273791016863, -4.1158914303669185, 0.0015227462494457568], [3.5304149994818843, -7.240390914959576, 0.00010802576416728263], [0.015110442256276002, -4.244924223159618, 53558748.59105391], [3.8573846240934344, 7.555361051815151, 26893.967868913725], [5.497697693195921, 9.768347229826592, 16995878.068408724], [9.96278261985784, 2.4264755213769007, 264.57342475037416], [5.854270187319637, -4.552233503055367, 0.0003208372455978718], [8.663084550775622, 3.691707011056092, 2894.7585031019976], [3.939839545687178, -2.7521255367971094, 0.022970387258241715], [7.560889276856056, -0.48060123540388844, 0.37823071118824736], [2.21897406629723, 0.04758759638377619, 1.0386579568206036], [8.185419099880864, 5.6526530285998895, 144911.72448774966], [5.150122679337985, -3.664177700481721, 0.002464755913556522]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-7.11705, x1=-3.17712, y=22.61175\nx0=-7.90516, x1=-7.30776, y=57.76899\nx0=-5.86821, x1=-5.67978, y=33.33010\nx0=-6.82165, x1=-9.05075, y=61.74110\nx0=-3.13889, x1=2.36606, y=-7.42681\nx0=4.70786, x1=-0.06109, y=-0.28760\nx0=5.29967, x1=-5.48003, y=-29.04235\nx0=1.80820, x1=7.62765, y=13.79229\nx0=2.19580, x1=-5.09311, y=-11.18345\nx0=-2.20990, x1=2.29306, y=-5.06742\nx0=7.47328, x1=-9.91462, y=-74.09475\nx0=5.38021, x1=3.04127, y=16.36270\nx0=-4.22987, x1=-7.35179, y=31.09711\nx0=6.52911, x1=3.14199, y=20.51436\nx0=5.43107, x1=-4.82141, y=-26.18541\nx0=1.96757, x1=7.80016, y=15.34735\nx0=3.36155, x1=1.80015, y=6.05132\nx0=-5.95292, x1=2.81114, y=-16.73449\nx0=-4.27594, x1=-7.80828, y=33.38773\nx0=5.01051, x1=-8.28170, y=-41.49554\nx0=-0.70977, x1=-6.07725, y=4.31345\nx0=3.65503, x1=0.54866, y=2.00538\nx0=1.91708, x1=5.52126, y=10.58467\nx0=-8.60651, x1=5.38785, y=-46.37064\nx0=5.54548, x1=-5.70664, y=-31.64609\nx0=-3.20257, x1=-1.03389, y=3.31110\nx0=5.87166, x1=-5.63445, y=-33.08357\nx0=9.34235, x1=-3.36109, y=-31.40045\nx0=2.02675, x1=5.65964, y=11.47065\nx0=6.60653, x1=5.26915, y=34.81079\nx0=-9.88635, x1=3.95958, y=-39.14580\nx0=-0.35459, x1=9.33238, y=-3.30919\nx0=-0.69547, x1=4.00343, y=-2.78428\nx0=5.96402, x1=-4.77701, y=-28.49018\nx0=-1.67734, x1=-7.79304, y=13.07155\nx0=-0.65259, x1=4.96375, y=-3.23930\nx0=-3.05534, x1=-0.01519, y=0.04641\nx0=-9.84127, x1=2.92117, y=-28.74804\nx0=-5.53639, x1=4.11652, y=-22.79065\nx0=1.59670, x1=1.77744, y=2.83803\nx0=6.57723, x1=3.05084, y=20.06610\nx0=6.06155, x1=-3.48863, y=-21.14653\nx0=0.19858, x1=-0.88395, y=-0.17554\nx0=4.92192, x1=3.67099, y=18.06830\nx0=1.70616, x1=6.37420, y=10.87542\nx0=-4.25806, x1=3.96324, y=-16.87569\nx0=2.27020, x1=-3.86394, y=-8.77192\nx0=-5.16797, x1=-9.00744, y=46.55017\nx0=-5.18983, x1=6.25462, y=-32.46042\nx0=3.54717, x1=-1.50430, y=-5.33603\nx0=-5.37417, x1=-5.05930, y=27.18952\nx0=6.05914, x1=0.93918, y=5.69062\nx0=9.99751, x1=5.85534, y=58.53887\nx0=-6.95035, x1=8.03661, y=-55.85730\nx0=-2.06292, x1=-1.47782, y=3.04863\nx0=-8.96978, x1=-4.60094, y=41.26944\nx0=-9.48585, x1=4.46253, y=-42.33090\nx0=-4.56964, x1=-1.74691, y=7.98277\nx0=-0.93244, x1=-6.06907, y=5.65907\nx0=8.31503, x1=-7.87114, y=-65.44882\nx0=-8.03929, x1=-2.43049, y=19.53942\nx0=-4.89057, x1=-1.32858, y=6.49753\nx0=5.85604, x1=5.50016, y=32.20921\nx0=-0.20363, x1=-2.22987, y=0.45406\nx0=0.95863, x1=-1.42638, y=-1.36738\nx0=5.22384, x1=-5.04190, y=-26.33807\nx0=7.01708, x1=-7.26097, y=-50.95082\nx0=-7.65534, x1=-2.44542, y=18.72051\nx0=9.17019, x1=-1.36138, y=-12.48413\nx0=0.16207, x1=-5.07146, y=-0.82192\nx0=0.95060, x1=5.08531, y=4.83411\nx0=-6.97671, x1=-4.98846, y=34.80303\nx0=4.64080, x1=9.50531, y=44.11223\nx0=2.42188, x1=4.05054, y=9.80991\nx0=3.01999, x1=4.10727, y=12.40392\nx0=-4.37374, x1=0.72835, y=-3.18561\nx0=-7.67071, x1=3.63004, y=-27.84497\nx0=-6.72614, x1=-6.72779, y=45.25208\nx0=1.63037, x1=7.18424, y=11.71299\nx0=-5.12956, x1=-9.26579, y=47.52944\nx0=4.70533, x1=7.74109, y=36.42436\nx0=0.81002, x1=4.50376, y=3.64814\nx0=-8.80420, x1=3.75493, y=-33.05914\nx0=7.73624, x1=-6.66303, y=-51.54678\nx0=9.84295, x1=0.29338, y=2.88772\nx0=-6.63147, x1=-8.57949, y=56.89465\nx0=2.07508, x1=7.62140, y=15.81502\nx0=-1.61206, x1=-8.44936, y=13.62088\nx0=0.68410, x1=9.30538, y=6.36583\nx0=0.42081, x1=0.26946, y=0.11339\nx0=-5.05124, x1=5.71464, y=-28.86605\nx0=4.56333, x1=-7.28549, y=-33.24608\nx0=5.85916, x1=1.28383, y=7.52215\nx0=-0.52742, x1=3.44256, y=-1.81567\nx0=6.62823, x1=6.96407, y=46.15949\nx0=-3.05256, x1=5.55482, y=-16.95643\nx0=9.50390, x1=2.21492, y=21.05040\nx0=1.84579, x1=3.42701, y=6.32555\nx0=4.23166, x1=-3.40995, y=-14.42977\nx0=-2.56056, x1=-8.53920, y=21.86515\nx0=9.07651, x1=5.19267, y=47.13126\nx0=-8.84893, x1=-0.70667, y=6.25328\nx0=-0.92516, x1=3.16283, y=-2.92612\nx0=-6.42731, x1=5.43748, y=-34.94836\nx0=1.18345, x1=-6.23603, y=-7.38000\nx0=-5.38256, x1=6.99309, y=-37.64072\nx0=7.59940, x1=-1.52666, y=-11.60166\nx0=-0.14991, x1=-7.28526, y=1.09210\nx0=9.15396, x1=4.22486, y=38.67420\nx0=-3.28722, x1=2.83715, y=-9.32633\nx0=3.19149, x1=0.20682, y=0.66005\nx0=-5.13296, x1=5.99916, y=-30.79347\nx0=-9.11186, x1=-8.28432, y=75.48558\nx0=3.66521, x1=-6.71782, y=-24.62220\nx0=-5.33327, x1=-3.36678, y=17.95594\nx0=7.90845, x1=-2.94269, y=-23.27212\nx0=-6.24678, x1=-9.59347, y=59.92830\nx0=-0.61533, x1=2.84022, y=-1.74768\nx0=1.95826, x1=9.70254, y=19.00007\nx0=9.29955, x1=5.89803, y=54.84901\nx0=0.67420, x1=5.90895, y=3.98383\nx0=8.21855, x1=-5.43333, y=-44.65415\nx0=3.40860, x1=1.15353, y=3.93191\nx0=-4.47559, x1=-4.84432, y=21.68122\nx0=5.47705, x1=9.79867, y=53.66784\nx0=-1.52693, x1=8.55871, y=-13.06860\nx0=-0.82532, x1=6.60414, y=-5.45052\nx0=-0.72198, x1=7.64632, y=-5.52051\nx0=-6.43443, x1=-1.04662, y=6.73440\nx0=4.58751, x1=1.81026, y=8.30461\nx0=7.66358, x1=8.58222, y=65.77051\nx0=-7.40237, x1=-6.69593, y=49.56578\nx0=4.50156, x1=-4.45101, y=-20.03651\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.74265, x1=2.01643, y=-1.49750\nx0=-3.54507, x1=-9.90605, y=35.11766\nx0=5.15779, x1=-6.40827, y=-33.05249\nx0=-3.15592, x1=-1.56517, y=4.93954\nx0=-5.30355, x1=7.21846, y=-38.28347\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1", "data": [[-7.117049447361685, -3.177124594351735, 22.611752838430235], [-7.9051586858583045, -7.307758267290351, 57.768988740823154], [-5.86820672364432, -5.679776608573026, 33.33010328322597], [-6.821652141257819, -9.050754862011292, 61.74110128443895], [-3.1388876125333613, 2.3660648090421823, -7.4268115195536195], [4.707863422458356, -0.061088676579277745, -0.2875971459939701], [5.299670336858647, -5.480028836900168, -29.04234627204981], [1.8081959640506344, 7.627651434236949, 13.792288538572285], [2.195799384400683, -5.093109565530494, -11.183446848677088], [-2.2098952744687628, 2.2930577913310763, -5.067417577146324], [7.47328145858501, -9.91462011617309, -74.09474668311032], [5.380211860658971, 3.041274949478602, 16.362703554709785], [-4.229866265494362, -7.351794803662994, 31.097108830850843], [6.529107947826805, 3.141985361940794, 20.514361598603116], [5.431072522033169, -4.821405918167116, -26.185405199725526], [1.9675687785713958, 7.800160082752008, 15.347351446681726], [3.3615540414591685, 1.8001547563749618, 6.051317496544198], [-5.952920314828109, 2.8111395526149714, -16.734489750578465], [-4.275939970380518, -7.808279487563321, 33.38773436077432], [5.010510769364576, -8.281698177366085, -41.49553790631975], [-0.7097707745468931, -6.0772484046918285, 4.313453307311989], [3.6550264058569724, 0.5486627543198708, 2.0053768549493443], [1.9170752634648949, 5.521257594462508, 10.584666357561764], [-8.606513009883292, 5.387853982505167, -46.37063539578222], [5.545484452991847, -5.706640945083567, -31.64608863976762], [-3.2025735854703052, -1.0338864944728527, 3.311097577573249], [5.871659397851854, -5.634449912737107, -33.083570781848394], [9.34235253799297, -3.3610854744293146, -31.40044541244601], [2.0267460033844493, 5.659640592300615, 11.470653951037669], [6.6065271063467215, 5.269150961811125, 34.810788656638096], [-9.886350117310297, 3.9595803344029576, -39.14579750352422], [-0.3545921447235951, 9.332377386283682, -3.3091877127723097], [-0.6954742799526663, 4.003432040505254, -2.7842840157098254], [5.964017214532227, -4.777011231059336, -28.490177216051666], [-1.6773367313902057, -7.793039860791621, 13.071552007693802], [-0.6525918183860426, 4.963748185136502, -3.239301454148649], [-3.0553442823381927, -0.015188686807656282, 0.04640666739399816], [-9.841268090911985, 2.9211723617120136, -28.74804035137044], [-5.536389297370386, 4.116519254521949, -22.790653143154437], [1.5966977781723557, 1.777437934740382, 2.8380312012392284], [6.577230072339727, 3.050842946822062, 20.066095975823618], [6.061554438945016, -3.488631252921368, -21.146528256987832], [0.19858109085234688, -0.8839501785638681, -0.17553579071833975], [4.921916124579042, 3.6709888475825014, 18.068299202066147], [1.7061629396615796, 6.3741983875025845, 10.87542105880751], [-4.258058510293916, 3.963236663368935, -16.875693602766958], [2.270201754846454, -3.863936387089586, -8.771915166585845], [-5.1679665705142686, -9.007444854589487, 46.55017389426922], [-5.189829034434168, 6.254621408343766, -32.46041578441601], [3.5471741012709774, -1.5043048261230467, -5.336031119640612], [-5.374169873726407, -5.059297052903107, 27.18952180394467], [6.059138689362435, 0.9391792354697532, 5.690617241880614], [9.997511067532685, 5.85534393072297, 58.53886575161323], [-6.950352077063311, 8.036614178099025, -55.85729804530701], [-2.062919260603204, -1.4778244907495406, 3.0486326057583484], [-8.969776936535794, -4.600943984592975, 41.26944123929517], [-9.485850372071438, 4.46253065064586, -42.33089803280922], [-4.569638905796234, -1.746913917879846, 7.982765804220672], [-0.9324446038611072, -6.069065412674577, 5.659067294528493], [8.315032898192232, -7.87114407097989, -65.44882189660852], [-8.039293766346205, -2.4304901298149613, 19.539424149787397], [-4.890568061148586, -1.3285829663376738, 6.497525421757074], [5.856044628569341, 5.500163944276563, 32.20920552213153], [-0.20362721735210698, -2.2298694263234413, 0.4540621063407815], [0.9586300818746718, -1.4263845876075756, -1.3673751740030202], [5.223842071483144, -5.041896307302018, -26.338070050139788], [7.017082379569924, -7.260968713395628, -50.95081561737697], [-7.655338588714877, -2.44541839681808, 18.720505818714717], [9.170192920706633, -1.3613809521660354, -12.484125969937832], [0.16206683256426047, -5.0714604495011955, -0.8219155315255794], [0.9506042408609297, 5.08530644677869, 4.834113874385248], [-6.976713609480781, -4.988455472222883, 34.803025183346264], [4.640796125055502, 9.505314222145984, 44.11222540957003], [2.421877541040443, 4.05053764766371, 9.809906158015526], [3.019994968369362, 4.107266256998033, 12.403923429887323], [-4.373743233607548, 0.728349610238963, -3.1856141794833595], [-7.670708286670019, 3.6300392227580467, -27.844971946947343], [-6.726140995746237, -6.727791777197023, 45.252076083449325], [1.6303723561379293, 7.184241723827917, 11.71298910634174], [-5.129562942764285, -9.265787115605972, 47.52943822375517], [4.705329025104344, 7.741085735353572, 36.42435539638037], [0.8100223159444742, 4.5037552324852115, 3.6481422438647146], [-8.804196725373, 3.7549294109054294, -33.05913722350035], [7.736237372613498, -6.663029405810197, -51.54677710405156], [9.842950235340538, 0.2933794198410027, 2.887719029568068], [-6.631474087834763, -8.579487629725978, 56.89464990342672], [2.0750803407941287, 7.621403097813488, 15.81502373754024], [-1.6120613693661738, -8.44935532765385, 13.620879319759041], [0.6841025497910742, 9.305378115144197, 6.365832895340206], [0.4208113815759056, 0.26946019798713294, 0.11339191819468247], [-5.051243146338811, 5.714642796625093, -28.866050260226952], [4.563326139793421, -7.285491769244898, -33.246075031845066], [5.859163212473213, 1.2838274186854814, 7.522154382726418], [-0.5274185074871784, 3.4425581525553746, -1.815668882758574], [6.628234979810582, 6.964069959639389, 46.159492108329864], [-3.052559422180847, 5.554823189618816, -16.95642786601958], [9.5038998744192, 2.214922514527027, 21.05040180766167], [1.845790558250453, 3.4270113811106384, 6.325545250270861], [4.231664536681032, -3.4099516375917815, -14.429771416594553], [-2.56056196018913, -8.539200591539153, 21.86515220511967], [9.0765050145326, 5.192666536078317, 47.13126385351047], [-8.84893224874249, -0.7066703253697071, 6.253277831393349], [-0.9251574073463757, 3.1628334830000107, -2.9261188250005974], [-6.427306367582055, 5.437481802347095, -34.948361411837034], [1.1834467077860538, -6.236025153521554, -7.380003437606104], [-5.3825612553368885, 6.993087553198084, -37.64072211902265], [7.599400846774984, -1.5266550779712258, -11.601663892267862], [-0.14990525552256173, -7.285255985317929, 1.0920981600263564], [9.153963974941796, 4.224858012801086, 38.674198048425325], [-3.287216096626919, 2.83715011712102, -9.326325533547164], [3.191490834272745, 0.20681562530317343, 0.6600501725394644], [-5.132963943176492, 5.999159988746975, -30.793471911585307], [-9.111864548969816, -8.284318021675432, 75.48558369409614], [3.6652088018493565, -6.717815298843133, -24.622195762518118], [-5.333266385014353, -3.3667802380252043, 17.955935869190444], [7.908445781788885, -2.942691463993743, -23.272115895527474], [-6.246780744167351, -9.593468802854971, 59.928296187444644], [-0.6153323070760734, 2.84021877889451, -1.7476783738179469], [1.958256422239593, 9.702544919218429, 19.00007090012762], [9.299546967994871, 5.8980305439189245, 54.84901206184237], [0.6742027368028136, 5.908953976515605, 3.9838329426086894], [8.218553777078206, -5.433334753476615, -44.65415386031552], [3.4085968216305584, 1.1535269920656894, 3.9319084388201673], [-4.4755922145105265, -4.844323230493708, 21.681215334970123], [5.477054833161352, 9.798668155258166, 53.66784277830097], [-1.5269344018356499, 8.558714914387995, -13.068596238282888], [-0.8253187291899611, 6.604136096182739, -5.450517210299089], [-0.7219828850459074, 7.646315847070412, -5.520509175240137], [-6.434434858077767, -1.0466185192694493, 6.734398683497081], [4.5875126940026725, 1.8102639631344797, 8.304608910375011], [7.663577808203751, 8.582219251776422, 65.77050500305279], [-7.402370771729085, -6.695933232661848, 49.565780450905514], [4.501561309962561, -4.451013596604232, -20.03651059659092], [-0.742652809577006, 2.0164259511529625, -1.4975043979277343], [-3.545073324415185, -9.906047295829785, 35.117664018841346], [5.15778728611356, -6.408268584779433, -33.0524862325763], [-3.1559188975819907, -1.5651683705513353, 4.939544438520571], [-5.3035526713947885, 7.218457769112089, -38.283470984724886]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-7.41617, x1=-3.29900, y=-2.41927\nx0=6.90933, x1=3.20389, y=-2.47030\nx0=7.45988, x1=9.57445, y=-2.13153\nx0=-0.36955, x1=-8.69065, y=-44.52495\nx0=-7.86353, x1=-1.12820, y=-3.53280\nx0=3.36140, x1=5.36608, y=-2.59850\nx0=-4.97681, x1=-9.55566, y=-2.20199\nx0=-6.98931, x1=-3.86201, y=-2.37511\nx0=-3.43416, x1=7.16329, y=-1.67391\nx0=2.34694, x1=8.24354, y=-2.55056\nx0=1.76029, x1=-7.74118, y=-1.45870\nx0=0.96706, x1=-7.28980, y=-1.10445\nx0=3.46068, x1=6.68242, y=-2.44719\nx0=-7.54581, x1=-5.32912, y=-2.24185\nx0=-8.32298, x1=5.78056, y=-1.82391\nx0=-2.83324, x1=8.72107, y=-1.67519\nx0=-5.10209, x1=4.70986, y=-1.66704\nx0=-9.48349, x1=-5.39501, y=-2.18686\nx0=5.09989, x1=9.02968, y=-2.20906\nx0=-0.47485, x1=6.45759, y=-0.51642\nx0=-3.91427, x1=1.85552, y=-1.12306\nx0=6.12438, x1=-2.73783, y=-1.54471\nx0=0.97419, x1=7.49033, y=-4.09449\nx0=-6.88935, x1=3.84102, y=-1.69452\nx0=6.40103, x1=6.11595, y=-2.24897\nx0=7.95662, x1=8.11865, y=-2.14611\nx0=-5.07285, x1=6.46355, y=-1.74852\nx0=-8.13867, x1=-1.93464, y=-2.70614\nx0=7.96190, x1=1.59001, y=-2.93172\nx0=-6.99790, x1=-0.45609, y=-48.95765\nx0=-9.89997, x1=5.80762, y=-1.85123\nx0=9.77142, x1=-2.39118, y=-1.65864\nx0=9.20706, x1=-3.25739, y=-1.72720\nx0=5.60338, x1=-2.33746, y=-1.44091\nx0=0.33000, x1=-8.23620, y=-0.42602\nx0=0.48086, x1=9.45704, y=-7.81593\nx0=-7.15643, x1=5.35815, y=-1.78232\nx0=-0.78510, x1=2.47105, y=-0.17814\nx0=2.52348, x1=-6.10586, y=-1.51108\nx0=-8.96916, x1=3.35041, y=-1.72769\nx0=4.52524, x1=-5.60279, y=-1.68258\nx0=5.18190, x1=-1.91592, y=-1.30384\nx0=-4.11854, x1=-7.02828, y=-2.34687\nx0=9.35035, x1=6.26871, y=-2.16183\nx0=-8.39737, x1=-3.45418, y=-2.34607\nx0=4.79663, x1=-6.20341, y=-1.72524\nx0=3.36750, x1=3.30201, y=-3.10844\nx0=3.39187, x1=-7.50259, y=-1.68363\nx0=-3.09441, x1=-1.38110, y=-9.06602\nx0=4.37861, x1=7.97709, y=-2.28188\nx0=-1.41256, x1=3.77378, y=-0.91966\nx0=-4.55434, x1=2.78634, y=-1.42638\nx0=6.87317, x1=8.44459, y=-2.16351\nx0=-7.09584, x1=-4.84264, y=-2.28697\nx0=3.97543, x1=-6.90249, y=-1.70434\nx0=6.28608, x1=-2.63949, y=-1.54063\nx0=-2.89960, x1=-0.06684, y=1.20721\nx0=-6.56824, x1=-5.60968, y=-2.26591\nx0=-7.51246, x1=-4.42679, y=-2.29746\nx0=8.72787, x1=1.19925, y=-3.20533\nx0=9.94815, x1=-5.32812, y=-1.83930\nx0=-4.04152, x1=1.12030, y=-0.80442\nx0=-2.50883, x1=0.97173, y=-0.34495\nx0=2.72758, x1=-2.67172, y=-1.12514\nx0=-5.03473, x1=0.52019, y=-0.39830\nx0=6.55037, x1=3.73065, y=-2.41983\nx0=-4.44937, x1=-9.85574, y=-2.22031\nx0=7.67402, x1=-1.71298, y=-1.44257\nx0=-7.54419, x1=4.89319, y=-1.77452\nx0=-3.85311, x1=2.51920, y=-1.29171\nx0=-6.93373, x1=-1.32022, y=-3.46245\nx0=8.81082, x1=-9.30031, y=-1.89405\nx0=7.06038, x1=-2.93624, y=-1.62075\nx0=7.39898, x1=-9.68817, y=-1.87949\nx0=-9.11368, x1=9.35458, y=-1.89802\nx0=7.71734, x1=6.89927, y=-2.17913\nx0=-8.80377, x1=-7.35757, y=-2.14569\nx0=7.42632, x1=4.45952, y=-2.29883\nx0=1.48787, x1=8.25361, y=-2.96979\nx0=-8.36243, x1=-8.13337, y=-2.13843\nx0=3.65820, x1=0.54171, y=6.83809\nx0=-2.41893, x1=7.52842, y=-1.57569\nx0=7.75554, x1=-6.76801, y=-1.83781\nx0=-8.95412, x1=-5.68846, y=-2.18775\nx0=1.18387, x1=9.90265, y=-3.03171\nx0=6.13339, x1=-6.04122, y=-1.77530\nx0=6.20690, x1=-6.29158, y=-1.78598\nx0=-6.77691, x1=-6.70669, y=-2.21201\nx0=6.26113, x1=5.71475, y=-2.27455\nx0=-6.61651, x1=4.02702, y=-1.69641\nx0=-9.61182, x1=9.23463, y=-1.90192\nx0=-1.10191, x1=-7.25402, y=-3.80242\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-1.49044, x1=-9.51023, y=-2.80541\nx0=1.24739, x1=6.11567, y=-3.94442\nx0=8.38163, x1=3.21452, y=-2.37589\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1 + x0 * x1 / (1 - (x0 * x1 / 3))", "data": [[-7.416165339033807, -3.2989988421028293, -2.419269224742313], [6.909333872485263, 3.203894261965324, -2.470298675214002], [7.459879854210904, 9.574451827793911, -2.131532295122327], [-0.3695514243854454, -8.690645615753471, -44.524948865104186], [-7.86352684846168, -1.128195437867511, -3.532803236977456], [3.3614006619820564, 5.366081343913326, -2.5985017752270645], [-4.976811738289735, -9.55566248519164, -2.2019896735891322], [-6.98931496308639, -3.862013124517187, -2.375112125408974], [-3.434160610043979, 7.1632850636549925, -1.6739115241436817], [2.3469361658435535, 8.243535446910425, -2.5505580020893697], [1.7602864710317903, -7.741184835519778, -1.4587020628928302], [0.9670596182675073, -7.289804184693276, -1.1044486737892951], [3.4606754847689185, 6.682423910295551, -2.4471894010823925], [-7.545814191751852, -5.329118262662287, -2.241853980276395], [-8.322978929399032, 5.78055998288912, -1.823914310697842], [-2.8332442438459937, 8.721071405392426, -1.6751949098265912], [-5.1020889522469055, 4.709855705968852, -1.667037891844307], [-9.483493519909384, -5.395011363367002, -2.1868632816479643], [5.099885746431298, 9.029675138605853, -2.2090577205889277], [-0.47485189860396027, 6.457589761877877, -0.5164180005649621], [-3.9142665110733628, 1.8555162135663306, -1.123062147954942], [6.124379266468665, -2.7378343450085696, -1.5447080482553015], [0.9741864576828423, 7.490333319356736, -4.0944936472232625], [-6.889347728657738, 3.8410181795229867, -1.6945228960363483], [6.401027437645951, 6.1159512658117485, -2.248973869000643], [7.956624042190828, 8.118645456285897, -2.146110989063028], [-5.072847543132674, 6.46354890602867, -1.7485232600406362], [-8.138674729190633, -1.9346385458662407, -2.706137457234323], [7.961900627625528, 1.5900132338771336, -2.9317226050679506], [-6.997897365237504, -0.45608872193469807, -48.95764899840157], [-9.899972815031246, 5.8076152554468035, -1.8512279475339741], [9.771424882380881, -2.3911811518487607, -1.658641544373249], [9.207059012972529, -3.257385967297914, -1.7271978706076654], [5.603377091005179, -2.337462627299834, -1.4409133823331048], [0.33000335934524827, -8.236203882289281, -0.42601618936227537], [0.4808557815512682, 9.457040556976555, -7.815934857952405], [-7.1564301565343875, 5.35814665242018, -1.782320571619607], [-0.7850979148166388, 2.4710546655574195, -0.17814497808620655], [2.5234808725191655, -6.1058641030013705, -1.5110829688424885], [-8.9691605673416, 3.350410562061331, -1.727688376289048], [4.525239630527819, -5.602787772335818, -1.6825839894348729], [5.181904416472529, -1.9159197676001156, -1.3038427242497863], [-4.11854120503113, -7.028276075205582, -2.346871007083093], [9.350346999919875, 6.26871085728737, -2.1618279458807503], [-8.397365963084845, -3.4541753380283335, -2.3460743234110515], [4.7966343303733705, -6.203411852235043, -1.7252369684718327], [3.367495342593646, 3.3020130096659095, -3.108440804516615], [3.3918673536200465, -7.502586903599742, -1.6836308446222747], [-3.0944128613748383, -1.3811026072275538, -9.066018838753697], [4.378614603660294, 7.9770886642032295, -2.281878969583732], [-1.4125621818694256, 3.7737771634744828, -0.9196579512523011], [-4.554335544676031, 2.7863444055457016, -1.4263843090023154], [6.873173632577583, 8.444589366166653, -2.1635140878921684], [-7.095842114454003, -4.8426432489003695, -2.2869657121121274], [3.975433512383823, -6.902486414743077, -1.7043400496892445], [6.286083596463726, -2.6394946407820825, -1.540630796786835], [-2.899597285955804, -0.06684496973887377, 1.2072109423691515], [-6.568244640568528, -5.609684574572384, -2.2659120229826977], [-7.512456305676418, -4.426790058936048, -2.297461002848727], [8.727872907645796, 1.1992451333436556, -3.205326077363508], [9.948152777558864, -5.3281207702313305, -1.8392999461107555], [-4.041524368263898, 1.1203005545862599, -0.8044191841047093], [-2.508831652464794, 0.9717270506489033, -0.34494920990821454], [2.727576921280047, -2.6717234584424983, -1.1251375322321455], [-5.034728721308113, 0.5201937808681194, -0.3983013649070215], [6.550368140164608, 3.7306514767551313, -2.4198321118596406], [-4.449365158298695, -9.855743724047262, -2.2203085151077535], [7.674021352204456, -1.7129844269618388, -1.4425684142405086], [-7.5441940743568185, 4.8931866279721525, -1.7745217016990256], [-3.8531133217652673, 2.5191952777859576, -1.2917147482319482], [-6.933732934900281, -1.3202175720476017, -3.4624548688799015], [8.810815891503449, -9.300312914949835, -1.8940470260697828], [7.060383565596503, -2.936236961033025, -1.6207485786783553], [7.398984628578834, -9.688168583255624, -1.879490018511782], [-9.113683319549782, 9.35457848237975, -1.8980223888375911], [7.71733938248375, 6.899266184660231, -2.179125941936283], [-8.803765979762058, -7.357570427199988, -2.145691588386811], [7.426324400191632, 4.459524566990854, -2.2988258524138274], [1.4878713004926158, 8.253612418267384, -2.969794872086224], [-8.362430097270872, -8.133366474087483, -2.138430213631477], [3.6582011680481212, 0.5417091390506297, 6.838094984097796], [-2.4189341529472896, 7.528421125772798, -1.5756869565014409], [7.755542194054467, -6.768012997903545, -1.8378074753245972], [-8.95411608097641, -5.688462554014835, -2.187753647233335], [1.1838651519993562, 9.90264964094358, -3.0317076048151987], [6.133391758322794, -6.041219264580597, -1.775298653074604], [6.206899957623296, -6.291582380540868, -1.7859753062110526], [-6.77690962760744, -6.706685965886674, -2.212011114220712], [6.261126518845302, 5.714745655136049, -2.2745514125305224], [-6.616512786945767, 4.02702446943306, -1.6964060435648585], [-9.611822988498979, 9.234628609081874, -1.901919773910222], [-1.1019116312839827, -7.254024825441967, -3.8024172835419217], [-1.4904381960241473, -9.510228353372387, -2.805411824017183], [1.2473919067615054, 6.115667137019244, -3.9444182885283663], [8.38163243605429, 3.2145184151466832, -2.375894129739021]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.39161, y=-55.87998\nx0=-4.88674, y=-2314.16828\nx0=5.60208, y=6715.25683\nx0=-6.99339, y=-14635.93309\nx0=-8.67025, y=-43929.92417\nx0=2.79799, y=265.30660\nx0=6.38047, y=12538.72429\nx0=-7.95011, y=-28211.42510\nx0=-2.95741, y=-169.81288\nx0=-2.48018, y=-67.59248\nx0=-4.54590, y=-1592.10688\nx0=-0.30570, y=-0.23475\nx0=5.14880, y=4489.46437\nx0=-2.56130, y=-79.99715\nx0=1.11656, y=7.04495\nx0=2.67998, y=218.94390\nx0=0.71959, y=2.07108\nx0=-1.85569, y=-14.94942\nx0=-9.98014, y=-89994.35608\nx0=5.40260, y=5646.93672\nx0=-6.71924, y=-11922.79212\nx0=8.35334, y=46202.56035\nx0=4.57734, y=2569.80684\nx0=7.33410, y=24568.36155\nx0=9.27547, y=76951.58905\nx0=-9.95175, y=-88698.95220\nx0=3.36801, y=614.96582\nx0=-7.59985, y=-22405.52006\nx0=-6.81537, y=-12823.75152\nx0=5.26815, y=5007.28630\nx0=-4.43968, y=-1408.60050\nx0=4.88388, y=3492.76365\nx0=-9.50215, y=-70090.27809\nx0=9.52531, y=87611.10404\nx0=-5.82907, y=-5745.09963\nx0=1.11934, y=7.10173\nx0=-5.05462, y=-2755.34000\nx0=3.85720, y=1151.28772\nx0=2.51703, y=165.96346\nx0=5.48651, y=6078.28002\nx0=3.98628, y=1342.29058\nx0=-4.75055, y=-1999.55639\nx0=-8.90997, y=-50488.43906\nx0=1.54439, y=22.08805\nx0=4.80325, y=3227.65718\nx0=-3.85019, y=-672.43145\nx0=-5.39866, y=-3870.08774\nx0=6.03335, y=9581.61742\nx0=-8.35512, y=-36364.55916\nx0=5.56024, y=6478.76189\nx0=-3.98627, y=-805.48103\nx0=-3.33247, y=-316.89685\nx0=-2.15058, y=-32.08327\nx0=-9.38149, y=-65671.70609\nx0=5.90341, y=8630.96317\nx0=-6.47317, y=-9845.41776\nx0=7.76816, y=32465.46720\nx0=3.08461, y=411.73386\nx0=3.95155, y=1288.56328\nx0=6.58484, y=14595.76755\nx0=3.18959, y=479.43686\nx0=9.03374, y=67652.14540\nx0=0.09770, y=0.10827\nx0=4.56465, y=2536.34862\nx0=3.48141, y=716.11080\nx0=7.44847, y=26480.53859\nx0=-0.72971, y=-0.50915\nx0=-7.85935, y=-26603.03403\nx0=9.73599, y=97490.59742\nx0=-3.04638, y=-198.28512\nx0=2.19367, y=91.51787\nx0=6.03184, y=9570.10727\nx0=2.15612, y=85.03866\nx0=-8.39732, y=-37312.12680\nx0=-8.75950, y=-46286.66792\nx0=2.01110, y=63.44518\nx0=-4.94238, y=-2453.59507\nx0=-7.49953, y=-20932.88061\nx0=7.87811, y=34757.56455\nx0=-6.52580, y=-10263.26905\nx0=-7.26325, y=-17768.76183\nx0=0.43595, y=0.76071\nx0=-9.76541, y=-80559.59156\nx0=-3.39412, y=-348.70340\nx0=-9.87934, y=-85461.52923\nx0=-5.66339, y=-4952.63951\nx0=-2.36709, y=-52.94644\nx0=5.46127, y=5945.84931\nx0=-1.70353, y=-9.67004\nx0=5.66371, y=7076.20131\nx0=-3.67585, y=-528.36648\nx0=-0.81007, y=-0.60365\nx0=9.37355, y=81004.59933\nx0=-0.39192, y=-0.28417\nx0=-5.91794, y=-6210.18500\nx0=-2.27125, y=-42.65846\nx0=5.80487, y=7961.73267\nx0=-4.78369, y=-2072.74556\nx0=-6.42617, y=-9483.95212\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=5.04414, y=4071.58527\nx0=3.81191, y=1089.72481\nx0=-7.93146, y=-27874.73795\nx0=-0.19019, y=-0.15984\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**5 + x0**4 + x0**3 + x0**2 + x0", "data": [[-2.391614899116041, -55.879980582892486], [-4.886736906180955, -2314.1682835350225], [5.6020791133418975, 6715.256831072331], [-6.9933867551340185, -14635.93308636353], [-8.670248319109175, -43929.92416606226], [2.7979875635612963, 265.30659620218336], [6.380465766456357, 12538.724290303575], [-7.950113213232477, -28211.425100035372], [-2.957406109653813, -169.81287980078937], [-2.480177405925157, -67.59247866137073], [-4.5459026934820335, -1592.1068753745083], [-0.30570334895806006, -0.23475436271598285], [5.1488023193890005, 4489.464374662233], [-2.561298047585434, -79.9971494214045], [1.1165571859086825, 7.044950710983848], [2.679980676623831, 218.94390157468143], [0.7195898928143425, 2.071078199890294], [-1.8556918731705103, -14.949420846695087], [-9.980135322789005, -89994.35608294873], [5.402599039104171, 5646.936720759808], [-6.719239656461193, -11922.792123550793], [8.353341648184792, 46202.56034789058], [4.5773352014319, 2569.8068414339555], [7.334102141319562, 24568.361552357837], [9.275474535344305, 76951.58904941965], [-9.951753676397637, -88698.95219537118], [3.3680058625456173, 614.9658233903194], [-7.599845388776407, -22405.520060656254], [-6.815365330889183, -12823.751523058047], [5.268150878093582, 5007.286300915779], [-4.43967895233818, -1408.6004977406483], [4.883883371539184, 3492.7636464230422], [-9.502146146194423, -70090.27808582493], [9.525310717640998, 87611.1040424363], [-5.829067328164578, -5745.099630854415], [1.1193427401211569, 7.101732652720979], [-5.054618676785669, -2755.3399967180258], [3.857200985957231, 1151.2877153156592], [2.5170253486749505, 165.96346363403137], [5.486509101669872, 6078.280021882244], [3.986283817327065, 1342.2905771172727], [-4.75055045563304, -1999.5563851985216], [-8.909966376782073, -50488.43905769234], [1.5443930375502255, 22.08805061035677], [4.803252394356436, 3227.657179521876], [-3.850191364311925, -672.4314510528374], [-5.398658293189014, -3870.087740605569], [6.033347584538394, 9581.617421553507], [-8.355123287245876, -36364.559163713464], [5.560240583626875, 6478.761892378271], [-3.986269266579219, -805.4810300580282], [-3.332470848536566, -316.8968508547055], [-2.150576148322127, -32.08327158701863], [-9.381494632698788, -65671.70609032654], [5.903411043208884, 8630.963172937922], [-6.473166295434818, -9845.417763880243], [7.768155040324384, 32465.46719552855], [3.0846065737001904, 411.7338635558417], [3.9515539050164854, 1288.5632815334534], [6.584844383637062, 14595.767545739704], [3.189594197235442, 479.4368551437879], [9.033744448041844, 67652.14539842171], [0.09769626330000669, 0.1082732896142588], [4.5646503375948875, 2536.3486248075337], [3.481406071705484, 716.110795394995], [7.44847001297677, 26480.53858804732], [-0.729710623692295, -0.5091517943825244], [-7.85934564333898, -26603.03402953985], [9.735985914819182, 97490.59742432767], [-3.0463803219280123, -198.28512362134404], [2.1936663303617188, 91.51786613007889], [6.031837532045071, 9570.10727322962], [2.1561238352922274, 85.03865697898243], [-8.397317725843312, -37312.12679838162], [-8.75949669215964, -46286.66791975275], [2.0110964665514235, 63.44517890628097], [-4.942378389663526, -2453.595074509245], [-7.499534455981955, -20932.88060653967], [7.878111956909397, 34757.564549449235], [-6.525797467987047, -10263.269053151707], [-7.263252016923792, -17768.761825392565], [0.4359463206074601, 0.760711271187746], [-9.765410216477585, -80559.59156213245], [-3.3941227667514813, -348.7033988278784], [-9.879344477635161, -85461.52922989319], [-5.6633864461824786, -4952.63950517144], [-2.367087709910818, -52.94643638903026], [5.461269794050459, 5945.849306270009], [-1.7035282007909398, -9.67004282778216], [5.663710534753694, 7076.201308747182], [-3.675854049177641, -528.3664819496864], [-0.8100736248192355, -0.603653470027932], [9.373553076909506, 81004.5993287506], [-0.3919217422901369, -0.2841724478057348], [-5.917935112200226, -6210.184995548505], [-2.271252569300122, -42.65846463304698], [5.804870389838317, 7961.732674074539], [-4.783688933219985, -2072.7455622775033], [-6.426173889139523, -9483.952118745643], [5.044139863372614, 4071.5852693383777], [3.811914455381631, 1089.7248127348487], [-7.931462089333556, -27874.737951743882], [-0.19018953499623592, -0.15983745241505531]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.65160, x1=-9.98509, y=1.52960\nx0=7.57034, x1=-5.53880, y=1.63757\nx0=7.39040, x1=3.27106, y=0.76535\nx0=0.01510, x1=3.20734, y=-0.05060\nx0=2.10053, x1=-8.69525, y=0.19642\nx0=0.35265, x1=2.75207, y=0.72513\nx0=-2.23950, x1=-5.25128, y=0.07365\nx0=-3.79977, x1=-2.25353, y=-0.16418\nx0=9.80565, x1=7.22078, y=0.43441\nx0=9.59335, x1=4.41446, y=-1.12372\nx0=-6.19983, x1=-4.62302, y=1.07927\nx0=8.44535, x1=3.42172, y=0.55370\nx0=-6.96216, x1=-1.05474, y=-1.49777\nx0=2.89246, x1=-7.03583, y=-0.43701\nx0=-1.89584, x1=-9.26568, y=-1.10607\nx0=7.41020, x1=-2.08273, y=0.03133\nx0=-5.41065, x1=6.22705, y=0.70985\nx0=-8.06126, x1=-7.68531, y=-1.96440\nx0=5.94589, x1=-3.48473, y=0.00550\nx0=-5.21152, x1=9.82586, y=0.48759\nx0=-1.93089, x1=-4.79527, y=0.06070\nx0=-6.17190, x1=3.24476, y=0.00808\nx0=-3.80660, x1=-8.75806, y=-0.00135\nx0=6.90235, x1=9.18006, y=0.82264\nx0=-4.55654, x1=8.87819, y=1.50765\nx0=-4.74822, x1=-3.30823, y=1.16522\nx0=-5.15930, x1=4.31549, y=-0.02048\nx0=3.57171, x1=-1.14488, y=-1.32764\nx0=6.54952, x1=0.52754, y=0.76661\nx0=5.01557, x1=-9.59263, y=-0.78733\nx0=3.59836, x1=0.20281, y=-0.23963\nx0=8.12446, x1=8.65405, y=1.66030\nx0=8.51458, x1=1.52879, y=1.78874\nx0=8.27368, x1=-2.07437, y=0.03735\nx0=-8.07124, x1=-0.47641, y=-1.43508\nx0=7.75443, x1=1.63583, y=1.99293\nx0=1.88108, x1=1.65551, y=1.94866\nx0=0.65862, x1=-0.73940, y=-0.06182\nx0=-8.46832, x1=2.18402, y=0.00064\nx0=0.76921, x1=-3.45707, y=1.00584\nx0=-5.01720, x1=-4.52974, y=1.93727\nx0=-0.31863, x1=-6.40988, y=-0.43962\nx0=-5.91899, x1=-7.31125, y=-0.50010\nx0=-8.52519, x1=2.75609, y=-0.40704\nx0=-2.93203, x1=-8.91153, y=-0.69904\nx0=-9.69899, x1=8.11239, y=1.23759\nx0=3.25488, x1=-6.58768, y=-0.41286\nx0=-2.13147, x1=-6.52924, y=-1.09048\nx0=2.81581, x1=-5.98474, y=0.61409\nx0=0.36159, x1=-3.53469, y=0.73681\nx0=2.03690, x1=4.25714, y=-0.00482\nx0=8.10737, x1=-3.31672, y=1.14230\nx0=1.20586, x1=8.86731, y=1.46319\nx0=6.33821, x1=9.21926, y=0.25907\nx0=6.37299, x1=-2.81883, y=-0.22751\nx0=-4.84371, x1=3.79995, y=0.37957\nx0=-3.96059, x1=9.81957, y=0.34585\nx0=-7.43623, x1=-5.73686, y=-0.39445\nx0=7.19853, x1=0.70562, y=1.44128\nx0=3.90617, x1=7.21258, y=0.10903\nx0=-9.45460, x1=-5.29768, y=0.86337\nx0=4.47256, x1=-9.99387, y=-0.43251\nx0=-6.85630, x1=5.33170, y=-1.35653\nx0=-1.96412, x1=4.44818, y=-1.88894\nx0=-3.16335, x1=-3.95956, y=0.75152\nx0=9.27016, x1=-1.00413, y=-0.68970\nx0=2.14245, x1=-9.02779, y=0.45437\nx0=6.25995, x1=4.96555, y=-0.99136\nx0=0.95397, x1=8.38009, y=1.68049\nx0=-1.94542, x1=4.19690, y=-1.80070\nx0=2.06983, x1=3.48907, y=0.53752\nx0=5.69668, x1=-0.31585, y=-0.86408\nx0=-7.27127, x1=-2.39265, y=-1.51584\nx0=-3.91631, x1=-7.03342, y=0.01771\nx0=-3.29855, x1=9.05761, y=0.51529\nx0=6.48714, x1=-1.40336, y=-0.78348\nx0=-6.98012, x1=-7.49600, y=-1.57847\nx0=-2.03978, x1=4.77243, y=-1.89023\nx0=-2.84874, x1=-3.84641, y=0.35921\nx0=-1.20544, x1=-4.24532, y=-0.04110\nx0=8.12410, x1=-7.08583, y=0.24454\nx0=-7.01217, x1=-0.08256, y=-0.74859\nx0=-5.94176, x1=6.96815, y=0.96748\nx0=-9.85650, x1=8.19627, y=1.36042\nx0=-5.86925, x1=9.77902, y=0.05534\nx0=9.56465, x1=-3.32782, y=0.04573\nx0=2.46251, x1=4.25531, y=-0.26927\nx0=-7.12964, x1=-1.93799, y=-1.68227\nx0=5.11349, x1=-6.26057, y=-0.89802\nx0=-5.79213, x1=1.27108, y=1.42698\nx0=-6.56737, x1=1.88706, y=0.67003\nx0=4.22981, x1=8.40654, y=-0.03461\nx0=-4.04581, x1=-0.83255, y=0.04629\nx0=-9.39551, x1=-6.81169, y=-0.53350\nx0=2.07682, x1=-5.71155, y=1.41569\nx0=-9.20880, x1=4.62506, y=-1.21049\nx0=-2.93368, x1=-0.61337, y=-0.78205\nx0=-7.64827, x1=-0.00181, y=-0.98073\nx0=1.60823, x1=-7.19651, y=0.20776\nx0=-5.78004, x1=-3.62227, y=0.94456\nx0=-2.78363, x1=1.72261, y=0.63813\nx0=6.51149, x1=4.56854, y=-0.76334\nx0=-3.90336, x1=9.91302, y=0.22113\nx0=-4.37407, x1=-0.68529, y=0.31042\nx0=9.25688, x1=6.43360, y=0.31696\nx0=5.98736, x1=-4.46543, y=0.67813\nx0=8.94489, x1=7.63112, y=1.43695\nx0=5.18728, x1=-5.18471, y=0.00117\nx0=5.12669, x1=6.83132, y=-0.39430\nx0=-7.95250, x1=-4.20015, y=-0.12350\nx0=-9.48108, x1=4.63609, y=-0.94082\nx0=-3.63449, x1=6.48171, y=0.67040\nx0=9.49399, x1=1.94555, y=0.86144\nx0=9.28720, x1=-4.06061, y=0.93216\nx0=8.04988, x1=-1.28527, y=0.02136\nx0=-9.72107, x1=-3.52218, y=0.66344\nx0=0.43001, x1=-9.94403, y=0.91311\nx0=1.33150, x1=6.05912, y=0.74931\nx0=0.40956, x1=3.15562, y=0.38418\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=8.94980, x1=-5.48940, y=1.17033\nx0=-2.67867, x1=-3.02714, y=-0.56076\nx0=-5.68344, x1=2.15850, y=1.39665\nx0=3.88849, x1=-6.23229, y=-0.62850\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0) + sin(x1)", "data": [[-4.651600455538858, -9.985085682858333, 1.5295998383844955], [7.570340671016066, -5.538796652899989, 1.637565160638658], [7.39040382944135, 3.2710595111039034, 0.7653529258795924], [0.015096960724088504, 3.2073406337644617, -0.05060423396599057], [2.1005331948389543, -8.695249491118009, 0.1964218740855841], [0.3526466909083332, 2.7520742995258267, 0.7251257251291379], [-2.2395013073101016, -5.251282151014641, 0.07365201934120924], [-3.799771225014683, -2.253527636028519, -0.16417547102389973], [9.80565231086753, 7.220784112948891, 0.4344072725389484], [9.593351903407594, 4.414464966082832, -1.1237246028963772], [-6.199828025826433, -4.623017380298715, 1.0792697971282748], [8.44534806567577, 3.421722695626432, 0.5536990504247653], [-6.962156417587173, -1.0547425965478396, -1.4977658952198518], [2.8924559114768478, -7.035834959991345, -0.43700764056392677], [-1.8958373831667341, -9.265675584834332, -1.106069599538353], [7.410195071518949, -2.0827272138869475, 0.031332068355703235], [-5.410650991403783, 6.227049677008068, 0.7098545225199879], [-8.061256505103856, -7.68531304066925, -1.9644045063358078], [5.945888452245978, -3.4847285013650087, 0.0055043085097064015], [-5.211518766985213, 9.825855130522083, 0.48758917684148234], [-1.9308876608763619, -4.795265697288549, 0.06070304502432777], [-6.171895663702753, 3.2447589563842545, 0.008076662775842597], [-3.806596439012953, -8.7580599618431, -0.001348032087224449], [6.902347657842835, 9.18005553082278, 0.8226402464031384], [-4.55654143641723, 8.878192829440707, 1.5076532597048007], [-4.748224017758764, -3.308228044844588, 1.1652232843318515], [-5.159298068087654, 4.3154914628889784, -0.020477483657633022], [3.5717092108412274, -1.1448766518913995, -1.3276358927998797], [6.54952195985793, 0.5275391731439267, 0.7666076211393084], [5.015565139408494, -9.592631338292875, -0.787326770342337], [3.598361809126633, 0.2028081659859744, -0.2396300552362051], [8.124455934494684, 8.654045911641962, 1.6603048750376954], [8.514583755841137, 1.5287931105994588, 1.7887409118508653], [8.273675187698906, -2.07437109619846, 0.03735073161228453], [-8.071244953963557, -0.4764104063249732, -1.4350832747461597], [7.754427686169038, 1.6358341609864286, 1.9929343826728352], [1.8810778431239505, 1.6555132337681897, 1.9486613216802577], [0.6586247446393596, -0.7394046342240657, -0.0618183017810261], [-8.468319923076685, 2.1840212517889928, 0.0006412564355247063], [0.7692077935796764, -3.4570734026711714, 1.0058398166944578], [-5.01719958701218, -4.52973544022798, 1.9372689764255675], [-0.31862635611874524, -6.409879963140657, -0.4396183400725504], [-5.9189858888657865, -7.311252443335965, -0.5001009758677113], [-8.525194879962738, 2.7560860415393336, -0.40703906464181605], [-2.932029785745236, -8.911532311271802, -0.6990396445775067], [-9.698990017719115, 8.11238821576261, 1.2375869044647283], [3.2548838433967866, -6.587682785311957, -0.4128628069158564], [-2.1314740811247157, -6.5292408050739255, -1.0904750700908075], [2.815811072833087, -5.984738279399238, 0.6140855936989309], [0.3615902359718408, -3.5346898161487044, 0.7368132648111998], [2.0368979199720876, 4.257137783551666, -0.004823564419678794], [8.107374596358575, -3.3167175724455173, 1.1422985609926912], [1.2058640050719909, 8.867305548630032, 1.4631909084124315], [6.338208436799093, 9.219259521034331, 0.25907008629922074], [6.3729853348499645, -2.818830732298892, -0.22750768659117837], [-4.843711401909068, 3.7999453440908955, 0.379574936793835], [-3.9605926675200642, 9.819567190836985, 0.3458496122352729], [-7.436226086882098, -5.736861340679393, -0.39445204310917625], [7.198530741223831, 0.7056172421837363, 1.4412769868457422], [3.9061677050656023, 7.212584762020182, 0.10903038437239654], [-9.454601440607046, -5.297681328955777, 0.8633696745631099], [4.472561578300143, -9.993870555389687, -0.4325111061590938], [-6.856297368090725, 5.3316983037031065, -1.356529048418559], [-1.9641196142555302, 4.448181287857565, -1.888940189947486], [-3.163349990923468, -3.9595641488255495, 0.751516058222912], [9.270163513687326, -1.0041343613343496, -0.6896984347110648], [2.1424520173040733, -9.027793094613621, 0.45436690371812394], [6.259947248629437, 4.965550042741215, -0.9913614899883041], [0.9539730589620294, 8.380088914980348, 1.6804885675892263], [-1.945422986452293, 4.196900032729323, -1.800696095889839], [2.069828650619181, 3.489070620480156, 0.5375184892499899], [5.696678739753322, -0.3158461701932058, -0.8640756944230005], [-7.271265000826506, -2.39264938782725, -1.5158359640682602], [-3.9163110988365286, -7.03341520050488, 0.017707946580593492], [-3.298553665608579, 9.05760971574729, 0.5152911667213421], [6.487136675540565, -1.403363463130125, -0.7834754591510079], [-6.980116425435138, -7.495995828567807, -1.578471920663619], [-2.0397787376927763, 4.772430789502064, -1.8902267106809822], [-2.848743519882766, -3.8464112948169182, 0.3592144682230881], [-1.2054389346351755, -4.245323884142341, -0.0411025065131333], [8.124100796979018, -7.085831882251328, 0.2445416419561709], [-7.01217415115408, -0.08256361795160672, -0.748585653942746], [-5.941755583682349, 6.96814736176281, 0.9674782547444902], [-9.856496682081612, 8.19626631868918, 1.3604227375897908], [-5.869246953943749, 9.779017116084663, 0.0553413117211205], [9.564653873482534, -3.3278178427164935, 0.04573043761940518], [2.462511400691591, 4.255309450973394, -0.2692668457358087], [-7.12963577109811, -1.9379855698236685, -1.6822731178145873], [5.113485528321494, -6.260568392659622, -0.8980184380750822], [-5.792128772740758, 1.2710751361288857, 1.4269766861629392], [-6.5673657885942305, 1.8870565869445421, 0.6700342782021111], [4.229808730412421, 8.40653792525788, -0.03461486848469142], [-4.045811745394725, -0.8325543210953974, 0.046289748192348656], [-9.395514263597484, -6.811690122479639, -0.5335022412967618], [2.0768240468235923, -5.711546487155587, 1.4156878413735532], [-9.208804503898849, 4.625060494347554, -1.2104876619247706], [-2.933678910453712, -0.6133739044077746, -0.7820486323359017], [-7.648270594585145, -0.0018117718217087742, -0.9807277635977936], [1.6082290239194812, -7.19651478526859, 0.20775666544496607], [-5.780044025832289, -3.622271659248728, 0.9445612460193142], [-2.783628692866637, 1.7226052768873217, 0.638131152451202], [6.5114923934458595, 4.568540649090311, -0.7633427926105917], [-3.9033645987449717, 9.913024786395827, 0.22112645021760702], [-4.374065347356524, -0.685287801391949, 0.310416523155125], [9.256878533891104, 6.433596425452464, 0.3169563061594458], [5.987358359282611, -4.46542622136451, 0.6781284008321702], [8.944885130492779, 7.63111755516066, 1.4369525346193763], [5.187278303949194, -5.184713390877982, 0.0011698542246385557], [5.126691009548896, 6.8313178257011735, -0.3943032677099515], [-7.952495774253867, -4.200153885757487, -0.12350019905017551], [-9.481076258225695, 4.636085909886869, -0.9408217702300369], [-3.6344881444913835, 6.481709069573615, 0.6704010022386642], [9.4939873922984, 1.9455486100811008, 0.861444131995409], [9.287195812054286, -4.060614846697588, 0.9321573787398628], [8.049876407614345, -1.2852664999394108, 0.02136134646221044], [-9.72106841011853, -3.5221799158980582, 0.663440087562321], [0.43001353474689985, -9.944031066225875, 0.913114934913692], [1.3314971429664002, 6.0591230233738855, 0.7493121381945458], [0.4095638038103786, 3.1556245656644073, 0.38417779385635425], [8.949799488640082, -5.48939828349652, 1.170332953643451], [-2.6786744922680183, -3.027143432974661, -0.5607605683879018], [-5.683441864306031, 2.158497601887584, 1.3966481125945855], [3.888491408236023, -6.232293290885941, -0.628496288277946]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.30345, x1=9.69882, y=56880697.53519\nx0=0.02603, x1=4.42182, y=0.00000\nx0=3.48205, x1=-7.27659, y=0.00011\nx0=5.42036, x1=2.11073, y=35.42720\nx0=9.41613, x1=6.30247, y=1373420.85402\nx0=4.41079, x1=2.02765, y=20.26994\nx0=7.79333, x1=-7.14948, y=0.00000\nx0=9.30627, x1=6.57639, y=2349870.46956\nx0=1.34440, x1=2.72957, y=2.24301\nx0=3.27090, x1=-9.16013, y=0.00002\nx0=7.89746, x1=-1.88617, y=0.02029\nx0=2.94958, x1=5.08468, y=244.66763\nx0=4.45215, x1=1.01482, y=4.55179\nx0=0.72837, x1=-4.13881, y=3.71273\nx0=9.88219, x1=-5.33145, y=0.00000\nx0=8.61588, x1=2.17779, y=108.86532\nx0=8.41669, x1=8.25220, y=43097132.18081\nx0=7.94695, x1=5.37841, y=69446.17707\nx0=0.54796, x1=0.45447, y=0.76080\nx0=0.41100, x1=-8.50953, y=1932.10561\nx0=1.84818, x1=-0.68176, y=0.65788\nx0=3.80572, x1=-0.98761, y=0.26715\nx0=5.15486, x1=8.39033, y=945660.57017\nx0=0.53541, x1=-2.10726, y=3.73012\nx0=3.59396, x1=6.39509, y=3572.25823\nx0=0.57243, x1=0.09330, y=0.94929\nx0=9.94853, x1=9.40127, y=2399950483.45232\nx0=9.58597, x1=5.24522, y=140894.81594\nx0=6.07302, x1=-4.97339, y=0.00013\nx0=6.86388, x1=5.23438, y=23928.75031\nx0=3.92614, x1=-8.15490, y=0.00001\nx0=2.71585, x1=3.63003, y=37.59194\nx0=5.47176, x1=1.18598, y=7.50595\nx0=9.74909, x1=-7.23021, y=0.00000\nx0=2.55934, x1=-4.69792, y=0.01210\nx0=9.05910, x1=8.27054, y=82339771.03155\nx0=9.96031, x1=-0.24060, y=0.57520\nx0=0.68603, x1=-3.29003, y=3.45488\nx0=2.32648, x1=-1.35219, y=0.31927\nx0=3.57610, x1=-2.59243, y=0.03676\nx0=5.36831, x1=-4.69928, y=0.00037\nx0=7.76346, x1=2.18869, y=88.72626\nx0=6.01354, x1=8.35105, y=3210407.37693\nx0=0.98830, x1=7.68612, y=0.91349\nx0=8.38840, x1=0.31869, y=1.96955\nx0=4.44011, x1=6.68322, y=21216.57703\nx0=4.61411, x1=3.36472, y=171.58126\nx0=8.25086, x1=3.08551, y=672.76414\nx0=1.72886, x1=6.98712, y=45.84063\nx0=0.31115, x1=7.48612, y=0.00016\nx0=6.04868, x1=-2.11403, y=0.02226\nx0=8.96579, x1=2.37704, y=183.80011\nx0=1.34746, x1=9.37550, y=16.37841\nx0=2.41253, x1=-8.49524, y=0.00056\nx0=7.85917, x1=-2.18028, y=0.01116\nx0=0.97884, x1=-8.07085, y=1.18840\nx0=8.87910, x1=6.31457, y=973956.71111\nx0=5.05718, x1=3.18426, y=174.35124\nx0=1.22033, x1=-6.75605, y=0.26047\nx0=7.14554, x1=-7.87147, y=0.00000\nx0=3.63011, x1=-7.36670, y=0.00008\nx0=0.47132, x1=-7.73457, y=336.30544\nx0=7.72293, x1=-7.11244, y=0.00000\nx0=3.38414, x1=3.71623, y=92.80120\nx0=0.60783, x1=1.88695, y=0.39084\nx0=2.89005, x1=-7.99127, y=0.00021\nx0=4.27795, x1=6.57928, y=14225.71654\nx0=9.15549, x1=3.80210, y=4533.24157\nx0=1.42853, x1=-8.18436, y=0.05399\nx0=5.73842, x1=-8.23413, y=0.00000\nx0=8.87271, x1=7.98046, y=36807027.71924\nx0=4.88548, x1=-3.18415, y=0.00640\nx0=0.25125, x1=-0.85664, y=3.26511\nx0=6.31382, x1=7.88773, y=2053487.77259\nx0=0.27580, x1=-6.45842, y=4100.86348\nx0=0.11521, x1=-1.65216, y=35.52839\nx0=9.99546, x1=7.16244, y=14488627.93746\nx0=1.49526, x1=0.56429, y=1.25485\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.03256, x1=-3.10443, y=0.00108\nx0=3.10423, x1=-0.86151, y=0.37686\nx0=5.83039, x1=7.46997, y=524496.63157\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**x1", "data": [[6.303448502941556, 9.698819733798395, 56880697.53519345], [0.02603334350673947, 4.421822195901674, 9.857236106968172e-08], [3.482048119778579, -7.276586865757011, 0.00011410173285530781], [5.420358529354674, 2.1107326135052347, 35.427203183640025], [9.41613203284341, 6.302471204584666, 1373420.854024935], [4.410788498760143, 2.0276487570969177, 20.269943573412572], [7.793325141657924, -7.149484110183595, 4.2134907231800583e-07], [9.306268784442665, 6.576387739449434, 2349870.4695620276], [1.3444034223989263, 2.7295739004625723, 2.243009263321638], [3.2709031607389534, -9.16012795683077, 1.930092560082714e-05], [7.897456622468997, -1.8861726978905313, 0.020285422330637293], [2.9495759133200075, 5.084678703095113, 244.66763404447508], [4.452148552531408, 1.0148210158293463, 4.551788851437471], [0.728372208725725, -4.138813582613801, 3.7127333155530033], [9.882192569856812, -5.33144941646345, 4.965807583766223e-06], [8.615875388992052, 2.1777941205031937, 108.8653201718335], [8.416692003750935, 8.25219591519987, 43097132.18081239], [7.946951503431986, 5.378410705152593, 69446.17707322497], [0.5479630441911993, 0.4544729992114753, 0.7607982518360621], [0.41099925839792384, -8.509528944486108, 1932.1056133217091], [1.8481761866906954, -0.6817614075192324, 0.6578769412141404], [3.8057241344208563, -0.9876123197346374, 0.26714863984032133], [5.15486224383962, 8.390328713327804, 945660.5701741425], [0.5354133443286901, -2.1072599293966965, 3.730116500101626], [3.5939641675033585, 6.395087766382694, 3572.258233496723], [0.5724331827752511, 0.09329536443262398, 0.9492854995288831], [9.948528281612809, 9.401272046581411, 2399950483.4523206], [9.585968836694772, 5.2452181327182235, 140894.81594288792], [6.073017283298707, -4.973391132572336, 0.00012700561490296228], [6.863880101084774, 5.234375662527366, 23928.750314854417], [3.9261404312322625, -8.154899579199524, 1.4330729776842397e-05], [2.7158540629967867, 3.630033182541295, 37.59193980390252], [5.471757931723516, 1.1859827842988935, 7.5059517392792054], [9.749093000435924, -7.230209465192063, 7.072640508929881e-08], [2.5593358725326, -4.6979200114077795, 0.012096247535634546], [9.059096997583612, 8.270540653450333, 82339771.0315458], [9.960309223443396, -0.24059906950721555, 0.5751968354355661], [0.6860314172599189, -3.2900283164858273, 3.4548791282607465], [2.3264808868927176, -1.3521915413504928, 0.3192655454569902], [3.576103951613259, -2.5924301098795155, 0.03675554816144982], [5.368310567292829, -4.699276072139076, 0.0003717846682188715], [7.76345861269408, 2.188686808940499, 88.72625839695858], [6.013542407056789, 8.351054366467427, 3210407.376930557], [0.9882972611432308, 7.686122310154751, 0.9134933820050777], [8.388398410516086, 0.318689401606882, 1.969548698378072], [4.440112342372801, 6.683218557641865, 21216.577032119392], [4.614106623863275, 3.3647214167326, 171.5812621071885], [8.250857579633053, 3.0855053368140783, 672.7641417212976], [1.7288572137750364, 6.98711588660872, 45.84062911433178], [0.31115267930334767, 7.486120718270513, 0.00016008061736346533], [6.0486831259957405, -2.114028805219615, 0.022261092890266423], [8.965792857649973, 2.377044530011016, 183.80010736824963], [1.3474583898237302, 9.375503224057937, 16.378408615021968], [2.412532680787807, -8.495243153487246, 0.0005633744184958766], [7.859172698639874, -2.1802771761678414, 0.011164269943119212], [0.978840117293986, -8.070846829263939, 1.188403601165563], [8.879103309246421, 6.3145663404195, 973956.711108965], [5.057182405739145, 3.1842557100161066, 174.35123871056797], [1.2203291088595378, -6.756054610513765, 0.2604694920411304], [7.145541316134178, -7.871471492511198, 1.8944658615008807e-07], [3.6301090967036522, -7.366702801876688, 7.503055260765331e-05], [0.47132397308172536, -7.734572847521209, 336.30544073749246], [7.722930551537207, -7.112440243964768, 4.849563546900022e-07], [3.3841395270462513, 3.7162339023986135, 92.80119645744935], [0.60782696877164, 1.8869520934797368, 0.390843733469942], [2.890049380816679, -7.991272659382633, 0.00020738644646651214], [4.277946381000488, 6.579280195633579, 14225.716543809605], [9.15548811001003, 3.8020996049364246, 4533.241568675242], [1.4285252573606417, -8.184355472691482, 0.05399358649939935], [5.738424676632725, -8.234134120387026, 5.649360106666681e-07], [8.872712044758952, 7.980464928937682, 36807027.71923884], [4.885483465855112, -3.18415172917903, 0.006403447310345356], [0.2512464540133248, -0.8566390760016347, 3.2651101141582277], [6.313823149489895, 7.88773205612565, 2053487.7725885191], [0.2758002139057183, -6.4584205003626955, 4100.863483123344], [0.11520851215339434, -1.652157706821649, 35.528388071031166], [9.995456547278959, 7.162440871491466, 14488627.937457263], [1.4952576555000157, 0.5642877287296848, 1.25484508611637], [9.032560495849484, -3.104427829225555, 0.0010783360090301417], [3.1042301090742956, -0.8615112623008425, 0.3768566373159183], [5.830393204869651, 7.469973622419499, 524496.6315739934]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-9.32063, x1=-1.60171, y=-0.68762\nx0=-8.15378, x1=-8.64141, y=-0.12576\nx0=7.68973, x1=-7.56430, y=0.68808\nx0=-9.58129, x1=-4.07047, y=0.43564\nx0=3.31751, x1=-2.27523, y=-0.40523\nx0=-0.64626, x1=-0.24094, y=-0.81857\nx0=-3.20616, x1=5.36813, y=-0.89294\nx0=4.67573, x1=-8.62578, y=-0.25950\nx0=-4.30111, x1=1.24956, y=-0.13600\nx0=4.89134, x1=8.43247, y=-0.41383\nx0=-8.81368, x1=3.42656, y=0.08641\nx0=3.94651, x1=0.38207, y=-0.34901\nx0=-8.21298, x1=0.62851, y=0.23243\nx0=7.93914, x1=8.94270, y=0.14592\nx0=2.74971, x1=5.05069, y=0.67907\nx0=-7.42334, x1=9.00416, y=-0.20674\nx0=3.09045, x1=8.70323, y=0.35196\nx0=-5.58834, x1=7.11061, y=0.79070\nx0=-0.19473, x1=-8.41133, y=0.13975\nx0=6.82838, x1=-6.74787, y=0.71003\nx0=-0.38492, x1=8.26761, y=0.29848\nx0=0.80606, x1=-3.90584, y=-0.34876\nx0=3.88425, x1=-7.01521, y=0.41187\nx0=5.33825, x1=-0.12381, y=0.98636\nx0=-2.75037, x1=8.16218, y=-0.49146\nx0=-1.02727, x1=-8.71273, y=0.34839\nx0=-3.44005, x1=2.36702, y=0.34046\nx0=-7.21818, x1=-0.62362, y=0.93833\nx0=-5.96716, x1=-7.21036, y=0.40831\nx0=8.41728, x1=8.81579, y=-0.01784\nx0=7.98587, x1=8.39371, y=0.27328\nx0=-1.59630, x1=8.88865, y=0.17999\nx0=-4.69900, x1=-5.41737, y=0.62885\nx0=0.79915, x1=9.89074, y=0.21508\nx0=-5.48846, x1=9.50193, y=-0.03583\nx0=-5.47632, x1=-1.53884, y=-0.67214\nx0=-2.59029, x1=2.27364, y=0.28472\nx0=-6.28776, x1=9.00061, y=-0.00144\nx0=-2.48203, x1=9.24391, y=-0.04960\nx0=1.81649, x1=0.75817, y=0.37615\nx0=0.35086, x1=0.61611, y=0.47869\nx0=-2.85437, x1=-6.59549, y=-0.89756\nx0=-0.02428, x1=-4.90750, y=0.02814\nx0=-6.02709, x1=-1.63940, y=-0.25576\nx0=1.61765, x1=0.53901, y=0.63204\nx0=-9.01864, x1=4.41252, y=0.48677\nx0=-5.84148, x1=-2.92997, y=-0.06497\nx0=8.24082, x1=-9.45430, y=-0.00301\nx0=9.29778, x1=-8.79384, y=-0.30465\nx0=-2.29687, x1=-9.24423, y=-0.02696\nx0=0.47531, x1=-1.65732, y=0.44207\nx0=-5.50947, x1=0.49476, y=-0.88911\nx0=2.33831, x1=-6.24998, y=0.35771\nx0=8.97561, x1=6.70316, y=-0.76432\nx0=-4.54665, x1=-5.62338, y=0.48381\nx0=6.63935, x1=4.79263, y=0.37421\nx0=-3.29261, x1=-0.32812, y=0.96137\nx0=6.45602, x1=-0.49814, y=-0.24845\nx0=8.50991, x1=-8.75992, y=-0.06435\nx0=8.41775, x1=7.50561, y=-0.04932\nx0=7.75710, x1=-3.60535, y=0.18432\nx0=-1.35365, x1=-1.63206, y=-0.61400\nx0=8.72643, x1=1.25492, y=0.40453\nx0=1.34377, x1=-1.67908, y=0.60281\nx0=-0.96874, x1=-0.58926, y=-0.95029\nx0=9.19865, x1=9.40567, y=-0.00901\nx0=2.36041, x1=5.46391, y=0.35637\nx0=8.33267, x1=6.95784, y=0.06353\nx0=3.24181, x1=8.20858, y=0.56486\nx0=8.53250, x1=-3.07556, y=0.00760\nx0=-2.73908, x1=-0.53489, y=0.79394\nx0=4.60381, x1=0.53439, y=0.56240\nx0=-7.07592, x1=-3.30178, y=-0.07425\nx0=7.61925, x1=1.25379, y=-0.73501\nx0=3.60513, x1=-3.26186, y=0.04615\nx0=-3.47928, x1=-3.87424, y=-0.31321\nx0=3.70073, x1=-8.62436, y=0.26043\nx0=8.14650, x1=7.75447, y=0.25187\nx0=-3.62685, x1=0.27447, y=0.73956\nx0=6.91698, x1=3.45413, y=0.12666\nx0=3.89491, x1=-3.03836, y=-0.02201\nx0=3.43951, x1=4.79109, y=0.66226\nx0=4.89278, x1=-7.51433, y=-0.71062\nx0=9.43131, x1=-5.80021, y=-0.97094\nx0=-6.11233, x1=3.62652, y=0.06086\nx0=-6.44210, x1=7.09699, y=-0.21684\nx0=-4.85449, x1=-0.12732, y=-0.83899\nx0=2.05100, x1=9.22228, y=-0.00657\nx0=-2.96854, x1=-4.96231, y=-0.76327\nx0=-8.14694, x1=2.43358, y=0.11755\nx0=7.49011, x1=-6.59998, y=0.95928\nx0=-4.27853, x1=-0.80977, y=-0.12335\nx0=-5.32962, x1=4.29316, y=0.53913\nx0=-8.27122, x1=3.06116, y=0.00639\nx0=8.24198, x1=-7.24925, y=0.17889\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=5.25458, x1=6.24303, y=-0.99941\nx0=8.91001, x1=-2.56505, y=0.20367\nx0=9.76300, x1=-0.48816, y=0.84814\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(1.5 * x0) * cos(0.5 * x1)", "data": [[-9.320632013493723, -1.6017098994546402, -0.6876165603814828], [-8.1537759772663, -8.641405035759833, -0.12576160794232621], [7.689727238440192, -7.564304612523392, 0.688082773328411], [-9.581288201699387, -4.070474654127228, 0.43563608417788624], [3.3175095718317476, -2.275231545429315, -0.4052303259034831], [-0.6462642493454389, -0.24094498106558504, -0.8185680050566468], [-3.2061649660877496, 5.368132572462541, -0.8929428837036876], [4.675731747331779, -8.625781168378698, -0.2595026193326064], [-4.301106447738611, 1.249559107738623, -0.1360027114800539], [4.891335409033665, 8.432471413560915, -0.4138348128219257], [-8.813682148529162, 3.4265627968661754, 0.08640724690347225], [3.946509339993886, 0.3820696812457296, -0.34900745694642826], [-8.212980775469749, 0.6285107998750217, 0.2324296334940027], [7.939139996933239, 8.94269880903487, 0.14591695745826727], [2.749705080749944, 5.050685121942733, 0.6790734446076379], [-7.423340892348005, 9.004159911505269, -0.20673596279476825], [3.0904549386752223, 8.703230096926873, 0.35196045375815543], [-5.588337759473598, 7.11060901361504, 0.7906981825110649], [-0.19472789881961994, -8.411330260107135, 0.13974952652414957], [6.828377522279258, -6.747866387806267, 0.7100299926870058], [-0.3849237239007799, 8.267610856497022, 0.29848375020750617], [0.8060577902810202, -3.905835810723943, -0.3487613556461601], [3.884253559716848, -7.015208472894252, 0.41186656605266236], [5.33825466454484, -0.12381290143346746, 0.9863641206887884], [-2.750374081167486, 8.16217555831484, -0.49145672801112655], [-1.0272747443555055, -8.71273162811242, 0.34839392414472303], [-3.440050440876041, 2.367016256860367, 0.3404589419085512], [-7.21818296018697, -0.6236159514831563, 0.9383327479850426], [-5.967156269952394, -7.210361429723093, 0.4083071485146483], [8.417280249925998, 8.815791733781072, -0.017843042414625695], [7.98587485628839, 8.393713765643398, 0.27328374205570577], [-1.5962973760400718, 8.888653366001272, 0.17998746549421116], [-4.698997574228983, -5.417373842799118, 0.6288545341977525], [0.7991483463343219, 9.890743108935776, 0.21508263371035155], [-5.48846405423822, 9.501931374390313, -0.035834299176288616], [-5.476316065790694, -1.5388432441864968, -0.6721423260274696], [-2.590291453863296, 2.273638603499286, 0.28471792817024627], [-6.287757545283272, 9.000613764796046, -0.0014436440772877782], [-2.482029458106183, 9.243913922343413, -0.04960098700598172], [1.8164876393732463, 0.758170560059682, 0.37614650872626376], [0.35086298623772194, 0.6161122739030347, 0.4786852959001486], [-2.8543706596340845, -6.595494571389329, -0.8975626820322198], [-0.024282583013846448, -4.907503003641103, 0.028135533602400717], [-6.027087917013246, -1.6394044576345408, -0.2557559806700331], [1.6176502644820445, 0.5390101919349739, 0.6320367931953752], [-9.018640768430568, 4.412517064290078, 0.4867716183568495], [-5.841479381332189, -2.9299661798466348, -0.06496817381057735], [8.2408158392149, -9.454299982517416, -0.0030068701784677775], [9.29778180326118, -8.793838319033679, -0.3046507210046644], [-2.296865790865197, -9.24423211473387, -0.026960248706280495], [0.4753124902785384, -1.657321337110556, 0.44207032591009016], [-5.509472867679803, 0.49476089544933544, -0.8891130717980621], [2.33830526143052, -6.249981694934856, 0.35770809924842645], [8.975612854456418, 6.703161337650577, -0.764322278533492], [-4.546651665903802, -5.623380436446659, 0.4838051776670032], [6.639353829949044, 4.792628812270362, 0.374209284850122], [-3.2926088676940086, -0.32811997326803777, 0.9613682463173755], [6.456020072552008, -0.4981351427531102, -0.2484472517045612], [8.509914950543337, -8.759918423194936, -0.06435464850190385], [8.417752398168762, 7.505611417560683, -0.04931856663924285], [7.757101927442704, -3.605351699325454, 0.18431655046049314], [-1.3536544007521307, -1.6320557379027374, -0.6139992051011518], [8.726425927801188, 1.254923816544169, 0.4045283808798063], [1.3437668403550092, -1.6790806064938497, 0.6028099564344589], [-0.9687425131596612, -0.5892568501451727, -0.9502915394883457], [9.198646934988503, 9.405674185698643, -0.009007506029030032], [2.3604093813315288, 5.463909061680043, 0.35637288738214956], [8.332666700339832, 6.957838666270359, 0.06352566798914613], [3.241808168585976, 8.20858479992705, 0.5648635065227169], [8.532495058859435, -3.075562637546634, 0.007601525949715561], [-2.739079456884596, -0.534892644842893, 0.7939354612566454], [4.603807252648085, 0.5343918969117851, 0.5623979277021383], [-7.075916712744775, -3.3017793959630577, -0.074249848893544], [7.619251261023635, 1.2537925499882512, -0.7350088889258186], [3.605129360362822, -3.2618567942638865, 0.04614508909284085], [-3.4792773389765337, -3.8742419359351583, -0.3132105701336083], [3.7007280235211333, -8.624356345275206, 0.2604279143686479], [8.146500151378394, 7.754468123871984, 0.2518694159525393], [-3.6268513647395313, 0.2744732220161161, 0.7395616386236132], [6.916982353309699, 3.4541345848321754, 0.12665943358669676], [3.8949124828759274, -3.0383602434127948, -0.022013727757307953], [3.439513294626712, 4.791093036724828, 0.6622618611977992], [4.892776036899811, -7.514329787174267, -0.7106178801679807], [9.431309811004724, -5.800209275859716, -0.970936589314877], [-6.112327267887554, 3.6265215759062492, 0.06086201923799706], [-6.442099783552919, 7.096985313100241, -0.2168419379437196], [-4.85449396370452, -0.12731711128490808, -0.838986880177391], [2.051001852614828, 9.222278142924015, -0.00657444484037622], [-2.9685406642649355, -4.962313421620276, -0.7632678132930822], [-8.146941354024815, 2.4335757043407273, 0.1175520955384768], [7.490105104628402, -6.599981129872685, 0.9592757567088647], [-4.278525565946452, -0.8097707276112232, -0.12334680276999666], [-5.329622960422958, 4.2931624287450205, 0.539131510603513], [-8.271217763677862, 3.0611554564630765, 0.006387725272224196], [8.24197738987834, -7.249254913121945, 0.17889335017245567], [5.254578051190448, 6.243032905195292, -0.9994097844244344], [8.910006057869285, -2.5650538363079933, 0.20366978612884046], [9.763001017318736, -0.48816452341585936, 0.8481355584066631]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.26617, y=6.51182\nx0=3.97824, y=4.52298\nx0=0.25273, y=0.81275\nx0=1.27572, y=2.05835\nx0=3.94796, y=4.50322\nx0=4.27042, y=4.70755\nx0=1.08614, y=1.81887\nx0=2.99417, y=3.80902\nx0=0.11495, y=0.68786\nx0=7.52416, y=6.24771\nx0=4.45553, y=4.81911\nx0=7.85628, y=6.36877\nx0=6.02234, y=5.63066\nx0=5.97316, y=5.60819\nx0=0.33398, y=0.89510\nx0=2.61863, y=3.48984\nx0=4.85736, y=5.04838\nx0=5.39549, y=5.33107\nx0=0.65151, y=1.26350\nx0=2.70248, y=3.56375\nx0=9.69636, y=6.96385\nx0=1.02746, y=1.74368\nx0=3.41466, y=4.13353\nx0=5.42911, y=5.34790\nx0=5.68802, y=5.47453\nx0=2.46007, y=3.34565\nx0=8.58945, y=6.62006\nx0=0.50527, y=1.08629\nx0=0.99322, y=1.69966\nx0=0.84871, y=1.51361\nx0=1.76760, y=2.64011\nx0=7.54104, y=6.25397\nx0=7.53006, y=6.24990\nx0=5.58804, y=5.42625\nx0=6.96448, y=6.03209\nx0=7.67097, y=6.30182\nx0=9.54753, y=6.91984\nx0=7.76292, y=6.33523\nx0=5.67467, y=5.46812\nx0=7.71386, y=6.31745\nx0=3.30462, y=4.05166\nx0=0.76156, y=1.40209\nx0=6.72784, y=5.93612\nx0=0.40378, y=0.97040\nx0=8.73514, y=6.66761\nx0=6.59580, y=5.88123\nx0=6.76679, y=5.95212\nx0=1.73750, y=2.60643\nx0=9.58211, y=6.93012\nx0=4.38828, y=4.77904\nx0=5.93524, y=5.59074\nx0=4.30137, y=4.72648\nx0=4.07574, y=4.58578\nx0=8.96222, y=6.74026\nx0=6.17725, y=5.70040\nx0=0.41355, y=0.98125\nx0=5.58293, y=5.42376\nx0=9.08869, y=6.77997\nx0=1.85932, y=2.74115\nx0=8.27786, y=6.51580\nx0=4.60156, y=4.90439\nx0=3.13437, y=3.92082\nx0=1.98536, y=2.87609\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.69314, y=4.33189\nx0=7.53059, y=6.25009\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = log(x0 + 1.4) + log(x0**2 + 1.3)", "data": [[8.266173989498986, 6.511822803377166], [3.9782426577040058, 4.522983664925288], [0.2527264488735034, 0.8127530468521368], [1.275720191902106, 2.0583544135182215], [3.9479559388426217, 4.503220384602521], [4.270421863290942, 4.707548176437611], [1.0861429044656223, 1.8188726448007575], [2.994166879250164, 3.8090214415456813], [0.11494610661559257, 0.6878563722744606], [7.524163924500042, 6.247705268166716], [4.455528709260374, 4.819108279683393], [7.856278803229656, 6.368771965686823], [6.022338077085744, 5.630661533928446], [5.973164625325715, 5.608188960222961], [0.3339774622023663, 0.8950998573190122], [2.6186262940612197, 3.489841548830624], [4.857357090150269, 5.0483814185322755], [5.395488776287385, 5.331073198202224], [0.6515138284161626, 1.2634978861788735], [2.7024798947761113, 3.5637488361219374], [9.696357343799605, 6.963849675600162], [1.0274635245576589, 1.743676877712835], [3.4146592355932444, 4.133525068327431], [5.429109012696101, 5.347904185558543], [5.688024573239233, 5.474527413850272], [2.4600663125038698, 3.345646718074243], [8.589446073185309, 6.620064492575514], [0.505267985832215, 1.0862883861026766], [0.9932200094788675, 1.6996558790877043], [0.8487143412657563, 1.513612600211737], [1.7675986658210865, 2.640109598112627], [7.541037907667326, 6.2539742079241005], [7.530062966777646, 6.249898323012383], [5.588039826957207, 5.426245675126521], [6.964478173952159, 6.032088373773341], [7.670967722346488, 6.3018164135365184], [9.547534928655347, 6.9198409274090125], [7.762921717364095, 6.335225379468634], [5.674665488066062, 5.468120178062144], [7.713859918146932, 6.3174458934445], [3.3046165644735326, 4.051658377749059], [0.7615627288500979, 1.4020914086135425], [6.72784161077427, 5.936119951627676], [0.40377705986610957, 0.9703965029741883], [8.735142569777755, 6.6676112697729994], [6.5957985102438546, 5.8812260925450826], [6.76678646503941, 5.952123400690086], [1.737504524239697, 2.6064335739848525], [9.582113493807343, 6.930123585733085], [4.388282315369744, 4.779038153701043], [5.935241090100219, 5.590744368917058], [4.301365317833374, 4.72647566990352], [4.075743501466703, 4.585781364013839], [8.962220809047288, 6.740258082577633], [6.177247803669033, 5.700396756931527], [0.4135522482348693, 0.9812472408391355], [5.582927904221071, 5.423756673899649], [9.088688569923862, 6.779973783401664], [1.8593182239824508, 2.741148765218628], [8.277858409462846, 6.51580324499892], [4.601560533492051, 4.904394598977945], [3.134373685284448, 3.920818727951718], [1.985355049165677, 2.876092199679695], [3.693138998191882, 4.33188803479772], [7.53059140148097, 6.250094699043723]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-0.39120, y=-0.27461\nx0=-9.50498, y=7384.27946\nx0=-1.84301, y=6.83107\nx0=-1.53321, y=2.73935\nx0=4.33038, y=455.93205\nx0=8.08195, y=4867.72358\nx0=-4.50199, y=335.30835\nx0=-0.92046, y=-0.13525\nx0=8.87597, y=6993.67994\nx0=5.23255, y=925.51840\nx0=1.53773, y=13.12993\nx0=-7.23147, y=2401.57620\nx0=4.75725, y=647.23307\nx0=6.60004, y=2235.18404\nx0=0.47716, y=0.86532\nx0=4.63463, y=587.04611\nx0=-7.98988, y=3621.10420\nx0=-6.51587, y=1561.85765\nx0=8.53356, y=6005.77569\nx0=-6.64914, y=1698.21022\nx0=-6.12504, y=1209.06574\nx0=-0.36142, y=-0.26094\nx0=-5.43260, y=734.77348\nx0=6.42007, y=2011.12416\nx0=-8.86979, y=5561.45190\nx0=3.33181, y=174.65007\nx0=8.09164, y=4890.28096\nx0=4.42573, y=494.35577\nx0=9.34213, y=8528.94608\nx0=3.63768, y=240.11160\nx0=3.14685, y=142.27474\nx0=5.96611, y=1520.88694\nx0=-5.51919, y=784.72120\nx0=9.93609, y=10836.42850\nx0=8.85652, y=6934.49110\nx0=-5.79142, y=958.46911\nx0=-2.08934, y=12.21140\nx0=3.63872, y=240.36203\nx0=-2.75592, y=41.59345\nx0=-8.72871, y=5207.38845\nx0=-2.01103, y=10.25606\nx0=8.35477, y=5533.69048\nx0=1.23909, y=7.03422\nx0=-8.66290, y=5048.13799\nx0=-2.75886, y=41.78571\nx0=-5.12807, y=577.85302\nx0=-7.70234, y=3114.25060\nx0=2.03853, y=31.93448\nx0=-0.36898, y=-0.26453\nx0=-4.69719, y=400.53059\nx0=-1.64009, y=3.87370\nx0=-7.36945, y=2596.15881\nx0=-9.16976, y=6374.08919\nx0=-3.09917, y=68.99157\nx0=9.63250, y=9605.24582\nx0=5.33075, y=992.75196\nx0=0.40876, y=0.67205\nx0=-8.22933, y=4088.44806\nx0=9.29965, y=8379.45599\nx0=7.94476, y=4556.57559\nx0=-9.28042, y=6695.27031\nx0=-8.69803, y=5132.68914\nx0=4.26483, y=430.85665\nx0=8.13174, y=4984.51712\nx0=1.12730, y=5.44559\nx0=2.57656, y=70.39235\nx0=-1.43143, y=1.88294\nx0=5.02987, y=797.65323\nx0=-8.35091, y=4342.36721\nx0=8.44754, y=5775.00967\nx0=-1.17205, y=0.47867\nx0=-5.12054, y=574.32389\nx0=-4.88778, y=472.98377\nx0=-7.59618, y=2941.31351\nx0=-4.50744, y=337.01245\nx0=6.24118, y=1805.58518\nx0=2.92263, y=109.39005\nx0=-2.58016, y=31.21891\nx0=4.72891, y=632.92554\nx0=-3.24128, y=83.58570\nx0=-7.21582, y=2380.21718\nx0=-7.14837, y=2289.80335\nx0=-1.79976, y=6.10167\nx0=4.36141, y=468.17846\nx0=-4.45443, y=320.70442\nx0=-3.30835, y=91.22356\nx0=5.67196, y=1255.29460\nx0=2.81419, y=95.74259\nx0=-4.61467, y=371.89377\nx0=-4.35338, y=291.26823\nx0=-4.06969, y=219.40028\nx0=3.96943, y=330.53157\nx0=-0.56155, y=-0.32385\nx0=6.71485, y=2387.61315\nx0=0.62710, y=1.42159\nx0=2.65112, y=77.71169\nx0=-8.18318, y=3995.04125\nx0=-2.41148, y=23.19742\nx0=-7.30501, y=2503.86809\nx0=-0.76940, y=-0.28246\nx0=1.79771, y=21.28353\nx0=-3.08216, y=67.38267\nx0=6.30714, y=1879.42935\nx0=9.58491, y=9422.22086\nx0=8.27374, y=5329.16187\nx0=9.31408, y=8430.01728\nx0=4.61979, y=580.06045\nx0=9.52079, y=9179.76427\nx0=2.36414, y=52.40556\nx0=-9.20106, y=6463.74147\nx0=-0.72136, y=-0.30559\nx0=-8.64954, y=5016.26261\nx0=4.82840, y=684.22348\nx0=6.77008, y=2463.66465\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-6.91455, y=1996.19215\nx0=8.74068, y=6589.80122\nx0=-1.98547, y=9.66990\nx0=9.70300, y=9881.27538\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**4 + x0**3 + x0**2 + x0", "data": [[-0.3912026705041711, -0.2746115161304009], [-9.504982825441811, 7384.279457174777], [-1.8430125502005783, 6.831069406890341], [-1.5332148275593305, 2.739346423049435], [4.330381806699791, 455.9320547205057], [8.08194890604728, 4867.7235770912375], [-4.501990127999118, 335.30835424416716], [-0.9204583266115414, -0.1352455575163135], [8.875973457506483, 6993.679941967591], [5.232549819097105, 925.5184013605989], [1.5377319661042588, 13.12992856234474], [-7.231468648391242, 2401.5761990041874], [4.757249061177127, 647.2330719317673], [6.600042040214927, 2235.1840368595463], [0.4771583122641303, 0.8653160054169577], [4.634628257052835, 587.046107794201], [-7.989880955517892, 3621.104200281219], [-6.515868737562922, 1561.8576474967995], [8.53356015797117, 6005.775690081483], [-6.649135993742816, 1698.2102168902902], [-6.125044259802039, 1209.0657386792282], [-0.36142320754336055, -0.2609446622453706], [-5.43260078821344, 734.7734824689961], [6.420072614729495, 2011.124160239365], [-8.869787916002439, 5561.451895504296], [3.3318087032352643, 174.65007113041437], [8.091635404737342, 4890.280963795378], [4.425734481408089, 494.3557709678069], [9.342128950733748, 8528.946084439132], [3.637680202065132, 240.11159690801617], [3.146851568488527, 142.27474214830636], [5.966109642458715, 1520.88693675495], [-5.519191803883556, 784.7211979077797], [9.936094004932645, 10836.428500365428], [8.856519320499089, 6934.491100533339], [-5.791418787944604, 958.4691065463863], [-2.0893353306950235, 12.211402296742415], [3.6387209952234816, 240.36202645604968], [-2.755924269895729, 41.59344894581967], [-8.728708677075659, 5207.388453034178], [-2.011032293396413, 10.256064680683956], [8.354773038858369, 5533.690482259152], [1.2390947499593956, 7.0342192903444], [-8.662896684408475, 5048.137992931784], [-2.7588566749602723, 41.7857126271655], [-5.128069573243312, 577.85302162443], [-7.702338220973905, 3114.250595644305], [2.038529450531094, 31.934480134283184], [-0.36897964461637756, -0.26453303374161696], [-4.697186922712675, 400.53058907057897], [-1.6400923287534237, 3.8736988193104622], [-7.369450257368639, 2596.1588100993204], [-9.16976218998953, 6374.089188521745], [-3.099167135691328, 68.99156737375326], [9.632502463934646, 9605.245818264537], [5.330751422770614, 992.7519649808469], [0.408755267756284, 0.6720473387450989], [-8.229334492389919, 4088.4480594829383], [9.299653604463462, 8379.455994432945], [7.944764419349113, 4556.575589023491], [-9.280416710168126, 6695.270313467475], [-8.698029321037238, 5132.68913685162], [4.264828606657856, 430.8566496781725], [8.131742458483703, 4984.51712041358], [1.127296735058911, 5.445588396104888], [2.5765641579466685, 70.39234944691529], [-1.4314299458967294, 1.8829406258691281], [5.029871236506022, 797.6532253869991], [-8.350913351323896, 4342.367206392698], [8.447537822555514, 5775.009667685016], [-1.172051624954877, 0.47866565438099773], [-5.1205399441159205, 574.3238874722562], [-4.887783084510167, 472.9837667356094], [-7.596184417439971, 2941.313512634969], [-4.507438370090586, 337.0124497744315], [6.241179404425033, 1805.5851806262665], [2.922625910694741, 109.39004528938455], [-2.5801581065787786, 31.218911232306667], [4.728905895902946, 632.9255419975428], [-3.241277997764202, 83.58569630046273], [-7.215817047443542, 2380.2171785697324], [-7.1483706665338875, 2289.803353641094], [-1.7997575581430691, 6.101671386316449], [4.361410727888607, 468.17846260179306], [-4.454425412339429, 320.7044150758697], [-3.3083521712637776, 91.223558936441], [5.67195585136629, 1255.2945954826646], [2.8141916176885324, 95.7425911312166], [-4.614666518496469, 371.8937673642374], [-4.353377926647708, 291.26823086537485], [-4.0696856194321445, 219.4002750216569], [3.9694254476704884, 330.5315736687412], [-0.561545619778121, -0.3238510673268855], [6.714853600707361, 2387.61315106747], [0.6270955452160631, 1.421593589660991], [2.651119717261148, 77.71168925044897], [-8.18318322569425, 3995.041245603602], [-2.4114804440896043, 23.19741714525153], [-7.3050102784154785, 2503.868085784586], [-0.7693968534603517, -0.2824560804622412], [1.7977101869470946, 21.283528505182353], [-3.08216272393593, 67.38267386486845], [6.307135141619611, 1879.4293486645588], [9.584911639736909, 9422.220858301984], [8.273740134899267, 5329.161874625863], [9.314083068090092, 8430.017280792834], [4.61978986475938, 580.0604515618003], [9.520786160615508, 9179.764273288181], [2.364140334187649, 52.405561445750706], [-9.201062919613443, 6463.741472991873], [-0.7213602466056024, -0.3055919362110994], [-8.649537168430365, 5016.262613117448], [4.828396607840158, 684.2234816634714], [6.770084910212599, 2463.664653913803], [-6.91454612429399, 1996.1921547604763], [8.740678628143616, 6589.801222336596], [-1.9854746022155627, 9.66990319919956], [9.703004760997182, 9881.275377785101]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.61926, x1=-4.58357, y=1.99054\nx0=1.38915, x1=-3.30238, y=1.14364\nx0=-3.71728, x1=5.71464, y=0.00600\nx0=-5.30529, x1=-8.54681, y=0.05988\nx0=-5.03678, x1=-6.45943, y=0.77251\nx0=-7.06388, x1=8.33874, y=0.18101\nx0=1.28348, x1=0.26796, y=1.22377\nx0=4.12830, x1=-8.07370, y=-1.81017\nx0=-8.66570, x1=8.00451, y=0.30044\nx0=-1.14470, x1=-2.87370, y=-1.17528\nx0=-6.69250, x1=-0.26730, y=-0.66211\nx0=9.86217, x1=7.04920, y=0.26969\nx0=-8.34026, x1=0.55794, y=-0.35464\nx0=3.93465, x1=9.18908, y=-0.47898\nx0=1.20703, x1=-2.43457, y=0.28499\nx0=8.26894, x1=3.62962, y=0.44625\nx0=2.09694, x1=7.20953, y=1.66418\nx0=2.83972, x1=-7.00454, y=-0.36309\nx0=9.13013, x1=7.56150, y=1.24793\nx0=-3.26459, x1=-4.05081, y=0.91171\nx0=5.37145, x1=-3.96693, y=-0.05579\nx0=8.98437, x1=4.60390, y=-0.56781\nx0=-6.77370, x1=3.02874, y=-0.35846\nx0=-4.25918, x1=-2.05469, y=0.01386\nx0=-7.92099, x1=-8.17945, y=-1.94526\nx0=-0.98767, x1=-7.73226, y=-1.82735\nx0=4.74563, x1=8.44157, y=-0.16717\nx0=3.56037, x1=1.74902, y=0.57752\nx0=-2.29494, x1=-7.04714, y=-1.44085\nx0=-7.05579, x1=3.77307, y=-1.28834\nx0=5.63298, x1=7.00870, y=0.05817\nx0=-3.16299, x1=-5.47102, y=0.74717\nx0=-0.74302, x1=6.50564, y=-0.45590\nx0=-7.04827, x1=-0.28459, y=-0.97336\nx0=-0.66855, x1=-0.94725, y=-1.43166\nx0=-1.94990, x1=4.56240, y=-1.91777\nx0=-9.84916, x1=3.18044, y=0.37291\nx0=-6.97094, x1=-0.21730, y=-0.85040\nx0=9.49399, x1=1.94555, y=0.86144\nx0=4.90265, x1=-2.51373, y=-1.56937\nx0=7.13759, x1=-8.74979, y=0.12929\nx0=-4.71815, x1=-1.10357, y=0.10716\nx0=9.54379, x1=-4.84828, y=0.87205\nx0=-0.53377, x1=-5.24655, y=0.35191\nx0=7.78034, x1=4.70663, y=-0.00269\nx0=9.69921, x1=-2.72300, y=-0.67748\nx0=6.50828, x1=-0.42780, y=-0.19168\nx0=2.88010, x1=-7.50202, y=-0.68017\nx0=6.96251, x1=-0.95663, y=-0.18899\nx0=9.79508, x1=8.06929, y=0.61502\nx0=-5.60135, x1=-5.86074, y=1.04020\nx0=-9.48108, x1=4.63609, y=-0.94082\nx0=5.93774, x1=-2.16807, y=-1.16548\nx0=-8.11826, x1=3.70670, y=-1.50079\nx0=-1.95741, x1=7.57237, y=0.03442\nx0=-4.12251, x1=-7.69640, y=-0.15660\nx0=-0.20383, x1=9.90321, y=-0.66280\nx0=3.94961, x1=-3.20919, y=-0.65537\nx0=1.88108, x1=1.65551, y=1.94866\nx0=4.40785, x1=-0.96378, y=-1.77534\nx0=3.03143, x1=7.11316, y=0.84785\nx0=-7.09002, x1=-5.89959, y=-0.34785\nx0=4.43088, x1=6.82285, y=-0.44678\nx0=-8.92317, x1=2.00391, y=0.42683\nx0=-5.01690, x1=7.10568, y=1.68684\nx0=7.88591, x1=-4.65419, y=1.99780\nx0=7.09855, x1=-0.32058, y=0.41286\nx0=-6.68509, x1=-0.54706, y=-0.91135\nx0=-5.31318, x1=-3.61249, y=1.27857\nx0=9.41804, x1=-5.01240, y=0.96207\nx0=-6.59950, x1=6.53118, y=-0.06560\nx0=-9.81107, x1=-1.91078, y=-0.56601\nx0=-0.52269, x1=-7.80723, y=-1.49812\nx0=-2.39917, x1=1.33165, y=0.29546\nx0=-9.39012, x1=3.28920, y=-0.18172\nx0=3.64439, x1=-6.21878, y=-0.41752\nx0=2.70220, x1=-4.14539, y=1.26891\nx0=8.37372, x1=-4.40148, y=1.82000\nx0=-1.79008, x1=1.11047, y=-0.08015\nx0=8.52479, x1=-7.69451, y=-0.20400\nx0=5.69885, x1=7.63610, y=0.42472\nx0=-5.53877, x1=9.72203, y=0.38465\nx0=-7.33567, x1=3.90482, y=-1.55992\nx0=-7.57278, x1=2.35631, y=-0.25370\nx0=2.68557, x1=-6.84314, y=-0.09077\nx0=0.22574, x1=3.28696, y=0.07897\nx0=-2.48009, x1=-7.57875, y=-1.57666\nx0=-0.21342, x1=-3.43439, y=0.07683\nx0=1.77593, x1=2.22280, y=1.77391\nx0=3.77342, x1=1.09729, y=0.29936\nx0=-1.93089, x1=-4.79527, y=0.06070\nx0=-0.20296, x1=9.80348, y=-0.57129\nx0=5.13253, x1=8.15967, y=0.04061\nx0=-6.66995, x1=5.90955, y=-0.74219\nx0=-8.80518, x1=-8.78808, y=-1.17525\nx0=-0.13276, x1=5.27200, y=-0.97983\nx0=-2.72914, x1=4.70986, y=-1.40085\nx0=-0.00057, x1=-0.88331, y=-0.77341\nx0=3.11829, x1=4.92893, y=-0.95334\nx0=3.40249, x1=-3.60853, y=0.19221\nx0=-4.39219, x1=-8.01371, y=-0.03810\nx0=-9.99617, x1=5.90857, y=0.17489\nx0=-3.49966, x1=-0.98810, y=-0.48452\nx0=8.81787, x1=-8.69862, y=-0.09367\nx0=-0.00326, x1=1.95655, y=0.92325\nx0=2.17251, x1=4.89553, y=-0.15891\nx0=-9.30813, x1=-9.26751, y=-0.27300\nx0=4.04200, x1=-3.65195, y=-0.29510\nx0=8.72933, x1=8.23630, y=1.56853\nx0=8.83300, x1=5.63609, y=-0.04504\nx0=8.47902, x1=9.63857, y=0.59877\nx0=4.04034, x1=-2.74665, y=-1.16730\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=8.12207, x1=-7.82975, y=-0.03543\nx0=-6.65170, x1=-4.86614, y=0.62797\nx0=6.26032, x1=6.28191, y=-0.02414\nx0=-0.66557, x1=-4.64451, y=0.38019\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0) + sin(x1)", "data": [[1.619257101243301, -4.583572659972576, 1.9905406507821837], [1.389153312837312, -3.302380693383795, 1.1436443483422183], [-3.7172812288316575, 5.714635245446203, 0.006001731273495903], [-5.305287699426873, -8.546805158267219, 0.05987879115844552], [-5.0367799891336595, -6.459428358056485, 0.7725129389797313], [-7.0638832932353, 8.338744733747674, 0.18100991356580143], [1.2834803003525899, 0.2679558579635035, 1.2237687075341548], [4.128298148707145, -8.07369704261835, -1.8101732995102777], [-8.665700471546856, 8.004514849729127, 0.3004387715814937], [-1.1446971053611001, -2.8737005244156055, -1.1752842918843844], [-6.692501790875525, -0.2672997216740658, -0.662110385636884], [9.862168856359048, 7.049195256429595, 0.2696877784027789], [-8.340255670457244, 0.5579411731865669, -0.3546395429966094], [3.934645201696462, 9.189081001374106, -0.4789777493027982], [1.2070290280536362, -2.4345719458611015, 0.284991563380542], [8.268942837807863, 3.629619758610943, 0.44624773870737744], [2.0969419649524745, 7.209533331489951, 1.6641804901421637], [2.8397198405086463, -7.004539087321639, -0.36309299306223414], [9.130134872268904, 7.561498413194766, 1.247929177211523], [-3.2645879772308106, -4.0508140071231935, 0.9117110584385181], [5.371453180544659, -3.966927862956826, -0.05579044053470428], [8.984372663857954, 4.603902318763367, -0.5678149683065584], [-6.77369732229764, 3.0287353771762326, -0.3584597380532827], [-4.259182698062167, -2.054686357677797, 0.013855973124441201], [-7.920985577870048, -8.179454956610744, -1.9452555596443202], [-0.987672685909903, -7.732255851642056, -1.827347302280191], [4.745630899199863, 8.441565917989493, -0.16716527483610877], [3.5603661057698055, 1.7490235192384347, 0.577519332198133], [-2.2949351658558825, -7.047142211679649, -1.440854361945486], [-7.055793843869411, 3.7730695474702713, -1.2883430502781357], [5.6329848985006965, 7.008696194030264, 0.058171818934101616], [-3.1629850689132404, -5.471021807309127, 0.7471679915867206], [-0.7430231642772434, 6.505635322882085, -0.45589740886770214], [-7.048265932669764, -0.28458700667721537, -0.9733562515928882], [-0.6685457159047203, -0.9472491925308386, -1.4316577624697506], [-1.9498978749646625, 4.5624019006861065, -1.9177705235292104], [-9.84915587644791, 3.1804435895119845, 0.3729127959959099], [-6.970943493754005, -0.21729700451955125, -0.8503975771544171], [9.4939873922984, 1.9455486100811008, 0.861444131995409], [4.902653961842924, -2.51372521954329, -1.56937440416452], [7.137589321855188, -8.74979141048059, 0.12929286915696148], [-4.718151466728848, -1.1035653789146664, 0.10716446271470903], [9.543794399398891, -4.848276790116113, 0.8720457887956788], [-0.533771732261032, -5.24654782385703, 0.3519131660969701], [7.780338641167738, 4.706628108864985, -0.0026938261385698326], [9.699208242324076, -2.7229983726379707, -0.6774750856187998], [6.5082760493261596, -0.42780079627777035, -0.19167597896089547], [2.8800951741236602, -7.502021578398552, -0.6801713978139765], [6.962506734883021, -0.9566252123738259, -0.18898615887588333], [9.79507723799464, 8.069286947631014, 0.6150167706818583], [-5.601354737578619, -5.8607437564764275, 1.040203959092127], [-9.481076258225695, 4.636085909886869, -0.9408217702300369], [5.937742745889034, -2.1680744782630246, -1.1654825547497827], [-8.118256512208585, 3.7067048505432254, -1.5007927361610518], [-1.9574082248105817, 7.572367013913887, 0.03441611049871618], [-4.122506142544262, -7.696404073235204, -0.15660446719293908], [-0.20382678421887412, 9.903207907027546, -0.6628043475296186], [3.949606045824156, -3.209186551112058, -0.6553735458315445], [1.8810778431239505, 1.6555132337681897, 1.9486613216802577], [4.407853971797435, -0.9637843562079915, -1.7753425842733237], [3.0314323333913933, 7.113158723152154, 0.8478510805980188], [-7.090023427513101, -5.899591015241555, -0.3478474883134491], [4.430875952152187, 6.822854427124906, -0.44678403970313274], [-8.923173041512808, 2.00391133625628, 0.42682941559982146], [-5.016904487309654, 7.10568115137762, 1.6868385991374728], [7.885907063696376, -4.654190123584447, 1.9977973512520633], [7.09854508902875, -0.32057649391269294, 0.4128585777399269], [-6.685089938869617, -0.5470629025944191, -0.9113529473535609], [-5.313175374703167, -3.6124852161126757, 1.2785732134361023], [9.418040050411452, -5.012401054200259, 0.9620707803746557], [-6.599499518281351, 6.531184577359738, -0.06560081707080576], [-9.811066861118645, -1.9107759815119465, -0.5660080749335643], [-0.5226888203729718, -7.80723068679454, -1.4981191222616943], [-2.399166734043499, 1.3316460948348574, 0.29546222515648324], [-9.390119269403543, 3.2891999510252674, -0.1817236248375502], [3.644392384209919, -6.218784021711425, -0.41752387414315245], [2.7021955238581477, -4.145389795669843, 1.2689104580378014], [8.373724187474593, -4.401480657882453, 1.82000315640819], [-1.7900779670930547, 1.1104714258287949, -0.0801457538174456], [8.524794915727057, -7.694511009772784, -0.20399511410064985], [5.698853265184551, 7.636103028466664, 0.4247158296586402], [-5.538774848653601, 9.722025090607524, 0.38464915495887825], [-7.335674876586866, 3.90482112601177, -1.5599172376428978], [-7.572776993695019, 2.3563137781151653, -0.2536994050672321], [2.6855735983245346, -6.843138320649292, -0.09076892466382869], [0.2257417413974565, 3.2869594460068736, 0.0789739825887415], [-2.480092390363586, -7.578749836905708, -1.576663585813586], [-0.21341925544937013, -3.434394548119397, 0.07683318513379847], [1.7759289024608904, 2.222796236265294, 1.7739058771723895], [3.7734171159357626, 1.0972911582767786, 0.29935737934979867], [-1.9308876608763619, -4.795265697288549, 0.06070304502432777], [-0.20295878782265575, 9.803484900637194, -0.5712876064435357], [5.132527554717505, 8.159666647181925, 0.04060859758684765], [-6.66995158739695, 5.909554671514101, -0.7421935179334103], [-8.805179643621354, -8.78807943242589, -1.1752522877870915], [-0.13275521301097548, 5.271999205337599, -0.9798277011290493], [-2.7291399737771194, 4.709858964800569, -1.4008543300251797], [-0.0005721804681044773, -0.8833062210964808, -0.7734134055453629], [3.1182893662223616, 4.9289346935377925, -0.9533442749926673], [3.4024885667445517, -3.6085337610471484, 0.19221070916097815], [-4.392189207554427, -8.013712567381537, -0.03809755755696098], [-9.996170518395271, 5.908572475809791, 0.1748916824649538], [-3.499659456034678, -0.9881027281340522, -0.48451915801146334], [8.817867468656374, -8.698618005170406, -0.09367080135204753], [-0.0032598777145604885, 1.9565528118739532, 0.9232541906868391], [2.172512842244201, 4.8955338484715405, -0.15891062216285445], [-9.308127417372013, -9.267512319595445, -0.27300435330375694], [4.042001732416214, -3.651945945365764, -0.2950955816859645], [8.729330470381843, 8.236300865023075, 1.5685309605642672], [8.833003642699147, 5.636090270731282, -0.045036761611551346], [8.479016699061042, 9.638572291390698, 0.598773239521184], [4.040335201871718, -2.746646626200442, -1.1673030177322568], [8.122068172734963, -7.829746791895593, -0.0354268386105796], [-6.6517000328065095, -4.866135059004188, 0.6279740628048915], [6.260321083832832, 6.2819072408831005, -0.02414029721537092], [-0.665571381084245, -4.6445085904711085, 0.380188349493791]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.80670, x1=-5.12833, y=231.61406\nx0=7.11869, x1=-9.81531, y=685.81610\nx0=-9.44186, x1=-3.62439, y=-124.03045\nx0=-6.16858, x1=9.78488, y=-590.60316\nx0=-3.96015, x1=2.95556, y=-34.59316\nx0=2.52650, x1=-2.96086, y=22.14896\nx0=6.38199, x1=4.81991, y=148.26352\nx0=5.92646, x1=-9.10048, y=490.82178\nx0=5.30100, x1=6.31492, y=211.39449\nx0=-8.98586, x1=2.10727, y=-39.90267\nx0=-1.48729, x1=-7.54360, y=-84.63539\nx0=-5.44705, x1=-8.64893, y=-407.46127\nx0=7.68319, x1=-2.80558, y=60.47654\nx0=-7.99125, x1=-0.48693, y=-1.89474\nx0=-7.27143, x1=-4.55488, y=-150.86021\nx0=0.13472, x1=-3.25938, y=1.43116\nx0=-3.59380, x1=9.73239, y=-340.40272\nx0=0.61045, x1=-1.50614, y=1.38479\nx0=-6.01516, x1=9.74008, y=-570.65369\nx0=-9.51443, x1=0.71674, y=-4.88777\nx0=8.15108, x1=-9.10345, y=675.50345\nx0=-5.46803, x1=1.72032, y=-16.18260\nx0=3.73690, x1=3.75394, y=52.66068\nx0=-2.09974, x1=-2.39558, y=-12.05003\nx0=-8.53785, x1=3.91215, y=-130.67071\nx0=-0.98048, x1=-9.34534, y=-85.63057\nx0=3.08214, x1=0.67382, y=1.39940\nx0=-8.85268, x1=8.81678, y=-688.16866\nx0=0.62966, x1=-6.35017, y=25.39095\nx0=3.73689, x1=4.64748, y=80.71349\nx0=-9.97559, x1=4.20822, y=-176.65909\nx0=0.32120, x1=8.25670, y=21.89717\nx0=3.98125, x1=5.81592, y=134.66554\nx0=8.08380, x1=-4.32585, y=151.27213\nx0=5.60285, x1=4.98698, y=139.34265\nx0=7.56113, x1=2.25744, y=38.53164\nx0=6.80638, x1=-7.02971, y=336.34991\nx0=-7.55392, x1=-7.52822, y=-428.11168\nx0=-2.89101, x1=-6.56774, y=-124.70421\nx0=1.18308, x1=-2.70508, y=8.65715\nx0=-3.52371, x1=-9.59975, y=-324.72849\nx0=-2.35464, x1=-9.66116, y=-219.77733\nx0=3.01149, x1=7.76933, y=181.78120\nx0=9.55672, x1=4.51735, y=195.01836\nx0=-3.26576, x1=-8.94565, y=-261.34090\nx0=6.86141, x1=6.17263, y=261.42930\nx0=6.89775, x1=1.21790, y=10.23122\nx0=8.41066, x1=-5.40539, y=245.74504\nx0=3.44384, x1=-4.42590, y=67.46006\nx0=-9.97625, x1=-8.85868, y=-782.89756\nx0=-7.90848, x1=0.16719, y=-0.22107\nx0=1.66856, x1=9.42287, y=148.15225\nx0=5.27368, x1=-3.20694, y=54.23708\nx0=-8.06943, x1=-6.38042, y=-328.50494\nx0=-2.12274, x1=-3.75430, y=-29.91944\nx0=-4.53533, x1=6.75614, y=-207.01659\nx0=7.80344, x1=6.38283, y=317.91622\nx0=1.03526, x1=3.59372, y=13.37021\nx0=8.17425, x1=2.73306, y=61.05839\nx0=-9.36327, x1=-0.40051, y=-1.50194\nx0=5.31787, x1=-8.67173, y=399.89727\nx0=5.99644, x1=0.99024, y=5.87993\nx0=-3.76575, x1=-4.08629, y=-62.87941\nx0=-0.71555, x1=-0.24220, y=-0.04197\nx0=7.32294, x1=5.54112, y=224.84403\nx0=-7.70521, x1=2.02404, y=-31.56630\nx0=0.17421, x1=3.73511, y=2.43038\nx0=9.62149, x1=0.16395, y=0.25862\nx0=4.90540, x1=-3.83935, y=72.30847\nx0=2.56828, x1=-1.79983, y=8.31966\nx0=4.74520, x1=-8.09453, y=310.91240\nx0=-9.50450, x1=8.70789, y=-720.70027\nx0=7.27332, x1=1.99880, y=29.05836\nx0=5.54895, x1=7.86564, y=343.30398\nx0=1.98673, x1=1.10647, y=2.43231\nx0=1.26063, x1=2.86468, y=10.34522\nx0=-6.67394, x1=-5.08428, y=-172.52074\nx0=-4.06904, x1=-8.49388, y=-293.56451\nx0=3.08109, x1=-4.75748, y=69.73616\nx0=-3.25349, x1=-7.13793, y=-165.76539\nx0=5.88951, x1=9.07850, y=485.40912\nx0=-6.66782, x1=1.76594, y=-20.79386\nx0=-1.18176, x1=0.06594, y=-0.00514\nx0=-2.69094, x1=7.66217, y=-157.98167\nx0=5.16864, x1=-8.53380, y=376.40995\nx0=-7.74639, x1=-3.16864, y=-77.77573\nx0=-0.45911, x1=-6.43488, y=-19.01061\nx0=9.77437, x1=-1.44471, y=20.40098\nx0=1.12437, x1=4.26589, y=20.46121\nx0=-5.04200, x1=1.83743, y=-17.02255\nx0=6.83310, x1=-5.59900, y=214.20957\nx0=3.68742, x1=9.70438, y=347.26310\nx0=-2.43275, x1=5.23316, y=-66.62316\nx0=3.66166, x1=-0.10858, y=0.04317\nx0=3.58811, x1=7.57226, y=205.73914\nx0=-7.96996, x1=0.27334, y=-0.59550\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=2.45999, x1=6.92351, y=117.91980\nx0=0.95135, x1=9.24982, y=81.39674\nx0=-7.49991, x1=3.27345, y=-80.36512\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1**2", "data": [[8.806704020146878, -5.1283275446181715, 231.6140559726712], [7.1186890026413, -9.815305651753711, 685.8161004853597], [-9.44186254246803, -3.624393337508927, -124.03045027418091], [-6.168579141426067, 9.784875727291428, -590.6031644117902], [-3.960148442112576, 2.9555571816669683, -34.59315697534431], [2.526498021070429, -2.9608556105898813, 22.14896416587865], [6.3819912025019505, 4.8199113264798665, 148.26351705583915], [5.926463888525921, -9.100475621054049, 490.82177721771507], [5.301000504357056, 6.314920823515056, 211.394490876371], [-8.98586400504984, 2.1072743294353398, -39.902673524212304], [-1.4872857049430106, -7.543602641607636, -84.63539229969382], [-5.447050019739925, -8.64893206390623, -407.46127046143573], [7.6831908469625105, -2.8055799441546725, 60.476537407093325], [-7.991247201604869, -0.48693104130342135, -1.8947394072829247], [-7.2714349503629405, -4.554883766323354, -150.86021459325607], [0.13471508200597526, -3.259381936007742, 1.4311551852183404], [-3.5938027760359548, 9.732387471848849, -340.4027201236933], [0.61045379767525, -1.5061426500278259, 1.3847934906150154], [-6.015164841688629, 9.74008051978435, -570.6536871132133], [-9.514427157414547, 0.7167442892624898, -4.887774127397394], [8.151080248855198, -9.103453967446969, 675.5034475474355], [-5.468028513925754, 1.7203179099886299, -16.182596000870333], [3.7369012274834894, 3.753940900067697, 52.66068220540633], [-2.09974289426688, -2.3955816151833993, -12.050028196229782], [-8.537846297837442, 3.9121452007959228, -130.67071366251528], [-0.9804808188276795, -9.345335067042246, -85.63057421554186], [3.082138429950813, 0.6738205489481999, 1.3993960473163043], [-8.852675705962179, 8.816783347231159, -688.1686648312377], [0.62966342628037, -6.350168707720538, 25.39095263344508], [3.7368938407787073, 4.647481625539982, 80.71348942092452], [-9.975589189761296, 4.20822268444949, -176.65908720799123], [0.32119917982488033, 8.256704336540945, 21.89716516620357], [3.9812457602348807, 5.815924276531279, 134.66553906661454], [8.083798425842925, -4.325852714889244, 151.27213377348775], [5.60284738003222, 4.986980137290768, 139.34265124101614], [7.561133085285469, 2.257435252579832, 38.531639450488505], [6.806378357426144, -7.029713277620928, 336.3499060576754], [-7.5539249009137155, -7.528218328684428, -428.1116777066221], [-2.891009118305597, -6.567738186654067, -124.70421283226062], [1.1830807913197887, -2.7050806587742304, 8.657147988632868], [-3.5237109606387484, -9.599753050934694, -324.72849494649626], [-2.3546368554637027, -9.661164578686998, -219.77733267238926], [3.0114928368166325, 7.769330036851322, 181.78120390302917], [9.556718319743077, 4.517345995693923, 195.0183585876911], [-3.2657565863446987, -8.945647604150812, -261.34090063119055], [6.861413609540904, 6.1726312487829595, 261.42930348886915], [6.897754716946935, 1.2178951694479245, 10.231223284026674], [8.410657489675398, -5.405394589890653, 245.74503527949486], [3.44384273790482, -4.42590105626437, 67.46005840619328], [-9.976245020332463, -8.858678009900721, -782.8975608637461], [-7.908483938018042, 0.16719176000975544, -0.2210665206970494], [1.6685606052435311, 9.422868622233185, 148.1522521174413], [5.273678254939595, -3.2069437700738863, 54.237082545124856], [-8.069430768998888, -6.38042344429453, -328.50493957891763], [-2.1227357548587733, -3.7542979757089956, -29.9194367654723], [-4.535325311374225, 6.756135499394567, -207.01658778585266], [7.803442806136221, 6.382829144789017, 317.91622322479304], [1.035261454228948, 3.5937187221375826, 13.3702093855294], [8.17425449685605, 2.733056479647848, 61.058392760141096], [-9.36327179073758, -0.40050855231481286, -1.501935278933179], [5.317865497629615, -8.671726004486114, 399.8972736064713], [5.996439617754563, 0.9902375349949928, 5.879931048921668], [-3.7657455450941573, -4.0862859183223215, -62.87941217526972], [-0.7155486171523666, -0.24220063524762736, -0.04197490312757688], [7.322943167475586, 5.541123753111208, 224.84403108271806], [-7.705206320376632, 2.0240430005426795, -31.56630451731], [0.17420768273247234, 3.7351084606009657, 2.430377516080547], [9.621486807374747, 0.16395062163828023, 0.25862370204255686], [4.905401214896923, -3.8393467132078607, 72.30847466016196], [2.568276983421349, -1.7998316044361484, 8.319660547891269], [4.745203893394843, -8.094529024294918, 310.9124029745566], [-9.50449857895389, 8.707886080535193, -720.7002749258971], [7.273317586053867, 1.998799743642648, 29.05836143958143], [5.548946235091313, 7.865641724096225, 343.3039798474382], [1.9867331207094718, 1.1064693308943063, 2.4323064599986597], [1.260630488345086, 2.864678830299427, 10.345218878936949], [-6.673938711740899, -5.084281095482266, -172.52074346083734], [-4.069038423754899, -8.49387531290995, -293.56451177246504], [3.0810925118133987, -4.757476474397944, 69.73616126186205], [-3.2534902094873814, -7.137928266445499, -165.76539103796148], [5.889514096934532, 9.078502797233693, 485.40911705367876], [-6.667816718021726, 1.7659389926246032, -20.79385665290401], [-1.1817634896319067, 0.06594326696535546, -0.005138915620676678], [-2.690937607552179, 7.662165659093819, -157.98167095803012], [5.168643367109899, -8.533796184245329, 376.40995400553317], [-7.746392902038915, -3.16863544662003, -77.77572593277623], [-0.4591082872339207, -6.434880782085958, -19.010613946250317], [9.774366647047707, -1.4447117820407396, 20.4009811724111], [1.1243748871391794, 4.265894266428184, 20.461209916380522], [-5.042004813631202, 1.8374297175058611, -17.022554300004032], [6.833095027570671, -5.59900299629154, 214.209565500698], [3.6874215775754227, 9.704382896864498, 347.2631018849734], [-2.432746096420648, 5.233162502381942, -66.62315972499825], [3.6616615048313506, -0.10858410167289634, 0.04317284610273291], [3.588111801528031, 7.572259239450169, 205.7391372422179], [-7.969960585370577, 0.27334498949498176, -0.5954953967957183], [2.4599917040308448, 6.923513499765942, 117.91979871873896], [0.9513497710139482, 9.249822653351501, 81.39674351647402], [-7.499911880735903, 3.273450038868365, -80.36511943746946]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.71024, y=241399.47048\nx0=9.03808, y=612885.71776\nx0=3.09147, y=1288.85857\nx0=-9.28309, y=577729.97405\nx0=1.90174, y=97.65586\nx0=1.98202, y=120.34157\nx0=6.94047, y=130586.23321\nx0=-8.74541, y=401476.52711\nx0=-6.38389, y=58520.00889\nx0=-7.83966, y=205893.09273\nx0=0.01162, y=0.01176\nx0=-6.29198, y=53537.51262\nx0=3.14240, y=1410.84157\nx0=-0.23126, y=-0.18780\nx0=5.69947, y=41569.91832\nx0=3.83190, y=4282.39126\nx0=-3.59631, y=1691.94906\nx0=1.52919, y=34.06077\nx0=9.04414, y=615304.87502\nx0=-6.52839, y=67132.80111\nx0=-5.54815, y=24711.81887\nx0=-8.19654, y=270264.12375\nx0=0.77840, y=2.73126\nx0=4.40311, y=9427.11478\nx0=4.61039, y=12262.07684\nx0=3.18825, y=1528.82886\nx0=-2.05927, y=50.65791\nx0=-5.16199, y=15848.04391\nx0=-2.45704, y=155.66904\nx0=-3.39292, y=1177.53635\nx0=-4.01659, y=3361.15537\nx0=-5.47628, y=22806.34590\nx0=-3.05009, y=605.59635\nx0=-0.92776, y=-0.17437\nx0=2.45413, y=367.01506\nx0=-8.47141, y=330577.34234\nx0=5.98921, y=55404.68385\nx0=-5.31622, y=18999.58203\nx0=2.04703, y=141.89477\nx0=-1.05268, y=0.18500\nx0=-2.30512, y=103.93412\nx0=-5.36415, y=20079.33342\nx0=-7.86275, y=209629.11577\nx0=3.75893, y=3841.98285\nx0=-3.67034, y=1920.51317\nx0=2.96857, y=1030.49660\nx0=9.43735, y=790212.23154\nx0=5.79802, y=45907.67621\nx0=6.02145, y=57156.71932\nx0=2.48412, y=391.63930\nx0=-8.25475, y=282203.20188\nx0=-4.35048, y=5511.93864\nx0=3.68511, y=3435.73826\nx0=-9.49611, y=663424.57173\nx0=-9.39356, y=620933.60422\nx0=-4.18072, y=4308.08872\nx0=-7.67612, y=180993.95821\nx0=0.09927, y=0.11021\nx0=6.61414, y=98633.32691\nx0=-1.44789, y=4.85795\nx0=5.71192, y=42098.38986\nx0=2.81492, y=770.07776\nx0=7.32362, y=178694.70308\nx0=4.75022, y=14551.35773\nx0=8.42230, y=405017.57237\nx0=-3.71740, y=2078.76682\nx0=-2.57518, y=209.34787\nx0=0.32715, y=0.48561\nx0=-8.46966, y=330160.88720\nx0=5.92620, y=52109.06935\nx0=7.28435, y=173169.71968\nx0=-1.41221, y=4.05850\nx0=-3.38559, y=1161.77965\nx0=-6.52206, y=66734.77602\nx0=1.11545, y=8.94857\nx0=-3.36593, y=1120.36907\nx0=-8.59666, y=361564.45399\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-8.32829, y=297912.43029\nx0=-1.80412, y=21.54150\nx0=0.54295, y=1.15751\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**6 + x0**5 + x0**4 + x0**3 + x0**2 + x0", "data": [[7.710243509672047, 241399.47048164307], [9.038077711921666, 612885.7177635804], [3.0914692729496966, 1288.8585722475098], [-9.283094518922972, 577729.9740473228], [1.9017406991554981, 97.65585642059979], [1.9820228580327566, 120.34156591860963], [6.940469775136382, 130586.23320947369], [-8.745410069758284, 401476.52710813173], [-6.383885811937555, 58520.00889112749], [-7.839655902652738, 205893.09272967908], [0.011621660755483987, 0.011758311867031171], [-6.291978403348095, 53537.51261592718], [3.142399763633213, 1410.8415691445969], [-0.23126220812512344, -0.18779657870455263], [5.699468681928632, 41569.918320941884], [3.83190358310328, 4282.391263437484], [-3.596306728051932, 1691.949063838449], [1.5291909675879989, 34.06076569781613], [9.044139414724071, 615304.8750166448], [-6.528389635596634, 67132.80110754156], [-5.548151790786083, 24711.818868379283], [-8.196541102937076, 270264.12374842394], [0.7783981021747195, 2.7312588099280135], [4.403105801599715, 9427.114784793945], [4.610389487926289, 12262.076835510701], [3.188253868710147, 1528.828864454389], [-2.059273591148429, 50.65791128696968], [-5.161989032954208, 15848.043906821815], [-2.4570394739373054, 155.66904483869405], [-3.392916294495272, 1177.5363549438964], [-4.016587194080783, 3361.1553738139523], [-5.476275715147107, 22806.34589956248], [-3.0500889620033345, 605.5963518553637], [-0.9277569374062882, -0.17436925081407828], [2.4541264620070073, 367.0150634705976], [-8.471406763131506, 330577.34233759256], [5.989212110326296, 55404.68384960494], [-5.3162198402641225, 18999.582033237424], [2.047029155374032, 141.89476985872153], [-1.052678150024466, 0.18499644891380385], [-2.3051159028857215, 103.93411501639159], [-5.364153074158509, 20079.33341648092], [-7.862751979599761, 209629.11577179393], [3.7589306444317536, 3841.982848164052], [-3.6703391688992255, 1920.513166699258], [2.96857177917863, 1030.496602054278], [9.43734997874628, 790212.2315437123], [5.79802191749623, 45907.67621191787], [6.021445114332195, 57156.71931866417], [2.484119383030709, 391.63929619346175], [-8.25475163889652, 282203.2018782796], [-4.350481529503682, 5511.93863728978], [3.68511362963779, 3435.7382568238163], [-9.49611129696845, 663424.5717264862], [-9.39355513093831, 620933.604223475], [-4.180717712155662, 4308.088721627895], [-7.676118448305216, 180993.95820970763], [0.09927269612273548, 0.11021382462459765], [6.61413587985729, 98633.32691057835], [-1.4478870653820035, 4.857950131766254], [5.711922468231361, 42098.389862757154], [2.814924148441216, 770.0777583355865], [7.323618972759579, 178694.70307721992], [4.750223812842648, 14551.357733430723], [8.422295501000185, 405017.57237314794], [-3.717397268178555, 2078.766817953622], [-2.5751847341230665, 209.3478684458559], [0.32714650308947313, 0.4856115884642067], [-8.46965792062245, 330160.88720261806], [5.926202951264312, 52109.06935090105], [7.284348830163648, 173169.71968187075], [-1.4122135972405268, 4.058500833570344], [-3.385589668829856, 1161.779651712884], [-6.522062728940727, 66734.77602369992], [1.115446038072367, 8.948567921835682], [-3.3659313267678375, 1120.3690709147636], [-8.596655647394499, 361564.45398892194], [-8.328293420731896, 297912.4302949617], [-1.804117237682739, 21.54150058189826], [0.542949133058876, 1.1575069463790513]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=0.33116, y=0.62658\nx0=3.70747, y=1.74068\nx0=7.90856, y=2.39825\nx0=3.49456, y=1.69768\nx0=8.14543, y=2.42838\nx0=0.34375, y=0.63655\nx0=9.15356, y=2.55125\nx0=9.67777, y=2.61206\nx0=7.93321, y=2.40141\nx0=8.59799, y=2.48456\nx0=4.09584, y=1.81560\nx0=2.57621, y=1.49226\nx0=2.93157, y=1.57610\nx0=2.47685, y=1.46764\nx0=0.08074, y=0.34491\nx0=3.07204, y=1.60761\nx0=0.54530, y=0.77374\nx0=3.95094, y=1.78815\nx0=8.17653, y=2.43230\nx0=6.13569, y=2.15410\nx0=5.36422, y=2.03508\nx0=8.85191, y=2.51534\nx0=5.06336, y=1.98599\nx0=5.69218, y=2.08681\nx0=3.67061, y=1.73334\nx0=1.15106, y=1.06131\nx0=8.10789, y=2.42364\nx0=3.34391, y=1.66632\nx0=9.37964, y=2.57771\nx0=1.86792, y=1.30252\nx0=1.28639, y=1.11241\nx0=0.27828, y=0.58212\nx0=2.90342, y=1.56968\nx0=5.51010, y=2.05831\nx0=1.49687, y=1.18605\nx0=2.45082, y=1.46110\nx0=1.10077, y=1.04145\nx0=7.37693, y=2.32869\nx0=2.46027, y=1.46348\nx0=6.40520, y=2.19363\nx0=5.87502, y=2.11491\nx0=3.15582, y=1.62602\nx0=8.13550, y=2.42713\nx0=4.82201, y=1.94539\nx0=4.99186, y=1.97408\nx0=1.53373, y=1.19832\nx0=2.49617, y=1.47247\nx0=3.69737, y=1.73868\nx0=3.51263, y=1.70138\nx0=7.74197, y=2.37675\nx0=3.50379, y=1.69957\nx0=3.30406, y=1.65790\nx0=9.17524, y=2.55380\nx0=8.00176, y=2.41017\nx0=0.59622, y=0.80352\nx0=0.89264, y=0.95310\nx0=0.43893, y=0.70588\nx0=7.90829, y=2.39822\nx0=8.06132, y=2.41774\nx0=3.10587, y=1.61508\nx0=9.66369, y=2.61045\nx0=3.20629, y=1.63696\nx0=8.92252, y=2.52381\nx0=1.59162, y=1.21724\nx0=8.20453, y=2.43582\nx0=5.19464, y=2.00761\nx0=1.51295, y=1.19142\nx0=4.56121, y=1.90016\nx0=5.93009, y=2.12327\nx0=1.58322, y=1.21453\nx0=2.28125, y=1.41745\nx0=6.59357, y=2.22069\nx0=5.63267, y=2.07755\nx0=8.06198, y=2.41783\nx0=6.87085, y=2.25972\nx0=9.60335, y=2.60354\nx0=0.58240, y=0.79559\nx0=9.16427, y=2.55251\nx0=0.21514, y=0.52209\nx0=2.95232, y=1.58081\nx0=1.23542, y=1.09355\nx0=6.29038, y=2.17691\nx0=2.83370, y=1.55362\nx0=4.82767, y=1.94635\nx0=3.25440, y=1.64731\nx0=7.23154, y=2.30916\nx0=2.40168, y=1.44863\nx0=6.24451, y=2.17018\nx0=9.31165, y=2.56979\nx0=3.24849, y=1.64604\nx0=4.28717, y=1.85101\nx0=4.83138, y=1.94698\nx0=0.22223, y=0.52930\nx0=0.21268, y=0.51955\nx0=7.33129, y=2.32258\nx0=3.73044, y=1.74524\nx0=9.37650, y=2.57735\nx0=7.19126, y=2.30371\nx0=8.42723, y=2.46357\nx0=2.99835, y=1.59119\nx0=2.93796, y=1.57755\nx0=3.09823, y=1.61340\nx0=4.61797, y=1.91013\nx0=7.38109, y=2.32924\nx0=1.40355, y=1.15419\nx0=0.87550, y=0.94531\nx0=5.04518, y=1.98297\nx0=6.93532, y=2.26867\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=6.92594, y=2.26737\nx0=4.58096, y=1.90364\nx0=1.41926, y=1.15964\nx0=1.36551, y=1.14085\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**0.423", "data": [[0.3311608291555146, 0.6265799310987764], [3.70746950716196, 1.7406835279831878], [7.90855721781552, 2.3982538008372214], [3.494562988440821, 1.6976774703901532], [8.145428369091977, 2.4283796897300918], [0.34375493143085123, 0.6365511402467978], [9.15356397181447, 2.5512479191545183], [9.67777229620048, 2.612059070143607], [7.933214296693141, 2.401413819866745], [8.597989716005046, 2.4845623379754573], [4.09583947536918, 1.8156036965125466], [2.5762124363821393, 1.4922625754686958], [2.9315718109802305, 1.576099122190199], [2.4768452347260332, 1.4676389269987897], [0.08074294383763991, 0.3449095640210487], [3.0720420307598424, 1.6076136528772342], [0.5452952168474425, 0.7737402761040394], [3.9509381946281685, 1.7881510408051848], [8.17653498589532, 2.4322981732033786], [6.135685365113634, 2.1541011040079807], [5.36421590510567, 2.035078394205231], [8.851908829093418, 2.51533956637151], [5.063358426983889, 1.9859922894873308], [5.692184470436141, 2.0868104491277877], [3.670608560228912, 1.733341778631533], [1.1510582245430108, 1.0613146390915957], [8.107885630657524, 2.4236389350457146], [3.343907952400171, 1.6663244810852569], [9.379640875173333, 2.5777142183869572], [1.8679198435744997, 1.3025203994586838], [1.2863909873204964, 1.112409718019102], [0.2782804895491626, 0.5821249410051318], [2.903418378251983, 1.5696787174206361], [5.510097249801802, 2.058308031439797], [1.4968721917444494, 1.1860503791791053], [2.4508213233602465, 1.461096256550447], [1.100766641095067, 1.0414468119548426], [7.376932142501246, 2.328688822277885], [2.460270808850833, 1.4634765654926796], [6.405203190806461, 2.1936302253233357], [5.8750249624805395, 2.1149061980005786], [3.1558230281021604, 1.6260153723643214], [8.135497979425562, 2.4271269462751617], [4.822014434710379, 1.9453854263592114], [4.991862873697608, 1.9740815955830244], [1.5337282181660932, 1.1983166028581733], [2.496171524905325, 1.472472123697567], [3.6973670495353588, 1.7386755848696793], [3.512628345886643, 1.7013843014845276], [7.741973342573235, 2.3767541291770673], [3.503786930976906, 1.6995715092532888], [3.304055858970239, 1.6578950777948316], [9.175235656889924, 2.5538012031115453], [8.001760718352408, 2.4101689767291297], [0.596220478763394, 0.803520782603799], [0.8926448444877462, 0.953096973644323], [0.438928256745033, 0.7058825850873474], [7.908285212928863, 2.3982189093674995], [8.061315968708648, 2.4177406603015488], [3.1058694910817692, 1.6150779753092284], [9.663687740912124, 2.610450375748267], [3.206288817828977, 1.63696395606762], [8.92252326069088, 2.5238078821423393], [1.5916167447223941, 1.2172441199226416], [8.204525688585491, 2.4358168009541012], [5.194643067275759, 2.007613309104109], [1.5129512374990224, 1.191422906811924], [4.561208379105262, 1.9001627643751238], [5.930087776402344, 2.123268195615865], [1.5832249393152242, 1.2145251969561022], [2.281254403139103, 1.4174491361243244], [6.593572723630789, 2.220690827088905], [5.632672147803371, 2.0775535289484837], [8.061982576194026, 2.417825227893303], [6.870852321189755, 2.25972447660808], [9.603346390414032, 2.603543014517702], [0.5823953792612535, 0.7955860883359682], [9.164268055854489, 2.552509473221016], [0.21514311003810782, 0.5220879962591501], [2.9523227372246215, 1.5808086389277107], [1.2354249878687806, 1.093549205125257], [6.290379580896591, 2.1769091699510876], [2.83369719963855, 1.5536225119956466], [4.827668940321539, 1.946350066431806], [3.2544024008721184, 1.6473100175191397], [7.231538423190081, 2.3091629742440123], [2.401679254382165, 1.4486312440484226], [6.244507519044259, 2.1701798940943275], [9.311652468404446, 2.5697940483867026], [3.2484853652259282, 1.6460424339419357], [4.28716768718717, 1.851007204491394], [4.831380348981968, 1.9469828662167077], [0.22223387448829257, 0.5292985924813874], [0.21268124712362102, 0.5195525142999399], [7.331288884299269, 2.3225832026819133], [3.730440390792346, 1.7452374525021812], [9.376502384330994, 2.5773493369922944], [7.191260838994033, 2.3037138462747486], [8.427229341617764, 2.4635686902096428], [2.9983516795901437, 1.591187385810781], [2.9379633967695185, 1.5775517656516627], [3.098233030105389, 1.6133970394262958], [4.617974126150841, 1.9101302505190145], [7.38108526113443, 2.3292432945723354], [1.4035489458196118, 1.1541898714930332], [0.8754953377513353, 0.945308087206914], [5.045181858242259, 1.9829734393261866], [6.935324476937733, 2.2686695917180435], [6.925938489515808, 2.2673703365416737], [4.580960249867815, 1.90363906889645], [1.419261296564292, 1.159637839502802], [1.3655125628271882, 1.1408540306759296]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=9.40284, x1=9.49204, y=14.20492\nx0=7.52112, x1=-1.95627, y=-2.34171\nx0=-2.87994, x1=5.29040, y=-2.42489\nx0=-6.84534, x1=-3.62096, y=3.94492\nx0=6.73413, x1=-3.34365, y=-3.58362\nx0=7.67140, x1=-9.33663, y=-11.39948\nx0=3.25408, x1=1.31021, y=0.67856\nx0=6.74612, x1=-4.52822, y=-4.86185\nx0=6.46427, x1=-2.25249, y=-2.31741\nx0=-8.81069, x1=4.52085, y=-6.33943\nx0=-3.94524, x1=-2.21435, y=1.39040\nx0=-8.38545, x1=5.22466, y=-6.97275\nx0=-3.11513, x1=-3.27556, y=1.62398\nx0=7.30782, x1=5.51119, y=6.40993\nx0=9.59871, x1=-3.63885, y=-5.55901\nx0=6.27613, x1=7.95946, y=7.95052\nx0=-4.29396, x1=4.30371, y=-2.94118\nx0=6.94190, x1=-6.39032, y=-7.06026\nx0=9.21583, x1=3.35054, y=4.91439\nx0=-7.58506, x1=6.92399, y=-8.35863\nx0=-3.33073, x1=2.77422, y=-1.47062\nx0=-0.61721, x1=7.98918, y=-0.78480\nx0=-4.08992, x1=-1.41904, y=0.92370\nx0=-6.03932, x1=2.65505, y=-2.55200\nx0=-6.25827, x1=3.53232, y=-3.51831\nx0=2.37695, x1=-5.37505, y=-2.03340\nx0=-8.82617, x1=-6.46716, y=9.08460\nx0=-6.76086, x1=-8.80065, y=9.46972\nx0=8.68232, x1=-4.52959, y=-6.25914\nx0=-5.88825, x1=1.02470, y=-0.96029\nx0=-0.79831, x1=-7.01088, y=0.89076\nx0=3.24381, x1=-9.77023, y=-5.04405\nx0=-5.74452, x1=0.64621, y=-0.59081\nx0=7.33312, x1=-0.82022, y=-0.95728\nx0=4.32009, x1=2.15539, y=1.48197\nx0=3.50717, x1=-9.44351, y=-5.27121\nx0=-5.57379, x1=-1.72627, y=1.53137\nx0=2.35388, x1=-3.99870, y=-1.49804\nx0=-4.76651, x1=-2.37378, y=1.80078\nx0=-8.32527, x1=9.88148, y=-13.09303\nx0=5.10998, x1=-4.35249, y=-3.53979\nx0=-2.42216, x1=0.70453, y=-0.27160\nx0=9.02092, x1=-6.28539, y=-9.02409\nx0=7.26224, x1=-4.93267, y=-5.70129\nx0=-4.74338, x1=-2.05595, y=1.55211\nx0=1.27253, x1=-0.19716, y=-0.03993\nx0=8.27986, x1=3.89328, y=5.13049\nx0=5.77374, x1=3.74808, y=3.44418\nx0=3.46521, x1=-1.14166, y=-0.62963\nx0=9.09758, x1=0.29232, y=0.42326\nx0=-2.35040, x1=-3.75743, y=1.40557\nx0=0.05366, x1=9.76572, y=0.08340\nx0=7.95033, x1=-6.72769, y=-8.51278\nx0=5.06521, x1=1.81293, y=1.46150\nx0=9.28538, x1=-9.16067, y=-13.53777\nx0=0.01427, x1=-6.41399, y=-0.01456\nx0=7.60932, x1=-1.87360, y=-2.26904\nx0=-2.53820, x1=-1.18159, y=0.47732\nx0=8.90400, x1=-0.28697, y=-0.40667\nx0=5.19812, x1=-8.15976, y=-6.75062\nx0=-5.07375, x1=7.22087, y=-5.83095\nx0=-7.36742, x1=-7.42521, y=8.70651\nx0=-8.95703, x1=8.75233, y=-12.47693\nx0=-1.01799, x1=5.78207, y=-0.93680\nx0=1.90117, x1=-6.65626, y=-2.01405\nx0=-8.54192, x1=6.41811, y=-8.72535\nx0=1.43109, x1=9.74582, y=2.21975\nx0=-9.74021, x1=-0.65566, y=1.01641\nx0=8.17426, x1=9.62821, y=12.52604\nx0=1.75139, x1=-1.22094, y=-0.34033\nx0=-3.60265, x1=-1.84951, y=1.06047\nx0=-2.29520, x1=-6.46538, y=2.36175\nx0=-6.69933, x1=-9.59515, y=10.23066\nx0=6.31861, x1=0.32731, y=0.32915\nx0=-1.51172, x1=6.44444, y=-1.55052\nx0=-0.24544, x1=-0.55752, y=0.02178\nx0=1.10432, x1=-6.58215, y=-1.15686\nx0=8.51992, x1=7.51280, y=10.18726\nx0=-4.97264, x1=3.03621, y=-2.40292\nx0=6.69278, x1=-2.36609, y=-2.52033\nx0=-5.92724, x1=3.60416, y=-3.39998\nx0=-7.25651, x1=7.46747, y=-8.62425\nx0=-7.39100, x1=8.93211, y=-10.50696\nx0=-7.37715, x1=-7.23882, y=8.49917\nx0=4.49717, x1=0.11834, y=0.08470\nx0=-9.93033, x1=-0.84810, y=1.34039\nx0=-0.39741, x1=8.01437, y=-0.50690\nx0=2.96018, x1=3.69299, y=1.73987\nx0=6.69007, x1=4.43391, y=4.72104\nx0=-2.38136, x1=-7.82777, y=2.96677\nx0=4.72218, x1=-8.36922, y=-6.28996\nx0=8.74767, x1=8.29717, y=11.55161\nx0=0.32609, x1=2.95386, y=0.15330\nx0=-7.35797, x1=4.91858, y=-5.75993\nx0=2.95716, x1=-2.23671, y=-1.05270\nx0=0.53706, x1=-9.18198, y=-0.78483\nx0=-4.67379, x1=7.45004, y=-5.54176\nx0=8.61508, x1=-6.21574, y=-8.52260\nx0=3.39996, x1=-2.85299, y=-1.54381\nx0=2.13985, x1=2.23212, y=0.76019\nx0=-3.86901, x1=-5.86545, y=3.61178\nx0=7.82453, x1=8.25554, y=10.28073\nx0=-5.86795, x1=2.55437, y=-2.38556\nx0=-2.16805, x1=1.63320, y=-0.56355\nx0=7.33210, x1=7.41477, y=8.65260\nx0=-5.14424, x1=-5.85208, y=4.79127\nx0=-7.99375, x1=-5.54693, y=7.05705\nx0=5.91271, x1=8.35729, y=7.86452\nx0=-7.23432, x1=-0.70748, y=0.81458\nx0=8.31843, x1=-4.57985, y=-6.06335\nx0=-8.98463, x1=9.56313, y=-13.67479\nx0=-9.39885, x1=-1.60336, y=2.39843\nx0=1.80262, x1=-2.36923, y=-0.67972\nx0=-3.34725, x1=-5.32597, y=2.83731\nx0=-2.19800, x1=-3.35080, y=1.17218\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.07034, x1=-1.16232, y=1.67791\nx0=-1.97768, x1=-3.38272, y=1.06474\nx0=8.42041, x1=0.98917, y=1.32564\nx0=-3.36253, x1=8.34249, y=-4.46460\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (x1 / (2 * pi)) * x0", "data": [[9.402837980440609, 9.492041322537432, 14.204917139318052], [7.521123738545587, -1.956272829693205, -2.3417055679807555], [-2.8799435801852997, 5.2903996013946575, -2.4248930476778527], [-6.845337256733625, -3.620958686160667, 3.944923185879292], [6.734129232577487, -3.3436450045266124, -3.583618255316368], [7.671402247692097, -9.33663416951193, -11.399484951053262], [3.2540845627110375, 1.3102068801937428, 0.6785609168528678], [6.746123507018197, -4.528216508056005, -4.861850532238544], [6.464273648710275, -2.2524922137074332, -2.317411527614183], [-8.810687780555977, 4.52085190967049, -6.339430198361723], [-3.9452416560995607, -2.2143491588054287, 1.3904002691892121], [-8.385453951165847, 5.224655372370128, -6.972754247063105], [-3.1151311190821263, -3.2755555189753016, 1.6239828097671483], [7.30781816488312, 5.511193795479521, 6.409933840845935], [9.598713325751355, -3.6388510809612606, -5.559009746431668], [6.276128328255048, 7.95945736677843, 7.950517677728684], [-4.293959405286493, 4.303713828491777, -2.9411789670435726], [6.941895875082199, -6.390315685941024, -7.060257485962946], [9.215829489665104, 3.350539724369737, 4.914386778129518], [-7.585059918812879, 6.9239850563385055, -8.358633234846824], [-3.330732190621517, 2.77422193891395, -1.4706219638804343], [-0.6172131200314386, 7.989184263672538, -0.7847976949291748], [-4.089924834724457, -1.4190366056191177, 0.923695987140944], [-6.0393222741002734, 2.6550451466898366, -2.5519975154677472], [-6.258268767773898, 3.5323209700867544, -3.518313231918641], [2.3769468941467675, -5.375051766203363, -2.033397389530471], [-8.826167243762985, -6.467155813055672, 9.084595791290717], [-6.7608648805938, -8.800650278629654, 9.469720290946471], [8.682323594299394, -4.529585897960187, -6.259139049954091], [-5.888245070361262, 1.0247042236635302, -0.9602947069968837], [-0.7983068421543926, -7.010878265646365, 0.8907634926160306], [3.2438051212073518, -9.770225503375459, -5.0440510622829775], [-5.74451616705918, 0.6462091306787698, -0.5908084223210306], [7.333122309350184, -0.8202194747234195, -0.9572803338753864], [4.3200904453846185, 2.155386777953831, 1.4819658135670106], [3.5071699603512876, -9.443511518302492, -5.271211702029026], [-5.573788787459264, -1.7262708031707685, 1.5313679887551526], [2.3538790379643117, -3.9986993338965977, -1.4980386668567232], [-4.766507068738653, -2.373779290400913, 1.8007802116535572], [-8.325266422761672, 9.881480953457185, -13.09303443509354], [5.10997506468434, -4.35249319412172, -3.5397860486075574], [-2.422164391088401, 0.7045328006691083, -0.27159699717666175], [9.02091939234625, -6.285394683666928, -9.024091447000897], [7.262243490650356, -4.932670247084523, -5.701288541097358], [-4.743379782748214, -2.0559547977697523, 1.5521067651532976], [1.272529178248691, -0.19716364339196346, -0.0399314164456366], [8.279858176412198, 3.8932818253336325, 5.130490313206406], [5.7737353713144675, 3.7480783979867702, 3.444178670997989], [3.4652141927343614, -1.1416566579401977, -0.6296304598566533], [9.09757595456913, 0.29232376704236884, 0.4232626516609134], [-2.350396373919752, -3.7574271185020507, 1.4055678199564743], [0.05365948982769986, 9.765715713423873, 0.08340090214845217], [7.950329279580547, -6.727691589227334, -8.512778282172201], [5.065209710060511, 1.8129289823610755, 1.461498433702486], [9.285383211785565, -9.160669616694667, -13.537771641141184], [0.014266019570371213, -6.413986238338967, -0.014563004069875035], [7.6093180090636885, -1.8735966838041875, -2.2690390766451607], [-2.538200554611403, -1.1815913666236213, 0.4773241143566356], [8.904004963806646, -0.2869682306014969, -0.40666738681267844], [5.198118648552574, -8.15976165823978, -6.750622044359221], [-5.073754571658302, 7.2208705485231235, -5.830947706580959], [-7.367415590927355, -7.4252128628318275, 8.706512117201507], [-8.957025500746932, 8.7523331635415, -12.476931286316685], [-1.0179871360302801, 5.782069144753603, -0.9367974556266793], [1.9011657598984968, -6.656260385158744, -2.0140507902532385], [-8.541919916247025, 6.418110978798605, -8.725349852699567], [1.4310862180897832, 9.745815222237614, 2.219750201009825], [-9.740206775259658, -0.6556614980146147, 1.0164078016195797], [8.17425588924668, 9.628209567971165, 12.526042909152741], [1.75138787818846, -1.220941731772422, -0.3403277866971762], [-3.6026506326760916, -1.8495097564706526, 1.0604712687171356], [-2.2951998211523943, -6.465380016105389, 2.361754163082049], [-6.699331646936346, -9.5951525917811, 10.230656310876356], [6.318613442146074, 0.3273089346818807, 0.3291544866665399], [-1.5117177653587692, 6.444444578020608, -1.5505163193789118], [-0.24544215306229233, -0.5575232927142633, 0.02177871742694032], [1.1043188614488813, -6.5821533146674005, -1.1568648223743574], [8.519918986236753, 7.512796657131318, 10.18725626406225], [-4.972638617429337, 3.0362121888039084, -2.40291909956945], [6.692777200990076, -2.366085236946864, -2.520326960807963], [-5.927242114149529, 3.6041594416739677, -3.3999833817393736], [-7.25650818416921, 7.4674745902707045, -8.624254710020473], [-7.391000283832114, 8.932105013836889, -10.506962227749522], [-7.377145422983342, -7.238823736932128, 8.499169256980453], [4.497169934729202, 0.11833522808555053, 0.08469806379219207], [-9.930334359781792, -0.8480984295409222, 1.3403871704569612], [-0.39740582468249386, 8.014372962472926, -0.5069018882548775], [2.960184155539933, 3.6929939882745533, 1.7398726531434607], [6.690069299315663, 4.433913594800261, 4.721043191658925], [-2.3813625959470697, -7.8277740273435565, 2.9667704145127973], [4.7221796090050105, -8.369224215019425, -6.289959311910854], [8.74767322640723, 8.297167674979427, 11.551610843387552], [0.3260864054335819, 2.953855774880264, 0.15329998475443699], [-7.357969194310621, 4.918577048064744, -5.759934910426677], [2.957162377996907, -2.2367052073462297, -1.0526986180522324], [0.5370565986096558, -9.181979654550714, -0.7848316611227911], [-4.6737918389883015, 7.450037717634814, -5.5417632590032095], [8.615083689474698, -6.215735520357417, -8.522601050510314], [3.399955305128856, -2.852986419765962, -1.54380713589013], [2.1398512760974437, 2.2321175699677873, 0.7601876113755968], [-3.8690079592840476, -5.865452466672847, 3.611779880569241], [7.824531979097667, 8.255538478438702, 10.280728909173432], [-5.8679537717068975, 2.554366896923689, -2.385558619447254], [-2.168051943376992, 1.6332045573513927, -0.5635473317095725], [7.332101182922447, 7.41477355110657, 8.652596934081904], [-5.144235620008293, -5.8520756701392145, 4.791272999526958], [-7.993754549872982, -5.546926859158406, 7.057053015377955], [5.912708257374755, 8.357290057353097, 7.864517042800507], [-7.234320436834222, -0.7074839997945599, 0.8145814118515089], [8.318430186069541, -4.579848672690796, -6.063349970437653], [-8.984633221744057, 9.563134320654353, -13.674792341899025], [-9.398853727922972, -1.6033603941976793, 2.3984251747261385], [1.8026224932267443, -2.369227177766624, -0.6797224645477364], [-3.347250197645182, -5.325967347041349, 2.8373101195448154], [-2.197996620119838, -3.3507963565265753, 1.1721823734753605], [-9.070335554758373, -1.16231927984472, 1.6779110235552026], [-1.977680730154157, -3.3827233101861998, 1.0647380872810088], [8.420407346553958, 0.989174424451706, 1.3256415629121856], [-3.3625337954461294, 8.342493057665521, -4.4646009107229485]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.49704, x1=-0.06552, y=0.53043\nx0=-5.65203, x1=0.60653, y=-0.59991\nx0=-0.92408, x1=-7.66489, y=-4.20426\nx0=7.67402, x1=-1.71298, y=-1.44257\nx0=-6.78122, x1=0.72886, y=-0.86687\nx0=-1.75538, x1=0.04875, y=0.91680\nx0=7.88074, x1=-6.80180, y=-1.84100\nx0=5.59874, x1=9.19375, y=-2.18567\nx0=-1.06327, x1=-7.07931, y=-3.98798\nx0=1.48787, x1=8.25361, y=-2.96979\nx0=-9.36266, x1=-1.17301, y=-3.12746\nx0=6.39421, x1=6.33375, y=-2.24000\nx0=3.23066, x1=-4.21275, y=-1.45816\nx0=5.75693, x1=6.31790, y=-2.26969\nx0=-0.43151, x1=0.37261, y=0.84739\nx0=-7.90434, x1=0.07588, y=0.50016\nx0=9.40333, x1=4.33541, y=-2.23830\nx0=0.61689, x1=3.94726, y=13.92949\nx0=3.47701, x1=0.26253, y=2.31206\nx0=-8.59837, x1=-7.45274, y=-2.14734\nx0=-5.19548, x1=-5.06993, y=-2.38559\nx0=7.02416, x1=2.56557, y=-2.59916\nx0=2.81473, x1=-3.42427, y=-1.28788\nx0=-3.44339, x1=4.84493, y=-1.54275\nx0=-9.48607, x1=-9.20795, y=-2.10670\nx0=3.42329, x1=-4.16356, y=-1.47835\nx0=-6.37938, x1=8.31962, y=-1.83950\nx0=-7.97250, x1=-2.10448, y=-2.65322\nx0=6.87502, x1=4.48254, y=-2.32354\nx0=-0.87295, x1=5.97711, y=-0.90481\nx0=3.27661, x1=4.39175, y=-2.79016\nx0=9.61356, x1=2.60446, y=-2.40838\nx0=1.60239, x1=-6.19101, y=-1.30343\nx0=5.40438, x1=-8.33417, y=-1.81266\nx0=3.57169, x1=-0.14569, y=0.55657\nx0=-6.18541, x1=-4.37413, y=-2.37413\nx0=-4.80262, x1=-4.66405, y=-2.46393\nx0=-8.06335, x1=9.98784, y=-1.89226\nx0=6.93182, x1=1.15256, y=-3.80384\nx0=9.63446, x1=-3.11555, y=-1.72741\nx0=-3.07877, x1=8.10482, y=-1.67803\nx0=0.60758, x1=4.18170, y=17.59494\nx0=-8.27478, x1=9.42043, y=-1.88882\nx0=-6.50517, x1=9.55941, y=-1.86193\nx0=-2.29557, x1=-1.54160, y=-18.70198\nx0=-5.76327, x1=3.64416, y=-1.62504\nx0=-9.83346, x1=-7.15813, y=-2.13355\nx0=-3.13561, x1=7.47320, y=-1.65952\nx0=8.16058, x1=9.46734, y=-2.12120\nx0=4.29352, x1=6.33948, y=-2.37161\nx0=3.24356, x1=-8.03043, y=-1.69016\nx0=-1.50918, x1=-3.37283, y=-6.30580\nx0=-1.05473, x1=-0.17530, y=1.19704\nx0=-8.77594, x1=5.06376, y=-1.81028\nx0=6.72104, x1=5.98210, y=-2.24190\nx0=4.89505, x1=-3.74171, y=-1.57778\nx0=8.59176, x1=-8.99341, y=-1.88788\nx0=2.30475, x1=-9.66631, y=-1.64397\nx0=-3.36286, x1=0.10178, y=0.69279\nx0=-9.97338, x1=3.46156, y=-1.76015\nx0=2.79723, x1=-4.24776, y=-1.39524\nx0=2.62482, x1=-6.96446, y=-1.57708\nx0=9.43471, x1=0.18949, y=5.42468\nx0=-1.53784, x1=-5.70557, y=-3.55863\nx0=0.60648, x1=6.35755, y=-12.51723\nx0=6.24930, x1=7.44180, y=-2.20687\nx0=-6.60077, x1=-3.19274, y=-2.49794\nx0=7.82460, x1=6.97485, y=-2.17450\nx0=6.85638, x1=-3.26606, y=-1.64558\nx0=-2.89660, x1=8.51596, y=-1.67471\nx0=6.29936, x1=-5.99557, y=-1.77924\nx0=2.52839, x1=2.37838, y=-4.98659\nx0=-4.48072, x1=-8.45784, y=-2.25790\nx0=-2.77047, x1=-8.09783, y=-2.46309\nx0=5.64968, x1=-4.77293, y=-1.69965\nx0=-8.86530, x1=6.29910, y=-1.84705\nx0=-2.88598, x1=5.25576, y=-1.50462\nx0=-4.35970, x1=0.35982, y=-0.03007\nx0=-2.28338, x1=-1.59584, y=-15.97730\nx0=-1.66872, x1=1.52017, y=-0.37450\nx0=9.81947, x1=-8.02177, y=-1.88993\nx0=0.89175, x1=4.84739, y=-8.80448\nx0=0.77638, x1=0.71853, y=1.68528\nx0=2.42022, x1=-5.17116, y=-1.41993\nx0=-1.41651, x1=-5.58582, y=-3.83212\nx0=-5.38067, x1=5.50679, y=-1.72418\nx0=4.64638, x1=2.78121, y=-2.90703\nx0=4.19456, x1=8.22778, y=-2.28561\nx0=-6.78911, x1=-4.02726, y=-2.36974\nx0=9.18800, x1=-5.88021, y=-1.84218\nx0=-3.05596, x1=-2.04038, y=-4.78180\nx0=-5.71787, x1=-4.45690, y=-2.40029\nx0=-1.81774, x1=2.19227, y=-0.71152\nx0=-9.12820, x1=-2.46827, y=-2.46081\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.69684, x1=-0.09570, y=1.06820\nx0=4.77268, x1=7.83134, y=-2.26181\nx0=-9.16202, x1=-3.71373, y=-2.29009\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1 + x0 * x1 / (1 - (x0 * x1 / 3))", "data": [[8.497040348162564, -0.06551793922015392, 0.5304294167123558], [-5.652028866610516, 0.6065342541301604, -0.5999080229961737], [-0.9240841215797264, -7.664887372859881, -4.204261186394456], [7.674021352204456, -1.7129844269618388, -1.4425684142405086], [-6.78121906326933, 0.7288639517997968, -0.8668678111947643], [-1.7553825817262698, 0.048750114769337216, 0.9167982309759841], [7.880743599679871, -6.801797065529456, -1.8409984412863136], [5.598738690866831, 9.193749814964782, -2.1856688303179563], [-1.0632687790110076, -7.079307087673006, -3.9879810186980693], [1.4878713004926158, 8.253612418267384, -2.969794872086224], [-9.36265644605511, -1.1730127392272536, -3.1274641738274154], [6.394206764442295, 6.333748412697457, -2.240004499637987], [3.2306553761565873, -4.21275112458122, -1.4581560096132664], [5.756926160387273, 6.317903994921011, -2.2696895324352573], [-0.4315103211398874, 0.3726129297077012, 0.8473927291230661], [-7.904341786121214, 0.07587935386694333, 0.5001553239035241], [9.403326577392935, 4.335413951062677, -2.238301304230568], [0.6168856657233306, 3.94726359029665, 13.929494716483903], [3.477014998432038, 0.262533163481816, 2.3120625216083663], [-8.598371436020837, -7.452735921976679, -2.1473443835132087], [-5.195484562317958, -5.06992830795194, -2.385591982723403], [7.024160302968074, 2.565568071200456, -2.599162714034208], [2.8147302236719227, -3.424271297401593, -1.2878845375492407], [-3.4433909532424707, 4.844927987513186, -1.5427521924677192], [-9.486070647058924, -9.207949762773481, -2.106701744554741], [3.4232889830588995, -4.163559991009727, -1.4783536786871383], [-6.379377917414519, 8.319623873223144, -1.8394978775073505], [-7.972498360243055, -2.104476414221912, -2.6532183636921696], [6.875023218970778, 4.482537776180081, -2.323536745049977], [-0.8729522591931911, 5.977107115279633, -0.9048069332692257], [3.276610219851438, 4.391753755885322, -2.7901622871048883], [9.613558436001888, 2.6044617160913184, -2.40838283077057], [1.6023900705280205, -6.191010409573492, -1.3034278720583599], [5.404377453341985, -8.334166389421753, -1.8126599451913252], [3.5716915271677223, -0.1456864020716857, 0.5565662380962534], [-6.185408032272777, -4.374130340229165, -2.374130443829711], [-4.802621535108729, -4.664051628002706, -2.463925302751417], [-8.063349880784523, 9.987837827965393, -1.8922612848628022], [6.931818426975948, 1.1525608110224184, -3.803844979251644], [9.634455414312978, -3.1155510056976627, -1.727410155965392], [-3.078774195552631, 8.104823469885044, -1.6780300747623351], [0.6075756221402138, 4.181698123219839, 17.594943722528953], [-8.274784801471585, 9.420431749914272, -1.888823068669534], [-6.505174532552793, 9.559411801848746, -1.8619327861732837], [-2.2955693388124114, -1.5416037680959676, -18.70197765877971], [-5.7632738420431995, 3.6441559701971027, -1.6250354463267107], [-9.833459764143782, -7.158131967295884, -2.1335525520582865], [-3.135609444575838, 7.473198244932316, -1.6595169127338498], [8.160577549423945, 9.467344711926838, -2.121197429457633], [4.293519501984379, 6.339476045260838, -2.3716142223143217], [3.243556859974211, -8.030432268110879, -1.6901590770894845], [-1.5091777045124886, -3.3728313051926655, -6.3058043344821595], [-1.0547336993346121, -0.175298249382978, 1.197036527376492], [-8.775937613668905, 5.063764733464968, -1.8102838121354865], [6.721038415034112, 5.982097981304786, -2.2418970512749556], [4.895052850195471, -3.741714493771071, -1.577779772898336], [8.59175609655005, -8.993409756629491, -1.8878772693102643], [2.3047510947130885, -9.666312653164045, -1.6439654370445043], [-3.3628608224479084, 0.10177637867937861, 0.6927888757761382], [-9.973382307085885, 3.461563993103491, -1.7601503127351252], [2.7972265087925514, -4.247756868141348, -1.395240060080027], [2.624815000760792, -6.964458261183461, -1.57707590737109], [9.434707092377497, 0.18949472541817514, 5.424684188411601], [-1.5378443146307745, -5.70557413027343, -3.5586346029763574], [0.6064816585295691, 6.357551993459417, -12.51722942995354], [6.24929814373888, 7.441801940475113, -2.206867832511746], [-6.600766329162182, -3.1927441909731886, -2.497937477864019], [7.824602682564418, 6.974849713899516, -2.1745017033705567], [6.856383197466162, -3.26605942967163, -1.645576569083309], [-2.896600714482666, 8.515963136708457, -1.674706769641948], [6.299362689878244, -5.995565203946784, -1.77923991678117], [2.5283868937527814, 2.3783826149851794, -4.986588790673757], [-4.480723495217546, -8.457836464271296, -2.2579001509891063], [-2.7704702038444555, -8.09782744955578, -2.4630870801894584], [5.649681229805065, -4.77292655014506, -1.699654738521073], [-8.865304004535115, 6.299099468650894, -1.8470517484586177], [-2.885980225274416, 5.255761125525542, -1.5046241321914775], [-4.359703368327819, 0.359818191931641, -0.030074452066467527], [-2.2833817128583123, -1.5958352231922053, -15.977304716101841], [-1.6687249958371204, 1.520174607686812, -0.37449866279834443], [9.81947334551679, -8.021771801340407, -1.8899346111623885], [0.8917502335070076, 4.847385802823155, -8.80448304546123], [0.7763792020811255, 0.7185328757785197, 1.6852833242227123], [2.42021955524889, -5.17115994222727, -1.4199290122653068], [-1.4165072976830366, -5.585816841000224, -3.832116892307244], [-5.380673747371794, 5.506788672583324, -1.7241821738445555], [4.646381857996442, 2.781205110073902, -2.907025733640225], [4.194563609406327, 8.227776020593321, -2.2856061191303807], [-6.789106541871273, -4.027256020005079, -2.3697393760238503], [9.187997012366797, -5.880208893672847, -1.8421809657566866], [-3.055959179701153, -2.040378324052618, -4.781802058458985], [-5.717870867213977, -4.456899071901721, -2.400285121110981], [-1.8177353153896902, 2.192270202717726, -0.7115186026258924], [-9.12820301592004, -2.4682732723551943, -2.4608082688007302], [-0.6968398199919239, -0.09569745531863916, 1.0682018286502888], [4.772675532408371, 7.8313370258603, -2.261807285994015], [-9.162021917519832, -3.713726996017903, -2.2900863181290347]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.69482, x1=1.80977, y=32.99538\nx0=6.82274, x1=8.87677, y=1879.80481\nx0=5.75371, x1=5.29071, y=914.18024\nx0=8.63414, x1=5.34001, y=4922.71402\nx0=-6.94803, x1=0.54747, y=2665.50145\nx0=-4.66393, x1=5.35065, y=583.57631\nx0=2.93972, x1=4.47297, y=54.80888\nx0=0.94848, x1=7.76119, y=22.31290\nx0=-0.54438, x1=-3.30678, y=9.02332\nx0=0.75847, x1=-7.85396, y=38.59092\nx0=3.65301, x1=-5.83568, y=152.19063\nx0=-6.59143, x1=0.00481, y=2174.00407\nx0=-1.98387, x1=6.24480, y=36.55221\nx0=-2.61764, x1=0.95386, y=64.38773\nx0=9.17195, x1=-3.07842, y=6313.19052\nx0=-8.43779, x1=3.86834, y=5673.27289\nx0=5.89515, x1=-9.98539, y=1062.72261\nx0=-6.37896, x1=-4.05074, y=1927.59000\nx0=-6.40347, x1=7.96291, y=1967.67135\nx0=-2.41967, x1=-4.67913, y=64.07153\nx0=8.30138, x1=5.74072, y=4187.65029\nx0=-2.77009, x1=3.35670, y=82.41442\nx0=7.79761, x1=2.56990, y=3223.59277\nx0=-6.80730, x1=-7.01259, y=2494.38605\nx0=-0.99893, x1=-5.98949, y=25.91902\nx0=-5.33618, x1=6.49773, y=977.37138\nx0=-6.64259, x1=8.37158, y=2266.69265\nx0=-1.03255, x1=-6.84229, y=32.48835\nx0=-7.88284, x1=-0.97415, y=4352.56565\nx0=0.93952, x1=-6.39006, y=26.75635\nx0=0.77332, x1=-2.62992, y=5.98333\nx0=-3.98074, x1=2.57794, y=314.93036\nx0=-5.24636, x1=1.53002, y=901.62876\nx0=-7.03496, x1=4.94113, y=2804.74952\nx0=2.43004, x1=-5.86662, y=43.59577\nx0=0.05881, x1=-6.43646, y=27.15025\nx0=-7.70172, x1=9.57026, y=4011.50515\nx0=-7.86701, x1=-6.16191, y=4342.39515\nx0=0.92154, x1=-6.09606, y=24.61562\nx0=-3.75979, x1=-4.97893, y=270.34984\nx0=6.27341, x1=-7.01729, y=1333.61143\nx0=7.11634, x1=7.05524, y=2222.09124\nx0=6.87057, x1=-3.89117, y=1915.41942\nx0=7.92296, x1=3.12032, y=3444.88899\nx0=-0.38311, x1=5.41250, y=9.31283\nx0=-7.20968, x1=-3.07032, y=3084.40720\nx0=4.94770, x1=-9.32214, y=530.91401\nx0=9.84228, x1=7.56008, y=8451.47714\nx0=-2.28007, x1=8.84978, y=69.18943\nx0=9.83009, x1=-5.57346, y=8408.71817\nx0=-4.15997, x1=6.12772, y=384.11216\nx0=0.03861, x1=-1.98393, y=3.95187\nx0=1.14794, x1=4.57699, y=6.12123\nx0=-1.69586, x1=-7.81351, y=51.48737\nx0=-7.74418, x1=0.48000, y=4060.74396\nx0=4.22321, x1=-4.20995, y=255.85485\nx0=9.51007, x1=4.87059, y=7326.54555\nx0=-8.43593, x1=-1.41100, y=5667.19881\nx0=9.76298, x1=4.55999, y=8160.38492\nx0=-8.20192, x1=0.19722, y=5077.03870\nx0=-5.39012, x1=8.55909, y=1028.77424\nx0=4.26405, x1=-6.48040, y=280.53715\nx0=-1.00171, x1=-1.99651, y=6.00153\nx0=7.29105, x1=1.30958, y=2437.88842\nx0=-5.65370, x1=-4.41958, y=1216.62057\nx0=6.95617, x1=5.18147, y=2013.07782\nx0=6.57433, x1=1.82258, y=1583.80596\nx0=-5.24370, x1=-4.15673, y=913.02944\nx0=-6.00531, x1=1.74465, y=1516.94854\nx0=-2.65550, x1=7.96877, y=92.23378\nx0=8.83253, x1=9.95762, y=5436.68615\nx0=2.12295, x1=-5.74689, y=33.00450\nx0=-1.87535, x1=-8.74547, y=65.95146\nx0=-8.37075, x1=-4.89004, y=5513.10370\nx0=2.70473, x1=1.45332, y=33.33358\nx0=1.32889, x1=9.43887, y=35.87914\nx0=0.40915, x1=7.78330, y=22.46611\nx0=4.67399, x1=-6.03378, y=399.38505\nx0=6.78407, x1=2.53289, y=1806.61710\nx0=-5.90595, x1=8.41657, y=1449.63123\nx0=9.13656, x1=1.19128, y=6205.19499\nx0=-7.91607, x1=8.67929, y=4451.82673\nx0=5.08822, x1=3.64972, y=541.56728\nx0=0.41326, x1=8.77555, y=29.68817\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.71487, x1=0.41445, y=9823.89732\nx0=9.46206, x1=0.94290, y=7168.08070\nx0=-5.70556, x1=-8.49478, y=1290.03471\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**4 - x0**3 + x1**2 / 2 - x1", "data": [[2.694820077395459, 1.8097728385716554, 32.995380182725285], [6.822738190245595, 8.876774075897401, 1879.8048061739664], [5.7537097824478405, 5.290714848485017, 914.1802357027996], [8.634138835010827, 5.340013736975282, 4922.714024216992], [-6.948026482016781, 0.5474726595443471, 2665.501445241861], [-4.663932615547806, 5.350645990122407, 583.5763087366907], [2.939715686786661, 4.472972101087008, 54.808880436750336], [0.9484800617418578, 7.761192496034408, 22.31290175466166], [-0.5443777185767988, -3.3067789354679107, 9.023318761927385], [0.7584728041361739, -7.853959935645529, 38.59091650462111], [3.6530080244062173, -5.835680163390458, 152.19063055890643], [-6.591425239884565, 0.004811178742547995, 2174.0040692508155], [-1.9838747190598802, 6.2447986269418045, 36.55220702865489], [-2.617640546185676, 0.9538574364531307, 64.38772757512179], [9.171950509094742, -3.0784195262886875, 6313.1905226305325], [-8.43779253048448, 3.8683416203060617, 5673.272887510725], [5.895149320657314, -9.985387915074678, 1062.7226148172347], [-6.3789598525067355, -4.050735175792697, 1927.5900028851527], [-6.4034670518407655, 7.9629108132175865, 1967.671348224326], [-2.419667956324661, -4.679132768314074, 64.07153085247161], [8.301378155056238, 5.740723766062976, 4187.650290040942], [-2.7700932254722765, 3.3567003272327796, 82.4144176594773], [7.797613162588355, 2.569897979257128, 3223.592767437537], [-6.807304075068757, -7.012588746927097, 2494.3860508456496], [-0.9989321101368951, -5.989490333429506, 25.919022588921614], [-5.336175518049171, 6.497732998975906, 977.3713788173261], [-6.6425879572864455, 8.371582436107502, 2266.692646771799], [-1.0325529062373384, -6.84229170371502, 32.48835075525055], [-7.882843677776814, -0.9741532248531666, 4352.565648093531], [0.9395151299059368, -6.390062692377407, 26.75635323401785], [0.7733226615339781, -2.6299210672315576, 5.983332335464379], [-3.9807417011784807, 2.577943900743948, 314.93036461321446], [-5.246358824137484, 1.5300239536953253, 901.6287564353415], [-7.034955323642871, 4.941131142424345, 2804.749524582143], [2.4300400009256293, -5.866621115300168, 43.59576709941857], [0.05880886957260856, -6.436455746686058, 27.15024560783176], [-7.701717686037726, 9.57026057689578, 4011.505147340797], [-7.867013530064524, -6.161913516193824, 4342.395153079103], [0.9215374640927738, -6.096058952294728, 24.61562166772425], [-3.759792001281128, -4.978925242016679, 270.34983897003906], [6.273407920709705, -7.017294818971996, 1333.611426907748], [7.1163431193939815, 7.055239245125126, 2222.091236859182], [6.8705650906520574, -3.891170163136568, 1915.4194177442757], [7.922962688338291, 3.1203165375787716, 3444.888991840054], [-0.38310957072545193, 5.412495608698864, 9.312831164499872], [-7.2096806442874595, -3.0703162242442765, 3084.4071957178585], [4.9477041494069685, -9.322136157681864, 530.914006554025], [9.842279177222917, 7.560082302580938, 8451.477139275315], [-2.280066214092729, 8.84978284515276, 69.18943187772359], [9.830094239497889, -5.573461191275378, 8408.718168441266], [-4.159971467026704, 6.127722751082672, 384.1121599171062], [0.03861310033281384, -1.9839329825443226, 3.9518726741212022], [1.1479430293790127, 4.576992087745353, 6.121233843358109], [-1.695864530959831, -7.8135137980744425, 51.487371200122226], [-7.744176394435314, 0.4799977426945077, 4060.743955995748], [4.223213862561748, -4.209953172129439, 255.85484645017087], [9.510072101466854, 4.870586091601918, 7326.54554909902], [-8.435931911014904, -1.4109967144840834, 5667.1988126850965], [9.76298482243935, 4.559988177882763, 8160.384917691513], [-8.201923109036318, 0.19721961499156038, 5077.038704142075], [-5.390124745476936, 8.559086099348228, 1028.7742360427176], [4.264045449832125, -6.480403723201427, 280.5371530686973], [-1.0017104354846378, -1.996507170131462, 6.0015270140517405], [7.29105397662007, 1.309580034219774, 2437.8884162966656], [-5.653699971495369, -4.4195774525674985, 1216.6205723489927], [6.956174198568775, 5.181469839547718, 2013.077820524287], [6.574326846344494, 1.8225819886404064, 1583.8059577892043], [-5.243698820368374, -4.1567345706770205, 913.029442680967], [-6.005313453071503, 1.744652686172417, 1516.9485404194984], [-2.6554996999519176, 7.968770213610107, 92.2337815751541], [8.83253175246083, 9.957615591386052, 5436.686149977832], [2.1229464803129723, -5.746887118104141, 33.00449512610368], [-1.8753521196587482, -8.745465161243207, 65.95146310040032], [-8.370747998816183, -4.89004497323802, 5513.103697155989], [2.704729500290684, 1.4533214829712922, 33.33357726792131], [1.3288947842239, 9.438873996577108, 35.87913982216548], [0.4091540400634912, 7.7832997463708935, 22.466107575703095], [4.673993417418432, -6.033778964750862, 399.3850471501219], [6.784067575001853, 2.532887956311459, 1806.617103404625], [-5.905945623984758, 8.416574446173573, 1449.6312291724184], [9.136560931535438, 1.1912814204010047, 6205.1949865013785], [-7.9160652037300006, 8.679290728793436, 4451.826725727078], [5.088218850863504, 3.649723632766193, 541.5672810237393], [0.4132588531957442, 8.775549108388638, 29.68817122346681], [-9.71487259355305, 0.41445060770917586, 9823.897319940448], [9.462059398711993, 0.942900209179756, 7168.080695161469], [-5.705558766109117, -8.494783607632403, 1290.0347051983822]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-3.39642, x1=0.21022, y=-1.40323\nx0=6.76819, x1=-0.39717, y=5.61366\nx0=3.74347, x1=-7.75596, y=-0.27705\nx0=4.00100, x1=5.14246, y=0.32568\nx0=-0.82642, x1=-7.34352, y=0.06514\nx0=-8.91304, x1=-6.97333, y=0.74607\nx0=-1.78011, x1=5.57161, y=-0.13544\nx0=-5.75673, x1=-0.87891, y=-23.76984\nx0=6.28995, x1=-5.12542, y=-0.76234\nx0=-8.90074, x1=9.62826, y=-0.41873\nx0=0.37589, x1=9.84220, y=0.01733\nx0=8.18139, x1=7.90629, y=0.45930\nx0=0.91115, x1=1.53353, y=0.17982\nx0=3.81126, x1=5.42404, y=0.29664\nx0=-3.91317, x1=4.47898, y=-0.35711\nx0=1.33878, x1=-4.33608, y=-0.20065\nx0=2.58486, x1=2.96329, y=0.32610\nx0=-3.49516, x1=7.19799, y=-0.21317\nx0=-6.13482, x1=7.86753, y=-0.34591\nx0=5.02975, x1=-8.99714, y=-0.31447\nx0=-5.83216, x1=2.82335, y=-0.76270\nx0=-8.33339, x1=0.02162, y=-4.07853\nx0=-7.50428, x1=-6.15342, y=0.72809\nx0=-2.07323, x1=-6.75997, y=0.17997\nx0=-0.96030, x1=6.95783, y=-0.06034\nx0=-4.13955, x1=-6.42553, y=0.38149\nx0=-1.00770, x1=-5.89967, y=0.10283\nx0=4.98092, x1=5.70459, y=0.37146\nx0=3.69447, x1=6.25613, y=0.25458\nx0=7.08279, x1=0.54653, y=2.28989\nx0=-6.88105, x1=-2.38497, y=2.48419\nx0=1.79628, x1=0.99032, y=0.45125\nx0=2.69336, x1=-7.60550, y=-0.20387\nx0=5.81775, x1=-0.09417, y=3.21128\nx0=3.44284, x1=0.64246, y=1.04807\nx0=-4.59145, x1=-1.83748, y=2.74122\nx0=-2.59803, x1=0.39695, y=-0.92990\nx0=2.54965, x1=8.74526, y=0.13081\nx0=6.98461, x1=-7.25388, y=-0.55842\nx0=7.33296, x1=2.61114, y=1.01532\nx0=5.60803, x1=2.41862, y=0.82022\nx0=-2.20325, x1=9.70062, y=-0.10295\nx0=3.33099, x1=-7.01086, y=-0.27708\nx0=5.17551, x1=-2.50244, y=-1.72237\nx0=2.86789, x1=5.20849, y=0.23096\nx0=3.63760, x1=1.43320, y=0.74749\nx0=-4.51461, x1=-4.98344, y=0.56667\nx0=9.42124, x1=4.80614, y=0.81132\nx0=-7.48558, x1=3.50823, y=-0.83021\nx0=9.96283, x1=7.41846, y=0.59173\nx0=7.42279, x1=7.36197, y=0.44384\nx0=-9.98128, x1=8.18296, y=-0.54347\nx0=5.20278, x1=-2.12087, y=-2.32087\nx0=-5.64193, x1=8.15282, y=-0.30821\nx0=5.87233, x1=-8.23855, y=-0.40563\nx0=-5.21057, x1=-1.99709, y=2.61290\nx0=4.76728, x1=-7.14471, y=-0.38792\nx0=-0.81543, x1=-2.45893, y=0.27946\nx0=9.30611, x1=4.79443, y=0.80302\nx0=-0.80556, x1=9.94849, y=-0.03679\nx0=-6.71139, x1=-6.24108, y=0.64027\nx0=4.62148, x1=-0.79036, y=11.02229\nx0=-6.33598, x1=6.87112, y=-0.40248\nx0=-7.72626, x1=-3.37321, y=1.62781\nx0=2.36971, x1=-0.46205, y=2.20251\nx0=3.39600, x1=6.27596, y=0.23337\nx0=1.13216, x1=5.61209, y=0.08561\nx0=-7.14556, x1=-5.16932, y=0.85692\nx0=-5.37871, x1=0.62751, y=-1.65243\nx0=9.59686, x1=-6.58542, y=-0.85910\nx0=-0.90670, x1=-2.01727, y=0.44565\nx0=9.90615, x1=6.60429, y=0.65135\nx0=-0.27705, x1=-6.94397, y=0.02331\nx0=-3.99882, x1=-7.37029, y=0.31386\nx0=-1.30094, x1=-8.96377, y=0.08168\nx0=-4.35571, x1=-0.72884, y=-8.03172\nx0=-8.56822, x1=6.17009, y=-0.59750\nx0=9.66304, x1=-7.35671, y=-0.76007\nx0=-7.98403, x1=4.57725, y=-0.71577\nx0=-0.18250, x1=2.05793, y=-0.02984\nx0=-9.70084, x1=-4.38881, y=1.43130\nx0=6.91177, x1=5.21870, y=0.55572\nx0=-3.34321, x1=4.41622, y=-0.30863\nx0=-5.24168, x1=-2.17233, y=2.23558\nx0=9.78640, x1=-6.28798, y=-0.92534\nx0=1.54236, x1=-0.98459, y=50.03231\nx0=-9.59771, x1=-4.35833, y=1.42894\nx0=4.01362, x1=-9.07837, y=-0.24842\nx0=6.32229, x1=-1.25872, y=-12.21852\nx0=-1.35421, x1=6.37265, y=-0.09184\nx0=4.23176, x1=4.53816, y=0.38205\nx0=-5.64443, x1=9.26110, y=-0.27504\nx0=-7.86327, x1=4.43796, y=-0.72300\nx0=3.17293, x1=-8.87023, y=-0.20158\nx0=4.59444, x1=4.67401, y=0.40487\nx0=7.00272, x1=-6.31354, y=-0.65895\nx0=-3.94109, x1=4.64064, y=-0.34935\nx0=1.64001, x1=6.47384, y=0.10972\nx0=0.11013, x1=-4.18845, y=-0.01727\nx0=8.13437, x1=-7.03023, y=-0.67447\nx0=-2.06582, x1=-3.07201, y=0.49851\nx0=-0.08673, x1=-4.17179, y=0.01367\nx0=7.35689, x1=3.43285, y=0.82981\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=6.07513, x1=-5.05788, y=-0.74856\nx0=-2.27666, x1=-3.86026, y=0.39798\nx0=9.81478, x1=-6.11669, y=-0.95909\nx0=8.25226, x1=3.91107, y=0.84017\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 / (2 * (1 + x1))", "data": [[-3.3964223372316127, 0.2102197567060351, -1.4032254548859637], [6.768185186643468, -0.39716813054974054, 5.613659072815427], [3.743472035868738, -7.755959327750315, -0.2770496279108956], [4.001004643981496, 5.142462906669982, 0.325684070443216], [-0.826421502487861, -7.343516084963284, 0.06513907203978063], [-8.913039364381705, -6.973331433645969, 0.7460693804948818], [-1.7801130794641136, 5.571610410655266, -0.1354396387054399], [-5.756729347045065, -0.8789068462652949, -23.76983821751434], [6.289948654913321, -5.125424718265812, -0.7623395267720945], [-8.900741203528003, 9.628261319656612, -0.41872988139021294], [0.3758930355953378, 9.84219690815403, 0.017334726475620548], [8.181394989250762, 7.906289806339046, 0.4593043325082269], [0.9111491046905318, 1.5335306363746781, 0.17981805540633375], [3.8112636516524407, 5.424035441502998, 0.2966409265918324], [-3.9131664077837858, 4.478981367544348, -0.35710711036216275], [1.33877923774582, -4.336083696548654, -0.200651326453658], [2.5848591042556386, 2.963285690547293, 0.3261005269467079], [-3.495164224436702, 7.197990538552482, -0.21317200892097168], [-6.134824104139522, 7.8675329195665356, -0.3459149325852971], [5.029750574180769, -8.99714059203629, -0.3144718112864924], [-5.832162755553194, 2.823348501735225, -0.7627035245291227], [-8.333394824982701, 0.02161667136043377, -4.0785331027759915], [-7.504279041791042, -6.153419771716868, 0.7280873065082163], [-2.073229239272263, -6.759974793842261, 0.17996860346408652], [-0.9603027089655374, 6.957829495834929, -0.06033697438906884], [-4.139552434877876, -6.425530606515412, 0.38148825756385646], [-1.0076958374896705, -5.899669311175755, 0.10283304581303035], [4.980921175904614, 5.704592766005341, 0.371455907147683], [3.6944718317297536, 6.256132526509234, 0.25457582384503963], [7.082785910201061, 0.546534927671809, 2.2898887647056436], [-6.881048869332553, -2.3849660615822117, 2.4841940391923796], [1.7962772863915575, 0.9903157571276751, 0.45125434995898733], [2.6933558986590107, -7.605501463821376, -0.2038721748387038], [5.817750984999591, -0.09416893079993827, 3.2112781195158386], [3.4428360323389953, 0.6424608378517238, 1.0480724876344978], [-4.591446932806642, -1.8374821407262836, 2.741220803123536], [-2.5980296487763006, 0.3969467192629583, -0.9298957551319654], [2.5496450989391946, 8.745259629437285, 0.13081463172297325], [6.984608617504858, -7.253884028053548, -0.5584216613366542], [7.332956312613149, 2.611144050137753, 1.015323151167761], [5.608033227683338, 2.418616554092832, 0.8202196910573804], [-2.203245963914058, 9.700619738351513, -0.10294945609633818], [3.3309948052626552, -7.010856855836209, -0.27708152807103065], [5.1755137874638635, -2.5024364253007487, -1.7223736393464568], [2.8678879228236287, 5.208492823641995, 0.23096490599962413], [3.637596003529058, 1.433199589429135, 0.7474923182077498], [-4.514614812369809, -4.983442907486612, 0.5666724636475766], [9.421240441389546, 4.806137549302626, 0.8113173655799051], [-7.485584327504792, 3.5082263665552453, -0.8302138933214837], [9.96283302251998, 7.418463436008061, 0.59172514665243], [7.422794742778944, 7.361973921828998, 0.4438422561568675], [-9.981284928227867, 8.18295673081975, -0.5434679276408204], [5.202784004546, -2.1208686990939736, -2.32087130667113], [-5.641932549004713, 8.1528207860786, -0.30820731012160035], [5.872332438511441, -8.238545602743914, -0.4056293046137208], [-5.210572490724932, -1.9970858636024165, 2.6129005940869625], [4.767284999516125, -7.144711539274806, -0.38791772152731163], [-0.8154318756684216, -2.4589340687789862, 0.27946152369684335], [9.306107752762664, 4.794431867444725, 0.803021587418073], [-0.805558367825645, 9.94848934383376, -0.03678856244580168], [-6.711387669797406, -6.241081716456501, 0.6402674135688711], [4.621479628743437, -0.790357609535274, 11.022292816111152], [-6.335983425092248, 6.871121047554958, -0.4024829110626131], [-7.726258926684149, -3.373211574165758, 1.6278065998814535], [2.3697058044283796, -0.4620454573723407, 2.202514912183344], [3.3959998008244536, 6.275962681318454, 0.23337116678346373], [1.1321639631287717, 5.6120900807044265, 0.08561316840137145], [-7.145559928456446, -5.1693249707387405, 0.8569204821650497], [-5.378714866110088, 0.6275137799657884, -1.652432972402591], [9.59685508841639, -6.585421797754969, -0.8590985100063343], [-0.9066959431644595, -2.0172651671622326, 0.44565368619363155], [9.906154191988257, 6.604289126097132, 0.6513530737535586], [-0.2770544650865574, -6.943970872434589, 0.023305503259732394], [-3.9988153714132313, -7.3702870372387075, 0.31386461457995585], [-1.300941879066917, -8.96376532986051, 0.0816788180704531], [-4.355711701375231, -0.7288430733898075, -8.03171756633176], [-8.56821933373752, 6.170093106183749, -0.5974970761779911], [9.663041186225815, -7.356708385254256, -0.7600664212189837], [-7.984028836913943, 4.57725349949566, -0.7157670740298897], [-0.18249590730517973, 2.057931622690216, -0.029839762594925018], [-9.700843087980964, -4.388812796062533, 1.4313040689725305], [6.9117748084538455, 5.218704324470764, 0.5557246693057774], [-3.343213733204262, 4.416222407654569, -0.30862965749702304], [-5.241675644148005, -2.1723282214370565, 2.235583665179827], [9.786397060660224, -6.2879835409212355, -0.9253429955793042], [1.5423625007130077, -0.9845863348775463, 50.032308618999025], [-9.597713439797431, -4.358333638974276, 1.4289398361755425], [4.0136228591644425, -9.078368301809437, -0.2484179174069997], [6.322287679658551, -1.2587174065568156, -12.218520129356168], [-1.3542083302014145, 6.372647641183292, -0.09184002790509511], [4.231761259860756, 4.5381630828653226, 0.3820545907137982], [-5.644425084708347, 9.261095409118841, -0.27504008391210616], [-7.863274116414589, 4.4379595439695905, -0.7229985854836437], [3.1729250638364803, -8.870230936843516, -0.20157763408077536], [4.594441254368807, 4.674008018516805, 0.40486735649430766], [7.0027219805988175, -6.3135397552940535, -0.6589507468746966], [-3.9410862115390337, 4.640643166816199, -0.3493472370956181], [1.6400122296694377, 6.47383552499501, 0.10971690667962168], [0.11012632195989092, -4.188453360433339, -0.0172695519599703], [8.134367183054795, -7.03022714159008, -0.6744660683635447], [-2.0658240979783287, -3.0720104205075094, 0.4985071690595877], [-0.08673041253181069, -4.171788775570935, 0.013672160832367984], [7.356889139843322, 3.4328495931859457, 0.8298148837659786], [6.075133042570432, -5.057882637106923, -0.7485594811216265], [-2.2766574278862457, -3.860264273817517, 0.3979802581052507], [9.814779028241961, -6.116689678100493, -0.9590946144583831], [8.252259274798647, 3.911067793637933, 0.8401695539093429]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.99949, x1=1.94384, y=-0.84914\nx0=4.12519, x1=-7.42671, y=-0.32094\nx0=9.13493, x1=7.41405, y=0.54284\nx0=-6.25523, x1=4.52245, y=-0.56635\nx0=-0.22202, x1=-2.35170, y=0.08213\nx0=-8.09171, x1=-7.65660, y=0.60780\nx0=-5.63700, x1=-1.32137, y=8.77032\nx0=-8.69467, x1=6.02300, y=-0.61901\nx0=9.27871, x1=-2.67032, y=-2.77752\nx0=-3.97401, x1=-0.10786, y=-2.22724\nx0=8.13676, x1=7.11483, y=0.50135\nx0=7.06403, x1=-9.43398, y=-0.41878\nx0=8.82484, x1=2.27112, y=1.34890\nx0=4.16247, x1=0.91378, y=1.08750\nx0=-1.66707, x1=-0.61215, y=-2.14915\nx0=9.09686, x1=-6.93053, y=-0.76695\nx0=-8.63490, x1=-8.84634, y=0.55025\nx0=8.07514, x1=6.66096, y=0.52703\nx0=3.09034, x1=4.44417, y=0.28382\nx0=-0.82642, x1=-7.34352, y=0.06514\nx0=-4.24603, x1=-1.21501, y=9.87387\nx0=-0.05394, x1=-3.85197, y=0.00946\nx0=8.28207, x1=-3.59794, y=-1.59397\nx0=6.25994, x1=0.96710, y=1.59116\nx0=0.06633, x1=-7.18020, y=-0.00537\nx0=-0.34902, x1=-5.83357, y=0.03610\nx0=-9.07116, x1=-9.35604, y=0.54279\nx0=-5.40071, x1=1.04692, y=-1.31923\nx0=-9.15264, x1=3.43246, y=-1.03246\nx0=9.96003, x1=-7.89043, y=-0.72274\nx0=-0.16766, x1=8.30080, y=-0.00901\nx0=-1.24088, x1=-3.01248, y=0.30830\nx0=-4.68827, x1=9.34139, y=-0.22668\nx0=6.23869, x1=7.78817, y=0.35495\nx0=-3.49516, x1=7.19799, y=-0.21317\nx0=-5.66180, x1=-3.08528, y=1.35757\nx0=8.41380, x1=-7.12655, y=-0.68667\nx0=8.31407, x1=5.43874, y=0.64563\nx0=7.69937, x1=0.54094, y=2.49827\nx0=0.72936, x1=-6.77404, y=-0.06316\nx0=-5.46891, x1=1.73825, y=-0.99861\nx0=-2.08383, x1=3.51420, y=-0.23081\nx0=-4.08766, x1=-8.07602, y=0.28884\nx0=-9.17640, x1=-8.65735, y=0.59919\nx0=4.00476, x1=-2.70782, y=-1.17248\nx0=-8.12912, x1=3.29840, y=-0.94560\nx0=-6.59926, x1=6.68282, y=-0.42948\nx0=5.88100, x1=1.36831, y=1.24160\nx0=0.89316, x1=-0.30885, y=0.64614\nx0=8.77661, x1=-5.11385, y=-1.06671\nx0=-4.34836, x1=3.84698, y=-0.44856\nx0=1.95507, x1=8.09022, y=0.10754\nx0=3.81126, x1=5.42404, y=0.29664\nx0=2.31271, x1=-3.81102, y=-0.41136\nx0=9.22090, x1=-4.80718, y=-1.21099\nx0=-3.29977, x1=-0.22820, y=-2.13770\nx0=8.83980, x1=-1.50885, y=-8.68608\nx0=-1.56445, x1=-0.45005, y=-1.42236\nx0=3.84562, x1=-3.42761, y=-0.79206\nx0=6.88383, x1=4.77921, y=0.59557\nx0=7.79438, x1=-1.39563, y=-9.85070\nx0=4.00749, x1=-3.54577, y=-0.78709\nx0=-2.08387, x1=-5.11451, y=0.25323\nx0=-3.73770, x1=0.64407, y=-1.13672\nx0=2.37912, x1=-2.23424, y=-0.96380\nx0=4.05500, x1=-1.67077, y=-3.02262\nx0=-6.46068, x1=-4.87397, y=0.83386\nx0=7.62716, x1=6.71015, y=0.49462\nx0=-4.15953, x1=-7.32702, y=0.32871\nx0=-1.16387, x1=6.12139, y=-0.08172\nx0=-1.80047, x1=-5.82488, y=0.18658\nx0=-3.26604, x1=4.14824, y=-0.31720\nx0=-4.02806, x1=-0.20348, y=-2.52853\nx0=-7.46336, x1=-6.17794, y=0.72069\nx0=-7.73362, x1=-0.23759, y=-5.07180\nx0=-2.00528, x1=-3.88202, y=0.34789\nx0=-6.52705, x1=-3.70203, y=1.20781\nx0=7.80155, x1=1.37569, y=1.64195\nx0=-5.86733, x1=-5.96000, y=0.59146\nx0=2.65900, x1=-5.65649, y=-0.28552\nx0=-0.94852, x1=8.34265, y=-0.05076\nx0=-0.96030, x1=6.95783, y=-0.06034\nx0=1.50682, x1=1.47046, y=0.30497\nx0=-4.41517, x1=-0.23109, y=-2.87107\nx0=1.23714, x1=7.93071, y=0.06926\nx0=-1.07874, x1=-7.60638, y=0.08164\nx0=1.98742, x1=1.55564, y=0.38883\nx0=2.95415, x1=1.64994, y=0.55740\nx0=7.83027, x1=1.00356, y=1.95409\nx0=-0.27578, x1=-8.23178, y=0.01907\nx0=-9.98947, x1=-2.81383, y=2.75370\nx0=-8.04400, x1=9.66873, y=-0.37699\nx0=7.64109, x1=5.60746, y=0.57822\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=2.32827, x1=9.10802, y=0.11517\nx0=-4.62850, x1=0.94574, y=-1.18939\nx0=-1.14539, x1=2.45450, y=-0.16578\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 / (2 * (1 + x1))", "data": [[-4.99948587452097, 1.9438445157672923, -0.8491423116512472], [4.125189079228779, -7.426706544462749, -0.3209411423011871], [9.134926316599067, 7.414054172087145, 0.5428373843196392], [-6.255227950634261, 4.522449763011867, -0.5663453919065392], [-0.22202476337244548, -2.3517025008853842, 0.0821278214795845], [-8.091706450351428, -7.6565997199545865, 0.6077957809371353], [-5.637000031490058, -1.321367813050827, 8.770324535578986], [-8.694665156292372, 6.0230029192793, -0.6190133519967708], [9.278712900889534, -2.6703220558044594, -2.7775221157636953], [-3.974011543849974, -0.10786384431939311, -2.227244977431846], [8.136764943637655, 7.11482739369346, 0.5013516954138324], [7.0640318741796975, -9.433981383307584, -0.418783938043824], [8.824843072712987, 2.2711208246329235, 1.3489020347793614], [4.1624738451535475, 0.9137794074049594, 1.0875009494426962], [-1.6670741683910357, -0.6121542501393069, -2.149145851140328], [9.096858309811637, -6.930527139475318, -0.7669519164038805], [-8.634897357622524, -8.846342266646296, 0.5502498530001849], [8.075137371421125, 6.660955401835238, 0.5270320050085833], [3.0903381235715557, 4.444166302707904, 0.2838210620085609], [-0.826421502487861, -7.343516084963284, 0.06513907203978063], [-4.246033817563277, -1.215013660433879, 9.873869895045614], [-0.053944189870826165, -3.8519743049359745, 0.009457341494533063], [8.282066997693502, -3.59793675709823, -1.5939700947424467], [6.259941802406775, 0.9670999188159932, 1.5911600988155863], [0.06632569268714761, -7.18019739860178, -0.005365984968550784], [-0.34901930884945287, -5.833565289979008, 0.03610371308866386], [-9.071156870968672, -9.356041393848663, 0.542790326388668], [-5.400711348291932, 1.0469183165398572, -1.3192298160244564], [-9.152638896670783, 3.4324557585292155, -1.032456881161046], [9.960034296270596, -7.890434731837224, -0.7227435338912871], [-0.167655639096294, 8.300799125396644, -0.009012969575834385], [-1.2408771114808825, -3.0124820082014487, 0.30829520622394335], [-4.688271995258326, 9.341385295565573, -0.22667524036981174], [6.238687698576459, 7.7881681355174734, 0.35494813039379264], [-3.495164224436702, 7.197990538552482, -0.21317200892097168], [-5.661800605423101, -3.085275867844719, 1.3575663279686287], [8.413797151182106, -7.126553429377196, -0.6866664306588298], [8.314071618151498, 5.438744943645897, 0.6456282777869835], [7.699374564583742, 0.5409423374815567, 2.498268227598716], [0.7293558547452683, -6.774044268143595, -0.06315814538946742], [-5.46891426813342, 1.7382539295834558, -0.9986134246076575], [-2.0838302881391524, 3.51419695103508, -0.2308085259396294], [-4.087664025259723, -8.07601500015258, 0.28883941209646824], [-9.176403737243287, -8.657351939873905, 0.5991891067105893], [4.004761702872337, -2.707821242558701, -1.1724768386392421], [-8.129119923255415, 3.2983997337883153, -0.9455984118176656], [-6.59925767963937, 6.68281932025177, -0.4294815096226361], [5.881002098533422, 1.3683086457649178, 1.2416038148258273], [0.8931593046353079, -0.30885384452604825, 0.646143581615401], [8.776608799917465, -5.113852551974302, -1.066714070209618], [-4.348363435573321, 3.846981557701527, -0.4485640582502387], [1.9550748990443303, 8.090215077842732, 0.1075373290016975], [3.8112636516524407, 5.424035441502998, 0.2966409265918324], [2.31270641629804, -3.811024091562212, -0.41136367760775144], [9.220897188776078, -4.807180988123401, -1.210987501978617], [-3.2997705698053608, -0.2281950475766532, -2.1376971989131435], [8.839797869083121, -1.5088483511554678, -8.686082846697], [-1.5644547996007692, -0.45004831235012865, -1.422356576707866], [3.8456169433580314, -3.4276076156840762, -0.7920590046168507], [6.883830207398248, 4.779212511969405, 0.5955681845183106], [7.794381474682627, -1.3956259154076562, -9.85069629052388], [4.007494646997099, -3.545765336925908, -0.7870903474230416], [-2.083871018142844, -5.114514208924681, 0.25323415017291423], [-3.737701518067067, 0.6440718825990039, -1.136720832473086], [2.3791198263488944, -2.2342377984468165, -0.9638012339853855], [4.054995481255945, -1.6707739897937106, -3.022624269094733], [-6.4606832267149805, -4.873974706400876, 0.8338571772345529], [7.6271567412759325, 6.7101532451815125, 0.4946177137297855], [-4.159530654311949, -7.327020687138573, 0.32871163696108585], [-1.1638686745259612, 6.121394323587573, -0.08171634806620527], [-1.8004653937334218, -5.824879723010685, 0.186581375816136], [-3.2660412790116418, 4.1482404054689415, -0.3171997635873946], [-4.028063982130585, -0.20347737348279438, -2.5285307962582877], [-7.463362048453259, -6.177937427574425, 0.7206887059611908], [-7.733623970488943, -0.23758516535006002, -5.071795313400354], [-2.00528219202591, -3.8820227634168747, 0.3478949260012928], [-6.527054672256696, -3.7020259040944374, 1.2078075680855078], [7.801549793452001, 1.3756894477702808, 1.6419548861435145], [-5.8673262939294375, -5.959997206255543, 0.5914646772915085], [2.659000924632007, -5.656492512007796, -0.2855154300984255], [-0.9485173524947577, 8.342648062856306, -0.050762768013588734], [-0.9603027089655374, 6.957829495834929, -0.06033697438906884], [1.5068230516897643, 1.470457705216857, 0.304968396849663], [-4.415165052657926, -0.23109442199824848, -2.8710710254776357], [1.2371386269699496, 7.930710791107604, 0.06926316705954584], [-1.0787376144762568, -7.606375118244535, 0.08164368471123859], [1.9874242724373818, 1.5556376290790848, 0.388831391787251], [2.954151255412693, 1.6499375734161248, 0.5574001601110166], [7.830266833875193, 1.00355890208564, 1.9540895018669375], [-0.2757763745485988, -8.231783219045319, 0.019066969113670736], [-9.989471219836917, -2.8138250456305602, 2.7537030773450826], [-8.043995033289047, 9.668725620072543, -0.37698949807813836], [7.641094600834663, 5.607460857853967, 0.5782171673217001], [2.3282708273451433, 9.108017377962398, 0.11516951051257901], [-4.628498557452161, 0.9457408051110168, -1.189392375719868], [-1.1453948380287482, 2.45450380139523, -0.16578283074491593]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.28495, x1=-8.22477, y=-0.69530\nx0=0.12662, x1=6.20108, y=0.25172\nx0=-3.21057, x1=-5.37600, y=0.08491\nx0=8.04489, x1=-3.01306, y=-1.94747\nx0=8.53893, x1=-3.27922, y=-1.53425\nx0=-1.14962, x1=-2.11945, y=0.95192\nx0=-7.41602, x1=5.67861, y=-1.49019\nx0=8.31020, x1=-0.34356, y=1.69052\nx0=-8.74968, x1=-7.10197, y=-0.85386\nx0=-5.40219, x1=8.94210, y=-1.36650\nx0=-0.43189, x1=-9.69165, y=0.80754\nx0=9.02247, x1=-1.39001, y=0.14080\nx0=4.32034, x1=-4.13238, y=1.01290\nx0=-4.02601, x1=-7.65295, y=0.30893\nx0=-4.90189, x1=-9.90606, y=-1.74107\nx0=-0.46238, x1=-0.61895, y=-0.72665\nx0=7.34238, x1=8.77504, y=-1.38858\nx0=6.74681, x1=-6.73584, y=0.80432\nx0=-2.78926, x1=5.91251, y=-0.64331\nx0=-8.02357, x1=7.42807, y=-0.81445\nx0=-4.06388, x1=7.61889, y=0.37128\nx0=4.43014, x1=-5.51195, y=-1.37735\nx0=-6.41445, x1=-4.15866, y=0.13766\nx0=3.47233, x1=-6.55443, y=-0.62574\nx0=-7.89427, x1=-0.11128, y=-1.98602\nx0=-3.42679, x1=4.22881, y=-0.26162\nx0=-3.70305, x1=-0.66314, y=0.83916\nx0=8.86349, x1=9.90792, y=-0.94270\nx0=-9.20270, x1=0.90868, y=-0.27082\nx0=-6.57258, x1=-0.44487, y=-0.51519\nx0=0.27062, x1=-6.44446, y=0.52772\nx0=6.76867, x1=-5.22458, y=0.45738\nx0=-3.71369, x1=1.78902, y=-0.23442\nx0=9.99695, x1=-2.98356, y=1.06942\nx0=-5.66314, x1=-6.55159, y=1.12054\nx0=5.74034, x1=-2.02771, y=0.45580\nx0=4.65656, x1=8.38336, y=1.00842\nx0=-6.68029, x1=4.00710, y=0.50142\nx0=-3.19710, x1=-3.70967, y=-0.09353\nx0=-3.60564, x1=-1.79341, y=-0.19763\nx0=-7.27783, x1=-8.01393, y=0.26712\nx0=-3.60463, x1=8.51935, y=-0.55150\nx0=4.18332, x1=-3.43149, y=1.65451\nx0=-1.55078, x1=4.10140, y=1.14713\nx0=9.71904, x1=3.61073, y=0.51739\nx0=-0.46023, x1=-3.13301, y=0.88827\nx0=-2.28831, x1=7.64510, y=-0.31247\nx0=6.57249, x1=6.52217, y=0.55435\nx0=1.55260, x1=0.20948, y=1.95596\nx0=3.32752, x1=-5.23052, y=-0.18310\nx0=8.71291, x1=1.43651, y=0.17492\nx0=-4.24716, x1=3.59803, y=-1.60446\nx0=9.24745, x1=-5.60419, y=0.27455\nx0=2.23696, x1=2.82824, y=-1.49583\nx0=5.10881, x1=-1.28616, y=-0.51805\nx0=3.04486, x1=-6.43900, y=0.19083\nx0=-4.75352, x1=-5.65738, y=1.61961\nx0=-0.99175, x1=8.14998, y=0.48830\nx0=7.50614, x1=3.29947, y=-1.85684\nx0=5.52955, x1=2.37073, y=0.98170\nx0=-2.64394, x1=-9.79797, y=0.88901\nx0=-6.34169, x1=4.00479, y=0.07602\nx0=1.96390, x1=7.33979, y=0.90864\nx0=1.07892, x1=-4.34697, y=-0.62996\nx0=0.16580, x1=2.46060, y=-0.25646\nx0=-3.55148, x1=-4.97952, y=0.21039\nx0=-4.61445, x1=-5.09620, y=0.74532\nx0=1.42557, x1=-3.80176, y=-1.56315\nx0=-0.66461, x1=9.96898, y=1.05532\nx0=0.60372, x1=-1.51936, y=0.05837\nx0=1.04585, x1=0.14298, y=1.71304\nx0=7.42234, x1=4.85833, y=0.26416\nx0=0.52870, x1=5.08820, y=0.37027\nx0=6.42421, x1=1.67303, y=-0.02869\nx0=9.09214, x1=-9.86040, y=-0.59208\nx0=3.09174, x1=-2.63490, y=-0.08713\nx0=9.17896, x1=-2.83013, y=-0.46329\nx0=6.96881, x1=-6.91255, y=1.02370\nx0=6.16649, x1=-0.20525, y=-0.22797\nx0=-6.60478, x1=0.46785, y=-0.56422\nx0=4.11822, x1=6.92903, y=-1.32345\nx0=-9.93060, x1=-1.42432, y=0.14144\nx0=0.87718, x1=-7.57166, y=0.42844\nx0=-0.76769, x1=-6.40397, y=-1.37883\nx0=-6.24543, x1=2.27004, y=-0.04860\nx0=3.04693, x1=6.27356, y=0.18902\nx0=7.10908, x1=8.09048, y=-0.34449\nx0=4.34449, x1=7.86121, y=0.01349\nx0=-3.27767, x1=-9.61133, y=-0.26661\nx0=-9.91966, x1=8.10762, y=-0.23834\nx0=0.13655, x1=0.34255, y=0.25644\nx0=-7.28071, x1=2.05768, y=0.78615\nx0=3.33263, x1=-4.99824, y=-0.10708\nx0=-8.01799, x1=-7.48705, y=-0.70788\nx0=5.71696, x1=-6.27606, y=-1.07286\nx0=6.91548, x1=-0.59978, y=0.97569\nx0=-5.38649, x1=8.88395, y=-1.33954\nx0=-7.40875, x1=1.57587, y=0.00916\nx0=4.59550, x1=-2.94934, y=1.94976\nx0=-0.34427, x1=4.70543, y=0.00469\nx0=-6.91041, x1=-3.67253, y=1.01220\nx0=-6.76191, x1=2.67909, y=0.82451\nx0=-3.38791, x1=2.37546, y=-0.35142\nx0=-4.99323, x1=0.64079, y=1.54043\nx0=9.16394, x1=4.62075, y=-0.04720\nx0=5.57436, x1=-8.68195, y=0.95891\nx0=4.89824, x1=1.95793, y=0.74207\nx0=1.05777, x1=2.32180, y=-1.18905\nx0=9.04920, x1=-4.85255, y=0.10249\nx0=3.53241, x1=-7.12595, y=-0.50696\nx0=-4.99123, x1=3.54907, y=-1.76533\nx0=4.55325, x1=3.72075, y=1.65270\nx0=-9.85852, x1=-4.32006, y=-0.32137\nx0=0.98170, x1=-7.39007, y=0.74406\nx0=-5.95228, x1=-8.03459, y=-0.11672\nx0=-8.02377, x1=-7.88367, y=0.05852\nx0=-4.97030, x1=3.66840, y=-1.67165\nx0=5.09164, x1=-1.49284, y=-0.14468\nx0=7.92388, x1=-6.29342, y=1.99501\nx0=-7.59702, x1=-7.99112, y=0.26444\nx0=-1.11302, x1=-2.42100, y=1.34810\nx0=4.06197, x1=-4.81293, y=-0.15975\nx0=-1.50607, x1=-7.23781, y=-1.15341\nx0=1.34275, x1=0.39437, y=1.79867\nx0=-3.06933, x1=-1.33509, y=-0.03372\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-5.87608, x1=-1.83396, y=-0.20601\nx0=6.10474, x1=8.35583, y=0.17078\nx0=-0.08463, x1=-0.80930, y=-0.11665\nx0=-3.62087, x1=9.11706, y=-0.87896\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 2 * sin(x0) * cos(x1)", "data": [[1.2849469649974132, -8.224773239880731, -0.6952999239058661], [0.1266220624592762, 6.201076020323029, 0.2517170303860813], [-3.210569717286738, -5.376002122345309, 0.08490785028748532], [8.044887954724192, -3.013064437938004, -1.947468259011558], [8.538932401306187, -3.2792221445329233, -1.5342539896196141], [-1.1496224997113345, -2.119445029514866, 0.9519152914248176], [-7.4160239671552475, 5.6786139670869495, -1.4901896360232851], [8.310204678690102, -0.34356259551284296, 1.6905209867315873], [-8.749676064094764, -7.101969435164999, -0.8538554955914834], [-5.402187738907312, 8.942097640314742, -1.3664954178101945], [-0.4318887189082403, -9.691646156013343, 0.8075390011161628], [9.022474269219757, -1.390013038951972, 0.14079759588047297], [4.3203408890191035, -4.132383422592714, 1.0128976257589264], [-4.026012155662329, -7.652945056394405, 0.30893177357033164], [-4.901887618699805, -9.906056580765647, -1.7410721306853036], [-0.46237822013070407, -0.6189507866959669, -0.7266498047693798], [7.3423832624675605, 8.775035744493355, -1.3885834198307798], [6.746813851772618, -6.735839642320078, 0.8043182116164966], [-2.789255342423167, 5.912510759092516, -0.6433098015804122], [-8.023572286769829, 7.428067323363422, -0.8144529100753405], [-4.0638843887311165, 7.618893052467087, 0.37128340268647125], [4.430142275467201, -5.51194563861409, -1.3773502172615493], [-6.41444652497412, -4.158655263453042, 0.1376557112571753], [3.4723319492077955, -6.5544340206771645, -0.6257376287745355], [-7.89426781832562, -0.1112764117741687, -1.9860176113047496], [-3.426788695839287, 4.2288118045225325, -0.26162277728487954], [-3.7030477945025853, -0.6631438345622147, 0.8391563071624367], [8.863492613079902, 9.907923477365458, -0.9426990848125621], [-9.202704591713971, 0.9086800321202144, -0.2708169537905672], [-6.572579937593012, -0.444866708547897, -0.515192510558284], [0.27061848427976365, -6.4444630994590675, 0.5277166561534774], [6.7686696547443645, -5.224578124644445, 0.4573849171096497], [-3.713687606129234, 1.789022483257284, -0.23442190586479317], [9.99694558139899, -2.9835553503338303, 1.0694162422794042], [-5.663137601586293, -6.55158526098753, 1.1205389441198264], [5.740341412317001, -2.027707600121735, 0.4558017552478457], [4.656559461966644, 8.3833623961, 1.0084242828017178], [-6.6802887089988605, 4.007103667769723, 0.5014206299835623], [-3.1971026004195435, -3.7096721008537425, -0.09353459158460199], [-3.605644491131712, -1.7934091621057249, -0.19763013369086238], [-7.277832817662622, -8.01393336035282, 0.26711804801171457], [-3.6046339269006378, 8.51934835566286, -0.5515028376579023], [4.183322065009939, -3.4314896924372125, 1.6545133042391755], [-1.5507783743268249, 4.101396382536821, 1.1471316404616336], [9.71903804646714, 3.610731050076426, 0.5173924985210976], [-0.46022764983225883, -3.133005856820379, 0.8882714148224677], [-2.288307857385403, 7.645103292071358, -0.3124725507207419], [6.572487583323305, 6.52217061575476, 0.554350854906837], [1.552600780334604, 0.2094780583442386, 1.955955339334798], [3.3275157690262898, -5.2305193374012955, -0.18310020597284507], [8.71290642508637, 1.4365067011724832, 0.17492305421193347], [-4.247163722557595, 3.5980310564717914, -1.6044571035528497], [9.2474519148275, -5.604185152935653, 0.2745464950744059], [2.2369556358435503, 2.8282404678657933, -1.4958346391734012], [5.108813510725881, -1.2861641265127624, -0.5180547367425105], [3.0448567779860056, -6.43899790038242, 0.19083003619772312], [-4.753518767028777, -5.657375350472192, 1.6196070222379033], [-0.9917533583684435, 8.149984672224253, 0.4882970829904155], [7.50613992836022, 3.299465752804842, -1.856838586571548], [5.529550827245313, 2.370732848771901, 0.9817037788767037], [-2.643940992563854, -9.797968070221476, 0.889011930184601], [-6.341692121008398, 4.004789977288219, 0.0760167677594388], [1.9638962933293485, 7.339788405005233, 0.9086370956196428], [1.078919514219141, -4.346967566469071, -0.6299584168188931], [0.16579878957072225, 2.460602203061903, -0.2564558477721827], [-3.551480077369577, -4.979523757610815, 0.2103864446214449], [-4.614447117328626, -5.09619967928584, 0.7453241126464808], [1.425566817086036, -3.8017621898332576, -1.5631457950489995], [-0.664613529836938, 9.968979925907345, 1.0553179941635011], [0.6037169490262215, -1.519363658241046, 0.05837155636508738], [1.0458536457455665, 0.14298348991430387, 1.7130439478517712], [7.422339338943413, 4.858325212358032, 0.2641618975778317], [0.5287011647905615, 5.0882046172991835, 0.3702702471484601], [6.424208256874529, 1.6730344632897864, -0.028690320868832248], [9.09214380112595, -9.860399651169672, -0.5920764643085811], [3.091744893409931, -2.6348966034723498, -0.0871329477481359], [9.17895591845685, -2.830134885197541, -0.46329093199589055], [6.968813696467919, -6.912548226072708, 1.0236957074387039], [6.1664896037664505, -0.20525052063515226, -0.22797426638891552], [-6.604775575460589, 0.46784574512483523, -0.5642215828816044], [4.118220304329975, 6.9290270148049835, -1.3234517096407092], [-9.930602766373761, -1.424317332820058, 0.14143961811176886], [0.8771817996734264, -7.571656020420199, 0.42843801319051983], [-0.7676914794234371, -6.403966874708926, -1.3788333106049975], [-6.245426099943341, 2.270040086950404, -0.048595054861032855], [3.0469346229825547, 6.273564299155527, 0.18902472259700873], [7.10908231368829, 8.090478162948955, -0.34449141100423414], [4.344486126610292, 7.861208320635001, 0.013486089023794277], [-3.2776696347165712, -9.611329267965196, -0.2666074386964185], [-9.919661531188357, 8.107615897377624, -0.23834188662729347], [0.13655437366534784, 0.3425513070192725, 0.2564426171542035], [-7.280713601509126, 2.0576760891141443, 0.7861468669754895], [3.3326252558046683, -4.998242443890324, -0.10707929932133556], [-8.01798920196454, -7.4870477903065495, -0.7078817947841229], [5.716964996851452, -6.276057014676537, -1.0728648964968799], [6.915482643343022, -0.5997823063293684, 0.9756911591618824], [-5.386488026556218, 8.88395267040326, -1.339540042016737], [-7.408746229045839, 1.5758735196413305, 0.009164388236508367], [4.595498483068926, -2.9493443216501314, 1.9497578661202244], [-0.3442728006904048, 4.705434683944315, 0.004694282479216541], [-6.910410853565958, -3.672534949198827, 1.0122044719462167], [-6.761914231915222, 2.679094766105001, 0.8245113762569566], [-3.387912063263827, 2.3754609617814726, -0.3514157201506916], [-4.99323439967565, 0.6407918366124203, 1.5404324399250149], [9.163936082954041, 4.620749494363839, -0.04720042705503943], [5.574360697989116, -8.681946814973125, 0.9589111706952819], [4.89824003652487, 1.9579292363464802, 0.7420673150933297], [1.057765485058475, 2.3217967865758666, -1.1890453927587703], [9.049197511584552, -4.852552999487953, 0.10249148960461758], [3.5324106993129725, -7.125950007127471, -0.5069626712042851], [-4.991226708194834, 3.549067141941098, -1.765325871507725], [4.5532450858025175, 3.7207453816807483, 1.652701391904849], [-9.858523436478912, -4.32006397643012, -0.32137203637495093], [0.9817026227047094, -7.390067300997645, 0.7440633081693899], [-5.952280733892588, -8.034586629553196, -0.11671968888523768], [-8.023773323489468, -7.883673491324215, 0.058521176510059905], [-4.9702974682779715, 3.6684042369003844, -1.6716489976092357], [5.091641402005763, -1.4928441021468597, -0.14467950989833364], [7.92387505909722, -6.293416833664319, 1.9950124698453535], [-7.597020795245351, -7.991119961181601, 0.2644405727279612], [-1.1130247096303059, -2.4210042971680963, 1.348102706218763], [4.061965911005723, -4.812928490474522, -0.15975479598188405], [-1.5060657268624311, -7.237807974950064, -1.1534128214805381], [1.3427450253193012, 0.3943728326703315, 1.7986679889900419], [-3.069332604117765, -1.3350917336330106, -0.033720149082073124], [-5.876076345073981, -1.833964760753858, -0.20600905949839043], [6.104737109171051, 8.35583391818745, 0.1707753661642841], [-0.08463039888618695, -0.8092989342771517, -0.11665160668769128], [-3.620873176344455, 9.117059255447561, -0.8789594436638113]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.11869, x1=-9.81531, y=685.81610\nx0=5.07524, x1=2.63281, y=35.17991\nx0=9.80249, x1=4.95852, y=241.01301\nx0=-1.13314, x1=9.16392, y=-95.15843\nx0=-6.17982, x1=-0.51092, y=-1.61317\nx0=9.21031, x1=-1.46911, y=19.87856\nx0=9.13468, x1=-1.09049, y=10.86264\nx0=0.11530, x1=4.77356, y=2.62728\nx0=4.28108, x1=-4.72409, y=95.54074\nx0=2.54852, x1=2.89561, y=21.36817\nx0=0.62966, x1=-6.35017, y=25.39095\nx0=-3.93895, x1=8.74932, y=-301.52874\nx0=2.20405, x1=6.96204, y=106.83001\nx0=7.78054, x1=-8.52657, y=565.66374\nx0=-5.81369, x1=6.62346, y=-255.04742\nx0=-5.93961, x1=-3.26138, y=-63.17728\nx0=4.48277, x1=6.91129, y=214.12350\nx0=6.85181, x1=5.79267, y=229.91292\nx0=6.70553, x1=-6.29898, y=266.05612\nx0=-5.16460, x1=-6.01713, y=-186.98855\nx0=-0.18418, x1=0.70483, y=-0.09150\nx0=5.17976, x1=-2.45067, y=31.10861\nx0=-9.38610, x1=8.96533, y=-754.42722\nx0=-8.17303, x1=-2.40549, y=-47.29208\nx0=1.05658, x1=-6.68199, y=47.17529\nx0=-1.15476, x1=-6.53119, y=-49.25799\nx0=-7.88658, x1=-9.45267, y=-704.68873\nx0=-4.85858, x1=2.15308, y=-22.52323\nx0=5.31883, x1=6.56595, y=229.30396\nx0=4.53530, x1=-3.97795, y=71.76697\nx0=9.09678, x1=-3.66341, y=122.08372\nx0=3.76540, x1=4.88623, y=89.89995\nx0=5.01504, x1=-5.45658, y=149.31918\nx0=0.75381, x1=-8.14694, y=50.03242\nx0=-7.46340, x1=6.32970, y=-299.02204\nx0=5.83278, x1=-3.95083, y=91.04421\nx0=0.83280, x1=3.84510, y=12.31278\nx0=-0.10038, x1=8.99012, y=-8.11280\nx0=3.27847, x1=1.26122, y=5.21496\nx0=-9.70503, x1=8.57018, y=-712.81589\nx0=2.55509, x1=-8.79529, y=197.65423\nx0=5.48895, x1=0.26792, y=0.39401\nx0=2.43818, x1=-1.72734, y=7.27479\nx0=-0.46325, x1=3.95840, y=-7.25860\nx0=-1.48729, x1=-7.54360, y=-84.63539\nx0=-5.78082, x1=-0.12157, y=-0.08543\nx0=2.66265, x1=5.81288, y=89.96984\nx0=-7.56590, x1=2.94391, y=-65.57045\nx0=-3.31114, x1=1.22598, y=-4.97673\nx0=-5.49785, x1=-4.62378, y=-117.54025\nx0=1.14502, x1=3.00667, y=10.35102\nx0=-6.73300, x1=3.72484, y=-93.41671\nx0=3.14940, x1=-0.47047, y=0.69708\nx0=1.00374, x1=7.66690, y=59.00107\nx0=-1.41846, x1=-4.25631, y=-25.69711\nx0=-7.76069, x1=-1.96139, y=-29.85577\nx0=-1.63355, x1=-8.74104, y=-124.81278\nx0=5.10562, x1=0.33222, y=0.56351\nx0=2.52445, x1=4.24013, y=45.38635\nx0=0.99223, x1=-1.50224, y=2.23920\nx0=8.86055, x1=-4.48811, y=178.47889\nx0=-8.63816, x1=-2.29814, y=-45.62198\nx0=-8.52695, x1=6.45727, y=-355.54230\nx0=3.71121, x1=4.95898, y=91.26423\nx0=-5.47176, x1=-9.10438, y=-453.55337\nx0=2.14475, x1=2.78832, y=16.67481\nx0=-1.44646, x1=-5.52074, y=-44.08616\nx0=-4.92271, x1=-2.91524, y=-41.83619\nx0=-4.76696, x1=6.68574, y=-213.07934\nx0=-1.41341, x1=-1.69972, y=-4.08340\nx0=-9.86353, x1=5.40914, y=-288.59465\nx0=-4.87732, x1=4.67678, y=-106.67814\nx0=9.84014, x1=-9.99601, y=983.22824\nx0=9.13707, x1=-4.11090, y=154.41163\nx0=-2.09275, x1=8.49144, y=-150.89676\nx0=3.51379, x1=-7.40212, y=192.52501\nx0=8.23018, x1=-5.22688, y=224.85068\nx0=-9.73443, x1=-8.68813, y=-734.79019\nx0=-5.08468, x1=-4.91842, y=-123.00254\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.74645, x1=-6.24811, y=-29.14062\nx0=-2.27552, x1=-5.98310, y=-81.45799\nx0=-9.08154, x1=4.34015, y=-171.06772\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1**2", "data": [[7.1186890026413, -9.815305651753711, 685.8161004853597], [5.075243420112885, 2.632806328845227, 35.179908321118646], [9.80248914520309, 4.958519882613064, 241.0130107899856], [-1.1331438718084144, 9.163915971711308, -95.15842625021595], [-6.179815635816408, -0.5109194579875158, -1.6131709937751497], [9.210309548111294, -1.4691133483959007, 19.878556116147227], [9.134682970535206, -1.0904879198249269, 10.862635256504408], [0.11529779161907783, 4.7735593999188435, 2.6272757133394875], [4.281076185455998, -4.724086402837373, 95.54074444408373], [2.548518079974709, 2.8956085608101034, 21.368174559490313], [0.62966342628037, -6.350168707720538, 25.39095263344508], [-3.9389452290662756, 8.749321700912265, -301.5287397109332], [2.2040456675812017, 6.962037104665118, 106.8300067712651], [7.780543157266983, -8.526567102492802, 565.6637449926284], [-5.81368653916231, 6.623456031830301, -255.04741566951876], [-5.9396122740902975, -3.261380124198306, -63.17728178269051], [4.482768135122475, 6.911288626538422, 214.12350144180547], [6.851808597275035, 5.792673906278365, 229.91292385362215], [6.705533655745189, -6.298976043945701, 266.05612406270495], [-5.164597354860929, -6.017128271383294, -186.98854745354052], [-0.18418102515732393, 0.7048300983558082, -0.09149845669629869], [5.179760091070946, -2.4506735379410305, 31.108607244708097], [-9.386095611499904, 8.965328129017625, -754.4272249904184], [-8.173029302631553, -2.405485111320413, -47.2920785632038], [1.056582507573955, -6.681986138968707, 47.17528767700419], [-1.1547603872784364, -6.531190973230949, -49.257985106377994], [-7.886576422590461, -9.452668027100007, -704.6887333507937], [-4.8585837747609695, 2.153081617392578, -22.523230511654642], [5.31883359111762, 6.565950110423842, 229.3039626648893], [4.535295324630297, -3.9779517619400035, 71.76696774570571], [9.096778378671054, -3.66340611894318, 122.08371805796368], [3.7653992206032765, 4.886233311428644, 89.89994554311433], [5.015041189615497, -5.456580208067545, 149.31917823951116], [0.7538108112695312, -8.146940980464958, 50.03241913685326], [-7.463395736140308, 6.329703461727746, -299.02203917797016], [5.832778945618713, -3.950830530637745, 91.04420750513539], [0.8328006396818317, 3.8450993693167526, 12.31278186994246], [-0.10037834386445077, 8.990117227845577, -8.112799363461882], [3.278473929821681, 1.261216859759248, 5.214963461929843], [-9.705033588246623, 8.570184387907176, -712.8158935882424], [2.5550850559286005, -8.79529428444168, 197.6542296486892], [5.488954149332834, 0.2679211767355518, 0.39400677262067213], [2.438180065110709, -1.7273376430349145, 7.274786481395186], [-0.46324724560024855, 3.958403579003596, -7.258602049193388], [-1.4872857049430106, -7.543602641607636, -84.63539229969382], [-5.78082325324962, -0.12156722834191847, -0.08543242254200602], [2.662652125483433, 5.812878784735256, 89.96984313015656], [-7.565896202569604, 2.943905698196488, -65.57045046039163], [-3.3111423588115425, 1.225979505671269, -4.976732221666533], [-5.497846674055095, -4.623778143460648, -117.54024710595154], [1.1450198750448397, 3.0066654761342537, 10.351022362903773], [-6.732995130101718, 3.724844430942449, -93.41671224455149], [3.149398831818921, -0.47046548006862743, 0.6970809077756885], [1.0037389647622792, 7.666895918139481, 59.00107420286527], [-1.4184604158957654, -4.25631276760144, -25.697110282370474], [-7.76069112052668, -1.9613898467493094, -29.85576779133938], [-1.6335519534598433, -8.741038897511284, -124.81278014988627], [5.105619344532313, 0.3322207573340279, 0.5635104317835643], [2.524448336813723, 4.24013226727563, 45.386353952212424], [0.9922342991888904, -1.50224143084111, 2.2392042318516707], [8.860545034264216, -4.4881070225685065, 178.47888584603444], [-8.63815648379352, -2.298140234291526, -45.62197891912588], [-8.526946836766104, 6.457268753658138, -355.542301856481], [3.711212406418829, 4.958980392546788, 91.26422991601355], [-5.471761662933778, -9.10438495208952, -453.55336862932916], [2.1447505688097195, 2.788316496211788, 16.674811299244567], [-1.4464619681959139, -5.520744275152354, -44.08616084232523], [-4.922711512257115, -2.915236855166339, -41.83618520898815], [-4.766963404479632, 6.685744372043882, -213.07934482257252], [-1.4134132774766641, -1.6997160590756355, -4.083399977893845], [-9.86352777873353, 5.40913727802989, -288.59465212555665], [-4.877321040987475, 4.676781079341714, -106.67813762373568], [9.84014274745379, -9.996005164830127, 983.228236814862], [9.137069996348796, -4.110896344526022, 154.4116289195411], [-2.092751743825181, 8.49143519065872, -150.89675867254414], [3.5137864724565624, -7.402116061737236, 192.52500672425006], [8.230175051430617, -5.226880425920253, 224.85067851584753], [-9.734430981044731, -8.688131588099964, -734.7901912244242], [-5.084680138170734, -4.918415572345829, -123.00253999226942], [-0.7464503455846501, -6.248113853315511, -29.140620344378554], [-2.2755232032577544, -5.983099221163213, -81.45798791661021], [-9.081536655453725, 4.34014619742549, -171.06771643394768]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=3.78303, x1=4.25897, y=0.05596\nx0=0.98657, x1=9.98332, y=0.00000\nx0=5.64014, x1=9.32189, y=0.01805\nx0=0.94219, x1=9.67725, y=0.00000\nx0=3.11421, x1=3.87337, y=0.05911\nx0=3.07280, x1=0.27418, y=0.12931\nx0=7.93980, x1=2.00434, y=0.04867\nx0=1.83920, x1=3.43534, y=0.03790\nx0=0.15629, x1=1.51011, y=0.00000\nx0=8.70471, x1=2.66463, y=0.04373\nx0=6.06152, x1=8.25441, y=0.02604\nx0=3.19182, x1=6.09135, y=0.02023\nx0=1.33155, x1=2.11693, y=0.08466\nx0=7.44347, x1=5.04841, y=0.04258\nx0=3.75364, x1=5.26867, y=0.03969\nx0=3.63657, x1=1.20787, y=0.10382\nx0=8.04646, x1=5.75045, y=0.03841\nx0=4.18062, x1=1.42006, y=0.09008\nx0=3.05068, x1=6.82803, y=0.01068\nx0=1.42602, x1=5.64667, y=0.00011\nx0=9.25578, x1=7.43481, y=0.03122\nx0=0.07448, x1=3.66434, y=0.00000\nx0=4.71417, x1=9.57503, y=0.01076\nx0=7.49308, x1=9.08757, y=0.02552\nx0=8.10406, x1=6.62848, y=0.03523\nx0=6.63570, x1=2.04523, y=0.05733\nx0=1.21215, x1=3.74654, y=0.00277\nx0=2.37772, x1=6.18687, y=0.00568\nx0=3.34749, x1=1.01449, y=0.11383\nx0=5.37206, x1=7.44841, y=0.02840\nx0=5.95342, x1=7.75425, y=0.02869\nx0=0.68775, x1=9.87023, y=0.00000\nx0=3.34793, x1=7.92373, y=0.00724\nx0=9.34884, x1=0.58508, y=0.04259\nx0=8.33162, x1=1.05665, y=0.04750\nx0=0.84795, x1=7.35152, y=0.00000\nx0=6.03939, x1=6.22733, y=0.03882\nx0=8.50503, x1=0.09863, y=0.04690\nx0=3.35356, x1=4.24561, y=0.05338\nx0=3.53603, x1=0.29811, y=0.11242\nx0=5.62151, x1=4.67616, y=0.05021\nx0=0.53798, x1=8.06676, y=0.00000\nx0=1.16728, x1=9.13895, y=0.00000\nx0=0.86312, x1=0.72229, y=0.32566\nx0=0.31578, x1=2.19422, y=0.00000\nx0=5.73093, x1=2.51232, y=0.06323\nx0=3.81976, x1=2.48122, y=0.08458\nx0=7.49005, x1=9.56284, y=0.02358\nx0=7.65311, x1=3.77728, y=0.04615\nx0=9.08592, x1=6.07911, y=0.03510\nx0=2.61144, x1=8.51182, y=0.00075\nx0=8.77736, x1=8.51111, y=0.02840\nx0=1.25694, x1=8.24274, y=0.00000\nx0=1.71508, x1=2.24935, y=0.09843\nx0=8.93386, x1=2.20664, y=0.04331\nx0=3.91682, x1=4.14228, y=0.05823\nx0=5.02599, x1=5.23619, y=0.04613\nx0=2.15953, x1=5.49619, y=0.00724\nx0=3.01041, x1=9.97471, y=0.00055\nx0=6.16430, x1=4.36308, y=0.05038\nx0=0.40641, x1=0.73236, y=0.19356\nx0=8.71086, x1=5.13295, y=0.03850\nx0=7.17291, x1=1.11668, y=0.05495\nx0=6.85033, x1=6.61992, y=0.03651\nx0=8.13843, x1=8.56521, y=0.02817\nx0=6.85539, x1=7.72028, y=0.03087\nx0=5.98502, x1=5.83255, y=0.04146\nx0=9.45998, x1=7.33272, y=0.03123\nx0=2.99341, x1=8.88387, y=0.00163\nx0=4.66797, x1=0.14748, y=0.08542\nx0=8.02483, x1=3.59256, y=0.04497\nx0=6.12353, x1=0.67010, y=0.06476\nx0=4.47881, x1=0.99854, y=0.08689\nx0=4.28997, x1=7.97863, y=0.01649\nx0=5.05669, x1=0.51701, y=0.07848\nx0=3.85202, x1=0.21659, y=0.10340\nx0=0.05422, x1=0.36584, y=0.00000\nx0=3.48261, x1=2.42160, y=0.08995\nx0=3.23264, x1=5.75208, y=0.02534\nx0=8.39192, x1=1.37515, y=0.04690\nx0=5.83538, x1=2.74430, y=0.06121\nx0=1.43985, x1=7.40440, y=0.00000\nx0=9.54617, x1=5.28777, y=0.03585\nx0=9.39608, x1=1.25760, y=0.04208\nx0=7.25823, x1=5.51991, y=0.04116\nx0=0.82998, x1=2.03631, y=0.02370\nx0=5.89283, x1=0.68615, y=0.06724\nx0=6.83391, x1=7.45864, y=0.03218\nx0=0.32214, x1=0.35977, y=0.66377\nx0=8.21300, x1=8.57783, y=0.02815\nx0=2.83931, x1=5.13826, y=0.02732\nx0=9.26353, x1=1.76605, y=0.04229\nx0=5.24467, x1=6.42132, y=0.03595\nx0=5.42924, x1=0.79897, y=0.07269\nx0=9.39349, x1=7.45443, y=0.03100\nx0=2.88941, x1=5.27428, y=0.02610\nx0=9.69694, x1=6.58251, y=0.03267\nx0=1.12523, x1=7.98656, y=0.00000\nx0=8.55539, x1=6.47493, y=0.03502\nx0=3.59225, x1=1.09295, y=0.10603\nx0=6.06332, x1=8.87657, y=0.02253\nx0=9.21152, x1=0.94968, y=0.04308\nx0=8.18514, x1=1.05295, y=0.04834\nx0=6.60615, x1=8.35740, y=0.02713\nx0=8.74707, x1=5.21573, y=0.03818\nx0=9.62988, x1=5.31175, y=0.03558\nx0=4.95645, x1=1.70347, y=0.07587\nx0=5.85212, x1=5.22704, y=0.04575\nx0=5.78858, x1=7.58454, y=0.02921\nx0=2.44177, x1=3.64038, y=0.05377\nx0=8.13645, x1=8.00332, y=0.03023\nx0=1.10048, x1=3.38530, y=0.00319\nx0=6.37571, x1=5.69286, y=0.04200\nx0=7.43468, x1=7.19157, y=0.03361\nx0=9.50186, x1=2.34981, y=0.04072\nx0=8.13561, x1=0.87253, y=0.04876\nx0=2.64718, x1=5.23612, y=0.02131\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=8.52189, x1=2.62474, y=0.04465\nx0=5.76080, x1=3.27997, y=0.05889\nx0=7.37312, x1=0.20302, y=0.05409\nx0=9.63825, x1=5.88060, y=0.03436\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = exp(-(x1/x0)**2/2) / (sqrt(2*pi)*x0)", "data": [[3.7830294382709306, 4.258973551522328, 0.05595608514924231], [0.9865727082460836, 9.983320200874259, 2.3513688637370462e-23], [5.640139042455985, 9.321887851663467, 0.018048694633005055], [0.9421864240535314, 9.677252047215903, 5.234820918217661e-24], [3.114208468444754, 3.8733675832382266, 0.059107417329028245], [3.0728042612379287, 0.27417780800917296, 0.12931424008053585], [7.939801769896016, 2.004344399804816, 0.0486700960535074], [1.8391978306139114, 3.4353374415446813, 0.03790427013082699], [0.1562855191899539, 1.510105375733664, 1.3594693053836045e-20], [8.704707396521588, 2.6646291279436416, 0.043732871388472386], [6.061520470379536, 8.254408036652855, 0.026040285159180974], [3.1918234996300536, 6.091352053836093, 0.020230342661609325], [1.33154804420573, 2.116934409470396, 0.08466442997587664], [7.443473232021781, 5.048407923202038, 0.042584029432271714], [3.7536420197034333, 5.268674689698853, 0.03968686304571882], [3.6365712526640843, 1.207869769373638, 0.10381549603896306], [8.046455071885227, 5.750454960053972, 0.03840615925834457], [4.180623152532317, 1.420058959045379, 0.0900771393911709], [3.0506755114083104, 6.828033349298864, 0.010683235127445324], [1.4260233022252984, 5.646668788609741, 0.00011016147617021002], [9.255782935841701, 7.434809416975815, 0.03121672764913967], [0.07448483669796664, 3.6643357910371814, 0.0], [4.71417127237159, 9.575033081279226, 0.010756665597105617], [7.493077123198227, 9.087565732169885, 0.025518443496444814], [8.104063007819283, 6.628475113995729, 0.03523199614024061], [6.6356997140505225, 2.0452331508239787, 0.057331709964727674], [1.2121484388137258, 3.7465362020472854, 0.002772721049640421], [2.3777247940635293, 6.186871474805337, 0.005682754978417681], [3.3474897970635067, 1.0144890813760465, 0.11382741751158645], [5.3720558302812975, 7.44840911678074, 0.028400339164485235], [5.95341643257228, 7.754254905826797, 0.02869186662649464], [0.6877459055598888, 9.87023182052733, 1.0919672874560325e-45], [3.347934217438855, 7.923729410150207, 0.0072406874056173826], [9.34883628822983, 0.5850838362972697, 0.04258944777771358], [8.331622361197873, 1.0566531093350051, 0.047499364477893845], [0.8479521909093153, 7.351517238877694, 2.243019326493263e-17], [6.039385009258716, 6.227329421813586, 0.038819028229807574], [8.505025786795782, 0.09863174075229711, 0.046903497404439054], [3.353561268718397, 4.24561266800959, 0.0533788366946778], [3.5360258734466448, 0.2981067182514119, 0.11242199106001301], [5.621505901283163, 4.676159399464599, 0.050211461250214626], [0.5379787752016767, 8.06676129017252, 1.1152490378688114e-49], [1.1672807554892939, 9.138954388871955, 1.6717210261406773e-14], [0.8631155946601518, 0.7222945368516023, 0.32566461736164964], [0.31577687355300404, 2.194215878323941, 4.1392085347482045e-11], [5.730932137107768, 2.512320698536649, 0.06323452586316736], [3.8197642991093796, 2.4812211989360153, 0.08457634012453757], [7.4900502564241105, 9.56284191463844, 0.023575535696738585], [7.653107277658132, 3.7772847118174138, 0.046150286168163954], [9.08591689723515, 6.079114515474538, 0.03510219924737111], [2.6114426668447073, 8.511823422941918, 0.0007534903417181261], [8.777360443944575, 8.511114788471906, 0.028403551482668307], [1.2569441548260094, 8.242735647240417, 1.456641709430901e-10], [1.7150821916069405, 2.2493499276330793, 0.09842792975517975], [8.93386074907063, 2.206637416236943, 0.04331349865481353], [3.9168151424739337, 4.142275737821597, 0.058225241051319675], [5.025986874604965, 5.2361894075129785, 0.04613155447667812], [2.159532143557907, 5.496191112788879, 0.007244179978314228], [3.010408813810263, 9.974714911618294, 0.0005473877166087645], [6.164303738141202, 4.363075245548561, 0.05037793633807889], [0.40641117994983283, 0.7323597939648692, 0.19355742854626684], [8.710861380923415, 5.1329541438808395, 0.03849902567416543], [7.172910813390868, 1.1166781779744186, 0.05494798902335538], [6.850328979509935, 6.619916083004037, 0.03651012814205525], [8.138429027134293, 8.565209318089018, 0.028174137946784285], [6.8553894351103555, 7.720283077624476, 0.030866163195387902], [5.985024448610568, 5.832546617182724, 0.04145913957868026], [9.45997535613794, 7.332716678531672, 0.031228564951490147], [2.993407985943924, 8.883874667309827, 0.001629784300389126], [4.667969127303269, 0.14747749366191162, 0.08542113651674121], [8.024831554236869, 3.5925647242686902, 0.04497320743552548], [6.1235271522099675, 0.6701040534381744, 0.06476017978686721], [4.4788148121527716, 0.9985412470398456, 0.08688674225482264], [4.28996576142562, 7.978630267211434, 0.016494782222446335], [5.056692466395189, 0.5170082791790975, 0.07848263473195068], [3.8520175923489686, 0.21659336811173802, 0.10340350508451258], [0.0542227555143289, 0.36583549991431236, 9.594963830381685e-10], [3.482606494342228, 2.421598375843735, 0.08995291148127543], [3.232643615005118, 5.75207597379814, 0.02534125975256725], [8.3919167497131, 1.375146554714174, 0.0469048849107686], [5.835376027849976, 2.7442950854712667, 0.06120896240119513], [1.439847292752152, 7.404399368517444, 5.012935638937377e-07], [9.546171860062637, 5.287771007038149, 0.0358471986625042], [9.396083331293418, 1.2575993029871626, 0.04207975918204192], [7.258228256695567, 5.519910225518367, 0.04116127832028348], [0.8299794401615535, 2.0363146730259913, 0.023699592840161383], [5.89283372523711, 0.6861462598672441, 0.06724219292845532], [6.833906301466291, 7.458639154410074, 0.0321793565392076], [0.3221355320035765, 0.3597722835950145, 0.6637723805789926], [8.212997156148909, 8.577831436269749, 0.028154033005447887], [2.839311382523764, 5.138263597202222, 0.027324193102674067], [9.263530393132514, 1.7660529479669043, 0.04229033663920196], [5.2446680335530775, 6.421315947793944, 0.03594847942617345], [5.4292398669435835, 0.798969001879194, 0.07268896032863954], [9.393493256457928, 7.454432825887146, 0.030997903957205003], [2.889411964657733, 5.274282104530869, 0.026095243532282777], [9.696940494520385, 6.582514195097475, 0.032674842301246114], [1.1252332523456496, 7.986556648721224, 4.077530506857391e-12], [8.555390153362271, 6.474931675288024, 0.03501803885456176], [3.592249525708739, 1.092952124366178, 0.10603330416536912], [6.063315668445681, 8.876569377670304, 0.022532125229923785], [9.211515002836277, 0.9496838408862112, 0.04307952688666708], [8.185137270667523, 1.0529506263091566, 0.04833821314793013], [6.606147247353363, 8.357397282382296, 0.02712849652447585], [8.747072287186805, 5.215730263078223, 0.03818035077163242], [9.629884767535138, 5.311747587787967, 0.03558128344028362], [4.956447406093604, 1.7034650279380386, 0.07587348167308192], [5.852120158532946, 5.227036312178391, 0.045746780850983146], [5.788580307773992, 7.5845414175634165, 0.02921084112015894], [2.441771339714775, 3.64037922558839, 0.05377113584404142], [8.136453819657186, 8.003321946593134, 0.030225648154992936], [1.100481383683369, 3.385299517389063, 0.003194943795532874], [6.375711409751472, 5.6928560828108, 0.04200078010111057], [7.434679930701715, 7.1915688104458155, 0.033610085705282663], [9.501858192991495, 2.349810564921943, 0.04072127548795153], [8.135610357968162, 0.8725263364090545, 0.048755349934377676], [2.6471844813903593, 5.23612324406295, 0.021308026956755557], [8.521893249222723, 2.624735344229667, 0.04464518658805238], [5.7608020813503575, 3.2799714991668916, 0.05888901110331011], [7.373121780922077, 0.20302332282146235, 0.054087139757341474], [9.638248209055622, 5.88060226373744, 0.03436184989067653]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.29978, y=648.92814\nx0=-6.67483, y=-259.50695\nx0=-3.68109, y=-40.01085\nx0=0.44030, y=0.71952\nx0=9.79953, y=1046.88616\nx0=2.93138, y=36.71361\nx0=-4.28245, y=-64.48071\nx0=4.21806, y=97.05788\nx0=6.65823, y=346.16299\nx0=-4.60389, y=-80.99105\nx0=-6.89802, y=-287.54168\nx0=5.13283, y=166.70813\nx0=0.84202, y=2.14803\nx0=7.22774, y=437.04748\nx0=-0.17899, y=-0.15269\nx0=4.91679, y=147.95414\nx0=-3.22452, y=-26.35397\nx0=8.18336, y=623.16990\nx0=4.25846, y=99.61818\nx0=-8.34547, y=-519.93431\nx0=-2.50931, y=-12.01286\nx0=-4.19764, y=-60.54064\nx0=5.67267, y=220.39331\nx0=6.84222, y=373.98385\nx0=2.44816, y=23.11462\nx0=-6.26444, y=-212.85845\nx0=-9.62440, y=-808.49340\nx0=1.52071, y=7.34995\nx0=4.46913, y=113.70441\nx0=-6.12287, y=-198.17675\nx0=7.43178, y=473.13087\nx0=-0.23403, y=-0.19208\nx0=-7.72395, y=-408.87072\nx0=1.88912, y=12.19981\nx0=7.06836, y=410.17721\nx0=5.71231, y=224.73779\nx0=8.07995, y=600.86960\nx0=4.31290, y=103.13845\nx0=7.37517, y=462.92739\nx0=3.84733, y=75.59722\nx0=-0.86149, y=-0.75869\nx0=-3.68997, y=-40.31644\nx0=-0.03688, y=-0.03557\nx0=-4.12615, y=-57.34938\nx0=8.97106, y=811.44243\nx0=2.53515, y=25.25542\nx0=-1.43978, y=-2.35142\nx0=7.19318, y=431.12274\nx0=6.22860, y=286.66545\nx0=-9.64419, y=-813.64466\nx0=-5.91011, y=-177.41714\nx0=-7.86895, y=-433.19682\nx0=5.62127, y=214.84435\nx0=-1.41038, y=-2.22671\nx0=1.98483, y=13.74373\nx0=8.15098, y=616.12866\nx0=-7.43213, y=-362.72054\nx0=-5.60682, y=-150.42899\nx0=3.40030, y=54.27671\nx0=-9.84056, y=-865.93140\nx0=8.54074, y=704.48356\nx0=4.60517, y=123.47735\nx0=9.72444, y=1023.87727\nx0=-3.75071, y=-42.44728\nx0=8.18761, y=624.09766\nx0=7.70515, y=524.52510\nx0=-4.93556, y=-100.80507\nx0=-7.21280, y=-330.43048\nx0=-1.06198, y=-1.13189\nx0=5.74580, y=228.45260\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-7.04248, y=-306.72805\nx0=-5.21048, y=-119.52115\nx0=6.54043, y=329.09869\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 + x0**2 + x0", "data": [[8.299782154144758, 648.928144939166], [-6.674825061713692, -259.50694949101165], [-3.681085713152239, -40.01084818589162], [0.44029981349222425, 0.719521989609077], [9.79952758572303, 1046.8861630488361], [2.9313778822951946, 36.71361480720775], [-4.282453518059233, -64.4807082677408], [4.218059007010545, 97.05787854362543], [6.658229363260197, 346.16299328694754], [-4.603886746492448, -80.991052771837], [-6.898020460784416, -287.5416777039781], [5.13283120439948, 166.70813333103806], [0.8420238074955932, 2.148026225288629], [7.2277443576859, 437.04748330794115], [-0.17898747111202695, -0.1526850910669422], [4.916789932327852, 147.95414068652147], [-3.2245176330099, -26.35397078893548], [8.18336446518897, 623.1699015785443], [4.258464290385838, 99.61818020827684], [-8.345469228237256, -519.9343115168052], [-2.509307978377433, -12.012856637495648], [-4.197639988380741, -60.54063686594308], [5.672665968765189, 220.3933129673002], [6.842222968267329, 373.9838522406252], [2.448158373222281, 23.114624621335363], [-6.264444665224196, -212.85845207801137], [-9.624395391685937, -808.4934010399656], [1.5207053400916344, 7.349949193690074], [4.469125312079447, 113.70440847057293], [-6.122868560405285, -198.17674888034963], [7.4317825603559164, 473.1308706159599], [-0.23402896813542462, -0.1920770733356726], [-7.723949554542527, -408.87072356177777], [1.8891244201591455, 12.199805864930097], [7.068358547009222, 410.1772076484122], [5.712305840130975, 224.73778546870324], [8.079948793774431, 600.8696041569754], [4.312895918295897, 103.13845118361682], [7.375172721312996, 462.927388686059], [3.847329219430989, 75.59721577506029], [-0.8614896262365956, -0.7586921611072629], [-3.68997483631672, -40.316441656992026], [-0.03687892520622249, -0.03556902745306418], [-4.126153930955736, -57.349381842820435], [8.971064929999763, 811.4424301061154], [2.5351465986956185, 25.255421642625393], [-1.4397783504388144, -2.351422026680629], [7.1931762731340925, 431.1227406157567], [6.228600002345914, 286.6654477142578], [-9.644193410722439, -813.6446554335917], [-5.910108212301706, -177.41713928908914], [-7.86894950106338, -433.1968183616245], [5.621267307302551, 214.8443499500896], [-1.41038271012971, -2.2267075387351616], [1.9848305676740843, 13.743726941535554], [8.150982424497961, 616.128660781679], [-7.432128012829679, -362.7205393686586], [-5.606822301268792, -150.42899033991682], [3.400299292293681, 54.27671493991221], [-9.840563224469218, -865.9313956557596], [8.540743367707027, 704.4835637874327], [4.605170410972104, 123.47735166926036], [9.72443677058811, 1023.8772663347403], [-3.7507116963179747, -42.447278854452605], [8.187612888182688, 624.0976622357083], [7.705154971999107, 524.5250969742985], [-4.9355638136164455, -100.80507246783367], [-7.212799795457743, -330.43048402363934], [-1.0619826116231756, -1.1318870390670814], [5.745795475969015, 228.45260477186912], [-7.042476757865015, -306.72804769283704], [-5.210478870932955, -119.52114895230821], [6.540427156758703, 329.098692663687]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=3.56111, y=222.22316\nx0=2.73635, y=86.77685\nx0=-8.20553, y=4040.07108\nx0=9.70300, y=9881.27538\nx0=5.07202, y=823.07333\nx0=-9.23711, y=6568.16428\nx0=-1.44865, y=2.01387\nx0=2.19039, y=40.51623\nx0=-2.11128, y=12.80455\nx0=-8.89773, y=5633.67571\nx0=8.35135, y=5524.93182\nx0=3.87422, y=302.32184\nx0=3.92381, y=316.77691\nx0=-6.39438, y=1444.87915\nx0=-6.08365, y=1175.56351\nx0=-4.29189, y=274.37988\nx0=3.21901, y=154.30891\nx0=0.03711, y=0.03855\nx0=-5.89955, y=1034.94151\nx0=-2.25014, y=17.05554\nx0=-8.18007, y=3988.80232\nx0=-9.32908, y=6840.30458\nx0=3.44745, y=197.55540\nx0=-6.30187, y=1360.31249\nx0=9.76726, y=10137.98045\nx0=2.53124, y=66.20816\nx0=9.29965, y=8379.45599\nx0=6.70544, y=2374.82742\nx0=0.56241, y=1.15667\nx0=5.95182, y=1507.08574\nx0=2.57618, y=70.35629\nx0=3.71558, y=259.40965\nx0=-3.03579, y=63.13773\nx0=-0.10230, y=-0.09279\nx0=4.49243, y=522.65209\nx0=2.38281, y=53.82716\nx0=-1.05607, y=0.12525\nx0=-5.63984, y=858.51401\nx0=-1.39196, y=1.60268\nx0=-0.81125, y=-0.25390\nx0=-7.59618, y=2941.31351\nx0=8.81198, y=6800.39681\nx0=5.39550, y=1039.05408\nx0=6.51473, y=2126.75727\nx0=4.16796, y=395.72701\nx0=-2.78803, y=43.73484\nx0=-7.69885, y=3108.45543\nx0=2.46877, y=60.75692\nx0=-8.79499, y=5371.55955\nx0=7.43866, y=3536.19580\nx0=-2.41269, y=23.24890\nx0=2.49905, y=63.35472\nx0=-4.43191, y=313.96059\nx0=2.78776, y=92.62285\nx0=-4.26984, y=268.50588\nx0=-0.40746, y=-0.28152\nx0=5.55901, y=1163.21947\nx0=-8.41980, y=4491.39637\nx0=7.94383, y=4554.50299\nx0=-9.93095, y=8835.90043\nx0=-3.92819, y=188.99277\nx0=5.05791, y=814.49861\nx0=-6.37932, y=1430.84352\nx0=8.08853, y=4883.04420\nx0=7.55653, y=3756.68321\nx0=-5.33045, y=678.96386\nx0=-5.38563, y=708.70247\nx0=9.28196, y=8317.76464\nx0=4.60829, y=574.69109\nx0=7.58539, y=3812.20410\nx0=2.02665, y=31.32814\nx0=-0.13910, y=-0.12207\nx0=-4.32270, y=282.74800\nx0=7.94264, y=4551.88284\nx0=-5.77391, y=946.49557\nx0=7.15957, y=3052.94689\nx0=0.15092, y=0.17766\nx0=9.87385, y=10574.85761\nx0=-8.69718, y=5130.62149\nx0=-2.02007, y=10.46943\nx0=-9.57988, y=7625.49630\nx0=0.71062, y=1.82946\nx0=-0.50551, y=-0.31385\nx0=0.52142, y=1.00898\nx0=8.30959, y=5418.94478\nx0=-2.47799, y=26.15155\nx0=-1.22071, y=0.67091\nx0=-7.74573, y=3187.10170\nx0=-0.85984, y=-0.20962\nx0=4.32835, y=455.13956\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.90108, y=-0.16151\nx0=-7.69749, y=3106.18795\nx0=-5.05873, y=545.96261\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**4 + x0**3 + x0**2 + x0", "data": [[3.5611089187416525, 222.22315610409208], [2.736348564525011, 86.77685070131878], [-8.205531952463371, 4040.0710823175905], [9.703004760997182, 9881.275377785101], [5.072021181768239, 823.0733349529804], [-9.237112373424747, 6568.164278086481], [-1.4486480053405142, 2.0138701911244663], [2.190389914736521, 40.51622950175961], [-2.1112811189999032, 12.80455168761132], [-8.89773312958874, 5633.675709276705], [8.351349439001947, 5524.931815517165], [3.874220396472312, 302.3218415744342], [3.923807067325402, 316.77691077121784], [-6.394383305229663, 1444.8791456561949], [-6.083647481295076, 1175.5635117168151], [-4.291894668040066, 274.3798776783952], [3.219014880407233, 154.30890784472214], [0.03711492749555845, 0.038545469368833594], [-5.899552632630439, 1034.94150601125], [-2.250140367092584, 17.055536670467827], [-8.18007189576263, 3988.802322572244], [-9.329081755982077, 6840.304584858859], [3.4474465105026297, 197.55539722306935], [-6.3018736207654875, 1360.3124882842658], [9.767256033350215, 10137.980454229753], [2.5312370957464925, 66.20815761658396], [9.299653604463462, 8379.455994432945], [6.705438652396229, 2374.827416935643], [0.5624127834623334, 1.156667502150817], [5.951820331001228, 1507.0857363800285], [2.5761825036207764, 70.3562943284209], [3.7155806796681734, 259.4096461860649], [-3.0357940686910023, 63.137731914212026], [-0.10229521473969783, -0.09279185091383495], [4.492433797730017, 522.6520878841856], [2.3828134562251364, 53.82716405408244], [-1.0560665797799338, 0.12524561576487914], [-5.639841736713828, 858.5140148468896], [-1.3919565942372198, 1.602684085281969], [-0.8112525381783549, -0.25389604976939406], [-7.596184417439971, 2941.313512634969], [8.81197945437468, 6800.396809216856], [5.395502345553565, 1039.05408335631], [6.514734877915412, 2126.757273837711], [4.167957810255995, 395.7270084715631], [-2.788032518670544, 43.73484394894636], [-7.698853582333369, 3108.4554333588653], [2.468766555663983, 60.756922063301815], [-8.794991144028701, 5371.559545660528], [7.438660525088025, 3536.1958014672705], [-2.4126916484429444, 23.24889974898378], [2.4990507958946484, 63.354723377869384], [-4.4319104812768355, 313.9605914488103], [2.787762176085426, 92.62284826281919], [-4.26984414738492, 268.5058762879746], [-0.4074619760214908, -0.2815213078127005], [5.559009806388229, 1163.2194712486992], [-8.419802874548397, 4491.396370203713], [7.943827329619641, 4554.502989685624], [-9.93094662838147, 8835.90043028736], [-3.928185713586978, 188.9927693077798], [5.057914237612168, 814.4986074739311], [-6.379315942032964, 1430.8435179358326], [8.088531487451391, 4883.044197245808], [7.556529049566361, 3756.683210690177], [-5.3304504079886, 678.9638600011701], [-5.385634953852685, 708.7024724597522], [9.281958934734408, 8317.764638159153], [4.608292719580483, 574.6910879807803], [7.585386693803432, 3812.2040998983975], [2.0266520751318886, 31.328142899072045], [-0.1390965174723462, -0.12206555466912167], [-4.322703977709121, 282.7480032766289], [7.942642217574377, 4551.882844033732], [-5.77390644116913, 946.4955717199973], [7.159571134355744, 3052.94689107836], [0.15092448252933544, 0.1776593162866397], [9.873848124494714, 10574.857607440852], [-8.697175376414199, 5130.62149336363], [-2.0200748278744607, 10.469434809998901], [-9.579880422353146, 7625.496304888871], [0.710620863993368, 1.8294604630377775], [-0.5055052116726451, -0.31384582779565723], [0.5214190594688048, 1.0089767378415004], [8.309594269615033, 5418.944783666489], [-2.477992270969203, 26.151549784576233], [-1.2207133051450434, 0.670912875973763], [-7.745733832110096, 3187.1016955764544], [-0.8598356064740198, -0.2096196237210428], [4.328352263678783, 455.1395636938613], [-0.9010756397320492, -0.16151306794487152], [-7.6974888162818855, 3106.1879537334194], [-5.058731859145842, 545.9626106605065]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-4.83656, x1=-0.12021, y=0.87213\nx0=-9.90371, x1=-1.68247, y=24.99402\nx0=-4.61893, x1=-0.30026, y=2.08030\nx0=4.90245, x1=-3.54416, y=-26.06258\nx0=7.65685, x1=-8.36987, y=-96.13030\nx0=5.62812, x1=8.22933, y=69.47348\nx0=-9.69055, x1=-7.55115, y=109.76223\nx0=-4.06344, x1=-1.43783, y=8.76381\nx0=-0.63132, x1=4.59866, y=-4.35484\nx0=-9.66162, x1=-3.43366, y=49.76210\nx0=-0.79499, x1=0.84515, y=-1.00782\nx0=7.54220, x1=0.97201, y=10.99663\nx0=8.26097, x1=9.41409, y=116.65429\nx0=3.48942, x1=-5.89440, y=-30.85209\nx0=-8.31391, x1=-0.23670, y=2.95179\nx0=-9.99957, x1=-0.24565, y=3.68460\nx0=8.96716, x1=-5.99934, y=-80.69560\nx0=7.88076, x1=-3.21829, y=-38.04382\nx0=-5.98502, x1=8.55362, y=-76.79043\nx0=-6.83333, x1=-7.10135, y=72.78877\nx0=2.89164, x1=-4.73716, y=-20.54723\nx0=-9.77747, x1=-4.38772, y=64.35114\nx0=7.12231, x1=5.89942, y=63.02627\nx0=-6.32533, x1=4.25780, y=-40.39791\nx0=-5.51928, x1=1.76735, y=-14.63173\nx0=9.40434, x1=1.35261, y=19.08063\nx0=-5.18300, x1=8.58153, y=-66.71713\nx0=7.14812, x1=6.50201, y=69.71564\nx0=-3.35595, x1=-3.42692, y=17.25085\nx0=-5.47169, x1=-7.36311, y=60.43293\nx0=7.29080, x1=3.61995, y=39.58848\nx0=2.85393, x1=6.26843, y=26.83443\nx0=8.11533, x1=7.02605, y=85.52813\nx0=8.70916, x1=-4.53667, y=-59.26584\nx0=4.51317, x1=-8.25927, y=-55.91327\nx0=-4.71558, x1=-4.33517, y=30.66425\nx0=1.72218, x1=2.35231, y=6.07664\nx0=7.35437, x1=-2.66150, y=-29.36046\nx0=-2.13208, x1=9.97788, y=-31.91037\nx0=-4.76687, x1=6.52326, y=-46.64328\nx0=-7.85329, x1=3.50360, y=-41.27217\nx0=7.86115, x1=-5.78950, y=-68.26821\nx0=4.63966, x1=-2.09926, y=-14.60980\nx0=-8.83807, x1=2.97865, y=-39.48825\nx0=-3.62469, x1=7.68525, y=-41.78501\nx0=-9.76432, x1=-3.02449, y=44.29811\nx0=2.00570, x1=-6.71189, y=-20.19300\nx0=6.59273, x1=7.50155, y=74.18345\nx0=0.76139, x1=-2.29252, y=-2.61824\nx0=2.43159, x1=-4.29948, y=-15.68189\nx0=0.48944, x1=-4.17554, y=-3.06554\nx0=2.84682, x1=-7.59793, y=-32.44497\nx0=-7.62351, x1=-6.90633, y=78.97571\nx0=7.74001, x1=4.69084, y=54.46072\nx0=-1.36460, x1=9.71787, y=-19.89154\nx0=7.00463, x1=-0.00895, y=-0.09402\nx0=-0.84422, x1=7.37832, y=-9.34335\nx0=-1.81442, x1=-6.17342, y=16.80172\nx0=2.40525, x1=-3.90378, y=-14.08438\nx0=6.08547, x1=7.16876, y=65.43793\nx0=7.86981, x1=-8.49122, y=-100.23638\nx0=1.80013, x1=-1.95760, y=-5.28590\nx0=-9.63410, x1=1.16429, y=-16.82540\nx0=3.15813, x1=-4.14575, y=-19.63927\nx0=-2.11220, x1=-2.23264, y=7.07370\nx0=-6.17629, x1=-6.04555, y=56.00863\nx0=9.75288, x1=4.25816, y=62.29401\nx0=-1.92248, x1=5.43088, y=-15.66116\nx0=-0.06728, x1=6.14332, y=-0.61995\nx0=-7.49128, x1=7.42858, y=-83.47439\nx0=2.84928, x1=-4.59532, y=-19.64000\nx0=4.83242, x1=8.26812, y=59.93257\nx0=-6.20963, x1=6.73253, y=-62.70979\nx0=-5.62297, x1=-5.62770, y=47.46654\nx0=5.32466, x1=-6.93237, y=-55.36877\nx0=-7.84084, x1=-0.08775, y=1.03207\nx0=5.22946, x1=-9.85848, y=-77.33176\nx0=-5.06311, x1=-1.34196, y=10.19171\nx0=8.76615, x1=-7.48381, y=-98.40630\nx0=1.38388, x1=3.60488, y=7.48311\nx0=4.79737, x1=3.63173, y=26.13409\nx0=-8.60707, x1=3.65836, y=-47.23164\nx0=-7.65366, x1=-0.64993, y=7.46152\nx0=2.73190, x1=-4.61745, y=-18.92162\nx0=-1.94613, x1=4.00066, y=-11.67871\nx0=-3.34233, x1=-2.85869, y=14.33202\nx0=-5.84187, x1=-3.13221, y=27.44694\nx0=2.27282, x1=8.69465, y=29.64200\nx0=-0.24887, x1=-1.84587, y=0.68907\nx0=4.54578, x1=-0.61130, y=-4.16824\nx0=7.54632, x1=9.68116, y=109.58565\nx0=-1.64879, x1=-3.88142, y=9.59950\nx0=-1.65678, x1=9.19633, y=-22.85445\nx0=5.54526, x1=0.17811, y=1.48147\nx0=0.58130, x1=-4.12757, y=-3.59904\nx0=-7.48421, x1=-4.01125, y=45.03150\nx0=-0.11102, x1=6.45016, y=-1.07415\nx0=7.08646, x1=3.54635, y=37.69667\nx0=6.22900, x1=-4.79045, y=-44.75960\nx0=-5.67094, x1=8.81281, y=-74.96543\nx0=0.39354, x1=-9.09496, y=-5.36889\nx0=1.19782, x1=-7.25353, y=-13.03264\nx0=0.88403, x1=6.68641, y=8.86644\nx0=0.03010, x1=1.27306, y=0.05748\nx0=1.45491, x1=8.76648, y=19.13166\nx0=-5.99380, x1=4.77370, y=-42.91892\nx0=5.08387, x1=3.19039, y=24.32928\nx0=0.83945, x1=7.83143, y=9.86117\nx0=8.40925, x1=3.70340, y=46.71416\nx0=5.01701, x1=-2.30154, y=-17.32026\nx0=-0.87158, x1=0.58644, y=-0.76670\nx0=9.87471, x1=0.99952, y=14.80491\nx0=6.14313, x1=-3.53011, y=-32.52890\nx0=1.51256, x1=-9.72334, y=-22.06072\nx0=9.45195, x1=-3.58052, y=-50.76434\nx0=8.57562, x1=7.63080, y=98.15826\nx0=-9.87227, x1=-9.57595, y=141.80463\nx0=8.67925, x1=5.90146, y=76.83032\nx0=6.79202, x1=3.98042, y=40.55262\nx0=5.12671, x1=-3.26108, y=-25.07792\nx0=-6.08900, x1=9.33104, y=-85.22505\nx0=6.45787, x1=-5.30825, y=-51.42000\nx0=4.77481, x1=-8.22998, y=-58.94493\nx0=-4.33058, x1=-5.54310, y=36.00725\nx0=6.71894, x1=-1.25549, y=-12.65331\nx0=-6.66284, x1=2.25082, y=-22.49527\nx0=-4.70799, x1=-2.86498, y=20.23243\nx0=-2.56355, x1=-8.66101, y=33.30434\nx0=0.97513, x1=-7.18731, y=-10.51287\nx0=-4.86094, x1=-1.91379, y=13.95421\nx0=2.75234, x1=-3.51271, y=-14.50224\nx0=-7.77934, x1=4.56377, y=-53.25470\nx0=-8.37263, x1=2.29242, y=-28.79041\nx0=1.11055, x1=-8.68174, y=-14.46228\nx0=7.48539, x1=-4.57049, y=-51.31782\nx0=7.53303, x1=4.91849, y=55.57669\nx0=2.95842, x1=-5.73499, y=-25.44978\nx0=-3.66660, x1=-0.07192, y=0.39554\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.75714, x1=-3.22627, y=47.21869\nx0=2.77010, x1=8.84635, y=36.75786\nx0=5.28102, x1=2.55353, y=20.22788\nx0=5.17525, x1=0.97519, y=7.57029\nx0=6.52736, x1=1.66133, y=16.26613\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = (3/2) * x0 * x1", "data": [[-4.836557449401521, -0.12021324173680803, 0.8721273747582972], [-9.903708897178022, -1.6824685672693143, 24.994018378331205], [-4.618926896625508, -0.3002567272389971, 2.080295810005429], [4.902446989780424, -3.544159236927575, -26.062579173567112], [7.656851404887721, -8.369872307320582, -96.13030280255765], [5.628116533929417, 8.229334259489399, 69.47347831359612], [-9.690554326461925, -7.551148979981896, 109.76222912658316], [-4.0634367113213266, -1.43783202894614, 8.76380917670006], [-0.6313204989468506, 4.598656617898136, -4.354839285745032], [-9.661617520727452, -3.4336624699636253, 49.76210022009729], [-0.7949877940175121, 0.8451490886101389, -1.0078248143551278], [7.542197568690302, 0.9720089786067643, 10.996625632789621], [8.26096942781161, 9.41409232418058, 116.65429332097756], [3.4894249415263108, -5.89439743785189, -30.852086152363754], [-8.313905415615167, -0.23669535441141143, 2.9517941833379773], [-9.999574090860383, -0.24565050919691345, 3.684600700758174], [8.967157624986317, -5.999344092291674, -80.69559618316485], [7.880756958009133, -3.2182878270253257, -38.04381627855889], [-5.985022469847506, 8.553621531611771, -76.79042559790182], [-6.833327441770589, -7.101349760755012, 72.78877229066734], [2.891637884257964, -4.73715955492321, -20.547225049185823], [-9.777469178111831, -4.387716294012181, 64.35114124050476], [7.122314176357715, 5.8994186444466585, 63.02626956541718], [-6.3253254765627, 4.257795124943165, -40.3979099666812], [-5.519275243528552, 1.767348668029209, -14.631725625205162], [9.404344237819412, 1.3526108167929696, 19.080626611378758], [-5.183002702495472, 8.581529289532938, -66.71713424878989], [7.1481167332581705, 6.502005594987285, 69.71564248990029], [-3.355945405150762, -3.426923872360925, 17.250854134876654], [-5.471687373899236, -7.3631068288309764, 60.432928001978546], [7.29079978236539, 3.619948219399065, 39.58847653525303], [2.8539252893989158, 6.268426744382097, 26.83443241580487], [8.115334189609055, 7.026051370238363, 85.5281323542674], [8.709158372391617, -4.53666809694419, -59.265841408895156], [4.513170257539855, -8.259274563845718, -55.91326846560593], [-4.7155827263781935, -4.335165848547462, 30.664249787092608], [1.722178458923242, 2.3523083142052386, 6.076642061205461], [7.354368146285264, -2.661498508324966, -29.360459776516315], [-2.132075133171889, 9.977876502340198, -31.91037355874946], [-4.766870226620583, 6.523257498722618, -46.64328292686045], [-7.853293139252838, 3.5035973601816988, -41.27216566712893], [7.861153250366371, -5.789498741610133, -68.26820527590077], [4.6396582846310395, -2.099263953127986, -14.609801087636349], [-8.838068172898037, 2.9786488950072414, -39.488252995802114], [-3.624692577371034, 7.685250613544042, -41.785006281223914], [-9.764324231517739, -3.0244869015085936, 44.29810611046254], [2.0056956739926246, -6.711887201472675, -20.19300468648031], [6.592725988086073, 7.50154566729444, 74.1834526073798], [0.761386857359243, -2.292520238190763, -2.618242169382792], [2.431593926876296, -4.2994802963296745, -15.681885265919302], [0.48944341933969504, -4.175539181727808, -3.0655352620375957], [2.846824114465356, -7.5979325070217545, -32.44496622160462], [-7.623508266019545, -6.906331533213881, 78.97571329699119], [7.740009910144302, 4.690839905733505, 54.460721035916535], [-1.364601534893172, 9.717874951845669, -19.891540612782762], [7.004627394222272, -0.00894877256814297, -0.09402422621321857], [-0.8442161878271985, 7.378323771599977, -9.343350550522395], [-1.8144169650773598, -6.173415169733896, 16.801723824646665], [2.4052528485927223, -3.90378423428759, -14.084382224717379], [6.085474628924246, 7.168756982555966, 65.43793310740179], [7.869807055719285, -8.491218411129388, -100.23637584533934], [1.8001259806986774, -1.9576019782197704, -5.285895271290802], [-9.63410422827298, 1.1642943507477082, -16.82539969123926], [3.158133294618766, -4.1457549004818635, -19.639269873811024], [-2.1122046448306104, -2.2326445215218405, 7.073703192921071], [-6.1762892346397695, -6.045553798981718, 56.008633269129525], [9.752876175807454, 4.258163507897784, 62.29401214330349], [-1.9224837876441914, 5.430878061515681, -15.661162538904616], [-0.06727645558892803, 6.143320840669372, -0.6199512775587435], [-7.491283650705649, 7.428578746591242, -83.47438576847766], [2.8492762710680335, -4.595319672334684, -19.640002950533017], [4.8324199669515355, 8.268123845291907, 59.93257013882508], [-6.209626945379676, 6.732534501738261, -62.70979147903836], [-5.622968872115535, -5.627696002361599, 47.466539164512454], [5.324657221109607, -6.932373078598532, -55.36876555857827], [-7.840844312189425, -0.08775191460581588, 1.0320736507811155], [5.229457644580396, -9.858480100688896, -77.3317561897369], [-5.0631109175628435, -1.3419565083017755, 10.191711972115849], [8.766148391792708, -7.483811363196802, -98.40630141895146], [1.3838838826566313, 3.6048826063900172, 7.483108406778561], [4.797366008352375, 3.6317269401215455, 26.134085061235027], [-8.607074209449923, 3.658357933245771, -47.2316373242643], [-7.6536613709844765, -0.6499303803785885, 7.461520569199275], [2.7318980004857174, -4.617454604804245, -18.921622503297428], [-1.9461285865958295, 4.0006627797900745, -11.6787063016191], [-3.3423295446764385, -2.85868829726752, 14.332017532467018], [-5.841869248865807, -3.13221026961525, 27.446944282570513], [2.2728164444053505, 8.694646483401794, 29.642003258650124], [-0.24887034607209912, -1.8458717584553632, 0.6890741149972506], [4.545782266859632, -0.6112983050043592, -4.16824349197525], [7.546317583127191, 9.68115899699098, 109.58565054606456], [-1.6487935251517207, -3.8814223057004344, 9.599495949027508], [-1.6567801841157603, 9.196332379360424, -22.854451878999736], [5.545256333042271, 0.1781065374157098, 1.4814696068410427], [0.5813013369627544, -4.127569242092244, -3.5990422782518467], [-7.484207504609293, -4.011246143099692, 45.03149773053269], [-0.11102093390196366, 6.450160185873962, -1.0741542114794862], [7.086464366496664, 3.5463539783962883, 37.69666664833346], [6.228998855838036, -4.790453662288037, -44.75959557200597], [-5.670944563601646, 8.812809052936661, -74.9654273832158], [0.39354315806519047, -9.094963252418948, -5.3688908412657135], [1.1978200261557088, -7.25353073269984, -13.03263655794564], [0.8840259964216877, 6.686409563200154, 8.866439814887277], [0.03010235291615615, 1.2730567841459361, 0.05748300689800169], [1.4549090949734733, 8.766484891609892, 19.131657899626163], [-5.993800345121196, 4.773701159751699, -42.91891748823778], [5.083871867887764, 3.190387641429961, 24.32928296688386], [0.8394526156184021, 7.831432476098502, 9.861174714149682], [8.40924546238914, 3.7033968558765533, 46.714159808559174], [5.017009281997238, -2.30153858515604, -17.320260666903962], [-0.871578460960281, 0.5864427279460127, -0.7666962753968019], [9.874708189396149, 0.9995169213042416, 14.804906892364532], [6.14312500180516, -3.530114786785113, -32.528904608912576], [1.5125620318925215, -9.723336246107168, -22.06072384377909], [9.451949602363236, -3.5805199180695624, -50.76434072377687], [8.575622651218406, 7.630797554423516, 98.15826053186449], [-9.87227132628697, -9.575954491866504, 141.80463142782392], [8.67924766424715, 5.901457832680169, 76.83032116491361], [6.792016546513878, 3.9804197969554487, 40.552615684489226], [5.126710637401722, -3.2610796161767963, -25.077917336501258], [-6.08899658408985, 9.331044673881323, -85.22504871787976], [6.457870480452957, -5.308251294152903, -51.419999003004364], [4.774812075208519, -8.229982120505548, -58.94492701161016], [-4.3305782741870225, -5.543101624237334, 36.007253198299495], [6.718941634394831, -1.2554859822398043, -12.653305556205167], [-6.66283675780976, 2.250820514209561, -22.495274485961595], [-4.707989253507813, -2.8649776340200006, 20.232425868759606], [-2.563546043317226, -8.661008877917533, 33.30434256018129], [0.9751324274120208, -7.1873096336328075, -10.512868034409243], [-4.860944004017648, -1.9137859326206197, 13.954209381218286], [2.752339381113856, -3.51270704894012, -14.502242917671195], [-7.779343313277531, 4.563770096814391, -53.25470157898348], [-8.372630469194629, 2.292422919923524, -28.790414981447725], [1.1105518603884548, -8.681739912240962, -14.462283616421852], [7.485388873341929, -4.570487589506911, -51.31781542236361], [7.5330266720088055, 4.918491344251246, 55.57668972343362], [2.958422942622432, -5.734987588363509, -25.44977828560425], [-3.6665992568823107, -0.07191825425056741, 0.39554312638710537], [-9.757142228661511, -3.226265123087833, 47.21869151000718], [2.770095362542925, 8.846351801695885, 36.757857151951534], [5.281024330022392, 2.5535301640852346, 20.227882385970293], [5.175252655231654, 0.9751907874386294, 7.570288068073822], [6.527359631918564, 1.6613277005237421, 16.266125051680152]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-5.74205, y=13.61453\nx0=-1.71517, y=0.61332\nx0=0.73027, y=0.63179\nx0=-4.58066, y=8.20090\nx0=6.34163, y=23.27894\nx0=-6.15008, y=15.83673\nx0=7.97200, y=35.76243\nx0=-2.87831, y=2.70317\nx0=-5.54715, y=12.61184\nx0=3.05971, y=6.21075\nx0=-5.27934, y=11.29602\nx0=-3.63021, y=4.77411\nx0=-2.99885, y=2.99714\nx0=4.72655, y=13.53342\nx0=-7.31452, y=23.09383\nx0=0.63661, y=0.52094\nx0=-2.09536, y=1.14758\nx0=5.20647, y=16.15692\nx0=4.11852, y=10.54038\nx0=0.48073, y=0.35591\nx0=3.35130, y=7.29127\nx0=0.49353, y=0.36855\nx0=-4.82264, y=9.21761\nx0=4.46930, y=12.22195\nx0=-5.70976, y=13.44582\nx0=4.34281, y=11.60139\nx0=-0.18355, y=-0.07493\nx0=7.05532, y=28.41640\nx0=-1.55614, y=0.43272\nx0=0.59587, y=0.47546\nx0=3.18223, y=6.65440\nx0=-5.03929, y=10.17759\nx0=-5.09523, y=10.43309\nx0=-4.44134, y=7.64207\nx0=-3.06883, y=3.17444\nx0=4.74413, y=13.62543\nx0=8.27027, y=38.33384\nx0=4.73105, y=13.55692\nx0=-3.63524, y=4.78987\nx0=-5.37515, y=11.75855\nx0=7.19962, y=29.51705\nx0=2.83771, y=5.44514\nx0=1.58587, y=2.05043\nx0=-7.12957, y=21.85059\nx0=0.23850, y=0.14769\nx0=2.24714, y=3.64840\nx0=-4.06749, y=6.23848\nx0=-2.77140, y=2.45464\nx0=-6.71081, y=19.16209\nx0=5.39056, y=17.22437\nx0=3.78117, y=9.03921\nx0=1.30897, y=1.51118\nx0=6.29259, y=22.94467\nx0=-2.55149, y=1.97931\nx0=-3.61918, y=4.73963\nx0=-4.01553, y=6.05447\nx0=1.09381, y=1.14511\nx0=-3.50615, y=4.39345\nx0=8.82373, y=43.34094\nx0=-6.38565, y=17.19547\nx0=-4.86410, y=9.39769\nx0=-3.70427, y=5.00867\nx0=1.52090, y=1.91701\nx0=-4.15543, y=6.55610\nx0=1.94106, y=2.85438\nx0=3.82031, y=9.20754\nx0=0.93324, y=0.90208\nx0=-3.29587, y=3.78345\nx0=-1.11255, y=0.06261\nx0=7.24396, y=29.85949\nx0=4.18908, y=10.86872\nx0=-8.69321, y=33.43936\nx0=-7.18388, y=22.21215\nx0=2.75331, y=5.16700\nx0=-8.10381, y=28.78396\nx0=6.34078, y=23.27316\nx0=8.96768, y=44.69346\nx0=-2.12265, y=1.19150\nx0=0.19639, y=0.11748\nx0=-4.16117, y=6.57707\nx0=-1.43423, y=0.31140\nx0=-5.26394, y=11.22255\nx0=2.31100, y=3.82586\nx0=7.85578, y=34.78454\nx0=-9.58003, y=41.09847\nx0=8.95004, y=44.52662\nx0=-3.85933, y=5.51755\nx0=-3.89633, y=5.64254\nx0=-1.67094, y=0.56055\nx0=-3.30036, y=3.79600\nx0=-0.40146, y=-0.12014\nx0=-3.18877, y=3.48974\nx0=-0.53935, y=-0.12423\nx0=-6.95915, y=20.73532\nx0=-0.24523, y=-0.09255\nx0=5.73255, y=19.29736\nx0=1.39644, y=1.67325\nx0=7.51685, y=32.00996\nx0=-4.60090, y=8.28368\nx0=-9.24666, y=38.12704\nx0=2.94365, y=5.80437\nx0=-6.45214, y=17.58898\nx0=-2.89167, y=2.73505\nx0=-1.96767, y=0.95203\nx0=-0.89357, y=-0.04755\nx0=-4.83319, y=9.26329\nx0=3.76822, y=8.98385\nx0=5.54197, y=18.12771\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=2.47847, y=4.31063\nx0=3.72369, y=8.79478\nx0=-0.95796, y=-0.02014\nx0=0.91816, y=0.88058\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * (x0 + 1) / 2", "data": [[-5.742046681045629, 13.614526703130748], [-1.7151687385124745, 0.6133175315289994], [0.7302742349907057, 0.631787346640983], [-4.580662333823662, 8.20090254134359], [6.341628606476988, 23.278940994482124], [-6.150084486336118, 15.836727351368035], [7.972004676037152, 35.76243161539768], [-2.8783059333511973, 2.703169556306755], [-5.547146339891304, 12.611843088139095], [3.059705633613138, 6.210752098988556], [-5.279335465114549, 11.296023744050853], [-3.6302115096856564, 4.774112047684278], [-2.998854092842236, 2.997135888657197], [4.726551778652798, 13.533421747469363], [-7.314517808762011, 23.093826482967298], [0.6366079388440085, 0.5209388033216127], [-2.0953575217776432, 1.1475828111462516], [5.206473466177046, 16.156919710091337], [4.118523557992562, 10.540379927866137], [0.48072812891673244, 0.3559138314242575], [3.3513030985046495, 7.291267778275757], [0.4935300216891392, 0.36855095199881066], [-4.822641149656368, 9.217613254351264], [4.469295975306796, 12.221951245100161], [-5.709764373100001, 13.445822411611026], [4.342808050159967, 11.601394905347089], [-0.18354744832494596, -0.07492889126917363], [7.055315496588101, 28.41639612649215], [-1.5561398239028374, 0.43271566381675824], [0.5958676374163545, 0.47546293936825135], [3.1822264083861302, 6.6543956613081106], [-5.0392922078309965, 10.177586874037601], [-5.095233453922194, 10.43308524802285], [-4.441337847484581, 7.642072014007195], [-3.0688286805061082, 3.1744403948953765], [4.744126849198814, 13.62543320524394], [8.270272768092259, 38.333842213370325], [4.7310460601633615, 13.556921441775314], [-3.635240169237905, 4.789865459401463], [-5.375152050018217, 11.758553755398411], [7.199616539361902, 29.51704742660767], [2.837706538245193, 5.445142467722356], [1.58587098154322, 2.0504288758220377], [-7.129569290951432, 21.850594491763136], [0.23850107140393462, 0.14769191623237968], [2.2471432669842315, 3.6483980646683984], [-4.067486376710095, 6.238479524006061], [-2.7714037635285482, 2.4546375284858266], [-6.71081192043353, 19.162092355499617], [5.390562926720593, 17.224365796827538], [3.781169830309919, 9.03920755797793], [1.3089685562074571, 1.511183618673646], [6.292594101314361, 22.944667312605322], [-2.551494413875483, 1.9793146650811562], [-3.6191750094776998, 4.739626369875104], [-4.015528571560559, 6.054470568729311], [1.0938060292816623, 1.1451088294872895], [-3.506145046122038, 4.393454019162035], [8.82372620798894, 43.34093520076991], [-6.38565467682392, 17.195465487409642], [-4.864102185536812, 9.397693942903588], [-3.7042698462898516, 5.0086726239211945], [1.520897340786826, 1.9170130309996325], [-4.155434152603636, 6.556099422010531], [1.9410555708708355, 2.85437615003977], [3.820310244869722, 9.207540305963139], [0.933236925083186, 0.902084041710953], [-3.2958735762087006, 3.7834545270710143], [-1.1125524269252889, 0.06261023786603069], [7.2439642604417, 29.859491233499185], [4.189077657712135, 10.86872464002756], [-8.693211992819403, 33.43936137963985], [-7.183883033104896, 22.212146200113754], [2.7533050097378258, 5.166996743192617], [-8.10380925939876, 28.783957626659163], [6.340783829828897, 23.273161703224257], [8.967677319196405, 44.69345691021301], [-2.1226507158577963, 1.1914976728369093], [0.19638534955075926, 0.11747627753446657], [-4.161165554783517, 6.57706660976665], [-1.4342349454702266, 0.3113974666688786], [-5.2639379383677465, 11.222552340309768], [2.310998702620193, 3.8258568530662034], [7.855780772191004, 34.784536156458444], [-9.580029437299462, 41.09846729111239], [8.950039389042146, 44.52662222722403], [-3.8593295375552223, 5.517547470945492], [-3.8963327849648755, 5.642538193113634], [-1.6709381966201953, 0.5605481301520775], [-3.300356243567963, 3.795997545445036], [-0.40145774157604386, -0.12014471165235312], [-3.188768310418353, 3.489737513554982], [-0.5393527774363207, -0.1242256794540237], [-6.959152306902363, 20.735324261881058], [-0.24522764020125543, -0.09254552234128952], [5.732553420687887, 19.29736107086414], [1.3964443904248114, 1.6732506629868673], [7.516852731643631, 32.00996386043097], [-4.600896938727401, 8.283677851031886], [-9.246660556897721, 38.127035448795176], [2.943651278497427, 5.804367063948481], [-6.452139374645693, 17.58898156760381], [-2.89167117876554, 2.735045513668873], [-1.9676744002998916, 0.9520340726478232], [-0.8935736977005391, -0.04754987223916234], [-4.833194646652618, 9.263287922889456], [3.768220689860069, 8.983853928674781], [5.541971718205389, 18.12771112179689], [2.478466531369598, 4.310631439244423], [3.7236894020178823, 8.794776082359089], [-0.9579571052033646, -0.020137644896877208], [0.9181567821817964, 0.8805843294241136]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=5.68218, x1=-3.39770, y=40.18000\nx0=-0.93105, x1=4.40126, y=6.05393\nx0=4.47276, x1=9.54748, y=49.45291\nx0=-7.47945, x1=9.02211, y=-44.52665\nx0=-2.09459, x1=-8.48825, y=44.77011\nx0=7.31455, x1=-6.90300, y=101.68365\nx0=-5.58895, x1=-8.40849, y=14.43318\nx0=-8.07776, x1=-9.84795, y=-38.99832\nx0=-4.16344, x1=3.25953, y=-8.21784\nx0=5.58248, x1=-4.82991, y=45.70597\nx0=3.80395, x1=-1.50645, y=9.84584\nx0=-2.36038, x1=-1.54524, y=2.46939\nx0=-9.82665, x1=-0.48348, y=-179.35111\nx0=8.62389, x1=7.76475, y=142.03134\nx0=7.00130, x1=-0.28102, y=61.95748\nx0=-9.42000, x1=-6.99642, y=-126.28779\nx0=8.15265, x1=-5.39871, y=120.19337\nx0=3.71702, x1=2.37868, y=7.00439\nx0=-5.19423, x1=6.44573, y=-8.50589\nx0=-2.49952, x1=7.60895, y=20.71546\nx0=2.35842, x1=8.14420, y=25.28497\nx0=-3.31014, x1=7.02647, y=13.71542\nx0=-6.11240, x1=-2.68402, y=-33.27525\nx0=2.48867, x1=5.75985, y=11.42214\nx0=0.42226, x1=7.76195, y=21.95479\nx0=2.61147, x1=-7.77022, y=38.90886\nx0=3.79876, x1=7.92023, y=30.60964\nx0=-8.42856, x1=-0.40205, y=-110.84273\nx0=-8.20819, x1=2.35729, y=-101.97511\nx0=8.50763, x1=-8.43505, y=158.65831\nx0=4.73045, x1=-5.80400, y=39.08760\nx0=-7.09158, x1=-4.72592, y=-48.34315\nx0=-0.26208, x1=1.64308, y=-0.03475\nx0=-9.17130, x1=8.77727, y=-115.37011\nx0=-3.31741, x1=2.17121, y=-3.79851\nx0=7.07171, x1=5.82627, y=74.80469\nx0=-7.38411, x1=-6.61093, y=-44.67646\nx0=-1.36002, x1=8.27969, y=26.85384\nx0=9.01234, x1=4.98966, y=144.84691\nx0=-5.67255, x1=-6.47309, y=-3.40997\nx0=-2.27978, x1=0.08770, y=-0.17387\nx0=-7.03828, x1=-2.49617, y=-57.08167\nx0=-7.26254, x1=8.89915, y=-38.65086\nx0=-3.51946, x1=7.19899, y=13.51438\nx0=-3.76542, x1=7.70483, y=15.06529\nx0=-1.93067, x1=6.86396, y=17.18437\nx0=8.90938, x1=7.13417, y=150.84453\nx0=-2.23702, x1=-5.84704, y=22.93908\nx0=-0.52517, x1=-1.82257, y=3.97964\nx0=2.22473, x1=2.55333, y=0.68391\nx0=-0.65366, x1=9.34223, y=34.89421\nx0=-1.99760, x1=-5.01205, y=17.97571\nx0=-2.10074, x1=1.23539, y=-0.22572\nx0=6.25204, x1=-4.21967, y=55.74639\nx0=9.86542, x1=3.32309, y=184.36648\nx0=3.80663, x1=-9.87817, y=65.89263\nx0=1.03692, x1=-5.28048, y=18.40829\nx0=-4.14746, x1=0.05978, y=-10.17902\nx0=-4.61827, x1=-8.09732, y=25.79888\nx0=-5.17531, x1=-0.38016, y=-22.09525\nx0=-3.92341, x1=1.12197, y=-8.64790\nx0=5.55862, x1=-3.87777, y=40.18800\nx0=-5.23650, x1=8.01563, y=0.62810\nx0=-3.66972, x1=6.71712, y=9.62852\nx0=7.10723, x1=-3.27144, y=73.31659\nx0=-7.77576, x1=-0.23984, y=-85.98402\nx0=-6.74048, x1=9.19347, y=-21.44243\nx0=-8.38231, x1=-8.06818, y=-68.79511\nx0=1.39786, x1=1.48311, y=-1.23487\nx0=-0.64924, x1=1.00426, y=0.09451\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.79164, x1=-4.10286, y=190.48486\nx0=4.88380, x1=5.67798, y=28.85523\nx0=0.46331, x1=0.76338, y=-0.91542\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 / 5 + x1**2 / 2 - x1 - x0", "data": [[5.6821788111082085, -3.3977046239803688, 40.180002954666506], [-0.9310536776953455, 4.401261820201231, 6.053925847225383], [4.472757696064939, 9.547475094208803, 49.452913297080215], [-7.479447086929538, 9.022111961318473, -44.526651100636975], [-2.094587845325549, -8.488249913742717, 44.77011474393247], [7.3145495218165735, -6.902995623615549, 101.68365461418605], [-5.588946932204115, -8.408493022991504, 14.433181715528857], [-8.077759705376819, -9.847949756884676, -38.99832359761929], [-4.163441298765584, 3.2595321542735896, -8.217836934210489], [5.5824779330764684, -4.829907836517178, 45.70597006760401], [3.803947788615522, -1.506453031358781, 9.84584479733815], [-2.360380747814612, -1.5452424074101518, 2.469386430950167], [-9.826647377295647, -0.48347606467639537, -179.35110954549765], [8.623890134058389, 7.764751820536297, 142.0313397893326], [7.00130160087636, -0.2810226830259701, 61.957482138035516], [-9.419995672506046, -6.996419366165556, -126.2877901840653], [8.152649524474928, -5.398706264932245, 120.19337356305006], [3.7170167465573556, 2.3786840328461807, 7.004387471036724], [-5.194232873971973, 6.445734734533556, -8.505891605931055], [-2.4995173654921636, 7.608953831479784, 20.715462268830592], [2.3584208901045045, 8.144202602566367, 25.284972247002315], [-3.310142523505464, 7.026466705327859, 13.715417857309053], [-6.1124026785232495, -2.6840230977334523, -33.27524981619244], [2.4886704411070575, 5.759854202942771, 11.422141977187499], [0.4222565119089303, 7.7619501950747996, 21.954786423090724], [2.6114736569372514, -7.770221129587494, 38.90885849451465], [3.798757487218449, 7.920225340243338, 30.609640281482225], [-8.428563328320324, -0.4020545337063126, -110.84273189563507], [-8.208191807295721, 2.3572929064544184, -101.97510671930783], [8.507625428351776, -8.435049225756494, 158.65831047610473], [4.730452011457121, -5.804002188966697, 39.08760254641472], [-7.091579643002824, -4.725922030517385, -48.343148614348635], [-0.2620775546424152, 1.6430798080110804, -0.0347467663639327], [-9.171295309860172, 8.77727463741428, -115.37010883787903], [-3.317414330983423, 2.1712055018762104, -3.7985112527286935], [7.071710983117388, 5.826267275356582, 74.8046919347869], [-7.384106148119671, -6.610933010121858, -44.676455617717906], [-1.3600183733738334, 8.279688883223663, 26.85384190132811], [9.012340135228019, 4.989661326748545, 144.84691187002093], [-5.672551781304264, -6.4730944691522225, -3.409974679187574], [-2.2797844830081555, 0.08769967170080761, -0.17386782990447364], [-7.038278419835868, -2.4961702008948228, -57.0816693011064], [-7.262536423188162, 8.89914965110139, -38.65085746620315], [-3.5194583833040998, 7.198990269671132, 13.514382854027552], [-3.7654207359810083, 7.7048333871692485, 15.065292869612616], [-1.9306714777026919, 6.863960069212396, 17.184372689802302], [8.909376237413774, 7.134169357021435, 150.84452529692555], [-2.2370182660017885, -5.847040965640316, 22.93908320383636], [-0.5251681589545303, -1.822566574307821, 3.979640748958976], [2.224725119072577, 2.553334447049993, 0.6839105595564932], [-0.6536631579122432, 9.342230923711437, 34.894212696511104], [-1.9976032165477182, -5.01204820622394, 17.97571042308204], [-2.1007408578039737, 1.2353908826734745, -0.22571570978032884], [6.252040115090804, -4.219669601353539, 55.746391065456166], [9.865422517755931, 3.3230904551818146, 184.36648230222784], [3.8066298707746355, -9.878172532053583, 65.89263042428797], [1.0369193585233933, -5.280481920266382, 18.408286719912716], [-4.147464662035314, 0.059777238378845965, -10.17901800467905], [-4.618266019597426, -8.097322829672432, 25.798879882523327], [-5.175313340218988, -0.38015937471388206, -22.095248757978545], [-3.9234123426588274, 1.1219685585722878, -8.647895740869211], [5.5586170174899365, -3.877774581373572, 40.18800321502336], [-5.236498056082062, 8.015627650158219, 0.6281033559027058], [-3.6697222021499947, 6.7171183635158584, 9.628515602324605], [7.107233718195552, -3.271442349741158, 73.3165901832838], [-7.7757626332124214, -0.23984016540285147, -85.98402112981312], [-6.740476391556678, 9.193471563447126, -21.4424259907861], [-8.382307772280038, -8.068179292679325, -68.79511272049768], [1.3978590528115724, 1.4831120912399047, -1.2348743120466534], [-0.6492359173900653, 1.0042584348820434, 0.09451345186405202], [9.79163754228112, -4.102855230574878, 190.48486102178103], [4.88380463458757, 5.677984974253551, 28.855226923566807], [0.4633067678089393, 0.7633751689095529, -0.915421060011031]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.68680, x1=0.50006, y=0.91875\nx0=5.41480, x1=1.81111, y=0.20798\nx0=-5.00576, x1=8.76035, y=1.57388\nx0=0.83266, x1=2.44755, y=1.37937\nx0=-2.00379, x1=6.96545, y=-0.27716\nx0=-3.02285, x1=-9.09994, y=-0.43762\nx0=1.45042, x1=6.05363, y=0.76522\nx0=-5.01720, x1=-4.52974, y=1.93727\nx0=3.45561, x1=2.69929, y=0.11914\nx0=-4.53546, x1=-6.98127, y=0.34163\nx0=0.88433, x1=-7.81933, y=-0.22591\nx0=-0.76787, x1=-9.11202, y=-1.00229\nx0=0.12786, x1=-3.17526, y=0.16118\nx0=8.91335, x1=8.89636, y=0.99359\nx0=8.33482, x1=5.81022, y=0.43108\nx0=6.67593, x1=5.97625, y=0.08059\nx0=-2.87512, x1=1.34337, y=0.71092\nx0=-2.33412, x1=-3.96517, y=0.01104\nx0=-4.12711, x1=5.56932, y=0.17880\nx0=-9.63805, x1=9.41757, y=0.21887\nx0=3.70119, x1=-4.31849, y=0.39257\nx0=2.87971, x1=-4.78044, y=1.25658\nx0=-4.25856, x1=0.20868, y=1.10595\nx0=0.11133, x1=4.78756, y=-0.88608\nx0=5.50689, x1=-8.12647, y=-1.66375\nx0=7.61102, x1=-9.62742, y=1.17189\nx0=4.99895, x1=-6.52070, y=-1.19451\nx0=3.88849, x1=-6.23229, y=-0.62850\nx0=1.57757, x1=6.44182, y=1.15795\nx0=-4.26563, x1=6.11059, y=0.73011\nx0=0.35265, x1=2.75207, y=0.72513\nx0=0.33278, x1=-5.32174, y=1.14669\nx0=-8.71863, x1=-1.52597, y=-1.64790\nx0=-0.08995, x1=-4.60938, y=0.90487\nx0=-6.66690, x1=-2.27100, y=-1.13908\nx0=-1.67844, x1=6.59359, y=-0.68876\nx0=0.08430, x1=7.28904, y=0.92882\nx0=-3.63717, x1=0.56583, y=1.01166\nx0=0.57094, x1=-0.53044, y=0.03451\nx0=-2.78770, x1=4.41527, y=-1.30273\nx0=-7.03764, x1=2.33989, y=0.03366\nx0=-3.21376, x1=3.74220, y=-0.49305\nx0=6.79037, x1=4.95984, y=-0.48382\nx0=5.09493, x1=-2.44629, y=-1.56834\nx0=-1.10310, x1=-3.92864, y=-0.18434\nx0=-6.58392, x1=-1.26408, y=-1.24956\nx0=4.66182, x1=-8.95681, y=-1.44980\nx0=1.85265, x1=0.41196, y=1.36095\nx0=9.27016, x1=-1.00413, y=-0.68970\nx0=-0.06815, x1=-0.04526, y=-0.11333\nx0=-5.30512, x1=3.50381, y=0.47507\nx0=-2.94967, x1=-0.07492, y=-0.26560\nx0=5.50703, x1=7.23025, y=0.11116\nx0=-0.81535, x1=4.08268, y=-1.53617\nx0=-3.02256, x1=0.48607, y=0.34840\nx0=-6.17190, x1=3.24476, y=0.00808\nx0=9.95310, x1=-0.11202, y=-0.61587\nx0=7.79117, x1=5.92579, y=0.64820\nx0=6.98713, x1=6.84784, y=1.18235\nx0=-4.09467, x1=-7.23275, y=0.00204\nx0=-1.49793, x1=-5.06576, y=-0.05914\nx0=8.99013, x1=-0.09270, y=0.32853\nx0=-0.33495, x1=3.60583, y=-0.77646\nx0=9.99794, x1=-5.22071, y=0.33127\nx0=9.22654, x1=4.78761, y=-0.80023\nx0=-1.90608, x1=-5.40791, y=-0.17660\nx0=4.64043, x1=6.87979, y=-0.43557\nx0=-3.94539, x1=-1.58475, y=-0.27990\nx0=-1.88229, x1=7.12041, y=-0.20909\nx0=-6.75483, x1=-4.55056, y=0.53258\nx0=5.62738, x1=1.81255, y=0.36112\nx0=2.45277, x1=2.73903, y=1.02741\nx0=-3.66662, x1=-7.22025, y=-0.30459\nx0=-3.12560, x1=8.76353, y=0.59811\nx0=8.53738, x1=0.08742, y=0.86274\nx0=4.22496, x1=-9.93747, y=-0.39301\nx0=1.07910, x1=-6.78990, y=0.39623\nx0=-1.95038, x1=5.24487, y=-1.79037\nx0=3.42392, x1=4.20029, y=-1.15031\nx0=6.02851, x1=-4.93923, y=0.72246\nx0=-0.84956, x1=4.27772, y=-1.65800\nx0=-5.39139, x1=8.42773, y=1.61807\nx0=3.69449, x1=-6.60642, y=-0.84279\nx0=-6.93149, x1=9.60094, y=-0.77909\nx0=-5.09020, x1=6.63362, y=1.27278\nx0=8.86977, x1=2.80690, y=0.85543\nx0=2.76897, x1=8.07291, y=1.34019\nx0=-3.27631, x1=-7.18843, y=-0.65227\nx0=3.78330, x1=-1.56187, y=-1.59852\nx0=-8.45029, x1=4.16479, y=-1.68119\nx0=6.99410, x1=4.22920, y=-0.23299\nx0=0.21246, x1=4.69908, y=-0.78904\nx0=8.12410, x1=-7.08583, y=0.24454\nx0=2.64214, x1=-4.88161, y=1.46466\nx0=-1.57730, x1=-0.04494, y=-1.04490\nx0=-4.97808, x1=-3.87662, y=1.63552\nx0=8.08351, x1=1.35038, y=1.94958\nx0=8.83067, x1=4.86950, y=-0.42791\nx0=8.04874, x1=9.57907, y=0.82741\nx0=-0.12609, x1=-4.36106, y=0.81316\nx0=5.11184, x1=9.31706, y=-0.81376\nx0=3.85344, x1=2.62277, y=-0.15738\nx0=-3.15724, x1=5.39911, y=-0.75769\nx0=-6.62071, x1=0.50557, y=0.15316\nx0=2.40977, x1=-8.63780, y=-0.03999\nx0=6.04432, x1=-8.17190, y=-1.18649\nx0=0.77863, x1=9.90508, y=0.24026\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.12362, x1=-0.08293, y=-0.37946\nx0=-7.10136, x1=-4.49013, y=0.24550\nx0=-1.53804, x1=9.61659, y=-1.19010\nx0=5.26674, x1=9.20384, y=-0.63110\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0) + sin(x1)", "data": [[2.686803021780875, 0.5000600015470642, 0.9187515325880276], [5.414801036956208, 1.8111095452104138, 0.20797740001235177], [-5.005759225794297, 8.760351781880445, 1.5738821877349638], [0.8326571645242815, 2.4475505525015055, 1.3793714478776715], [-2.0037863004791667, 6.965449446788799, -0.2771633117484015], [-3.0228453705807183, -9.0999397127512, -0.43762390273262586], [1.450422549439308, 6.053630456520768, 0.7652197467827737], [-5.01719958701218, -4.52973544022798, 1.9372689764255675], [3.4556072769684594, 2.6992932247258743, 0.11913932082682743], [-4.535461341653941, -6.981273574917082, 0.34163475457911985], [0.8843339032281001, -7.819329173146505, -0.2259066801747469], [-0.7678672790174197, -9.112015672724795, -1.0022906423536009], [0.12786126890573613, -3.1752623942303053, 0.16117654287434433], [8.913352681711139, 8.896363610519835, 0.9935852515199264], [8.334824013356407, 5.810221715765717, 0.4310790780467467], [6.675933526465855, 5.976247246836179, 0.08058760607212972], [-2.8751150709250233, 1.3433727221322087, 0.710915537405201], [-2.334120972574336, -3.9651693539004818, 0.011039659352319653], [-4.12710650923122, 5.569324846120443, 0.17879953917631308], [-9.638054223866872, 9.417569265636562, 0.21887169461428801], [3.7011922398168657, -4.318494772114438, 0.39257461494899737], [2.8797104807901004, -4.780437491386618, 1.2565846017585347], [-4.258562158757817, 0.20868173477612117, 1.1059463925266404], [0.11132562773173404, 4.787559431060171, -0.8860802120444046], [5.506885944105445, -8.12646581189596, -1.663749091636061], [7.611020159594744, -9.627420984455764, 1.17188873921785], [4.998949037578605, -6.520700273721262, -1.1945099509207826], [3.888491408236023, -6.232293290885941, -0.628496288277946], [1.5775663211803277, 6.44181934333027, 1.1579466252964985], [-4.265634286436281, 6.11058857906912, 0.7301128829369877], [0.3526466909083332, 2.7520742995258267, 0.7251257251291379], [0.3327796589711074, -5.321737996262403, 1.1466922200011624], [-8.71862910757004, -1.5259657999789162, -1.64790366177435], [-0.08994564811831474, -4.60937883648138, 0.9048747277749993], [-6.666899517627467, -2.270995077341005, -1.1390812924486462], [-1.6784375790944779, 6.593593918228741, -0.6887645270153677], [0.08430038971048148, 7.289040439718562, 0.9288206621022961], [-3.6371688607921833, 0.5658339379719539, 1.011658580948609], [0.5709362899944086, -0.5304410750039157, 0.03450622089742983], [-2.787702633636153, 4.415274243721434, -1.3027345475278351], [-7.0376366537011865, 2.3398854013870825, 0.033655502124517844], [-3.2137557491742292, 3.7422039664624567, -0.49304642595676357], [6.7903747308408455, 4.959841164413582, -0.4838172090946534], [5.094929262133949, -2.446289667919368, -1.5683375171411746], [-1.1031021632610898, -3.928636101017875, -0.18434098369904905], [-6.583924905324253, -1.2640762279152824, -1.249555698642156], [4.661816289711755, -8.956805409935127, -1.4497992204398604], [1.8526464477267108, 0.41195904437456754, 1.3609477447335556], [9.270163513687326, -1.0041343613343496, -0.6896984347110648], [-0.06814645218758919, -0.045256661065435466, -0.1133349335659462], [-5.3051158845689095, 3.503808707353267, 0.47507308407540183], [-2.949671832672653, -0.07492173327698026, -0.26559646003208354], [5.507031401788385, 7.230247125806642, 0.11116292214987378], [-0.8153531994787695, 4.082679839970581, -1.5361666340925306], [-3.0225593216138673, 0.4860660013423299, 0.3483987239196369], [-6.171895663702753, 3.2447589563842545, 0.008076662775842597], [9.953096816446596, -0.11201933768392003, -0.6158673329542418], [7.7911713010902375, 5.925792981477523, 0.6481955552381526], [6.987126421511107, 6.8478418252205415, 1.1823526903145687], [-4.09466702619, -7.2327509485773, 0.0020371994095584878], [-1.497930812337298, -5.065762683706716, -0.05913594909430597], [8.990128591170759, -0.09269640142792568, 0.32852869168092974], [-0.3349496819577986, 3.6058293995386492, -0.7764621065449668], [9.997937963656923, -5.220713981557143, 0.3312712197433568], [9.226537109055243, 4.787607550149421, -0.8002274750820252], [-1.9060757547055935, -5.407909699532172, -0.1765982687631109], [4.6404290341792915, 6.879790634143539, -0.43557451932586666], [-3.945391581796307, -1.584753257956999, -0.2799049566977141], [-1.882292740694913, 7.120408719335721, -0.2090890270189718], [-6.754834958817176, -4.550559407013859, 0.5325777013307353], [5.627383260235694, 1.8125549328712953, 0.3611233387599073], [2.4527679548837984, 2.739031883498912, 1.0274059847193497], [-3.6666159184171976, -7.220251914374954, -0.3045914123542933], [-3.1255971872390447, 8.763526330362708, 0.5981103654924631], [8.537380643978455, 0.08742348878116601, 0.8627431276601315], [4.224957438752874, -9.937473870376918, -0.39301041959969124], [1.0791022077508412, -6.789897524419207, 0.3962290773184866], [-1.9503758802052573, 5.244867377075513, -1.7903720154999274], [3.4239198839619274, 4.200285495294324, -1.1503071996287908], [6.0285145561871225, -4.939225230113069, 0.7224559921029352], [-0.8495608151848995, 4.2777191923164715, -1.6579996257159921], [-5.391385047047277, 8.427732328382646, 1.6180746562715154], [3.6944880362941586, -6.6064201802236795, -0.8427889847859124], [-6.931492458746467, 9.600939800139816, -0.7790900039032164], [-5.090203519552281, 6.633618387954485, 1.272777648876145], [8.869767712538849, 2.806902602434418, 0.8554284453533925], [2.7689713421039475, 8.07290605759837, 1.3401897145891104], [-3.276311629463871, -7.188434301411117, -0.6522670922030133], [3.783297471125058, -1.5618730457443402, -1.5985221875597806], [-8.450292479328251, 4.164785764590297, -1.681187887904], [6.994098137123466, 4.229197065076205, -0.23299069198979594], [0.21246135383426612, 4.699076022857016, -0.7890448377844339], [8.124100796979018, -7.085831882251328, 0.2445416419561709], [2.6421442004089357, -4.881605306002417, 1.4646584859593008], [-1.5772984495577465, -0.044935336657324854, -1.0448990773358315], [-4.978084523994973, -3.8766232469030415, 1.6355199485161247], [8.083514774581168, 1.3503833461845431, 1.949579963849917], [8.830665713014511, 4.869503781430321, -0.42790949540323175], [8.048736865028655, 9.579072986354355, 0.8274115300561259], [-0.1260867742368621, -4.361062290363986, 0.813164012773423], [5.111843126862405, 9.31705581110944, -0.8137594873867675], [3.853444633254968, 2.622767452085469, -0.15737684062655366], [-3.1572367500078364, 5.399107538599628, -0.7576871603160961], [-6.620707567209141, 0.505574843950761, 0.15316027916960567], [2.4097660321916052, -8.637799350241124, -0.03999376925942211], [6.044315482786249, -8.171899019097413, -1.1864931724238708], [0.7786276316630403, 9.905075656720317, 0.24025991212796582], [-9.123619202293657, -0.08293134760622145, -0.37946333100191804], [-7.101364703177606, -4.490132679461536, 0.24550000992869792], [-1.5380441437816206, 9.616591687947317, -1.1901033663323806], [5.2667411118502265, 9.203844795136582, -0.631101449971115]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=0.59947, x1=3.66742, y=2.19850\nx0=-1.53064, x1=-3.10776, y=4.75687\nx0=6.18582, x1=-4.91466, y=-30.40123\nx0=-3.42306, x1=8.90214, y=-30.47259\nx0=6.00781, x1=9.86979, y=59.29582\nx0=1.11019, x1=2.24903, y=2.49685\nx0=5.11191, x1=6.37032, y=32.56445\nx0=-1.93674, x1=5.74181, y=-11.12040\nx0=-8.98656, x1=0.19690, y=-1.76949\nx0=8.01212, x1=-3.98710, y=-31.94514\nx0=3.52005, x1=2.14483, y=7.54993\nx0=-5.52011, x1=-5.95323, y=32.86244\nx0=-0.98863, x1=8.54690, y=-8.44973\nx0=-3.03717, x1=3.02245, y=-9.17968\nx0=-2.00752, x1=5.29186, y=-10.62351\nx0=-9.70885, x1=-7.95711, y=77.25441\nx0=-5.71780, x1=1.40784, y=-8.04976\nx0=7.28012, x1=3.97906, y=28.96804\nx0=2.39252, x1=-4.66991, y=-11.17286\nx0=2.62898, x1=-0.25854, y=-0.67971\nx0=-6.23589, x1=5.23668, y=-32.65535\nx0=-0.75265, x1=4.94119, y=-3.71897\nx0=-7.50441, x1=6.38675, y=-47.92881\nx0=7.53441, x1=9.54614, y=71.92458\nx0=5.71797, x1=8.55208, y=48.90060\nx0=9.95591, x1=9.74110, y=96.98159\nx0=6.95510, x1=-6.11751, y=-42.54793\nx0=8.57519, x1=0.37135, y=3.18439\nx0=0.36283, x1=4.35015, y=1.57837\nx0=-8.64050, x1=-5.81406, y=50.23642\nx0=2.32497, x1=4.14597, y=9.63924\nx0=9.96693, x1=-1.36711, y=-13.62594\nx0=-4.54887, x1=4.94846, y=-22.50989\nx0=4.74966, x1=-3.66458, y=-17.40552\nx0=-9.48585, x1=4.46253, y=-42.33090\nx0=1.96404, x1=-7.48597, y=-14.70275\nx0=-4.11351, x1=-8.26995, y=34.01855\nx0=7.61528, x1=2.55542, y=19.46027\nx0=9.70651, x1=-7.61864, y=-73.95043\nx0=-7.05956, x1=-4.82225, y=34.04298\nx0=5.59231, x1=2.42211, y=13.54517\nx0=-4.45069, x1=-0.83828, y=3.73092\nx0=4.97148, x1=5.49709, y=27.32868\nx0=9.43861, x1=3.12600, y=29.50511\nx0=0.75803, x1=-6.18520, y=-4.68857\nx0=7.07714, x1=5.26891, y=37.28876\nx0=-4.40378, x1=3.75647, y=-16.54267\nx0=-3.06982, x1=-6.91666, y=21.23288\nx0=-5.99340, x1=2.82087, y=-16.90660\nx0=6.05031, x1=1.70002, y=10.28567\nx0=3.54522, x1=7.28412, y=25.82376\nx0=-6.01967, x1=-2.96505, y=17.84862\nx0=-5.37394, x1=-4.06356, y=21.83733\nx0=1.00952, x1=1.02600, y=1.03577\nx0=2.61305, x1=0.58126, y=1.51886\nx0=1.43155, x1=7.94059, y=11.36737\nx0=-3.08642, x1=-8.79252, y=27.13744\nx0=3.08611, x1=-1.57010, y=-4.84551\nx0=-8.13540, x1=-1.40549, y=11.43418\nx0=-8.50876, x1=6.96408, y=-59.25573\nx0=4.98104, x1=-6.36995, y=-31.72896\nx0=-1.21956, x1=1.56658, y=-1.91053\nx0=-2.82518, x1=-1.82021, y=5.14243\nx0=-1.75764, x1=-9.45464, y=16.61788\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-5.41711, x1=8.94797, y=-48.47214\nx0=0.42081, x1=0.26946, y=0.11339\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1", "data": [[0.5994661721036199, 3.6674241946708452, 2.198496743459532], [-1.5306443880170022, -3.107757319982314, 4.756871301149688], [6.185819700723293, -4.914664504452699, -30.401228514088988], [-3.4230633646095177, 8.902141029552702, -30.47259282484911], [6.007807630911607, 9.869793065906986, 59.295818096874456], [1.1101877644427667, 2.2490320369230066, 2.4968478492317145], [5.111905943271488, 6.37031558063185, 32.56445407714691], [-1.9367429230496427, 5.741806647176624, -11.120403389438723], [-8.986563553022515, 0.1969044663666093, -1.7694945008775187], [8.012116333025887, -3.987103851564857, -31.94513989059321], [3.520052677700864, 2.144834129086652, 7.54992911931567], [-5.520106660113784, -5.953226438629697, 32.86244491304525], [-0.9886314192162793, 8.546896023501915, -8.449729945608672], [-3.037167248982917, 3.0224464950035888, -9.17967550642811], [-2.0075197925199966, 5.291860518032575, -10.623514729205516], [-9.70885237007084, -7.957110662357801, 77.25441271314848], [-5.717802813150268, 1.407841136000096, -8.049758007890018], [7.280122154411064, 3.9790591532820425, 28.968036695520727], [2.3925207525596885, -4.669913030153648, -11.172863837291501], [2.62898349877357, -0.2585446771261797, -0.6797096898604668], [-6.235887980464385, 5.236679934072733, -32.65534945842318], [-0.7526457045648804, 4.941190273181466, -3.718965634547798], [-7.504410088957276, 6.386752357860701, -47.928808830001515], [7.53441391019409, 9.54614129196134, 71.92457973883171], [5.7179745682672305, 8.552084355714264, 48.9006008516502], [9.955914548640852, 9.741102923781408, 96.98158831868327], [6.955104171582057, -6.117512025649412, -42.54793340929763], [8.575188600867886, 0.3713497486247608, 3.1843941313422035], [0.36283135671631683, 4.350146377686517, 1.5783695121305703], [-8.640504982572143, -5.814060348909824, 50.236417413730464], [2.324966191309306, 4.145971474657761, 9.639243508712083], [9.966929886280194, -1.367114821878543, -13.625937576157874], [-4.548866290428313, 4.948461831893978, -22.509891216573653], [4.74965802288564, -3.664584589761912, -17.40552359730575], [-9.485850372071438, 4.46253065064586, -42.33089803280922], [1.9640394376919446, -7.485973145490763, -14.702746487246676], [-4.113512253428768, -8.269953399981983, 34.018554646110786], [7.615275473044804, 2.555424965279691, 19.460265061300802], [9.706514156371163, -7.618638779734814, -73.9504251677743], [-7.059562759502209, -4.822250353259323, 34.042979010865885], [5.592313366207334, 2.4221055984150635, 13.545173512382172], [-4.450691402899986, -0.8382786148275123, 3.730919424247718], [4.971483870635016, 5.4970880555066834, 27.32868460341188], [9.438609286499371, 3.126001911286153, 29.505110669480267], [0.7580306146305755, -6.185199562673511, -4.688570626106169], [7.077135370938208, 5.268906498640112, 37.288764547692125], [-4.4037775167085735, 3.756473707306558, -16.542674454343523], [-3.069819726105374, -6.91665533087148, 21.23288497338116], [-5.993395290078221, 2.820872144413677, -16.906601824241783], [6.050309579759041, 1.7000231610828003, 10.285666417311514], [3.5452157021654322, 7.284115408715579, 25.823760323363643], [-6.01967344513562, -2.965047666275586, 17.848618700240486], [-5.373940095569898, -4.063560516045688, 21.837330787952627], [1.009517163822851, 1.0260011519335333, 1.0357657729789187], [2.6130466833424038, 0.5812588832025121, 1.5188565969156338], [1.4315516912964021, 7.940591829499024, 11.36736766341372], [-3.086423371559384, -8.792519842530623, 27.13743873688615], [3.0861107765683453, -1.5701040371994637, -4.845514989534731], [-8.135397233711874, -1.4054855875528034, 11.434183560998985], [-8.508760675834008, 6.964084877347432, -59.25573154754413], [4.98104017530064, -6.369946921841589, -31.7289615322256], [-1.219555899463094, 1.5665769844620119, -1.9105282033637503], [-2.8251819452507343, -1.8202136890528386, 5.1424348508103135], [-1.757642302023184, -9.45464436510295, 16.617882886690076], [-5.417111232520564, 8.947968636699894, -48.47214141010871], [0.4208113815759056, 0.26946019798713294, 0.11339191819468247]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.32450, x1=9.45383, y=0.00004\nx0=6.57270, x1=0.40515, y=0.06058\nx0=5.99445, x1=2.79485, y=0.05970\nx0=3.94433, x1=6.60087, y=0.02493\nx0=3.40796, x1=9.90148, y=0.00172\nx0=7.66333, x1=8.37866, y=0.02864\nx0=8.18367, x1=8.95621, y=0.02678\nx0=7.62878, x1=1.33770, y=0.05150\nx0=8.13672, x1=3.00397, y=0.04580\nx0=2.43039, x1=5.81385, y=0.00939\nx0=5.24450, x1=3.87705, y=0.05788\nx0=2.73976, x1=4.55916, y=0.03647\nx0=7.58616, x1=1.29785, y=0.05182\nx0=6.43218, x1=7.64101, y=0.03063\nx0=2.82569, x1=9.81469, y=0.00034\nx0=5.24852, x1=1.48301, y=0.07304\nx0=9.50875, x1=0.01008, y=0.04196\nx0=6.36609, x1=6.27921, y=0.03853\nx0=6.37571, x1=5.69286, y=0.04200\nx0=5.31170, x1=9.14066, y=0.01709\nx0=2.21447, x1=0.40341, y=0.17719\nx0=6.55010, x1=1.93254, y=0.05831\nx0=5.17310, x1=4.25180, y=0.05501\nx0=0.79979, x1=0.90803, y=0.26184\nx0=4.51044, x1=4.98633, y=0.04801\nx0=6.41717, x1=5.89900, y=0.04074\nx0=5.93705, x1=4.57225, y=0.04995\nx0=4.89955, x1=1.45398, y=0.07792\nx0=7.61224, x1=2.52695, y=0.04960\nx0=6.19506, x1=6.32525, y=0.03824\nx0=7.07415, x1=3.78254, y=0.04888\nx0=8.00689, x1=2.85347, y=0.04676\nx0=0.87969, x1=2.98931, y=0.00141\nx0=2.69531, x1=7.96628, y=0.00188\nx0=1.17764, x1=4.94613, y=0.00005\nx0=1.13583, x1=3.54948, y=0.00266\nx0=9.88455, x1=5.74703, y=0.03408\nx0=2.62316, x1=4.46746, y=0.03567\nx0=6.22139, x1=0.56143, y=0.06386\nx0=5.11558, x1=1.09944, y=0.07621\nx0=9.90003, x1=4.60668, y=0.03616\nx0=6.67788, x1=9.90233, y=0.01990\nx0=6.07168, x1=7.55459, y=0.03030\nx0=9.20899, x1=8.32324, y=0.02879\nx0=0.52398, x1=9.25865, y=0.00000\nx0=2.22536, x1=3.81137, y=0.04136\nx0=3.24069, x1=8.84964, y=0.00296\nx0=2.02421, x1=4.39365, y=0.01869\nx0=1.31497, x1=5.10247, y=0.00016\nx0=1.87634, x1=9.83107, y=0.00000\nx0=1.99126, x1=1.28843, y=0.16251\nx0=3.73224, x1=2.99235, y=0.07751\nx0=4.91752, x1=9.05059, y=0.01491\nx0=1.21875, x1=4.11982, y=0.00108\nx0=4.37400, x1=1.32350, y=0.08713\nx0=6.44325, x1=3.92424, y=0.05143\nx0=8.43838, x1=9.87758, y=0.02383\nx0=6.85578, x1=4.29012, y=0.04784\nx0=4.41653, x1=8.18583, y=0.01621\nx0=1.04233, x1=9.02293, y=0.00000\nx0=0.36119, x1=9.51403, y=0.00000\nx0=9.82252, x1=5.22188, y=0.03526\nx0=6.16893, x1=3.76266, y=0.05369\nx0=1.00100, x1=0.10764, y=0.39625\nx0=7.61102, x1=1.92886, y=0.05076\nx0=8.50503, x1=0.09863, y=0.04690\nx0=3.59840, x1=8.69246, y=0.00599\nx0=3.81183, x1=9.10051, y=0.00605\nx0=4.25302, x1=1.80061, y=0.08576\nx0=5.75472, x1=0.71422, y=0.06879\nx0=2.88941, x1=5.27428, y=0.02610\nx0=1.14087, x1=1.18932, y=0.20309\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.07224, x1=4.83413, y=0.00000\nx0=8.37709, x1=0.75316, y=0.04743\nx0=5.93442, x1=4.80276, y=0.04845\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = exp(-(x1/x0)**2/2) / (sqrt(2*pi)*x0)", "data": [[2.324496975982508, 9.45382788785223, 4.393236086818426e-05], [6.572702588778486, 0.40515408363587524, 0.06058163419553543], [5.9944471860440585, 2.79484945775728, 0.05969769617161076], [3.9443276516564887, 6.600870563976572, 0.02493371459511825], [3.407956544310124, 9.901480111730487, 0.0017194880604304277], [7.6633300353191505, 8.378657297344711, 0.02863613487547943], [8.183673970492615, 8.956213442042314, 0.026784404288435534], [7.628782153867786, 1.337702394987127, 0.051496550227170375], [8.136722511237517, 3.0039749941632996, 0.045799796060678986], [2.4303887647897566, 5.8138539644345, 0.009389341993720388], [5.24449768541389, 3.8770536985405877, 0.05788068353802261], [2.739759152200314, 4.559163405472595, 0.03646579581064676], [7.586161802631594, 1.297849736656417, 0.05182416692935566], [6.4321770413395125, 7.641007879986341, 0.030627826925968032], [2.825691064537084, 9.81469177222823, 0.0003388791074057684], [5.248524636699165, 1.483009007359663, 0.07303584976602337], [9.50874634859118, 0.010078961822456682, 0.04195527377261309], [6.366088463295547, 6.279206640098016, 0.038528028577614226], [6.375711409751472, 5.6928560828108, 0.04200078010111057], [5.311696486467408, 9.140656034221852, 0.017085593380162918], [2.214468733800236, 0.4034101322269787, 0.17718798586933762], [6.550100312348681, 1.9325427732091847, 0.058312240449242235], [5.17310028114334, 4.251797437047948, 0.05501360858081402], [0.7997850478505906, 0.9080264436961026, 0.2618397597645036], [4.510443208033011, 4.986328450164678, 0.048007055658604664], [6.417170074013135, 5.89900320705476, 0.0407447269944371], [5.937046524837211, 4.572249970231939, 0.04995192431463787], [4.89955148394398, 1.4539752065607277, 0.07791673685933423], [7.612243223811214, 2.5269506375744255, 0.04959849760341296], [6.19506167898629, 6.325246964367603, 0.038237974093158635], [7.0741536798779165, 3.7825438032636174, 0.04888239699075159], [8.006890741253377, 2.853466818612964, 0.04675925324199226], [0.8796879559611522, 2.989309188747839, 0.0014095950791967468], [2.6953140211208364, 7.966280347600296, 0.0018766816433595415], [1.1776354837386713, 4.946134094397083, 5.0040434988919215e-05], [1.1358316113339093, 3.5494770460051326, 0.0026608089553398144], [9.88454817619139, 5.747032531305828, 0.03408378742958432], [2.6231583560407525, 4.467460523023811, 0.0356656894529251], [6.22138824184645, 0.561425947013095, 0.06386375147979464], [5.11557982336572, 1.099438497432962, 0.07620528160831926], [9.900025850355714, 4.6066824479770725, 0.036162327949352716], [6.677879217805936, 9.902333465560217, 0.019897324753317604], [6.071684893474375, 7.554589746513269, 0.030299248806838576], [9.20898804662033, 8.323237046845657, 0.028794790264068722], [0.5239787449462969, 9.25865055963823, 1.2098765997132313e-68], [2.225361528188862, 3.8113694014093475, 0.041356612446972967], [3.2406910530693214, 8.849644292722024, 0.002957739176356007], [2.024213279821387, 4.393647506860861, 0.01869023555430477], [1.3149708546934633, 5.102471984686378, 0.00016310942317852525], [1.876339927040312, 9.831074585022241, 2.3249013129319612e-07], [1.991257677967508, 1.2884329640913441, 0.1625063062493414], [3.7322383950247286, 2.992354417364313, 0.07750946978905145], [4.9175245469887185, 9.05058606124087, 0.01491452353589606], [1.2187473778297213, 4.119819548016021, 0.0010806207260332398], [4.374000411047695, 1.323501474315697, 0.08712642848591778], [6.443250361203166, 3.924236320245003, 0.0514348037923293], [8.438383922193793, 9.87757697884289, 0.023829601821921904], [6.855784127037995, 4.290123073225488, 0.047843339767026996], [4.41652808361129, 8.185829792918607, 0.016213071036645314], [1.0423279175240616, 9.022933460822603, 2.0459739289097816e-17], [0.3611850897135391, 9.514028833159204, 2.3674521402265246e-151], [9.822516760567751, 5.221878886917655, 0.03526276863156914], [6.168929562649763, 3.762661127812709, 0.053692835256878416], [1.00099530998172, 0.10763675519292118, 0.3962481313700759], [7.611018294674658, 1.9288593070530013, 0.05075988745294507], [8.505025786795782, 0.09863174075229711, 0.046903497404439054], [3.5984014020859107, 8.692455889461353, 0.005993404823731302], [3.8118297048807563, 9.1005087563458, 0.00605434554989169], [4.253016966931327, 1.8006116928551816, 0.08576113030560462], [5.754718261534001, 0.714215396752022, 0.0687925237161955], [2.889411964657733, 5.274282104530869, 0.026095243532282777], [1.1408668622137585, 1.1893217698097154, 0.20309105436536753], [0.072239389220285, 4.834127237247472, 0.0], [8.377089642010931, 0.7531614959974012, 0.047430929099993996], [5.934422263246518, 4.802760648221834, 0.04845130924589778]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.49955, x1=-2.97805, y=6.05004\nx0=5.36302, x1=-2.98450, y=-12.26215\nx0=-9.49284, x1=-6.42651, y=54.49818\nx0=-7.56285, x1=4.52761, y=-36.91947\nx0=-6.19434, x1=5.77222, y=-39.52614\nx0=2.49917, x1=-1.08185, y=-4.78023\nx0=-0.23693, x1=-6.60442, y=8.74933\nx0=-1.77386, x1=-9.26391, y=20.12276\nx0=-2.91034, x1=6.00235, y=-13.99107\nx0=8.41078, x1=3.21689, y=29.05921\nx0=-1.50046, x1=3.29836, y=-6.32372\nx0=2.95431, x1=6.22812, y=23.24812\nx0=-2.77446, x1=3.89608, y=-9.09660\nx0=3.52528, x1=-6.15345, y=-25.82756\nx0=0.93812, x1=3.69329, y=3.29821\nx0=2.89526, x1=-7.49413, y=-29.74835\nx0=4.82309, x1=0.54659, y=2.92187\nx0=4.02402, x1=-0.76497, y=-3.28529\nx0=1.52164, x1=3.45669, y=6.48402\nx0=0.46940, x1=-4.56361, y=0.67329\nx0=4.47841, x1=-5.33087, y=-21.78157\nx0=-0.00313, x1=-6.51417, y=6.35600\nx0=0.63837, x1=5.42307, y=1.89706\nx0=1.99825, x1=3.35033, y=8.67030\nx0=-5.95840, x1=-8.17277, y=54.43013\nx0=-8.64086, x1=-6.18660, y=51.91670\nx0=-6.26761, x1=-5.94518, y=43.04707\nx0=-0.99057, x1=3.36982, y=-5.50212\nx0=7.20410, x1=5.49326, y=39.21901\nx0=-1.42531, x1=-6.63915, y=14.47859\nx0=-2.94213, x1=-9.76712, y=21.00825\nx0=0.73710, x1=1.36105, y=0.90940\nx0=8.73082, x1=1.44463, y=13.05410\nx0=2.23127, x1=4.38898, y=12.98851\nx0=-8.34899, x1=3.32426, y=-27.93022\nx0=5.50104, x1=9.61398, y=44.46457\nx0=2.17801, x1=-2.82436, y=-9.68461\nx0=0.95738, x1=-8.11675, y=-7.38239\nx0=-0.55414, x1=0.58903, y=0.08450\nx0=-6.13931, x1=-9.03218, y=63.02876\nx0=-9.91752, x1=1.69639, y=-16.12975\nx0=8.69943, x1=0.51438, y=3.99500\nx0=7.25550, x1=-7.24864, y=-52.36416\nx0=-8.23493, x1=-7.02446, y=59.36024\nx0=-8.28267, x1=-0.42242, y=3.70019\nx0=6.68156, x1=0.30114, y=2.40763\nx0=-9.91258, x1=1.76094, y=-16.69717\nx0=9.72961, x1=8.88630, y=91.51150\nx0=8.52173, x1=4.75584, y=44.07846\nx0=-3.26901, x1=0.47697, y=-2.03167\nx0=-1.04046, x1=-9.19559, y=18.65925\nx0=0.55169, x1=-7.03949, y=-0.39901\nx0=-4.06291, x1=-3.37560, y=9.60523\nx0=3.13361, x1=8.97788, y=34.88055\nx0=-3.39855, x1=0.15210, y=-1.32341\nx0=-7.56163, x1=-3.67507, y=31.34210\nx0=0.98729, x1=2.03608, y=1.99703\nx0=0.00975, x1=-7.81049, y=7.29086\nx0=-9.67914, x1=-8.76383, y=75.54726\nx0=-6.16449, x1=-3.17016, y=22.75999\nx0=1.43674, x1=0.16603, y=-0.11421\nx0=-2.70188, x1=0.00057, y=-0.53267\nx0=-2.13472, x1=-2.97042, y=6.36830\nx0=8.36529, x1=-6.90481, y=-64.74035\nx0=5.11450, x1=9.12954, y=39.97380\nx0=1.93517, x1=2.15068, y=5.08788\nx0=-1.56232, x1=-7.64006, y=16.66592\nx0=3.26262, x1=4.09617, y=15.74856\nx0=-0.46244, x1=-4.21433, y=7.13263\nx0=-1.00371, x1=-2.47739, y=5.64316\nx0=-7.00384, x1=-7.96614, y=64.65919\nx0=1.55316, x1=8.61755, y=17.38658\nx0=-3.39166, x1=9.03867, y=-23.02737\nx0=-7.48145, x1=1.04869, y=-7.88516\nx0=-5.52174, x1=0.13223, y=-0.52507\nx0=-4.17708, x1=0.32747, y=-1.96909\nx0=9.35934, x1=0.34650, y=2.67124\nx0=-3.01084, x1=2.96596, y=-7.42833\nx0=7.50968, x1=6.38969, y=49.19488\nx0=4.86135, x1=1.58763, y=7.33064\nx0=-4.00599, x1=-8.54253, y=25.08705\nx0=-7.78009, x1=7.09068, y=-58.82628\nx0=-3.16714, x1=1.91523, y=-5.28328\nx0=7.96027, x1=-8.96192, y=-77.58067\nx0=0.39935, x1=5.11719, y=-0.28340\nx0=5.29423, x1=-6.89083, y=-29.27071\nx0=2.26072, x1=-3.40955, y=-11.90733\nx0=-4.36489, x1=-5.24463, y=17.93041\nx0=-1.58178, x1=8.17149, y=-16.73375\nx0=2.15106, x1=2.79419, y=7.64892\nx0=2.77703, x1=-2.64078, y=-10.89714\nx0=4.76656, x1=0.85928, y=4.17816\nx0=-6.53183, x1=-4.84752, y=37.20989\nx0=3.54943, x1=-1.94675, y=-8.55459\nx0=8.81632, x1=-6.12945, y=-61.16361\nx0=0.96154, x1=-4.96565, y=-4.54530\nx0=6.71222, x1=-0.05517, y=0.19993\nx0=1.22691, x1=8.56037, y=12.20362\nx0=0.56500, x1=3.87750, y=0.97816\nx0=4.10887, x1=6.14179, y=25.40403\nx0=-0.52662, x1=6.41242, y=-8.78406\nx0=4.83252, x1=8.64028, y=36.88556\nx0=4.64183, x1=-6.63432, y=-27.13371\nx0=2.90971, x1=6.67758, y=24.78445\nx0=-7.93024, x1=-6.11972, y=51.91008\nx0=3.44857, x1=-9.48277, y=-39.39906\nx0=3.00435, x1=-5.14281, y=-21.02529\nx0=-1.24341, x1=-2.09620, y=5.02827\nx0=-3.89154, x1=9.67664, y=-29.11928\nx0=2.46434, x1=0.21386, y=-0.25468\nx0=3.76564, x1=3.97023, y=16.04099\nx0=-3.21226, x1=9.65049, y=-23.40893\nx0=-1.84240, x1=-5.42436, y=11.88741\nx0=3.02584, x1=0.05742, y=-0.67291\nx0=-7.72517, x1=-9.62930, y=81.23236\nx0=-9.23969, x1=-7.06581, y=59.41665\nx0=3.44789, x1=0.61619, y=1.87916\nx0=-7.40612, x1=-8.61284, y=71.97215\nx0=-8.94877, x1=-4.15633, y=34.61413\nx0=-0.82757, x1=6.62720, y=-10.92719\nx0=2.68584, x1=6.71980, y=23.73031\nx0=2.01473, x1=4.78704, y=12.86108\nx0=5.99320, x1=1.52130, y=8.61659\nx0=-5.97406, x1=-6.67670, y=44.77866\nx0=1.62578, x1=-0.81435, y=-2.38667\nx0=-8.32785, x1=-9.85160, y=83.09287\nx0=1.59858, x1=-3.88406, y=-8.96097\nx0=-2.35026, x1=6.82231, y=-14.82807\nx0=0.00492, x1=3.10046, y=-1.74661\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-4.81141, x1=-8.19662, y=35.25773\nx0=2.32644, x1=-5.51545, y=-19.15326\nx0=-1.97947, x1=-1.88702, y=4.20130\nx0=-8.26635, x1=2.98564, y=-24.99360\nx0=3.59872, x1=1.76872, y=6.76224\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1 + sin(x0 - 1) * (x1 - 1)", "data": [[-2.499550510430648, -2.9780549322591217, 6.05003839063495], [5.363015423289269, -2.984504432629011, -12.26215340425605], [-9.492836253341757, -6.426507416574636, 54.49818225350772], [-7.562849576421082, 4.527613642400684, -36.919469975660604], [-6.194339878831507, 5.772217816485266, -39.526141968408716], [2.499174905930385, -1.0818459498606856, -4.7802309343740195], [-0.23693342336348167, -6.604416042767751, 8.749334020667252], [-1.773861642709928, -9.2639079448086, 20.122756246814557], [-2.910339585348183, 6.002350257006455, -13.9910680705547], [8.410779152415365, 3.216885870595938, 29.059213541981936], [-1.5004593777987694, 3.298363331024113, -6.323720615846164], [2.954311916701167, 6.228117651318485, 23.24812269229939], [-2.774461094250147, 3.8960751915023017, -9.096596087768798], [3.5252775017304554, -6.153453546248732, -25.82755786503096], [0.9381226036809576, 3.693287947665615, 3.298209587095813], [2.8952569953825975, -7.494125778735945, -29.748346179939706], [4.823094489651618, 0.5465853107848275, 2.92186576407635], [4.024024140397254, -0.7649707042198379, -3.2852878576736657], [1.5216426593578305, 3.4566884849120942, 6.484024809623429], [0.46940193880603687, -4.563608275765459, 0.6732932904806552], [4.4784105385398565, -5.330872145325114, -21.781572833900398], [-0.003127661229868295, -6.5141683016734735, 6.355995827452661], [0.6383709618784366, 5.423070477373191, 1.8970555617062248], [1.9982493928686278, 3.3503271872770632, 8.670295297832403], [-5.958396036151925, -8.172767901124672, 54.43013486906556], [-8.640860635436718, -6.186598977279871, 51.91669645231828], [-6.267610710116807, -5.945176800542498, 43.04706852557082], [-0.9905719668489592, 3.369820484645981, -5.502123329291525], [7.2041022331208175, 5.493256234408863, 39.21900926516967], [-1.4253074978459495, -6.6391460157414635, 14.478590756280244], [-2.9421328679550633, -9.767120072174425, 21.0082545201617], [0.7371008763062132, 1.3610467703277163, 0.9093995166188996], [8.730817598912498, 1.444633963263776, 13.054101444002653], [2.231268386394067, 4.388981452122266, 12.988506795021769], [-8.348991612037103, 3.3242623121307187, -27.930216943611033], [5.501041083560196, 9.613976747022267, 44.46457353304273], [2.1780111711515016, -2.824361666195898, -9.684614744651098], [0.9573809303863605, -8.116751747171637, -7.3823934766848875], [-0.5541377684217501, 0.5890339821819346, 0.0845030196359971], [-6.139309396888562, -9.032184410521896, 63.02876464874772], [-9.917521742681451, 1.6963939393361542, -16.129750046956598], [8.699434256448935, 0.5143820679939921, 3.99500298299439], [7.25549899989327, -7.248640181479738, -52.36415637546661], [-8.234933728608633, -7.024461715852155, 59.36024020404615], [-8.282665237347654, -0.422415288128029, 3.700188004624513], [6.681563085300898, 0.3011401181962583, 2.40762783759357], [-9.912581802404716, 1.7609436949927542, -16.69717382318314], [9.72960837981703, 8.886298761498786, 91.51150489041942], [8.521732308045365, 4.755842506139539, 44.078456244251086], [-3.2690052685694155, 0.4769672266656517, -2.0316666165689714], [-1.0404569507582941, -9.19559281341639, 18.65925221724412], [0.551694206917535, -7.039490348168318, -0.39901443816708904], [-4.062909842646207, -3.375603693046722, 9.605232809273629], [3.1336127326670358, 8.977884203410728, 34.88055342516104], [-3.3985547410703187, 0.1521014733255761, -1.3234097213656038], [-7.561625284567162, -3.675074269353223, 31.342103433296508], [0.9872884923197986, 2.0360787359850434, 1.9970273373591778], [0.009749141537255923, -7.810485456630605, 7.290861671866997], [-9.679143357792876, -8.763825940504208, 75.54725534911077], [-6.164492661565042, -3.170158754013068, 22.759994778893702], [1.4367429180320492, 0.16603317604994494, -0.11421293777921465], [-2.7018846369250777, 0.0005683728115801756, -0.5326671850287632], [-2.134719817553825, -2.9704171767524272, 6.368296225037441], [8.365293747706449, -6.904814033350366, -64.74035015853025], [5.1145037835573515, 9.1295449137797, 39.97379651242053], [1.9351682216167294, 2.1506799365853624, 5.087878416207822], [-1.5623235719489603, -7.640061021813402, 16.66592400491828], [3.262620478268099, 4.096169538148221, 15.748555977714158], [-0.4624399598594273, -4.2143313996972775, 7.132625582782002], [-1.003705244892581, -2.477387251975509, 5.643162292266166], [-7.00383787579371, -7.966137710515562, 64.65918719716223], [1.5531635875874894, 8.617546480119177, 17.386578506545092], [-3.391663175794351, 9.038670851072684, -23.02737334719133], [-7.481454208860736, 1.048691663488876, -7.885155240214989], [-5.52174420907553, 0.13222685415495938, -0.525065827120285], [-4.17708276543048, 0.32747225909126243, -1.9690908470334003], [9.359335652667433, 0.34650478897304104, 2.671244261861098], [-3.0108353577427094, 2.965956287273775, -7.428329235294585], [7.50968139476706, 6.389691952709946, 49.19488419621273], [4.861350436850341, 1.5876252031073115, 7.330638440762239], [-4.00598595413064, -8.542527053175316, 25.087049501814324], [-7.780091154746335, 7.090675062804511, -58.826278162050876], [-3.1671442276639876, 1.915227714664077, -5.283282356484066], [7.960270857813278, -8.961916679856884, -77.58066566086067], [0.3993500441701343, 5.117185421540334, -0.2833976332882968], [5.294230337954211, -6.89083199740407, -29.270707910278553], [2.26072318547471, -3.40955476119837, -11.907328129181192], [-4.364885126176814, -5.2446296493536115, 17.930406281207958], [-1.5817808241081934, 8.17148655063135, -16.733751998215922], [2.15105581730689, 2.7941944726843637, 7.648917193434598], [2.7770255716035823, -2.6407777149029084, -10.897136918402804], [4.766555950698738, 0.8592848577365864, 4.178157209591211], [-6.531831823750847, -4.847520206223955, 37.209892778605855], [3.549431150010241, -1.9467467635386644, -8.554587409963391], [8.816323409430694, -6.129450578431658, -61.16361451119673], [0.9615410037562206, -4.9656496590534775, -4.545299414274886], [6.712219541199165, -0.05517329235869717, 0.19992774830967786], [1.2269080956229317, 8.560372310459236, 12.203616467936413], [0.5649967267917333, 3.877499741272244, 0.9781577995622328], [4.108874605819199, 6.141787170333732, 25.40403256432505], [-0.5266221010632162, 6.412421511491107, -8.784064462023316], [4.832520137947991, 8.640284822735637, 36.885561885645444], [4.64182922969073, -6.634320136381291, -27.13370818751926], [2.909708874472667, 6.677584997280793, 24.78445389015336], [-7.93024189023974, -6.119724181818567, 51.91008045366141], [3.44857064243425, -9.48276641907601, -39.399062304848876], [3.004353503123049, -5.142814049414291, -21.02529460173551], [-1.2434129666062184, -2.0961992034673145, 5.028269981610798], [-3.891541407289485, 9.676641957210762, -29.11927986289919], [2.4643405339786035, 0.21385527871843735, -0.25468207037207435], [3.765641932133569, 3.970225558927652, 16.040987000707492], [-3.2122646510046664, 9.650490774252642, -23.40892620940877], [-1.8423964654168206, -5.424356045490324, 11.887407486612801], [3.0258422367254205, 0.05742284398830222, -0.6729088405725927], [-7.72516932974238, -9.629297907382925, 81.23235632536397], [-9.239687705651548, -7.0658059815131065, 59.41664649438566], [3.4478865585086993, 0.6161938505569804, 1.8791642528265315], [-7.406115846371668, -8.612842925950785, 71.97215476942706], [-8.948765152492332, -4.156331275278267, 34.614132557715], [-0.8275733058376531, 6.627195491500139, -10.927189715500806], [2.685840389342804, 6.719803522921961, 23.730313772262257], [2.014732302058963, 4.7870366234890405, 12.861076270168514], [5.993203021736482, 1.521302434003216, 8.616591245987435], [-5.974058022674251, -6.6766988028946965, 44.77865543140279], [1.625779751190219, -0.8143498758346794, -2.3866716833468073], [-8.327848101547586, -9.851604965532347, 83.09286794167325], [1.598575352425268, -3.8840605098688874, -8.960965869437409], [-2.350260218854774, 6.822306952572177, -14.828067593686036], [0.004921580147739135, 3.100458198111827, -1.7466086770173124], [-4.811410956449844, -8.196617559209542, 35.25773149612699], [2.326438938291627, -5.515453020474075, -19.15326308853696], [-1.979466566724879, -1.8870151247735922, 4.201296023850216], [-8.266346704070749, 2.9856390839275466, -24.993600699269553], [3.5987171977756702, 1.7687190257762921, 6.762239952547552]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=2.83872, x1=-0.54205, y=0.41703\nx0=9.04930, x1=6.24070, y=176.21873\nx0=9.75390, x1=-8.73831, y=372.39463\nx0=3.52547, x1=-3.35717, y=19.86711\nx0=4.41226, x1=-1.40586, y=4.36028\nx0=-4.98609, x1=3.17420, y=-25.11886\nx0=-4.48738, x1=-8.30342, y=-154.69514\nx0=2.59133, x1=5.84696, y=44.29474\nx0=-6.69410, x1=-3.84202, y=-49.40615\nx0=-6.30582, x1=7.65109, y=-184.56875\nx0=0.02732, x1=-5.97308, y=0.48728\nx0=-6.84995, x1=-2.80527, y=-26.95294\nx0=-0.28493, x1=-3.26569, y=-1.51935\nx0=5.59070, x1=-3.69703, y=38.20689\nx0=-3.90659, x1=-6.41830, y=-80.46508\nx0=8.85480, x1=-1.76978, y=13.86717\nx0=-1.62357, x1=1.39585, y=-1.58169\nx0=-9.18891, x1=8.56730, y=-337.22642\nx0=-1.36880, x1=-4.64070, y=-14.73935\nx0=-8.46946, x1=-5.08510, y=-109.50249\nx0=-2.47532, x1=8.61296, y=-91.81359\nx0=0.30203, x1=-2.58150, y=1.00637\nx0=7.47355, x1=6.96751, y=181.40635\nx0=3.95818, x1=4.57552, y=41.43294\nx0=7.19115, x1=6.86274, y=169.34139\nx0=-3.69830, x1=-8.35336, y=-129.03137\nx0=9.05220, x1=3.27363, y=48.50471\nx0=-0.96193, x1=5.35319, y=-13.78288\nx0=-0.35765, x1=-5.73546, y=-5.88257\nx0=-4.93640, x1=5.92835, y=-86.74591\nx0=8.20451, x1=-0.70947, y=2.06488\nx0=1.77572, x1=-0.69742, y=0.43185\nx0=7.40417, x1=-8.84185, y=289.42253\nx0=5.12014, x1=6.52303, y=108.93073\nx0=5.88672, x1=0.18699, y=0.10292\nx0=-1.57287, x1=-1.14141, y=-1.02459\nx0=-1.07062, x1=-0.83399, y=-0.37233\nx0=-8.80222, x1=-4.47322, y=-88.06501\nx0=-8.84614, x1=5.56472, y=-136.96499\nx0=2.31115, x1=-5.39121, y=33.58686\nx0=1.62805, x1=1.64155, y=2.19353\nx0=-4.26590, x1=-4.23330, y=-38.22425\nx0=-5.44209, x1=-1.14676, y=-3.57831\nx0=6.78849, x1=-0.39171, y=0.52079\nx0=-2.28745, x1=-7.56294, y=-65.41888\nx0=-2.01097, x1=0.32457, y=-0.10592\nx0=6.91615, x1=3.18632, y=35.10861\nx0=6.66939, x1=-5.89053, y=115.70843\nx0=-6.72126, x1=8.32160, y=-232.72048\nx0=5.04990, x1=6.37564, y=102.63612\nx0=-6.52145, x1=-9.85659, y=-316.78735\nx0=4.58307, x1=-8.18506, y=153.52195\nx0=9.28113, x1=0.58794, y=1.60414\nx0=4.92653, x1=1.58560, y=6.19298\nx0=-4.13506, x1=-5.27083, y=-57.43930\nx0=-0.40299, x1=2.04697, y=-0.84427\nx0=9.87538, x1=-9.81311, y=475.48482\nx0=5.33295, x1=4.56560, y=55.58178\nx0=0.03364, x1=-0.72796, y=0.00891\nx0=-8.55000, x1=2.38695, y=-24.35701\nx0=9.23005, x1=1.55938, y=11.22219\nx0=-6.94608, x1=5.66817, y=-111.58244\nx0=-8.35698, x1=3.41564, y=-48.74880\nx0=3.38353, x1=-7.05636, y=84.23665\nx0=0.43690, x1=8.27413, y=14.95528\nx0=2.50676, x1=-7.86570, y=77.54570\nx0=7.97599, x1=2.37597, y=22.51320\nx0=-2.35666, x1=-5.98564, y=-42.21706\nx0=-6.37788, x1=-0.74805, y=-1.78446\nx0=2.43082, x1=6.01980, y=44.04406\nx0=-5.08449, x1=-4.31917, y=-47.42616\nx0=5.44632, x1=6.75848, y=124.38599\nx0=-0.75710, x1=6.37106, y=-15.36550\nx0=7.84050, x1=1.33903, y=7.02897\nx0=7.29276, x1=5.55061, y=112.34243\nx0=1.53041, x1=6.71136, y=34.46675\nx0=-1.04167, x1=-0.19658, y=-0.02013\nx0=-9.45590, x1=4.75347, y=-106.83033\nx0=-8.51411, x1=4.50409, y=-86.36226\nx0=-8.86256, x1=8.67728, y=-333.65403\nx0=4.61956, x1=-3.84212, y=34.09668\nx0=-6.53710, x1=0.40543, y=-0.53726\nx0=-0.63983, x1=9.45490, y=-28.59885\nx0=1.41708, x1=8.05159, y=45.93336\nx0=6.45717, x1=-0.88418, y=2.52405\nx0=-8.54303, x1=9.76968, y=-407.70223\nx0=7.43346, x1=2.39315, y=21.28626\nx0=2.76206, x1=-4.68570, y=30.32157\nx0=4.24589, x1=1.39536, y=4.13342\nx0=-6.31561, x1=3.12561, y=-30.85004\nx0=-5.64977, x1=1.64896, y=-7.68108\nx0=-5.30374, x1=-9.06087, y=-217.71717\nx0=-8.27119, x1=-9.74842, y=-393.01298\nx0=-8.34262, x1=-0.02975, y=-0.00369\nx0=-2.28071, x1=-7.48943, y=-63.96433\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=1.11563, x1=6.00934, y=20.14394\nx0=9.28270, x1=1.16581, y=6.30811\nx0=7.02528, x1=-1.64944, y=9.55664\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1/2 * x0 * x1**2", "data": [[2.8387235771237513, -0.5420464340363811, 0.41702884237487475], [9.049304125031608, 6.24070184777279, 176.2187260780347], [9.753896974634536, -8.73831348261199, 372.3946301202439], [3.5254676582469173, -3.3571746018446813, 19.867105453566243], [4.412257034718785, -1.4058586681112253, 4.360277546585044], [-4.986090614040426, 3.174204320389311, -25.118860151665007], [-4.487376781342043, -8.303421171099604, -154.6951417895654], [2.5913271051918603, 5.846957885896691, 44.29474170989044], [-6.694104214980716, -3.8420168180331027, -49.40614820449785], [-6.305815377861689, 7.651092523740637, -184.56874677427516], [0.027315479577383783, -5.9730822676168716, 0.4872769036887201], [-6.849948606188123, -2.805268471441453, -26.952942126654424], [-0.28493112700433443, -3.2656874625505434, -1.5193545755147069], [5.59070381688792, -3.6970268991715383, 38.20689194887791], [-3.906590381459843, -6.418296583328544, -80.46507934833407], [8.854802947312642, -1.7697806386299408, 13.867168238841995], [-1.6235697891115723, 1.395854187668423, -1.5816889241791652], [-9.188906032819183, 8.56729827832677, -337.22641820458284], [-1.3688047208145289, -4.640698532048699, -14.739345946978109], [-8.469458305579131, -5.085096149956534, -109.50248546586229], [-2.475322622424252, 8.61296281881431, -91.81358811174928], [0.30202573340254446, -2.5815001740594816, 1.0063713609881686], [7.473552277965169, 6.9675116269531365, 181.40635007563034], [3.958180763600044, 4.575515734953326, 41.4329384266506], [7.191146719826186, 6.86273901850279, 169.34139031466117], [-3.698302155475062, -8.353364970699516, -129.03137002011005], [9.052203403989985, 3.2736316471582754, 48.50471190006096], [-0.9619313611555409, 5.353193635887251, -13.782880610916312], [-0.35765233458086954, -5.735456815948314, -5.8825699070880075], [-4.936403685082411, 5.9283545744843575, -86.74591132169577], [8.204513589879912, -0.709473456414873, 2.064881563532442], [1.7757205042700939, -0.6974205550458397, 0.43185116965024767], [7.404165451603639, -8.841849356019878, 289.42253409045617], [5.120143146297041, 6.523026683673507, 108.93073084542081], [5.886724134044005, 0.18698980874373383, 0.1029152097150362], [-1.5728694287312663, -1.1414141197843524, -1.0245877448366192], [-1.0706198731700827, -0.8339942193938992, -0.372332876783536], [-8.802216633716299, -4.473224124351414, -88.06500701898285], [-8.846135819785276, 5.564715735506923, -136.96499166467638], [2.3111466572608457, -5.39120624423596, 33.58685986362124], [1.628050112548081, 1.6415450577171082, 2.1935290420779796], [-4.265896691942245, -4.233302568720925, -38.224248727441086], [-5.442092871480632, -1.1467557595225593, -3.578308773870278], [6.7884889612258235, -0.391705097850938, 0.5207887185835529], [-2.2874517506191054, -7.562938929434564, -65.41888436995977], [-2.010970947994841, 0.32457066576146687, -0.10592399045877415], [6.916147450355069, 3.186322204135301, 35.10860939992387], [6.669385346736394, -5.890532941747042, 115.70842802084296], [-6.721259454913833, 8.321602625922068, -232.72048412712132], [5.0499004091443105, 6.375638825599118, 102.63612122416428], [-6.521451292264555, -9.856592124931199, -316.7873493835905], [4.583070399997506, -8.185062082312253, 153.52195365143717], [9.281134838497206, 0.5879443763628149, 1.6041448008781232], [4.926526468810319, 1.5856026584779244, 6.192978259218802], [-4.135057381538434, -5.270827390750172, -57.439299285610176], [-0.4029860875153375, 2.0469680086094897, -0.8442715754983946], [9.875377453149081, -9.81310567083428, 475.4848231641608], [5.332948843848202, 4.5655963377110815, 55.58177917225314], [0.0336434010644826, -0.7279624724804172, 0.008914313019700044], [-8.550001002367932, 2.386953318784709, -24.357012629913886], [9.230053773067155, 1.5593791003237296, 11.222190947893239], [-6.946079568109871, 5.668172432193092, -111.58244288751636], [-8.356983548465703, 3.4156407038985552, -48.748798058903745], [3.3835285325184454, -7.056358060976573, 84.2366462323333], [0.4368975542467357, 8.27413256170366, 14.955280635059587], [2.5067600960584038, -7.865701686636006, 77.54569985948521], [7.975990217610676, 2.375971976126799, 22.51320079940186], [-2.3566618657382588, -5.985636810479297, -42.2170615883068], [-6.377879990395165, -0.7480501336905014, -1.7844638615908657], [2.430819636767506, 6.019803198177847, 44.04405812303083], [-5.084490518884481, -4.319169404444181, -47.42615565309434], [5.446315430236606, 6.758484793396779, 124.38599275297756], [-0.7571011696028229, 6.371055253121931, -15.365498851551857], [7.840500180609563, 1.3390260817031674, 7.02897253175436], [7.292762852970821, 5.550611968369987, 112.34243457299284], [1.5304139854069234, 6.711362519319916, 34.46674939771282], [-1.0416676532113698, -0.19658090219154545, -0.020127129013313816], [-9.455899174853066, 4.753471295093387, -106.83033456552569], [-8.51411119693735, 4.504093006679453, -86.36226459917565], [-8.862559545419222, 8.677279876872916, -333.65403497710224], [4.619564414506858, -3.8421163264018565, 34.0966766439755], [-6.537100477676738, 0.40542872088283133, -0.5372596032428303], [-0.639830421581733, 9.454897586809825, -28.598848541816007], [1.4170805532521626, 8.051593504652171, 45.93336097708312], [6.45716762240178, -0.8841839052416933, 2.5240460561236517], [-8.543030967051891, 9.769684735746718, -407.7022270610444], [7.433457379019373, 2.393146393104306, 21.2862614460822], [2.7620573686686214, -4.685700334027112, 30.321572490788927], [4.245885068230919, 1.3953587099149374, 4.133424160411968], [-6.315614935319425, 3.1256116959176055, -30.85003734503063], [-5.649773472436972, 1.6489614229608502, -7.681075440139023], [-5.303742212322438, -9.060874897091924, -217.71716963101545], [-8.271191228652349, -9.748424087185779, -393.01298026423905], [-8.342620004180494, -0.029749494257369946, -0.0036917445380390906], [-2.280709720026442, -7.489432781869148, -63.96433253643735], [1.1156312368506054, 6.009341088665106, 20.14393819784151], [9.282700722462728, 1.165809587604068, 6.308114946856512], [7.025284722021553, -1.64943625951339, 9.556635222425486]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=0.25034, y=-1.38494\nx0=1.77163, y=0.57190\nx0=6.36675, y=1.85109\nx0=6.31058, y=1.84223\nx0=8.75284, y=2.16938\nx0=8.39723, y=2.12790\nx0=9.67147, y=2.26918\nx0=6.63692, y=1.89265\nx0=2.25908, y=0.81496\nx0=7.33796, y=1.99306\nx0=4.38234, y=1.47758\nx0=1.18060, y=0.16602\nx0=6.41157, y=1.85810\nx0=5.79627, y=1.75722\nx0=0.92184, y=-0.08138\nx0=4.44623, y=1.49206\nx0=5.60993, y=1.72454\nx0=7.42444, y=2.00478\nx0=3.99031, y=1.38387\nx0=0.55963, y=-0.58049\nx0=7.14721, y=1.96672\nx0=5.77770, y=1.75401\nx0=5.63301, y=1.72864\nx0=0.06254, y=-2.77201\nx0=5.97619, y=1.78778\nx0=5.97893, y=1.78824\nx0=1.55888, y=0.44397\nx0=5.98909, y=1.78994\nx0=6.15720, y=1.81762\nx0=9.58741, y=2.26045\nx0=6.92224, y=1.93474\nx0=9.27318, y=2.22713\nx0=9.53734, y=2.25521\nx0=0.12812, y=-2.05478\nx0=3.74467, y=1.32033\nx0=4.07986, y=1.40606\nx0=4.82609, y=1.57404\nx0=3.80849, y=1.33723\nx0=0.26871, y=-1.31413\nx0=4.99301, y=1.60804\nx0=3.94132, y=1.37151\nx0=7.90879, y=2.06797\nx0=4.50596, y=1.50540\nx0=4.90145, y=1.58953\nx0=6.52006, y=1.87488\nx0=7.67281, y=2.03768\nx0=2.43520, y=0.89003\nx0=5.83442, y=1.76377\nx0=8.37682, y=2.12547\nx0=1.63401, y=0.49104\nx0=5.57215, y=1.71778\nx0=5.97827, y=1.78813\nx0=6.32486, y=1.84449\nx0=5.75505, y=1.75008\nx0=6.65861, y=1.89591\nx0=1.96203, y=0.67398\nx0=0.39747, y=-0.92264\nx0=8.77851, y=2.17231\nx0=4.35946, y=1.47235\nx0=6.71287, y=1.90403\nx0=1.10030, y=0.09558\nx0=3.82772, y=1.34227\nx0=9.20899, y=2.22018\nx0=1.53237, y=0.42681\nx0=6.28553, y=1.83825\nx0=0.31935, y=-1.14146\nx0=0.67710, y=-0.38994\nx0=5.55821, y=1.71528\nx0=1.00490, y=0.00488\nx0=6.90395, y=1.93209\nx0=1.51741, y=0.41700\nx0=2.42435, y=0.88556\nx0=0.68801, y=-0.37395\nx0=8.66370, y=2.15914\nx0=6.18198, y=1.82164\nx0=9.34760, y=2.23512\nx0=9.97338, y=2.29992\nx0=8.14276, y=2.09713\nx0=2.98557, y=1.09379\nx0=4.57759, y=1.52117\nx0=4.07660, y=1.40526\nx0=4.64577, y=1.53596\nx0=0.71845, y=-0.33066\nx0=0.62764, y=-0.46579\nx0=2.32876, y=0.84534\nx0=9.29869, y=2.22987\nx0=8.17783, y=2.10143\nx0=0.54785, y=-0.60175\nx0=3.33195, y=1.20356\nx0=4.68339, y=1.54402\nx0=8.40663, y=2.12902\nx0=4.86668, y=1.58241\nx0=1.98108, y=0.68364\nx0=8.80535, y=2.17536\nx0=6.80757, y=1.91803\nx0=2.89818, y=1.06408\nx0=1.15272, y=0.14213\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=4.39330, y=1.48008\nx0=1.88282, y=0.63277\nx0=8.40391, y=2.12870\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = log(x0)", "data": [[0.250338883291182, -1.3849397458608357], [1.7716336073585126, 0.571902062947099], [6.3667455033524645, 1.8510884290333272], [6.31057689534041, 1.8422270979430624], [8.752842239760406, 2.169378475025714], [8.397230159868478, 2.1279019085993327], [9.671465106708588, 2.269179808506595], [6.636917045081114, 1.8926475552279267], [2.25908196410683, 0.8149585201861316], [7.337957243187522, 1.9930604991496281], [4.382338313866411, 1.4775824435482776], [1.1806017534545097, 0.1660242690465488], [6.411565138260788, 1.8581034124631461], [5.796274565004442, 1.757215394800288], [0.9218390425152646, -0.08138464494386113], [4.446228919476441, 1.4920563030775968], [5.6099302395520665, 1.7245382844398325], [7.424441484499561, 2.0047774609167064], [3.990313853004109, 1.3838698877090236], [0.5596254828275058, -0.5804874996516575], [7.1472055368474114, 1.9667214463030447], [5.7776985977100965, 1.7540054369088207], [5.633008889367202, 1.7286437379988877], [0.0625363825702076, -2.772006770483236], [5.976187865612758, 1.7877828840185825], [5.97892905104521, 1.78824146347031], [1.5588844237096622, 0.4439704524395476], [5.989091705124216, 1.7899397654249396], [6.1571990889897, 1.8176219807952352], [9.587409263076939, 2.2604507025627427], [6.9222383237301655, 1.9347391745150204], [9.273177661101851, 2.227126110601651], [9.53733657470687, 2.255214261439588], [0.12812138067585163, -2.0547771778720545], [3.744674615604999, 1.320334728175769], [4.0798584017994886, 1.4060622823725208], [4.826086411883975, 1.574035872530308], [3.808492044935567, 1.3372333220627548], [0.26870862518368144, -1.3141276641971202], [4.993014330487264, 1.6080398016299682], [3.941316136192818, 1.3715147122483164], [7.908788448107625, 2.067974602931673], [4.505963701651852, 1.5054017864187632], [4.9014485050544225, 1.589530774707998], [6.5200586234147515, 1.8748833672194207], [7.672806890652803, 2.0376825054935517], [2.4351955614033645, 0.8900270660009817], [5.834417820673061, 1.763774487097225], [8.37681747796794, 2.1254680664620476], [1.6340070204290487, 0.4910352928967874], [5.572151858587078, 1.7177813094203855], [5.97827344110161, 1.7881318040504437], [6.324858998202562, 1.8444877415907979], [5.755054220991076, 1.7500784636743942], [6.65860772984456, 1.8959104131255011], [1.9620335474805013, 0.6739814596109067], [0.3974692592459223, -0.9226376831086577], [8.778507571703717, 2.1723064127549443], [4.359459360832205, 1.4723480498632038], [6.712869916021227, 1.90402656684859], [1.1002973523318766, 0.09558046357608119], [3.827717832139898, 1.342268759311677], [9.20899456492086, 2.220180676546946], [1.5323682181580773, 0.42681439371677693], [6.285525391059263, 1.838249432989005], [0.3193524836548071, -1.1414598217860334], [0.6770968779636038, -0.3899409173952691], [5.558213616087174, 1.7152767645664833], [1.0048955948949791, 0.004883650437910758], [6.9039465479907065, 1.9320932115713627], [1.5174083938901353, 0.41700387566489716], [2.4243475025888106, 0.8855624170859263], [0.6880109441498288, -0.3739505339807929], [8.66369609717499, 2.1591414325801463], [6.181984230884278, 1.8216392928953282], [9.347603838595864, 2.23512003650985], [9.973375450988783, 2.2999190874562], [8.142760969865662, 2.0971293079912376], [2.9855661396285718, 1.0937893903782032], [4.577590020461485, 1.5211726632303915], [4.076601415061865, 1.4052636547855863], [4.645767323707336, 1.5359565521012977], [0.718452930740421, -0.33065508606070604], [0.6276365575847117, -0.4657940100034113], [2.328761018684875, 0.8453363745101753], [9.298690242687611, 2.2298735561215426], [8.177825693932048, 2.1014263076937882], [0.5478541303622199, -0.6017462129381637], [3.3319544549924296, 1.203559055241316], [4.683388934724455, 1.544021979224329], [8.406625402857575, 2.1290201333939973], [4.866680730363303, 1.5824121298426843], [1.981075582745744, 0.6836399208228727], [8.80535054460193, 2.175359553149098], [6.807566042394139, 1.9180346469354124], [2.8981818030686624, 1.0640835759089413], [1.1527245901061516, 0.1421283490130225], [4.3933007657991565, 1.4800808274347292], [1.8828216400675333, 0.6327715240349572], [8.403910922556006, 2.1286971835162998]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-2.45209, y=-63.68130\nx0=9.04437, y=68040.86115\nx0=-7.18769, y=-16842.17577\nx0=9.11138, y=70534.73704\nx0=-0.36655, y=-0.27000\nx0=4.31024, y=1935.77812\nx0=3.65329, y=894.65228\nx0=-4.85921, y=-2247.57337\nx0=-3.16692, y=-242.86888\nx0=6.89899, y=18277.09192\nx0=-7.17209, y=-16655.74218\nx0=0.96300, y=4.47164\nx0=-1.00092, y=-1.00276\nx0=-2.47269, y=-66.53060\nx0=-1.13103, y=-1.51306\nx0=-7.49799, y=-20910.89758\nx0=-1.89620, y=-16.70498\nx0=-8.90997, y=-50488.43906\nx0=2.07493, y=72.31012\nx0=-3.38047, y=-341.44633\nx0=-8.32630, y=-35728.47396\nx0=-7.42476, y=-19886.34093\nx0=-3.33330, y=-317.30646\nx0=6.87285, y=17944.98147\nx0=-5.90127, y=-6120.73196\nx0=2.62580, y=199.99097\nx0=-3.71473, y=-558.10801\nx0=-1.73667, y=-10.65947\nx0=-7.96819, y=-28540.79652\nx0=5.45669, y=5922.05548\nx0=5.97146, y=9118.86303\nx0=-0.72971, y=-0.50915\nx0=-7.49413, y=-20855.83728\nx0=0.24563, y=0.32532\nx0=5.70010, y=7296.51385\nx0=-4.63055, y=-1751.65983\nx0=6.81795, y=17263.33146\nx0=5.85987, y=8329.93956\nx0=0.25425, y=0.34057\nx0=-2.21056, y=-37.03264\nx0=-6.55527, y=-10503.40477\nx0=1.85607, y=45.59097\nx0=9.49418, y=86221.90234\nx0=2.12329, y=79.68591\nx0=-5.97260, y=-6510.94577\nx0=-9.04601, y=-54545.21029\nx0=-6.65123, y=-11316.53387\nx0=9.97090, y=109538.40503\nx0=-6.19490, y=-7856.51804\nx0=4.63952, y=2738.99549\nx0=-5.52973, y=-4379.38679\nx0=-2.41843, y=-59.23632\nx0=2.13755, y=81.97594\nx0=-1.47454, y=-4.74967\nx0=-3.46170, y=-386.46491\nx0=-1.85940, y=-15.10340\nx0=-2.05351, y=-25.22971\nx0=-8.21198, y=-33292.45620\nx0=-1.71998, y=-10.15103\nx0=-0.29347, y=-0.22738\nx0=2.33946, y=120.64754\nx0=8.22176, y=42769.48275\nx0=0.72661, y=2.11948\nx0=-7.06046, y=-15369.56677\nx0=9.42374, y=83143.70365\nx0=9.71734, y=96581.98852\nx0=-1.33138, y=-2.95999\nx0=-4.22904, y=-1094.83259\nx0=-4.17644, y=-1026.00284\nx0=4.14652, y=1614.04452\nx0=-9.82185, y=-82959.01838\nx0=-2.04502, y=-24.69260\nx0=7.00222, y=19637.10478\nx0=-8.53224, y=-40475.52528\nx0=7.12989, y=21429.97081\nx0=-2.55337, y=-78.70936\nx0=9.14027, y=71632.21201\nx0=-2.93509, y=-163.21472\nx0=7.32066, y=24351.00600\nx0=7.81066, y=33336.70168\nx0=-6.91077, y=-13771.07394\nx0=7.59696, y=29139.25309\nx0=2.91665, y=319.66772\nx0=-0.56644, y=-0.38270\nx0=-7.06683, y=-15440.76884\nx0=3.81767, y=1097.40122\nx0=8.67639, y=55573.56938\nx0=-5.42317, y=-3961.51187\nx0=1.29045, y=11.45641\nx0=-1.20072, y=-1.90733\nx0=-9.84731, y=-84059.79552\nx0=1.50456, y=20.00825\nx0=5.90764, y=8660.64994\nx0=-5.03215, y=-2692.67061\nx0=-6.61589, y=-11011.43341\nx0=-1.65895, y=-8.46340\nx0=9.46000, y=84716.97964\nx0=1.35967, y=13.78653\nx0=-5.82907, y=-5745.09963\nx0=-9.84275, y=-83861.63155\nx0=5.22634, y=4820.68224\nx0=-9.66636, y=-76483.46205\nx0=-3.17812, y=-247.38808\nx0=-8.16038, y=-32237.43967\nx0=0.37536, y=0.59645\nx0=8.07665, y=39223.58790\nx0=3.88419, y=1189.28609\nx0=-7.88994, y=-27136.72397\nx0=7.17093, y=22033.36370\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-8.97307, y=-52339.04788\nx0=-1.26258, y=-2.34841\nx0=-6.60925, y=-10954.81680\nx0=5.45001, y=5887.52667\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**5 + x0**4 + x0**3 + x0**2 + x0", "data": [[-2.4520944072091, -63.68130141386064], [9.044366116799775, 68040.86114764768], [-7.187692976131455, -16842.175767769593], [9.11137895452785, 70534.73704395565], [-0.3665454609066856, -0.2700025578676544], [4.310236557866947, 1935.778124802807], [3.653293604103249, 894.6522817477063], [-4.859207085227828, -2247.573372766485], [-3.166924579267045, -242.868875766696], [6.8989881985541714, 18277.091920532937], [-7.172089553059484, -16655.742175099538], [0.9630008225706845, 4.4716425514723355], [-1.0009181501292659, -1.0027595138066017], [-2.4726860733034357, -66.53059771397605], [-1.1310287293795227, -1.5130620036850977], [-7.497994804101942, -20910.897576199517], [-1.896204734736294, -16.70498160507742], [-8.909966376782073, -50488.43905769234], [2.0749298740850293, 72.31012475913788], [-3.380466976465617, -341.446330251936], [-8.326302508270523, -35728.47395529813], [-7.424755496391833, -19886.340928337617], [-3.3332958073056895, -317.3064602978132], [6.872846890628338, 17944.98147193553], [-5.901266805718441, -6120.731959155971], [2.625801126599459, 199.99096911591485], [-3.714726754633473, -558.1080089803808], [-1.7366684044512084, -10.659473532376172], [-7.968187425105606, -28540.79652457057], [5.456687337601696, 5922.055477681442], [5.971456214706537, 9118.86303048111], [-0.729710623692295, -0.5091517943825244], [-7.494132784114829, -20855.837277762916], [0.2456294463404145, 0.32531733873310875], [5.700099559063549, 7296.513852376468], [-4.630552416123567, -1751.6598250722418], [6.81795390798165, 17263.33145533253], [5.859874148917575, 8329.9395615749], [0.25424837341309114, 0.3405668175725748], [-2.2105609151250043, -37.03263538716429], [-6.555272085975796, -10503.404767723643], [1.85606920666282, 45.59096837426502], [9.494179654739892, 86221.90233677022], [2.1232890743212813, 79.685909203094], [-5.972602968364487, -6510.945765863001], [-9.04601276088859, -54545.21028933423], [-6.651228586316902, -11316.53387440673], [9.970903152554492, 109538.40502893747], [-6.194904093648638, -7856.518039512768], [4.639518187767823, 2738.995486233864], [-5.529732422175011, -4379.386794988893], [-2.4184253755646274, -59.23632462911816], [2.137552219123007, 81.97593747895715], [-1.4745396622991436, -4.749672489165206], [-3.4617016756268004, -386.4649132673384], [-1.8593996260820163, -15.103395276457253], [-2.053507550484812, -25.22970656784404], [-8.211979617178297, -33292.45619798524], [-1.7199814745499928, -10.15102917839343], [-0.2934736178795987, -0.22738190142443576], [2.3394556107879954, 120.64754112864166], [8.221759370650258, 42769.4827496257], [0.7266100468084105, 2.1194770811172052], [-7.060455937471475, -15369.566767693528], [9.423741737200377, 83143.70365033278], [9.717343430840202, 96581.98851775298], [-1.331381568618994, -2.9599913084088225], [-4.229036226992395, -1094.8325903988248], [-4.176441141929141, -1026.002837482231], [4.146515640195087, 1614.0445225909107], [-9.821852573985588, -82959.01838019978], [-2.0450163794357596, -24.692596121420088], [7.002222193440371, 19637.104780971564], [-8.532237996548952, -40475.52528090571], [7.1298928993926545, 21429.97080838422], [-2.553371369274706, -78.70936495556066], [9.140269271129345, 71632.21200511156], [-2.935085142116627, -163.21471983809778], [7.320655025414954, 24351.005999139205], [7.810661368174841, 33336.701676870005], [-6.910771183391054, -13771.073939634914], [7.596961410681008, 29139.253094355092], [2.9166473158480315, 319.667723817641], [-0.5664426588605114, -0.3826981599560595], [-7.066827844945807, -15440.768841062234], [3.817672127331681, 1097.401217592756], [8.676389033643169, 55573.569375606334], [-5.423166358400935, -3961.5118691282087], [1.2904540719429125, 11.456409057275158], [-1.2007214866609743, -1.9073260538360568], [-9.847310136763333, -84059.79552162724], [1.5045578937056412, 20.008249253074922], [5.907638319722533, 8660.649939959934], [-5.03214847925642, -2692.6706051492174], [-6.615891786944101, -11011.433407180828], [-1.6589487945108807, -8.463403380910181], [9.459998843096898, 84716.9796400138], [1.3596668366519467, 13.786529116394345], [-5.829067328164578, -5745.099630854415], [-9.842746992423253, -83861.63155360814], [5.22633589100044, 4820.682243296648], [-9.666363660252193, -76483.4620538275], [-3.178120731274097, -247.38807947101668], [-8.160379023070497, -32237.43967222853], [0.37536027560650176, 0.5964450832527348], [8.076650349507265, 39223.58789625263], [3.884187922377059, 1189.28609479584], [-7.889939430038437, -27136.723974271066], [7.1709348773729715, 22033.363702045874], [-8.97307358533919, -52339.0478829004], [-1.2625783696448867, -2.3484113880553648], [-6.60924839310749, -10954.816795531648], [5.450011082242849, 5887.5266717447985]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.33754, y=-0.13321\nx0=-3.06209, y=50.91755\nx0=5.44320, y=0.57275\nx0=7.50149, y=-0.08265\nx0=-3.46332, y=-193.59502\nx0=-6.48371, y=-66585.00118\nx0=-0.37743, y=-0.02332\nx0=-1.45948, y=-1.33799\nx0=-1.66062, y=2.22558\nx0=-6.83127, y=-81801.81401\nx0=-7.31956, y=-281686.00062\nx0=-3.06291, y=50.24029\nx0=2.65048, y=0.87261\nx0=6.52883, y=-0.18678\nx0=-3.22051, y=-12.54935\nx0=-3.49391, y=-304.74166\nx0=-7.52154, y=-240528.94360\nx0=2.69943, y=0.90155\nx0=8.06504, y=0.03945\nx0=-5.18392, y=5553.65396\nx0=2.68968, y=0.89921\nx0=-8.36401, y=1458819.63264\nx0=-2.24284, y=21.15822\nx0=8.48998, y=0.06638\nx0=2.09241, y=0.25847\nx0=-1.51059, y=-0.89496\nx0=-0.09534, y=-0.00009\nx0=6.95124, y=-0.27063\nx0=6.30842, y=-0.00156\nx0=-2.33405, y=31.94569\nx0=1.52981, y=-0.03081\nx0=2.17816, y=0.23561\nx0=2.55664, y=0.72135\nx0=7.29536, y=-0.10690\nx0=5.93034, y=0.27656\nx0=6.37786, y=-0.03475\nx0=6.20364, y=0.01127\nx0=-8.66874, y=1549611.30107\nx0=-5.52530, y=33032.67433\nx0=-1.20461, y=-1.25628\nx0=-7.19586, y=-93631.43088\nx0=3.26795, y=-0.00949\nx0=-1.95275, y=13.94198\nx0=-7.61973, y=-156397.05358\nx0=0.00062, y=-0.00000\nx0=-5.18894, y=5640.77647\nx0=-9.18960, y=2334736.46591\nx0=-6.54694, y=-92018.03723\nx0=5.29253, y=0.29301\nx0=3.04012, y=0.15989\nx0=-3.26996, y=-6.23479\nx0=6.16598, y=0.03929\nx0=4.41797, y=-0.34073\nx0=-8.06387, y=396962.08364\nx0=-1.38958, y=-1.58695\nx0=3.46714, y=-0.20044\nx0=0.66559, y=-0.04879\nx0=7.34943, y=-0.13780\nx0=-2.59721, y=143.97161\nx0=4.09514, y=-0.26692\nx0=-7.08632, y=-219884.96714\nx0=-5.96187, y=44172.11084\nx0=-9.96538, y=-1804486.59095\nx0=-4.68497, y=-305.62451\nx0=6.51111, y=-0.17833\nx0=4.76172, y=0.04688\nx0=5.97208, y=0.29301\nx0=-3.85003, y=-2103.98594\nx0=3.53547, y=-0.42830\nx0=2.80660, y=0.80617\nx0=-6.58386, y=-91482.46488\nx0=-8.31466, y=942390.86227\nx0=-8.29142, y=739847.69296\nx0=-3.67152, y=-1428.31151\nx0=-3.05952, y=53.06671\nx0=6.78581, y=-0.03405\nx0=-0.04062, y=-0.00000\nx0=5.74304, y=0.03812\nx0=-7.73282, y=-128222.39847\nx0=1.54630, y=-0.01896\nx0=-5.20348, y=5976.73767\nx0=-0.10773, y=-0.00015\nx0=4.70384, y=-0.00806\nx0=8.39924, y=0.08950\nx0=-0.11298, y=-0.00018\nx0=-1.35557, y=-1.60065\nx0=-3.37910, y=-29.42516\nx0=-1.55487, y=-0.28044\nx0=8.03092, y=0.03431\nx0=5.20026, y=0.17918\nx0=6.12482, y=0.09255\nx0=-8.15576, y=453922.04744\nx0=0.69031, y=-0.05234\nx0=-4.39257, y=-2321.86656\nx0=8.42234, y=0.09068\nx0=-0.79582, y=-0.32715\nx0=8.02736, y=0.03364\nx0=8.97766, y=0.00724\nx0=8.59686, y=0.01904\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.59147, y=-0.03793\nx0=-3.00658, y=100.58065\nx0=7.97747, y=0.02319\nx0=7.14404, y=-0.07762\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**3 * exp(-x0) * cos(x0) * sin(x0) * (sin(x0**2) * cos(x0) - 1)", "data": [[7.337538025117716, -0.13320780442799102], [-3.0620947960260736, 50.91755173915504], [5.443204859266173, 0.5727487543899973], [7.501491822661251, -0.08264769174291114], [-3.463323022847211, -193.59502348890663], [-6.483705839578715, -66585.0011766814], [-0.3774270545684111, -0.023319582945566058], [-1.4594815936794543, -1.3379864139321742], [-1.6606248563317028, 2.2255792572739277], [-6.831266410932408, -81801.8140066707], [-7.3195593043957246, -281686.0006181728], [-3.062911872863612, 50.240285068076645], [2.6504830125997714, 0.872610214319669], [6.528833529567404, -0.18677507086293124], [-3.220513562393328, -12.549348909209783], [-3.4939060769995445, -304.74165668579], [-7.521542181049439, -240528.94359698624], [2.6994314169548836, 0.9015460978576266], [8.065043556397566, 0.03944588061314983], [-5.183921656211976, 5553.653959609631], [2.689681852445405, 0.8992060033436982], [-8.364009882012834, 1458819.632641092], [-2.2428417852123284, 21.158221789919537], [8.489975297466824, 0.06638103042135599], [2.0924065307796162, 0.258472512707187], [-1.5105913279956802, -0.8949555526623457], [-0.09533545507094843, -8.950341556590919e-05], [6.951244591887821, -0.27062813986552714], [6.308419748236513, -0.0015633370953013874], [-2.3340536130271383, 31.94569222002488], [1.5298111095388816, -0.03081009214674166], [2.1781634380068517, 0.23561008189862026], [2.5566380334049796, 0.7213511628411579], [7.295355302085266, -0.10689836576002881], [5.930338712026483, 0.27655789652687623], [6.377855863321521, -0.03474671961254269], [6.2036446758725035, 0.011266160281052706], [-8.668735955585994, 1549611.3010684957], [-5.5253037393265085, 33032.674329398964], [-1.2046139138340823, -1.2562767891154014], [-7.195855389899581, -93631.43087845536], [3.267948565504062, -0.009490971241911101], [-1.9527534737933543, 13.941983868438463], [-7.61972981741166, -156397.05357766576], [0.0006197299419579139, -1.4741459861300848e-13], [-5.1889422386588535, 5640.776472604243], [-9.189601870038063, 2334736.465914037], [-6.546938522003034, -92018.03723420114], [5.2925320003328675, 0.29301296891930584], [3.0401177918099442, 0.15988597091203902], [-3.269964809738113, -6.234787379539139], [6.165982258134932, 0.03929212286492186], [4.417969091446585, -0.3407257342337064], [-8.063865382421401, 396962.08363922377], [-1.38957764216115, -1.5869460348027917], [3.4671397442039584, -0.20043728299298386], [0.6655937966464691, -0.04879217608019554], [7.349428443835318, -0.13779524031518733], [-2.597212860880438, 143.97160967400987], [4.09513783070132, -0.2669197352947055], [-7.0863201106945395, -219884.9671358876], [-5.961867309760351, 44172.11084302254], [-9.96538392326289, -1804486.5909468282], [-4.684965049852316, -305.6245064988229], [6.511113450526452, -0.17832929178576779], [4.761718379835964, 0.04688247054191264], [5.9720832347989905, 0.2930066327465596], [-3.850025511406967, -2103.9859421427373], [3.535472626150842, -0.42830459215282957], [2.8066001444969917, 0.8061703586820343], [-6.5838637024749875, -91482.46488369438], [-8.314662193549653, 942390.8622656771], [-8.29141869514311, 739847.6929627117], [-3.671524149084499, -1428.311505270231], [-3.0595199464841505, 53.06670529138073], [6.785813169539075, -0.0340529061585978], [-0.040619920391570474, -2.8275017380153836e-06], [5.743044874720969, 0.03812047228991089], [-7.732823867411351, -128222.39847438055], [1.5462999506626502, -0.018964580281327432], [-5.203481835681667, 5976.737673366251], [-0.10772797922440525, -0.00014712771702832126], [4.703835812983462, -0.008055868544787296], [8.399236859825184, 0.08950179700701211], [-0.11297512984100067, -0.00017854651825284008], [-1.355571043544943, -1.6006460878607076], [-3.379104609325559, -29.425164858199395], [-1.5548682290298075, -0.28043733905342066], [8.030920361440707, 0.0343055440002432], [5.200258160282946, 0.17918106444784762], [6.12482379789245, 0.09255182015586844], [-8.155756462042046, 453922.047435642], [0.690305966726438, -0.05234170346314561], [-4.392572780905599, -2321.8665580978964], [8.422337485856197, 0.09067787734687804], [-0.7958154354912477, -0.3271546143881193], [8.027361778107355, 0.03363696313328257], [8.977658757356195, 0.007242881527578204], [8.596858818974958, 0.01903858071131908], [0.5914704967710982, -0.03792932244113269], [-3.0065804398882046, 100.58065017895808], [7.9774677344687746, 0.023188275437616743], [7.1440367193514405, -0.07761810132762113]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.34069, x1=6.53414, y=174288.51539\nx0=8.97475, x1=9.36487, y=841254662.89255\nx0=1.53502, x1=9.59383, y=61.03203\nx0=4.61411, x1=3.36472, y=171.58126\nx0=3.55276, x1=-4.70136, y=0.00258\nx0=0.48705, x1=9.06454, y=0.00147\nx0=1.11723, x1=7.66742, y=2.33946\nx0=0.52124, x1=6.69905, y=0.01272\nx0=0.74136, x1=-9.14532, y=15.43961\nx0=3.37511, x1=4.54619, y=252.17272\nx0=2.59509, x1=1.85634, y=5.87230\nx0=5.55285, x1=-7.73801, y=0.00000\nx0=9.90633, x1=-1.36471, y=0.04374\nx0=2.22687, x1=6.02918, y=124.82711\nx0=2.14650, x1=7.07370, y=222.10838\nx0=0.83698, x1=-2.37184, y=1.52512\nx0=4.19920, x1=9.84263, y=1360194.38269\nx0=3.41730, x1=-5.28143, y=0.00152\nx0=1.66259, x1=-2.53338, y=0.27585\nx0=6.51086, x1=6.78365, y=330700.91340\nx0=5.59739, x1=-8.58189, y=0.00000\nx0=3.54231, x1=3.92729, y=143.61820\nx0=1.76022, x1=-7.42224, y=0.01504\nx0=1.05039, x1=0.71883, y=1.03597\nx0=2.63913, x1=6.66961, y=647.10350\nx0=6.07282, x1=-8.08496, y=0.00000\nx0=2.39276, x1=-7.34009, y=0.00166\nx0=6.80684, x1=3.25786, y=517.15092\nx0=6.04179, x1=-3.99575, y=0.00076\nx0=0.97349, x1=5.33472, y=0.86648\nx0=3.08625, x1=6.45124, y=1436.93742\nx0=8.16627, x1=8.97564, y=153459037.98563\nx0=4.96876, x1=7.05578, y=81765.49418\nx0=1.66234, x1=-7.09069, y=0.02722\nx0=7.66155, x1=-9.38921, y=0.00000\nx0=1.64416, x1=-9.62700, y=0.00834\nx0=3.63011, x1=-7.36670, y=0.00008\nx0=0.00492, x1=-3.42453, y=79960350.85991\nx0=3.78425, x1=-7.88068, y=0.00003\nx0=2.57255, x1=0.09105, y=1.08984\nx0=9.33466, x1=-4.29757, y=0.00007\nx0=1.82306, x1=1.47715, y=2.42796\nx0=5.51043, x1=-5.01136, y=0.00019\nx0=1.82607, x1=-3.51105, y=0.12073\nx0=2.32648, x1=-1.35219, y=0.31927\nx0=2.71198, x1=-3.36413, y=0.03486\nx0=8.07591, x1=-4.35564, y=0.00011\nx0=5.58442, x1=-5.18676, y=0.00013\nx0=9.31079, x1=-5.13939, y=0.00001\nx0=4.97756, x1=5.73674, y=9967.79469\nx0=6.27032, x1=-0.41559, y=0.46629\nx0=2.68070, x1=-8.74721, y=0.00018\nx0=8.21071, x1=-8.51381, y=0.00000\nx0=3.13317, x1=1.93396, y=9.10363\nx0=3.15535, x1=4.04715, y=104.64509\nx0=9.91603, x1=9.14937, y=1305752101.06571\nx0=3.71239, x1=-8.22885, y=0.00002\nx0=1.95851, x1=-7.17008, y=0.00807\nx0=3.76166, x1=7.59422, y=23418.76532\nx0=3.47325, x1=-0.10312, y=0.87950\nx0=2.56051, x1=3.24307, y=21.09746\nx0=3.12858, x1=8.44132, y=15183.82925\nx0=5.68459, x1=-8.64613, y=0.00000\nx0=1.64446, x1=7.69648, y=45.98631\nx0=6.50188, x1=-5.56477, y=0.00003\nx0=1.03138, x1=1.17809, y=1.03707\nx0=9.76089, x1=-3.03204, y=0.00100\nx0=3.13367, x1=-0.67234, y=0.46396\nx0=5.70445, x1=-5.90882, y=0.00003\nx0=7.26748, x1=7.03332, y=1143897.39174\nx0=2.91921, x1=-2.59467, y=0.06206\nx0=9.39295, x1=-8.78861, y=0.00000\nx0=8.21264, x1=-9.09742, y=0.00000\nx0=7.91827, x1=2.06632, y=71.92204\nx0=3.74180, x1=7.06750, y=11226.68665\nx0=4.80288, x1=0.12570, y=1.21804\nx0=1.20251, x1=-2.35036, y=0.64828\nx0=7.40408, x1=4.93661, y=19599.10503\nx0=1.25107, x1=-9.31381, y=0.12415\nx0=3.71629, x1=8.79095, y=102755.03753\nx0=1.57233, x1=-9.35478, y=0.01450\nx0=5.39221, x1=-5.40719, y=0.00011\nx0=3.25904, x1=0.60505, y=2.04382\nx0=4.20770, x1=-7.52287, y=0.00002\nx0=5.47579, x1=-8.30560, y=0.00000\nx0=1.01003, x1=-1.22162, y=0.98788\nx0=9.96031, x1=-0.24060, y=0.57520\nx0=6.85072, x1=-2.69152, y=0.00563\nx0=8.90226, x1=-5.05636, y=0.00002\nx0=5.26177, x1=-3.13957, y=0.00544\nx0=9.86181, x1=2.45143, y=273.28223\nx0=9.25177, x1=7.91813, y=44739505.16973\nx0=7.94695, x1=5.37841, y=69446.17707\nx0=0.87756, x1=2.78022, y=0.69550\nx0=2.10691, x1=-6.74305, y=0.00657\nx0=7.44991, x1=-9.54391, y=0.00000\nx0=1.18138, x1=-9.35335, y=0.21034\nx0=4.45246, x1=-4.64847, y=0.00097\nx0=0.57243, x1=0.09330, y=0.94929\nx0=4.76282, x1=-7.71356, y=0.00001\nx0=2.17542, x1=-5.13368, y=0.01850\nx0=4.49731, x1=-0.58391, y=0.41566\nx0=3.19120, x1=3.10906, y=36.88291\nx0=2.87946, x1=-0.14427, y=0.85849\nx0=1.07319, x1=7.18237, y=1.66082\nx0=2.62296, x1=1.36637, y=3.73444\nx0=6.15797, x1=1.80682, y=26.69159\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.60523, x1=-9.25947, y=104.53962\nx0=6.87795, x1=-6.37274, y=0.00000\nx0=7.79637, x1=-8.58071, y=0.00000\nx0=3.03912, x1=-3.63193, y=0.01765\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**x1", "data": [[6.34068818010504, 6.534136582895652, 174288.51538635854], [8.974750978837733, 9.364866363962147, 841254662.8925469], [1.535024147540927, 9.5938304384702, 61.032025562886226], [4.614106623863275, 3.3647214167326, 171.5812621071885], [3.552763825382355, -4.701357985764762, 0.0025798267964163256], [0.48705496304633655, 9.064541177059692, 0.0014724402233993856], [1.1172250877937646, 7.667418607136117, 2.339455243898905], [0.5212416653679579, 6.699046183973142, 0.012718386578085605], [0.7413578109748897, -9.145316180634058, 15.43960711696013], [3.3751072837425227, 4.546194495093388, 252.17271718956073], [2.595085998191289, 1.8563445707257102, 5.8723017092936205], [5.552851451242738, -7.738005232129527, 1.7335280262708416e-06], [9.9063250650416, -1.3647052410120928, 0.04373940688479195], [2.226865187430926, 6.029179022629968, 124.82711262047435], [2.1465000874749247, 7.073699985015505, 222.10837602890473], [0.8369819952920583, -2.371838347389639, 1.525123033738489], [4.1992031975833655, 9.842629752684925, 1360194.382686577], [3.4172983237577057, -5.281426309975499, 0.001518424228248511], [1.662585008191753, -2.533377589029202, 0.275848811328136], [6.51086066375867, 6.783646624472588, 330700.9134046938], [5.597387970304208, -8.581890309205304, 3.8095287695537384e-07], [3.5423132941065703, 3.9272904879409793, 143.61820306282405], [1.7602170317898285, -7.422236978157059, 0.015043515212834086], [1.0503882066077637, 0.7188278034807265, 1.0359692302399006], [2.639125193549363, 6.669609927989356, 647.1035027283832], [6.072822734771304, -8.084963431682935, 4.6378383951299586e-07], [2.3927562666394504, -7.34009282205073, 0.0016551986232437314], [6.806837692786118, 3.257857377491508, 517.1509186070083], [6.041787165378281, -3.995749993972888, 0.00075623760357444], [0.9734937647844504, 5.334719602550361, 0.8664844151741173], [3.0862500838932974, 6.451240550066309, 1436.9374176967103], [8.166269485884222, 8.975635615754022, 153459037.98562902], [4.968757291461856, 7.055778393370154, 81765.49418212319], [1.6623366411893485, -7.090686381937625, 0.02722393822567042], [7.66155297631806, -9.389207201352264, 4.9769840589856146e-09], [1.644160327082984, -9.627000172155068, 0.00833883709677273], [3.6301090967036522, -7.366702801876688, 7.503055260765331e-05], [0.004923502980304306, -3.4245293391075693, 79960350.85991038], [3.7842515999962707, -7.880677085480039, 2.7869311049259483e-05], [2.5725452457627362, 0.0910472987080162, 1.0898392497153475], [9.334664247194901, -4.297572261681433, 6.775334300291517e-05], [1.823058800687189, 1.4771482682380324, 2.4279585473073193], [5.510429343143084, -5.011355635329149, 0.00019304394232099635], [1.8260708588601098, -3.5110508388237545, 0.12072530749578103], [2.3264808868927176, -1.3521915413504928, 0.3192655454569902], [2.7119754077146236, -3.3641294498679564, 0.03486347381452689], [8.075911362038841, -4.355643950355805, 0.00011183986677404574], [5.584418247813714, -5.186764314580488, 0.00013353696141740336], [9.310786218745235, -5.139393440617452, 1.0471234426756023e-05], [4.977558446942744, 5.736736275116288, 9967.794690397439], [6.270324559351895, -0.41558985808660687, 0.4662881227848185], [2.680697992692485, -8.74720930993485, 0.00017948413944943113], [8.210708122641613, -8.513806733755152, 1.64111937140588e-08], [3.133166574410996, 1.9339648943464276, 9.103631032930869], [3.1553518786754964, 4.047145073570299, 104.64508545139044], [9.916033594864793, 9.149365807354314, 1305752101.0657105], [3.7123881922893336, -8.2288526927282, 2.0530816815514015e-05], [1.958513102798447, -7.170075001903806, 0.008069845745922661], [3.7616626796075394, 7.594224940064404, 23418.765320740593], [3.473249880706156, -0.1031229832323195, 0.8795037337413801], [2.5605089531413068, 3.243068464391925, 21.09745856540155], [3.128578719079453, 8.441316043396593, 15183.829254306796], [5.684586874231389, -8.646125527485909, 2.9838604391542006e-07], [1.6444649881453, 7.6964766732102845, 45.98630728211256], [6.5018776946096715, -5.564772803551879, 2.9896739051508454e-05], [1.0313798414798825, 1.1780853786027397, 1.0370705512021179], [9.760885547712892, -3.0320358987030698, 0.0009996159156748755], [3.133672707642747, -0.6723431463844776, 0.463961280245982], [5.704451531261396, -5.908822888188194, 3.401465200787393e-05], [7.267483636847068, 7.033316882388373, 1143897.3917447992], [2.9192069175109463, -2.5946697062408237, 0.06205707644883397], [9.392949312514446, -8.788608966068557, 2.821134599918076e-09], [8.212644087793532, -9.097416160244746, 4.792559990009663e-09], [7.918267775431179, 2.0663249543116162, 71.92203626489024], [3.7418038415310413, 7.067502646871418, 11226.686649899015], [4.80287520647628, 0.12569752760749076, 1.2180441457571103], [1.202507126007104, -2.3503621816934483, 0.648283541347668], [7.4040826974445935, 4.936605076664563, 19599.105025222703], [1.251067183358895, -9.313810091674771, 0.1241499832155965], [3.7162858517349093, 8.790954252630506, 102755.03753337356], [1.572332529464136, -9.354782115917036, 0.01450006558787479], [5.392210570613376, -5.407188381308767, 0.00011045841988068195], [3.259041562936913, 0.6050457933587534, 2.0438211313529098], [4.2076975713076195, -7.522865849402924, 2.0202113755852883e-05], [5.475789935177676, -8.305602019055296, 7.35791793885638e-07], [1.0100307282653525, -1.2216218638503324, 0.9878813220698707], [9.960309223443396, -0.24059906950721555, 0.5751968354355661], [6.85072389440591, -2.6915215535036623, 0.0056311525525307785], [8.902257781054498, -5.056360519833416, 1.58119287059165e-05], [5.261767188295064, -3.1395746710629657, 0.0054444423675241846], [9.861809384278502, 2.4514263332036954, 273.2822300401894], [9.251770549120046, 7.918127079265549, 44739505.16973081], [7.946951503431986, 5.378410705152593, 69446.17707322497], [0.8775594061514731, 2.7802202459574055, 0.6954985806003617], [2.1069067609761145, -6.743053530832121, 0.006571163966220639], [7.449913482732789, -9.543914221887533, 4.745297877689574e-09], [1.1813781615618186, -9.353351205971336, 0.21033949918771108], [4.452463446667132, -4.648465205620331, 0.0009660592906630367], [0.5724331827752511, 0.09329536443262398, 0.9492854995288831], [4.7628245261260265, -7.7135577228308705, 5.905442203680937e-06], [2.1754161552089393, -5.133675906875121, 0.018499797447092802], [4.497311952527355, -0.583906088166108, 0.41565859028589747], [3.1912045236301516, 3.109060022323826, 36.88291357647644], [2.879455263164319, -0.14427425517312287, 0.8584862496219501], [1.073187272316492, 7.182367484540663, 1.6608209335789599], [2.6229613501184605, 1.3663732282913976, 3.73444466247333], [6.157974022648695, 1.8068230259651425, 26.69159272178671], [0.6052330394853112, -9.259470071873954, 104.53961573295388], [6.87795124373401, -6.372744073750265, 4.6034934423821785e-06], [7.7963678475103215, -8.580706003705947, 2.2229730618467103e-08], [3.0391232413058766, -3.6319259764300993, 0.01764793381620976]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.65754, x1=-7.32239, y=178.48004\nx0=-0.71632, x1=-9.62182, y=-33.15820\nx0=9.01921, x1=2.74471, y=33.97277\nx0=-0.99319, x1=3.03987, y=-4.58892\nx0=-6.98348, x1=9.73576, y=-330.96452\nx0=8.38362, x1=-0.24585, y=0.25335\nx0=0.45515, x1=-1.77776, y=0.71924\nx0=-1.16215, x1=-2.84620, y=-4.70718\nx0=9.65333, x1=1.93826, y=18.13304\nx0=2.41545, x1=2.70222, y=8.81876\nx0=-4.40800, x1=-5.83916, y=-75.14699\nx0=2.01660, x1=-5.09452, y=26.16956\nx0=-2.37043, x1=6.62227, y=-51.97700\nx0=-0.42168, x1=-8.08758, y=-13.79096\nx0=0.12220, x1=3.93538, y=0.94630\nx0=8.09290, x1=-0.21386, y=0.18506\nx0=0.93433, x1=-8.74804, y=35.75127\nx0=-3.15129, x1=-2.36338, y=-8.80088\nx0=3.24904, x1=6.61330, y=71.04960\nx0=9.71870, x1=-0.99353, y=4.79668\nx0=6.00223, x1=3.67246, y=40.47589\nx0=9.32780, x1=9.94986, y=461.72428\nx0=0.53441, x1=-7.15636, y=13.68447\nx0=-1.27110, x1=-5.80844, y=-21.44215\nx0=-6.90875, x1=-2.87818, y=-28.61582\nx0=1.15077, x1=6.90126, y=27.40411\nx0=1.01206, x1=9.11515, y=42.04388\nx0=5.88968, x1=1.46068, y=6.28306\nx0=6.54245, x1=8.76587, y=251.36251\nx0=0.50702, x1=-3.41259, y=2.95233\nx0=-7.91884, x1=0.98473, y=-3.83943\nx0=1.19672, x1=7.41306, y=32.88204\nx0=-9.71547, x1=2.21420, y=-23.81584\nx0=9.97775, x1=0.96090, y=4.60639\nx0=8.11913, x1=-6.65918, y=180.02038\nx0=-0.78305, x1=-8.18692, y=-26.24214\nx0=1.48707, x1=3.90539, y=11.34044\nx0=2.78752, x1=8.04489, y=90.20435\nx0=-4.43858, x1=-6.63736, y=-97.76969\nx0=-8.67958, x1=-3.17396, y=-43.71916\nx0=-6.62225, x1=-6.06286, y=-121.71118\nx0=2.83573, x1=9.16137, y=119.00242\nx0=-6.18023, x1=8.85593, y=-242.34997\nx0=4.40678, x1=3.38635, y=25.26712\nx0=8.75573, x1=-2.45638, y=26.41520\nx0=-3.95119, x1=-7.77946, y=-119.56307\nx0=-5.88157, x1=9.12170, y=-244.68941\nx0=6.21171, x1=-2.08878, y=13.55092\nx0=-1.26937, x1=-6.19769, y=-24.37919\nx0=-7.01044, x1=4.98975, y=-87.27163\nx0=-9.48971, x1=-0.36563, y=-0.63431\nx0=-5.56380, x1=-2.77826, y=-21.47265\nx0=-6.50177, x1=-1.37529, y=-6.14880\nx0=5.68406, x1=1.93437, y=10.63425\nx0=7.56668, x1=4.74404, y=85.14739\nx0=-9.67440, x1=7.32492, y=-259.53762\nx0=0.30451, x1=-1.64105, y=0.41003\nx0=8.86378, x1=-4.81095, y=102.57738\nx0=-2.81163, x1=-0.51232, y=-0.36899\nx0=-3.85416, x1=4.47739, y=-38.63226\nx0=0.15449, x1=-8.16379, y=5.14820\nx0=0.27330, x1=5.11423, y=3.57407\nx0=2.56392, x1=0.00350, y=0.00002\nx0=4.62873, x1=-0.26186, y=0.15869\nx0=5.59703, x1=3.52302, y=34.73422\nx0=8.19215, x1=9.41548, y=363.12218\nx0=0.35253, x1=7.16775, y=9.05583\nx0=-6.04994, x1=-1.83362, y=-10.17050\nx0=-4.07919, x1=9.75838, y=-194.22240\nx0=-4.33653, x1=-4.77667, y=-49.47239\nx0=-9.00059, x1=-0.05776, y=-0.01501\nx0=-1.54231, x1=8.48788, y=-55.55718\nx0=-9.41943, x1=-9.33660, y=-410.55558\nx0=-2.77785, x1=-5.10079, y=-36.13716\nx0=-4.70175, x1=-1.17043, y=-3.22045\nx0=6.00949, x1=8.74783, y=229.93662\nx0=-3.82983, x1=2.52905, y=-12.24794\nx0=-4.24159, x1=-8.22905, y=-143.61460\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.46886, x1=-1.77698, y=-14.94980\nx0=-3.79797, x1=4.80980, y=-43.93145\nx0=3.13729, x1=-4.26243, y=28.49966\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1**2 / 2", "data": [[6.657539439616851, -7.322391662181598, 178.48004299978322], [-0.7163186764702907, -9.621822145455516, -33.15819862875258], [9.019214874151224, 2.7447076424791312, 33.97276705109931], [-0.9931876065057565, 3.0398666478457805, -4.588918672103737], [-6.983479632012859, 9.735758230805093, -330.9645177069885], [8.383624710864126, -0.24584564662977648, 0.25335348235181304], [0.4551498364163358, -1.7777629589799702, 0.7192371335551804], [-1.1621459851983111, -2.8461983246222156, -4.707182190415652], [9.653327558107915, 1.9382586624915916, 18.133035613894915], [2.415447721947121, 2.7022153920252485, 8.818761015735499], [-4.407999022090943, -5.839155443563859, -75.14698612093493], [2.0166021049000076, -5.0945182506068925, 26.169562685684276], [-2.3704286642900874, 6.622273970502196, -51.97699679210586], [-0.42168434011046685, -8.087579076412597, -13.790961863286503], [0.12220375529146565, 3.9353795261889424, 0.9462977336230417], [8.092903092992678, -0.21385772017003646, 0.18506496516643037], [0.9343296805875028, -8.748038448079834, 35.751273440927456], [-3.1512898321986738, -2.363381499561843, -8.800878302521456], [3.2490444858560803, 6.613296168701957, 71.04959506593677], [9.718696569107419, -0.9935311691165403, 4.7966830232257305], [6.002227706195924, 3.672459113551289, 40.47589030977439], [9.327795509415413, 9.949857151668148, 461.72427957833725], [0.5344085689656666, -7.156361093693578, 13.684467719789243], [-1.271100694001932, -5.8084354236714635, -21.44214807929113], [-6.908746786370584, -2.87818311067773, -28.615815082215228], [1.1507725375980442, 6.901255334435266, 27.40410893456814], [1.0120574823140274, 9.115149668664692, 42.04388044840663], [5.889678589646037, 1.4606786225337203, 6.283056225193961], [6.542453597424384, 8.76586802315257, 251.36251374733945], [0.5070211900572481, -3.4125933844700036, 2.9523320670757816], [-7.918838632335408, 0.984730672492109, -3.839427123576299], [1.1967241801150958, 7.413056940408538, 32.88203917918871], [-9.715466026170423, 2.2141962095809973, -23.81583691590828], [9.97774817086728, 0.9609018867170409, 4.606389261683712], [8.119133443974299, -6.659183619945646, 180.02037593068724], [-0.7830469767286701, -8.186923550653182, -26.24214261775582], [1.487070761747125, 3.905387489791174, 11.340439880571601], [2.7875153821097562, 8.044890049446, 90.20435443836232], [-4.4385792579255146, -6.637356101614291, -97.76968612556026], [-8.679576451916484, -3.1739615237168994, -43.719164394091855], [-6.622245075019764, -6.062861042393093, -121.71118265671826], [2.8357287473267707, 9.161372538854057, 119.00241573654174], [-6.180232904212383, 8.855927751483922, -242.34997313153846], [4.406783372279843, 3.3863516355999774, 25.267124024836008], [8.755729356852285, -2.4563814708231213, 26.415203369773327], [-3.951191914208321, -7.779460092198418, -119.56306599260513], [-5.881571510654693, 9.121702212382672, -244.68940580566263], [6.211711621205232, -2.088784953694267, 13.550919040516336], [-1.2693741475331102, -6.197689226622385, -24.37918844149281], [-7.010437791637987, 4.989752064949348, -87.2716279583423], [-9.48970872062376, -0.3656273678584565, -0.6343081311384806], [-5.563797289936357, -2.7782556489671517, -21.472653453196514], [-6.50176513310252, -1.3752908919601268, -6.148800680374884], [5.684060123733445, 1.9343677784821303, 10.63424755715841], [7.566678638895688, 4.744036502052829, 85.14738954858528], [-9.674400584296519, 7.324924000196482, -259.5376192284554], [0.30451259406705944, -1.6410505590722746, 0.4100333544307966], [8.863781917522836, -4.810954803653649, 102.57738430557511], [-2.8116292669596854, -0.512321779604104, -0.368989236015592], [-3.854160046913253, 4.4773927969728415, -38.63226237384326], [0.15449062032321947, -8.163787227625125, 5.14820077597766], [0.2732953628567074, 5.1142325715733055, 3.574071322782309], [2.5639160226607753, 0.003500098892686765, 1.5704873085238917e-05], [4.628732759781908, -0.2618571107703751, 0.15869412726717685], [5.597033867689712, 3.5230174215583787, 34.73421760664705], [8.192145308462067, 9.4154821520527, 363.1221827137651], [0.3525270660881201, 7.167749367736803, 9.055826495730313], [-6.049943310187514, -1.833624795024523, -10.170498863335666], [-4.079185440436248, 9.758384549454906, -194.2223971380647], [-4.336525708501071, -4.776672597045232, -49.47238862400039], [-9.000585704292504, -0.05776157948604066, -0.01501477736316958], [-1.5423112795094234, 8.487876802166092, -55.55717748002216], [-9.419429660464802, -9.336598315301472, -410.5555819186757], [-2.777849957647504, -5.100792357809921, -36.13716493187033], [-4.701746440749002, -1.170425669152726, -3.2204524017911176], [6.009486201379708, 8.747831287718832, 229.93662037169025], [-3.829830506440879, 2.52904659457311, -12.24794479055409], [-4.241591599646835, -8.229053232251818, -143.61460167936616], [-9.468864142762804, -1.776984875233392, -14.949798959496087], [-3.79797447537581, 4.809796849211505, -43.9314474973828], [3.13728978142019, -4.262432540427521, 28.49965984952251]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.13443, x1=-8.20877, y=0.10297\nx0=7.16711, x1=-2.01540, y=-0.66514\nx0=7.60105, x1=-0.46465, y=1.73107\nx0=2.08872, x1=-9.34291, y=-1.73187\nx0=1.74688, x1=-7.53529, y=0.61696\nx0=5.70874, x1=9.47307, y=1.08547\nx0=8.68876, x1=-7.51705, y=0.44388\nx0=-3.01275, x1=-2.92629, y=0.25104\nx0=0.45919, x1=-5.94593, y=0.83651\nx0=-7.66158, x1=5.39995, y=-1.24589\nx0=-2.17652, x1=-8.04251, y=0.30814\nx0=9.52964, x1=-2.22427, y=0.12726\nx0=-8.88221, x1=-5.42464, y=-0.67489\nx0=2.59192, x1=-3.07962, y=-1.04281\nx0=3.07885, x1=-1.30487, y=0.03296\nx0=-8.21725, x1=-8.08794, y=0.43339\nx0=2.60587, x1=4.89121, y=0.18159\nx0=-2.71674, x1=2.61923, y=0.71443\nx0=-9.69808, x1=-8.09087, y=-0.12668\nx0=5.92311, x1=-6.28035, y=-0.70469\nx0=-8.93391, x1=-4.05152, y=0.57869\nx0=8.62068, x1=6.98421, y=1.10074\nx0=-8.62095, x1=6.04838, y=-1.40052\nx0=1.92340, x1=2.62489, y=-1.63193\nx0=-5.50635, x1=7.88923, y=-0.04941\nx0=0.68778, x1=-1.18988, y=0.47202\nx0=-4.68939, x1=-0.43098, y=1.81664\nx0=-4.24679, x1=-1.76303, y=-0.34144\nx0=-4.00057, x1=-0.99079, y=0.82991\nx0=-3.05172, x1=9.26707, y=0.17727\nx0=-3.30744, x1=-6.92511, y=0.26446\nx0=-6.04355, x1=0.54406, y=0.40615\nx0=2.74173, x1=4.99593, y=0.21781\nx0=-2.00728, x1=2.40742, y=1.34557\nx0=6.16295, x1=-1.52434, y=-0.01114\nx0=-3.38791, x1=2.37546, y=-0.35142\nx0=6.94312, x1=0.56439, y=1.03597\nx0=1.55802, x1=7.92497, y=-0.14185\nx0=-8.89167, x1=4.18630, y=0.51040\nx0=0.34606, x1=8.53789, y=-0.42862\nx0=-8.85090, x1=4.19639, y=0.53573\nx0=-8.61517, x1=9.08257, y=1.36407\nx0=-3.20997, x1=-3.84304, y=-0.10439\nx0=-7.68077, x1=-7.51630, y=-0.65268\nx0=-7.29224, x1=-7.60435, y=-0.41816\nx0=9.83456, x1=-5.97934, y=-0.76032\nx0=3.28326, x1=9.53958, y=0.28052\nx0=-3.07368, x1=3.55418, y=0.12433\nx0=-1.48793, x1=-0.80990, y=-1.37441\nx0=-3.61143, x1=-8.20339, y=-0.30998\nx0=7.24508, x1=-1.07641, y=0.77843\nx0=2.12086, x1=-8.89010, y=-1.46702\nx0=-7.47700, x1=0.85763, y=-1.21658\nx0=5.42847, x1=8.05311, y=0.29846\nx0=2.67762, x1=-7.65422, y=0.17760\nx0=-6.56970, x1=-4.59355, y=0.06701\nx0=-6.86238, x1=6.28562, y=-1.09469\nx0=6.20542, x1=2.37850, y=0.11229\nx0=5.50801, x1=-3.14523, y=1.39967\nx0=4.86461, x1=-4.54028, y=0.33857\nx0=-0.84573, x1=-4.46581, y=0.36537\nx0=-1.92553, x1=-3.18055, y=1.87406\nx0=-4.95347, x1=0.17069, y=1.91394\nx0=-2.19981, x1=-7.89014, y=0.05846\nx0=8.67576, x1=-8.77849, y=-1.08719\nx0=-1.90172, x1=-3.64628, y=1.65566\nx0=-1.59200, x1=2.42030, y=1.50157\nx0=-6.16531, x1=8.68379, y=-0.17353\nx0=0.97085, x1=-2.84416, y=-1.57825\nx0=5.14002, x1=8.25418, y=0.70904\nx0=-9.50042, x1=6.18561, y=0.15043\nx0=0.24771, x1=2.82091, y=-0.46536\nx0=-6.61545, x1=-7.11302, y=-0.44035\nx0=-2.74358, x1=-6.67337, y=-0.71691\nx0=-5.65793, x1=-1.30958, y=0.30232\nx0=2.13289, x1=-0.51881, y=1.46959\nx0=-3.88855, x1=2.03387, y=-0.60698\nx0=1.62861, x1=-1.83952, y=-0.53011\nx0=-6.86117, x1=-9.99469, y=0.91997\nx0=-2.67250, x1=-7.85596, y=0.00179\nx0=5.66131, x1=0.40440, y=-1.07114\nx0=-0.11810, x1=5.03843, y=-0.07548\nx0=9.09763, x1=-0.51306, y=0.55994\nx0=-9.19407, x1=6.81556, y=-0.39404\nx0=-8.93234, x1=-9.90982, y=0.83649\nx0=-9.81359, x1=7.04246, y=0.54994\nx0=-6.79665, x1=-7.51393, y=-0.32767\nx0=8.17088, x1=1.52295, y=0.09089\nx0=-5.35879, x1=-3.99220, y=-1.05294\nx0=-3.20397, x1=1.09343, y=0.05728\nx0=-1.36254, x1=5.06649, y=-0.67852\nx0=-6.58663, x1=-8.98532, y=0.54083\nx0=-1.21017, x1=-6.46421, y=-1.84077\nx0=-5.89833, x1=-6.40988, y=0.74484\nx0=-0.65666, x1=1.45495, y=-0.14113\nx0=2.29399, x1=-8.00935, y=-0.23202\nx0=4.60084, x1=2.73968, y=1.82919\nx0=8.54763, x1=1.76014, y=-0.28945\nx0=-8.60827, x1=4.89371, y=-0.26284\nx0=6.41341, x1=1.87605, y=-0.07806\nx0=-3.26817, x1=7.77262, y=0.02052\nx0=6.54667, x1=-5.11950, y=0.20625\nx0=3.31938, x1=-4.65128, y=0.02160\nx0=4.54258, x1=8.61631, y=1.36134\nx0=-7.98585, x1=7.94939, y=0.18887\nx0=0.24090, x1=-7.88714, y=-0.01582\nx0=7.58999, x1=2.75328, y=-1.78697\nx0=-5.88544, x1=8.28410, y=-0.32303\nx0=5.44080, x1=-8.10785, y=0.37483\nx0=-3.30280, x1=-5.29974, y=0.17790\nx0=-9.20251, x1=4.51250, y=0.08754\nx0=-9.65924, x1=8.37412, y=-0.23093\nx0=-7.36542, x1=3.00269, y=1.74901\nx0=1.01568, x1=-7.31837, y=0.86746\nx0=6.84731, x1=5.95980, y=1.01392\nx0=-9.04034, x1=-4.52040, y=0.14312\nx0=1.12467, x1=-5.19642, y=0.83960\nx0=-7.62612, x1=-4.06675, y=1.17231\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=8.19481, x1=-2.01361, y=-0.80768\nx0=-6.60478, x1=0.46785, y=-0.56422\nx0=0.12058, x1=8.68212, y=-0.17723\nx0=-8.48886, x1=-0.35280, y=-1.51110\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 2 * sin(x0) * cos(x1)", "data": [[6.134430026829939, -8.208768595079778, 0.10297162848849477], [7.167107552350952, -2.015401956665208, -0.6651370861684311], [7.601047775146576, -0.46464874348881935, 1.7310695179663909], [2.088724949895129, -9.342907572614369, -1.731872668405879], [1.7468787055285162, -7.535287265966466, 0.6169642528019428], [5.708743350613595, 9.473069139304457, 1.085465895732806], [8.688764283697687, -7.517048006406172, 0.44388207946678815], [-3.0127507735101178, -2.926293745543398, 0.2510386095138085], [0.45918973422855736, -5.945929201815079, 0.8365070636049733], [-7.661578061322329, 5.399954936533277, -1.2458940011849515], [-2.1765158966497555, -8.042506018592967, 0.30813614664136624], [9.529636932817358, -2.2242726213135944, 0.12726453839722027], [-8.882213800479715, -5.424642285300585, -0.6748902898268567], [2.591918556030979, -3.0796183490799, -1.0428128874282367], [3.0788462426603207, -1.3048663425300884, 0.03295871436107187], [-8.217247514724251, -8.087935240829099, 0.43339324873160495], [2.6058747267674516, 4.891208975566849, 0.18158899072461065], [-2.7167440885471184, 2.6192343165465104, 0.7144323137611627], [-9.698079797908377, -8.090867453505723, -0.12668412754022484], [5.923106766054524, -6.280353599456721, -0.704692651833266], [-8.93390722738295, -4.051516744360444, 0.5786886111065118], [8.620676835129114, 6.984208776989508, 1.100739606115382], [-8.62095313942607, 6.048379993715095, -1.4005162769880597], [1.923398402495275, 2.6248920800333586, -1.6319254240808714], [-5.50635028293557, 7.889229480353581, -0.04940907225860842], [0.6877810075990372, -1.1898803443573396, 0.4720184175571007], [-4.689392880662724, -0.43097774310649584, 1.8166350025491], [-4.246792449425431, -1.7630345411873964, -0.34143830747607473], [-4.00056557956761, -0.9907854172355002, 0.8299106471924569], [-3.051721793684095, 9.267074120195552, 0.17727235859961996], [-3.307441968092233, -6.92511252987204, 0.2644555539398003], [-6.043554242440039, 0.5440576784459914, 0.40615080292069683], [2.7417279270878208, 4.9959278162806235, 0.21781368681438942], [-2.0072790749291087, 2.4074248981136943, 1.3455707059242161], [6.162952406448472, -1.5243372022253094, -0.011140924637039949], [-3.387912063263827, 2.3754609617814726, -0.3514157201506916], [6.943118723939524, 0.5643937196858921, 1.035971980141795], [1.5580222392997012, 7.9249698686020125, -0.14184568114444152], [-8.891672758947664, 4.186303093347725, 0.5103977848022903], [0.3460593914294172, 8.537887546812616, -0.4286220470128143], [-8.850901085811635, 4.196387893270899, 0.5357320984899003], [-8.615169662366814, 9.08256841155653, 1.3640705626606298], [-3.2099697831733316, -3.843039173667546, -0.10438649322327213], [-7.680771529372499, -7.516302539477506, -0.6526816071590817], [-7.292235243124523, -7.604354873345935, -0.41815673236821155], [9.834562887817619, -5.979335743150626, -0.7603230536336174], [3.2832578265214565, 9.539581488683226, 0.28052475877376337], [-3.0736801970903427, 3.5541843695972517, 0.12433149643317148], [-1.487932496668595, -0.8098965474686004, -1.37441452950036], [-3.6114266460786526, -8.203392466537993, -0.30998473384125363], [7.24508467294379, -1.0764105178646695, 0.7784305512813375], [2.1208588142867857, -8.890095377862082, -1.4670198534618086], [-7.4770031021011345, 0.8576331301782218, -1.2165802014040923], [5.428470458623181, 8.053113409226281, 0.2984618846860197], [2.6776192304910733, -7.654219349453069, 0.17760251152578402], [-6.569699760655512, -4.5935519304223815, 0.06701120910097864], [-6.862376556575618, 6.285621818687208, -1.0946912865606844], [6.205421583416399, 2.378497088450642, 0.11228642742616599], [5.508014996692934, -3.145226692598044, 1.3996662349696478], [4.864613110741459, -4.540275947155528, 0.33856817001044015], [-0.8457251363416987, -4.465812764355399, 0.3653721686686926], [-1.9255280284792047, -3.180551350441762, 1.8740563233318666], [-4.953465016331807, 0.17068747865746658, 1.9139401918417402], [-2.1998142402226524, -7.890139700946078, 0.058462497832118925], [8.675763561280718, -8.778494284502429, -1.087189789145524], [-1.901723609694546, -3.6462811857496664, 1.655662513769465], [-1.5920042667145058, 2.420299684899625, 1.5015673261347777], [-6.165311541562144, 8.683788407841664, -0.17353225168001302], [0.9708498468835103, -2.8441558612597433, -1.5782494089417531], [5.140021563302305, 8.254184711371579, 0.7090429173989107], [-9.500424531788159, 6.185611687063364, 0.15042994566389253], [0.24770623344229747, 2.820910317501415, -0.4653633364260399], [-6.61545330966506, -7.113019055032879, -0.44035253436630445], [-2.7435819161561037, -6.6733656725184325, -0.7169092191710459], [-5.65793265187996, -1.3095793070096295, 0.30231614157872005], [2.1328912811996474, -0.5188085140122833, 1.469594639210113], [-3.8885523823621204, 2.0338662942401964, -0.6069815962078484], [1.6286069163527976, -1.839519229040043, -0.5301137074480716], [-6.861165445853496, -9.99469322051076, 0.9199670076124852], [-2.6724972685757686, -7.855960745058688, 0.001789430224120214], [5.661311677386557, 0.40439940006206143, -1.0711383619386028], [-0.11809929658214813, 5.038434939582883, -0.07547862412703261], [9.097628440587556, -0.5130628739951568, 0.5599406431409436], [-9.194072486132912, 6.815561483361119, -0.3940359862342691], [-8.932337305751739, -9.909818060578031, 0.8364919478560061], [-9.813593553708701, 7.042455116037164, 0.5499413058964341], [-6.796645507945868, -7.5139255293055935, -0.32766580482688035], [8.1708791310215, 1.5229495318459119, 0.09089400893557473], [-5.358792464551618, -3.99219871786525, -1.0529428430869683], [-3.2039719190147835, 1.0934260072812592, 0.057282525493477586], [-1.3625444312031494, 5.066494494101306, -0.6785190842960876], [-6.586626959040657, -8.985316184206706, 0.5408280734066548], [-1.210169061392243, -6.464209895266779, -1.8407729818773164], [-5.898326298837788, -6.409882064027201, 0.7448385780981487], [-0.6566632996435988, 1.4549461160772186, -0.14113169907227835], [2.293993530323686, -8.009346841329313, -0.23201658380687207], [4.600836138312783, 2.7396784973849684, 1.8291872505262017], [8.54763059390891, 1.7601432321651593, -0.28944773777619587], [-8.608268414928498, 4.893713519201157, -0.26283834865952765], [6.413414736596668, 1.8760475198780586, -0.07805535119652825], [-3.2681702154020904, 7.772618502063633, 0.02051987837872043], [6.54666613387905, -5.119504000509103, 0.20625081736266163], [3.319375097403615, -4.651284217550133, 0.02159899076557673], [4.542583573358632, 8.61630575868389, 1.3613433896477163], [-7.985847582014786, 7.949389486488478, 0.1888722514304328], [0.24089780624324142, -7.8871412670050205, -0.015819193224694463], [7.58999290261734, 2.7532775732848958, -1.78696888101334], [-5.885435023316365, 8.284097461067741, -0.3230273954985711], [5.440802139712632, -8.107846068146145, 0.37482680106296157], [-3.3028037943143573, -5.299735313989748, 0.1778986937640985], [-9.2025089322807, 4.512502956377901, 0.08754143550917075], [-9.659242884962824, 8.374116491232307, -0.23092733055916378], [-7.365417783716346, 3.0026881301198536, 1.7490058861217348], [1.0156789623899858, -7.318371655290483, 0.8674569169027302], [6.8473098745268075, 5.95980186087103, 1.0139232902598794], [-9.040344552870534, -4.5203960158678775, 0.14312467378785085], [1.1246666154730338, -5.196416284027922, 0.8396023212625258], [-7.626116696319894, -4.066749063129755, 1.1723120652461945], [8.194812680149496, -2.013613456203844, -0.8076776503666212], [-6.604775575460589, 0.46784574512483523, -0.5642215828816044], [0.12058044593524997, 8.682117519235813, -0.17722628963398532], [-8.488864396546841, -0.35280212383907994, -1.511102245763916]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.23479, x1=5.37892, y=0.19119\nx0=-8.09917, x1=0.48040, y=0.39394\nx0=5.80062, x1=-1.02742, y=0.57679\nx0=-9.65220, x1=4.72947, y=0.67203\nx0=9.36002, x1=-6.39251, y=-0.99380\nx0=7.34339, x1=-4.69372, y=0.70034\nx0=8.09989, x1=3.40979, y=0.05409\nx0=-7.27708, x1=-3.06368, y=0.03882\nx0=-0.06176, x1=7.68067, y=0.07083\nx0=-2.86401, x1=-2.51114, y=0.28354\nx0=9.40302, x1=5.35249, y=-0.89319\nx0=3.03682, x1=7.92493, y=0.67318\nx0=-6.39887, x1=6.10872, y=-0.17199\nx0=-3.08839, x1=-4.15043, y=-0.48176\nx0=-7.42048, x1=0.58782, y=0.94839\nx0=1.42904, x1=3.66464, y=-0.21729\nx0=7.42979, x1=8.75216, y=0.32635\nx0=2.71931, x1=-3.55860, y=0.16684\nx0=8.74296, x1=-1.06687, y=0.44865\nx0=-0.38492, x1=8.26761, y=0.29848\nx0=7.57248, x1=0.44674, y=-0.91156\nx0=-1.67574, x1=0.49564, y=-0.56957\nx0=-9.70943, x1=5.58344, y=0.85507\nx0=-8.61369, x1=-4.97044, y=0.27475\nx0=-4.13136, x1=-9.12783, y=-0.01273\nx0=5.91752, x1=9.41695, y=-0.00204\nx0=7.61650, x1=-4.29633, y=0.49632\nx0=1.91037, x1=7.18934, y=-0.24504\nx0=-6.21954, x1=-8.54697, y=0.04050\nx0=1.98671, x1=-2.62803, y=0.04084\nx0=-1.03187, x1=6.51841, y=0.99283\nx0=-5.74660, x1=-0.39285, y=-0.70688\nx0=3.77452, x1=9.88697, y=-0.13334\nx0=1.16220, x1=8.11375, y=-0.60052\nx0=6.31360, x1=-3.26607, y=0.00284\nx0=-7.43577, x1=7.63565, y=-0.77021\nx0=4.77615, x1=-6.65299, y=-0.75825\nx0=-5.58834, x1=7.11061, y=0.79070\nx0=-3.69796, x1=3.34369, y=-0.06774\nx0=-6.26575, x1=-0.91011, y=-0.02349\nx0=0.18445, x1=0.28500, y=0.27039\nx0=8.62438, x1=2.79993, y=0.06151\nx0=-8.10874, x1=1.55186, y=0.28009\nx0=2.02643, x1=-0.16078, y=0.10144\nx0=7.55066, x1=-7.44153, y=0.79164\nx0=-1.01965, x1=-4.19591, y=0.50265\nx0=-6.18010, x1=-8.18845, y=0.08925\nx0=1.95610, x1=-5.69343, y=-0.19707\nx0=-7.79323, x1=9.78327, y=0.13702\nx0=3.63190, x1=-4.85863, y=0.56124\nx0=-2.13027, x1=7.94460, y=-0.03627\nx0=9.09257, x1=-5.64479, y=-0.83402\nx0=9.17595, x1=-6.52973, y=-0.92409\nx0=-0.56686, x1=-3.48771, y=0.12940\nx0=5.02144, x1=-1.22572, y=0.77601\nx0=0.76427, x1=3.65420, y=-0.23102\nx0=-2.89067, x1=-3.75318, y=-0.27998\nx0=-3.39550, x1=-9.44058, y=0.00734\nx0=8.40812, x1=-2.07612, y=0.02326\nx0=-6.44059, x1=-2.99123, y=0.01757\nx0=-6.89589, x1=4.66275, y=-0.54805\nx0=-3.67772, x1=6.88687, y=-0.66233\nx0=-6.33112, x1=-2.93529, y=0.00740\nx0=-8.09570, x1=-9.53980, y=0.02358\nx0=1.44313, x1=0.30615, y=0.81907\nx0=-7.99208, x1=4.28097, y=-0.29480\nx0=3.45153, x1=4.11519, y=0.41815\nx0=4.27979, x1=-0.73061, y=0.12709\nx0=0.90349, x1=-3.34314, y=-0.09828\nx0=2.19984, x1=4.37133, y=0.09086\nx0=3.48672, x1=-5.09631, y=0.72039\nx0=8.50991, x1=-8.75992, y=-0.06435\nx0=9.13816, x1=-7.86067, y=-0.64060\nx0=-3.31576, x1=-6.77892, y=-0.93654\nx0=-0.13256, x1=-3.11634, y=-0.00249\nx0=-2.73908, x1=-0.53489, y=0.79394\nx0=-4.51621, x1=-9.66438, y=-0.05637\nx0=-8.69092, x1=-0.52337, y=-0.43748\nx0=-6.61962, x1=8.35112, y=-0.24727\nx0=-5.41502, x1=-9.82617, y=-0.19221\nx0=7.36039, x1=-1.49678, y=-0.73204\nx0=-1.49874, x1=-4.94019, y=0.61008\nx0=7.50647, x1=-1.75984, y=-0.61511\nx0=4.40080, x1=-7.25774, y=-0.27629\nx0=-6.21590, x1=-1.34598, y=-0.07878\nx0=1.24227, x1=7.89600, y=-0.66268\nx0=1.80488, x1=-5.78661, y=-0.40785\nx0=0.88317, x1=7.60375, y=-0.76603\nx0=4.26705, x1=8.82614, y=-0.03454\nx0=-2.92401, x1=3.58341, y=-0.20755\nx0=-6.01883, x1=-2.73743, y=-0.07752\nx0=9.75365, x1=-0.14215, y=0.87855\nx0=3.57280, x1=1.08593, y=-0.68324\nx0=-6.96068, x1=-6.01835, y=-0.84269\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.52177, x1=-9.61597, y=-0.09444\nx0=-8.86229, x1=-0.04028, y=-0.66455\nx0=9.78103, x1=-7.11622, y=-0.78701\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(1.5 * x0) * cos(0.5 * x1)", "data": [[8.234789736831495, 5.378922123940928, 0.1911944232267616], [-8.099171687985955, 0.4804021784838479, 0.39393569185636995], [5.800624657982441, -1.0274179609237084, 0.5767871937219394], [-9.652200271493466, 4.729471114307529, 0.6720275602735039], [9.360019170487647, -6.392514449073456, -0.9937991012244833], [7.343386923514068, -4.693719599850789, 0.7003421901239488], [8.0998861148752, 3.4097902284982204, 0.05409391145735263], [-7.277084436693107, -3.063684626582564, 0.038819770737881315], [-0.06176137009137328, 7.680674469029594, 0.07083000315854167], [-2.864009099089846, -2.511144519272417, 0.28354087468619804], [9.40301822338347, 5.3524907230427115, -0.8931897895988431], [3.036822130692599, 7.924934226904071, 0.6731820670088682], [-6.3988659232028215, 6.108722474039151, -0.1719949986363341], [-3.088386867445516, -4.1504307759142005, -0.4817605844355526], [-7.420476656818944, 0.5878155254810764, 0.9483924845695209], [1.4290373663127411, 3.6646432314460213, -0.2172912208105704], [7.429789720307319, 8.752155728654998, 0.326345241575156], [2.719312563341191, -3.558603033926282, 0.16684176510691553], [8.742960102379516, -1.0668683997383894, 0.4486501906123647], [-0.3849237239007799, 8.267610856497022, 0.29848375020750617], [7.57247982366647, 0.44674105385734464, -0.9115606935839157], [-1.675735577691654, 0.4956421970869016, -0.5695696798269453], [-9.709432806988234, 5.583435488276473, 0.8550745025136945], [-8.613694605841282, -4.970442954060362, 0.2747495607100922], [-4.131358991500667, -9.127828511825788, -0.0127279262345428], [5.91752082482129, 9.416948985311919, -0.002041028491727952], [7.6164959448367355, -4.296330559764893, 0.4963216087687293], [1.9103742540889002, 7.1893407261419355, -0.24504122702983658], [-6.219543905301752, -8.546971878144706, 0.040504723311185896], [1.9867134409852039, -2.628032417818429, 0.04084333446839459], [-1.0318734591967864, 6.518407011613348, 0.9928294675436056], [-5.746604806370723, -0.39285258877429996, -0.7068814215866276], [3.774521649792895, 9.886965952666102, -0.13334316366921378], [1.1621991914637153, 8.113749640457854, -0.6005199127469686], [6.313599049682779, -3.2660688500548085, 0.0028365233728207028], [-7.435772002006549, 7.635651145659761, -0.7702107094603997], [4.7761483286067445, -6.6529905759690955, -0.7582501560500555], [-5.588337759473598, 7.11060901361504, 0.7906981825110649], [-3.6979562750033175, 3.3436886498122824, -0.06773978841071869], [-6.265749816401924, -0.9101109077456542, -0.02348911748073598], [0.18444908101598045, 0.2849960894100452, 0.2703886570923575], [8.624375907151482, 2.799928860040037, 0.061506045215347235], [-8.108743123438432, 1.5518584025187927, 0.2800943999568666], [2.0264305735107673, -0.16078252735742637, 0.1014416125261627], [7.550664873137961, -7.441533882832414, 0.791642116508477], [-1.019645324048815, -4.1959132866848226, 0.5026516290908553], [-6.180102313803459, -8.188449564706069, 0.08925443202170784], [1.9561015294517006, -5.693430674932918, -0.19706630698109787], [-7.793229769538632, 9.783273722364179, 0.13701922152022794], [3.6319033426570524, -4.858630997118587, 0.5612369882801853], [-2.1302728820229655, 7.944595501012849, -0.03627403954785087], [9.09256993153791, -5.644791454320344, -0.8340210612324829], [9.17595248500259, -6.529726578108828, -0.9240856999144081], [-0.5668592713537102, -3.4877147153382593, 0.1294021549782766], [5.021436338676599, -1.225724191273308, 0.776007930088468], [0.7642653390726277, 3.6542018362434554, -0.23101809142748087], [-2.8906659224546782, -3.753182899347376, -0.2799771684202069], [-3.395499188685516, -9.440584258164503, 0.007336775156952817], [8.408117878004326, -2.0761218203473604, 0.023256450003875277], [-6.4405888953348285, -2.9912281700784433, 0.01756990497809398], [-6.895894197000601, 4.662747605651262, -0.5480485387432498], [-3.6777190705117384, 6.886871851012444, -0.6623332912598348], [-6.331122188473188, -2.9352927853608035, 0.00739750496997788], [-8.09570218863924, -9.539795118883166, 0.02358456534936044], [1.443134903478425, 0.30615426309790195, 0.8190701118699946], [-7.992082117632768, 4.280967084084633, -0.29479580954262724], [3.4515290397667027, 4.115192855944416, 0.418149839340215], [4.2797880618564115, -0.7306073907455097, 0.12709457084442272], [0.9034945300119936, -3.343143949547951, -0.0982769484751764], [2.1998438147167914, 4.37133405873279, 0.09086260845976597], [3.486720768985869, -5.0963068600036365, 0.7203902027126318], [8.509914950543337, -8.759918423194936, -0.06435464850190385], [9.138155289575579, -7.860672298673106, -0.6406014743324341], [-3.3157601616227605, -6.7789163053541905, -0.9365428781501128], [-0.13255693775925437, -3.116337856693585, -0.002494196168610543], [-2.739079456884596, -0.534892644842893, 0.7939354612566454], [-4.5162064645094, -9.664382537403293, -0.05636581815803921], [-8.690920131247115, -0.5233745101349836, -0.43747595295420816], [-6.619618400859391, 8.3511236643937, -0.24726811590211253], [-5.415019242874668, -9.8261689016142, -0.19220563152065664], [7.3603898969573045, -1.4967796716898079, -0.7320433020325918], [-1.4987366492908034, -4.940189369720985, 0.6100770308456863], [7.506468077868014, -1.759843948433259, -0.615113151582797], [4.4008013136943, -7.257738402018427, -0.27629049194938277], [-6.215902812107585, -1.3459753822875697, -0.07878471395060173], [1.242269424552859, 7.8959979868029855, -0.6626791788672992], [1.804876085603496, -5.786607590014443, -0.4078532497682991], [0.8831729985704069, 7.603751304997104, -0.7660335467795536], [4.267050362545717, 8.826139708841158, -0.03453537421268787], [-2.924007503067438, 3.583406760815693, -0.20754763785875358], [-6.01883402428663, -2.737426637749585, -0.07751777984871264], [9.753652052603975, -0.14214776584508648, 0.8785460511168731], [3.572795998412186, 1.085932730927892, -0.6832428567227657], [-6.960677510050877, -6.018354499779681, -0.842691088161517], [-9.521765730381196, -9.615966750194156, -0.09444056321896327], [-8.862294153006031, -0.040282830184821705, -0.6645490554302053], [9.781033319274883, -7.116218652143582, -0.7870064069135362]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-6.47611, x1=-9.90847, y=2089.56468\nx0=7.51521, x1=-4.11219, y=2777.92369\nx0=-1.69031, x1=3.55076, y=15.74592\nx0=-7.79687, x1=7.07326, y=4187.49170\nx0=1.32204, x1=3.39877, y=3.12117\nx0=-7.29940, x1=4.36829, y=3232.97639\nx0=2.45849, x1=9.69690, y=58.99045\nx0=7.07612, x1=-7.42078, y=2187.79610\nx0=-8.66438, x1=5.90869, y=6297.72767\nx0=-2.35165, x1=0.50948, y=43.20960\nx0=-9.23838, x1=7.15518, y=8091.14751\nx0=-2.70063, x1=-0.45774, y=73.45264\nx0=-6.19352, x1=-4.43500, y=1723.31233\nx0=-0.70480, x1=-8.14080, y=41.87396\nx0=1.70267, x1=6.46796, y=17.91785\nx0=-7.85261, x1=-0.41624, y=4287.10959\nx0=0.34563, x1=-7.30488, y=33.95853\nx0=-7.79545, x1=-8.62023, y=4212.36931\nx0=-7.92038, x1=-0.07039, y=4432.29331\nx0=-5.73617, x1=-2.69515, y=1277.71667\nx0=-3.94441, x1=3.84374, y=306.97384\nx0=-8.92026, x1=1.94589, y=7041.28012\nx0=1.94340, x1=-7.46417, y=42.24546\nx0=-5.57321, x1=6.04744, y=1150.11056\nx0=7.71409, x1=7.16239, y=3100.54483\nx0=-3.40166, x1=-1.25041, y=175.28849\nx0=-1.84095, x1=2.50681, y=18.36027\nx0=-6.53823, x1=6.85759, y=2123.59040\nx0=5.05560, x1=1.32104, y=523.60176\nx0=-8.33517, x1=3.70864, y=5409.03514\nx0=-0.04094, x1=6.31430, y=13.62094\nx0=-4.22075, x1=4.59125, y=398.50314\nx0=9.92039, x1=-6.45949, y=8736.34055\nx0=-1.09991, x1=-8.16690, y=44.31032\nx0=6.72734, x1=-1.46582, y=1746.28340\nx0=6.30990, x1=-4.03684, y=1346.17595\nx0=4.22199, x1=-0.27916, y=242.79816\nx0=-1.13717, x1=8.27269, y=29.08882\nx0=9.84653, x1=-7.03085, y=8477.18324\nx0=5.72432, x1=-4.48925, y=900.72326\nx0=8.69101, x1=-3.82763, y=5060.02160\nx0=-9.05173, x1=-7.74228, y=7492.49413\nx0=-2.25560, x1=-5.62888, y=58.83178\nx0=1.94524, x1=2.26950, y=7.26354\nx0=-0.37679, x1=-1.09600, y=1.77024\nx0=-7.51579, x1=8.70658, y=3644.53876\nx0=-9.87619, x1=9.14829, y=10509.88654\nx0=-3.98882, x1=-6.63185, y=345.23792\nx0=-6.08124, x1=9.23215, y=1625.90904\nx0=4.35148, x1=-3.93634, y=287.83590\nx0=-9.77448, x1=-4.26018, y=10075.18424\nx0=-7.76508, x1=8.95373, y=4134.99881\nx0=6.59647, x1=-5.76594, y=1628.77634\nx0=-0.90159, x1=0.03941, y=1.35496\nx0=-1.40031, x1=9.42458, y=41.57761\nx0=7.98452, x1=2.84941, y=3556.57154\nx0=-0.73247, x1=-9.55038, y=55.83606\nx0=1.20000, x1=2.68763, y=1.26964\nx0=9.93340, x1=-4.76297, y=8772.18980\nx0=-5.78547, x1=-5.59022, y=1335.21497\nx0=-3.43843, x1=5.19785, y=188.74145\nx0=6.98245, x1=-7.85097, y=2075.25748\nx0=6.62606, x1=-5.79623, y=1659.29835\nx0=-1.27952, x1=0.26929, y=4.54213\nx0=-1.91269, x1=-5.12069, y=38.61247\nx0=-8.36117, x1=5.74926, y=5482.58800\nx0=1.48154, x1=7.14178, y=19.92668\nx0=-8.25548, x1=2.28620, y=5207.77670\nx0=6.92391, x1=-1.27148, y=1968.44165\nx0=2.01942, x1=-1.07290, y=10.04372\nx0=9.15061, x1=-2.85314, y=6252.03251\nx0=9.91960, x1=0.13020, y=8706.06086\nx0=8.69045, x1=0.47201, y=5047.16417\nx0=2.56482, x1=-0.43049, y=26.92513\nx0=-1.25364, x1=-0.43150, y=4.96484\nx0=-6.07746, x1=7.73636, y=1610.89907\nx0=6.95219, x1=-6.73735, y=2029.48857\nx0=-8.66840, x1=-6.84446, y=6327.82599\nx0=9.65721, x1=-7.91115, y=7836.29302\nx0=6.43636, x1=-3.63812, y=1459.78925\nx0=8.87231, x1=0.25851, y=5497.86265\nx0=-6.07985, x1=9.46746, y=1626.46757\nx0=-9.37883, x1=-4.52710, y=8577.15161\nx0=8.63556, x1=-9.57505, y=4972.56379\nx0=-6.93926, x1=0.07983, y=2652.81382\nx0=-7.51459, x1=-8.10762, y=3654.07427\nx0=4.32974, x1=-1.65027, y=273.28032\nx0=4.42150, x1=-1.91234, y=299.49013\nx0=-5.75433, x1=-2.79318, y=1293.66100\nx0=-4.03360, x1=5.77389, y=341.23052\nx0=8.46152, x1=-2.28393, y=4525.25344\nx0=-0.15928, x1=2.65782, y=0.87886\nx0=-6.75290, x1=5.98200, y=2399.37095\nx0=-3.41306, x1=5.02563, y=183.05945\nx0=3.59842, x1=4.75415, y=127.61910\nx0=1.72282, x1=-1.54406, y=6.43224\nx0=-0.36990, x1=6.14483, y=12.80398\nx0=-1.06301, x1=-8.05119, y=42.94007\nx0=-9.79977, x1=-5.74264, y=10186.19208\nx0=-3.41768, x1=3.02686, y=177.91019\nx0=-8.02794, x1=-4.39402, y=4684.94227\nx0=9.07735, x1=3.35339, y=6043.79274\nx0=-3.29029, x1=-0.57076, y=153.55733\nx0=-2.00295, x1=1.13316, y=23.63897\nx0=2.17491, x1=-5.17317, y=30.64132\nx0=-0.65762, x1=-0.92028, y=1.81516\nx0=-1.48333, x1=1.51830, y=7.73924\nx0=-9.79270, x1=5.09691, y=10143.22678\nx0=-4.98575, x1=-4.59566, y=756.99361\nx0=-3.23982, x1=8.35940, y=170.76222\nx0=-7.73385, x1=7.22192, y=4058.96374\nx0=-0.64853, x1=-3.30062, y=9.19734\nx0=2.50867, x1=-9.18617, y=75.19813\nx0=-4.14739, x1=9.01661, y=398.84048\nx0=1.96895, x1=1.28305, y=6.93623\nx0=8.44959, x1=-7.87018, y=4532.90945\nx0=-4.79615, x1=2.40793, y=639.95893\nx0=0.88792, x1=6.80044, y=16.24406\nx0=8.21754, x1=4.18087, y=4009.66267\nx0=-5.76289, x1=-6.54498, y=1322.32006\nx0=-9.66844, x1=-9.50061, y=9696.71218\nx0=-1.57790, x1=5.07874, y=17.94571\nx0=0.89162, x1=1.90552, y=-0.16684\nx0=-0.05632, x1=9.05692, y=31.95717\nx0=-3.42688, x1=-8.74683, y=225.15329\nx0=-4.89356, x1=8.98935, y=722.05788\nx0=-7.74684, x1=6.78677, y=4082.77272\nx0=5.58837, x1=-4.62236, y=816.08690\nx0=-4.60646, x1=3.23823, y=550.01684\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.72653, x1=0.04650, y=141.05336\nx0=-7.32383, x1=-4.22115, y=3283.06111\nx0=5.59191, x1=1.97259, y=802.89592\nx0=6.98139, x1=5.00317, y=2042.80492\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**4 - x0**3 + 0.5 * x1**2 - x1", "data": [[-6.476106384307205, -9.908468163401887, 2089.564675257558], [7.515207224226799, -4.112194533604725, 2777.9236871059884], [-1.6903085140125196, 3.5507639719814303, 15.745916737713701], [-7.7968703564561626, 7.073258336490824, 4187.491700113353], [1.322037738805209, 3.3987733261865323, 3.121168766552101], [-7.299395348805557, 4.368294885229854, 3232.9763861535994], [2.4584886735127895, 9.696898240949686, 58.9904538618789], [7.07612042365167, -7.420782038391769, 2187.7960954575824], [-8.664381757039791, 5.9086943297916115, 6297.727671016075], [-2.351654495690916, 0.5094785912023543, 43.209595134421654], [-9.238381845156516, 7.155182481884776, 8091.147514292144], [-2.700626371773205, -0.4577401961595573, 73.4526378347661], [-6.193515698379142, -4.4349955050801455, 1723.312328414865], [-0.7048036176045507, -8.14079810620698, 41.87396360888376], [1.7026731640062582, 6.467962252043357, 17.91784985750745], [-7.852611036793682, -0.4162392952499534, 4287.109592272915], [0.34563145896110825, -7.304883802983042, 33.9585289300774], [-7.795448362440314, -8.62022673314813, 4212.369305914922], [-7.920379725274511, -0.07039025989739933, 4432.293306274858], [-5.736168544587241, -2.6951490020726165, 1277.716667032521], [-3.94440633617831, 3.843743414840384, 306.97384388982226], [-8.920256184423849, 1.9458868966567557, 7041.280121505575], [1.943399751349089, -7.464166941523072, 42.24546161639702], [-5.573209212125246, 6.0474424840924, 1150.110556319725], [7.714087641358567, 7.162386798361339, 3100.5448290827844], [-3.4016596893778273, -1.2504126001704563, 175.28848540860153], [-1.8409470854344114, 2.506812016105261, 18.36027461237593], [-6.538234352451107, 6.857585918074857, 2123.590397333887], [5.05559912484728, 1.321041495294324, 523.6017574576581], [-8.335168629521055, 3.708639443377015, 5409.035143779129], [-0.040937280985147595, 6.314295828291566, 13.620941489000181], [-4.220745670497232, 4.5912455371683, 398.5031377380786], [9.920385204217013, -6.459488270363827, 8736.340551415178], [-1.0999106845638522, -8.166898648600364, 44.31031577067621], [6.727337935130915, -1.4658215534884196, 1746.2833961439737], [6.309897040587629, -4.036841542330563, 1346.1759453071957], [4.2219904830707815, -0.2791560644498361, 242.79816477217946], [-1.1371742693515152, 8.272687080186113, 29.08881955173705], [9.846527199364033, -7.030853389737475, 8477.183238381698], [5.724319405283083, -4.4892528436648105, 900.7232648831135], [8.691009727729437, -3.827627411256329, 5060.021601068719], [-9.051726069188842, -7.742284980866017, 7492.494129517224], [-2.2555972177381545, -5.628884160618632, 58.83177967299134], [1.9452446191088484, 2.269504445784147, 7.263539716699167], [-0.37678638600058534, -1.0959953713301367, 1.7702448082222026], [-7.515792958859739, 8.706577443571302, 3644.5387603205913], [-9.876188219675344, 9.148285402045822, 10509.886535812502], [-3.9888219249274908, -6.631852451599989, 345.23792190241016], [-6.081241779194622, 9.232147480323832, 1625.9090374077334], [4.351481943663952, -3.9363431819480184, 287.83589992652907], [-9.774482945427248, -4.260177151558753, 10075.184244435664], [-7.765078563042815, 8.953727338883574, 4134.998813007232], [6.59647484925204, -5.76593511989995, 1628.7763394435367], [-0.9015850387746553, 0.03941313469012542, 1.3549561918667754], [-1.4003088492287592, 9.424583939613235, 41.57761476297907], [7.984523314789193, 2.84940694525077, 3556.5715404133484], [-0.7324733031107549, -9.550376767125782, 55.83606008696354], [1.1999973644639965, 2.6876292116979617, 1.2696393468138285], [9.933396442965677, -4.762973033983808, 8772.189804248494], [-5.7854676813846195, -5.590215291281702, 1335.2149748922384], [-3.438429902897613, 5.197851075360848, 188.74145106079092], [6.982452026933984, -7.850969371527025, 2075.257481861317], [6.62605887970917, -5.796225715232561, 1659.298347233175], [-1.2795230888414366, 0.2692890981478335, 4.542134145146348], [-1.912688605182984, -5.120687838764368, 38.61247454956435], [-8.361168708454269, 5.749255438409531, 5482.588004684563], [1.4815449808917833, 7.141778587281877, 19.926684706423835], [-8.255475776426358, 2.286197650968303, 5207.77669709581], [6.923912845419956, -1.2714797703122578, 1968.4416527939577], [2.019421362954043, -1.0728970058742746, 10.04371908665318], [9.150608893693136, -2.853138769843671, 6252.032510746924], [9.919599512590509, 0.13020025484297548, 8706.060860655007], [8.690449572767896, 0.47201458121325146, 5047.164172254486], [2.5648218098155517, -0.43048697143206205, 26.925125687296344], [-1.2536430289663834, -0.4314996566563085, 4.964839226391901], [-6.077462958398085, 7.7363633236529346, 1610.8990667366163], [6.952191219884121, -6.737348059006689, 2029.4885671272632], [-8.668403843392118, -6.844460336986479, 6327.825987617156], [9.657207286847626, -7.911148966281272, 7836.293019225358], [6.4363563708409615, -3.638115635569128, 1459.7892530630695], [8.872306810989375, 0.2585050069122925, 5497.862652975455], [-6.07984965463044, 9.467463062050008, 1626.4675746357343], [-9.378829804576178, -4.527101729219289, 8577.151607147181], [8.635564143698286, -9.575052473400888, 4972.5637864173], [-6.939259235386768, 0.0798296129224223, 2652.8138238044785], [-7.514591596275643, -8.107620107559042, 3654.0742682389937], [4.329738642296091, -1.650270562346737, 273.28031760679966], [4.4214958363345715, -1.9123410514590518, 299.49013223776905], [-5.754332787950506, -2.793176941373634, 1293.6609996379555], [-4.033595342417446, 5.77388624586024, 341.2305187862461], [8.461523252743767, -2.283925687896371, 4525.253439410316], [-0.15928389382575148, 2.657817031332879, 0.8788636093641347], [-6.7529044614559215, 5.98199826929328, 2399.3709480563684], [-3.413056011889159, 5.025632568792087, 183.059449522158], [3.5984194935234566, 4.75415498186713, 127.61909667829845], [1.7228166966064045, -1.544062634171885, 6.432241635351947], [-0.369901570124334, 6.144831569652315, 12.803980200531534], [-1.0630118646106013, -8.051185950634975, 42.940067770819354], [-9.799774698574279, -5.742635760410105, 10186.19207779636], [-3.417684244281027, 3.0268641092282706, 177.9101866387502], [-8.027935468845842, -4.394016166252099, 4684.942274734684], [9.077351649985072, 3.353390035434556, 6043.792741603122], [-3.290292994498434, -0.5707575496556334, 153.5573257250617], [-2.002950931272127, 1.1331555084340028, 23.638967641894034], [2.1749121003561385, -5.1731663333689815, 30.64132479878755], [-0.6576249261721401, -0.9202755056403777, 1.8151631890520885], [-1.4833310736557301, 1.5183007960960317, 7.739241111655598], [-9.792703626432802, 5.096910008873465, 10143.226777821434], [-4.9857468369956575, -4.595663356719502, 756.9936148958932], [-3.239821001248508, 8.359399281224569, 170.7622212252851], [-7.73384987387439, 7.221915089376836, 4058.963743491652], [-0.648529443882417, -3.3006238332646305, 9.19734427937469], [2.508671415364379, -9.186166298922178, 75.19812803412955], [-4.147389587496615, 9.016606176779746, 398.8404837670483], [1.968951273050406, 1.2830483560468497, 6.936227476388103], [8.449592321790202, -7.870181790046253, 4532.909446036077], [-4.7961522779070265, 2.4079287693716225, 639.9589267113436], [0.8879150220627459, 6.800435373328959, 16.244062854064502], [8.217535825300601, 4.180868786333223, 4009.662674965388], [-5.762892288497863, -6.544978766555143, 1322.3200577687035], [-9.668443572986886, -9.500610195216922, 9696.712180760327], [-1.5779040284087422, 5.078740967940094, 17.945709645199265], [0.8916224450991539, 1.9055224826497668, -0.16683593597390134], [-0.05631777543834815, 9.05692052775261, 31.95717287751802], [-3.4268771794757757, -8.746826566745717, 225.153294057263], [-4.8935634309697225, 8.989350203492293, 722.0578804737087], [-7.746835290541827, 6.786765790833492, 4082.7727192449806], [5.588370373030653, -4.622355524665192, 816.0869043428404], [-4.6064583934896035, 3.238233228861482, 550.0168360134846], [3.7265282519577436, 0.046499103297515276, 141.05336125681328], [-7.323832660864049, -4.22114598470801, 3283.061110309124], [5.591909973485471, 1.9725852122315928, 802.8959222398455], [6.981385986106453, 5.003167312470076, 2042.8049226852643]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=5.24824, x1=6.76790, y=74642.04304\nx0=8.05157, x1=-3.61581, y=0.00053\nx0=1.76634, x1=-1.53313, y=0.41802\nx0=7.38880, x1=-7.16803, y=0.00000\nx0=4.96571, x1=4.63837, y=1691.28692\nx0=4.36945, x1=-8.22565, y=0.00001\nx0=3.99550, x1=-0.19817, y=0.75996\nx0=5.15012, x1=-3.66418, y=0.00246\nx0=9.24139, x1=-1.41948, y=0.04258\nx0=3.49118, x1=8.02523, y=22775.89750\nx0=8.75366, x1=4.04016, y=6406.16338\nx0=3.86372, x1=-3.19626, y=0.01330\nx0=6.38234, x1=-5.72481, y=0.00002\nx0=7.36007, x1=-8.40874, y=0.00000\nx0=0.47342, x1=3.02584, y=0.10408\nx0=3.31653, x1=-5.66949, y=0.00112\nx0=6.29127, x1=-0.62779, y=0.31518\nx0=8.65799, x1=-9.33998, y=0.00000\nx0=5.37367, x1=5.96566, y=22727.29727\nx0=2.73929, x1=1.93246, y=7.01001\nx0=8.56920, x1=-3.42545, y=0.00064\nx0=1.85222, x1=1.61319, y=2.70295\nx0=6.20563, x1=7.33960, y=658769.07630\nx0=3.77672, x1=-1.45170, y=0.14528\nx0=5.21570, x1=-4.05797, y=0.00123\nx0=7.65242, x1=-2.30378, y=0.00920\nx0=8.54492, x1=-3.78740, y=0.00030\nx0=8.33844, x1=-4.62768, y=0.00005\nx0=9.72989, x1=-9.76690, y=0.00000\nx0=0.58895, x1=3.94628, y=0.12379\nx0=5.91908, x1=-0.64841, y=0.31569\nx0=2.78288, x1=8.36005, y=5199.91805\nx0=1.43150, x1=3.43953, y=3.43435\nx0=8.18542, x1=5.65265, y=144911.72449\nx0=3.97835, x1=8.31448, y=96875.44297\nx0=7.75180, x1=1.93516, y=52.61850\nx0=2.84961, x1=-4.32933, y=0.01074\nx0=1.25028, x1=-7.63602, y=0.18166\nx0=1.22415, x1=-8.13875, y=0.19281\nx0=8.63453, x1=-2.36782, y=0.00607\nx0=4.65889, x1=1.00016, y=4.66002\nx0=4.43377, x1=-1.36392, y=0.13118\nx0=4.63676, x1=2.34844, y=36.69124\nx0=3.16970, x1=8.57620, y=19807.80055\nx0=4.97960, x1=5.86426, y=12260.99085\nx0=7.56560, x1=1.79986, y=38.17674\nx0=0.04417, x1=1.53306, y=0.00837\nx0=0.37066, x1=-0.23018, y=1.25666\nx0=3.16943, x1=8.47607, y=17633.87479\nx0=4.34848, x1=7.25493, y=42765.81144\nx0=2.13409, x1=9.63018, y=1480.43138\nx0=3.31810, x1=-7.49449, y=0.00012\nx0=4.43624, x1=8.14399, y=185900.46925\nx0=3.27326, x1=1.14327, y=3.87935\nx0=9.81684, x1=4.49684, y=28889.24717\nx0=3.05466, x1=5.83044, y=672.26967\nx0=5.95838, x1=-8.41389, y=0.00000\nx0=0.27586, x1=3.72484, y=0.00825\nx0=9.19037, x1=9.93352, y=3709290928.76675\nx0=6.53937, x1=5.29582, y=20841.64045\nx0=4.28698, x1=-1.59729, y=0.09779\nx0=2.85948, x1=-0.75070, y=0.45443\nx0=9.80547, x1=-0.90416, y=0.12693\nx0=6.33046, x1=3.48969, y=626.26672\nx0=8.78379, x1=1.04370, y=9.65883\nx0=1.43706, x1=1.36135, y=1.63825\nx0=0.12312, x1=-9.23446, y=251439022.85022\nx0=9.70134, x1=0.35305, y=2.23051\nx0=8.83584, x1=-1.18160, y=0.07619\nx0=8.43812, x1=-6.83963, y=0.00000\nx0=5.43055, x1=5.67655, y=14838.03826\nx0=3.93109, x1=8.83907, y=179861.77160\nx0=7.85897, x1=-0.23231, y=0.61944\nx0=6.07359, x1=2.76966, y=147.86988\nx0=6.25065, x1=9.95469, y=83789442.75059\nx0=8.24020, x1=-9.06087, y=0.00000\nx0=1.67835, x1=7.40257, y=46.20733\nx0=2.39831, x1=5.12438, y=88.46702\nx0=4.90371, x1=8.03013, y=350754.00462\nx0=9.93888, x1=0.15254, y=1.41949\nx0=5.09759, x1=-1.23656, y=0.13344\nx0=6.27435, x1=2.17658, y=54.44697\nx0=3.46439, x1=9.42754, y=122280.01440\nx0=2.45680, x1=9.66069, y=5905.26372\nx0=4.83446, x1=-3.16286, y=0.00685\nx0=5.74667, x1=4.03039, y=1150.12209\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.12625, x1=-7.27368, y=0.00025\nx0=0.79447, x1=-6.62826, y=4.59523\nx0=0.18131, x1=9.67706, y=0.00000\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 ** x1", "data": [[5.24824062405829, 6.7679035231002835, 74642.04303756611], [8.051565430920956, -3.6158089336080863, 0.0005302855859325166], [1.7663447392418714, -1.5331260094300436, 0.4180249194694156], [7.3888033756269, -7.168026490600459, 5.943438497435857e-07], [4.965705223739363, 4.63837028571583, 1691.286916755611], [4.369453798559244, -8.22564809560241, 5.395996013191221e-06], [3.9955008628474964, -0.19816669627186378, 0.7599562954298175], [5.150122679337985, -3.664177700481721, 0.002464755913556522], [9.241387905906937, -1.4194784215041683, 0.04257521832065277], [3.4911779826765006, 8.02523072969235, 22775.897497643775], [8.753663551222733, 4.040160280628108, 6406.163378342577], [3.8637232839281452, -3.196259122673082, 0.013297704232098096], [6.382340038549927, -5.724814858306608, 2.4639896857360725e-05], [7.360072692097901, -8.408741012181643, 5.1358567518988364e-08], [0.4734213379379, 3.025841026924798, 0.10407623085386256], [3.3165312342207187, -5.669486728728359, 0.0011168335507683268], [6.291265766334661, -0.6277900379681398, 0.3151811390456441], [8.65798773492211, -9.339981652264777, 1.7560736839585201e-09], [5.373665151180083, 5.965662300903995, 22727.29727127226], [2.7392884214485385, 1.9324630719529523, 7.010012842207274], [8.569200004800837, -3.4254475811779255, 0.0006371797668502295], [1.8522165804225903, 1.6131889870180984, 2.7029462610951267], [6.205631022007111, 7.339601828550169, 658769.0762969145], [3.7767229825348743, -1.45169696783951, 0.14527929179908525], [5.215696492111999, -4.0579700808505255, 0.0012279144270828824], [7.6524241861641435, -2.3037767002429943, 0.009202893028220926], [8.544924319964728, -3.7874020159613497, 0.0002959691238265313], [8.338438018697715, -4.6276802491595825, 5.464047968077939e-05], [9.729890887374157, -9.766904041177295, 2.2348288762672733e-10], [0.5889539251983837, 3.9462759901991955, 0.12378768344708961], [5.919081476832824, -0.6484103706020967, 0.31569106583558454], [2.78287990909174, 8.360051223602948, 5199.918053729292], [1.4314952773859329, 3.4395334464287703, 3.4343506826815338], [8.185419099880864, 5.6526530285998895, 144911.72448774966], [3.978346354788851, 8.314477515350433, 96875.44296569249], [7.7517993678846295, 1.9351625826935717, 52.618502605820034], [2.849613299284739, -4.329327171769455, 0.010741944897240983], [1.2502790327945945, -7.636016215788479, 0.1816575159421165], [1.2241517263933126, -8.138751320266861, 0.19281052984654337], [8.634525349116206, -2.367817215970735, 0.006069577138151559], [4.6588898160745735, 1.0001569334073466, 4.660015006480817], [4.43377414033373, -1.363922159310249, 0.13117503875661762], [4.636761162836445, 2.3484356691156947, 36.69124313045321], [3.1697018445753056, 8.576204280092494, 19807.800552491295], [4.979597947203505, 5.864255760797832, 12260.990851709103], [7.565603992194706, 1.799863848561504, 38.176739410917776], [0.04417219185429211, 1.5330645296252836, 0.008373864168762686], [0.3706554214142326, -0.23018494846430926, 1.2566563676824556], [3.169427637618787, 8.476068160644218, 17633.874792341754], [4.348482545838095, 7.254931817769986, 42765.81143552165], [2.1340946478025895, 9.630184000934449, 1480.431378002027], [3.3181049184377684, -7.494486260708387, 0.00012479471544293936], [4.4362388632878655, 8.143986028729952, 185900.46924741822], [3.2732554564319685, 1.1432659352776593, 3.879350121687813], [9.816836275406917, 4.49683888013209, 28889.247171908093], [3.054656101374608, 5.830439557725489, 672.2696667052846], [5.958379866102042, -8.413886311235888, 3.007180899103463e-07], [0.27585901548754244, 3.724838360594198, 0.008253728132390097], [9.190369012587759, 9.933523919961043, 3709290928.7667503], [6.539374784689841, 5.295818566077738, 20841.640454570763], [4.286980540157671, -1.5972857887156842, 0.09778525516510689], [2.8594776588351998, -0.7507031200867509, 0.45442701837071403], [9.80546864652208, -0.904160815308952, 0.1269267510327117], [6.330461390385665, 3.48968795358725, 626.2667240570847], [8.783788033980024, 1.0437037836587155, 9.658825373894148], [1.4370607500382668, 1.3613507420234825, 1.6382451167347623], [0.12311676516277181, -9.234463533958568, 251439022.8502171], [9.701337348158233, 0.3530525729166474, 2.230506215564109], [8.835836876909518, -1.1815990645931862, 0.07619291955820444], [8.438120642382504, -6.839633759511104, 4.621877528062588e-07], [5.430545554207523, 5.67655113928393, 14838.038256828699], [3.931087649962471, 8.83906874681806, 179861.77160296612], [7.858971332881065, -0.2323105483971517, 0.6194369418380306], [6.073588653563512, 2.769663056342706, 147.86987713599225], [6.250647631267327, 9.954693133728927, 83789442.75058569], [8.240202823157006, -9.060867790122852, 5.021202896023172e-09], [1.6783515351524336, 7.40256680498636, 46.207334181929276], [2.3983137626374234, 5.124376516017666, 88.46701684146299], [4.903705432354952, 8.0301331083841, 350754.00461632916], [9.938877795542648, 0.15253927483822416, 1.4194925457900336], [5.097594300949721, -1.2365649738360052, 0.13344333435289069], [6.274350847330009, 2.176581748054671, 54.446967038850254], [3.4643924284436327, 9.42753924430615, 122280.01439578123], [2.4567991367455733, 9.660687732822517, 5905.2637170805865], [4.834455024325061, -3.162862693609007, 0.0068470381238231875], [5.746666074207113, 4.03039190608702, 1150.1220945105067], [3.126252324341685, -7.273683180336096, 0.0002508141628312343], [0.7944715157507751, -6.6282614043292165, 4.595226702657378], [0.1813143155485477, 9.677064190001555, 6.664994277348236e-08]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=5.55168, x1=6.61954, y=84673.16145\nx0=6.02935, x1=0.71276, y=3.59872\nx0=5.37765, x1=5.74023, y=15623.10109\nx0=7.30572, x1=-4.53100, y=0.00012\nx0=3.62588, x1=-4.64968, y=0.00251\nx0=2.68389, x1=-3.06844, y=0.04835\nx0=5.31111, x1=-3.29072, y=0.00411\nx0=3.01348, x1=-7.76161, y=0.00019\nx0=0.78375, x1=-5.24338, y=3.58818\nx0=2.44422, x1=-6.18044, y=0.00399\nx0=8.63627, x1=3.75709, y=3295.02774\nx0=4.44190, x1=7.80645, y=113558.51792\nx0=4.28795, x1=2.72915, y=53.15041\nx0=9.88730, x1=9.11416, y=1173007110.39655\nx0=7.55939, x1=-0.39880, y=0.44633\nx0=5.90607, x1=-6.68360, y=0.00001\nx0=2.99317, x1=-7.12051, y=0.00041\nx0=3.29119, x1=5.76346, y=958.84419\nx0=2.21789, x1=-6.78332, y=0.00450\nx0=8.69859, x1=0.71748, y=4.72100\nx0=9.61423, x1=9.22850, y=1177146664.06818\nx0=3.21363, x1=3.10039, y=37.31523\nx0=1.61327, x1=6.74390, y=25.16221\nx0=5.42225, x1=-1.01519, y=0.17975\nx0=4.59512, x1=-9.76969, y=0.00000\nx0=6.02629, x1=-4.49018, y=0.00031\nx0=4.06129, x1=1.23796, y=5.66893\nx0=7.30228, x1=4.26983, y=4862.03037\nx0=4.41755, x1=2.72714, y=57.47831\nx0=4.73794, x1=-1.40753, y=0.11197\nx0=0.03800, x1=-3.13296, y=28142.80766\nx0=5.85099, x1=-5.85412, y=0.00003\nx0=6.90109, x1=-1.96318, y=0.02255\nx0=9.61781, x1=-4.41308, y=0.00005\nx0=0.03447, x1=4.13953, y=0.00000\nx0=8.39423, x1=-6.64947, y=0.00000\nx0=7.11032, x1=7.15286, y=1240079.54277\nx0=1.23424, x1=-7.76417, y=0.19514\nx0=7.00412, x1=-0.00602, y=0.98834\nx0=0.60783, x1=1.88695, y=0.39084\nx0=5.77775, x1=-7.87105, y=0.00000\nx0=6.93868, x1=-9.90942, y=0.00000\nx0=1.97971, x1=-7.30920, y=0.00679\nx0=9.50276, x1=9.38329, y=1497777284.65892\nx0=1.24477, x1=5.90279, y=3.64159\nx0=8.10289, x1=5.22851, y=56342.14707\nx0=4.56290, x1=-4.76885, y=0.00072\nx0=6.49055, x1=-8.68199, y=0.00000\nx0=0.39248, x1=6.31540, y=0.00272\nx0=3.65812, x1=5.86645, y=2015.23860\nx0=4.04240, x1=8.93007, y=261416.96963\nx0=8.66396, x1=-8.62243, y=0.00000\nx0=4.53694, x1=-5.37947, y=0.00029\nx0=4.33204, x1=-2.94558, y=0.01332\nx0=4.20770, x1=-7.52287, y=0.00002\nx0=8.50151, x1=-8.91860, y=0.00000\nx0=4.04509, x1=-7.98707, y=0.00001\nx0=0.78500, x1=-3.31298, y=2.22990\nx0=2.14474, x1=8.67430, y=748.93176\nx0=8.25484, x1=8.39922, y=50076782.36985\nx0=3.22887, x1=6.05844, y=1213.53177\nx0=4.33382, x1=1.13794, y=5.30546\nx0=1.84753, x1=5.16757, y=23.85796\nx0=1.19693, x1=-6.09835, y=0.33413\nx0=9.08091, x1=-7.37201, y=0.00000\nx0=5.81922, x1=-4.72038, y=0.00025\nx0=9.90108, x1=-7.21843, y=0.00000\nx0=8.03871, x1=-7.98503, y=0.00000\nx0=2.33933, x1=-2.52205, y=0.11726\nx0=5.69547, x1=-1.43133, y=0.08291\nx0=5.05718, x1=3.18426, y=174.35124\nx0=4.41798, x1=-6.58525, y=0.00006\nx0=3.05111, x1=-2.57142, y=0.05679\nx0=1.18627, x1=6.49746, y=3.03385\nx0=3.50705, x1=-3.44457, y=0.01327\nx0=4.43756, x1=-2.21774, y=0.03671\nx0=5.92384, x1=9.88403, y=43295061.94226\nx0=2.60693, x1=7.18250, y=974.64646\nx0=4.77832, x1=-4.67879, y=0.00066\nx0=3.36931, x1=6.30809, y=2127.04909\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=1.78514, x1=-5.76383, y=0.03543\nx0=3.54934, x1=9.82757, y=255043.21457\nx0=5.22512, x1=6.42478, y=41077.96000\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**x1", "data": [[5.551681443447787, 6.619537000881184, 84673.161452027], [6.029353387551183, 0.7127625811252951, 3.5987177502758785], [5.377651109727239, 5.740226649381864, 15623.10108634376], [7.305717683025534, -4.530997270814923, 0.00012210847918354381], [3.625884708300898, -4.649679263567226, 0.0025055574624515283], [2.6838890302733667, -3.0684401970951214, 0.04834611753668517], [5.311107681788146, -3.2907224358105918, 0.004107873858006759], [3.013476767736451, -7.761608225011596, 0.00019127713289351274], [0.7837478818037411, -5.243382626705109, 3.5881759427722564], [2.4442152633791565, -6.1804377406607935, 0.003991427851266096], [8.636273525603546, 3.757086329877893, 3295.0277418752426], [4.441904256908311, 7.80645492105797, 113558.51792139083], [4.287949400605955, 2.7291539894810253, 53.15041498980654], [9.8873013335098, 9.114162646997496, 1173007110.3965514], [7.559388938152097, -0.39880373333756935, 0.44633015329778764], [5.9060732175196495, -6.683603588297407, 6.9975239705054405e-06], [2.993168794547632, -7.120514349256153, 0.00040709980609446685], [3.2911945544209793, 5.763462931015413, 958.8441897374372], [2.2178883986416693, -6.783319568149853, 0.0045017413295369655], [8.698590617175025, 0.7174779837931933, 4.720998875210828], [9.614232571064232, 9.228503023709244, 1177146664.0681794], [3.2136280473740513, 3.100393962691726, 37.3152302363312], [1.6132667684970734, 6.7438956773861065, 25.16221464969984], [5.422254293089004, -1.0151866060963233, 0.1797506287007213], [4.595117145743679, -9.769685068691771, 3.3850954375354985e-07], [6.026285044033209, -4.490183767184663, 0.00031436459934520793], [4.061290826517288, 1.2379593503525665, 5.668934011093894], [7.30227537844884, 4.269827582467343, 4862.030371953015], [4.417552807363542, 2.7271447215309497, 57.47831171179914], [4.737935550877644, -1.4075264141380028, 0.11196709948873171], [0.03800299365856574, -3.132955371032362, 28142.807658146452], [5.850991138197921, -5.854122705670188, 3.2251113441328915e-05], [6.901092391603047, -1.9631786380876814, 0.022545216696014687], [9.617809560942447, -4.413075614224303, 4.5878637501563566e-05], [0.0344746932374278, 4.139527566376998, 8.829632602858366e-07], [8.39422754378301, -6.649474807208444, 7.178163784736671e-07], [7.110323976278401, 7.152864701081285, 1240079.5427652402], [1.2342401930701676, -7.764168818865967, 0.19514499390878323], [7.004117990078544, -0.0060229807904033095, 0.9883447334164857], [0.60782696877164, 1.8869520934797368, 0.390843733469942], [5.77775429377628, -7.871053163300545, 1.0096105273933964e-06], [6.938679567157674, -9.909423776832087, 4.60713945896346e-09], [1.9797065309505069, -7.3091995388624635, 0.006793372892361016], [9.502760297538831, 9.38328921138421, 1497777284.6589153], [1.2447703225945403, 5.902785742069836, 3.6415923184728642], [8.102892284496725, 5.228509695376104, 56342.147072413536], [4.562899616404257, -4.768848340821384, 0.0007180919514521826], [6.490553648548062, -8.68199165821512, 8.866999307918615e-08], [0.3924751005344156, 6.315395551777641, 0.0027212146625724813], [3.658120751892673, 5.8664524168994525, 2015.238600609709], [4.042401390117147, 8.930071912881715, 261416.9696284], [8.663955486550876, -8.622432698504795, 8.214952734216243e-09], [4.536943390980477, -5.379470509144413, 0.00029306291895344374], [4.332039582934517, -2.9455803128749913, 0.013322059021281253], [4.2076975713076195, -7.522865849402924, 2.0202113755852883e-05], [8.501513088061593, -8.918598939004942, 5.1309281054806605e-09], [4.045090252332228, -7.987071052641054, 1.4204345134166233e-05], [0.7850046270122988, -3.3129764354265294, 2.22990247287273], [2.1447388696227243, 8.67430330708919, 748.9317641678367], [8.254844788623913, 8.399216279299207, 50076782.36984723], [3.228867673504798, 6.058441519021137, 1213.531772940181], [4.333816555368452, 1.1379436445975966, 5.305456591220701], [1.8475328742219723, 5.167568768508719, 23.85796495801527], [1.1969301545060134, -6.098347038488427, 0.3341252629738366], [9.080905869499873, -7.372009584810999, 8.642960863742871e-08], [5.8192169864889, -4.720376236505414, 0.00024521754901029046], [9.901081204357581, -7.218426495962252, 6.497378645765119e-08], [8.038708111943848, -7.985027234029101, 5.916475431259933e-08], [2.339327588107512, -2.522054353714392, 0.11725525869668948], [5.695466826609836, -1.4313346321384834, 0.08290576082662973], [5.057182405739145, 3.1842557100161066, 174.35123871056797], [4.417978275036258, -6.585250061467431, 5.6369139720710853e-05], [3.051107370504937, -2.571419591970507, 0.05678799247373179], [1.1862654420109937, 6.49745622234709, 3.0338458479513255], [3.5070541070291927, -3.444574402808291, 0.013271045242700166], [4.4375602066663955, -2.2177392316435363, 0.036711555778160765], [5.92384145922601, 9.884033773819052, 43295061.942256466], [2.6069274696235887, 7.182502250565012, 974.6464557664808], [4.778318909024788, -4.67878609529309, 0.0006634633841094324], [3.3693129948048135, 6.308088398212121, 2127.049091710452], [1.785141050898563, -5.763827554246812, 0.035432589767396286], [3.549339204514455, 9.827571175462186, 255043.21456715904], [5.225115282449561, 6.42478117025497, 41077.959995966805]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.72381, y=-0.77580\nx0=-1.57633, y=-0.75338\nx0=8.38868, y=-1.23439\nx0=-1.33859, y=-0.52548\nx0=-2.85634, y=-1.66539\nx0=-2.49833, y=-0.71677\nx0=-9.36531, y=-0.49770\nx0=4.55896, y=-0.89283\nx0=2.68672, y=-1.47292\nx0=-3.19481, y=-0.04630\nx0=0.34865, y=-0.63604\nx0=-0.40670, y=-0.59878\nx0=-8.36281, y=-1.10671\nx0=-3.67084, y=-1.43081\nx0=2.59639, y=-1.12809\nx0=4.29944, y=-0.60698\nx0=-9.33735, y=-0.05044\nx0=-3.04285, y=-0.91430\nx0=1.96241, y=-0.50137\nx0=6.17329, y=-0.35339\nx0=-9.77881, y=-1.67049\nx0=7.11195, y=-0.54109\nx0=-6.35074, y=-0.26401\nx0=-2.64706, y=-1.33285\nx0=-7.24676, y=-0.30607\nx0=2.00194, y=-0.43161\nx0=-0.69986, y=-0.39014\nx0=0.83120, y=-0.32052\nx0=-8.54747, y=-0.29032\nx0=-1.34456, y=-0.53196\nx0=0.26297, y=-0.68328\nx0=2.52342, y=-0.81877\nx0=9.65944, y=0.03711\nx0=3.54643, y=-0.75989\nx0=-7.81492, y=-0.78837\nx0=-7.02280, y=-1.34906\nx0=7.22422, y=-0.19736\nx0=-9.78237, y=-1.67957\nx0=6.46720, y=-1.56862\nx0=-4.49620, y=-0.96004\nx0=-3.18906, y=-0.07254\nx0=-1.59111, y=-0.76164\nx0=3.28506, y=0.21921\nx0=4.01124, y=-0.50946\nx0=-9.35070, y=-0.24678\nx0=-8.58761, y=-0.08259\nx0=-4.41836, y=-0.93050\nx0=9.35654, y=-0.34341\nx0=-1.47529, y=-0.67160\nx0=-6.84889, y=-0.56862\nx0=2.82134, y=-1.69383\nx0=8.30634, y=-0.69775\nx0=-0.46462, y=-0.55851\nx0=2.27145, y=-0.16866\nx0=4.03073, y=-0.42670\nx0=5.13915, y=-0.35367\nx0=-4.39267, y=-0.88557\nx0=-4.64747, y=-0.77479\nx0=5.03364, y=-0.68578\nx0=-1.60009, y=-0.76608\nx0=-4.01330, y=-0.50024\nx0=8.46427, y=-1.07961\nx0=6.70403, y=-0.00142\nx0=-5.01774, y=-0.73648\nx0=-9.41943, y=-1.43972\nx0=9.59512, y=0.05746\nx0=5.54784, y=-1.19131\nx0=-8.70463, y=-1.02353\nx0=-2.13528, y=-0.22127\nx0=-2.46667, y=-0.59587\nx0=1.12065, y=-0.33630\nx0=-2.14368, y=-0.21165\nx0=-3.69362, y=-1.49953\nx0=8.44940, y=-1.17659\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.21608, y=-0.63965\nx0=3.48158, y=-0.34424\nx0=7.99002, y=-0.86475\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0**2) * cos(x0) - 0.75", "data": [[1.7238108917737467, -0.7757967775232625], [-1.5763278088217252, -0.753377353645292], [8.388684814088453, -1.2343854701653354], [-1.338592971500372, -0.5254763212205626], [-2.856339547247857, -1.6653905759831535], [-2.4983270789307577, -0.7167660015156314], [-9.365312152376289, -0.4976956908283801], [4.558960415743602, -0.8928267332712516], [2.686715120071252, -1.4729181378906144], [-3.1948051974988, -0.046296009095352364], [0.3486541338368916, -0.6360352905790269], [-0.4066977113151147, -0.5987802650182356], [-8.362811926905188, -1.1067084263187181], [-3.6708428648851887, -1.4308080628599948], [2.5963890646610626, -1.1280912413027433], [4.299437584764389, -0.6069789279890422], [-9.3373468065992, -0.05043526926341235], [-3.042846207382553, -0.9143011352117258], [1.9624067394012776, -0.5013697189652273], [6.173293778771335, -0.35339016213073376], [-9.778810330485083, -1.67048704284321], [7.111945464944398, -0.5410880070523404], [-6.350742594091503, -0.26400512769318557], [-2.64705753785345, -1.3328465264278726], [-7.246761845484402, -0.3060687807114899], [2.001942041544435, -0.431609746211066], [-0.6998567885169571, -0.39013736390580145], [0.831195156193516, -0.32051811238898664], [-8.547465747137547, -0.29032177899702577], [-1.3445574897187402, -0.5319585355716843], [0.2629747409746823, -0.6832750082119312], [2.523423804835234, -0.8187663005219232], [9.659442592334845, 0.03711271288034501], [3.5464253416234257, -0.7598919805068788], [-7.814915094043737, -0.7883672659325168], [-7.022801101606548, -1.349059555565874], [7.224216133873917, -0.19736390849046692], [-9.78237092928072, -1.6795733358176865], [6.467196591670273, -1.5686209540109073], [-4.496197009593521, -0.9600391264310567], [-3.189062960617351, -0.07253893699992842], [-1.5911110453942392, -0.7616361464190801], [3.285057705137028, 0.21920960311828253], [4.011242841772516, -0.5094604325093987], [-9.350704584274897, -0.24678414631676426], [-8.587609222974066, -0.08259424697838835], [-4.418356434537516, -0.9304964670687546], [9.356539640553539, -0.34340695091306805], [-1.4752906525737597, -0.6716029824036224], [-6.848894378189463, -0.5686239290534764], [2.821341227310338, -1.693830466357026], [8.306335648749773, -0.6977510132920809], [-0.4646201061243609, -0.5585077340914276], [2.2714531244294314, -0.16865590709773448], [4.030726508188902, -0.4267032815090701], [5.139153920309099, -0.3536691743544539], [-4.39266628524601, -0.8855669570373654], [-4.647472268360753, -0.7747921988367794], [5.033642950854203, -0.6857779279681155], [-1.600092070740791, -0.7660842621536776], [-4.013297134203164, -0.5002360293165583], [8.464269896122254, -1.0796105932035058], [6.704025060377909, -0.001420749902836027], [-5.017740909104756, -0.736481492407081], [-9.419432427814609, -1.4397178785837133], [9.595124371403887, 0.057461684223957143], [5.547842618416645, -1.1913140303368905], [-8.704634162788496, -1.0235340571356237], [-2.135276781422446, -0.22127102692183065], [-2.46667178576174, -0.5958705842355885], [1.12064789662276, -0.3363018076603372], [-2.143679566540058, -0.21165037752725646], [-3.6936212348902515, -1.4995315036826762], [8.44940182872223, -1.1765886785237316], [9.216075282854916, -0.6396463547219314], [3.4815848849446596, -0.34423606195316614], [7.990023298359233, -0.8647496808369349]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=7.14676, x1=2.86888, y=1.02952\nx0=3.98512, x1=-9.93357, y=-0.25987\nx0=-7.60645, x1=4.11925, y=-1.79871\nx0=-6.04113, x1=-8.86364, y=-0.29244\nx0=8.47902, x1=9.63857, y=0.59877\nx0=-2.22030, x1=0.18332, y=-0.61408\nx0=8.59708, x1=-8.87877, y=0.21709\nx0=8.68738, x1=-7.58217, y=-0.29092\nx0=4.12104, x1=-3.91542, y=-0.13132\nx0=-2.66371, x1=9.90099, y=-0.91832\nx0=4.46361, x1=-5.15951, y=-0.06752\nx0=-4.12251, x1=-7.69640, y=-0.15660\nx0=7.71726, x1=9.13697, y=1.27452\nx0=9.71065, x1=-2.23121, y=-1.07173\nx0=4.44196, x1=-4.21267, y=-0.08594\nx0=6.55298, x1=3.05509, y=0.35292\nx0=7.20638, x1=-9.36913, y=0.74192\nx0=9.76696, x1=-7.44645, y=-1.25364\nx0=1.74210, x1=1.09217, y=1.87299\nx0=4.22806, x1=-5.11997, y=0.03309\nx0=9.41650, x1=2.49453, y=0.61112\nx0=-8.03674, x1=9.96753, y=-1.49984\nx0=-9.33559, x1=-6.71874, y=-0.51099\nx0=-2.48262, x1=5.49085, y=-1.32430\nx0=-0.00326, x1=1.95655, y=0.92325\nx0=-7.30757, x1=5.92154, y=-1.20820\nx0=2.03690, x1=4.25714, y=-0.00482\nx0=-6.81319, x1=-6.15325, y=-0.37597\nx0=4.57708, x1=-4.02478, y=-0.21809\nx0=5.52939, x1=2.92630, y=-0.47078\nx0=8.18651, x1=6.03215, y=0.69682\nx0=4.42392, x1=-6.61508, y=-1.28451\nx0=-3.14646, x1=-6.65311, y=-0.35668\nx0=-6.19704, x1=-2.32938, y=-0.63978\nx0=6.74355, x1=-5.66365, y=1.02493\nx0=2.40977, x1=-8.63780, y=-0.03999\nx0=-6.82154, x1=-7.81643, y=-1.51202\nx0=4.72342, x1=4.82711, y=-1.99337\nx0=5.98296, x1=9.72692, y=-0.59330\nx0=6.52967, x1=-4.30078, y=1.16047\nx0=-4.99086, x1=1.74989, y=1.94548\nx0=4.17672, x1=1.74912, y=0.12421\nx0=2.30536, x1=-1.48807, y=-0.25446\nx0=6.07671, x1=5.30914, y=-1.03218\nx0=-3.12560, x1=8.76353, y=0.59811\nx0=1.83566, x1=0.59233, y=1.52343\nx0=-2.31581, x1=7.87712, y=0.26466\nx0=-5.68564, x1=5.68470, y=-0.00078\nx0=-2.93368, x1=-0.61337, y=-0.78205\nx0=2.76035, x1=5.15698, y=-0.53071\nx0=-6.65170, x1=-4.86614, y=0.62797\nx0=-8.80266, x1=5.31646, y=-1.40579\nx0=6.11038, x1=7.94200, y=0.82418\nx0=4.92606, x1=-8.66111, y=-1.66884\nx0=3.07644, x1=7.13707, y=0.81895\nx0=-1.96412, x1=4.44818, y=-1.88894\nx0=-3.90294, x1=1.65600, y=1.68627\nx0=-8.20140, x1=6.17950, y=-1.04375\nx0=2.43842, x1=-9.66809, y=0.88756\nx0=1.90981, x1=3.26422, y=0.82076\nx0=6.25892, x1=-5.49284, y=0.68633\nx0=-2.83365, x1=-3.68113, y=0.21064\nx0=-4.56309, x1=0.63829, y=1.58470\nx0=1.07997, x1=-8.65204, y=0.18385\nx0=-3.09527, x1=-9.09257, y=-0.37244\nx0=0.73045, x1=-9.60126, y=0.84277\nx0=-0.59640, x1=-3.87201, y=0.10551\nx0=-4.67943, x1=9.23593, y=1.18719\nx0=4.94239, x1=1.25158, y=-0.02418\nx0=-5.58323, x1=-2.16210, y=-0.18603\nx0=2.63630, x1=4.24726, y=-0.40970\nx0=1.26379, x1=-5.42119, y=1.71239\nx0=-2.56906, x1=9.70929, y=-0.82246\nx0=6.86881, x1=8.62532, y=1.26970\nx0=-4.67138, x1=8.89582, y=1.50380\nx0=0.11121, x1=4.74450, y=-0.88850\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.68137, x1=0.68242, y=0.37689\nx0=-8.61033, x1=-2.91412, y=-0.95287\nx0=-2.67561, x1=9.47333, y=-0.49783\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(x0) + sin(x1)", "data": [[7.146758940218405, 2.8688785964838477, 1.0295154712236259], [3.9851187784550923, -9.933565370378052, -0.25987343644784305], [-7.606451778161447, 4.119253340825583, -1.7987126379060028], [-6.041125013119304, -8.863644348007877, -0.2924429532433046], [8.479016699061042, 9.638572291390698, 0.598773239521184], [-2.2203037977762374, 0.18332378490784684, -0.6140831105398968], [8.597083821806567, -8.878766759446187, 0.21709070982444034], [8.687380194966249, -7.582165510728558, -0.29092092741580755], [4.121042114110789, -3.9154162567916178, -0.13131543299384718], [-2.6637121578235323, 9.900992037182267, -0.9183159294074579], [4.463610091892821, -5.1595069542788625, -0.06751686402437884], [-4.122506142544262, -7.696404073235204, -0.15660446719293908], [7.717264752271685, 9.136967445397833, 1.2745222763853237], [9.71064749188091, -2.231210504501493, -1.0717300249784136], [4.441956092284553, -4.212668354279765, -0.0859388745819043], [6.552980089626871, 3.0550947107090654, 0.35292377018440557], [7.206383542696244, -9.369129822561604, 0.7419156817079875], [9.766956107370795, -7.446446201568227, -1.253640193419948], [1.7420955197749528, 1.0921740146905652, 1.8729944030557923], [4.2280631059900635, -5.1199696053959265, 0.03309349213023227], [9.41650105128404, 2.4945315324755164, 0.6111210167196696], [-8.036743409528597, 9.967529514966191, -1.4998395761563668], [-9.335585288084596, -6.718744380533139, -0.5109918025062988], [-2.4826177203580873, 5.490846958362113, -1.324303899930297], [-0.0032598777145604885, 1.9565528118739532, 0.9232541906868391], [-7.307567626107634, 5.921542584277574, -1.208204565305219], [2.0368979199720876, 4.257137783551666, -0.004823564419678794], [-6.8131920111448725, -6.1532506984911395, -0.3759698226122703], [4.577082265386927, -4.024782583455247, -0.2180925821956674], [5.529393666977205, 2.926303588629036, -0.4707783254843032], [8.186510183793892, 6.032154859598048, 0.6968177199809401], [4.4239200450648415, -6.615075779221176, -1.2845114784400673], [-3.146459633586039, -6.65310671382672, -0.35667519533430136], [-6.197042967691355, -2.329376865858741, -0.6397773348345709], [6.74355135683696, -5.66365383577303, 1.0249298483736597], [2.4097660321916052, -8.637799350241124, -0.03999376925942211], [-6.821538271473965, -7.816431335490053, -1.5120176884919494], [4.7234248525384785, 4.827114698606012, -1.9933653252537598], [5.982956215259879, 9.726916560575255, -0.5933016705122287], [6.529666929238868, -4.300778269058611, 1.160471023743868], [-4.990855328355335, 1.749885319999878, 1.9454845229634719], [4.17672352068009, 1.749117199030234, 0.12421375906262044], [2.3053600792432363, -1.488065201887018, -0.25445650716327883], [6.076706671872422, 5.309136374549897, -1.032182416263597], [-3.1255971872390447, 8.763526330362708, 0.5981103654924631], [1.8356560745346293, 0.5923324977937447, 1.523426899758931], [-2.3158118960858154, 7.8771155691025285, 0.26465507570465785], [-5.685639159118468, 5.684701337131305, -0.0007750674265161184], [-2.933678910453712, -0.6133739044077746, -0.7820486323359017], [2.7603509426281008, 5.156979126473452, -0.5307136982034021], [-6.6517000328065095, -4.866135059004188, 0.6279740628048915], [-8.802656993321374, 5.316460894100601, -1.4057896656724287], [6.110380798067702, 7.941998870709575, 0.8241832214912032], [4.926061385160434, -8.661108503422204, -1.668835328022682], [3.0764355517791273, 7.137071549637046, 0.8189505880474948], [-1.9641196142555302, 4.448181287857565, -1.888940189947486], [-3.9029399381378216, 1.6559971024919555, 1.6862699889439057], [-8.201399715467712, 6.179504572021145, -1.0437499939187413], [2.43841609858608, -9.668090755954019, 0.8875631561530182], [1.9098116394383169, 3.2642249640516923, 0.8207574188632345], [6.258916993215188, -5.492839376073102, 0.6863307800051983], [-2.8336496958595365, -3.6811281688048965, 0.21063854157262735], [-4.563092939587161, 0.6382897467824229, 1.584698813071349], [1.079972023113669, -8.652044306987474, 0.1838494658995996], [-3.095266065737725, -9.092568013318532, -0.3724429582417768], [0.7304499910325131, -9.601257897085276, 0.8427701682342188], [-0.5964002574521299, -3.8720074664840443, 0.10551085984511943], [-4.679426122722841, 9.235926986670098, 1.187187196449451], [4.942393934166571, 1.2515781480636683, -0.02418420286502987], [-5.583232845985256, -2.1621045105334424, -0.18603081902631147], [2.636297248268713, 4.247263055179356, -0.4096991403795274], [1.2637890618166985, -5.421188969441733, 1.7123858008514667], [-2.569056983316571, 9.709291902392458, -0.8224560614237256], [6.868806231711176, 8.625319730490688, 1.2696954791749442], [-4.671383348563198, 8.895816621733424, 1.5037962915310839], [0.11120926712561285, 4.744500185122419, -0.8885043008528714], [9.68136942476185, 0.6824208624836459, 0.376888486421403], [-8.61032557444915, -2.914117922938231, -0.9528679279293641], [-2.675608784822936, 9.473327012438869, -0.49783196953607384]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.51870, x1=-9.99051, y=-65.12517\nx0=6.93440, x1=-8.65867, y=-60.04268\nx0=5.23864, x1=-0.63720, y=-3.33808\nx0=-5.09222, x1=-2.36915, y=12.06423\nx0=-4.62950, x1=2.36154, y=-10.93276\nx0=-4.96775, x1=-1.53136, y=7.60741\nx0=2.46559, x1=-3.75909, y=-9.26840\nx0=5.52167, x1=-5.30000, y=-29.26485\nx0=-9.51173, x1=-3.87065, y=36.81659\nx0=8.80945, x1=-7.73814, y=-68.16878\nx0=-0.77552, x1=-0.71221, y=0.55234\nx0=6.44521, x1=3.19535, y=20.59467\nx0=2.07455, x1=8.96577, y=18.59993\nx0=-6.53018, x1=7.60374, y=-49.65377\nx0=-1.48158, x1=9.95246, y=-14.74539\nx0=9.49025, x1=-8.73791, y=-82.92489\nx0=-9.27548, x1=-5.56463, y=51.61460\nx0=5.29884, x1=2.69606, y=14.28600\nx0=8.46751, x1=-7.09255, y=-60.05619\nx0=-0.75310, x1=-7.23090, y=5.44560\nx0=-8.91109, x1=3.14807, y=-28.05272\nx0=6.81579, x1=-4.69004, y=-31.96637\nx0=-2.39901, x1=5.67783, y=-13.62115\nx0=9.50312, x1=1.95292, y=18.55881\nx0=-5.40745, x1=0.07099, y=-0.38386\nx0=-5.66031, x1=3.03046, y=-17.15337\nx0=8.53776, x1=-8.42375, y=-71.91995\nx0=9.38993, x1=-8.99974, y=-84.50697\nx0=-0.06544, x1=-0.66726, y=0.04366\nx0=7.36328, x1=-4.29479, y=-31.62374\nx0=-1.51951, x1=0.58467, y=-0.88841\nx0=2.49319, x1=0.71982, y=1.79466\nx0=5.78615, x1=8.87987, y=51.38027\nx0=4.61607, x1=-6.08459, y=-28.08689\nx0=1.94980, x1=1.28838, y=2.51208\nx0=-1.29886, x1=-8.59224, y=11.16012\nx0=0.87434, x1=0.54488, y=0.47641\nx0=-1.80141, x1=-6.64884, y=11.97729\nx0=6.23667, x1=8.29969, y=51.76244\nx0=-7.35108, x1=4.75930, y=-34.98605\nx0=6.54937, x1=-3.19095, y=-20.89871\nx0=-1.07994, x1=3.95720, y=-4.27353\nx0=-2.93002, x1=7.71855, y=-22.61547\nx0=9.91885, x1=-0.11879, y=-1.17829\nx0=2.07316, x1=-9.13189, y=-18.93185\nx0=-7.57332, x1=-5.74665, y=43.52124\nx0=-7.07322, x1=0.01068, y=-0.07554\nx0=9.60178, x1=5.80922, y=55.77883\nx0=-9.24150, x1=-2.76702, y=25.57137\nx0=7.92859, x1=-9.43938, y=-74.84095\nx0=-2.47176, x1=-5.30824, y=13.12069\nx0=2.44461, x1=7.34603, y=17.95815\nx0=-8.65812, x1=-7.21880, y=62.50126\nx0=1.76348, x1=4.31141, y=7.60307\nx0=8.46439, x1=6.95496, y=58.86951\nx0=4.33110, x1=-0.13480, y=-0.58385\nx0=-9.19670, x1=1.33766, y=-12.30205\nx0=-8.67636, x1=9.22390, y=-80.02995\nx0=-0.64177, x1=-4.47000, y=2.86869\nx0=0.08529, x1=-4.06337, y=-0.34658\nx0=-9.82902, x1=5.77254, y=-56.73840\nx0=5.05799, x1=3.48616, y=17.63296\nx0=4.49367, x1=-0.04196, y=-0.18857\nx0=-2.79327, x1=1.16702, y=-3.25980\nx0=0.73433, x1=8.20369, y=6.02424\nx0=-1.24360, x1=-1.66333, y=2.06852\nx0=-4.89900, x1=-0.07643, y=0.37443\nx0=-4.09037, x1=8.66000, y=-35.42265\nx0=-6.14785, x1=-9.69282, y=59.58999\nx0=-1.70448, x1=2.63800, y=-4.49642\nx0=-6.83673, x1=1.19216, y=-8.15050\nx0=9.06510, x1=-3.72794, y=-33.79410\nx0=9.99763, x1=-5.84889, y=-58.47501\nx0=-3.73002, x1=3.56144, y=-13.28422\nx0=9.44782, x1=-3.14574, y=-29.72035\nx0=-6.15405, x1=8.85454, y=-54.49129\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-9.49853, x1=-1.80616, y=17.15586\nx0=-5.66525, x1=-8.24259, y=46.69630\nx0=9.26469, x1=-3.48878, y=-32.32248\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 * x1", "data": [[6.5187012012395655, -9.990512772799535, -65.12516761304755], [6.934402041609609, -8.658666784923527, -60.04267663099101], [5.2386443774011955, -0.6372026353783617, -3.3380780030900787], [-5.0922184813234335, -2.3691502842167056, 12.064230862320974], [-4.6294955549231265, 2.361544587909723, -10.93276017248083], [-4.967750719975717, -1.531358408287094, 7.607406835309079], [2.465594296219587, -3.7590944771069745, -9.268401901705507], [5.521668989023061, -5.300000461429271, -29.264848189681917], [-9.511725333734034, -3.870652668374664, 36.81658504386453], [8.809450917468752, -7.738141423377907, -68.16877706167945], [-0.775522894766592, -0.712214230460793, 0.5523384417009148], [6.445208795002042, 3.195345764496306, 20.594670624404113], [2.074549140870756, 8.965767462674116, 18.599925186937565], [-6.530181041830849, 7.603736249095917, -49.65377430092816], [-1.4815821254326664, 9.952464361523766, -14.745393302039247], [9.490247896633356, -8.737905743744047, -82.92489160554747], [-9.275481631297156, -5.56462753939714, 51.61460052668846], [5.2988351410352195, 2.6960647333196732, 14.286002551420031], [8.467507513935292, -7.0925468937985485, -60.05619411617762], [-0.7531011342815681, -7.230900336282627, 5.445599245131419], [-8.911094682489122, 3.1480671066337056, -28.052724054042528], [6.815794779724133, -4.690042781092365, -31.966369104052195], [-2.399006257703906, 5.677828582579265, -13.621146299777756], [9.503120580591997, 1.952917146107815, 18.558807123368165], [-5.407451456449975, 0.07098805779289918, -0.38386447650276767], [-5.660308996457546, 3.0304644822333344, -17.153365372230404], [8.537763472565455, -8.42374645583747, -71.91995479280186], [9.389933517882383, -8.999740975730784, -84.50696944027399], [-0.06543821128550498, -0.6672636174311659, 0.043664537580590995], [7.363283450907254, -4.2947873601433795, -31.623736694109397], [-1.519514653381595, 0.5846673508874449, -0.8884106070272713], [2.4931919085245013, 0.7198222472111766, 1.7946550023228287], [5.7861497744262245, 8.879871832334445, 51.38026839959573], [4.6160657201508855, -6.084594327197457, -28.08688729480072], [1.9498044196374558, 1.288376339548698, 2.512081881008379], [-1.2988595735897395, -8.592243678121767, 11.160117959944373], [0.874341067080465, 0.5448789527768998, 0.4764100450006409], [-1.8014114133646864, -6.648839177762557, 11.977294780447748], [6.236673414645857, 8.29968718207213, 51.762438398306244], [-7.351084434745072, 4.759304770128441, -34.98605121589916], [6.54936589402309, -3.190951320096551, -20.89870774532831], [-1.0799377402708075, 3.9571987491246325, -4.273528274932121], [-2.9300167886107946, 7.718547391132226, -22.61547343970547], [9.918848122530154, -0.11879281383804674, -1.1782878785075839], [2.0731575431677722, -9.131892031547137, -18.93185084859562], [-7.573320955125366, -5.746652094664821, 43.52124073034017], [-7.073218606111116, 0.010679366083456543, -0.07553749088297682], [9.60178330027004, 5.809215937739564, 55.7788325786503], [-9.241498250211063, -2.7670158613343148, 25.571372240827326], [7.928588469189069, -9.439378338117683, -74.84094624791294], [-2.4717605815539656, -5.3082381012646955, 13.120693696208942], [2.4446071525326936, 7.346026852364339, 17.958149785987093], [-8.65811781079371, -7.218804530264422, 62.501260076120715], [1.763475214699259, 4.311414576218041, 7.603072745453625], [8.4643862526056, 6.954964485000101, 58.86950577419504], [4.331104315263012, -0.13480344076019435, -0.5838477639887796], [-9.196699681896739, 1.337658995638943, -12.30204805967898], [-8.676363779036919, 9.223904646498106, -80.0299521761665], [-0.6417653290343672, -4.46999888124868, 2.868690302807812], [0.08529416461449735, -4.063367267726767, -0.3465815166226472], [-9.829018450211542, 5.772539522589666, -56.738397472109156], [5.057990467160639, 3.4861589051817443, 17.632958509416433], [4.493668800285789, -0.04196330972338558, -0.18856921566070706], [-2.7932686618322533, 1.1670190253368329, -3.2597976712353955], [0.7343328043008306, 8.203689618381727, 6.024238403079864], [-1.2435981117925028, -1.663334305935539, 2.0685194021411295], [-4.898995749330927, -0.07643028572518595, 0.37443164488783426], [-4.090374355830939, 8.66000224584807, -35.42265110785528], [-6.147851086523901, -9.692815810866826, 59.589988214313664], [-1.7044784437064777, 2.6380017516693233, -4.49641712018029], [-6.836729302961706, 1.1921637797403086, -8.150501046880153], [9.065096199924898, -3.727936031497567, -33.7940987526917], [9.997625650036468, -5.848890108955398, -58.475013777537086], [-3.730015179514627, 3.5614391612033245, -13.28422213220624], [9.447822052060019, -3.145735456290815, -29.720348813891448], [-6.1540492241163065, 8.854542639532024, -54.49129126071681], [-9.498527309230367, -1.8061598109253012, 17.15585828890833], [-5.6652482724687285, -8.242587541748376, 46.69630483156225], [9.26469153313246, -3.4887811480871234, -32.32248116363491]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.57393, x1=9.92334, y=90.10450\nx0=7.67482, x1=8.98158, y=88984278.71489\nx0=6.43131, x1=-2.54310, y=0.00880\nx0=1.50216, x1=5.54581, y=9.55063\nx0=7.64219, x1=-5.64790, y=0.00001\nx0=0.26043, x1=-0.72855, y=2.66502\nx0=3.05558, x1=-8.14506, y=0.00011\nx0=9.29931, x1=-9.97932, y=0.00000\nx0=6.21788, x1=-1.62038, y=0.05176\nx0=0.83219, x1=6.42434, y=0.30724\nx0=3.71560, x1=-8.15873, y=0.00002\nx0=4.95296, x1=1.40679, y=9.49575\nx0=4.13621, x1=7.58140, y=47283.51218\nx0=8.05970, x1=-7.10820, y=0.00000\nx0=8.09451, x1=8.55057, y=58284124.05853\nx0=7.92782, x1=-6.83461, y=0.00000\nx0=1.24356, x1=5.34091, y=3.20343\nx0=7.69312, x1=7.29545, y=2914162.33022\nx0=2.64168, x1=-2.70072, y=0.07255\nx0=8.83868, x1=-8.03869, y=0.00000\nx0=9.88578, x1=-6.86044, y=0.00000\nx0=8.16143, x1=3.27641, y=971.22227\nx0=0.69209, x1=7.13682, y=0.07232\nx0=8.17579, x1=-0.96351, y=0.13206\nx0=5.76747, x1=-5.24999, y=0.00010\nx0=2.03490, x1=3.52316, y=12.21920\nx0=1.66707, x1=-9.15644, y=0.00928\nx0=5.91582, x1=0.50091, y=2.43617\nx0=2.36196, x1=8.46111, y=1439.77970\nx0=0.29306, x1=-1.47593, y=6.11978\nx0=4.04286, x1=-8.30291, y=0.00001\nx0=3.98601, x1=3.89161, y=217.29888\nx0=0.44497, x1=2.28185, y=0.15760\nx0=4.12456, x1=-2.89161, y=0.01662\nx0=1.17564, x1=6.64373, y=2.93007\nx0=4.63676, x1=2.34844, y=36.69124\nx0=9.47843, x1=8.00117, y=65318463.16949\nx0=0.23295, x1=-5.80736, y=4726.59378\nx0=3.27124, x1=-0.77182, y=0.40062\nx0=5.73634, x1=-1.07580, y=0.15271\nx0=5.09869, x1=-4.39090, y=0.00078\nx0=2.86422, x1=-3.64380, y=0.02162\nx0=6.50514, x1=3.27157, y=457.74923\nx0=7.56548, x1=-3.74610, y=0.00051\nx0=2.04213, x1=3.49039, y=12.08683\nx0=7.75856, x1=2.63391, y=220.59761\nx0=9.87809, x1=-1.47617, y=0.03402\nx0=5.17157, x1=4.20587, y=1003.24025\nx0=7.40170, x1=-8.02605, y=0.00000\nx0=4.11600, x1=-6.50951, y=0.00010\nx0=7.11438, x1=1.63261, y=24.61547\nx0=6.04427, x1=0.99377, y=5.97690\nx0=6.34841, x1=-5.48156, y=0.00004\nx0=2.33588, x1=-8.54963, y=0.00071\nx0=9.33003, x1=8.35477, y=126807461.19574\nx0=8.60902, x1=-5.81464, y=0.00000\nx0=7.99959, x1=6.85206, y=1541242.45227\nx0=5.73028, x1=-3.47259, y=0.00233\nx0=6.82039, x1=6.88034, y=545627.06863\nx0=7.24438, x1=-4.40823, y=0.00016\nx0=9.18005, x1=-1.23136, y=0.06522\nx0=6.40662, x1=-5.71493, y=0.00002\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=5.24723, x1=5.04203, y=4264.90193\nx0=4.84497, x1=-6.44182, y=0.00004\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0 ** x1", "data": [[1.5739274512142707, 9.923341184959554, 90.10450106855473], [7.674823914937036, 8.981580523575943, 88984278.71488601], [6.431306614356256, -2.543101122223204, 0.008798595632311222], [1.5021582247782472, 5.545813704091309, 9.550634828702531], [7.64218555948683, -5.647904388558436, 1.0272391480638833e-05], [0.260428503244043, -0.7285510254744327, 2.6650215896099945], [3.0555847984804494, -8.145060077493122, 0.00011191220465226616], [9.299308267209728, -9.9793247951684, 2.165291991330411e-10], [6.21787685724825, -1.6203768127394298, 0.051760768578536655], [0.8321899173326912, 6.424336726370942, 0.30724311060481585], [3.715596206433304, -8.158731030518913, 2.2350677939565072e-05], [4.952959263396561, 1.4067908354758973, 9.495752154427617], [4.1362069854602055, 7.581402150177272, 47283.51218206273], [8.059702893266788, -7.108202279291609, 3.611611163072307e-07], [8.094511157760124, 8.550573030810344, 58284124.058527775], [7.927820627049908, -6.834606753412585, 7.155455106258991e-07], [1.2435649181073494, 5.340905391213052, 3.203430438514], [7.693118042200695, 7.2954477579422665, 2914162.330219463], [2.6416758484660328, -2.7007249835380236, 0.0725469944868292], [8.838683810418154, -8.038694446368762, 2.467625627050361e-08], [9.885777064360997, -6.860437891613196, 1.4920731665211338e-07], [8.16142626746726, 3.2764091113067124, 971.2222676272464], [0.6920908638779757, 7.1368212630583905, 0.07232238332593435], [8.175792927870507, -0.9635058024999879, 0.1320602643973232], [5.767465204734902, -5.249988101771333, 0.00010112019376878144], [2.0348954745900567, 3.5231585293670715, 12.219199409508477], [1.6670719176854583, -9.156440814637211, 0.009282998091419248], [5.915819126778461, 0.5009062570667062, 2.436167176924496], [2.3619581562371685, 8.46110706765877, 1439.7796981937538], [0.2930602349172631, -1.4759321662536706, 6.119775167429425], [4.042863708031195, -8.30291008538529, 9.177300377863088e-06], [3.986005699907862, 3.891606872860349, 217.29887553879286], [0.4449744422038755, 2.281851920480733, 0.15759872440061293], [4.124557880602227, -2.891613320939057, 0.016617531301410002], [1.17563730151862, 6.64373318429697, 2.930066219424087], [4.636761162836445, 2.3484356691156947, 36.69124313045321], [9.478433203516545, 8.001170763031489, 65318463.16949082], [0.23294868529816704, -5.807361334681618, 4726.593781285988], [3.2712427670914206, -0.7718233105317189, 0.40062005082928487], [5.73634265339556, -1.0758015670252359, 0.15270708471184005], [5.098694645019307, -4.390900776872058, 0.000782740332817781], [2.864215137465777, -3.64379795636947, 0.021615425980270837], [6.5051427581351575, 3.271571189781021, 457.7492282244881], [7.565482880427226, -3.746100281044229, 0.0005102579356830324], [2.042130122981513, 3.4903908862637056, 12.08682721139132], [7.758556892182064, 2.6339075955760336, 220.59760863182336], [9.878093433782041, -1.4761729649140616, 0.034016561919382085], [5.171572526985489, 4.205871374422811, 1003.2402512060224], [7.401697590306398, -8.026050987573623, 1.0536645343518534e-07], [4.115996933151127, -6.5095148619624865, 0.00010001510116379861], [7.114379295699209, 1.632610928886411, 24.61547407068513], [6.044266875773019, 0.9937698452206156, 5.976896563397274], [6.348406473781274, -5.481561870439158, 3.982388673478158e-05], [2.335879564297688, -8.549629076278212, 0.0007077589066250524], [9.330029756438986, 8.354765024852743, 126807461.195738], [8.609016964759281, -5.814637723683744, 3.6608652117174895e-06], [7.999587408783238, 6.852057414050783, 1541242.4522714037], [5.730281691842421, -3.4725856269249196, 0.002328997475853946], [6.820392742745362, 6.8803446211138315, 545627.0686299609], [7.244376757350633, -4.408228328802288, 0.00016177786632919232], [9.180048210759697, -1.2313564252598557, 0.06522208371463747], [6.4066238020038355, -5.7149286490969775, 2.4556787089916914e-05], [5.247231379228239, 5.0420290376456816, 4264.90193184219], [4.8449669255809, -6.441817584112577, 3.8501847277124094e-05]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-1.68579, x1=4.57655, y=-1.16006\nx0=3.36838, x1=4.92237, y=-2.66272\nx0=-8.32298, x1=5.78056, y=-1.82391\nx0=-4.00266, x1=6.54209, y=-1.69163\nx0=6.53907, x1=5.70116, y=-2.26254\nx0=-1.73051, x1=-8.13532, y=-2.81240\nx0=-7.44872, x1=-3.86540, y=-2.34894\nx0=-4.14518, x1=-1.49831, y=-4.80309\nx0=2.49383, x1=0.08170, y=1.21858\nx0=-1.85968, x1=-8.18377, y=-2.73654\nx0=1.95206, x1=-9.92029, y=-1.59759\nx0=4.48229, x1=-0.50378, y=-0.28835\nx0=8.45425, x1=-1.93302, y=-1.53470\nx0=-4.09024, x1=-6.85078, y=-2.35969\nx0=-4.33986, x1=-4.79939, y=-2.50481\nx0=0.48086, x1=9.45704, y=-7.81593\nx0=-0.54901, x1=-1.29937, y=1.93593\nx0=-6.50633, x1=4.09061, y=-1.69610\nx0=0.77638, x1=0.71853, y=1.68528\nx0=-8.65157, x1=9.73302, y=-1.89680\nx0=-8.81774, x1=-9.31572, y=-2.11372\nx0=9.82435, x1=4.43120, y=-2.22204\nx0=-5.04811, x1=-3.66387, y=-2.58081\nx0=7.72243, x1=7.13253, y=-2.17281\nx0=-0.22658, x1=-7.91968, y=5.46523\nx0=-5.06318, x1=5.58843, y=-1.71242\nx0=5.47561, x1=9.95269, y=-2.17477\nx0=-2.79329, x1=-1.13467, y=-55.11066\nx0=-4.13245, x1=-2.99363, y=-2.96041\nx0=5.14331, x1=1.73398, y=-3.52068\nx0=-2.08033, x1=2.11193, y=-0.78272\nx0=2.75046, x1=1.50537, y=-9.89161\nx0=-5.03473, x1=0.52019, y=-0.39830\nx0=-0.00829, x1=0.05514, y=0.99954\nx0=-9.40153, x1=1.56006, y=-1.49058\nx0=-1.32281, x1=3.34044, y=-0.78686\nx0=3.07810, x1=6.26607, y=-2.55257\nx0=-9.15676, x1=2.79828, y=-1.68557\nx0=1.42375, x1=8.84112, y=-2.93871\nx0=9.91649, x1=3.04975, y=-2.33036\nx0=-8.85745, x1=9.03454, y=-1.89160\nx0=-6.37227, x1=8.34018, y=-1.83970\nx0=7.74271, x1=3.74874, y=-2.34582\nx0=-0.09955, x1=-9.37256, y=2.35423\nx0=-6.41175, x1=-7.36638, y=-2.20348\nx0=2.09425, x1=-6.36888, y=-1.44914\nx0=-7.05046, x1=9.29854, y=-1.86873\nx0=4.79663, x1=-6.20341, y=-1.72524\nx0=1.35509, x1=-6.19310, y=-1.20999\nx0=-3.30704, x1=-0.09705, y=1.35942\nx0=3.46068, x1=6.68242, y=-2.44719\nx0=1.62075, x1=8.92732, y=-2.78473\nx0=2.73049, x1=-3.62846, y=-1.30273\nx0=-8.54832, x1=7.60532, y=-1.86767\nx0=0.63440, x1=-8.39135, y=-0.91872\nx0=-6.97791, x1=0.91513, y=-1.04110\nx0=0.35956, x1=-3.42103, y=0.12762\nx0=3.10874, x1=-9.53129, y=-1.72418\nx0=7.20549, x1=-2.63505, y=-1.59066\nx0=-1.73365, x1=-2.81020, y=-6.80797\nx0=8.11986, x1=-2.97893, y=-1.66898\nx0=5.18096, x1=-3.08313, y=-1.52566\nx0=5.58857, x1=0.56016, y=-70.96649\nx0=-5.83797, x1=1.68568, y=-1.29912\nx0=-6.01903, x1=3.39179, y=-1.61564\nx0=-6.77691, x1=-6.70669, y=-2.21201\nx0=7.17578, x1=-2.21891, y=-1.52437\nx0=3.95940, x1=-7.72307, y=-1.73197\nx0=-3.07355, x1=1.73898, y=-0.92149\nx0=-5.91560, x1=-4.17218, y=-2.41511\nx0=-0.88536, x1=-5.15516, y=-7.75391\nx0=-8.96916, x1=3.35041, y=-1.72769\nx0=5.59874, x1=9.19375, y=-2.18567\nx0=-2.94271, x1=2.43702, y=-1.11517\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=0.90788, x1=-3.82743, y=-0.61000\nx0=4.00144, x1=-3.31160, y=-1.44619\nx0=8.04272, x1=-2.96258, y=-1.66452\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1 + x0 * x1 / (1 - (x0 * x1 / 3))", "data": [[-1.6857891927797635, 4.576546639760426, -1.1600632758931226], [3.368379879865417, 4.922368380224896, -2.662719479343773], [-8.322978929399032, 5.78055998288912, -1.823914310697842], [-4.002658741876042, 6.542086143206468, -1.6916302095839009], [6.539069238222929, 5.7011615506331985, -2.2625415353560405], [-1.7305119510521987, -8.135318741363726, -2.812401485047106], [-7.448720812661163, -3.8653954352235376, -2.3489420078465453], [-4.1451750592663235, -1.4983064275852271, -4.803089996429298], [2.493833105705292, 0.0816965802686358, 1.2185821035493865], [-1.8596849224721073, -8.183767594591234, -2.736544003655736], [1.952063579855114, -9.920292041050509, -1.597586247100971], [4.482292103863497, -0.5037795647462229, -0.28835093118057453], [8.454253274562177, -1.9330200717868777, -1.5346971494369317], [-4.0902396597580415, -6.850778691716122, -2.359693157204643], [-4.339856493200161, -4.799388273347374, -2.504805287483552], [0.4808557815512682, 9.457040556976555, -7.815934857952405], [-0.5490143536227983, -1.2993701087657215, 1.9359280598673516], [-6.506325830818939, 4.090608103170974, -1.696098196287779], [0.7763792020811255, 0.7185328757785197, 1.6852833242227123], [-8.651567484948144, 9.733018715380972, -1.8967959360903786], [-8.817735003584488, -9.315720291730042, -2.11371741184494], [9.824350606600433, 4.431201405556127, -2.222037595403311], [-5.048110706644335, -3.663871753880792, -2.5808089033658814], [7.722431648893362, 7.132531005549314, -2.1728094566622365], [-0.22657623395605775, -7.91967816363595, 5.465229774479472], [-5.063175333714542, 5.588434542096168, -1.7124161814334538], [5.47560999835885, 9.952687513112007, -2.1747673425280865], [-2.793293589715238, -1.1346668019154809, -55.11066063236862], [-4.132453784352952, -2.993626734609043, -2.96040730198828], [5.14331062014506, 1.7339820491515674, -3.520679135541175], [-2.080331642758888, 2.1119312700317217, -0.7827174193017876], [2.7504562030757267, 1.5053691428432519, -9.891608602557193], [-5.034728721308113, 0.5201937808681194, -0.3983013649070215], [-0.008285106093540051, 0.055137269648646736, 0.9995432514215965], [-9.401532219753461, 1.5600628281356634, -1.4905751000268017], [-1.32280763681565, 3.340441992227671, -0.7868596155968659], [3.0781049884157525, 6.266068515451909, -2.55256702900654], [-9.156761058284442, 2.798275371462111, -1.6855690769915932], [1.4237549463953503, 8.841121773315969, -2.938713398888167], [9.916488721218364, 3.0497529390143825, -2.3303620251939945], [-8.857451173739985, 9.034536891864292, -1.8915962646799667], [-6.372273724977027, 8.340178842736602, -1.8397033514634327], [7.742705295433424, 3.7487444300062407, -2.3458157002543087], [-0.09955049860435494, -9.372557674014192, 2.3542265678830447], [-6.4117526210071425, -7.366381344655297, -2.20347529061827], [2.0942515457282056, -6.36887938224612, -1.4491381779006467], [-7.050459115456502, 9.298539202055615, -1.8687261500966468], [4.7966343303733705, -6.203411852235043, -1.7252369684718327], [1.3550928131557995, -6.193100011493041, -1.209987535377866], [-3.3070403690527765, -0.09705455107992833, 1.35941648798088], [3.4606754847689185, 6.682423910295551, -2.4471894010823925], [1.6207466577157952, 8.927315417207549, -2.7847297433942333], [2.7304901228019105, -3.6284587572968263, -1.3027293928459773], [-8.548322015391161, 7.605322439046095, -1.8676718610863063], [0.6343978829361152, -8.391348523613804, -0.9187180847149596], [-6.977913098579442, 0.9151332222888833, -1.0410964843076864], [0.35956237748500364, -3.4210284079137114, 0.1276228024094972], [3.108744887538119, -9.531285613830981, -1.724183037558559], [7.205489041428486, -2.635048869527507, -1.5906637822819651], [-1.7336482575187873, -2.810197201903244, -6.807965883098896], [8.119864613239123, -2.9789262729880006, -1.6689774252813905], [5.180959244884216, -3.0831344587039355, -1.5256565513687397], [5.588566842267806, 0.5601611727896021, -70.96649145103599], [-5.837967129465911, 1.6856828436855036, -1.2991178793025515], [-6.019034166951627, 3.391791144402241, -1.6156360417347995], [-6.77690962760744, -6.706685965886674, -2.212011114220712], [7.175780708637561, -2.2189131697612456, -1.524374092207867], [3.9594032321808683, -7.723067608244307, -1.7319732572420987], [-3.0735519873840467, 1.7389795475404668, -0.9214897304067255], [-5.915603409519545, -4.172177531650883, -2.4151110068170762], [-0.8853564289263574, -5.155158919819569, -7.753912482854808], [-8.9691605673416, 3.350410562061331, -1.727688376289048], [5.598738690866831, 9.193749814964782, -2.1856688303179563], [-2.9427148270681736, 2.437024694745439, -1.1151720304458], [0.9078788117353636, -3.8274255630557157, -0.6100039561368826], [4.001435156027499, -3.3116031097197407, -1.4461935534299886], [8.04271783844506, -2.962581254136449, -1.6645196558385842]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=-9.73165, x1=2.70366, y=-1.69295\nx0=-3.58268, x1=-9.31126, y=-2.29645\nx0=4.59906, x1=8.05587, y=-2.26432\nx0=8.89259, x1=5.35131, y=-2.20185\nx0=4.77268, x1=7.83134, y=-2.26181\nx0=7.54619, x1=-4.17174, y=-1.73898\nx0=-4.69631, x1=1.46738, y=-1.09011\nx0=-7.35791, x1=4.53563, y=-1.75256\nx0=4.61014, x1=-7.68097, y=-1.76569\nx0=5.32894, x1=-9.07763, y=-1.82481\nx0=4.37892, x1=-1.72957, y=-1.14883\nx0=9.40402, x1=-4.63863, y=-1.80696\nx0=2.99356, x1=7.84679, y=-2.43924\nx0=-9.40153, x1=1.56006, y=-1.49058\nx0=9.56959, x1=0.51514, y=-6.66389\nx0=-4.84610, x1=-8.48702, y=-2.23604\nx0=6.93124, x1=2.98108, y=-2.50955\nx0=-9.06827, x1=2.65665, y=-1.66779\nx0=5.02402, x1=0.54235, y=30.70247\nx0=-0.64621, x1=9.46125, y=-1.01250\nx0=3.69362, x1=-5.90848, y=-1.63744\nx0=1.75590, x1=-5.74574, y=-1.31240\nx0=-2.06908, x1=2.52093, y=-0.90458\nx0=-2.83324, x1=8.72107, y=-1.67519\nx0=-0.91879, x1=4.55418, y=-0.74727\nx0=-4.38042, x1=7.72467, y=-1.75568\nx0=5.92963, x1=6.35222, y=-2.25962\nx0=1.83120, x1=-2.17233, y=-0.71023\nx0=5.19742, x1=-8.30516, y=-1.80505\nx0=6.20048, x1=3.40747, y=-2.49647\nx0=-1.87980, x1=0.92979, y=-0.10439\nx0=-1.05473, x1=-0.17530, y=1.19704\nx0=3.01641, x1=-2.92019, y=-1.23784\nx0=8.70121, x1=9.09109, y=-2.11826\nx0=5.87392, x1=2.80625, y=-2.66747\nx0=-3.88265, x1=-4.82167, y=-2.57249\nx0=-9.95439, x1=1.32555, y=-1.44427\nx0=-7.56250, x1=2.75247, y=-1.62210\nx0=-6.47645, x1=-7.84048, y=-2.18837\nx0=7.35070, x1=4.49089, y=-2.29989\nx0=1.26082, x1=-3.43990, y=-0.77336\nx0=0.85149, x1=-9.46795, y=-1.18640\nx0=7.18050, x1=8.10274, y=-2.16310\nx0=6.34728, x1=0.89253, y=-5.37694\nx0=6.51879, x1=-8.84923, y=-1.85170\nx0=2.62482, x1=-6.96446, y=-1.57708\nx0=9.76911, x1=-9.62123, y=-1.90721\nx0=-1.11423, x1=-1.50134, y=4.78141\nx0=-2.45529, x1=2.87342, y=-1.10493\nx0=-2.15239, x1=-5.93424, y=-2.92092\nx0=-0.34881, x1=9.68708, y=-0.58911\nx0=-2.08033, x1=2.11193, y=-0.78272\nx0=9.18800, x1=-5.88021, y=-1.84218\nx0=-2.98089, x1=-5.22547, y=-2.71562\nx0=5.19343, x1=8.28835, y=-2.22475\nx0=9.16697, x1=1.14916, y=-3.19454\nx0=-9.65316, x1=3.43396, y=-1.75103\nx0=1.00422, x1=9.79178, y=-3.31711\nx0=2.45919, x1=0.60605, y=3.96185\nx0=4.73816, x1=-2.86862, y=-1.45757\nx0=6.12438, x1=-2.73783, y=-1.54471\nx0=-5.48836, x1=-5.60268, y=-2.32433\nx0=3.05416, x1=-7.67360, y=-1.65956\nx0=9.21692, x1=-0.39726, y=-0.64896\nx0=7.10050, x1=3.31672, y=-2.43795\nx0=-5.94963, x1=-2.66231, y=-2.70095\nx0=0.53407, x1=4.07169, y=8.90347\nx0=-5.48410, x1=-6.70475, y=-2.26651\nx0=-8.60110, x1=3.41180, y=-1.72175\nx0=4.54884, x1=-6.62563, y=-1.72842\nx0=-9.96575, x1=-7.87244, y=-2.11928\nx0=-8.77594, x1=5.06376, y=-1.81028\nx0=-1.89232, x1=-5.44426, y=-3.23250\nx0=-8.30235, x1=9.00606, y=-1.88428\nx0=-5.87204, x1=7.44181, y=-1.80727\nx0=-4.66849, x1=7.80270, y=-1.77173\nx0=1.35997, x1=2.66194, y=-16.51267\nx0=9.26257, x1=0.17119, y=4.36347\nx0=-9.07206, x1=8.38658, y=-1.88620\nx0=0.47349, x1=5.53335, y=21.68475\nx0=7.47228, x1=-6.07808, y=-1.81412\nx0=-8.10032, x1=9.62911, y=-1.88889\nx0=-6.85848, x1=-5.55301, y=-2.25652\nx0=-9.68451, x1=3.17796, y=-1.73355\nx0=9.25520, x1=9.06697, y=-2.11123\nx0=9.19072, x1=-9.05942, y=-1.89567\nx0=-8.46162, x1=5.94451, y=-1.83114\nx0=-2.88537, x1=2.08042, y=-1.00031\nx0=-7.87847, x1=8.33922, y=-1.86900\nx0=4.79539, x1=-3.16986, y=-1.50551\nx0=-6.00547, x1=-3.24680, y=-2.54550\nx0=4.56262, x1=2.56289, y=-3.03526\nx0=5.82621, x1=-7.80736, y=-1.81438\nx0=8.00024, x1=8.79269, y=-2.13364\nx0=-5.97891, x1=6.58001, y=-1.78744\nx0=-0.27576, x1=-8.25026, y=10.41571\nx0=-7.25835, x1=-5.72032, y=-2.23364\nx0=-7.25059, x1=-8.90885, y=-2.14612\nx0=-5.72274, x1=5.41270, y=-1.73510\nx0=-6.62694, x1=7.60213, y=-1.83139\nx0=8.76377, x1=0.63551, y=-5.50266\nx0=-7.73837, x1=-2.57009, y=-2.53291\nx0=5.28997, x1=4.66292, y=-2.41538\nx0=4.13827, x1=7.97249, y=-2.30008\nx0=-5.61978, x1=6.19505, y=-1.76200\nx0=3.52562, x1=-9.54944, y=-1.75455\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.03154, x1=-6.84761, y=-1.86121\nx0=3.22706, x1=8.95938, y=-2.34732\nx0=-2.81824, x1=-0.99523, y=44.10693\nx0=-6.79524, x1=6.14007, y=-1.79876\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 1 + x0 * x1 / (1 - (x0 * x1 / 3))", "data": [[-9.731648851762607, 2.7036640643068885, -1.692949184833386], [-3.5826782582125833, -9.311261114436519, -2.2964499842518284], [4.59905825343621, 8.055865292156707, -2.2643218867071386], [8.89259480796769, 5.351310848289703, -2.2018523810655957], [4.772675532408371, 7.8313370258603, -2.261807285994015], [7.546186266387721, -4.171739873879343, -1.7389846152711552], [-4.696313791298666, 1.4673847463061875, -1.090109418518753], [-7.357906266279812, 4.5356330163145575, -1.7525620998084817], [4.610136433251068, -7.680968834554798, -1.7656879363841052], [5.328940826422649, -9.07762818843281, -1.8248145975040337], [4.378919394941175, -1.7295667053840376, -1.1488261567823788], [9.404019304852195, -4.638626931141252, -1.8069570003417432], [2.9935592960989243, 7.846786821415403, -2.4392424766242735], [-9.401532219753461, 1.5600628281356634, -1.4905751000268017], [9.569587003607985, 0.5151446602972314, -6.663885083072274], [-4.846101275396554, -8.48702283454738, -2.2360409810379114], [6.931236165690738, 2.981075603851613, -2.5095530139012836], [-9.068270085443103, 2.6566471860732506, -1.6677887312060942], [5.0240161547122035, 0.5423532457824098, 30.70247454445391], [-0.6462085593683415, 9.461248809586642, -1.0125017241204275], [3.6936181732153663, -5.9084813747447456, -1.6374428727163943], [1.7558978743228142, -5.745736190482116, -1.3123958355907988], [-2.069081016281224, 2.52093255118025, -0.904578260810166], [-2.8332442438459937, 8.721071405392426, -1.6751949098265912], [-0.9187882063189114, 4.554182072719149, -0.7472733670323939], [-4.380423700613234, 7.724666835254975, -1.7556825104815155], [5.929627257805061, 6.35222078730088, -2.259618119133278], [1.831203327022596, -2.1723312129032513, -0.7102284882336813], [5.19742142695293, -8.305159990419034, -1.805048872411958], [6.20047883103474, 3.407465141181458, -2.496471864744788], [-1.879802335694853, 0.9297855376894653, -0.10439038947654411], [-1.0547336993346121, -0.175298249382978, 1.197036527376492], [3.016414346114221, -2.920189995746174, -1.2378373446125228], [8.701208494807304, 9.091088076855726, -2.1182600745263027], [5.873920454783699, 2.8062519832441186, -2.66747253217965], [-3.8826490740874853, -4.821668486662862, -2.5724882495302563], [-9.954390431319407, 1.3255450039719268, -1.4442726665124206], [-7.562498510685652, 2.7524710722941297, -1.622095780643332], [-6.476449355229241, -7.840484338995681, -2.188369246598455], [7.35070155594995, 4.490891415104892, -2.299888016690343], [1.260820962621274, -3.4398965592188047, -0.7733562662689479], [0.8514937121981525, -9.467945284860352, -1.1863962471107357], [7.180503808712455, 8.102740915045143, -2.1630973653896137], [6.347277850874303, 0.8925300775130758, -5.376937865623774], [6.518788121532186, -8.849228892566703, -1.851696220008789], [2.624815000760792, -6.964458261183461, -1.57707590737109], [9.769113632469598, -9.621228694346149, -1.9072077670174687], [-1.1142323265340863, -1.5013402153933342, 4.781407075338992], [-2.4552925460249098, 2.8734161137648435, -1.1049297930152182], [-2.152389764368852, -5.93423980639254, -2.9209236601231443], [-0.3488099623121226, 9.687078825841745, -0.5891094045045742], [-2.080331642758888, 2.1119312700317217, -0.7827174193017876], [9.187997012366797, -5.880208893672847, -1.8421809657566866], [-2.980885221445533, -5.225468174718189, -2.71561921633377], [5.193432005169168, 8.288347112643887, -2.22474734372915], [9.166974237130812, 1.1491552790443027, -3.1945406565431913], [-9.653161768050078, 3.433959409836376, -1.7510274659951266], [1.0042228109045919, 9.791783484239751, -3.3171119129080413], [2.459194837212717, 0.6060529953141796, 3.961853664203074], [4.7381625556456015, -2.868617350124274, -1.457569106195963], [6.124379266468665, -2.7378343450085696, -1.5447080482553015], [-5.488356496821085, -5.602683406457116, -2.324329889083521], [3.054160756537925, -7.673596732929752, -1.659560277504272], [9.216923235977745, -0.39726344082780685, -0.6489623974273335], [7.100504426951154, 3.316723439184006, -2.437947478187645], [-5.949633814781247, -2.662307886148616, -2.7009478436877346], [0.5340719815285162, 4.071689057976853, 8.90347454074316], [-5.484097599587365, -6.70475240211625, -2.266512550913647], [-8.60109539045219, 3.4117966374401636, -1.7217515041874107], [4.54883972726725, -6.625625732664195, -1.7284159279224958], [-9.965749279429897, -7.872440884040763, -2.1192767502093943], [-8.775937613668905, 5.063764733464968, -1.8102838121354865], [-1.8923165304609348, -5.444257868274094, -3.2324952870777217], [-8.302346802939509, 9.00605957334911, -1.8842762694360622], [-5.872039949114145, 7.441814035823569, -1.807274857259202], [-4.66848900637588, 7.802704179342847, -1.7717290987299825], [1.3599684209611382, 2.661935234049217, -16.512668066375355], [9.262570848866293, 0.17119188260667428, 4.3634683357830655], [-9.072063439395668, 8.386580009726629, -1.8861963592196251], [0.47349443418778137, 5.533346206444119, 21.684748493301456], [7.472280477714939, -6.078078945911145, -1.8141153018166496], [-8.100316881828869, 9.62911217744821, -1.888887324982114], [-6.85848489699195, -5.553014108870671, -2.2565179544980065], [-9.684511848039081, 3.1779617130059705, -1.7335465581583867], [9.255203152973106, 9.066966655346704, -2.1112256070579627], [9.190717022431155, -9.059419021142068, -1.895667363064708], [-8.461615078519532, 5.944506489648877, -1.831144863659579], [-2.885371018567417, 2.0804226478449745, -1.0003100387864925], [-7.878467617795433, 8.339215854357601, -1.8689960947836797], [4.795393506315165, -3.1698645059640373, -1.5055148192662995], [-6.005468739524533, -3.2468007755765687, -2.5455021343602207], [4.562620681459684, 2.562885280329592, -3.0352593954351175], [5.826210640035219, -7.8073632039894525, -1.814384548151673], [8.00024426493189, 8.792687550967567, -2.133642893529575], [-5.978910759613787, 6.5800053968574055, -1.7874414005802897], [-0.2757624121432105, -8.25026098747346, 10.415708902418402], [-7.258349331055323, -5.720317715979806, -2.233644469997994], [-7.250589570573311, -8.908850961178166, -2.146117127614883], [-5.722741764513999, 5.412701596037753, -1.7351031853404413], [-6.6269397180682805, 7.602130247117508, -1.83139392281101], [8.763772268348099, 0.635511225079668, -5.502660162581632], [-7.738367309112901, -2.5700887388093925, -2.5329136128480885], [5.289967765736868, 4.662922082732205, -2.415383832319707], [4.138271922276736, 7.97248641913178, -2.300076852692489], [-5.61977504580959, 6.195046738570895, -1.7619977532173432], [3.525615848439813, -9.549443872338912, -1.7545521753092364], [9.0315401275681, -6.847607745881826, -1.8612063050260148], [3.2270616933180207, 8.959381852530662, -2.3473230159495637], [-2.8182424190191524, -0.9952307751358198, 44.10693227957301], [-6.795243961112263, 6.14007028215336, -1.7987625034559116]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=6.31081, y=2.17990\nx0=3.68512, y=1.73624\nx0=8.85191, y=2.51534\nx0=8.01261, y=2.41155\nx0=2.32660, y=1.42930\nx0=1.23563, y=1.09363\nx0=8.42312, y=2.46306\nx0=6.21173, y=2.16535\nx0=5.76891, y=2.09866\nx0=2.16067, y=1.38526\nx0=4.73172, y=1.92989\nx0=8.77546, y=2.50613\nx0=1.90122, y=1.31229\nx0=9.58121, y=2.60100\nx0=6.10042, y=2.14886\nx0=8.56541, y=2.48058\nx0=5.43664, y=2.04666\nx0=1.30843, y=1.12043\nx0=2.79627, y=1.54491\nx0=2.45237, y=1.46149\nx0=2.13546, y=1.37840\nx0=8.05280, y=2.41666\nx0=1.81505, y=1.28680\nx0=9.03459, y=2.53717\nx0=2.50166, y=1.47384\nx0=7.19541, y=2.30428\nx0=0.52430, y=0.76100\nx0=0.08634, y=0.35483\nx0=3.87343, y=1.77323\nx0=5.36398, y=2.03504\nx0=3.05511, y=1.60386\nx0=2.28339, y=1.41801\nx0=1.70686, y=1.25377\nx0=1.49938, y=1.18689\nx0=1.71620, y=1.25667\nx0=4.02235, y=1.80175\nx0=7.17848, y=2.30198\nx0=4.48171, y=1.88608\nx0=0.52146, y=0.75925\nx0=9.26556, y=2.56441\nx0=2.15569, y=1.38391\nx0=1.37834, y=1.14537\nx0=9.94761, y=2.64262\nx0=0.43674, y=0.70439\nx0=4.64311, y=1.91452\nx0=7.76898, y=2.38026\nx0=7.81583, y=2.38632\nx0=8.17969, y=2.43270\nx0=9.93733, y=2.64147\nx0=7.44026, y=2.33712\nx0=3.22007, y=1.63994\nx0=7.56669, y=2.35384\nx0=2.77802, y=1.54064\nx0=3.59997, y=1.71915\nx0=8.44180, y=2.46537\nx0=2.05687, y=1.35671\nx0=5.54169, y=2.06329\nx0=9.81628, y=2.62781\nx0=3.27810, y=1.65237\nx0=1.04818, y=1.02011\nx0=4.28361, y=1.85036\nx0=1.61091, y=1.22346\nx0=0.38751, y=0.66964\nx0=8.19813, y=2.43501\nx0=4.39019, y=1.86969\nx0=6.97363, y=2.27396\nx0=1.40682, y=1.15533\nx0=4.61814, y=1.91016\nx0=2.45409, y=1.46192\nx0=4.08211, y=1.81303\nx0=2.35960, y=1.43784\nx0=3.65653, y=1.73053\nx0=7.18150, y=2.30239\nx0=9.22513, y=2.55967\nx0=5.26808, y=2.01957\nx0=6.59145, y=2.22039\nx0=5.23985, y=2.01499\nx0=6.55900, y=2.21576\nx0=3.51263, y=1.70138\nx0=9.86546, y=2.63337\nx0=9.16785, y=2.55293\nx0=6.77911, y=2.24691\nx0=2.99835, y=1.59119\nx0=5.96545, y=2.12861\nx0=9.55747, y=2.59827\nx0=6.98355, y=2.27533\nx0=8.55636, y=2.47947\nx0=7.75459, y=2.37839\nx0=3.07406, y=1.60806\nx0=9.60955, y=2.60425\nx0=0.85631, y=0.93649\nx0=2.30667, y=1.42411\nx0=7.69645, y=2.37083\nx0=3.68980, y=1.73717\nx0=4.39394, y=1.87037\nx0=2.40572, y=1.44966\nx0=4.49242, y=1.88799\nx0=4.40118, y=1.87167\nx0=2.22802, y=1.40336\nx0=4.82667, y=1.94618\nx0=9.38915, y=2.57882\nx0=9.73378, y=2.61844\nx0=5.24069, y=2.01512\nx0=0.06845, y=0.32163\nx0=9.19567, y=2.55621\nx0=9.01752, y=2.53514\nx0=4.65254, y=1.91616\nx0=7.25995, y=2.31300\nx0=1.12575, y=1.05138\nx0=9.96690, y=2.64479\nx0=5.55944, y=2.06609\nx0=6.16766, y=2.15884\nx0=8.35257, y=2.45431\nx0=4.89319, y=1.95748\nx0=5.76811, y=2.09854\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=3.43926, y=1.68626\nx0=8.89211, y=2.52017\nx0=0.63216, y=0.82366\nx0=6.80638, y=2.25073\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = x0**0.423", "data": [[6.310811956721928, 2.1798974150483934], [3.685116012007432, 1.7362363427674026], [8.851908829093418, 2.51533956637151], [8.01260520846391, 2.411550129495529], [2.326601664755003, 1.4293000884852518], [1.2356322415726613, 1.0936268018870952], [8.423118516952389, 2.463060284623238], [6.211734038924895, 2.1653546489810247], [5.7689134129174455, 2.098663313352036], [2.160669727970987, 1.3852587045842573], [4.731721377016809, 1.9298924461517928], [8.77546046507194, 2.5061275665593192], [1.9012239338539842, 1.3122937922194193], [9.58120670204331, 2.6010023744496213], [6.100418755504798, 2.1488550974788074], [8.565409596384914, 2.4805755652470696], [5.4366422750933, 2.0466562713596774], [1.3084293128979478, 1.1204316341320013], [2.796274067037256, 1.544910155082707], [2.4523658446615553, 1.4614856803640348], [2.1354551527995085, 1.3783974548114828], [8.052798922300582, 2.4166598099156507], [1.8150491373448947, 1.2867962530374932], [9.034593340284765, 2.537168680231335], [2.501664845051927, 1.473841971859848], [7.195414149825005, 2.3042765579750832], [0.5243029405822348, 0.7609976403545301], [0.0863433821632178, 0.35483372536085667], [3.8734287848706828, 1.7732273798821028], [5.36398142586714, 2.035040764992399], [3.0551082396052216, 1.6038592471434836], [2.283392534072643, 1.4180109481569243], [1.7068550304478443, 1.2537737625482281], [1.4993757500799667, 1.186889080013753], [1.716197686360438, 1.2566720995391667], [4.022347640517799, 1.8017514156952625], [7.178479160372017, 2.3019809418949384], [4.4817056242891145, 1.88608181308778], [0.5214643457313546, 0.7592521214942781], [9.26555506757882, 2.564405028213942], [2.1556873398442082, 1.3839066021352164], [1.3783350010484412, 1.1453733499099414], [9.947609740762967, 2.642621880537859], [0.4367445810224808, 0.7043949652321688], [4.6431077990833085, 1.9145208851977793], [7.768978861321255, 2.380257523383013], [7.815829229703283, 2.3863187362767544], [8.17969327058001, 2.432695539260256], [9.937329030331753, 2.641466275776784], [7.4402631937586285, 2.3371245118498], [3.2200661457136803, 1.6399356517545574], [7.566691397175372, 2.3538416720430337], [2.7780203356093836, 1.5406361457706508], [3.599965500956017, 1.7191516853603845], [8.441797750142953, 2.4653692845667474], [2.0568674120821058, 1.3567076187626703], [5.541689764448892, 2.063291811316493], [9.81627524251779, 2.6278070026834706], [3.278102091964909, 1.6523738255168963], [1.048184515695727, 1.0201056757472882], [4.283611901750742, 1.8503576471365928], [1.6109102765453631, 1.223463963372459], [0.3875054374245046, 0.6696401881593735], [8.198126115508096, 2.4350129412264088], [4.390186345144215, 1.8696929472054467], [6.973628204167021, 2.2739612930527144], [1.4068240185311414, 1.1553283344558656], [4.618141228094794, 1.9101594872507661], [2.4540928299245195, 1.4619209417040724], [4.082106907116254, 1.8130262427124997], [2.3595981205456535, 1.4378397691891807], [3.656533427043499, 1.7305271560839186], [7.1815045223965654, 2.302391272775199], [9.225129202488542, 2.5596662930166785], [5.268084553004048, 2.019570915552709], [6.591453100354816, 2.2203888273076973], [5.239853456709904, 2.0149858315686737], [6.558999006054201, 2.215757816493652], [3.512628345886643, 1.7013843014845276], [9.865464486858045, 2.6333689978434505], [9.167849766236444, 2.5529314139510717], [6.779105307519739, 2.246911240601196], [2.9983516795901437, 1.591187385810781], [5.965445605368577, 2.1286141386370905], [9.557465373959772, 2.5982741714850133], [6.98355382736586, 2.2753297911406425], [8.55635781252634, 2.479466361494287], [7.7545920022365, 2.378392009215438], [3.0740614201298584, 1.6080605757946882], [9.609548965114378, 2.604254184847564], [0.8563056440159826, 0.9364875005640131], [2.3066684755706497, 1.4241073610820651], [7.696453904079441, 2.3708329503083694], [3.689800314783529, 1.7371695622884975], [4.393938662405867, 1.8703687503359632], [2.405716921990159, 1.449660926389893], [4.492415747244285, 1.8879870670638026], [4.401181282554203, 1.8716722260042251], [2.2280219701549733, 1.4033627199472143], [4.826670227716765, 1.9461797367660387], [9.389154143734565, 2.5788198021481814], [9.733781502702364, 2.6184429374324405], [5.240687202307786, 2.0151214462918174], [0.06844703332182434, 0.3216288576564854], [9.195673710346227, 2.55620595846052], [9.017522145735835, 2.5351396807782933], [4.6525371242325235, 1.916164568214128], [7.259951149982545, 2.3129963873721215], [1.1257484465531142, 1.051379957367454], [9.966903609171176, 2.6447887519158653], [5.559441861236255, 2.066085047092678], [6.167660301142874, 2.158842447317591], [8.352565401784833, 2.4543122289440196], [4.893190804177085, 1.957480659659609], [5.768109661446143, 2.0985396251274038], [3.4392585589299802, 1.6862603243367356], [8.892114203863827, 2.520165885890573], [0.6321600488229393, 0.8236635368214674], [6.806378610380868, 2.2507305807264473]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=8.61046, y=2.93436\nx0=5.77411, y=2.40294\nx0=5.07255, y=2.25223\nx0=1.90090, y=1.37873\nx0=3.35925, y=1.83283\nx0=4.11636, y=2.02888\nx0=4.76727, y=2.18341\nx0=3.19649, y=1.78787\nx0=3.09815, y=1.76016\nx0=2.46212, y=1.56911\nx0=0.04280, y=0.20688\nx0=3.70791, y=1.92559\nx0=5.55494, y=2.35689\nx0=8.04202, y=2.83585\nx0=6.14957, y=2.47983\nx0=0.16951, y=0.41171\nx0=8.69791, y=2.94922\nx0=4.74705, y=2.17877\nx0=2.34548, y=1.53150\nx0=3.96550, y=1.99136\nx0=4.95399, y=2.22576\nx0=8.03094, y=2.83389\nx0=5.48657, y=2.34234\nx0=0.75187, y=0.86711\nx0=5.05352, y=2.24800\nx0=9.55844, y=3.09167\nx0=5.50665, y=2.34663\nx0=6.01158, y=2.45185\nx0=6.14008, y=2.47792\nx0=5.99297, y=2.44806\nx0=4.10248, y=2.02546\nx0=4.82708, y=2.19706\nx0=5.81851, y=2.41216\nx0=1.87943, y=1.37092\nx0=3.52174, y=1.87663\nx0=8.94822, y=2.99136\nx0=9.02780, y=3.00463\nx0=9.10047, y=3.01670\nx0=3.99841, y=1.99960\nx0=4.03059, y=2.00763\nx0=8.13118, y=2.85152\nx0=0.10446, y=0.32320\nx0=0.64314, y=0.80196\nx0=6.95489, y=2.63721\nx0=9.28482, y=3.04710\nx0=7.11480, y=2.66736\nx0=2.93460, y=1.71307\nx0=1.98249, y=1.40801\nx0=0.38660, y=0.62177\nx0=9.17038, y=3.02826\nx0=8.79486, y=2.96561\nx0=1.42210, y=1.19252\nx0=5.95070, y=2.43940\nx0=1.68851, y=1.29943\nx0=4.88672, y=2.21059\nx0=9.35944, y=3.05932\nx0=9.40194, y=3.06626\nx0=9.41990, y=3.06918\nx0=4.40210, y=2.09812\nx0=9.69962, y=3.11442\nx0=1.20262, y=1.09664\nx0=8.88924, y=2.98148\nx0=0.67452, y=0.82129\nx0=0.93845, y=0.96874\nx0=0.78752, y=0.88742\nx0=5.42954, y=2.33014\nx0=1.55676, y=1.24770\nx0=4.70801, y=2.16980\nx0=9.51222, y=3.08419\nx0=4.42298, y=2.10309\nx0=5.05306, y=2.24790\nx0=8.87119, y=2.97845\nx0=8.16713, y=2.85782\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=9.74652, y=3.12194\nx0=9.74998, y=3.12250\nx0=9.86614, y=3.14104\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sqrt(x0)", "data": [[8.610458119856128, 2.9343582126005217], [5.774105103076073, 2.4029367663498915], [5.072552908832311, 2.2522328718035154], [1.900895596068859, 1.3787297037740425], [3.3592529279367582, 1.8328264860419161], [4.116363664294196, 2.0288823682742665], [4.767270056799097, 2.1834078997748216], [3.196490197764695, 1.7878730933051974], [3.098152656962211, 1.760156997816448], [2.4621162139722026, 1.5691131934861178], [0.042798506990080046, 0.2068780002563831], [3.7079075314376753, 1.9255927740406784], [5.554942318275077, 2.356892513093263], [8.042020707119306, 2.835845677592366], [6.149565222788288, 2.479831692431623], [0.16950527923609196, 0.411710188404528], [8.697914798346906, 2.94922274478326], [4.74704507086864, 2.178771459072438], [2.3454829499294694, 1.5314969637349822], [3.965497966701269, 1.9913558111752077], [4.953992284752916, 2.2257565645759456], [8.030943919972572, 2.8338920092291047], [5.486572379252356, 2.342343352126745], [0.751871963321242, 0.8671055087595984], [5.053516185396063, 2.2480027102732913], [9.55843665078527, 3.0916721447762323], [5.506650267177988, 2.346625293304832], [6.011579069513383, 2.4518521712194197], [6.14008268584173, 2.4779190232616015], [5.992974914274619, 2.448055333172561], [4.1024831115468325, 2.025458741013214], [4.82708090474322, 2.1970618800441692], [5.8185107408806465, 2.412158937732057], [1.8794331511649722, 1.3709241959951586], [3.521737503654234, 1.8766292930822097], [8.948218019549884, 2.9913572203182093], [9.027802399939405, 3.00463016025923], [9.100469451317924, 3.016698435594437], [3.9984066283111694, 1.9996016174006186], [4.030587339698641, 2.0076322720305733], [8.131176111142956, 2.851521718511531], [0.10446125198802612, 0.3232046596013525], [0.6431419714505745, 0.8019613279021467], [6.95488677111356, 2.63721193139906], [9.284821455624787, 3.0471004997578905], [7.1148028349628145, 2.667358775073727], [2.934604393647192, 1.7130687066335641], [1.9824941149850008, 1.4080106942012198], [0.38659954100577093, 0.6217712931663627], [9.170376856330359, 3.0282630097682004], [8.794855891973782, 2.9656122288616533], [1.4220977017625591, 1.1925173800672924], [5.95069588374055, 2.4394048216195174], [1.6885141194422069, 1.2994283818057104], [4.886721709503551, 2.2105930673698295], [9.359440508364472, 3.059320269008211], [9.401943626716474, 3.066258897535639], [9.419895445707843, 3.069184817782703], [4.402103890158776, 2.0981191315458654], [9.69961802529453, 3.114420977532506], [1.2026162013462658, 1.0966385919464379], [8.889235099835151, 2.9814820307751564], [0.6745156011968969, 0.8212889876267043], [0.9384519341864496, 0.9687372885289641], [0.7875174859732258, 0.8874218196400322], [5.4295408309922895, 2.330137513322398], [1.5567572539531478, 1.247700787029145], [4.708013383324388, 2.1697957008263216], [9.512221109378, 3.084188890028949], [4.422980250953577, 2.1030882651361966], [5.053061913515675, 2.2479016690050466], [8.871187827656625, 2.978453932438208], [8.167131281608329, 2.8578193227718804], [9.746522708301976, 3.121942137244375], [9.749981794971522, 3.1224960840602383], [9.866136124923877, 3.141040611791557]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=1.29154, x1=7.45624, y=-0.77755\nx0=8.53743, x1=7.01663, y=-0.22169\nx0=-1.72484, x1=-3.81615, y=0.17419\nx0=3.67513, x1=-1.27518, y=-0.55965\nx0=-7.18369, x1=2.57916, y=0.27083\nx0=-7.54760, x1=-5.87357, y=-0.92759\nx0=6.56277, x1=-1.52129, y=-0.29497\nx0=6.84867, x1=-9.18424, y=0.09000\nx0=3.21718, x1=0.10450, y=-0.99222\nx0=-6.44278, x1=5.18526, y=-0.20227\nx0=4.48814, x1=8.91701, y=-0.10903\nx0=0.83147, x1=0.89895, y=0.85393\nx0=3.70073, x1=-8.62436, y=0.26043\nx0=-4.46731, x1=6.03945, y=0.40272\nx0=-3.12315, x1=-4.67241, y=-0.69257\nx0=2.74982, x1=-3.43947, y=0.12349\nx0=7.52623, x1=3.38653, y=0.11693\nx0=2.65000, x1=-7.22407, y=0.65981\nx0=5.74244, x1=-3.48012, y=-0.12214\nx0=2.13770, x1=-5.90648, y=0.06377\nx0=-8.07619, x1=3.85085, y=-0.15169\nx0=-6.81312, x1=-8.41964, y=-0.34382\nx0=6.11167, x1=-0.44215, y=0.24825\nx0=-0.86723, x1=5.78157, y=0.93363\nx0=-2.40378, x1=9.34886, y=-0.01699\nx0=7.40763, x1=3.94222, y=0.38709\nx0=9.83408, x1=9.52448, y=0.04073\nx0=-2.53934, x1=6.20196, y=-0.61845\nx0=-4.98181, x1=-6.48190, y=0.92361\nx0=-1.86806, x1=8.35669, y=0.16951\nx0=-5.24987, x1=-8.30528, y=0.53086\nx0=5.06464, x1=1.40434, y=0.73836\nx0=-7.97767, x1=9.07977, y=-0.09690\nx0=8.88004, x1=-0.79605, y=0.63083\nx0=-5.08667, x1=5.40971, y=0.88350\nx0=-1.06567, x1=-4.21604, y=0.51155\nx0=3.63429, x1=0.09152, y=-0.73833\nx0=8.16599, x1=2.28197, y=-0.13005\nx0=-3.38401, x1=5.38213, y=-0.84135\nx0=3.68652, x1=-7.62414, y=0.53603\nx0=5.32272, x1=-0.87204, y=0.89878\nx0=7.50667, x1=0.57994, y=-0.92495\nx0=-5.85731, x1=7.71064, y=0.45072\nx0=-2.31910, x1=-8.84041, y=-0.09526\nx0=8.05618, x1=-2.92843, y=-0.04932\nx0=7.40519, x1=-5.50927, y=0.92024\nx0=-9.19057, x1=-1.48425, y=-0.69202\nx0=-5.03107, x1=-3.67366, y=0.25058\nx0=-6.42845, x1=-2.27491, y=0.09078\nx0=-1.60340, x1=-1.72705, y=-0.43644\nx0=-4.60988, x1=-8.63387, y=0.22746\nx0=7.16897, x1=-2.53400, y=-0.29042\nx0=-9.04364, x1=-5.18868, y=0.71816\nx0=-6.83104, x1=-7.92201, y=-0.49995\nx0=-8.15378, x1=-8.64141, y=-0.12576\nx0=-0.59984, x1=-2.26556, y=-0.33218\nx0=-4.37081, x1=5.15471, y=0.22785\nx0=9.44954, x1=-4.44191, y=-0.60489\nx0=1.42904, x1=3.66464, y=-0.21729\nx0=-5.98166, x1=-9.28648, y=0.03020\nx0=8.24863, x1=-3.97592, y=0.07788\nx0=-1.09233, x1=3.99439, y=0.41265\nx0=9.99736, x1=2.89974, y=0.07881\nx0=-1.60217, x1=-8.97888, y=0.14882\nx0=9.71205, x1=-1.63187, y=0.62255\nx0=4.88712, x1=-0.42566, y=0.84663\nx0=6.31360, x1=-3.26607, y=0.00284\nx0=-9.88391, x1=8.61747, y=0.30325\nx0=5.06372, x1=-3.01205, y=0.06258\nx0=4.98344, x1=3.05472, y=0.04034\nx0=-9.32716, x1=-2.56847, y=-0.27963\nx0=-7.26864, x1=2.65855, y=0.23816\nx0=-5.04413, x1=9.03290, y=0.18668\nx0=8.23119, x1=-9.57923, y=-0.01681\nx0=6.22089, x1=-1.08305, y=0.07995\nx0=2.42032, x1=5.19787, y=0.40217\nx0=7.61591, x1=1.93268, y=-0.51698\nx0=-0.06073, x1=-6.92434, y=0.08633\nx0=5.99640, x1=-6.85146, y=-0.40032\nx0=5.35880, x1=-8.75551, y=-0.32287\nx0=-4.33725, x1=-1.78216, y=-0.13882\nx0=-8.68362, x1=-3.14371, y=0.00047\nx0=8.98554, x1=-3.11720, y=0.00964\nx0=1.52493, x1=-9.02405, y=-0.15007\nx0=-2.65521, x1=-9.20360, y=-0.08227\nx0=6.45596, x1=7.69210, y=0.19527\nx0=-1.24736, x1=8.37127, y=0.48024\nx0=-0.70750, x1=0.46011, y=-0.84997\nx0=8.96916, x1=-2.97600, y=0.06413\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=6.72750, x1=-3.34869, y=0.06390\nx0=-7.80027, x1=4.09259, y=-0.34870\nx0=-3.29319, x1=-2.99364, y=0.07201\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = sin(1.5 * x0) * cos(0.5 * x1)", "data": [[1.2915441090412383, 7.45623702536405, -0.777549557100909], [8.537431746207925, 7.016632706507778, -0.2216948830752511], [-1.7248444383433732, -3.81615354908011, 0.1741875226081164], [3.6751261753638875, -1.275178286391462, -0.5596538424415239], [-7.183691917981574, 2.5791634825333283, 0.2708315174982851], [-7.547599958884672, -5.873572293568545, -0.9275867188596919], [6.562772397565691, -1.5212900895432497, -0.2949684707378487], [6.8486730073933515, -9.184238264962964, 0.0899985305405318], [3.2171800985598242, 0.10449911129678924, -0.9922233031302388], [-6.442775861343399, 5.185259329298955, -0.20226710357758376], [4.4881360348504735, 8.917013815535903, -0.10902548199004305], [0.8314740272112608, 0.898953087202873, 0.8539310081053116], [3.7007280235211333, -8.624356345275206, 0.2604279143686479], [-4.467311504160742, 6.039446888021175, 0.402724898050989], [-3.1231463456991815, -4.67240782401962, -0.6925657673463674], [2.749821502270942, -3.43946699963539, 0.12349403841782008], [7.526233027845159, 3.3865314105944773, 0.11692967292769249], [2.6499985618522626, -7.224068081711841, 0.6598132519595761], [5.742441534724605, -3.480117236719038, -0.1221394691170561], [2.137703851711109, -5.906481171810228, 0.06376931911101365], [-8.076190298284256, 3.8508536335383425, -0.15169076633565862], [-6.813119798989849, -8.419641882007578, -0.34381897688660756], [6.111668575143231, -0.44215397411164936, 0.24825353174331516], [-0.8672342173466578, 5.781566216345642, 0.9336304682079734], [-2.403779800045484, 9.34886041996991, -0.016986176784040446], [7.407632216140172, 3.9422186212953747, 0.3870932716605479], [9.834076086101522, 9.524475447065278, 0.040728514173104996], [-2.5393430741215255, 6.201955307419862, -0.6184527562195092], [-4.981807471613811, -6.481899714733221, 0.9236149356289126], [-1.8680579044752914, 8.356691339042715, 0.16951368645862033], [-5.249868708437329, -8.305280209490016, 0.530858321979603], [5.06464227486973, 1.4043410821858906, 0.7383647219076516], [-7.977666394756406, 9.07977287154121, -0.09690164032575119], [8.88003650718138, -0.7960531274767213, 0.6308341390211054], [-5.086672489930912, 5.409711016972974, 0.8835038183773116], [-1.06567208484803, -4.216036652600332, 0.5115548101458431], [3.6342943217275074, 0.09151752078044417, -0.7383334535257701], [8.165987128628604, 2.281969121532324, -0.13004693868424375], [-3.38401494634891, 5.3821338552341995, -0.8413536439610431], [3.6865155350895744, -7.624139951511055, 0.5360341008840471], [5.322715938094493, -0.8720447507355527, 0.8987792560496601], [7.506668453872557, 0.579938729564681, -0.9249457403066355], [-5.857307084323306, 7.710641693735418, 0.45071843351096086], [-2.319102868424432, -8.840413476161597, -0.0952601768534923], [8.056184809492638, -2.928430746844956, -0.04932115888437286], [7.405185051973092, -5.509273560354964, 0.9202388617266835], [-9.190567778883679, -1.4842496936722291, -0.6920167498606707], [-5.0310657638563345, -3.6736615703261926, 0.25058464750105974], [-6.428454547518885, -2.274906134924624, 0.09077705779757272], [-1.6034016023194226, -1.7270537213561248, -0.4364389547938675], [-4.609876792075003, -8.63387201287376, 0.22746105841985756], [7.168965251278465, -2.533995157321085, -0.2904211235426157], [-9.0436376297484, -5.188676767675466, 0.7181574941824694], [-6.83104263182432, -7.92200696611353, -0.4999490320678489], [-8.1537759772663, -8.641405035759833, -0.12576160794232621], [-0.5998448097720974, -2.2655599840036844, -0.3321819500819064], [-4.370810417335331, 5.154714140707865, 0.22785423796276147], [9.449537909685574, -4.4419090094324565, -0.6048948930197738], [1.4290373663127411, 3.6646432314460213, -0.2172912208105704], [-5.9816555645067115, -9.286476518936507, 0.030196899216341742], [8.248625596735234, -3.9759206056910124, 0.07788497243437931], [-1.0923263510485377, 3.994392293023223, 0.4126484051026012], [9.997356099228437, 2.8997405549385906, 0.07880804922429471], [-1.6021651490946205, -8.978876919159289, 0.14882005578391944], [9.712052010284157, -1.631872628528857, 0.622550761755264], [4.88712310444032, -0.425661931249941, 0.8466326016046639], [6.313599049682779, -3.2660688500548085, 0.0028365233728207028], [-9.88391346916549, 8.61747190025254, 0.30325427304599156], [5.063722791911946, -3.0120494723982745, 0.06257744335100454], [4.983436692823229, 3.0547185823124874, 0.04034462696100098], [-9.327156350015585, -2.568470941160548, -0.2796300049066198], [-7.268642350351239, 2.6585477905442474, 0.23815617998761432], [-5.044132109031172, 9.032895289923864, 0.1866833866631313], [8.231191928762843, -9.579233223799402, -0.01680519042414382], [6.220892071645611, -1.0830454400085614, 0.07995446202839765], [2.4203156721947714, 5.197871003970892, 0.40216969404650627], [7.615907902596749, 1.9326803557173413, -0.5169835148187318], [-0.06073012254309518, -6.924343800187362, 0.08633464049567167], [5.9963968386498046, -6.8514587811436485, -0.4003153591567742], [5.358797387328105, -8.755506856315806, -0.32286815632597704], [-4.337250386118539, -1.7821559486819716, -0.1388232449581013], [-8.68362081272293, -3.143705043602756, 0.0004680064304515962], [8.985536777949001, -3.1171992092965546, 0.00964358207181139], [1.5249273173416373, -9.024050554587932, -0.15007474601365542], [-2.655205971115187, -9.203603576301347, -0.08226978338585732], [6.455964697846646, 7.69209626794914, 0.19527428934575153], [-1.2473625880951964, 8.371270598169072, 0.4802392673628505], [-0.7075041184773596, 0.46010681556821, -0.8499698555397073], [8.96915577355134, -2.9760000073175297, 0.06412771336415003], [6.727496265125435, -3.348693786409809, 0.06390190417093612], [-7.800272415934073, 4.092588115247578, -0.34870045278076256], [-3.2931891306580336, -2.993640306200045, 0.07200609053484208]]}}
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{"data_source": "SymbolicRegression", "prompt": "You will be provided with a set of input-output pairs. Based on these data, infer the mathematical relationship between y and multiple input variables. Please note that the possible mathematical operations include: +, -, *, /, exp, sqrt, sin, arcsin, and constant terms. The input sample data are as follows:\nx0=4.68545, y=-1.29160\nx0=5.58048, y=-0.81094\nx0=-8.35205, y=2.00794\nx0=8.48855, y=0.18304\nx0=7.47944, y=0.28911\nx0=5.99556, y=-0.05012\nx0=5.19296, y=1.45891\nx0=3.26714, y=0.97446\nx0=-2.07674, y=0.28889\nx0=0.75994, y=-0.22754\nx0=-8.00576, y=0.08694\nx0=5.93445, y=-0.71274\nx0=5.54420, y=-0.45602\nx0=-5.56950, y=-0.70668\nx0=-3.63673, y=-0.82616\nx0=-8.39078, y=1.59498\nx0=-4.79930, y=-1.37126\nx0=-7.09458, y=1.19164\nx0=7.48431, y=0.22097\nx0=-3.95019, y=-0.36482\nx0=8.01228, y=0.18525\nx0=-3.49863, y=0.00904\nx0=6.09691, y=1.04617\nx0=-5.67329, y=-1.50810\nx0=0.96432, y=-0.06431\nx0=-2.85347, y=-0.68143\nx0=-4.84904, y=-1.18204\nx0=7.19607, y=2.03604\nx0=-2.47895, y=0.09806\nx0=-7.73253, y=-2.30580\nx0=7.19260, y=2.01896\nx0=-6.29990, y=1.79783\nx0=-6.69990, y=-1.91120\nx0=4.69351, y=-1.32030\nx0=-2.16311, y=0.55460\nx0=8.39326, y=1.56492\nx0=-2.81900, y=-0.76746\nx0=4.10999, y=0.78589\nx0=-3.73561, y=-1.11610\nx0=-1.24065, y=0.37155\nx0=9.38715, y=1.83363\nx0=1.13588, y=0.25686\nx0=-3.18057, y=0.86481\nx0=-5.05007, y=0.46878\nx0=-2.41146, y=0.38203\nx0=2.14766, y=0.51562\nx0=5.15182, y=1.26066\nx0=5.10683, y=0.95290\nx0=-0.59787, y=-0.10347\nx0=-2.23390, y=0.66675\nx0=1.34085, y=0.33848\nx0=9.53696, y=-0.65854\nx0=0.61283, y=-0.11969\nx0=-4.40052, y=0.77246\nx0=2.84329, y=-0.71060\nx0=1.92980, y=-0.24715\nx0=7.99533, y=-0.07037\nx0=-6.72427, y=-1.99097\nx0=6.67530, y=-1.78602\nx0=-8.61456, y=-1.70370\nx0=-0.93531, y=-0.11094\nx0=-1.22009, y=0.35958\nx0=7.69414, y=-2.16750\nx0=-3.20029, y=0.91364\nx0=-2.24558, y=0.67342\nx0=6.03710, y=0.41839\nx0=1.93743, y=-0.22267\nx0=2.64429, y=-0.62464\nx0=-8.15538, y=2.02682\nx0=-7.14308, y=1.67731\nx0=-4.08000, y=0.58969\nx0=-5.34253, y=1.33943\nx0=-6.65613, y=-1.65951\nx0=3.97732, y=-0.16943\nx0=-5.39943, y=0.95679\nx0=-1.94368, y=-0.20207\nx0=3.89149, y=-0.73573\nx0=-6.04045, y=0.45558\nx0=7.22543, y=2.14184\n\nBased on the above data, please infer the possible formula. Ensure that your inference applies to all the provided data points, and consider both linear and nonlinear combinations. Verify whether your formula applies to the following new data point and adjust it to ensure accuracy:\nx0=-0.59562, y=-0.10101\nx0=-0.09324, y=0.01546\nx0=3.68227, y=-1.00616\nFinally, please output the formula string you inferred within \\boxed{}(e.g. \\boxed{y=sqrt(x0 + x1) / (2 * pi)}). Note that you should express mathematical formulas using Python syntax(sqrt(x0)) instead of LaTeX format(\\sqrt(x_0)).", "ground_truth": {"true_formula": "y = 0.3 * x0 * sin(2 * pi * x0)", "data": [[4.685450415692255, -1.2916028282866285], [5.580478972611225, -0.8109363038886279], [-8.352051020830782, 2.0079381458006473], [8.4885507710744, 0.1830358951480955], [7.479436421261401, 0.28910771439399524], [5.99556490955689, -0.050116127269991685], [5.192961535697284, 1.4589082398940014], [3.267144532831459, 0.9744620215857438], [-2.0767364119364906, 0.28888504882816934], [0.7599397134539139, -0.2275374499225682], [-8.005762205819346, 0.08693560739518212], [5.934445734241461, -0.7127416613405507], [5.544201713995731, -0.45601779179967167], [-5.569501606681779, -0.7066757598982735], [-3.6367251272720402, -0.8261566854484392], [-8.390783011202476, 1.5949842652747432], [-4.799302248098892, -1.371259712183906], [-7.094577074555957, 1.1916411612751892], [7.484311086912292, 0.22097453140950288], [-3.9501949887333137, -0.3648221252819604], [8.012278140989835, 0.18525028650063236], [-3.498629038655528, 0.009041049734864316], [6.096909463794354, 1.0461667411802815], [-5.673292309857684, -1.508104286716826], [0.9643236323035715, -0.06430746097253728], [-2.853467150173339, -0.6814261822821388], [-4.8490363349830705, -1.1820415118176357], [7.196065570502597, 2.0360423607136435], [-2.478953037649763, 0.09806009029795269], [-7.732532445622143, -2.3058024479188957], [7.192598968621883, 2.0189560300651737], [-6.299902298799611, 1.7978271244332982], [-6.69989964232343, -1.9112029301602829], [4.693514587482872, -1.3203021099291756], [-2.1631112684503373, 0.5546048381977693], [8.393261701896918, 1.5649247448804773], [-2.8190012191554814, -0.7674571883148389], [4.109990540395959, 0.7858855019998897], [-3.735608429133559, -1.116103927726331], [-1.2406543972007338, 0.3715548265468381], [9.387151448133423, 1.8336254968982457], [1.1358844064276674, 0.2568601441619806], [-3.1805695516890804, 0.8648079441573912], [-5.050067507585374, 0.46877812585687], [-2.41145576660511, 0.38203358670040266], [2.147659475338104, 0.5156224697269847], [5.151815889269267, 1.2606553770051627], [5.106834897357345, 0.9528983413294917], [-0.5978704455634887, -0.10347487292553041], [-2.2339033774107815, 0.6667463751916699], [1.3408482628294216, 0.3384810944452698], [9.536964450363683, -0.6585428399204308], [0.6128346593878504, -0.11969498106846478], [-4.400521708808929, 0.7724633742452397], [2.843290317989368, -0.7105986225803137], [1.9298033235282084, -0.24714823878141928], [7.995330274203795, -0.07036660483466177], [-6.7242685141644305, -1.9909730551897542], [6.675298513820163, -1.7860224486747305], [-8.614559401686924, -1.703699920244364], [-0.9353051781564155, -0.11094235789122349], [-1.2200927670172028, 0.3595843871820157], [7.694135496476825, -2.167500127956133], [-3.200291377444449, 0.9136390214778934], [-2.2455833155000926, 0.673415609534242], [6.037101413512488, 0.4183882216382283], [1.9374288797049246, -0.22266651618527836], [2.644290066521645, -0.6246446713281676], [-8.155379377585339, 2.026819071755915], [-7.143083811885331, 1.6773075088834903], [-4.080003259525215, 0.5896889351316109], [-5.342529737882888, 1.3394332639132724], [-6.6561344038757735, -1.6595058502827849], [3.977323380961826, -0.16943374222194632], [-5.39943068791197, 0.9567932885439686], [-1.9436764694040054, -0.2020745984840594], [3.8914858255534046, -0.7357278394830299], [-6.040446331713114, 0.4555798594112135], [7.225426238596068, 2.1418412303058667], [-0.5956213789030826, -0.10101289590898904], [-0.09323680241919696, 0.015464804171960453], [3.6822719168183724, -1.0061579022732505]]}}
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