Bouland and Aaronson, Equation (26)

Time bar (total: 37.5s)

analyze50.0ms (0.1%)

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 20 to 13 computations (35% saved)

sample36.8s (98.2%)

Results
5.5s8256×0valid
1.0s8236×0valid-sollya
15.0ms20×0exit-sollya
Sollya Eval
PtRival-outSollya-intervalSollya-pointstatusSollya statusRival itersollya-timecheck
(-4.1500264005873467e+307 -4.404439727074594e-116)+inf.0(+inf.0 +inf.0)+nan.0validexit00.352803#f
(-3.827547330957663e-262 6.324010517037796e-226)-1.0(-1.0 -1.0)+nan.0validexit00.175508#f
(-3.6070448354354795e-258 2.591204644803938e+273)+inf.0(+inf.0 +inf.0)+nan.0validexit00.30301100000000003#f
(-4.893227732926573e+189 1.3466360807421356e+250)+inf.0(+inf.0 +inf.0)+nan.0validexit00.337798#f
(2.0691148306034094e-204 1.1330407707051497e+57)1.6480946523809186e+228(+nan.0 +nan.0)+nan.0validexit05.0#f
(-3.535517435237893e+234 -5.189660548153434e-153)+inf.0(+inf.0 +inf.0)+nan.0validexit00.321477#f
(3.6575808099899277e+77 5.2782435528463876e+20)+inf.0(+inf.0 +inf.0)+nan.0validexit00.195131#f
(-7.27630985280465e-108 -1.2286116427153288e+67)2.278549700831076e+268(2.278549700831076e+268 2.278549700831076e+268)+nan.0validexit00.34376300000000004#f
(-1.0296806098281229e-161 1.1758301028399658e-286)-1.0(-1.0 -1.0)+nan.0validexit00.109173#f
(1.5437384781250215e+37 5.860357764478589e+274)+inf.0(+inf.0 +inf.0)+nan.0validexit00.309899#f
(-3.07635006723759e+241 -8.757652317556867e-301)+inf.0(+inf.0 +inf.0)+nan.0validexit00.33981#f
(-3.797137859219833e-251 -4.64884133070918e-137)-1.0(-1.0 -1.0)+nan.0validexit00.15607#f
(1.6797412491972807e+302 -3.68481497855107e-267)+inf.0(+inf.0 +inf.0)+nan.0validexit00.258545#f
(-6.813227593826497e+217 -1.0959322842321572e-149)+inf.0(+inf.0 +inf.0)+nan.0validexit00.29641999999999996#f
(1.6154370192984198e+111 1.0321724460034209e+301)+inf.0(+inf.0 +inf.0)+nan.0validexit00.170328#f
(9.215290259646168e+135 9.586804029520141e+185)+inf.0(+inf.0 +inf.0)+nan.0validexit00.241057#f
(-5.381505130649299e-110 -3.2892941281240373e+301)+inf.0(+inf.0 +inf.0)+nan.0validexit00.25672100000000003#f
(4.565926794250142e-45 9.234099179167198e+72)7.270732039944481e+291(+nan.0 +nan.0)+nan.0validexit05.0#f
(-4.8377610440908975e+249 -7.050181827796405e+226)+inf.0(+inf.0 +inf.0)+nan.0validexit00.302324#f
(-5.792270257671093e+179 -2.5643142894632506e+206)+inf.0(+inf.0 +inf.0)+nan.0validexit00.27092700000000003#f
Sollya timings
Total time spent in Sollya 1.0s
Bogosity

preprocess420.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
821×unsub-neg
800×fma-neg
601×sub-neg
410×fma-define
374×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038449
199421
2233413
3700413
42734413
57202413
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 b b))) #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 b b))) #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 b b))) #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 (neg.f64 b) (neg.f64 b)))) #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 b b))) #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 (neg.f64 b) (neg.f64 b)))) #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 a 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 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 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 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 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 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 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 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 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 b b))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 (*.f64 b b) #s(literal 4 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 b (*.f64 b #s(literal 4 binary64)) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(-.f64 (fma.f64 b (*.f64 b #s(literal -4 binary64)) #s(literal 1 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 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 (*.f64 b b) #s(literal 4 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 b (*.f64 b #s(literal 4 binary64)) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(-.f64 (fma.f64 b (*.f64 b #s(literal -4 binary64)) #s(literal 1 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 a a))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 a a) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 a a) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 a (*.f64 a #s(literal 4 binary64)) #s(literal -1 binary64)))
Symmetry

(abs a)

(abs b)

Compiler

Compiled 19 to 12 computations (36.8% saved)

eval1.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune3.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.9%
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
Compiler

Compiled 38 to 24 computations (36.8% saved)

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
3×1-exp
2×unsub-neg
2×sub-neg
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01767
12867
23267
33567
43867
54167
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 b 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 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 (*.f64 b b) #s(literal 4 binary64))) #s(literal 1 binary64))
(+.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 (*.f64 b b) #s(literal 4 binary64))) #s(literal -1 binary64))

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 19 to 12 computations (36.8% saved)

preprocess199.0ms (0.5%)

Remove

(abs b)

(abs a)

Compiler

Compiled 228 to 144 computations (36.8% saved)

end0.0ms (0%)

Profiling

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