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

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

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Source and history

task_id
d3d3c4a8-dbb6-5139-aeeb-1cc538cf7de3
task_key
bbeh~5fmultistep~5farithmetic--full--d3d3c4a8-dbb6-5139-aeeb-1cc538cf7de3
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import