Bouland and Aaronson, Equation (24)

Time bar (total: 3.0s)

analyze13.0ms (0.4%)

Memory
3.9MiB live, 3.9MiB allocated
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 63 to 39 computations (38.1% saved)

sample2.8s (94.7%)

Memory
5.1MiB live, 896.1MiB allocated
Samples
699.0ms8 256×0valid-baseline
675.0ms8 256×0valid-rival
546.0ms8 256×0valid-sollya
Bogosity

preprocess116.0ms (3.9%)

Memory
-8.1MiB live, 22.3MiB allocated
Algorithm
1×egg-herbie
Rules
641×sub-neg
559×unsub-neg
452×fmm-def
366×fma-define
315×distribute-lft-neg-out
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057765
1194729
2770713
33534713
47886713
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%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
76.4%
(-.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 (0.1%)

Memory
1.0MiB live, 1.0MiB allocated
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%)

Memory
0.4MiB live, 0.4MiB allocated
Stop Event
1×fuel
Compiler

Compiled 31 to 19 computations (38.7% saved)

preprocess25.0ms (0.8%)

Memory
-11.7MiB live, 26.5MiB allocated
Remove

(abs b)

Compiler

Compiled 248 to 150 computations (39.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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