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

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

$a ][ b$ 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 $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ otherwise.
$a >< b$ equals $a - b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a ~ b$ equals $(a + a) - b$ if $b < 2$ and $(b + b) - a$ otherwise.
$a ; b$ equals $(b * a) ~ b$ if $|a-b| < 2$ and $(a * b) ~ a$ otherwise.

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

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Source and history

task_id
7dfa8b5d-9189-5e4b-b386-d6c347b87b30
task_key
bbeh~5fmultistep~5farithmetic--full--7dfa8b5d-9189-5e4b-b386-d6c347b87b30
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import