Toniolo and Linder, Equation (3b), real

Time bar (total: 15.9s)

analyze451.0ms (2.8%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
0%0%99.9%0.1%0%0%0%3
0%0%99.9%0.1%0%0%0%4
25%25%74.9%0.1%0%0%0%5
43.8%43.7%56.2%0.1%0%0%0%6
43.8%43.7%56.2%0.1%0%0%0%7
53.1%53%46.8%0.1%0%0%0%8
60.9%60.8%39%0.1%0%0%0%9
60.9%60.8%39%0.1%0%0%0%10
64.8%64.7%35.1%0.1%0%0%0%11
68.4%68.3%31.6%0.1%0%0%0%12
Compiler

Compiled 20 to 14 computations (30% saved)

sample15.2s (95.5%)

Results
3.2s8256×0valid
1.2s8240×0valid-sollya
5.0ms16×0exit-sollya
Sollya Eval
PtRival-outSollya-intervalSollya-pointstatusSollya statusRival itersollya-timecheck
(1.029016643476364e+237 9.020897234843871e+231 -7.00129789933612e+52)0.48948156140037474(0.48948156140037474 0.48948156140037474)+nan.0validexit00.48758599999999996#f
(1.367774199397468e-105 -1.7621108557407097e-167 -8211153.313673702)-9.84123904643588e-63(-9.84123904643588e-63 -9.84123904643588e-63)+nan.0validexit00.28738199999999997#f
(1.1071104445512305e+124 -4.147802373864286e-196 2.207166528592259e+27)-3.29422323898865e-196(-3.29422323898865e-196 -3.29422323898865e-196)+nan.0validexit00.20344199999999998#f
(8.048325865356477e+158 4.21850366996888e+82 -1.2543811763670086e-186)1.2358116527774718e-186(1.2358116527774718e-186 1.2358116527774718e-186)+nan.0validexit00.195691#f
(-7.507340768968524e+242 1.5100067210499188e-300 -2.5208072849161034e+303)2.1907939890590765e-299(2.1907939890590765e-299 2.1907939890590765e-299)+nan.0validexit00.352156#f
(-7.788901420427517e-247 2.6290853263145723e-114 -1.7549820601773166e+143)-0.6985263509024798(-0.6985263509024798 -0.6985263509024798)+nan.0validexit00.263743#f
(9.153636654156409e-81 -1.4898157645164754e+256 -8.598005305143631e+90)0.5301463567904763(0.5301463567904763 0.5301463567904763)+nan.0validexit00.35966#f
(9.264044268302364e+270 -1.151720716646837e-294 -8.465474918531059e-22)5.25449386e-315(5.25449386e-315 5.25449386e-315)+nan.0validexit00.381938#f
(2.7633562956542838e-49 -7.32739492463612e+187 8.376256090011183e+191)0.14777780286749345(0.14777780286749345 0.14777780286749345)+nan.0validexit00.428657#f
(-5.165595402958202e+209 -6.778361097011955e-288 6.605439691514385e-158)-0.0(-0.0 -0.0)+nan.0validexit00.355773#f
(2.3878264955400042e-254 2.4378318873977983e-99 5.72164701079125e+162)0.9998715503606121(0.9998715503606121 0.9998715503606121)+nan.0validexit00.283736#f
(-2.4142976074942136e-83 4.046889869987919e-200 1.1380860535896197e-308)0.0(0.0 0.0)+nan.0validexit00.25738999999999995#f
(6.347323176532791e-39 -1.5945928929664571e-46 1.1803862680062811e-225)-2.965400534318124e-233(-2.965400534318124e-233 -2.965400534318124e-233)+nan.0validexit00.22929#f
(-2.679103380075091e-297 -1.0485158765348312e-60 -3.491693637351159e+173)-0.9575915814851577(-0.9575915814851577 -0.9575915814851577)+nan.0validexit00.2691#f
(-16618.936226938567 -3.2332335345068307e-201 2.5082424373335305e-33)-9.13325581986753e-233(-9.13325581986753e-233 -9.13325581986753e-233)+nan.0validexit00.23236900000000002#f
(4.871048791150787e-97 -2.598909188930857e+281 3.8944998317593867e-162)3.8944998317593867e-162(3.8944998317593867e-162 3.8944998317593867e-162)+nan.0validexit00.227113#f
Sollya timings
Total time spent in Sollya 1.2s
Bogosity

preprocess213.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
968×fma-define
307×fma-neg
195×unsub-neg
181×times-frac
170×associate-*l*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
053717
1111529
2240529
3420529
4940529
52219529
63233529
73758529
84126529
94217529
104256529
114256529
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 (neg.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 (neg.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 (neg.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))) (sin.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 (neg.f64 th))))
(*.f64 (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 th) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 kx))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))) (sin.f64 ky))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 (neg.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 (neg.f64 th)))
(*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)))
(*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 (neg.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(neg.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 (neg.f64 th))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 th) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 kx))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 th))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 th)))
Symmetry

(abs kx)

(negabs ky)

(negabs th)

Compiler

Compiled 19 to 13 computations (31.6% saved)

eval0.0ms (0%)

Compiler

Compiled 3 to 3 computations (0% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
93.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×*-commutative
1×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02063
12263
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 19 to 13 computations (31.6% saved)

preprocess49.0ms (0.3%)

Remove

(negabs th)

(negabs ky)

(abs kx)

Compiler

Compiled 304 to 208 computations (31.6% saved)

end0.0ms (0%)

Profiling

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