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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 min(a,b)min(a, b) if either aa or bb is prime and max(a,b)max(a, b) otherwise. a][ba ][ b equals $(b * a) <> b$ if |a−b|<2|a-b| < 2 and $(a * b) <> a$ otherwise. $a ~ b$ equals (a−b)(a - b) if a+b>0a + b > 0; otherwise, it equals a+ba + b. a[]ba [] 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. Let A = (((((((((((((((((10 - 4) - five) <> four) + -4) [] -6) <> 3) <> 1) [] 6) ~ ten) * -1) <> -9) <> -4) + -8) [] -4) - 5) [] -9) - -6) Let B = (((((((((((((((((((((-7 * six) <> -10) ~ ten) * 8) ~ -2) [] -8) - five) * one) + -5) <> 9) * -1) ][ five) <> -2) [] three) ][ 10) + -8) [] 5) <> -4) * four) * -1) [] five) Let C = ((((-10 <> nine) ][ (-5 ][ -8)) ][ ((10 [] 10) <> (ten [] 2))) - (((-1 ~ -6) + (10 ][ 6)) + ((one ~ -6) [] (-5 * -4)))). 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 min(a,b) if either a or b is prime and max(a,b) otherwise.
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 gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.

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

$a <> b$ equals $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ otherwise.
$a ][ b$ 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 $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.

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

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Source and history

task_id
ffdd5850-c198-5c82-ac2d-fb79b8ed5850
task_key
bbeh~5fmultistep~5farithmetic--full--ffdd5850-c198-5c82-ac2d-fb79b8ed5850
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import