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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 (b+a)−b(b + a) - b if |a−b|<2|a-b| < 2 and (a+b)−a(a + b) - a otherwise. a[]ba [] b equals $(a # a) + b$ if b<2b < 2 and $(b # b) + a$ otherwise. a!ba ! b equals min(a,b)min(a, b) if either aa or bb is prime and max(a,b)max(a, b) otherwise. a;ba ; b equals (a!b)(a ! b) if $a * b > 0$; otherwise, it equals $a # b$. $a @ b$ 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. Let A = ((((-4 + -2) + (-3 - -7)) [] ((-9 >< 5) ! (-10 ; two))) [] (((-5 - -4) ! (10 - 8)) [] ((five @ nine) [] (10 # -4)))) Let B = ((((-2 - -8) * (-9 + -6)) ! ((-4 - -2) ; (eight >< six))) @ (((7 # -1) ; (-8 ! 5)) ; ((two >< -7) >< (-2 [] -7)))) Let C = (((((((((((((((((((((-7 ; six) # 6) * -4) ! 7) + -10) * -5) * -9) + 3) ! 3) ! -4) ! -8) # -7) + -9) ; 8) ; -8) @ -2) ; -9) * 10) * 2) >< seven) - three). 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 (b+a)−b if |a−b|<2 and (a+b)−a otherwise.
a[]b equals $(a # a) + b$ if b<2 and $(b # b) + a$ otherwise.
a!b equals min(a,b) if either a or b is prime and max(a,b) 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 = ((((-4 + -2) + (-3 - -7)) [] ((-9 >< 5) ! (-10 ; two))) [] (((-5 - -4) ! (10 - 8)) [] ((five @ nine) [] (10 # -4))))
Let B = ((((-2 - -8) * (-9 + -6)) ! ((-4 - -2) ; (eight >< six))) @ (((7 # -1) ; (-8 ! 5)) ; ((two >< -7) >< (-2 [] -7))))
Let C = (((((((((((((((((((((-7 ; six) # 6) * -4) ! 7) + -10) * -5) * -9) + 3) ! 3) ! -4) ! -8) # -7) + -9) ; 8) ; -8) @ -2) ; -9) * 10) * 2) >< seven) - three).
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 $(b + a) - b$ if $|a-b| < 2$ and $(a + b) - a$ otherwise.
$a [] b$ equals $(a # a) + b$ if $b < 2$ and $(b # b) + a$ otherwise.
$a ! b$ equals $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ 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 = ((((-4 + -2) + (-3 - -7)) [] ((-9 >< 5) ! (-10 ; two))) [] (((-5 - -4) ! (10 - 8)) [] ((five @ nine) [] (10 # -4))))
Let B = ((((-2 - -8) * (-9 + -6)) ! ((-4 - -2) ; (eight >< six))) @ (((7 # -1) ; (-8 ! 5)) ; ((two >< -7) >< (-2 [] -7))))
Let C = (((((((((((((((((((((-7 ; six) # 6) * -4) ! 7) + -10) * -5) * -9) + 3) ! 3) ! -4) ! -8) # -7) + -9) ; 8) ; -8) @ -2) ; -9) * 10) * 2) >< seven) - three).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
a898a34d-c538-5e54-990a-6f0955ec3f66
task_key
bbeh~5fmultistep~5farithmetic--full--a898a34d-c538-5e54-990a-6f0955ec3f66
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import