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BIG-Bench Extra Hard (BBEH) / Consider the following new operations:

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Consider the following new operations: $a & b$ equals (a−b)(a - b) if $a * b > 0$; otherwise, it equals −a−−b-a - -b. $a @ b$ 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 $(a * a) @ b$ if b<2b < 2 and $(b * b) @ a$ otherwise. a;ba ; b equals (a><b)(a >< b) if a−b>0a - b > 0; otherwise, it equals $a @ b$. Let A = ((((-6 * -3) >< (four * -1)) + ((-8 * -9) ; (-4 & 10))) & (((-7 + -1) & (-4 * -6)) @ ((-2 + five) ; (3 ; -5)))) Let B = ((((((((((((((((((7 - 6) & 7) + -5) + -5) >< three) @ eight) + 8) >< 7) ; -5) @ -3) - -10) * -5) - 4) + -6) @ nine) ; -10) + 4) @ one) Let C = ((((-5 * -7) * (10 @ 2)) + ((2 >< -5) & (-9 >< two))) @ (((4 & -4) & (4 * one)) >< ((-10 - -5) - (-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 $(a * a) @ b$ if b<2 and $(b * b) @ a$ otherwise.
a;b equals (a><b) if a−b>0; otherwise,  it equals $a @ b$.

Let A = ((((-6 * -3) >< (four * -1)) + ((-8 * -9) ; (-4 & 10))) & (((-7 + -1) & (-4 * -6)) @ ((-2 + five) ; (3 ; -5))))
Let B = ((((((((((((((((((7 - 6) & 7) + -5) + -5) >< three) @ eight) + 8) >< 7) ; -5) @ -3) - -10) * -5) - 4) + -6) @ nine) ; -10) + 4) @ one)
Let C = ((((-5 * -7) * (10 @ 2)) + ((2 >< -5) & (-9 >< two))) @ (((4 & -4) & (4 * one)) >< ((-10 - -5) - (-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 $(a * a) @ b$ if $b < 2$ and $(b * b) @ a$ otherwise.
$a ; b$ equals $(a >< b)$ if $a - b > 0$; otherwise,  it equals $a @ b$.

Let A = ((((-6 * -3) >< (four * -1)) + ((-8 * -9) ; (-4 & 10))) & (((-7 + -1) & (-4 * -6)) @ ((-2 + five) ; (3 ; -5))))
Let B = ((((((((((((((((((7 - 6) & 7) + -5) + -5) >< three) @ eight) + 8) >< 7) ; -5) @ -3) - -10) * -5) - 4) + -6) @ nine) ; -10) + 4) @ one)
Let C = ((((-5 * -7) * (10 @ 2)) + ((2 >< -5) & (-9 >< two))) @ (((4 & -4) & (4 * one)) >< ((-10 - -5) - (-4 - 3)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
18d31422-2d4f-5cad-90bd-b1461ed3e449
task_key
bbeh~5fmultistep~5farithmetic--full--18d31422-2d4f-5cad-90bd-b1461ed3e449
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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