Bouland and Aaronson, Equation (24)

Time bar (total: 27.1s)

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)

sample26.4s (97.7%)

Results
3.8s8256×0valid
1.2s8247×0valid-sollya
3.0ms9×0exit-sollya
Sollya Eval
PtRival-outSollya-intervalSollya-pointstatusSollya statusRival itersollya-timecheck
(-1.3005083225979014e-5 -2.6711700809921897e+62)5.091035983703884e+249(5.091035983703884e+249 5.091035983703884e+249)+nan.0validexit00.132476#f
(-1.0399752374136801e-288 -7.291644622310478e+268)+inf.0(+inf.0 +inf.0)+nan.0validexit00.370892#f
(60.759187934831004 -2.3396632558163996e+103)+inf.0(+inf.0 +inf.0)+nan.0validexit00.33065#f
(-2.8397217177019043e-95 8.843264316967179e+92)+inf.0(+inf.0 +inf.0)+nan.0validexit00.30424100000000004#f
(-5.3658437677755875e+200 -1.53480610911963e+297)+inf.0(+inf.0 +inf.0)+nan.0validexit00.296641#f
(8.837084713782439e+95 -3.013531052958669e-132)+inf.0(+inf.0 +inf.0)+nan.0validexit00.23352099999999998#f
(-2.4108539780569775e+297 9.538869027439046e-122)+inf.0(+inf.0 +inf.0)+nan.0validexit00.360145#f
(-7.929359972908233e+157 -6.593600624002301e+183)+inf.0(+inf.0 +inf.0)+nan.0validexit00.388028#f
(3.1732881949556866e-220 -3.821980818846523e-193)-1.0(-1.0 -1.0)+nan.0validexit00.265096#f
Sollya timings
Total time spent in Sollya 1.2s
Bogosity

preprocess423.0ms (1.6%)

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)

eval1.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune4.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
71.7%
(-.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)

simplify12.0ms (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))

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 31 to 19 computations (38.7% saved)

preprocess185.0ms (0.7%)

Remove

(abs b)

Compiler

Compiled 248 to 150 computations (39.5% saved)

end0.0ms (0%)

Profiling

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