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InternBootcamp/examples/data/InternBootcamp_eval/BbehMultistepArithmetic.jsonl
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{"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 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 @ 9) &[] 3) ][ -8) @ 8) & -6)\nLet B = (((((10 @ 9) ][@ 5) ][@ 8) []][ -1) & 2)\nLet C = (((((7 [] 5) ][ -3) &[] -9) & -1) ][ -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": "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)"}], "A": "(((((-4 @ 9) &[] 3) ][ -8) @ 8) & -6)", "B": "(((((10 @ 9) ][@ 5) ][@ 8) []][ -1) & 2)", "C": "(((((7 [] 5) ][ -3) &[] -9) & -1) ][ -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 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 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 = ((((((-4 ; 1) & 4) <><> -5) &:* -8) &:* 10) ; 7)\nLet B = ((((((7 :*<> 8) <>~ -3) ~& -7) ;; 8) &<> -4) && 8)\nLet C = ((((((2 :* -1) ;& -6) <> -6) <> 1) :*& 9) &:* 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": "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": "((((((-4 ; 1) & 4) <><> -5) &:* -8) &:* 10) ; 7)", "B": "((((((7 :*<> 8) <>~ -3) ~& -7) ;; 8) &<> -4) && 8)", "C": "((((((2 :* -1) ;& -6) <> -6) <> 1) :*& 9) &:* 7)", "A_val": 83, "B_val": -60, "C_val": -181, "answer": 204}}
{"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 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 = ((((((-10 ><<> 7) >< 7) :* 9) :*][ 6) :* -2) <>][ 10)\nLet B = ((((((10 & 1) <>& 8) <>& 2) <> -9) && 3) ><][ -3)\nLet C = ((((((4 ][ 9) :* -9) <>:* -8) :* 4) ][ 4) ][ 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": "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": "((((((-10 ><<> 7) >< 7) :* 9) :*][ 6) :* -2) <>][ 10)", "B": "((((((10 & 1) <>& 8) <>& 2) <> -9) && 3) ><][ -3)", "C": "((((((4 ][ 9) :* -9) <>:* -8) :* 4) ][ 4) ][ 1)", "A_val": 0, "B_val": -3, "C_val": 3, "answer": -6}}
{"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 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 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 = ((((((((-8 <>! 4) # 8) @@ -5) # -8) @ -9) !! -9) ! 10) #<> 3)\nLet B = ((((((((-7 :*<> 7) #<> 5) :* 3) <>@ -4) :* 9) #:* -5) #! 3) <> 3)\nLet C = ((((((((8 <> -2) @@ 6) :* 10) ! -3) <> -7) #! 4) <># -5) <>:* -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": "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)"}, {"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)"}], "A": "((((((((-8 <>! 4) # 8) @@ -5) # -8) @ -9) !! -9) ! 10) #<> 3)", "B": "((((((((-7 :*<> 7) #<> 5) :* 3) <>@ -4) :* 9) #:* -5) #! 3) <> 3)", "C": "((((((((8 <> -2) @@ 6) :* 10) ! -3) <> -7) #! 4) <># -5) <>:* -8)", "A_val": 12, "B_val": 0, "C_val": 0, "answer": 12}}
{"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, (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) :* 2) ><:* 8)\nLet B = (((7 ;; 1) :*:* 9) >< 5)\nLet C = (((-4 ><>< -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": "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": "(((-4 >< 5) :* 2) ><:* 8)", "B": "(((7 ;; 1) :*:* 9) >< 5)", "C": "(((-4 ><>< -7) ;>< -9) :* -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 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 ~>< 7) >< -5) ><~ 3) # -1)\nLet B = ((((-10 ~ 8) ~# 7) ><>< -1) ; 9)\nLet C = ((((4 ><; -4) ><~ 6) ~ 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": "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 ~>< 7) >< -5) ><~ 3) # -1)", "B": "((((-10 ~ 8) ~# 7) ><>< -1) ; 9)", "C": "((((4 ><; -4) ><~ 6) ~ 5) # 6)", "A_val": -1, "B_val": 14, "C_val": 6, "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 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)\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 @! -8) @ 4) [] 9) @ -7) []! -1) && 7)\nLet B = ((((((-4 & 1) [] 4) ][ 3) []][ 8) [][] -5) @ 5)\nLet C = ((((((-7 ][ -1) ][ -2) &][ -4) ! -7) @ -6) && 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": "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 @! -8) @ 4) [] 9) @ -7) []! -1) && 7)", "B": "((((((-4 & 1) [] 4) ][ 3) []][ 8) [][] -5) @ 5)", "C": "((((((-7 ][ -1) ][ -2) &][ -4) ! -7) @ -6) && 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 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 = (((-4 ~~ -4) <>~ 6) <> -6)\nLet B = (((-5 ~ -3) <><> 8) !! 8)\nLet C = (((-5 ~ -7) ~ -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": "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": "(((-4 ~~ -4) <>~ 6) <> -6)", "B": "(((-5 ~ -3) <><> 8) !! 8)", "C": "(((-5 ~ -7) ~ -5) <> -6)", "A_val": 24, "B_val": -32, "C_val": 30, "answer": -38}}
{"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, (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 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) [] 2) ><~ 7) @ -7) @[] -10) !>< 7) ! -4)\nLet B = (((((((7 >< -6) @ -7) >< -6) ><! 4) [] -9) [] -3) @ -6)\nLet C = (((((((-3 >< 10) ~@ -5) [] -5) >< 8) !@ -1) ~>< 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", "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)"}, {"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": "(((((((2 ~ -9) [] 2) ><~ 7) @ -7) @[] -10) !>< 7) ! -4)", "B": "(((((((7 >< -6) @ -7) >< -6) ><! 4) [] -9) [] -3) @ -6)", "C": "(((((((-3 >< 10) ~@ -5) [] -5) >< 8) !@ -1) ~>< 8) @ 4)", "A_val": 2, "B_val": -79, "C_val": -4, "answer": -73}}
{"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\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 <> 4) <> 1) & 4)\nLet B = (((4 & 3) <> 1) & 9)\nLet C = (((-7 & 7) <># 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": "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"}], "A": "(((-7 <> 4) <> 1) & 4)", "B": "(((4 & 3) <> 1) & 9)", "C": "(((-7 & 7) <># 8) #<> 1)", "A_val": 0, "B_val": 0, "C_val": 16, "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)\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 ][][ 3) @ 3) ! 8) ! -9)\nLet B = ((((3 ][ -1) @ 1) @ -4) ][ -1)\nLet C = ((((1 ][& 9) @ 6) @@ -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": "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": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "((((-10 ][][ 3) @ 3) ! 8) ! -9)", "B": "((((3 ][ -1) @ 1) @ -4) ][ -1)", "C": "((((1 ][& 9) @ 6) @@ -1) ! -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 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 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 >< -6) ~][ 7) ][& 4) >< -2) ><~ 3) >< -4) && 8)\nLet B = (((((((4 ][& -9) ][~ -4) ;& -1) ><~ -6) ~>< 10) ; -3) ><; -3)\nLet C = (((((((-3 ><& 4) ;; -6) ][][ 5) >< -5) ][][ -4) ][& -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": "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": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((((((8 >< -6) ~][ 7) ][& 4) >< -2) ><~ 3) >< -4) && 8)", "B": "(((((((4 ][& -9) ][~ -4) ;& -1) ><~ -6) ~>< 10) ; -3) ><; -3)", "C": "(((((((-3 ><& 4) ;; -6) ][][ 5) >< -5) ][][ -4) ][& -8) ][~ 3)", "A_val": -16, "B_val": -3, "C_val": 3, "answer": -22}}
{"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)\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) !! -2) ][<> -10)\nLet B = (((-10 ! 2) <> -7) ][ 5)\nLet C = (((9 ! -1) !! -6) <>][ -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": "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": "(((4 ! 9) !! -2) ][<> -10)", "B": "(((-10 ! 2) <> -7) ][ 5)", "C": "(((9 ! -1) !! -6) <>][ -1)", "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 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)\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) ][ 3) #:* 1) & -3) ][ 7) ][ 6) ][][ -7) #& 7)\nLet B = ((((((((5 @# -6) # -9) @:* -5) ][ -4) ][:* 4) @@ -5) # 10) @ -9)\nLet C = ((((((((-5 :*@ 8) :*# -2) :*# -10) && 3) ][ 3) :* -3) :*@ 8) :* 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": "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)"}, {"symbol": "][", "condition": "math.gcd(a, b) == 1", "true_expr": "(a # b)", "false_expr": "math.gcd(a, b)"}], "A": "((((((((7 # -2) ][ 3) #:* 1) & -3) ][ 7) ][ 6) ][][ -7) #& 7)", "B": "((((((((5 @# -6) # -9) @:* -5) ][ -4) ][:* 4) @@ -5) # 10) @ -9)", "C": "((((((((-5 :*@ 8) :*# -2) :*# -10) && 3) ][ 3) :* -3) :*@ 8) :* 9)", "A_val": 49, "B_val": 0, "C_val": -9, "answer": 58}}
{"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 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)\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 :*:* -10) # -3) [] 4) [] -3) ][ -4) @[] 10) #][ 6) # -6)\nLet B = ((((((((1 :* 9) @ -10) ][ 10) [] 3) [] -8) # 5) ][ -10) ][ 7)\nLet C = ((((((((7 [][] 8) ][# -1) :*][ -2) ][ -5) []# -7) :*][ 7) ][:* -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": "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", "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": "((((((((8 :*:* -10) # -3) [] 4) [] -3) ][ -4) @[] 10) #][ 6) # -6)", "B": "((((((((1 :* 9) @ -10) ][ 10) [] 3) [] -8) # 5) ][ -10) ][ 7)", "C": "((((((((7 [][] 8) ][# -1) :*][ -2) ][ -5) []# -7) :*][ 7) ][:* -5) @[] -6)", "A_val": 2, "B_val": -57, "C_val": -63, "answer": 8}}
{"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 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 []; -5) ~ -10) []! -1) ~[] -3) ;[] -4) ;& 5) &! -10)\nLet B = (((((((8 []! 5) &; -3) ; -4) ~ -3) && 3) ! -8) []~ 4)\nLet C = (((((((3 ;~ 4) ~; -6) ; 3) && -7) ![] 9) ; -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": "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": "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 []; -5) ~ -10) []! -1) ~[] -3) ;[] -4) ;& 5) &! -10)", "B": "(((((((8 []! 5) &; -3) ; -4) ~ -3) && 3) ! -8) []~ 4)", "C": "(((((((3 ;~ 4) ~; -6) ; 3) && -7) ![] 9) ; -1) ;! 9)", "A_val": 0, "B_val": 16, "C_val": -2, "answer": 18}}
{"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 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 = (((((((5 &; -7) :* -4) ][:* 3) []& 8) & -8) &:* -3) ; -9)\nLet B = (((((((-7 [] -6) ][ -4) & 4) :*][ 4) ][:* -3) :*; 6) &][ 8)\nLet C = (((((((-9 &:* 2) :* -8) ][ 5) &][ -9) ;][ -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": "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": "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": "(((((((5 &; -7) :* -4) ][:* 3) []& 8) & -8) &:* -3) ; -9)", "B": "(((((((-7 [] -6) ][ -4) & 4) :*][ 4) ][:* -3) :*; 6) &][ 8)", "C": "(((((((-9 &:* 2) :* -8) ][ 5) &][ -9) ;][ -3) :* 3) []][ 2)", "A_val": 3, "B_val": -8, "C_val": -2, "answer": -3}}
{"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, 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 = (((3 @ 1) <><> 2) [] 10)\nLet B = (((4 @ 8) [][] 7) [] -1)\nLet C = (((-8 []<> -1) [] 10) <> -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": "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": "(((3 @ 1) <><> 2) [] 10)", "B": "(((4 @ 8) [][] 7) [] -1)", "C": "(((-8 []<> -1) [] 10) <> -8)", "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 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 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 :* 10) ;& 3) ~:* -5) ~ 10) ~ -3)\nLet B = (((((9 ~ -10) && -6) :*~ -8) & -2) & 2)\nLet C = (((((-5 && 7) :*; -5) ~:* 5) :* 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": "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": "is_prime(a) or is_prime(b)", "true_expr": "min(a, b)", "false_expr": "max(a, b)"}], "A": "(((((3 :* 10) ;& 3) ~:* -5) ~ 10) ~ -3)", "B": "(((((9 ~ -10) && -6) :*~ -8) & -2) & 2)", "C": "(((((-5 && 7) :*; -5) ~:* 5) :* 1) :*; 6)", "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 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\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 ! 5) &][ 9) # -4) ][# -4) &! 7)\nLet B = (((((3 ][ -1) ! 7) ! 10) !# 8) !][ -1)\nLet C = (((((-7 ][# -4) #& -8) ][& -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": "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"}, {"symbol": "][", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((((2 ! 5) &][ 9) # -4) ][# -4) &! 7)", "B": "(((((3 ][ -1) ! 7) ! 10) !# 8) !][ -1)", "C": "(((((-7 ][# -4) #& -8) ][& -6) & -1) #! 4)", "A_val": -58, "B_val": -36, "C_val": -385, "answer": 291}}
{"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 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 = ((((-4 []][ 8) []~ 9) ~~ 2) @[] 3)\nLet B = ((((3 ~@ -1) ][[] -8) [] -10) [] 4)\nLet C = ((((8 [] -3) [] 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": "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"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "(a [] b)", "false_expr": "math.gcd(a, b)"}], "A": "((((-4 []][ 8) []~ 9) ~~ 2) @[] 3)", "B": "((((3 ~@ -1) ][[] -8) [] -10) [] 4)", "C": "((((8 [] -3) [] 8) ][ -8) ][][ 10)", "A_val": 2, "B_val": -2, "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 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 <> -9) !! -1) !<> -1)\nLet B = (((-4 &<> -2) <> 5) ! 5)\nLet C = (((-8 ! -3) ! 1) ! -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": "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 <> -9) !! -1) !<> -1)", "B": "(((-4 &<> -2) <> 5) ! 5)", "C": "(((-8 ! -3) ! 1) ! -7)", "A_val": 5, "B_val": -2, "C_val": -17, "answer": 20}}
{"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 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 ;; -5) # -1) [] -4) ~# 5) ~ -10)\nLet B = (((((-9 ;; 4) # -3) [] 5) ;~ 1) ~ -5)\nLet C = (((((3 ;~ 10) ~ 9) ~ 9) #~ 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 > 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": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((((2 ;; -5) # -1) [] -4) ~# 5) ~ -10)", "B": "(((((-9 ;; 4) # -3) [] 5) ;~ 1) ~ -5)", "C": "(((((3 ;~ 10) ~ 9) ~ 9) #~ 5) ~[] -7)", "A_val": 6, "B_val": 5, "C_val": -224, "answer": 235}}
{"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\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) ][<> -7)\nLet B = (((3 <>][ 8) ][][ -10) # -7)\nLet C = (((-4 <> 5) ][][ 9) <>][ -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 > 0", "true_expr": "(a ][ b)", "false_expr": "(a ][ b)"}, {"symbol": "<>", "condition": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "(((-5 # 4) # 3) ][<> -7)", "B": "(((3 <>][ 8) ][][ -10) # -7)", "C": "(((-4 <> 5) ][][ 9) <>][ -10)", "A_val": 0, "B_val": 0, "C_val": -910, "answer": 910}}
{"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 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 = (((((-8 ! 1) <>& -1) & -4) ! 7) & 4)\nLet B = (((((10 <>! -5) :* -4) && -2) ! 5) :* 4)\nLet C = (((((9 ! 3) ! 1) :*<> 2) !& -6) !:* -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", "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": "(((((-8 ! 1) <>& -1) & -4) ! 7) & 4)", "B": "(((((10 <>! -5) :* -4) && -2) ! 5) :* 4)", "C": "(((((9 ! 3) ! 1) :*<> 2) !& -6) !:* -9)", "A_val": 2, "B_val": 0, "C_val": 0, "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 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 = (((((7 :*:* 10) :* -2) ><~ 10) <> 5) ~ -7)\nLet B = (((((8 <>>< 2) <>>< 1) >< 6) :*<> -3) ~ -8)\nLet C = (((((-9 :*:* -2) ~:* -8) ~ 9) ~>< -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": "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": "(((((7 :*:* 10) :* -2) ><~ 10) <> 5) ~ -7)", "B": "(((((8 <>>< 2) <>>< 1) >< 6) :*<> -3) ~ -8)", "C": "(((((-9 :*:* -2) ~:* -8) ~ 9) ~>< -9) <> 5)", "A_val": 507, "B_val": -7, "C_val": -5, "answer": 505}}
{"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 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\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) #][ -3) # -10) ][ 7) :*; 1) # -9) :*# 1) :*:* -6)\nLet B = ((((((((-1 # 9) ][ -9) :* 5) ][ -5) :*][ -8) :* 9) ;>< 2) #][ 1)\nLet C = ((((((((7 #; -4) ;; 6) ><>< 6) ][# -6) # 6) ><][ 2) :*:* 1) ][>< 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": "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"}], "A": "((((((((-2 >< -9) #][ -3) # -10) ][ 7) :*; 1) # -9) :*# 1) :*:* -6)", "B": "((((((((-1 # 9) ][ -9) :* 5) ][ -5) :*][ -8) :* 9) ;>< 2) #][ 1)", "C": "((((((((7 #; -4) ;; 6) ><>< 6) ][# -6) # 6) ><][ 2) :*:* 1) ][>< 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 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, (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 = (((((((6 [] -2) >< 4) # 6) [] -8) ><; -7) [] -4) [] -5)\nLet B = (((((((6 ><# 4) ! -10) [] 10) [] -10) ><! -4) >< -7) ;! 8)\nLet C = (((((((6 # -9) ; -9) >< 6) !# -1) ;>< 4) [] -1) ;[] 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": "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": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((((6 [] -2) >< 4) # 6) [] -8) ><; -7) [] -4) [] -5)", "B": "(((((((6 ><# 4) ! -10) [] 10) [] -10) ><! -4) >< -7) ;! 8)", "C": "(((((((6 # -9) ; -9) >< 6) !# -1) ;>< 4) [] -1) ;[] 3)", "A_val": 0, "B_val": 12, "C_val": 0, "answer": 12}}
{"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 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 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 = ((((((((-6 & 7) >< -5) ; -4) & -3) ! 6) ;>< 8) :*>< -2) ! -4)\nLet B = ((((((((-1 & -3) !:* 1) :* -8) !! 10) !; -4) :*; -7) & 9) ! 7)\nLet C = ((((((((-2 && 10) ; -3) :* -1) ; -10) &>< -4) ! -3) ! 10) >< -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": "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": "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": "((((((((-6 & 7) >< -5) ; -4) & -3) ! 6) ;>< 8) :*>< -2) ! -4)", "B": "((((((((-1 & -3) !:* 1) :* -8) !! 10) !; -4) :*; -7) & 9) ! 7)", "C": "((((((((-2 && 10) ; -3) :* -1) ; -10) &>< -4) ! -3) ! 10) >< -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 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 = ((((8 @ 10) ~ -4) ~ -8) ><~ -4)\nLet B = ((((3 @ 7) @ -3) ><@ -8) & 1)\nLet C = ((((2 &@ -6) ><~ -7) >< 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": "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": "((((8 @ 10) ~ -4) ~ -8) ><~ -4)", "B": "((((3 @ 7) @ -3) ><@ -8) & 1)", "C": "((((2 &@ -6) ><~ -7) >< 9) ~ 5)", "A_val": -80, "B_val": 0, "C_val": -4, "answer": -76}}
{"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 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 @ 9) @ 10) # 6) #:* 8)\nLet B = ((((2 :* -7) @:* 2) ## 1) &:* 7)\nLet C = ((((-7 :* 7) &:* -9) &:* -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": "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": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "((((-5 @ 9) @ 10) # 6) #:* 8)", "B": "((((2 :* -7) @:* 2) ## 1) &:* 7)", "C": "((((-7 :* 7) &:* -9) &:* -5) &:* -2)", "A_val": 8, "B_val": 1, "C_val": -11, "answer": 20}}
{"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\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 = (((((((-9 & -9) #@ -4) ~ -8) @# 3) ; 9) @ -1) ;; -7)\nLet B = (((((((-9 && 3) # -2) &~ -4) @ -9) ~@ -6) ;@ -7) ~ 10)\nLet C = (((((((-6 ## 2) & -9) #@ 9) ~; 8) ## 8) #; 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": "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 > 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": "(((((((-9 & -9) #@ -4) ~ -8) @# 3) ; 9) @ -1) ;; -7)", "B": "(((((((-9 && 3) # -2) &~ -4) @ -9) ~@ -6) ;@ -7) ~ 10)", "C": "(((((((-6 ## 2) & -9) #@ 9) ~; 8) ## 8) #; 8) @& -1)", "A_val": 0, "B_val": 17, "C_val": -2, "answer": 19}}
{"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 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 > 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 = ((((((-7 !@ -7) ~ -4) ][:* 4) ][ 8) ][ 10) ][~ -4)\nLet B = ((((((-10 @! -1) ~:* 3) ][! 4) :*:* 3) !:* -7) :* -8)\nLet C = ((((((-8 :*~ 8) !@ 7) ! 6) ~ 4) ~ 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", "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": "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": "((((((-7 !@ -7) ~ -4) ][:* 4) ][ 8) ][ 10) ][~ -4)", "B": "((((((-10 @! -1) ~:* 3) ][! 4) :*:* 3) !:* -7) :* -8)", "C": "((((((-8 :*~ 8) !@ 7) ! 6) ~ 4) ~ 9) ~ -3)", "A_val": -6, "B_val": -1, "C_val": -4, "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 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 <> 4) :* -6) :*:* 1)\nLet B = (((-1 <>:* 8) ; -8) <> 6)\nLet C = (((-6 <> 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": "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 <> 4) :* -6) :*:* 1)", "B": "(((-1 <>:* 8) ; -8) <> 6)", "C": "(((-6 <> 6) <> -5) :* 9)", "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 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 ! 2) !; 4) ; -5) ;[] -10) [] -5)\nLet B = (((((-5 ;! 3) ; -2) !; 10) [] -5) [] 9)\nLet C = (((((-2 &; 6) [][] -10) && 4) ! 6) []! -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": "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 ! 2) !; 4) ; -5) ;[] -10) [] -5)", "B": "(((((-5 ;! 3) ; -2) !; 10) [] -5) [] 9)", "C": "(((((-2 &; 6) [][] -10) && 4) ! 6) []! -6)", "A_val": 5, "B_val": 0, "C_val": -36, "answer": 41}}
{"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 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 = ((((((5 ~>< 3) >< 8) ][ 7) <>~ 10) ][ -3) ][ -4)\nLet B = ((((((-6 []][ -2) ~][ -3) ][ 1) ][~ -2) ~ -5) >< -1)\nLet C = ((((((8 <>~ -10) <> 1) ~ -10) ][ -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": "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": "((((((5 ~>< 3) >< 8) ][ 7) <>~ 10) ][ -3) ][ -4)", "B": "((((((-6 []][ -2) ~][ -3) ][ 1) ][~ -2) ~ -5) >< -1)", "C": "((((((8 <>~ -10) <> 1) ~ -10) ][ -2) ][ 5) ][ -3)", "A_val": 0, "B_val": 2, "C_val": 0, "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 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 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 ~ -6) !; -3) <>! 7) ~[] -8) <><> 1) ~ -5) ; -4)\nLet B = (((((((1 ; -1) ~<> 10) <> 9) ;; 5) <> -6) ~~ 3) <>~ -3)\nLet C = (((((((4 <> 2) ~ 10) <> -6) !<> 8) [] -7) <> -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": "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": "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": "(((((((5 ~ -6) !; -3) <>! 7) ~[] -8) <><> 1) ~ -5) ; -4)", "B": "(((((((1 ; -1) ~<> 10) <> 9) ;; 5) <> -6) ~~ 3) <>~ -3)", "C": "(((((((4 <> 2) ~ 10) <> -6) !<> 8) [] -7) <> -9) ! 4)", "A_val": 12, "B_val": 3, "C_val": 36, "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 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 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) &][ 7) :*[] 6) ; -8) :* 6) ][ 3)\nLet B = ((((((-8 &; -3) [][] -4) [] 7) ;:* 9) ][ 3) &[] 5)\nLet C = ((((((-5 :* 7) ][ -5) & 7) ][[] -8) :* -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": "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": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "((((((-2 ][ 9) &][ 7) :*[] 6) ; -8) :* 6) ][ 3)", "B": "((((((-8 &; -3) [][] -4) [] 7) ;:* 9) ][ 3) &[] 5)", "C": "((((((-5 :* 7) ][ -5) & 7) ][[] -8) :* -3) []][ -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 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\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 = ((((((5 @~ -5) ~ -7) [] 4) :* 7) ~[] -7) ~~ 3)\nLet B = ((((((2 ~ 4) @@ 2) :*~ -1) [] -10) @@ 2) ~ -8)\nLet C = ((((((-4 [] -5) []~ -7) ;@ 10) ; -5) ; -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": "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"}], "A": "((((((5 @~ -5) ~ -7) [] 4) :* 7) ~[] -7) ~~ 3)", "B": "((((((2 ~ 4) @@ 2) :*~ -1) [] -10) @@ 2) ~ -8)", "C": "((((((-4 [] -5) []~ -7) ;@ 10) ; -5) ; -9) ~ -9)", "A_val": -482, "B_val": 10, "C_val": 9, "answer": -481}}
{"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 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) :* -4) [][] 3) :* -9)\nLet B = ((((5 && 6) &~ 8) ~ 10) [] 3)\nLet C = ((((8 :* -6) :* 6) :* -9) ~[] -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": "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": "a > b", "true_expr": "a * b", "false_expr": "a + b"}], "A": "((((-4 && -4) :* -4) [][] 3) :* -9)", "B": "((((5 && 6) &~ 8) ~ 10) [] 3)", "C": "((((8 :* -6) :* 6) :* -9) ~[] -1)", "A_val": -27, "B_val": 3, "C_val": -51, "answer": 27}}
{"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 > 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)\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 & -5) ][][ 10) # -2) ][& 4) ][# -9) ][<> -10) # -9) & 10)\nLet B = ((((((((-5 ][ -2) ~ -9) #][ 7) ~ -3) ][][ -9) & 6) #~ 6) ][& 4)\nLet C = ((((((((-4 ][ -3) # -4) <> -9) & -3) & -8) & -3) ~ -5) &~ -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": "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)"}], "A": "((((((((5 & -5) ][][ 10) # -2) ][& 4) ][# -9) ][<> -10) # -9) & 10)", "B": "((((((((-5 ][ -2) ~ -9) #][ 7) ~ -3) ][][ -9) & 6) #~ 6) ][& 4)", "C": "((((((((-4 ][ -3) # -4) <> -9) & -3) & -8) & -3) ~ -5) &~ -4)", "A_val": 19, "B_val": 4, "C_val": 0, "answer": 23}}
{"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 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 = ((((((((6 ><][ -4) ][>< -1) &~ -10) ][:* -9) ~][ 3) & -2) ][ 2) ><:* 10)\nLet B = ((((((((9 >< 9) >< 9) ][:* 10) :* -10) ~ -9) ][][ 3) :*>< 2) ><~ 1)\nLet C = ((((((((-1 ~>< 2) &>< 6) &~ 2) :* -5) ][ -4) &>< -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": "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"}], "A": "((((((((6 ><][ -4) ][>< -1) &~ -10) ][:* -9) ~][ 3) & -2) ][ 2) ><:* 10)", "B": "((((((((9 >< 9) >< 9) ][:* 10) :* -10) ~ -9) ][][ 3) :*>< 2) ><~ 1)", "C": "((((((((-1 ~>< 2) &>< 6) &~ 2) :* -5) ][ -4) &>< -6) >< 4) & 9)", "A_val": -10, "B_val": 1, "C_val": 9, "answer": -18}}
{"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\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 ;! -10) ; -2) ;][ 6) ! 10) ;; 3) :* -9) ;& 9) :* -5)\nLet B = ((((((((-8 ][ 4) ][ 5) ! -8) !][ -9) ;& 5) &][ 4) ! -8) &; 6)\nLet C = ((((((((3 !][ 1) ; 4) ! 1) ! -2) ][ 10) ][ -9) ;:* 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": "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"}, {"symbol": ";", "condition": "math.gcd(a, b) == 1", "true_expr": "(a ][ b)", "false_expr": "math.gcd(a, b)"}], "A": "((((((((2 ;! -10) ; -2) ;][ 6) ! 10) ;; 3) :* -9) ;& 9) :* -5)", "B": "((((((((-8 ][ 4) ][ 5) ! -8) !][ -9) ;& 5) &][ 4) ! -8) &; 6)", "C": "((((((((3 !][ 1) ; 4) ! 1) ! -2) ][ 10) ][ -9) ;:* 2) ! 9)", "A_val": 0, "B_val": 0, "C_val": 9, "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 > 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 > 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 ><; -3) # -9) #>< -9) ;; 6) #! -9) !][ 6) !! 3)\nLet B = (((((((6 >< 3) ;# 5) ><! 4) ! 3) # 8) ><][ 6) >< 3)\nLet C = (((((((-4 ! -8) >< 9) ><][ -7) !# -9) ][ 2) !! 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": "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 > 0", "true_expr": "(a ; b)", "false_expr": "a + b"}, {"symbol": "][", "condition": "a * b > 0", "true_expr": "a - b", "false_expr": "a + b"}], "A": "(((((((6 ><; -3) # -9) #>< -9) ;; 6) #! -9) !][ 6) !! 3)", "B": "(((((((6 >< 3) ;# 5) ><! 4) ! 3) # 8) ><][ 6) >< 3)", "C": "(((((((-4 ! -8) >< 9) ><][ -7) !# -9) ][ 2) !! 4) >< -8)", "A_val": 0, "B_val": -8, "C_val": 12, "answer": -20}}
{"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 is_prime(a) or is_prime(b); 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, 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 ;; 10) ~ -5) @ 9) ! 4) ; 3) ;<> 7)\nLet B = ((((((-8 ;~ -8) ;! 4) ; -2) ~~ -10) ~ -6) <> -7)\nLet C = ((((((-3 !@ 2) ~ 4) ; -4) ;! 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": "is_prime(a) or is_prime(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": "is_prime(a) or is_prime(b)", "true_expr": "(a @ b)", "false_expr": "max(a, b)"}], "A": "((((((-9 ;; 10) ~ -5) @ 9) ! 4) ; 3) ;<> 7)", "B": "((((((-8 ;~ -8) ;! 4) ; -2) ~~ -10) ~ -6) <> -7)", "C": "((((((-3 !@ 2) ~ 4) ; -4) ;! 6) !; -2) ~ 6)", "A_val": -7, "B_val": 33, "C_val": -6, "answer": 32}}
{"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 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 = (((((1 ~@ -9) ~ -9) :* -3) ~ 8) ~~ 5)\nLet B = (((((8 @:* 4) @~ 3) :* -4) []~ -2) ~~ 1)\nLet C = (((((4 @~ 10) :*~ -6) :*:* -2) @ 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 > 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)"}, {"symbol": "~", "condition": "math.gcd(a, b) == 1", "true_expr": "a + b", "false_expr": "math.gcd(a, b)"}], "A": "(((((1 ~@ -9) ~ -9) :* -3) ~ 8) ~~ 5)", "B": "(((((8 @:* 4) @~ 3) :* -4) []~ -2) ~~ 1)", "C": "(((((4 @~ 10) :*~ -6) :*:* -2) @ 8) :*[] -1)", "A_val": 18, "B_val": 4, "C_val": 0, "answer": 22}}
{"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 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 = ((((-7 ><# -9) >< -6) #<> 10) ~ 5)\nLet B = ((((3 # -9) <><> 4) ~# -6) ><>< 6)\nLet C = ((((-7 <> 10) # -4) <> -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", "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)"}, {"symbol": "#", "condition": "a > b", "true_expr": "(a ~ b)", "false_expr": "(a ~ b)"}], "A": "((((-7 ><# -9) >< -6) #<> 10) ~ 5)", "B": "((((3 # -9) <><> 4) ~# -6) ><>< 6)", "C": "((((-7 <> 10) # -4) <> -3) ><~ 2)", "A_val": -5, "B_val": 12, "C_val": 4, "answer": 3}}
{"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, 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 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 @ 8) !@ 1) @>< -8) @ -2) # 10) @ 6) #! -6) :* 1)\nLet B = ((((((((2 @ 4) @ -10) #>< 5) ! -2) :*@ -3) ! 3) @@ -3) >< -2)\nLet C = ((((((((7 >< 5) :* -1) @ -6) !! -9) !! 5) !>< 10) ><@ -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": "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", "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": "(a >< b)", "false_expr": "max(a, b)"}], "A": "((((((((6 @ 8) !@ 1) @>< -8) @ -2) # 10) @ 6) #! -6) :* 1)", "B": "((((((((2 @ 4) @ -10) #>< 5) ! -2) :*@ -3) ! 3) @@ -3) >< -2)", "C": "((((((((7 >< 5) :* -1) @ -6) !! -9) !! 5) !>< 10) ><@ -8) @ -4)", "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 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\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) ;@ -6) :* 3) @ 3) # 9) ;>< -7) @; 5) @ 4)\nLet B = ((((((((6 # 1) @>< 6) # -6) >< -10) ; 9) >< -2) @ -5) #:* 8)\nLet C = ((((((((7 @ -8) ><; 10) # -4) :* -4) ;:* 1) >< -7) @; 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": "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": "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"}], "A": "((((((((5 ;:* 6) ;@ -6) :* 3) @ 3) # 9) ;>< -7) @; 5) @ 4)", "B": "((((((((6 # 1) @>< 6) # -6) >< -10) ; 9) >< -2) @ -5) #:* 8)", "C": "((((((((7 @ -8) ><; 10) # -4) :* -4) ;:* 1) >< -7) @; 7) :* -7)", "A_val": 2, "B_val": 4, "C_val": 6, "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 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 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 & 9) ;; -4) ~ -3) ~][ 9) >< 9) ><][ 1) &>< 4)\nLet B = (((((((10 ; -2) ><][ -7) >< -3) && -5) & 2) ; 2) ][ 2)\nLet C = (((((((-4 ~ 8) & -8) ><; -6) >< 5) ~~ 2) & 6) & -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": "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": "abs(a - b) < 2", "true_expr": "a * b", "false_expr": "a - b"}], "A": "(((((((4 & 9) ;; -4) ~ -3) ~][ 9) >< 9) ><][ 1) &>< 4)", "B": "(((((((10 ; -2) ><][ -7) >< -3) && -5) & 2) ; 2) ][ 2)", "C": "(((((((-4 ~ 8) & -8) ><; -6) >< 5) ~~ 2) & 6) & -4)", "A_val": 4, "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 > 0; otherwise, 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 > 0; 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 = ((((((-3 !# 1) #; 10) :* 5) #:* -7) ;[] 8) !# 7)\nLet B = ((((((-1 ! -2) ## -8) ; -2) :* -8) ;[] -1) :* -1)\nLet C = ((((((1 # -9) !# 3) #; 4) #:* -4) ;# 8) []; -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": "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"}], "A": "((((((-3 !# 1) #; 10) :* 5) #:* -7) ;[] 8) !# 7)", "B": "((((((-1 ! -2) ## -8) ; -2) :* -8) ;[] -1) :* -1)", "C": "((((((1 # -9) !# 3) #; 4) #:* -4) ;# 8) []; -9)", "A_val": -8, "B_val": -1, "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 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 = (((10 <><> -1) # -7) #; -7)\nLet B = (((-10 #<> -1) <><> -7) ; -3)\nLet C = (((9 #; -2) ; 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": "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": "(((10 <><> -1) # -7) #; -7)", "B": "(((-10 #<> -1) <><> -7) ; -3)", "C": "(((9 #; -2) ; 6) #<> 5)", "A_val": -32, "B_val": -29, "C_val": 2, "answer": -63}}
{"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, (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 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 ><][ -6) :*<> -9) ; -1) ;; 5) ;<> 4) >< -8)\nLet B = ((((((10 ; -2) :*<> -3) ><][ -9) ][ -7) >< -3) ][ -10)\nLet C = ((((((4 :*>< 8) :*][ 10) <> 4) ><<> -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": "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": "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": "abs(a - b) < 2", "true_expr": "(a >< b)", "false_expr": "a - b"}], "A": "((((((-2 ><][ -6) :*<> -9) ; -1) ;; 5) ;<> 4) >< -8)", "B": "((((((10 ; -2) :*<> -3) ><][ -9) ][ -7) >< -3) ][ -10)", "C": "((((((4 :*>< 8) :*][ 10) <> 4) ><<> -1) ><:* 2) <> -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 (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 # 3) >< 10) ][ -8) # 3)\nLet B = ((((-6 #>< -1) ][][ 8) ><>< -4) ][# 4)\nLet C = ((((-10 ][ -1) ][ 6) ][][ 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": "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": "math.gcd(a, b) == 1", "true_expr": "(a # b)", "false_expr": "math.gcd(a, b)"}], "A": "((((-7 # 3) >< 10) ][ -8) # 3)", "B": "((((-6 #>< -1) ][][ 8) ><>< -4) ][# 4)", "C": "((((-10 ][ -1) ][ 6) ][][ 6) ~ 5)", "A_val": 12, "B_val": 16, "C_val": 0, "answer": 28}}
{"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 a > 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\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) ][ 5) [] 9) [] -9) [] 9) ; 7) ; 9) ;][ 9)\nLet B = ((((((((6 [] 7) []:* -1) [][] 2) ][ -8) @ 5) [] -3) []@ -1) @ 9)\nLet C = ((((((((-1 @ -5) []][ 6) []][ -8) @ 6) ][; -8) :*; 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": "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": "a > b", "true_expr": "a * b", "false_expr": "a - b"}, {"symbol": "@", "condition": "a * b > 0", "true_expr": "(a ; b)", "false_expr": "a + b"}], "A": "((((((((5 ][; -1) ][ 5) [] 9) [] -9) [] 9) ; 7) ; 9) ;][ 9)", "B": "((((((((6 [] 7) []:* -1) [][] 2) ][ -8) @ 5) [] -3) []@ -1) @ 9)", "C": "((((((((-1 @ -5) []][ 6) []][ -8) @ 6) ][; -8) :*; 4) ;@ -1) ;@ -5)", "A_val": 0, "B_val": 8, "C_val": 0, "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 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, (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) ;<> -6) ][][ -6) ;<> -6) ; -1)\nLet B = (((((-9 ][ -5) ][; 7) ~ 8) ][][ -3) ~ -10)\nLet C = (((((-6 <> -5) ~ -10) ;; -9) ][<> 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": "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": "(a ; b)"}], "A": "(((((-9 ; 2) ;<> -6) ][][ -6) ;<> -6) ; -1)", "B": "(((((-9 ][ -5) ][; 7) ~ 8) ][][ -3) ~ -10)", "C": "(((((-6 <> -5) ~ -10) ;; -9) ][<> 2) <>; -7)", "A_val": -1, "B_val": -10, "C_val": -7, "answer": -4}}
{"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)\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) <># 8) #:* -9) <> -4)\nLet B = ((((-9 @ 3) :* -8) :*@ 2) :*:* -7)\nLet C = ((((-9 # 10) @ 7) # 3) @ -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": "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 @ -7) <># 8) #:* -9) <> -4)", "B": "((((-9 @ 3) :* -8) :*@ 2) :*:* -7)", "C": "((((-9 # 10) @ 7) # 3) @ -7)", "A_val": 59, "B_val": 7, "C_val": -21, "answer": 87}}
{"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 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 = ((((((((-1 <>>< -5) ><~ 2) ][ 2) <> 10) ~<> 10) @@ -6) ~ -8) ><~ 3)\nLet B = ((((((((-8 @<> -9) <>~ -7) @ -9) ><<> 4) ~ -6) ><][ 1) ][>< 5) ><~ 10)\nLet C = ((((((((7 <> -2) @ -2) ><@ 8) @<> 1) ~<> -3) <>][ 6) >< -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": "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": "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": "((((((((-1 <>>< -5) ><~ 2) ][ 2) <> 10) ~<> 10) @@ -6) ~ -8) ><~ 3)", "B": "((((((((-8 @<> -9) <>~ -7) @ -9) ><<> 4) ~ -6) ><][ 1) ][>< 5) ><~ 10)", "C": "((((((((7 <> -2) @ -2) ><@ 8) @<> 1) ~<> -3) <>][ 6) >< -10) <>>< 7)", "A_val": -3, "B_val": -10, "C_val": 0, "answer": -13}}
{"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 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\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 &][ -5) & -9) ][& -3) && -3) & 3) ][ -7) []][ 9) ][ 7)\nLet B = ((((((((6 ~~ -10) ][~ -2) ][~ -4) <>& -3) <> 4) [] 6) ~ -9) []][ 5)\nLet C = ((((((((-8 [] -4) & 2) &][ -1) ][ 6) & 6) []~ 9) <> -6) <><> -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": "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"}, {"symbol": "&", "condition": "a > b", "true_expr": "a * b", "false_expr": "a - b"}], "A": "((((((((-9 &][ -5) & -9) ][& -3) && -3) & 3) ][ -7) []][ 9) ][ 7)", "B": "((((((((6 ~~ -10) ][~ -2) ][~ -4) <>& -3) <> 4) [] 6) ~ -9) []][ 5)", "C": "((((((((-8 [] -4) & 2) &][ -1) ][ 6) & 6) []~ 9) <> -6) <><> -6)", "A_val": 16, "B_val": 5, "C_val": -6, "answer": 27}}
{"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 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)\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 ; 4) ;][ -7) @@ 8) @ -5) ][; 8) ><; 7) >< -2) >< -8)\nLet B = ((((((((7 ; 4) ][ -3) ;][ 9) ][][ 10) ;>< 1) ][ -2) :* -3) ][; -4)\nLet C = ((((((((2 @@ 6) @][ 6) ; -5) ; -5) ; 9) ; 3) @ 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": "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": "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)"}], "A": "((((((((7 ; 4) ;][ -7) @@ 8) @ -5) ][; 8) ><; 7) >< -2) >< -8)", "B": "((((((((7 ; 4) ][ -3) ;][ 9) ][][ 10) ;>< 1) ][ -2) :* -3) ][; -4)", "C": "((((((((2 @@ 6) @][ 6) ; -5) ; -5) ; 9) ; 3) @ 10) ><; 9)", "A_val": 0, "B_val": 4, "C_val": 9, "answer": -5}}
{"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, 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\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) ! -8) !<> -10) <><> -1) @ 10)\nLet B = (((((4 <> -1) ! 4) &! -4) & 3) @@ -10)\nLet C = (((((8 <>& -3) <> -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": "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", "true_expr": "a * b", "false_expr": "a + b"}, {"symbol": "&", "condition": "a > b", "true_expr": "(a ! b)", "false_expr": "a - b"}], "A": "(((((-10 <> -5) ! -8) !<> -10) <><> -1) @ 10)", "B": "(((((4 <> -1) ! 4) &! -4) & 3) @@ -10)", "C": "(((((8 <>& -3) <> -4) !<> -4) & -1) & -4)", "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 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 ][ -1) ][][ -10) ][ -1)\nLet B = (((-4 [][] 4) ][ -8) ! -5)\nLet C = (((-10 [] -7) !! 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": "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 ][ -1) ][][ -10) ][ -1)", "B": "(((-4 [][] 4) ][ -8) ! -5)", "C": "(((-10 [] -7) !! 8) ][][ -1)", "A_val": 0, "B_val": 5, "C_val": 0, "answer": 5}}
{"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 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 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) :* -10) ;; 6) @:* -10) :*@ -8) # 7) :*; 4)\nLet B = (((((((-5 ; 8) # 8) # -5) ;; -3) #@ -2) :*:* -4) ~ 2)\nLet C = (((((((-1 # 3) ;# 2) ;@ 4) #; -1) ~:* 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": "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": "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)"}], "A": "(((((((3 :* 5) :* -10) ;; 6) @:* -10) :*@ -8) # 7) :*; 4)", "B": "(((((((-5 ; 8) # 8) # -5) ;; -3) #@ -2) :*:* -4) ~ 2)", "C": "(((((((-1 # 3) ;# 2) ;@ 4) #; -1) ~:* 9) ;~ 10) :*~ -6)", "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 > 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 = ((((1 ][ 10) &][ 1) &][ -1) []][ -4)\nLet B = ((((5 ][ 9) # 6) #[] 4) []][ 3)\nLet C = ((((-6 []& -8) ][[] -4) []][ -4) ][ 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": "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": "((((1 ][ 10) &][ 1) &][ -1) []][ -4)", "B": "((((5 ][ 9) # 6) #[] 4) []][ 3)", "C": "((((-6 []& -8) ][[] -4) []][ -4) ][ 5)", "A_val": 4, "B_val": 3, "C_val": 9, "answer": -2}}
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