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

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

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Source and history

task_id
299cdddc-2f7f-5a89-b445-f3785cb8d4ea
task_key
bbeh~5fmultistep~5farithmetic--full--299cdddc-2f7f-5a89-b445-f3785cb8d4ea
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import