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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 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 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(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. 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 = ((((-2 <> six) [][]* (-9 *+ -10)) -<>[] ((-10 []<>][ -9) ][<>+ (7 * seven))) []-][ (((7 ][>< 3) ][<>][ (nine ><><[] -5)) -<> ((8 - -5) ][ (-6 [] two)))) Let B = ((((four *<>+ ten) *<>+ (eight +<> four)) +<> ((-2 * six) * (-1 -<>- three))) []][- (((5 -- 3) <>][ (-3 * -5)) <>+ ((3 +->< nine) ** (ten ** 4)))) Let C = (((((((((((((((((10 [][]<> -1) ><[] 6) *][ two) ][<> -7) - 7) *<>- -6) + one) <>->< seven) <>+ -2) <>* -5) ><+ -5) ** 8) --<> 8) ][+[] -9) ][][>< six) <> 1) ** 5). 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 min(a,b) if either a or b is prime and max(a,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 (2<>b)+a if a>b and b otherwise.
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 = ((((-2 <> six) [][]* (-9 *+ -10)) -<>[] ((-10 []<>][ -9) ][<>+ (7 * seven))) []-][ (((7 ][>< 3) ][<>][ (nine ><><[] -5)) -<> ((8 - -5) ][ (-6 [] two))))
Let B = ((((four *<>+ ten) *<>+ (eight +<> four)) +<> ((-2 * six) * (-1 -<>- three))) []][- (((5 -- 3) <>][ (-3 * -5)) <>+ ((3 +->< nine) ** (ten ** 4))))
Let C = (((((((((((((((((10 [][]<> -1) ><[] 6) *][ two) ][<> -7) - 7) *<>- -6) + one) <>->< seven) <>+ -2) <>* -5) ><+ -5) ** 8) --<> 8) ][+[] -9) ][][>< six) <> 1) ** 5).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a <> b$ equals $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ 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 $(2 <> b) + a$ if $a > b$ and $b$ otherwise.
$a >< b$ 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 = ((((-2 <> six) [][]* (-9 *+ -10)) -<>[] ((-10 []<>][ -9) ][<>+ (7 * seven))) []-][ (((7 ][>< 3) ][<>][ (nine ><><[] -5)) -<> ((8 - -5) ][ (-6 [] two))))
Let B = ((((four *<>+ ten) *<>+ (eight +<> four)) +<> ((-2 * six) * (-1 -<>- three))) []][- (((5 -- 3) <>][ (-3 * -5)) <>+ ((3 +->< nine) ** (ten ** 4))))
Let C = (((((((((((((((((10 [][]<> -1) ><[] 6) *][ two) ][<> -7) - 7) *<>- -6) + one) <>->< seven) <>+ -2) <>* -5) ><+ -5) ** 8) --<> 8) ][+[] -9) ][][>< six) <> 1) ** 5).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
95789e9a-653b-5f8b-958a-8abdd9ee7391
task_key
bbeh~5fmultistep~5farithmetic--full--95789e9a-653b-5f8b-958a-8abdd9ee7391
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import