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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 (a−b)(a - b) if a+b>0a + b > 0; otherwise, it equals a+ba + b. $a @ b$ equals $(a + a) * b$ if b<2b < 2 and $(b + b) * a$ otherwise. $a & b$ equals (a:b)(a : b) if a+b>0a + b > 0; otherwise, it equals $a * b$. a[]ba [] b equals (a:b)(a : b) if a−b>0a - b > 0; otherwise, it equals −a:−b-a : -b. $a # b$ equals $(b * a) - b$ if |a−b|<2|a-b| < 2 and $(a * b) - a$ otherwise. a][ba ][ b equals $(2 @ b) * a$ if a>ba > b and bb otherwise. Let A = ((((two [] 5) & (1 # -2)) : ((-6 : -2) * (5 [] 7))) [] (((5 - -1) - (-4 - 2)) : ((six ][ eight) [] (-1 & -7)))) Let B = (((((((((((((((((9 [] 6) * 3) @ -8) @ 9) * -3) ][ two) * 7) @ -1) ][ one) * four) @ -4) * -3) @ -1) [] -9) * -1) [] three) ][ -7) Let C = ((((-2 : 10) + (three + six)) : ((4 + -7) & (four + two))) & (((nine + -9) @ (-8 * -1)) & ((-2 @ -10) @ (-1 ][ six)))). 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 a+b>0; otherwise,  it equals a+b.
$a @ b$ equals $(a + a) * b$ if b<2 and $(b + b) * a$ 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 $(b * a) - b$ if |a−b|<2 and $(a * b) - a$ otherwise.
a][b equals $(2 @ b) * a$ if a>b and b otherwise.

Let A = ((((two [] 5) & (1 # -2)) : ((-6 : -2) * (5 [] 7))) [] (((5 - -1) - (-4 - 2)) : ((six ][ eight) [] (-1 & -7))))
Let B = (((((((((((((((((9 [] 6) * 3) @ -8) @ 9) * -3) ][ two) * 7) @ -1) ][ one) * four) @ -4) * -3) @ -1) [] -9) * -1) [] three) ][ -7)
Let C = ((((-2 : 10) + (three + six)) : ((4 + -7) & (four + two))) & (((nine + -9) @ (-8 * -1)) & ((-2 @ -10) @ (-1 ][ six)))).
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 $a + b > 0$; otherwise,  it equals $a + b$.
$a @ b$ equals $(a + a) * b$ if $b < 2$ and $(b + b) * a$ 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 $(b * a) - b$ if $|a-b| < 2$ and $(a * b) - a$ otherwise.
$a ][ b$ equals $(2 @ b) * a$ if $a > b$ and $b$ otherwise.

Let A = ((((two [] 5) & (1 # -2)) : ((-6 : -2) * (5 [] 7))) [] (((5 - -1) - (-4 - 2)) : ((six ][ eight) [] (-1 & -7))))
Let B = (((((((((((((((((9 [] 6) * 3) @ -8) @ 9) * -3) ][ two) * 7) @ -1) ][ one) * four) @ -4) * -3) @ -1) [] -9) * -1) [] three) ][ -7)
Let C = ((((-2 : 10) + (three + six)) : ((4 + -7) & (four + two))) & (((nine + -9) @ (-8 * -1)) & ((-2 @ -10) @ (-1 ][ six)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
019c7e27-f8b6-52de-ad66-609c2eba55a7
task_key
bbeh~5fmultistep~5farithmetic--full--019c7e27-f8b6-52de-ad66-609c2eba55a7
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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