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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+ba + b. a><ba >< b equals $a * b$ if gcd(a,b)==1gcd(a, b) == 1 and gcd(a,b)gcd(a, b) otherwise, where gcd stands for greatest common divisor. $a ~ b$ equals $(a * b)$ if a−b>0a - b > 0; otherwise, it equals $-a * -b$. $a @ b$ equals min(a,b)min(a, b) if either aa or bb is prime and max(a,b)max(a, b) otherwise. $a # b$ equals $(2 : b) ~ a$ if a>ba > b and bb otherwise. Let A = ((((four @ 1) ~ (six + 3)) >< ((-4 - -9) ~ (seven : -9))) ! (((-9 ~ -10) - (-10 * 10)) : ((6 - -5) - (5 @ 5)))) Let B = ((((((((((((((((((((7 ~ five) ~ -5) * three) @ -4) >< -4) + 3) : 3) + -8) - one) >< 8) + -8) # 7) # -3) : -5) ! one) - -10) >< four) * four) ! one) ! two) Let C = ((((5 ~ three) # (-8 ~ -10)) ! ((8 # -3) : (-1 : 7))) >< (((-5 ~ 10) ! (7 # five)) - ((9 * 7) >< (-5 + 5)))). 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 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 min(a,b) if either a or b is prime and max(a,b) otherwise.
$a # b$ equals $(2 : b) ~ a$ if a>b and b otherwise.

Let A = ((((four @ 1) ~ (six + 3)) >< ((-4 - -9) ~ (seven : -9))) ! (((-9 ~ -10) - (-10 * 10)) : ((6 - -5) - (5 @ 5))))
Let B = ((((((((((((((((((((7 ~ five) ~ -5) * three) @ -4) >< -4) + 3) : 3) + -8) - one) >< 8) + -8) # 7) # -3) : -5) ! one) - -10) >< four) * four) ! one) ! two)
Let C = ((((5 ~ three) # (-8 ~ -10)) ! ((8 # -3) : (-1 : 7))) >< (((-5 ~ 10) ! (7 # five)) - ((9 * 7) >< (-5 + 5)))).
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 $gcd(a, b) == 1$ 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 $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ otherwise.
$a # b$ equals $(2 : b) ~ a$ if $a > b$ and $b$ otherwise.

Let A = ((((four @ 1) ~ (six + 3)) >< ((-4 - -9) ~ (seven : -9))) ! (((-9 ~ -10) - (-10 * 10)) : ((6 - -5) - (5 @ 5))))
Let B = ((((((((((((((((((((7 ~ five) ~ -5) * three) @ -4) >< -4) + 3) : 3) + -8) - one) >< 8) + -8) # 7) # -3) : -5) ! one) - -10) >< four) * four) ! one) ! two)
Let C = ((((5 ~ three) # (-8 ~ -10)) ! ((8 # -3) : (-1 : 7))) >< (((-5 ~ 10) ! (7 # five)) - ((9 * 7) >< (-5 + 5)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
213d8392-4d81-5220-8f82-b9f7ceee84d5
task_key
bbeh~5fmultistep~5farithmetic--full--213d8392-4d81-5220-8f82-b9f7ceee84d5
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import