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

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Source and history

task_id
61db466c-7157-5120-bc36-e1b5258e664f
task_key
bbeh~5fmultistep~5farithmetic--full--61db466c-7157-5120-bc36-e1b5258e664f
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import