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

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

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

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Source and history

task_id
3cc49ae4-5e71-5f1a-b9c4-be249f2591ac
task_key
bbeh~5fmultistep~5farithmetic--full--3cc49ae4-5e71-5f1a-b9c4-be249f2591ac
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import