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

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

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

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Source and history

task_id
02ac5e65-3a00-5fb8-b359-37fa92287665
task_key
bbeh~5fmultistep~5farithmetic--full--02ac5e65-3a00-5fb8-b359-37fa92287665
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import