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

Let A = ((((10 ; -4) : (three ][ four)) - ((three : -1) * (-6 ; -6))) @ (((eight >< seven) ! (2 ][ -4)) ! ((-5 * 10) >< (-5 ][ 2))))
Let B = (((((((((((((((one >< -3) ][ -6) + 1) @ -8) @ 5) ][ 4) @ -8) - 9) >< four) ][ -3) + -8) : 8) ][ 3) * -9) >< -4)
Let C = ((((five * four) >< (-4 - -10)) ! ((-9 @ 2) ! (-9 - -5))) : (((10 - -2) : (two >< 9)) + ((-8 ][ -5) ! (-2 ; five)))).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a ; b$ equals $(b - a) * b$ if $|a-b| < 2$ and $(a - b) * a$ otherwise.
$a : b$ 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 $(a - b)$ 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.

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

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Source and history

task_id
1ae731c2-abce-5a8a-a6fa-bf4c6be95b94
task_key
bbeh~5fmultistep~5farithmetic--full--1ae731c2-abce-5a8a-a6fa-bf4c6be95b94
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import