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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: $a @ b$ equals $(a * a) - b$ if b<2b < 2 and $(b * b) - a$ otherwise. 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><b)(a >< b) if $a @ b > 0$; otherwise, it equals −a><−b-a >< -b. a<>ba <> b equals $(a @ b)$ if $a * b > 0$; otherwise, it equals a!ba ! b. $a ~ b$ equals (a−b)(a - b) if $a @ b > 0$; otherwise, it equals a+ba + b. a][ba ][ b equals (2!b)><a(2 ! b) >< a if a>ba > b and bb otherwise. Let A = ((((((((((((-7 ][ -3) ~ -3) + -4) ][ nine) - nine) <> -2) * -2) >< -4) <> -7) @ -10) @ -10) * -8) Let B = ((((-9 ][ -9) ][ (-10 + 2)) @ ((-9 >< 9) * (1 >< -3))) * (((8 ~ 8) >< (-5 ][ two)) + ((nine @ -8) ][ (-1 * eight)))) Let C = ((((nine @ -2) >< (-10 + -10)) - ((-5 - ten) + (nine ~ -5))) ][ (((4 * 4) >< (three ][ -5)) ~ ((-2 + -7) >< (3 ! -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 a+b if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
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 (2!b)><a if a>b and b otherwise.

Let A = ((((((((((((-7 ][ -3) ~ -3) + -4) ][ nine) - nine) <> -2) * -2) >< -4) <> -7) @ -10) @ -10) * -8)
Let B = ((((-9 ][ -9) ][ (-10 + 2)) @ ((-9 >< 9) * (1 >< -3))) * (((8 ~ 8) >< (-5 ][ two)) + ((nine @ -8) ][ (-1 * eight))))
Let C = ((((nine @ -2) >< (-10 + -10)) - ((-5 - ten) + (nine ~ -5))) ][ (((4 * 4) >< (three ][ -5)) ~ ((-2 + -7) >< (3 ! -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 $a + b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a ! b$ 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 $(2 ! b) >< a$ if $a > b$ and $b$ otherwise.

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

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Source and history

task_id
d54ee069-a9ef-544b-9ae4-c2027c53d47f
task_key
bbeh~5fmultistep~5farithmetic--full--d54ee069-a9ef-544b-9ae4-c2027c53d47f
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import