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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: $a # b$ equals (a+b)(a + b) if a−b>0a - b > 0; otherwise, it equals −a+−b-a + -b. a[]ba [] b equals $a * b$ 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 (2[]b)+a(2 [] b) + a if a>ba > b and bb otherwise. $a ~ b$ equals (a−b)(a - b) if a−b>0a - b > 0; otherwise, it equals a+ba + b. a!ba ! b equals $(b * a) ; b$ if |a−b|<2|a-b| < 2 and $(a * b) ; a$ otherwise. Let A = (((((((((((((((((((((7 + -1) * 5) # 9) + 9) # five) # 5) ~ 7) ! nine) # three) + -8) ; -8) ; nine) [] 8) ; 7) + -4) ! two) + 8) ~ -10) ! 4) ; -8) ~ -2) Let B = (((((((((((((-9 # -9) ! -5) * 4) ; -6) ! nine) ! -3) ! -10) ~ 8) ; 8) - one) ; six) - -2) ; -6) Let C = ((((7 * -3) # (one - ten)) ~ ((two # three) - (-5 # -3))) * (((five + -8) - (-6 * 3)) ! ((four ! 10) - (-4 * -3)))). 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 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 (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 $(b * a) ; b$ if |a−b|<2 and $(a * b) ; a$ otherwise.

Let A = (((((((((((((((((((((7 + -1) * 5) # 9) + 9) # five) # 5) ~ 7) ! nine) # three) + -8) ; -8) ; nine) [] 8) ; 7) + -4) ! two) + 8) ~ -10) ! 4) ; -8) ~ -2)
Let B = (((((((((((((-9 # -9) ! -5) * 4) ; -6) ! nine) ! -3) ! -10) ~ 8) ; 8) - one) ; six) - -2) ; -6)
Let C = ((((7 * -3) # (one - ten)) ~ ((two # three) - (-5 # -3))) * (((five + -8) - (-6 * 3)) ! ((four ! 10) - (-4 * -3)))).
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 $a - b > 0$; 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 $(2 [] b) + a$ if $a > b$ and $b$ otherwise.
$a ~ b$ equals $(a - b)$ if $a - b > 0$; otherwise,  it equals $a + b$.
$a ! b$ equals $(b * a) ; b$ if $|a-b| < 2$ and $(a * b) ; a$ otherwise.

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

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Source and history

task_id
12a6197c-ef29-5ff0-a196-78e7acfc25bc
task_key
bbeh~5fmultistep~5farithmetic--full--12a6197c-ef29-5ff0-a196-78e7acfc25bc
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import