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

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

$a <> b$ equals $a - b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a [] b$ equals $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ 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 $a <> b > 0$; otherwise,  it equals $a + b$.

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

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Source and history

task_id
98ab74a3-8b75-5a81-a9da-230aefb44aea
task_key
bbeh~5fmultistep~5farithmetic--full--98ab74a3-8b75-5a81-a9da-230aefb44aea
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import