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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. $a ~ b$ equals $(a * b)$ if a+b>0a + b > 0; otherwise, it equals a:ba : b. 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:−b-a : -b. $a @ b$ equals $(b * a) ~ b$ if |a−b|<2|a-b| < 2 and $(a * b) ~ a$ otherwise. Let A = ((((5 ][ 4) # (5 - five)) + ((-2 # -8) @ (-6 <> -4))) <> (((-6 - 2) + (5 - -7)) : ((-2 @ two) ~ (one : -2)))) Let B = (((((((((((((((((((((8 <> -10) # -6) <> -1) ~ one) <> -1) - three) - 7) - 8) # -1) + 5) * -7) <> -6) ~ -5) @ -1) + 2) - eight) * nine) <> -1) + 4) ][ four) + -4) Let C = ((((-6 : ten) ~ (ten * -7)) <> ((eight : -4) + (five ][ five))) # (((8 @ eight) <> (-2 * -3)) # ((-6 * -2) - (two # 5)))). 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 (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 = ((((5 ][ 4) # (5 - five)) + ((-2 # -8) @ (-6 <> -4))) <> (((-6 - 2) + (5 - -7)) : ((-2 @ two) ~ (one : -2))))
Let B = (((((((((((((((((((((8 <> -10) # -6) <> -1) ~ one) <> -1) - three) - 7) - 8) # -1) + 5) * -7) <> -6) ~ -5) @ -1) + 2) - eight) * nine) <> -1) + 4) ][ four) + -4)
Let C = ((((-6 : ten) ~ (ten * -7)) <> ((eight : -4) + (five ][ five))) # (((8 @ eight) <> (-2 * -3)) # ((-6 * -2) - (two # 5)))).
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 $(2 <> b) - a$ 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 = ((((5 ][ 4) # (5 - five)) + ((-2 # -8) @ (-6 <> -4))) <> (((-6 - 2) + (5 - -7)) : ((-2 @ two) ~ (one : -2))))
Let B = (((((((((((((((((((((8 <> -10) # -6) <> -1) ~ one) <> -1) - three) - 7) - 8) # -1) + 5) * -7) <> -6) ~ -5) @ -1) + 2) - eight) * nine) <> -1) + 4) ][ four) + -4)
Let C = ((((-6 : ten) ~ (ten * -7)) <> ((eight : -4) + (five ][ five))) # (((8 @ eight) <> (-2 * -3)) # ((-6 * -2) - (two # 5)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
b93fab6f-dbf5-5788-a2cb-4cd850edd664
task_key
bbeh~5fmultistep~5farithmetic--full--b93fab6f-dbf5-5788-a2cb-4cd850edd664
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import