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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: $a # b$ equals min(a,b)min(a, b) if either aa or bb is prime and max(a,b)max(a, b) otherwise. $a & b$ equals $(b - a) * b$ if |a−b|<2|a-b| < 2 and $(a - b) * a$ otherwise. a!ba ! b equals $(a & a) # b$ if b<2b < 2 and $(b & b) # a$ otherwise. a;ba ; b equals $a # b$ 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 (a!b)(a ! b) if a;b>0a ; b > 0; otherwise, it equals a+ba + b. a><ba >< b equals (2−b)!a(2 - b) ! a if a>ba > b and bb otherwise. Let A = ((((three - 10) # (one + seven)) & ((-5 + -9) >< (three ; one))) ; (((-5 # nine) + (3 ; five)) + ((-7 + two) # (five & -3)))) Let B = ((((((((((((((((((((one ! 3) ; -4) * 4) ! -4) ; -10) * -6) ! -4) * -5) + -5) + 2) ; -3) + four) & -4) ! -9) - -10) + -6) ! 1) & 8) # -1) & -7) Let C = ((((8 : 2) - (-9 ; -8)) ! ((nine & 2) & (-1 - -3))) : (((4 >< 3) - (9 & -6)) # ((-4 - -4) + (7 ! -7)))). 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 $(b - a) * b$ 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 $a # b$ if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
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.

Let A = ((((three - 10) # (one + seven)) & ((-5 + -9) >< (three ; one))) ; (((-5 # nine) + (3 ; five)) + ((-7 + two) # (five & -3))))
Let B = ((((((((((((((((((((one ! 3) ; -4) * 4) ! -4) ; -10) * -6) ! -4) * -5) + -5) + 2) ; -3) + four) & -4) ! -9) - -10) + -6) ! 1) & 8) # -1) & -7)
Let C = ((((8 : 2) - (-9 ; -8)) ! ((nine & 2) & (-1 - -3))) : (((4 >< 3) - (9 & -6)) # ((-4 - -4) + (7 ! -7)))).
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 $(b - a) * b$ 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 $a # b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a : b$ equals $(a ! b)$ if $a ; b > 0$; otherwise,  it equals $a + b$.
$a >< b$ equals $(2 - b) ! a$ if $a > b$ and $b$ otherwise.

Let A = ((((three - 10) # (one + seven)) & ((-5 + -9) >< (three ; one))) ; (((-5 # nine) + (3 ; five)) + ((-7 + two) # (five & -3))))
Let B = ((((((((((((((((((((one ! 3) ; -4) * 4) ! -4) ; -10) * -6) ! -4) * -5) + -5) + 2) ; -3) + four) & -4) ! -9) - -10) + -6) ! 1) & 8) # -1) & -7)
Let C = ((((8 : 2) - (-9 ; -8)) ! ((nine & 2) & (-1 - -3))) : (((4 >< 3) - (9 & -6)) # ((-4 - -4) + (7 ! -7)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
13161680-c4c5-5e1b-b239-b391d557fdbe
task_key
bbeh~5fmultistep~5farithmetic--full--13161680-c4c5-5e1b-b239-b391d557fdbe
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import