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

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Source and history

task_id
e2c6fb06-38b1-5068-8d39-1d4a2c7ec888
task_key
bbeh~5fmultistep~5farithmetic--full--e2c6fb06-38b1-5068-8d39-1d4a2c7ec888
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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