Bouland and Aaronson, Equation (24)

Time bar (total: 7.1s)

analyze1.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 32 to 19 computations (40.6% saved)

sample6.9s (97.7%)

Results
1.6s8256×0valid-rival
828.0ms8240×0valid-sollya
80.0ms16×0exit-sollya
Bogosity

preprocess127.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
664×unsub-neg
633×sub-neg
452×fma-neg
366×fma-define
320×distribute-lft-neg-out
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057765
1194729
2770713
33528713
47880713
Stop Event
1×node limit
Calls
Call 1
Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (-.f64 #s(literal 1 binary64) (neg.f64 a))) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) (neg.f64 a)))))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (-.f64 #s(literal 1 binary64) (neg.f64 a))) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) (neg.f64 a)))))) #s(literal 1 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 b b) (-.f64 #s(literal 1 binary64) b)) (*.f64 (*.f64 a a) (+.f64 #s(literal 3 binary64) b))))) #s(literal 1 binary64))
Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 b (*.f64 b (+.f64 a #s(literal 3 binary64)))))) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 a (*.f64 a (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 b (*.f64 b (+.f64 a #s(literal 3 binary64)))))) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 a (*.f64 a (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (-.f64 #s(literal 1 binary64) (neg.f64 a))) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) (neg.f64 a)))))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) (neg.f64 a)) (*.f64 b (*.f64 b (-.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (+.f64 a #s(literal 1 binary64)) (*.f64 (*.f64 b b) (-.f64 #s(literal 3 binary64) a))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 b (*.f64 b (-.f64 #s(literal 3 binary64) a)) (fma.f64 a a (pow.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 b (*.f64 b (+.f64 a #s(literal 3 binary64)))))) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 a (*.f64 a (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (-.f64 #s(literal 1 binary64) (neg.f64 a))) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) (neg.f64 a)))))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) (neg.f64 a)) (*.f64 b (*.f64 b (-.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (+.f64 a #s(literal 1 binary64)) (*.f64 (*.f64 b b) (-.f64 #s(literal 3 binary64) a))) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (fma.f64 b (*.f64 b (-.f64 #s(literal 3 binary64) a)) (fma.f64 a a (pow.f64 a #s(literal 3 binary64)))) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 b (*.f64 b (+.f64 a #s(literal 3 binary64)))))) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (fma.f64 a (*.f64 a (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (fma.f64 a (*.f64 a (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 b b) (-.f64 #s(literal 1 binary64) b)) (*.f64 (*.f64 a a) (+.f64 #s(literal 3 binary64) b))))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (*.f64 b b) (-.f64 #s(literal 1 binary64) b) (*.f64 (*.f64 a a) (+.f64 b #s(literal 3 binary64))))) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 a (*.f64 a (+.f64 b #s(literal 3 binary64))) (*.f64 (*.f64 b b) (-.f64 #s(literal 1 binary64) b))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 #s(literal 4 binary64) (fma.f64 (*.f64 b b) (-.f64 #s(literal 1 binary64) b) (*.f64 a (*.f64 a (+.f64 b #s(literal 3 binary64))))) #s(literal -1 binary64)))
Symmetry

(abs b)

Compiler

Compiled 31 to 18 computations (41.9% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
71.4%
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
Compiler

Compiled 62 to 36 computations (41.9% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
8×+-commutative
6×unsub-neg
5×*-commutative
5×neg-mul-1
4×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023115
140115
247115
353115
461115
572115
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 #s(literal 3 binary64) a))))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))))) #s(literal 1 binary64))
(+.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (+.f64 (*.f64 (*.f64 a a) (-.f64 #s(literal 1 binary64) a)) (*.f64 (*.f64 b b) (+.f64 a #s(literal 3 binary64)))))) #s(literal -1 binary64))

soundness0.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 31 to 19 computations (38.7% saved)

preprocess33.0ms (0.5%)

Remove

(abs b)

Compiler

Compiled 248 to 150 computations (39.5% saved)

end0.0ms (0%)

Profiling

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