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

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input

Consider the following new operations: a!ba ! 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. a][ba ][ b equals $(2 * b) - a$ if a>ba > b and bb otherwise. a;ba ; b equals (a][b)(a ][ b) if a!b>0a ! b > 0; otherwise, it equals −a][−b-a ][ -b. $a ~ b$ equals (a+a);b(a + a) ; b if b<2b < 2 and (b+b);a(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 = (((((((((((-10 -* -1) ][~ 5) !!- -3) -* 1) ! 2) ++; 5) ~+! -5) ++][ 3) ][][ 10) ][* 4) +~ -2) Let B = ((((6 !- eight) +~ (-10 ; -1)) ; ((6 ; -1) +- (two *- five))) ;~- (((-3 + 1) *! (-6 ][; 1)) ][ ((-9 ;! three) - (8 -~+ four)))) Let C = (((((((((((((-1 ~; -10) ! nine) ][+~ 6) ! one) -- six) ! -10) !*- -3) ][ -9) ! -3) ][ six) ][ one) ~ -6) * -3). 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 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.
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 = (((((((((((-10 -* -1) ][~ 5) !!- -3) -* 1) ! 2) ++; 5) ~+! -5) ++][ 3) ][][ 10) ][* 4) +~ -2)
Let B = ((((6 !- eight) +~ (-10 ; -1)) ; ((6 ; -1) +- (two *- five))) ;~- (((-3 + 1) *! (-6 ][; 1)) ][ ((-9 ;! three) - (8 -~+ four))))
Let C = (((((((((((((-1 ~; -10) ! nine) ][+~ 6) ! one) -- six) ! -10) !*- -3) ][ -9) ! -3) ][ six) ][ one) ~ -6) * -3).
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 $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a ][ b$ equals $(2 * b) - a$ if $a > b$ and $b$ otherwise.
$a ; b$ 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 = (((((((((((-10 -* -1) ][~ 5) !!- -3) -* 1) ! 2) ++; 5) ~+! -5) ++][ 3) ][][ 10) ][* 4) +~ -2)
Let B = ((((6 !- eight) +~ (-10 ; -1)) ; ((6 ; -1) +- (two *- five))) ;~- (((-3 + 1) *! (-6 ][; 1)) ][ ((-9 ;! three) - (8 -~+ four))))
Let C = (((((((((((((-1 ~; -10) ! nine) ][+~ 6) ! one) -- six) ! -10) !*- -3) ][ -9) ! -3) ][ six) ][ one) ~ -6) * -3).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
b50dd6f7-5b70-599f-a999-da9a77d58e13
task_key
bbeh~5fmultistep~5farithmetic--full--b50dd6f7-5b70-599f-a999-da9a77d58e13
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import