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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 $(2 - b) * a$ if a>ba > b and bb otherwise. a;ba ; b equals (a−a)+b(a - a) + b if b<2b < 2 and (b−b)+a(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. $a @ b$ equals (b[]a)+b(b [] a) + b if |a−b|<2|a-b| < 2 and (a[]b)+a(a [] b) + a 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 @*+ 4) <>+[] (-4 *<>* -1)) @; ((-1 <> six) ; (2 ;* one))) @@@ (((five ;- five) []@@ (-8 - one)) ; ((two +; -5) +[]- (three - -8)))) Let B = (((((((((((8 *; 8) + 10) -+ nine) +[] seven) +- four) []<>[] four) @@ 9) -+ seven) @ three) ; -5) ;[] three) Let C = ((((9 @+ -1) <> (-3 + -5)) [];- ((8 <><> -5) <>- (-9 <>* 3))) ; (((-4 <>@+ -5) ; (four @; -9)) *+ ((-5 [];- 3) @[]+ (ten *+<> two)))). 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 $(2 - b) * a$ if a>b and b 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 (b[]a)+b if |a−b|<2 and (a[]b)+a 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 @*+ 4) <>+[] (-4 *<>* -1)) @; ((-1 <> six) ; (2 ;* one))) @@@ (((five ;- five) []@@ (-8 - one)) ; ((two +; -5) +[]- (three - -8))))
Let B = (((((((((((8 *; 8) + 10) -+ nine) +[] seven) +- four) []<>[] four) @@ 9) -+ seven) @ three) ; -5) ;[] three)
Let C = ((((9 @+ -1) <> (-3 + -5)) [];- ((8 <><> -5) <>- (-9 <>* 3))) ; (((-4 <>@+ -5) ; (four @; -9)) *+ ((-5 [];- 3) @[]+ (ten *+<> two)))).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a [] b$ equals $(2 - b) * a$ if $a > b$ and $b$ 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 $(b [] a) + b$ if $|a-b| < 2$ and $(a [] b) + a$ 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 @*+ 4) <>+[] (-4 *<>* -1)) @; ((-1 <> six) ; (2 ;* one))) @@@ (((five ;- five) []@@ (-8 - one)) ; ((two +; -5) +[]- (three - -8))))
Let B = (((((((((((8 *; 8) + 10) -+ nine) +[] seven) +- four) []<>[] four) @@ 9) -+ seven) @ three) ; -5) ;[] three)
Let C = ((((9 @+ -1) <> (-3 + -5)) [];- ((8 <><> -5) <>- (-9 <>* 3))) ; (((-4 <>@+ -5) ; (four @; -9)) *+ ((-5 [];- 3) @[]+ (ten *+<> two)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
90d56bff-20e0-5082-88b6-f94608456e7a
task_key
bbeh~5fmultistep~5farithmetic--full--90d56bff-20e0-5082-88b6-f94608456e7a
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import