mirror of
https://github.com/InternLM/InternBootcamp.git
synced 2026-04-19 12:58:04 +00:00
update to tech report version (#10)
* 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
This commit is contained in:
Yongkang Chen
GitHub
parent
125a7818e0
commit
a8249acc18
2952 changed files with 105460 additions and 17649 deletions
100
examples/data/Intenbootcamp_eval/BbehMultistepArithmetic.jsonl
Normal file
100
examples/data/Intenbootcamp_eval/BbehMultistepArithmetic.jsonl
Normal file
|
|
@ -0,0 +1,100 @@
|
|||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if a > b; otherwise, a + b\n$~ b$ equals (a ! b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$][ b$ equals a * b if a > b; otherwise, a - b\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((5 !& -8) ][ -7) && -8) ~][ -2) ~ 8) ~! 1)\nLet B = ((((((7 !~ -9) ][ 9) ][! 6) [][] -2) ! 7) ][ 7)\nLet C = ((((((-9 ~~ 9) &[] 7) !~ 8) &[] -7) !! -4) ~ 10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ! b)", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((5 !& -8) ][ -7) && -8) ~][ -2) ~ 8) ~! 1)", "B": "((((((7 !~ -9) ][ 9) ][! 6) [][] -2) ! 7) ][ 7)", "C": "((((((-9 ~~ 9) &[] 7) !~ 8) &[] -7) !! -4) ~ 10)", "A_val": 1, "B_val": 0, "C_val": 10, "answer": -9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals (a >< b) if abs(a - b) < 2; otherwise, (a >< b)\n$:* b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((5 :*[] 8) [] 4) ><:* 7) [] 2) & -1) :*>< 3)\nLet B = ((((((4 >< 1) :*:* -2) >< -2) >< 10) :* -1) [][] -4)\nLet C = ((((((-7 >< -8) & 1) & -8) []>< -6) >< 2) [] 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "(a >< b)", "false_expr": "(a >< b)"}, {"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((5 :*[] 8) [] 4) ><:* 7) [] 2) & -1) :*>< 3)", "B": "((((((4 >< 1) :*:* -2) >< -2) >< 10) :* -1) [][] -4)", "C": "((((((-7 >< -8) & 1) & -8) []>< -6) >< 2) [] 7)", "A_val": 0, "B_val": 0, "C_val": 0, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$# b$ equals a - b if a * b > 0; otherwise, a + b\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\n$<> b$ equals (a # b) if abs(a - b) < 2; otherwise, (a # b)\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$>< b$ equals (a :* b) if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-3 []>< 1) <> -10) >< -4) <>[] -3) ><# -5) :* -4) ><:* -5) <># -4)\nLet B = ((((((((10 :* -5) :*# 5) #[] -9) ><[] -8) #<> 9) # -6) <>>< -4) #[] -1)\nLet C = ((((((((-3 ## -1) # 5) ><[] 8) []<> -10) []:* -10) <><> -8) ><# 8) :* -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "#", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "(a # b)", "false_expr": "(a # b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "(a :* b)", "false_expr": "a + b"}], "A": "((((((((-3 []>< 1) <> -10) >< -4) <>[] -3) ><# -5) :* -4) ><:* -5) <># -4)", "B": "((((((((10 :* -5) :*# 5) #[] -9) ><[] -8) #<> 9) # -6) <>>< -4) #[] -1)", "C": "((((((((-3 ## -1) # 5) ><[] 8) []<> -10) []:* -10) <><> -8) ><# 8) :* -4)", "A_val": -4, "B_val": -2, "C_val": -4, "answer": -2}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-10 >< -5) ; 2) ; 10) ;[] 6) ; 9) [] -5) []>< -8)\nLet B = (((((((-4 ><>< 5) &>< 2) @; 3) @[] 8) @ 6) >< 7) []& 4)\nLet C = (((((((-6 & -6) ><@ 1) &>< -3) ; 6) >< -4) & -8) []; 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((((-10 >< -5) ; 2) ; 10) ;[] 6) ; 9) [] -5) []>< -8)", "B": "(((((((-4 ><>< 5) &>< 2) @; 3) @[] 8) @ 6) >< 7) []& 4)", "C": "(((((((-6 & -6) ><@ 1) &>< -3) ; 6) >< -4) & -8) []; 7)", "A_val": 7, "B_val": 0, "C_val": 7, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a - b if a * b > 0; otherwise, a + b\n$; b$ equals a * b if a > b; otherwise, a - b\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-4 ; -10) <> 6) >< -3) <> 10)\nLet B = ((((6 ><<> -8) ;<> 1) ><! -9) <>; 3)\nLet C = ((((7 >< -10) ;! -7) ! 3) <> 5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": ";", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((-4 ; -10) <> 6) >< -3) <> 10)", "B": "((((6 ><<> -8) ;<> 1) ><! -9) <>; 3)", "C": "((((7 >< -10) ;! -7) ! 3) <> 5)", "A_val": 0, "B_val": -3, "C_val": 0, "answer": -3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if a > b; otherwise, a + b\n$>< b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals (a ][ b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((6 ][ 10) ! 9) @@ -4) ][ -1) ][ -9)\nLet B = (((((-5 ><@ 8) @>< 8) @ -5) @! -5) ! -6)\nLet C = (((((-9 ][ -2) ][ -6) @>< 6) ][! -4) ><>< 9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "><", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ][ b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((6 ][ 10) ! 9) @@ -4) ][ -1) ][ -9)", "B": "(((((-5 ><@ 8) @>< 8) @ -5) @! -5) ! -6)", "C": "(((((-9 ][ -2) ][ -6) @>< 6) ][! -4) ><>< 9)", "A_val": 0, "B_val": 1, "C_val": 0, "answer": 1}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$[] b$ equals a - b if a * b > 0; otherwise, a + b\n$! b$ equals (a [] b) if abs(a - b) < 2; otherwise, a - b\n$# b$ equals a - b if a * b > 0; otherwise, a + b\n$@ b$ equals (a [] b) if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((7 [] -2) [] -10) @@ -3) ![] -2) []! 3)\nLet B = (((((-3 []@ 6) ! -5) [][] 7) @# 9) @ -1)\nLet C = (((((3 !@ 4) ![] 6) @@ -1) @# 2) ! -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "[]", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "(a [] b)", "false_expr": "a - b"}, {"symbol": "#", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "(a [] b)", "false_expr": "a - b"}], "A": "(((((7 [] -2) [] -10) @@ -3) ![] -2) []! 3)", "B": "(((((-3 []@ 6) ! -5) [][] 7) @# 9) @ -1)", "C": "(((((3 !@ 4) ![] 6) @@ -1) @# 2) ! -2)", "A_val": 0, "B_val": 3, "C_val": 0, "answer": 3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals a * b if a > b; otherwise, a - b\n$! b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((6 :*# -5) ~# -9) #:* -3) :* -8)\nLet B = ((((10 # 5) ! -1) # -5) !! -7)\nLet C = ((((-4 ~ -4) #~ -4) :*! -10) :* 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((6 :*# -5) ~# -9) #:* -3) :* -8)", "B": "((((10 # 5) ! -1) # -5) !! -7)", "C": "((((-4 ~ -4) #~ -4) :*! -10) :* 7)", "A_val": -23, "B_val": 0, "C_val": -7, "answer": -16}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals (a <> b) if abs(a - b) < 2; otherwise, (a <> b)\n$; b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((9 ; -7) ;~ 7) <> -1) ~ 3)\nLet B = ((((6 ;; 1) @ -1) ;~ 6) <> -5)\nLet C = ((((-6 @ -8) ;@ -3) ~ 8) ~ 3)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}, {"symbol": ";", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((9 ; -7) ;~ 7) <> -1) ~ 3)", "B": "((((6 ;; 1) @ -1) ;~ 6) <> -5)", "C": "((((-6 @ -8) ;@ -3) ~ 8) ~ 3)", "A_val": -59, "B_val": 5, "C_val": 5, "answer": -59}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$[] b$ equals a - b if a * b > 0; otherwise, a + b\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((4 [] 2) ][<> -4) !@ 1) <>][ 3) []<> -8) @ -7) []][ -5) <><> 7)\nLet B = ((((((((-2 [] 10) !@ -10) ][ -1) ][! 1) ! -2) [] -1) [] 8) []@ 5)\nLet C = ((((((((-4 ][<> 3) ][ 2) ][ 10) ![] -7) [][] -9) @ 4) ! 4) ![] -7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((((4 [] 2) ][<> -4) !@ 1) <>][ 3) []<> -8) @ -7) []][ -5) <><> 7)", "B": "((((((((-2 [] 10) !@ -10) ][ -1) ][! 1) ! -2) [] -1) [] 8) []@ 5)", "C": "((((((((-4 ][<> 3) ][ 2) ][ 10) ![] -7) [][] -9) @ 4) ! 4) ![] -7)", "A_val": 7, "B_val": 3, "C_val": 16, "answer": -6}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals (a ~ b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$& b$ equals a * b if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((-8 !! 7) # -2) !# -7) ! 7) ~& -2)\nLet B = (((((4 !! 9) ~ 5) && -2) ~! 9) #& 8)\nLet C = (((((-1 # 8) ~# -8) # -2) && -3) # 9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ~ b)", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((((-8 !! 7) # -2) !# -7) ! 7) ~& -2)", "B": "(((((4 !! 9) ~ 5) && -2) ~! 9) #& 8)", "C": "(((((-1 # 8) ~# -8) # -2) && -3) # 9)", "A_val": 0, "B_val": 576, "C_val": -42, "answer": 618}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$[] b$ equals a * b if a > b; otherwise, a - b\n$:* b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((5 :*[] 7) []:* 2) :*:* 3)\nLet B = (((-8 []@ -6) [] 10) @ 6)\nLet C = (((1 @ 6) @[] 1) [][] -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((5 :*[] 7) []:* 2) :*:* 3)", "B": "(((-8 []@ -6) [] 10) @ 6)", "C": "(((1 @ 6) @[] 1) [][] -6)", "A_val": -19, "B_val": -12, "C_val": 6, "answer": -37}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals (a ; b) if is_prime(a) or is_prime(b); otherwise, (a ; b)\n$@ b$ equals (a <> b) if a * b > 0; otherwise, a + b\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((10 ~; 3) ;; 3) !~ -5) ~ -2) <><> -10) ;! 10) ! -10) @; 10)\nLet B = ((((((((2 <>~ 1) @ -8) ;~ -6) ~ -7) <><> 10) ~; 1) @! 4) ! -5)\nLet C = ((((((((2 @ 7) !; 7) ; -5) ~ -8) ! -6) ~~ 9) ~~ 10) @~ 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "(a <> b)", "false_expr": "a + b"}, {"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((((10 ~; 3) ;; 3) !~ -5) ~ -2) <><> -10) ;! 10) ! -10) @; 10)", "B": "((((((((2 <>~ 1) @ -8) ;~ -6) ~ -7) <><> 10) ~; 1) @! 4) ! -5)", "C": "((((((((2 @ 7) !; 7) ; -5) ~ -8) ! -6) ~~ 9) ~~ 10) @~ 7)", "A_val": 10, "B_val": 20, "C_val": 0, "answer": 30}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$# b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$][ b$ equals (a # b) if math.gcd(a, b) == 1; otherwise, (a # b)\n$>< b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-8 ][][ -5) ][ -5) #][ 7)\nLet B = (((-10 ><>< -2) ][# 6) ## 6)\nLet C = (((-2 ][ 7) ][ -1) >< -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "][", "condition": "math.gcd(a, b) == 1", "true_expr": "(a # b)", "false_expr": "(a # b)"}, {"symbol": "><", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((-8 ][][ -5) ][ -5) #][ 7)", "B": "(((-10 ><>< -2) ][# 6) ## 6)", "C": "(((-2 ][ 7) ][ -1) >< -6)", "A_val": 0, "B_val": 0, "C_val": 6, "answer": -6}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if a > b; otherwise, a + b\n$>< b$ equals (a ~ b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((6 &; 7) & -3) ;>< 7) ;; 7) # -6) # 6) # 8) #~ 1)\nLet B = ((((((((8 ><~ -3) #~ 7) ~; -4) ; 7) >< 2) ;# 8) ~ 4) & -10)\nLet C = ((((((((-5 ; 5) # 7) >< -2) ><& 9) #; 8) ; 8) ;# 3) &# 4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ~ b)", "false_expr": "math.gcd(a, b)"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((((((6 &; 7) & -3) ;>< 7) ;; 7) # -6) # 6) # 8) #~ 1)", "B": "((((((((8 ><~ -3) #~ 7) ~; -4) ; 7) >< 2) ;# 8) ~ 4) & -10)", "C": "((((((((-5 ; 5) # 7) >< -2) ><& 9) #; 8) ; 8) ;# 3) &# 4)", "A_val": 13, "B_val": 2, "C_val": 28, "answer": -13}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if a > b; otherwise, a - b\n$~ b$ equals (a <> b) if a > b; otherwise, (a <> b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-10 <> 4) :* 2) @ -7) ~ 4) ~:* 2) :* 8) :* -3) :* 7)\nLet B = ((((((((4 @ 7) :* -8) @# -8) ~ -4) :* -4) ~<> 7) :*:* 1) <>~ -7)\nLet C = ((((((((-6 @ -10) :*# 3) @~ 9) ~@ 8) ~:* 8) #@ -2) @ -6) <><> -7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a > b", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}], "A": "((((((((-10 <> 4) :* 2) @ -7) ~ 4) ~:* 2) :* 8) :* -3) :* 7)", "B": "((((((((4 @ 7) :* -8) @# -8) ~ -4) :* -4) ~<> 7) :*:* 1) <>~ -7)", "C": "((((((((-6 @ -10) :*# 3) @~ 9) ~@ 8) ~:* 8) #@ -2) @ -6) <><> -7)", "A_val": 6, "B_val": 0, "C_val": -22, "answer": 28}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a - b if a * b > 0; otherwise, a + b\n$# b$ equals (a ; b) if is_prime(a) or is_prime(b); otherwise, (a ; b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-8 && -2) [] -9) & 2) []~ 4) # 3) ~& 10) ; 4)\nLet B = (((((((5 #; 8) & 3) # 7) [] -4) &; -3) && 7) ;[] -5)\nLet C = (((((((7 #& -1) ;# 3) ;# -6) [] 5) ~ -8) [] 8) ~ 10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}], "A": "(((((((-8 && -2) [] -9) & 2) []~ 4) # 3) ~& 10) ; 4)", "B": "(((((((5 #; 8) & 3) # 7) [] -4) &; -3) && 7) ;[] -5)", "C": "(((((((7 #& -1) ;# 3) ;# -6) [] 5) ~ -8) [] 8) ~ 10)", "A_val": 96, "B_val": 0, "C_val": 10, "answer": 86}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals (a <> b) if math.gcd(a, b) == 1; otherwise, (a <> b)\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$:* b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-10 ~:* -8) :*<> -1) !:* 5) ~; 7) :*! 1) <>; -6) !<> -9)\nLet B = (((((((-10 ~ 2) ; 6) ; 7) <>:* 3) ~ 6) ! 10) ~ 7)\nLet C = (((((((-3 ! -7) ;:* -4) :* -9) :* 10) !<> 7) <>; 8) !:* -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((((-10 ~:* -8) :*<> -1) !:* 5) ~; 7) :*! 1) <>; -6) !<> -9)", "B": "(((((((-10 ~ 2) ; 6) ; 7) <>:* 3) ~ 6) ! 10) ~ 7)", "C": "(((((((-3 ! -7) ;:* -4) :* -9) :* 10) !<> 7) <>; 8) !:* -6)", "A_val": 0, "B_val": -7, "C_val": 6, "answer": -13}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$>< b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$<> b$ equals (a >< b) if is_prime(a) or is_prime(b); otherwise, (a >< b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((4 &<> -2) &>< 9) <> 2)\nLet B = (((4 ><<> -9) & 9) ><& 10)\nLet C = (((-4 & 2) <>& -10) &>< -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "><", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a >< b)", "false_expr": "(a >< b)"}], "A": "(((4 &<> -2) &>< 9) <> 2)", "B": "(((4 ><<> -9) & 9) ><& 10)", "C": "(((-4 & 2) <>& -10) &>< -2)", "A_val": 0, "B_val": 10, "C_val": 0, "answer": 10}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a - b if a * b > 0; otherwise, a + b\n$# b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((5 @ 6) #@ -10) @ 9) ## 8) >< 6)\nLet B = (((((-10 @ -5) ><<> -2) <> -7) <>>< 9) <> 4)\nLet C = (((((7 <> -8) <>>< -5) # -6) # -9) ><>< 3)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((5 @ 6) #@ -10) @ 9) ## 8) >< 6)", "B": "(((((-10 @ -5) ><<> -2) <> -7) <>>< 9) <> 4)", "C": "(((((7 <> -8) <>>< -5) # -6) # -9) ><>< 3)", "A_val": 6, "B_val": -2, "C_val": 3, "answer": 1}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$:* b$ equals (a <> b) if abs(a - b) < 2; otherwise, a - b\n$& b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((4 <> -2) <> 9) <> 10)\nLet B = (((-8 <><> -5) &<> 7) <>& 4)\nLet C = (((-1 <>:* -6) && -2) <> 6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "(a <> b)", "false_expr": "a - b"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((4 <> -2) <> 9) <> 10)", "B": "(((-8 <><> -5) &<> 7) <>& 4)", "C": "(((-1 <>:* -6) && -2) <> 6)", "A_val": 0, "B_val": 4, "C_val": 0, "answer": 4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$:* b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$; b$ equals (a ][ b) if math.gcd(a, b) == 1; otherwise, (a ][ b)\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-1 ;:* -8) ~ 9) ;:* 1) ; -5) ][ -9) ;; -1) ~; 1) ][; 3)\nLet B = ((((((((6 ~@ 3) ~ 4) ][][ 6) ~ 5) ; -7) ; 9) ;~ 1) ; -7)\nLet C = ((((((((-3 ~][ -4) ;@ 5) @ 6) :*:* 1) ~ 3) ~@ 8) ][:* 2) :*:* 6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((((((-1 ;:* -8) ~ 9) ;:* 1) ; -5) ][ -9) ;; -1) ~; 1) ][; 3)", "B": "((((((((6 ~@ 3) ~ 4) ][][ 6) ~ 5) ; -7) ; 9) ;~ 1) ; -7)", "C": "((((((((-3 ~][ -4) ;@ 5) @ 6) :*:* 1) ~ 3) ~@ 8) ][:* 2) :*:* 6)", "A_val": 0, "B_val": 0, "C_val": 0, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a * b if a > b; otherwise, a - b\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$][ b$ equals (a >< b) if a > b; otherwise, a + b\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\n$<> b$ equals (a :* b) if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-7 >< -8) ;<> -7) <>; -6) >< -1) ][ -7) ; 10) :*>< -8) <>; 7)\nLet B = ((((((((-7 <> -3) ; 2) <> -4) ;][ 5) :*:* 1) ][; -6) ][ 3) >< -7)\nLet C = ((((((((6 ][<> 8) ;:* -7) :* 8) ;>< -6) :*<> 8) ><:* 3) ][ -2) ;; -5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "(a >< b)", "false_expr": "a + b"}, {"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "(a :* b)", "false_expr": "a - b"}], "A": "((((((((-7 >< -8) ;<> -7) <>; -6) >< -1) ][ -7) ; 10) :*>< -8) <>; 7)", "B": "((((((((-7 <> -3) ; 2) <> -4) ;][ 5) :*:* 1) ][; -6) ][ 3) >< -7)", "C": "((((((((6 ][<> 8) ;:* -7) :* 8) ;>< -6) :*<> 8) ><:* 3) ][ -2) ;; -5)", "A_val": 0, "B_val": -21, "C_val": 0, "answer": -21}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals (a >< b) if is_prime(a) or is_prime(b); otherwise, (a >< b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((1 :* 1) ><:* 5) !! 9) :* -4)\nLet B = ((((-5 :* 7) !>< -2) :* -2) <>! -9)\nLet C = ((((-1 >< 3) ><:* -1) <><> -3) :*:* -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a >< b)", "false_expr": "(a >< b)"}], "A": "((((1 :* 1) ><:* 5) !! 9) :* -4)", "B": "((((-5 :* 7) !>< -2) :* -2) <>! -9)", "C": "((((-1 >< 3) ><:* -1) <><> -3) :*:* -6)", "A_val": 0, "B_val": 9, "C_val": 0, "answer": 9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals (a <> b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$@ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals (a & b) if a * b > 0; otherwise, (a & b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((4 # -5) &# 3) <> -10) <> -9) # 4) & 5) & -9)\nLet B = (((((((-10 <> 8) !! 4) @ 8) !# 5) @ -9) <>@ 8) #@ -8)\nLet C = (((((((3 <># -1) @ 6) <><> 9) # 1) #@ -2) !# -5) # 10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "(a <> b)", "false_expr": "math.gcd(a, b)"}, {"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "a * b > 0", "true_expr": "(a & b)", "false_expr": "(a & b)"}], "A": "(((((((4 # -5) &# 3) <> -10) <> -9) # 4) & 5) & -9)", "B": "(((((((-10 <> 8) !! 4) @ 8) !# 5) @ -9) <>@ 8) #@ -8)", "C": "(((((((3 <># -1) @ 6) <><> 9) # 1) #@ -2) !# -5) # 10)", "A_val": 0, "B_val": 0, "C_val": 0, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$# b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$& b$ equals (a # b) if a * b > 0; otherwise, a + b\n$[] b$ equals (a & b) if abs(a - b) < 2; otherwise, a - b\n$~ b$ equals (a [] b) if a > b; otherwise, (a [] b)\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-2 []~ -9) && 5) @[] -7) # -4) & -2) ~ -1)\nLet B = ((((((8 @ -6) []# -6) [] 6) &@ 2) @~ 10) [] 4)\nLet C = ((((((8 @[] -3) &[] -5) &@ -6) & 9) []@ -4) [][] 8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "&", "condition": "a * b > 0", "true_expr": "(a # b)", "false_expr": "a + b"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "(a & b)", "false_expr": "a - b"}, {"symbol": "~", "condition": "a > b", "true_expr": "(a [] b)", "false_expr": "(a [] b)"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((-2 []~ -9) && 5) @[] -7) # -4) & -2) ~ -1)", "B": "((((((8 @ -6) []# -6) [] 6) &@ 2) @~ 10) [] 4)", "C": "((((((8 @[] -3) &[] -5) &@ -6) & 9) []@ -4) [][] 8)", "A_val": 0, "B_val": -4, "C_val": -11, "answer": 7}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\n$][ b$ equals a * b if a > b; otherwise, a + b\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((5 !][ -8) ][; -5) ;][ 8) ;][ -2)\nLet B = ((((9 ][ 6) :* -2) ][:* 6) ;][ 5)\nLet C = ((((-9 ! 9) ][ 6) ! -9) ;! 9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "((((5 !][ -8) ][; -5) ;][ 8) ;][ -2)", "B": "((((9 ][ 6) :* -2) ][:* 6) ;][ 5)", "C": "((((-9 ! 9) ][ 6) ! -9) ;! 9)", "A_val": -4, "B_val": 1555, "C_val": -6, "answer": 1557}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals (a @ b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-9 @ 9) @& 8) &>< 2)\nLet B = (((-5 @>< -6) >< -2) &>< 5)\nLet C = (((1 & 8) ><& -7) & 3)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "(a @ b)", "false_expr": "math.gcd(a, b)"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((-9 @ 9) @& 8) &>< 2)", "B": "(((-5 @>< -6) >< -2) &>< 5)", "C": "(((1 & 8) ><& -7) & 3)", "A_val": 2, "B_val": 5, "C_val": 0, "answer": 7}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals (a <> b) if abs(a - b) < 2; otherwise, a - b\n$>< b$ equals a * b if a > b; otherwise, a - b\n$; b$ equals (a # b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-10 <> 5) #; 3) ; 1) #<> -2)\nLet B = ((((7 # -3) <> -9) ; -3) <>; -7)\nLet C = ((((-4 >< 7) ;# 2) ; 7) ; -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "(a <> b)", "false_expr": "a - b"}, {"symbol": "><", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a # b)", "false_expr": "max(a, b)"}], "A": "((((-10 <> 5) #; 3) ; 1) #<> -2)", "B": "((((7 # -3) <> -9) ; -3) <>; -7)", "C": "((((-4 >< 7) ;# 2) ; 7) ; -4)", "A_val": 4, "B_val": 0, "C_val": 0, "answer": 4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$:* b$ equals (a [] b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals (a :* b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-7 @ 2) ~~ 7) :*! 6) ~@ 9) !~ -2) ~ 7) ![] 7) [][] 3)\nLet B = ((((((((-1 :* 9) ! -2) !! -9) !:* -3) ~@ -9) ~~ -4) :* 7) ~ 6)\nLet C = ((((((((-10 :*~ -5) @[] -3) @ -10) ~[] 1) !~ 9) []! 5) !~ 3) ~@ -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a [] b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "(a :* b)", "false_expr": "math.gcd(a, b)"}], "A": "((((((((-7 @ 2) ~~ 7) :*! 6) ~@ 9) !~ -2) ~ 7) ![] 7) [][] 3)", "B": "((((((((-1 :* 9) ! -2) !! -9) !:* -3) ~@ -9) ~~ -4) :* 7) ~ 6)", "C": "((((((((-10 :*~ -5) @[] -3) @ -10) ~[] 1) !~ 9) []! 5) !~ 3) ~@ -2)", "A_val": 0, "B_val": 0, "C_val": 2, "answer": -2}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals a * b if a > b; otherwise, a - b\n$~ b$ equals (a ; b) if a * b > 0; otherwise, (a ; b)\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((3 & -9) []; -2) ;; 9) []~ -3) [] 5) & -8) ; -3)\nLet B = (((((((-4 & -6) ~ 10) ;& 5) ; 6) ;~ 4) [] -8) <>& 9)\nLet C = (((((((8 <><> 3) & -6) &; 8) ~ -8) <>[] 6) []~ -4) <>[] 4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}, {"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "(((((((3 & -9) []; -2) ;; 9) []~ -3) [] 5) & -8) ; -3)", "B": "(((((((-4 & -6) ~ 10) ;& 5) ; 6) ;~ 4) [] -8) <>& 9)", "C": "(((((((8 <><> 3) & -6) &; 8) ~ -8) <>[] 6) []~ -4) <>[] 4)", "A_val": -24, "B_val": -18, "C_val": 0, "answer": -42}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$~ b$ equals (a >< b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$& b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((9 ~ -9) &>< -6) &~ 4)\nLet B = (((6 ~ 3) ><& 3) ><>< -8)\nLet C = (((3 & -4) & -6) &>< -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a >< b)", "false_expr": "max(a, b)"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((9 ~ -9) &>< -6) &~ 4)", "B": "(((6 ~ 3) ><& 3) ><>< -8)", "C": "(((3 & -4) & -6) &>< -2)", "A_val": 0, "B_val": 19, "C_val": -7, "answer": 26}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a * b if a > b; otherwise, a - b\n$# b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$; b$ equals (a # b) if a > b; otherwise, (a # b)\n$][ b$ equals a * b if a > b; otherwise, a + b\n$! b$ equals a * b if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-7 ;# -8) ;# 9) ][ 5) ! -3) ; 10) ][ -2) ><; 8)\nLet B = (((((((4 ;>< 7) !; 8) ][; 4) >< -7) ;][ 5) >< 9) ;! -1)\nLet C = (((((((6 ][ -4) ## 2) ][ -7) !][ -3) ][ 8) ! -4) >< 4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ";", "condition": "a > b", "true_expr": "(a # b)", "false_expr": "(a # b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "!", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((((((-7 ;# -8) ;# 9) ][ 5) ! -3) ; 10) ][ -2) ><; 8)", "B": "(((((((4 ;>< 7) !; 8) ][; 4) >< -7) ;][ 5) >< 9) ;! -1)", "C": "(((((((6 ][ -4) ## 2) ][ -7) !][ -3) ][ 8) ! -4) >< 4)", "A_val": 0, "B_val": 0, "C_val": -36, "answer": 36}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\n$>< b$ equals (a ; b) if a > b; otherwise, a + b\n$:* b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((-5 @; 4) :* 1) ;; 1) :* 5) ; -3)\nLet B = (((((-5 @:* 6) @ -7) @ -1) :* -5) @ 3)\nLet C = (((((-8 >< 8) :*; 6) @ 4) :*@ 4) ><:* 8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "><", "condition": "a > b", "true_expr": "(a ; b)", "false_expr": "a + b"}, {"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "(((((-5 @; 4) :* 1) ;; 1) :* 5) ; -3)", "B": "(((((-5 @:* 6) @ -7) @ -1) :* -5) @ 3)", "C": "(((((-8 >< 8) :*; 6) @ 4) :*@ 4) ><:* 8)", "A_val": 0, "B_val": 3, "C_val": 0, "answer": 3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals (a <> b) if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((2 ; -10) ; 6) & 4)\nLet B = (((-4 <>; -5) & -10) ; 4)\nLet C = (((-5 ;; 8) ; -1) <> -10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "a > b", "true_expr": "(a <> b)", "false_expr": "a - b"}], "A": "(((2 ; -10) ; 6) & 4)", "B": "(((-4 <>; -5) & -10) ; 4)", "C": "(((-5 ;; 8) ; -1) <> -10)", "A_val": -2, "B_val": 4, "C_val": 10, "answer": -8}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a * b if a > b; otherwise, a + b\n$# b$ equals (a <> b) if a > b; otherwise, (a <> b)\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$& b$ equals (a # b) if math.gcd(a, b) == 1; otherwise, (a # b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((-2 & -9) ; -8) <> 5) # -7) ;<> 1)\nLet B = (((((8 ;# -8) ; -6) ;# 6) <>& -1) <>& -7)\nLet C = (((((-2 # -3) ; 5) <> -10) #& 8) ;<> 1)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "#", "condition": "a > b", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "(a # b)", "false_expr": "(a # b)"}], "A": "(((((-2 & -9) ; -8) <> 5) # -7) ;<> 1)", "B": "(((((8 ;# -8) ; -6) ;# 6) <>& -1) <>& -7)", "C": "(((((-2 # -3) ; 5) <> -10) #& 8) ;<> 1)", "A_val": 1, "B_val": 0, "C_val": 1, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$# b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a - b if a * b > 0; otherwise, a + b\n$~ b$ equals (a ; b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals (a # b) if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-10 #[] -2) ;; -1) ;; -8) []# -10)\nLet B = ((((6 # -9) ~ -10) ;# 5) [] -4)\nLet C = ((((-7 ~ -5) ; -6) [] -7) # -8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ; b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "a > b", "true_expr": "(a # b)", "false_expr": "a + b"}], "A": "((((-10 #[] -2) ;; -1) ;; -8) []# -10)", "B": "((((6 # -9) ~ -10) ;# 5) [] -4)", "C": "((((-7 ~ -5) ; -6) [] -7) # -8)", "A_val": 10, "B_val": 0, "C_val": 8, "answer": 2}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals (a ~ b) if a > b; otherwise, (a ~ b)\n$[] b$ equals a * b if a > b; otherwise, a + b\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-3 ; -2) # -3) # 3) # 5) ; 9) # 7) <>; 9) ~ -8)\nLet B = ((((((((-1 #<> -10) ; 6) [] -4) ## -9) [] -4) ;[] 2) [] -2) ~; -2)\nLet C = ((((((((-4 #[] -1) <> -8) <># 1) <> -9) ; 5) ~<> 7) ; 9) <> -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "a > b", "true_expr": "(a ~ b)", "false_expr": "(a ~ b)"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((((-3 ; -2) # -3) # 3) # 5) ; 9) # 7) <>; 9) ~ -8)", "B": "((((((((-1 #<> -10) ; 6) [] -4) ## -9) [] -4) ;[] 2) [] -2) ~; -2)", "C": "((((((((-4 #[] -1) <> -8) <># 1) <> -9) ; 5) ~<> 7) ; 9) <> -9)", "A_val": 0, "B_val": -2, "C_val": 11, "answer": -13}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals a - b if a * b > 0; otherwise, a + b\n$:* b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals a * b if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((6 :*][ 7) ][ 1) ][& -6) ; -6)\nLet B = ((((-2 :*:* -1) ; 3) ;& -10) & -8)\nLet C = ((((3 &; -6) ][][ -9) ][:* -3) :* 1)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "((((6 :*][ 7) ][ 1) ][& -6) ; -6)", "B": "((((-2 :*:* -1) ; 3) ;& -10) & -8)", "C": "((((3 &; -6) ][][ -9) ][:* -3) :* 1)", "A_val": -132, "B_val": -42, "C_val": 8, "answer": -182}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals a * b if a > b; otherwise, a - b\n$[] b$ equals a * b if a > b; otherwise, a - b\n$][ b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((9 :*@ -2) [][] 10) ][ 10) @ 5)\nLet B = ((((4 ][ -5) [] 4) []@ -9) :* 7)\nLet C = ((((-10 [] -3) [] 6) []][ -5) :* -7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((9 :*@ -2) [][] 10) ][ 10) @ 5)", "B": "((((4 ][ -5) [] 4) []@ -9) :* 7)", "C": "((((-10 [] -3) [] 6) []][ -5) :* -7)", "A_val": -23, "B_val": -4, "C_val": 21, "answer": -48}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a - b if a * b > 0; otherwise, a + b\n$[] b$ equals a * b if a > b; otherwise, a + b\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((3 @@ -8) ! 8) @ -3)\nLet B = (((8 []! -4) [] 1) @@ 3)\nLet C = (((-2 @ 9) [][] 6) @ 2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((3 @@ -8) ! 8) @ -3)", "B": "(((8 []! -4) [] 1) @@ 3)", "C": "(((-2 @ 9) [][] 6) @ 2)", "A_val": 14, "B_val": -33, "C_val": 2, "answer": -21}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\n$# b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((4 ~ -9) []# -5) #[] 5)\nLet B = (((-3 [] 7) # -2) #~ -3)\nLet C = (((-6 []~ -7) ~[] -3) #~ -10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "#", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((4 ~ -9) []# -5) #[] 5)", "B": "(((-3 [] 7) # -2) #~ -3)", "C": "(((-6 []~ -7) ~[] -3) #~ -10)", "A_val": 0, "B_val": 2, "C_val": -8, "answer": 10}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals (a :* b) if a * b > 0; otherwise, a + b\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\n$][ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((2 >< -8) #][ -2) #>< -7) #:* -8) :* -10) # 2) # -5)\nLet B = (((((((6 ][ -1) # -3) ][][ 6) & -6) & -9) ><>< -8) & -5)\nLet C = (((((((10 :* -4) ][ 5) # 7) ## 9) >< -2) #>< 5) >< 6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "a * b > 0", "true_expr": "(a :* b)", "false_expr": "a + b"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "][", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((((2 >< -8) #][ -2) #>< -7) #:* -8) :* -10) # 2) # -5)", "B": "(((((((6 ][ -1) # -3) ][][ 6) & -6) & -9) ><>< -8) & -5)", "C": "(((((((10 :* -4) ][ 5) # 7) ## 9) >< -2) #>< 5) >< 6)", "A_val": -3, "B_val": 12, "C_val": -1, "answer": 10}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$:* b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$! b$ equals (a :* b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-6 ! -1) ;~ 3) :*<> 2) ~<> 6) !~ -6) :*<> -8) ! -6) ~ 7)\nLet B = ((((((((-5 ; 8) ~ -3) ;! 7) <>:* 4) :* 6) <> 3) ~~ 3) <>; -10)\nLet C = ((((((((1 ~~ -1) ~ -2) !~ -4) ; -6) :* -6) ;; -3) ~! 5) ~! -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a :* b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((((((-6 ! -1) ;~ 3) :*<> 2) ~<> 6) !~ -6) :*<> -8) ! -6) ~ 7)", "B": "((((((((-5 ; 8) ~ -3) ;! 7) <>:* 4) :* 6) <> 3) ~~ 3) <>; -10)", "C": "((((((((1 ~~ -1) ~ -2) !~ -4) ; -6) :* -6) ;; -3) ~! 5) ~! -9)", "A_val": 0, "B_val": 0, "C_val": 0, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$& b$ equals (a ; b) if math.gcd(a, b) == 1; otherwise, (a ; b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((-3 ;& -7) ][; -2) ~; 10) ;][ -4) && -8)\nLet B = (((((5 & 5) ][& -8) && -6) ~& 8) ~; -9)\nLet C = (((((-3 ][; -6) ][ -7) & 9) ][; -10) ~ -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}], "A": "(((((-3 ;& -7) ][; -2) ~; 10) ;][ -4) && -8)", "B": "(((((5 & 5) ][& -8) && -6) ~& 8) ~; -9)", "C": "(((((-3 ][; -6) ][ -7) & 9) ][; -10) ~ -6)", "A_val": 0, "B_val": 9, "C_val": 0, "answer": 9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\n$@ b$ equals (a >< b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$:* b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((10 :*>< 3) :*@ 8) :* -6)\nLet B = (((3 ><:* -3) :*>< 1) :*@ 10)\nLet C = (((-7 @ -2) :*>< -5) :* 3)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a >< b)", "false_expr": "max(a, b)"}, {"symbol": ":*", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((10 :*>< 3) :*@ 8) :* -6)", "B": "(((3 ><:* -3) :*>< 1) :*@ 10)", "C": "(((-7 @ -2) :*>< -5) :* 3)", "A_val": 6, "B_val": 0, "C_val": -3, "answer": 9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a - b if a * b > 0; otherwise, a + b\n$! b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$][ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$:* b$ equals a * b if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((5 :* 8) ][ 5) :*! -10) <><> 6) ][ 4) :* -3) ][ 3) <>:* -1)\nLet B = ((((((((7 ][ -6) [] -4) <> 4) []<> 3) <><> 9) <> -8) !<> -2) [][] 3)\nLet C = ((((((((6 []:* -2) <>:* -8) ][ -3) !<> -9) [] 4) <> -4) []! -2) <>[] 5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "][", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ":*", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "((((((((5 :* 8) ][ 5) :*! -10) <><> 6) ][ 4) :* -3) ][ 3) <>:* -1)", "B": "((((((((7 ][ -6) [] -4) <> 4) []<> 3) <><> 9) <> -8) !<> -2) [][] 3)", "C": "((((((((6 []:* -2) <>:* -8) ][ -3) !<> -9) [] 4) <> -4) []! -2) <>[] 5)", "A_val": -2, "B_val": -8, "C_val": 25, "answer": -35}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals a * b if a > b; otherwise, a + b\n$~ b$ equals (a ][ b) if abs(a - b) < 2; otherwise, a - b\n$; b$ equals (a @ b) if a * b > 0; otherwise, a + b\n$>< b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((2 ][>< -1) ][; 10) ;][ 2) @ 9) ;@ -7) ;~ -4) ><~ 8) ><>< 7)\nLet B = ((((((((-7 @ -8) @@ 6) ; -8) ][ 9) >< 8) @][ 2) ;>< -10) @ -6)\nLet C = ((((((((2 @~ 2) ~ -2) @ -2) ~@ -5) ~~ 2) >< -10) @ 2) ;~ -8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "(a ][ b)", "false_expr": "a - b"}, {"symbol": ";", "condition": "a * b > 0", "true_expr": "(a @ b)", "false_expr": "a + b"}, {"symbol": "><", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((((((2 ][>< -1) ][; 10) ;][ 2) @ 9) ;@ -7) ;~ -4) ><~ 8) ><>< 7)", "B": "((((((((-7 @ -8) @@ 6) ; -8) ][ 9) >< 8) @][ 2) ;>< -10) @ -6)", "C": "((((((((2 @~ 2) ~ -2) @ -2) ~@ -5) ~~ 2) >< -10) @ 2) ;~ -8)", "A_val": 0, "B_val": 6, "C_val": 2, "answer": 4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$>< b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((10 :*>< -7) ; -5) ><@ 4) @ 9) @# -8) ><# -7) @>< 10) ><; 5)\nLet B = ((((((((-7 ## 6) @# -8) :*>< -1) :* -3) # 2) :* -5) :*# 2) @ -9)\nLet C = ((((((((3 # 10) ;@ 9) @@ 4) >< -9) #>< -4) ;@ 4) ><>< 1) # -5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "><", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((((10 :*>< -7) ; -5) ><@ 4) @ 9) @# -8) ><# -7) @>< 10) ><; 5)", "B": "((((((((-7 ## 6) @# -8) :*>< -1) :* -3) # 2) :* -5) :*# 2) @ -9)", "C": "((((((((3 # 10) ;@ 9) @@ 4) >< -9) #>< -4) ;@ 4) ><>< 1) # -5)", "A_val": 5, "B_val": -7, "C_val": -5, "answer": 3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$# b$ equals a * b if a > b; otherwise, a - b\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$<> b$ equals (a ; b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-3 <>; -1) <>; -7) #; 3)\nLet B = (((1 #<> -6) <> -9) <><> 8)\nLet C = (((-2 # 8) # -5) <>; 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ; b)", "false_expr": "max(a, b)"}], "A": "(((-3 <>; -1) <>; -7) #; 3)", "B": "(((1 #<> -6) <> -9) <><> 8)", "C": "(((-2 # 8) # -5) <>; 7)", "A_val": 0, "B_val": 0, "C_val": 0, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if a > b; otherwise, a + b\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals (a [] b) if is_prime(a) or is_prime(b); otherwise, (a [] b)\n$~ b$ equals (a ][ b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-4 []~ 2) ~ -5) [] 3) [] 4) ~ -1) &# -10) &[] 5) & -6)\nLet B = ((((((((-9 [][] -4) ## -2) &[] 3) ][ -3) # 9) # -4) & 3) [] -8)\nLet C = ((((((((9 & 7) #][ -10) [][] 3) [] -5) ~][ 10) ~ 6) ## -4) [][] -3)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a [] b)", "false_expr": "(a [] b)"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ][ b)", "false_expr": "math.gcd(a, b)"}], "A": "((((((((-4 []~ 2) ~ -5) [] 3) [] 4) ~ -1) &# -10) &[] 5) & -6)", "B": "((((((((-9 [][] -4) ## -2) &[] 3) ][ -3) # 9) # -4) & 3) [] -8)", "C": "((((((((9 & 7) #][ -10) [][] 3) [] -5) ~][ 10) ~ 6) ## -4) [][] -3)", "A_val": 0, "B_val": 0, "C_val": 0, "answer": 0}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-4 ><][ 7) ][ -4) >< -5)\nLet B = (((10 ][ -8) # -2) ][ -7)\nLet C = (((-9 ][ -5) >< -4) # 10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((-4 ><][ 7) ][ -4) >< -5)", "B": "(((10 ][ -8) # -2) ][ -7)", "C": "(((-9 ][ -5) >< -4) # 10)", "A_val": 5, "B_val": 0, "C_val": -6, "answer": 11}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a - b if a * b > 0; otherwise, a + b\n$][ b$ equals (a ! b) if abs(a - b) < 2; otherwise, (a ! b)\n$@ b$ equals a * b if a > b; otherwise, a - b\n$:* b$ equals (a ! b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((-3 ! -4) :* 3) !:* -4) ! 10) :* 5)\nLet B = (((((7 ][ -4) @ -5) ][@ -5) @! -3) ! -7)\nLet C = (((((1 !@ 7) !][ 8) ][][ 1) !! 2) @ 4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "][", "condition": "abs(a - b) < 2", "true_expr": "(a ! b)", "false_expr": "(a ! b)"}, {"symbol": "@", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ! b)", "false_expr": "math.gcd(a, b)"}], "A": "(((((-3 ! -4) :* 3) !:* -4) ! 10) :* 5)", "B": "(((((7 ][ -4) @ -5) ][@ -5) @! -3) ! -7)", "C": "(((((1 !@ 7) !][ 8) ][][ 1) !! 2) @ 4)", "A_val": 0, "B_val": 4, "C_val": -4, "answer": 8}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals (a & b) if abs(a - b) < 2; otherwise, (a & b)\n$; b$ equals (a @ b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals a * b if a > b; otherwise, a + b\n$! b$ equals (a @ b) if math.gcd(a, b) == 1; otherwise, (a @ b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-3 []& -8) ;! 8) @! -7) &; 1) [] -8) []; 4)\nLet B = ((((((4 &! 3) ! 10) & 1) ! 8) @ 3) []! -9)\nLet C = ((((((10 &; -4) &; -5) @ 10) !@ -6) &@ 2) &! 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "(a & b)", "false_expr": "(a & b)"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "(a @ b)", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "(a @ b)", "false_expr": "(a @ b)"}], "A": "((((((-3 []& -8) ;! 8) @! -7) &; 1) [] -8) []; 4)", "B": "((((((4 &! 3) ! 10) & 1) ! 8) @ 3) []! -9)", "C": "((((((10 &; -4) &; -5) @ 10) !@ -6) &@ 2) &! 7)", "A_val": 4, "B_val": 0, "C_val": 0, "answer": 4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals a * b if a > b; otherwise, a - b\n$[] b$ equals a * b if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-4 ][ 1) ][][ 5) :*:* -6)\nLet B = (((-3 :*:* -6) []][ 1) :* 1)\nLet C = (((-10 ][][ 3) [] -3) [] -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((-4 ][ 1) ][][ 5) :*:* -6)", "B": "(((-3 :*:* -6) []][ 1) :* 1)", "C": "(((-10 ][][ 3) [] -3) [] -6)", "A_val": 3, "B_val": 4, "C_val": -25, "answer": 32}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-4 @ -8) @@ -8) ; -6) []; 2) ; -6) :* 5)\nLet B = ((((((1 ;@ 4) @ 3) @[] 4) [][] -8) @@ 3) @:* 8)\nLet C = ((((((-4 :*; 1) :* 3) @@ -3) ;:* 1) ][[] -4) ][ 4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((-4 @ -8) @@ -8) ; -6) []; 2) ; -6) :* 5)", "B": "((((((1 ;@ 4) @ 3) @[] 4) [][] -8) @@ 3) @:* 8)", "C": "((((((-4 :*; 1) :* 3) @@ -3) ;:* 1) ][[] -4) ][ 4)", "A_val": 7, "B_val": 8, "C_val": 0, "answer": 15}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-3 ~ 2) ~# 2) # -5) &~ -9) ~ 1) @# -2)\nLet B = ((((((-2 &~ 3) ~ -3) ~ 9) & -7) []# -4) [] -6)\nLet C = ((((((3 # 10) @ -2) & 1) &@ 5) ~~ 6) [] -5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((-3 ~ 2) ~# 2) # -5) &~ -9) ~ 1) @# -2)", "B": "((((((-2 &~ 3) ~ -3) ~ 9) & -7) []# -4) [] -6)", "C": "((((((3 # 10) @ -2) & 1) &@ 5) ~~ 6) [] -5)", "A_val": 8, "B_val": 0, "C_val": 0, "answer": 8}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$; b$ equals a * b if a > b; otherwise, a + b\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((-4 && -6) && 4) @ 9) <> 10) & -8)\nLet B = (((((-3 & -9) ;<> -1) & -4) ;& 3) &; 9)\nLet C = (((((-5 <><> 6) & -5) @; -10) <> 2) @& -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ";", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((-4 && -6) && 4) @ 9) <> 10) & -8)", "B": "(((((-3 & -9) ;<> -1) & -4) ;& 3) &; 9)", "C": "(((((-5 <><> 6) & -5) @; -10) <> 2) @& -9)", "A_val": 0, "B_val": 9, "C_val": 0, "answer": 9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if a > b; otherwise, a - b\n$>< b$ equals (a ][ b) if a * b > 0; otherwise, (a ][ b)\n$& b$ equals a * b if a > b; otherwise, a - b\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-8 & -1) ][& 2) ][][ -10) &][ -9) []>< 5) & -9) []][ -2)\nLet B = (((((((5 ][>< -8) [][] 9) :*][ -6) ][& 6) ][ -2) ][ -7) ><][ -9)\nLet C = (((((((4 >< -1) >< 7) ><:* 1) & 6) ][ 3) ><:* -8) &][ -6)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((((-8 & -1) ][& 2) ][][ -10) &][ -9) []>< 5) & -9) []][ -2)", "B": "(((((((5 ][>< -8) [][] 9) :*][ -6) ][& 6) ][ -2) ][ -7) ><][ -9)", "C": "(((((((4 >< -1) >< 7) ><:* 1) & 6) ][ 3) ><:* -8) &][ -6)", "A_val": -4, "B_val": 0, "C_val": 12, "answer": -16}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a - b if a * b > 0; otherwise, a + b\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\n$@ b$ equals a * b if a > b; otherwise, a + b\n$; b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-6 :* -6) :* -8) & -1) @ 8) ; -4) &:* -9) !; -1) :* 6)\nLet B = ((((((((-10 &! -1) &; 3) :* 7) & -6) ! 7) :* 10) & -6) :*; 1)\nLet C = ((((((((-6 & -6) ; -3) ; -5) @ 7) & 8) ! 2) & -3) :* -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "@", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": ";", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((((-6 :* -6) :* -8) & -1) @ 8) ; -4) &:* -9) !; -1) :* 6)", "B": "((((((((-10 &! -1) &; 3) :* 7) & -6) ! 7) :* 10) & -6) :*; 1)", "C": "((((((((-6 & -6) ; -3) ; -5) @ 7) & 8) ! 2) & -3) :* -2)", "A_val": 5, "B_val": -2, "C_val": 1, "answer": 2}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\n$@ b$ equals (a >< b) if is_prime(a) or is_prime(b); otherwise, (a >< b)\n$! b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((6 ! -2) :*>< -1) :*~ -3) >< -10) ! 1) ! -7)\nLet B = ((((((-10 ~:* 9) >< 10) ! -7) !! -9) >< 9) :* -6)\nLet C = ((((((-3 >< -5) @>< -2) :* -4) @ -3) >< 8) ~:* 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a >< b)", "false_expr": "(a >< b)"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((6 ! -2) :*>< -1) :*~ -3) >< -10) ! 1) ! -7)", "B": "((((((-10 ~:* 9) >< 10) ! -7) !! -9) >< 9) :* -6)", "C": "((((((-3 >< -5) @>< -2) :* -4) @ -3) >< 8) ~:* 7)", "A_val": -16, "B_val": 0, "C_val": 0, "answer": -16}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals a - b if a * b > 0; otherwise, a + b\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-3 @ 4) @ -2) ;; 2)\nLet B = (((8 ;! -7) @ 3) ; 5)\nLet C = (((-5 @; -1) !@ -10) @; 1)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((-3 @ 4) @ -2) ;; 2)", "B": "(((8 ;! -7) @ 3) ; 5)", "C": "(((-5 @; -1) !@ -10) @; 1)", "A_val": 2, "B_val": 5, "C_val": 1, "answer": 6}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$][ b$ equals a * b if a > b; otherwise, a - b\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$~ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((4 ][][ 1) ~<> 8) ; 9) ;; -3) ;][ 4) ><<> 9) ~ 8)\nLet B = (((((((-4 >< 6) ~ 9) ><~ -8) ~; 7) ][<> 1) <>~ -10) <>; 8)\nLet C = (((((((4 ;~ 4) ][][ -4) <> -10) <> -7) ~ 3) >< -1) ;~ 5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((((((4 ][][ 1) ~<> 8) ; 9) ;; -3) ;][ 4) ><<> 9) ~ 8)", "B": "(((((((-4 >< 6) ~ 9) ><~ -8) ~; 7) ][<> 1) <>~ -10) <>; 8)", "C": "(((((((4 ;~ 4) ][][ -4) <> -10) <> -7) ~ 3) >< -1) ;~ 5)", "A_val": 8, "B_val": 8, "C_val": 14, "answer": 2}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals a - b if a * b > 0; otherwise, a + b\n$>< b$ equals (a :* b) if math.gcd(a, b) == 1; otherwise, (a :* b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((1 # -2) :* -6) ~ -2) #>< -7) ~ -5)\nLet B = (((((10 ~>< -7) # -2) :* 7) ~:* -3) #:* 8)\nLet C = (((((3 ~ 7) #:* 7) ~ -5) :* -2) ~:* 8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "(a :* b)", "false_expr": "(a :* b)"}], "A": "(((((1 # -2) :* -6) ~ -2) #>< -7) ~ -5)", "B": "(((((10 ~>< -7) # -2) :* 7) ~:* -3) #:* 8)", "C": "(((((3 ~ 7) #:* 7) ~ -5) :* -2) ~:* 8)", "A_val": 5, "B_val": 5, "C_val": 13, "answer": -3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if a > b; otherwise, a - b\n$>< b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$][ b$ equals a * b if a > b; otherwise, a - b\n$; b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((2 ;! 7) ][][ 2) ; -7) ;! 6) ; -3)\nLet B = (((((-1 ][ -2) !][ 10) >< -7) >< -10) ;! -8)\nLet C = (((((1 !][ 2) ! 2) ; -6) ][][ -6) ;! -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "><", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((2 ;! 7) ][][ 2) ; -7) ;! 6) ; -3)", "B": "(((((-1 ][ -2) !][ 10) >< -7) >< -10) ;! -8)", "C": "(((((1 !][ 2) ! 2) ; -6) ][][ -6) ;! -2)", "A_val": -18, "B_val": -64, "C_val": -170, "answer": 88}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$; b$ equals (a # b) if math.gcd(a, b) == 1; otherwise, (a # b)\n$~ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((6 ~ 9) ; -6) ## -1) ~~ -7) &@ 5) @ -7)\nLet B = ((((((-4 #& -2) ~ 1) && -7) &; -6) #& -9) ~& 8)\nLet C = ((((((9 ;@ 4) @ 1) ; -3) #@ -3) @ -3) &@ 2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "(a # b)", "false_expr": "(a # b)"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "((((((6 ~ 9) ; -6) ## -1) ~~ -7) &@ 5) @ -7)", "B": "((((((-4 #& -2) ~ 1) && -7) &; -6) #& -9) ~& 8)", "C": "((((((9 ;@ 4) @ 1) ; -3) #@ -3) @ -3) &@ 2)", "A_val": -2, "B_val": 0, "C_val": 2, "answer": -4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a - b if a * b > 0; otherwise, a + b\n$; b$ equals (a ][ b) if math.gcd(a, b) == 1; otherwise, (a ][ b)\n$<> b$ equals a * b if a > b; otherwise, a + b\n$[] b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-7 ; 8) [] -7) <>[] -6) ;[] -7)\nLet B = ((((9 <><> -4) ; 4) <> -5) []][ 3)\nLet C = ((((10 <>; 9) ; 5) <> -10) <> -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": "<>", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "[]", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "((((-7 ; 8) [] -7) <>[] -6) ;[] -7)", "B": "((((9 <><> -4) ; 4) <> -5) []][ 3)", "C": "((((10 <>; 9) ; 5) <> -10) <> -9)", "A_val": 7, "B_val": 0, "C_val": 0, "answer": 7}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$@ b$ equals (a ][ b) if math.gcd(a, b) == 1; otherwise, (a ][ b)\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$& b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((10 @:* -9) <> -5) <> 2) :*@ 4) & 9) &<> 3) <>:* -1)\nLet B = (((((((9 @@ 4) :* -2) @ -2) @ 3) <> -2) <> -8) <> -4)\nLet C = (((((((7 & 4) ][@ -9) <><> 3) &:* -5) &][ 6) ][ -5) @:* 2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((((10 @:* -9) <> -5) <> 2) :*@ 4) & 9) &<> 3) <>:* -1)", "B": "(((((((9 @@ 4) :* -2) @ -2) @ 3) <> -2) <> -8) <> -4)", "C": "(((((((7 & 4) ][@ -9) <><> 3) &:* -5) &][ 6) ][ -5) @:* 2)", "A_val": -15, "B_val": 14, "C_val": 2, "answer": -3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if a > b; otherwise, a + b\n$<> b$ equals a * b if a > b; otherwise, a - b\n$& b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-2 &! -10) & 5) ! 6)\nLet B = (((5 && 1) <> 4) <> 1)\nLet C = (((4 & -4) !! -10) !& 10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((-2 &! -10) & 5) ! 6)", "B": "(((5 && 1) <> 4) <> 1)", "C": "(((4 & -4) !! -10) !& 10)", "A_val": -199, "B_val": 20, "C_val": -36, "answer": -143}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals (a ! b) if a * b > 0; otherwise, (a ! b)\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$; b$ equals (a [] b) if abs(a - b) < 2; otherwise, (a [] b)\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((4 ! -2) ! 1) @ 4) @ -6) []@ 9) [] -5) []! 2) [] 3)\nLet B = ((((((((1 @@ 5) !! 3) !! 9) @; -10) @ 10) !<> -3) ! -3) !@ -3)\nLet C = ((((((((-9 ! -9) [] 4) <><> -1) ! 9) [] 6) []; 8) !<> -9) ; -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "a * b > 0", "true_expr": "(a ! b)", "false_expr": "(a ! b)"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ";", "condition": "abs(a - b) < 2", "true_expr": "(a [] b)", "false_expr": "(a [] b)"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((((4 ! -2) ! 1) @ 4) @ -6) []@ 9) [] -5) []! 2) [] 3)", "B": "((((((((1 @@ 5) !! 3) !! 9) @; -10) @ 10) !<> -3) ! -3) !@ -3)", "C": "((((((((-9 ! -9) [] 4) <><> -1) ! 9) [] 6) []; 8) !<> -9) ; -2)", "A_val": 0, "B_val": 3, "C_val": 0, "answer": 3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$<> b$ equals a * b if a > b; otherwise, a + b\n$& b$ equals (a ; b) if is_prime(a) or is_prime(b); otherwise, (a ; b)\n$# b$ equals (a <> b) if math.gcd(a, b) == 1; otherwise, (a <> b)\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-9 <><> 3) :*:* -1) :*# -8) #; -9) & -6) :*<> 6)\nLet B = ((((((7 & -4) <> -10) :* 7) ; 2) :* 10) <> -7)\nLet C = ((((((8 # 1) :* -3) <># -10) <> -7) <>; 1) #; -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}, {"symbol": "#", "condition": "math.gcd(a, b) == 1", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}, {"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((-9 <><> 3) :*:* -1) :*# -8) #; -9) & -6) :*<> 6)", "B": "((((((7 & -4) <> -10) :* 7) ; 2) :* 10) <> -7)", "C": "((((((8 # 1) :* -3) <># -10) <> -7) <>; 1) #; -9)", "A_val": 12, "B_val": 35, "C_val": 9, "answer": 38}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals (a [] b) if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((9 ><[] -3) [] 6) [] -1) ><>< -10)\nLet B = ((((-8 <><> -5) <>>< -5) <> -2) @ -5)\nLet C = ((((8 [] -1) @ 3) <> -1) @ 8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "abs(a - b) < 2", "true_expr": "(a [] b)", "false_expr": "a - b"}], "A": "((((9 ><[] -3) [] 6) [] -1) ><>< -10)", "B": "((((-8 <><> -5) <>>< -5) <> -2) @ -5)", "C": "((((8 [] -1) @ 3) <> -1) @ 8)", "A_val": 20, "B_val": 5, "C_val": -8, "answer": 33}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a * b if a > b; otherwise, a + b\n$@ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$! b$ equals (a @ b) if a > b; otherwise, a + b\n$~ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$<> b$ equals (a @ b) if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((-6 <>! -9) @~ 1) ~ 6) <>! 4) <> 9) ~ -3) <> -7) ~ -3)\nLet B = ((((((((3 <> 6) <>! -3) @<> -6) !! 1) &~ 10) ! 5) <>& -6) !! 2)\nLet C = ((((((((-2 <> -6) @! -6) & -4) @<> -10) !<> 10) &@ -1) @! -9) ~@ 5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "@", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "!", "condition": "a > b", "true_expr": "(a @ b)", "false_expr": "a + b"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "<>", "condition": "a * b > 0", "true_expr": "(a @ b)", "false_expr": "a + b"}], "A": "((((((((-6 <>! -9) @~ 1) ~ 6) <>! 4) <> 9) ~ -3) <> -7) ~ -3)", "B": "((((((((3 <> 6) <>! -3) @<> -6) !! 1) &~ 10) ! 5) <>& -6) !! 2)", "C": "((((((((-2 <> -6) @! -6) & -4) @<> -10) !<> 10) &@ -1) @! -9) ~@ 5)", "A_val": 0, "B_val": 2, "C_val": 5, "answer": -3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals (a & b) if a * b > 0; otherwise, (a & b)\n$; b$ equals (a & b) if abs(a - b) < 2; otherwise, a - b\n$! b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((2 ;! 9) ; -8) @ -10) ;! 9) @ -9) :* 6) ;& -5) ; 7)\nLet B = ((((((((10 !@ -5) ;& -3) @! -3) @& -2) ! 5) ;@ 10) @; 5) @ 3)\nLet C = ((((((((9 :* 3) !; 7) ! 8) ! 5) !:* -8) !! 7) ; 3) && -10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "(a & b)", "false_expr": "(a & b)"}, {"symbol": ";", "condition": "abs(a - b) < 2", "true_expr": "(a & b)", "false_expr": "a - b"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "((((((((2 ;! 9) ; -8) @ -10) ;! 9) @ -9) :* 6) ;& -5) ; 7)", "B": "((((((((10 !@ -5) ;& -3) @! -3) @& -2) ! 5) ;@ 10) @; 5) @ 3)", "C": "((((((((9 :* 3) !; 7) ! 8) ! 5) !:* -8) !! 7) ; 3) && -10)", "A_val": 5, "B_val": 3, "C_val": 39, "answer": -31}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$@ b$ equals a * b if a > b; otherwise, a - b\n$~ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if a > b; otherwise, a - b\n$& b$ equals (a # b) if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((8 @& 7) @~ -2) # -5) # -1) <> -7) ~# -2) ~# 8) <> 9)\nLet B = ((((((((-7 <> 7) <># 8) ~ 8) <><> -5) ~ 9) <><> -7) ~ 4) @ -4)\nLet C = ((((((((1 @# 10) &~ -2) #& -1) <> 2) &~ 8) ~ -8) ~ -7) <> 5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "@", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "a > b", "true_expr": "(a # b)", "false_expr": "a - b"}], "A": "((((((((8 @& 7) @~ -2) # -5) # -1) <> -7) ~# -2) ~# 8) <> 9)", "B": "((((((((-7 <> 7) <># 8) ~ 8) <><> -5) ~ 9) <><> -7) ~ 4) @ -4)", "C": "((((((((1 @# 10) &~ -2) #& -1) <> 2) &~ 8) ~ -8) ~ -7) <> 5)", "A_val": 5, "B_val": -44, "C_val": 5, "answer": -44}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals a * b if a > b; otherwise, a + b\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals a * b if a > b; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((4 & -4) :* 6) & 2) & -3) >< -1) <>& -4)\nLet B = ((((((-8 # -4) &<> 6) <> -6) <>:* -3) # 7) # 9)\nLet C = ((((((-5 #>< -3) >< -4) :*:* -5) ><:* -8) & 1) <>& 5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "((((((4 & -4) :* 6) & 2) & -3) >< -1) <>& -4)", "B": "((((((-8 # -4) &<> 6) <> -6) <>:* -3) # 7) # 9)", "C": "((((((-5 #>< -3) >< -4) :*:* -5) ><:* -8) & 1) <>& 5)", "A_val": 4, "B_val": 16, "C_val": -5, "answer": 25}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a * b if a > b; otherwise, a - b\n$# b$ equals (a :* b) if a > b; otherwise, (a :* b)\n$& b$ equals a * b if a > b; otherwise, a + b\n$>< b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((10 :*& 1) ><& 5) >< -3) :*# -3) & -6)\nLet B = (((((-1 & -2) & 4) :* 6) >< 8) &# 9)\nLet C = (((((-5 >< -10) >< -5) & -7) :*:* -7) :* -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "a > b", "true_expr": "(a :* b)", "false_expr": "(a :* b)"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "><", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((10 :*& 1) ><& 5) >< -3) :*# -3) & -6)", "B": "(((((-1 & -2) & 4) :* 6) >< 8) &# 9)", "C": "(((((-5 >< -10) >< -5) & -7) :*:* -7) :* -4)", "A_val": 0, "B_val": 0, "C_val": -239, "answer": 239}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals (a ][ b) if a > b; otherwise, (a ][ b)\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\n$! b$ equals (a # b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((7 !; 5) ! -10) # -7) # -3) ! -1) ><; 1)\nLet B = ((((((2 ; 9) ;][ 5) >< -4) !; 5) ;! -3) ;>< 9)\nLet C = ((((((-7 ;][ -3) ## 5) ][ 6) ][ 4) ][ -1) ! 2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "a > b", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "(a # b)", "false_expr": "math.gcd(a, b)"}], "A": "((((((7 !; 5) ! -10) # -7) # -3) ! -1) ><; 1)", "B": "((((((2 ; 9) ;][ 5) >< -4) !; 5) ;! -3) ;>< 9)", "C": "((((((-7 ;][ -3) ## 5) ][ 6) ][ 4) ][ -1) ! 2)", "A_val": 0, "B_val": 9, "C_val": 0, "answer": 9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals (a <> b) if a > b; otherwise, (a <> b)\n$& b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$@ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-5 & 1) ][& -9) @ -3) <> 10) <>[] -7) ][ -7)\nLet B = ((((((5 <>@ -5) @@ -8) ][ 8) & -9) &<> -4) <>[] -3)\nLet C = ((((((-7 ][[] 7) @][ -9) @ 8) &[] -4) &[] 4) ][@ 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "a > b", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}, {"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((-5 & 1) ][& -9) @ -3) <> 10) <>[] -7) ][ -7)", "B": "((((((5 <>@ -5) @@ -8) ][ 8) & -9) &<> -4) <>[] -3)", "C": "((((((-7 ][[] 7) @][ -9) @ 8) &[] -4) &[] 4) ][@ 7)", "A_val": 0, "B_val": 6, "C_val": 0, "answer": 6}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals (a ~ b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$@ b$ equals (a ][ b) if a > b; otherwise, (a ][ b)\n$[] b$ equals (a & b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((1 ~ 3) [] 7) ~ -2) [] 6) ][@ 2) & -4) ][][ -7)\nLet B = (((((((5 ][ -10) & -7) ][ 4) ][][ -4) ~@ -2) ~][ 8) [][] 3)\nLet C = (((((((-1 []@ -5) ~ -4) &@ 4) @& 8) @~ 2) @[] 3) & 10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a ~ b)", "false_expr": "max(a, b)"}, {"symbol": "@", "condition": "a > b", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a & b)", "false_expr": "max(a, b)"}], "A": "(((((((1 ~ 3) [] 7) ~ -2) [] 6) ][@ 2) & -4) ][][ -7)", "B": "(((((((5 ][ -10) & -7) ][ 4) ][][ -4) ~@ -2) ~][ 8) [][] 3)", "C": "(((((((-1 []@ -5) ~ -4) &@ 4) @& 8) @~ 2) @[] 3) & 10)", "A_val": 14, "B_val": 0, "C_val": 0, "answer": 14}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a - b if a * b > 0; otherwise, a + b\n$~ b$ equals (a & b) if is_prime(a) or is_prime(b); otherwise, (a & b)\n$! b$ equals a * b if a > b; otherwise, a - b\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\n$# b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((3 !@ -5) @# -9) @ -4) ## -3) ~ -4) &# -7) ~ -1)\nLet B = (((((((-2 ~ 10) !@ -4) # -3) ~ -9) ~ -8) ! 7) !# -10)\nLet C = (((((((10 # -1) # 6) @! -10) # -7) # 4) & -3) && 3)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "~", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a & b)", "false_expr": "(a & b)"}, {"symbol": "!", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "#", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((((((3 !@ -5) @# -9) @ -4) ## -3) ~ -4) &# -7) ~ -1)", "B": "(((((((-2 ~ 10) !@ -4) # -3) ~ -9) ~ -8) ! 7) !# -10)", "C": "(((((((10 # -1) # 6) @! -10) # -7) # 4) & -3) && 3)", "A_val": 0, "B_val": 10, "C_val": 2, "answer": 8}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a - b if a * b > 0; otherwise, a + b\n$! b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals (a <> b) if a * b > 0; otherwise, (a <> b)\n$][ b$ equals (a <> b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((5 <>][ 8) ! 8) && 4) ! 8) ][! -7)\nLet B = (((((5 ][& 3) & -6) !<> -5) <><> 7) ][ 6)\nLet C = (((((6 & -10) !& 9) ! -1) !][ -9) ][! -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "a * b > 0", "true_expr": "(a <> b)", "false_expr": "(a <> b)"}, {"symbol": "][", "condition": "math.gcd(a, b) == 1", "true_expr": "(a <> b)", "false_expr": "math.gcd(a, b)"}], "A": "(((((5 <>][ 8) ! 8) && 4) ! 8) ][! -7)", "B": "(((((5 ][& 3) & -6) !<> -5) <><> 7) ][ 6)", "C": "(((((6 & -10) !& 9) ! -1) !][ -9) ][! -4)", "A_val": 7, "B_val": 6, "C_val": 4, "answer": 9}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\n$@ b$ equals a * b if a > b; otherwise, a + b\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-5 >< 4) :* 3) # 6) # 7)\nLet B = ((((-9 >< -6) # 1) :*# -3) #>< -4)\nLet C = ((((6 :* 4) ><# 4) :* -1) @ -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "@", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((-5 >< 4) :* 3) # 6) # 7)", "B": "((((-9 >< -6) # 1) :*# -3) #>< -4)", "C": "((((6 :* 4) ><# 4) :* -1) @ -4)", "A_val": -11, "B_val": 4, "C_val": 4, "answer": -11}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a * b if a > b; otherwise, a + b\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$! b$ equals (a & b) if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((10 >< 3) [] 8) & -1) >< -9) & -8)\nLet B = (((((6 &>< -6) []! -4) >< 2) []>< -2) ><& 1)\nLet C = (((((-2 ! -7) [] 3) & 1) & 10) [] 9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "!", "condition": "a > b", "true_expr": "(a & b)", "false_expr": "a - b"}], "A": "(((((10 >< 3) [] 8) & -1) >< -9) & -8)", "B": "(((((6 &>< -6) []! -4) >< 2) []>< -2) ><& 1)", "C": "(((((-2 ! -7) [] 3) & 1) & 10) [] 9)", "A_val": -17, "B_val": 0, "C_val": 0, "answer": -17}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$; b$ equals (a & b) if a > b; otherwise, (a & b)\n$@ b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((((6 @& 7) @ 6) ~ 5) #@ -4) ;@ 3) # -1) ;# 9) & 4)\nLet B = ((((((((5 # -2) #~ 6) #@ -6) ~ -7) ; 4) @ -6) ~ 2) @& -10)\nLet C = ((((((((9 @~ -5) ## 5) ~@ -3) & -10) ;; -1) ~@ 6) @ -5) # -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ";", "condition": "a > b", "true_expr": "(a & b)", "false_expr": "(a & b)"}, {"symbol": "@", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((((6 @& 7) @ 6) ~ 5) #@ -4) ;@ 3) # -1) ;# 9) & 4)", "B": "((((((((5 # -2) #~ 6) #@ -6) ~ -7) ; 4) @ -6) ~ 2) @& -10)", "C": "((((((((9 @~ -5) ## 5) ~@ -3) & -10) ;; -1) ~@ 6) @ -5) # -9)", "A_val": -5, "B_val": 10, "C_val": 9, "answer": -4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$:* b$ equals a * b if a > b; otherwise, a - b\n$~ b$ equals a - b if a * b > 0; otherwise, a + b\n$][ b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((4 ! 9) ~ -4) :* -4) ~! 7) !:* 3)\nLet B = (((((7 ~ -10) :* 1) ][][ 4) !! 2) ! -10)\nLet C = (((((3 ][ -7) ~:* 1) ~ -6) ~! 1) ~~ -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": ":*", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "][", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((4 ! 9) ~ -4) :* -4) ~! 7) !:* 3)", "B": "(((((7 ~ -10) :* 1) ][][ 4) !! 2) ! -10)", "C": "(((((3 ][ -7) ~:* 1) ~ -6) ~! 1) ~~ -4)", "A_val": -3, "B_val": 0, "C_val": 0, "answer": -3}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$~ b$ equals (a ; b) if a * b > 0; otherwise, a + b\n$<> b$ equals a - b if a * b > 0; otherwise, a + b\n$# b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals (a ; b) if abs(a - b) < 2; otherwise, (a ; b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-2 ## 10) <> 3) #~ 9) []# -10) ;# 6) [] -9) []; -9)\nLet B = (((((((7 ;[] 10) ;<> -1) ~# -8) [] -3) []~ -7) #; 3) <>~ -8)\nLet C = (((((((-8 [] 3) # -6) # 5) [] 1) <><> 4) <> 10) []# 2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "~", "condition": "a * b > 0", "true_expr": "(a ; b)", "false_expr": "a + b"}, {"symbol": "<>", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "#", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}], "A": "(((((((-2 ## 10) <> 3) #~ 9) []# -10) ;# 6) [] -9) []; -9)", "B": "(((((((7 ;[] 10) ;<> -1) ~# -8) [] -3) []~ -7) #; 3) <>~ -8)", "C": "(((((((-8 [] 3) # -6) # 5) [] 1) <><> 4) <> 10) []# 2)", "A_val": 9, "B_val": -1, "C_val": 2, "answer": 6}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$[] b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$! b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals a * b if a > b; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((4 & -8) :*! -8) !! -6) &[] -6)\nLet B = ((((5 :*[] 2) &! -8) & 6) & -9)\nLet C = ((((6 & -7) :* 10) []& 2) && 8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "[]", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((4 & -8) :*! -8) !! -6) &[] -6)", "B": "((((5 :*[] 2) &! -8) & 6) & -9)", "C": "((((6 & -7) :* 10) []& 2) && 8)", "A_val": 6, "B_val": -432, "C_val": -16, "answer": -410}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$[] b$ equals a * b if a > b; otherwise, a - b\n$~ b$ equals (a ! b) if a > b; otherwise, a - b\n$& b$ equals a * b if a > b; otherwise, a + b\n$# b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((-7 ![] -3) # 7) ~& 3) []# -8) &~ -1) []& -8) [] 2)\nLet B = (((((((-8 ! -3) ~ 3) # -4) # 6) ~[] 4) !& 1) &[] 6)\nLet C = (((((((-7 !~ 3) ![] 7) #[] -1) [] 5) &! -4) ~ 3) ~ 8)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "~", "condition": "a > b", "true_expr": "(a ! b)", "false_expr": "a - b"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "(((((((-7 ![] -3) # 7) ~& 3) []# -8) &~ -1) []& -8) [] 2)", "B": "(((((((-8 ! -3) ~ 3) # -4) # 6) ~[] 4) !& 1) &[] 6)", "C": "(((((((-7 !~ 3) ![] 7) #[] -1) [] 5) &! -4) ~ 3) ~ 8)", "A_val": -2, "B_val": -8, "C_val": -16, "answer": 6}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals (a ! b) if a > b; otherwise, a - b\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$][ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals (a & b) if is_prime(a) or is_prime(b); otherwise, (a & b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((8 &! -3) !& -8) # 8) # 1) [][] 5) [] 10) []][ 9)\nLet B = (((((((-7 ][ 4) ][[] 10) !][ 9) & 2) #! 3) ! -1) [] -8)\nLet C = (((((((-5 []& 10) ! 1) #][ -3) #[] -9) []! 3) ][ -1) ][ -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "a > b", "true_expr": "(a ! b)", "false_expr": "a - b"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "][", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a & b)", "false_expr": "(a & b)"}], "A": "(((((((8 &! -3) !& -8) # 8) # 1) [][] 5) [] 10) []][ 9)", "B": "(((((((-7 ][ 4) ][[] 10) !][ 9) & 2) #! 3) ! -1) [] -8)", "C": "(((((((-5 []& 10) ! 1) #][ -3) #[] -9) []! 3) ][ -1) ][ -2)", "A_val": -38, "B_val": 10, "C_val": 6, "answer": -34}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$# b$ equals (a & b) if is_prime(a) or is_prime(b); otherwise, (a & b)\n$:* b$ equals (a # b) if a > b; otherwise, a - b\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-9 :*# -3) :*<> 10) [] -5) ## 6) #:* -2) [][] 10)\nLet B = ((((((-10 :*[] 7) :*<> -4) &:* 9) # -8) <> -5) <> 4)\nLet C = ((((((3 [] 2) [] -1) :* 7) #& -9) & 7) :* 7)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "(a & b)", "false_expr": "(a & b)"}, {"symbol": ":*", "condition": "a > b", "true_expr": "(a # b)", "false_expr": "a - b"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((((-9 :*# -3) :*<> 10) [] -5) ## 6) #:* -2) [][] 10)", "B": "((((((-10 :*[] 7) :*<> -4) &:* 9) # -8) <> -5) <> 4)", "C": "((((((3 [] 2) [] -1) :* 7) #& -9) & 7) :* 7)", "A_val": 0, "B_val": 9, "C_val": -7, "answer": 16}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$[] b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$>< b$ equals (a ~ b) if math.gcd(a, b) == 1; otherwise, (a ~ b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((-4 ><>< 2) ~[] 8) ~ -2)\nLet B = (((-1 ~[] -8) ~>< 8) []>< 7)\nLet C = (((1 >< -2) ~ -5) ~ -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "[]", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ~ b)", "false_expr": "(a ~ b)"}], "A": "(((-4 ><>< 2) ~[] 8) ~ -2)", "B": "(((-1 ~[] -8) ~>< 8) []>< 7)", "C": "(((1 >< -2) ~ -5) ~ -2)", "A_val": 2, "B_val": 0, "C_val": 3, "answer": -1}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$][ b$ equals a * b if a > b; otherwise, a - b\n$:* b$ equals a - b if a * b > 0; otherwise, a + b\n$; b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$>< b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((2 >< -7) ;>< 1) ; -6) ><][ 1)\nLet B = ((((-3 :*>< 9) ><>< 10) ; 7) >< 6)\nLet C = ((((-6 ><; 6) :* -2) :* -1) ][ -9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": ":*", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "><", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((2 >< -7) ;>< 1) ; -6) ><][ 1)", "B": "((((-3 :*>< 9) ><>< 10) ; 7) >< 6)", "C": "((((-6 ><; 6) :* -2) :* -1) ][ -9)", "A_val": 2, "B_val": -2, "C_val": -27, "answer": 27}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$& b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$[] b$ equals a - b if a * b > 0; otherwise, a + b\n$][ b$ equals (a [] b) if a * b > 0; otherwise, a + b\n$>< b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((1 >< -1) ][ 6) & 4) ][][ 10) [] 5)\nLet B = (((((-9 ][ 1) ][[] -7) ][ -8) ><>< 8) ][][ -1)\nLet C = (((((4 &>< -2) []& 3) ][ 9) []][ 8) [] -5)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "][", "condition": "a * b > 0", "true_expr": "(a [] b)", "false_expr": "a + b"}, {"symbol": "><", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((((1 >< -1) ][ 6) & 4) ][][ 10) [] 5)", "B": "(((((-9 ][ 1) ][[] -7) ][ -8) ><>< 8) ][][ -1)", "C": "(((((4 &>< -2) []& 3) ][ 9) []][ 8) [] -5)", "A_val": 5, "B_val": 6, "C_val": 0, "answer": 11}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$; b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$[] b$ equals (a ; b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$:* b$ equals (a ; b) if a > b; otherwise, (a ; b)\n$<> b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-10 ;<> 5) :*[] -6) ; 5) ;:* -2)\nLet B = ((((3 [] 2) <>; -2) [] 3) :* -1)\nLet C = ((((10 :*<> 2) <> -6) <>:* 2) <> -1)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": ";", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "[]", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ; b)", "false_expr": "math.gcd(a, b)"}, {"symbol": ":*", "condition": "a > b", "true_expr": "(a ; b)", "false_expr": "(a ; b)"}, {"symbol": "<>", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "((((-10 ;<> 5) :*[] -6) ; 5) ;:* -2)", "B": "((((3 [] 2) <>; -2) [] 3) :* -1)", "C": "((((10 :*<> 2) <> -6) <>:* 2) <> -1)", "A_val": 0, "B_val": 0, "C_val": -1, "answer": 1}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals (a <> b) if a * b > 0; otherwise, a + b\n$! b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$>< b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = (((((((10 ~@ -8) <> 2) !~ -6) @<> -8) <> 9) >< -9) >< 10)\nLet B = (((((((-3 ~ 2) @ 4) ! 7) <> 10) ~ 10) >< 7) <>! -6)\nLet C = (((((((2 @<> -1) ! -9) !@ 8) @ 8) <> 10) <> -1) <>@ -4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "(a <> b)", "false_expr": "a + b"}, {"symbol": "!", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "><", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "(((((((10 ~@ -8) <> 2) !~ -6) @<> -8) <> 9) >< -9) >< 10)", "B": "(((((((-3 ~ 2) @ 4) ! 7) <> 10) ~ 10) >< 7) <>! -6)", "C": "(((((((2 @<> -1) ! -9) !@ 8) @ 8) <> 10) <> -1) <>@ -4)", "A_val": 0, "B_val": 0, "C_val": -4, "answer": 4}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$! b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$# b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$& b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((-2 ~~ 1) #! -8) ! 10) !! -9)\nLet B = ((((-2 #& -4) # 1) # -4) &! -2)\nLet C = ((((-10 ~# -1) ~ 2) # -8) ~ 4)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "!", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "#", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "&", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "((((-2 ~~ 1) #! -8) ! 10) !! -9)", "B": "((((-2 #& -4) # 1) # -4) &! -2)", "C": "((((-10 ~# -1) ~ 2) # -8) ~ 4)", "A_val": 16, "B_val": 2, "C_val": -4, "answer": 22}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$[] b$ equals a - b if a * b > 0; otherwise, a + b\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\n$@ b$ equals a - b if a * b > 0; otherwise, a + b\n$& b$ equals (a @ b) if abs(a - b) < 2; otherwise, (a @ b)\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-8 & -10) ~ -1) ~ 1) [] -10) <>& 9) <> 10)\nLet B = ((((((-6 <>& 1) ~<> -1) ~ -4) @<> -7) <> -4) &<> -10)\nLet C = ((((((5 @& 10) && -9) [] -8) ~ -3) &~ 1) []<> -10)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "[]", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "&", "condition": "abs(a - b) < 2", "true_expr": "(a @ b)", "false_expr": "(a @ b)"}], "A": "((((((-8 & -10) ~ -1) ~ 1) [] -10) <>& 9) <> 10)", "B": "((((((-6 <>& 1) ~<> -1) ~ -4) @<> -7) <> -4) &<> -10)", "C": "((((((5 @& 10) && -9) [] -8) ~ -3) &~ 1) []<> -10)", "A_val": -10, "B_val": 10, "C_val": 100, "answer": -100}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$~ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$][ b$ equals a - b if a * b > 0; otherwise, a + b\n$>< b$ equals a * b if a > b; otherwise, a + b\n$[] b$ equals min(a, b) if is_prime(a) or is_prime(b); otherwise, max(a, b)\n$<> b$ equals a * b if abs(a - b) < 2; otherwise, a - b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-2 >< 9) ][<> 9) <> -1) <><> 10) <> -1) >< 10)\nLet B = ((((((-2 []<> 7) <> 7) ~][ 5) ~ -6) <> 10) []][ -3)\nLet C = ((((((4 ][>< 10) >< 3) ><[] 3) []<> 3) ~[] 9) []][ 9)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "][", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}, {"symbol": "><", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "[]", "condition": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}, {"symbol": "<>", "condition": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((-2 >< 9) ][<> 9) <> -1) <><> 10) <> -1) >< 10)", "B": "((((((-2 []<> 7) <> 7) ~][ 5) ~ -6) <> 10) []][ -3)", "C": "((((((4 ][>< 10) >< 3) ><[] 3) []<> 3) ~[] 9) []][ 9)", "A_val": -19, "B_val": -3, "C_val": 9, "answer": -31}}
|
||||
{"data_source": "BbehMultistepArithmetic", "prompt": "Consider the following new operations:\n\n$<> b$ equals a * b if a > b; otherwise, a + b\n$! b$ equals (a <> b) if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$# b$ equals a * b if a > b; otherwise, a - b\n$][ b$ equals a + b if math.gcd(a, b) == 1; otherwise, math.gcd(a, b)\n$& b$ equals a - b if a * b > 0; otherwise, a + b\nFor brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.\nLet A = ((((((-8 <> 1) ][# 5) &# 2) ][ -5) # 6) !# 10)\nLet B = ((((((-1 # -9) #<> 2) ][ -10) !! 8) # -3) &# -6)\nLet C = ((((((-9 ][ 4) & 3) # -5) ! 6) # -2) <>& -2)\nCompute A + B - C. Your final answer must be in number form. Please put your final answer within [answer] and [/answer] tags.", "ground_truth": {"operators": [{"symbol": "<>", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "!", "condition": "math.gcd(a, b) == 1", "true_expr": "(a <> b)", "false_expr": "math.gcd(a, b)"}, {"symbol": "#", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "][", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}, {"symbol": "&", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((((-8 <> 1) ][# 5) &# 2) ][ -5) # 6) !# 10)", "B": "((((((-1 # -9) #<> 2) ][ -10) !! 8) # -3) &# -6)", "C": "((((((-9 ][ 4) & 3) # -5) ! 6) # -2) <>& -2)", "A_val": -8, "B_val": 0, "C_val": -4, "answer": -4}}
|
||||
Loading…
Add table
Add a link
Reference in a new issue