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

Problem

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input

Consider the following new operations: a><ba >< b equals $(b * a) + b$ if |a−b|<2|a-b| < 2 and $(a * b) + a$ otherwise. $a @ b$ equals $(a >< a) * b$ if b<2b < 2 and $(b >< b) * a$ otherwise. a<>ba <> b equals $(2 >< b) @ a$ if a>ba > b and bb otherwise. a[]ba [] b equals (a<>b)(a <> b) if $a * b > 0$; otherwise, it equals −a<>−b-a <> -b. a][ba ][ b equals (a−b)(a - b) if $a * b > 0$; otherwise, it equals a+ba + b. $a ~ b$ equals min(a,b)min(a, b) if either aa or bb is prime and max(a,b)max(a, b) otherwise. Let A = ((((10 [] -2) - (seven [] four)) @ ((-10 <> -2) * (6 * -10))) <> (((one * 10) [] (-9 >< 3)) ~ ((-6 - 6) >< (9 [] -8)))) Let B = (((((((((((((((((-10 ][ -10) <> -10) >< -6) @ -7) ][ -4) >< one) <> five) ][ -7) @ three) * -4) <> -10) ][ five) @ -9) - 10) - -3) @ nine) <> -6) Let C = (((((((((((((-7 <> five) - -6) - -3) ][ -1) >< seven) ][ two) ~ -1) <> -8) - 8) ~ -7) [] one) @ 9) <> -10). 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 $(a >< a) * b$ if b<2 and $(b >< b) * a$ 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−b) if $a * b > 0$; otherwise,  it equals a+b.
$a ~ b$ equals min(a,b) if either a or b is prime and max(a,b) otherwise.

Let A = ((((10 [] -2) - (seven [] four)) @ ((-10 <> -2) * (6 * -10))) <> (((one * 10) [] (-9 >< 3)) ~ ((-6 - 6) >< (9 [] -8))))
Let B = (((((((((((((((((-10 ][ -10) <> -10) >< -6) @ -7) ][ -4) >< one) <> five) ][ -7) @ three) * -4) <> -10) ][ five) @ -9) - 10) - -3) @ nine) <> -6)
Let C = (((((((((((((-7 <> five) - -6) - -3) ][ -1) >< seven) ][ two) ~ -1) <> -8) - 8) ~ -7) [] one) @ 9) <> -10).
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 $(a >< a) * b$ if $b < 2$ and $(b >< b) * a$ 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 $(a - b)$ if $a * b > 0$; otherwise,  it equals $a + b$.
$a ~ b$ equals $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ otherwise.

Let A = ((((10 [] -2) - (seven [] four)) @ ((-10 <> -2) * (6 * -10))) <> (((one * 10) [] (-9 >< 3)) ~ ((-6 - 6) >< (9 [] -8))))
Let B = (((((((((((((((((-10 ][ -10) <> -10) >< -6) @ -7) ][ -4) >< one) <> five) ][ -7) @ three) * -4) <> -10) ][ five) @ -9) - 10) - -3) @ nine) <> -6)
Let C = (((((((((((((-7 <> five) - -6) - -3) ][ -1) >< seven) ][ two) ~ -1) <> -8) - 8) ~ -7) [] one) @ 9) <> -10).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
e2419c8a-7c05-59ec-bfc6-81cd17d203b6
task_key
bbeh~5fmultistep~5farithmetic--full--e2419c8a-7c05-59ec-bfc6-81cd17d203b6
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import