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

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input

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

Let A = ((((-3 # -6) >< (-3 @ -9)) * ((-6 - -9) - (8 >< -4))) * (((-7 - 3) + (10 + 9)) [] ((nine @ -8) * (three - -9))))
Let B = ((((9 @ -9) + (two >< -2)) + ((-7 + ten) - (-10 >< nine))) [] (((three >< -10) # (6 [] 8)) ~ ((6 >< two) - (-5 - -10))))
Let C = (((((((((((3 # -7) @ -5) [] 7) # -6) >< -6) * -2) @ -1) - -4) @ 3) - four) [] -8).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a >< b$ equals $(a - a) * b$ if $b < 2$ and $(b - b) * a$ otherwise.
$a @ b$ equals $(2 - b) + a$ if $a > b$ and $b$ 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 $(b @ a) # b$ if $|a-b| < 2$ and $(a @ b) # a$ otherwise.
$a ~ b$ equals $(a * b)$ if $a >< b > 0$; otherwise,  it equals $a @ b$.

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

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Source and history

task_id
43babfd1-e0ea-537d-8069-6035929083f5
task_key
bbeh~5fmultistep~5farithmetic--full--43babfd1-e0ea-537d-8069-6035929083f5
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import