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

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Consider the following new operations: $a @ b$ equals $(a * b)$ if a−b>0a - b > 0; otherwise, it equals a+ba + 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: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 (2+b)−a(2 + b) - a if a>ba > b and bb otherwise. For brevity, we use a<op1><op2>ba <op1><op2> b to denote (aop1b)op2b(a op1 b) op2 b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$. Let A = ((((((((((((((((((-1 *~ -10) &: nine) --@ -1) ~ -4) - 8) :~* -2) & -3) * -3) && three) +@~ three) +~ 6) *+ four) - 7) +@+ 3) -& -8) -:: nine) ~ 2) : -4) Let B = ((((five +:: nine) :-~ (-5 :@ -4)) &-& ((-10 :~~ -1) @& (9 @@+ -2))) & (((-6 : -1) & (7 + -8)) ~&- ((seven -+@ 5) *& (-2 ::- 7)))) Let C = (((((((((((((9 *-+ 2) *:& five) -:~ 9) &&* -6) ++ -6) &~ three) @@+ one) * three) ~& -4) &+- 10) -- -10) &@* seven) :~ -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 $(a * b)$ 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 $a @ b$ if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
$a & b$ equals (2+b)−a if a>b and b otherwise.
For brevity, we use a<op1><op2>b to denote (aop1b)op2b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = ((((((((((((((((((-1 *~ -10) &: nine) --@ -1) ~ -4) - 8) :~* -2) & -3) * -3) && three) +@~ three) +~ 6) *+ four) - 7) +@+ 3) -& -8) -:: nine) ~ 2) : -4)
Let B = ((((five +:: nine) :-~ (-5 :@ -4)) &-& ((-10 :~~ -1) @& (9 @@+ -2))) & (((-6 : -1) & (7 + -8)) ~&- ((seven -+@ 5) *& (-2 ::- 7))))
Let C = (((((((((((((9 *-+ 2) *:& five) -:~ 9) &&* -6) ++ -6) &~ three) @@+ one) * three) ~& -4) &+- 10) -- -10) &@* seven) :~ -5).
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 $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ 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 $(2 + b) - a$ if $a > b$ and $b$ otherwise.
For brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = ((((((((((((((((((-1 *~ -10) &: nine) --@ -1) ~ -4) - 8) :~* -2) & -3) * -3) && three) +@~ three) +~ 6) *+ four) - 7) +@+ 3) -& -8) -:: nine) ~ 2) : -4)
Let B = ((((five +:: nine) :-~ (-5 :@ -4)) &-& ((-10 :~~ -1) @& (9 @@+ -2))) & (((-6 : -1) & (7 + -8)) ~&- ((seven -+@ 5) *& (-2 ::- 7))))
Let C = (((((((((((((9 *-+ 2) *:& five) -:~ 9) &&* -6) ++ -6) &~ three) @@+ one) * three) ~& -4) &+- 10) -- -10) &@* seven) :~ -5).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
ebf52795-877b-5e05-8f9c-549d027aedf0
task_key
bbeh~5fmultistep~5farithmetic--full--ebf52795-877b-5e05-8f9c-549d027aedf0
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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