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BIG-Bench Extra Hard (BBEH) / Consider the following new operations:

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Consider the following new operations: a<>ba <> b equals $(2 + b) * a$ if a>ba > b and bb otherwise. a:ba : b equals (a+b)(a + b) if a<>b>0a <> b > 0; otherwise, it equals −a+−b-a + -b. $a & b$ equals (a+a):b(a + a) : b if b<2b < 2 and (b+b):a(b + b) : a otherwise. $a # b$ equals a+ba + b if gcd(a,b)==1gcd(a, b) == 1 and gcd(a,b)gcd(a, b) otherwise, where gcd stands for greatest common divisor. For brevity, we use a<op1><op2>ba <op1><op2> b to denote (aop1b)op2b(a op1 b) op2 b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$. Let A = (((((((((((((((((((((((five -:& 3) --# -2) * nine) &&: 3) #+& -10) - 2) &+* 6) *- 6) * seven) :* -9) +&- six) - two) # -2) # 4) +& 6) *# -7) <><> 3) : -3) :*# -2) +<> 5) <>-: 1) * -10) *#- 10) Let B = ((((-9 -*& -10) # (4 -#* 7)) ##<> ((five +<>- -6) &+: (-2 + ten))) & (((2 <>:+ -7) #+ (-9 - -7)) <> ((ten +<> four) :: (-6 <> 5)))) Let C = (((((((((((three :& 4) <>&# 6) <>#& -10) --- nine) -+ -10) +&& ten) *+: -8) <> 9) +# -7) * 7) + 1). Compute A + B - C. Your final answer must be in number form.
Plain-text mathematical notation (without MathML)
Consider the following new operations:

a<>b equals $(2 + b) * a$ if a>b and b otherwise.
a:b equals (a+b) if a<>b>0; otherwise,  it equals −a+−b.
$a & b$ equals (a+a):b if b<2 and (b+b):a otherwise.
$a # b$ equals a+b if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
For brevity, we use a<op1><op2>b to denote (aop1b)op2b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = (((((((((((((((((((((((five -:& 3) --# -2) * nine) &&: 3) #+& -10) - 2) &+* 6) *- 6) * seven) :* -9) +&- six) - two) # -2) # 4) +& 6) *# -7) <><> 3) : -3) :*# -2) +<> 5) <>-: 1) * -10) *#- 10)
Let B = ((((-9 -*& -10) # (4 -#* 7)) ##<> ((five +<>- -6) &+: (-2 + ten))) & (((2 <>:+ -7) #+ (-9 - -7)) <> ((ten +<> four) :: (-6 <> 5))))
Let C = (((((((((((three :& 4) <>&# 6) <>#& -10) --- nine) -+ -10) +&& ten) *+: -8) <> 9) +# -7) * 7) + 1).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a <> b$ equals $(2 + b) * a$ if $a > b$ and $b$ otherwise.
$a : b$ equals $(a + b)$ if $a <> b > 0$; otherwise,  it equals $-a + -b$.
$a & b$ equals $(a + a) : b$ if $b < 2$ and $(b + b) : a$ otherwise.
$a # b$ equals $a + b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
For 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 $(4 * -5) -- -5$.
Let A = (((((((((((((((((((((((five -:& 3) --# -2) * nine) &&: 3) #+& -10) - 2) &+* 6) *- 6) * seven) :* -9) +&- six) - two) # -2) # 4) +& 6) *# -7) <><> 3) : -3) :*# -2) +<> 5) <>-: 1) * -10) *#- 10)
Let B = ((((-9 -*& -10) # (4 -#* 7)) ##<> ((five +<>- -6) &+: (-2 + ten))) & (((2 <>:+ -7) #+ (-9 - -7)) <> ((ten +<> four) :: (-6 <> 5))))
Let C = (((((((((((three :& 4) <>&# 6) <>#& -10) --- nine) -+ -10) +&& ten) *+: -8) <> 9) +# -7) * 7) + 1).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
99ce260b-f536-5ba2-a5f2-d9d489716b2b
task_key
bbeh~5fmultistep~5farithmetic--full--99ce260b-f536-5ba2-a5f2-d9d489716b2b
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import