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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 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)(a + b) if $a * b > 0$; otherwise, it equals $a ~ b$. a:ba : b equals $(b @ a) * b$ if |a−b|<2|a-b| < 2 and $(a @ b) * a$ otherwise. $a & b$ equals $(2 - b) @ a$ if a>ba > b and bb otherwise. a][ba ][ b equals $(a @ b)$ if a:b>0a : b > 0; otherwise, it equals $-a @ -b$. a;ba ; 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 = (((((((((((((((-9 @ one) *&~ nine) @+- -4) -* -3) @][ -5) -: -8) ; 1) :+ -8) +-][ eight) +@+ two) :: -4) : -7) - -7) +;+ -3) -@* -8) Let B = ((((three + -4) ][- (-3 ;; -7)) +;- ((eight &; -2) + (-4 - five))) &~ (((7 ;;@ -5) *& (seven ~:- 10)) ~; ((four * -6) @ (-5 ++~ -4)))) Let C = (((((((((((((((((((((((seven ~~ 9) *&* 6) ~ 3) ][ -6) ;& 5) &@ 6) ][* -3) ][@ eight) ; -7) :@ 8) ~-+ -8) *: 3) @+ ten) ;; 2) & -6) -:; 8) ;* -6) : -1) *:: one) + seven) @* 1) @:: -10) -: 4). 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 (a+b) if $a * b > 0$; otherwise,  it equals $a ~ b$.
a:b equals $(b @ a) * b$ if |a−b|<2 and $(a @ b) * a$ 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 $(a * a) - b$ 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 = (((((((((((((((-9 @ one) *&~ nine) @+- -4) -* -3) @][ -5) -: -8) ; 1) :+ -8) +-][ eight) +@+ two) :: -4) : -7) - -7) +;+ -3) -@* -8)
Let B = ((((three + -4) ][- (-3 ;; -7)) +;- ((eight &; -2) + (-4 - five))) &~ (((7 ;;@ -5) *& (seven ~:- 10)) ~; ((four * -6) @ (-5 ++~ -4))))
Let C = (((((((((((((((((((((((seven ~~ 9) *&* 6) ~ 3) ][ -6) ;& 5) &@ 6) ][* -3) ][@ eight) ; -7) :@ 8) ~-+ -8) *: 3) @+ ten) ;; 2) & -6) -:; 8) ;* -6) : -1) *:: one) + seven) @* 1) @:: -10) -: 4).
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 $(a + b)$ if $a * b > 0$; otherwise,  it equals $a ~ b$.
$a : b$ equals $(b @ a) * b$ if $|a-b| < 2$ and $(a @ b) * a$ 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 $(a * a) - b$ 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 = (((((((((((((((-9 @ one) *&~ nine) @+- -4) -* -3) @][ -5) -: -8) ; 1) :+ -8) +-][ eight) +@+ two) :: -4) : -7) - -7) +;+ -3) -@* -8)
Let B = ((((three + -4) ][- (-3 ;; -7)) +;- ((eight &; -2) + (-4 - five))) &~ (((7 ;;@ -5) *& (seven ~:- 10)) ~; ((four * -6) @ (-5 ++~ -4))))
Let C = (((((((((((((((((((((((seven ~~ 9) *&* 6) ~ 3) ][ -6) ;& 5) &@ 6) ][* -3) ][@ eight) ; -7) :@ 8) ~-+ -8) *: 3) @+ ten) ;; 2) & -6) -:; 8) ;* -6) : -1) *:: one) + seven) @* 1) @:: -10) -: 4).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
01638b37-2610-5725-a150-4e82daebc0ed
task_key
bbeh~5fmultistep~5farithmetic--full--01638b37-2610-5725-a150-4e82daebc0ed
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import