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

Problem

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input

Consider the following new operations: a<>ba <> b equals (b−a)+b(b - a) + b if |a−b|<2|a-b| < 2 and (a−b)+a(a - b) + a otherwise. a:ba : b equals $(a * b)$ if a+b>0a + b > 0; otherwise, it equals a−ba - b. a[]ba [] b equals (a−b)(a - b) if a−b>0a - b > 0; otherwise, it equals a+ba + b. $a # b$ 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. $a & b$ equals (a[]b)(a [] b) if a<>b>0a <> b > 0; otherwise, it equals −a[]−b-a [] -b. Let A = (((((((((((((((((-5 <> -8) <> -7) # seven) # five) * -1) - -3) [] -1) <> four) : -9) [] -5) # three) * -5) + -7) <> four) : 8) * 4) + -5) Let B = ((((-1 : -8) + (-4 [] -5)) [] ((-2 : -7) & (4 : three))) * (((1 <> 9) * (-10 [] -10)) : ((-1 * -9) & (ten # -6)))) Let C = ((((-1 * -7) # (9 * nine)) + ((-6 + -2) [] (9 # -9))) : (((-2 [] ten) + (2 # -6)) * ((ten : 4) <> (5 * -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 (b−a)+b if |a−b|<2 and (a−b)+a otherwise.
a:b equals $(a * b)$ if a+b>0; otherwise,  it equals a−b.
a[]b equals (a−b) if a−b>0; otherwise,  it equals a+b.
$a # b$ equals a−b if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
$a & b$ equals (a[]b) if a<>b>0; otherwise,  it equals −a[]−b.

Let A = (((((((((((((((((-5 <> -8) <> -7) # seven) # five) * -1) - -3) [] -1) <> four) : -9) [] -5) # three) * -5) + -7) <> four) : 8) * 4) + -5)
Let B = ((((-1 : -8) + (-4 [] -5)) [] ((-2 : -7) & (4 : three))) * (((1 <> 9) * (-10 [] -10)) : ((-1 * -9) & (ten # -6))))
Let C = ((((-1 * -7) # (9 * nine)) + ((-6 + -2) [] (9 # -9))) : (((-2 [] ten) + (2 # -6)) * ((ten : 4) <> (5 * -1)))).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a <> b$ equals $(b - a) + b$ if $|a-b| < 2$ and $(a - b) + a$ otherwise.
$a : b$ equals $(a * b)$ if $a + b > 0$; otherwise,  it equals $a - b$.
$a [] b$ equals $(a - b)$ if $a - b > 0$; otherwise,  it equals $a + b$.
$a # b$ equals $a - b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a & b$ equals $(a [] b)$ if $a <> b > 0$; otherwise,  it equals $-a [] -b$.

Let A = (((((((((((((((((-5 <> -8) <> -7) # seven) # five) * -1) - -3) [] -1) <> four) : -9) [] -5) # three) * -5) + -7) <> four) : 8) * 4) + -5)
Let B = ((((-1 : -8) + (-4 [] -5)) [] ((-2 : -7) & (4 : three))) * (((1 <> 9) * (-10 [] -10)) : ((-1 * -9) & (ten # -6))))
Let C = ((((-1 * -7) # (9 * nine)) + ((-6 + -2) [] (9 # -9))) : (((-2 [] ten) + (2 # -6)) * ((ten : 4) <> (5 * -1)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
22165a9b-2c8f-588d-bf87-eef45349af3f
task_key
bbeh~5fmultistep~5farithmetic--full--22165a9b-2c8f-588d-bf87-eef45349af3f
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import