Falkner and Boettcher, Appendix B, 1

Time bar (total: 1.5min)

analyze902.0ms (1%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
0%0%100%0%0%0%0%4
0%0%100%0%0%0%0%5
0%0%100%0%0%0%0%6
0%0%100%0%0%0%0%7
0%0%100%0%0%0%0%8
0%0%100%0%0%0%0%9
0%0%100%0%0%0%0%10
0%0%100%0%0%0%0%11
0%0%100%0%0%0%0%12
Compiler

Compiled 16 to 10 computations (37.5% saved)

sample1.5min (98.3%)

Results
4.1s8335×0invalid
827.0ms8252×0invalid-sollya
10.1s3799×3valid
407.0ms3772×3valid-sollya
3.7s2195×1valid
228.0ms2184×1valid-sollya
3.9s2067×2valid
217.0ms2056×2valid-sollya
24.0ms195×0valid-sollya
397.0ms195×0valid
9.0ms83×0exit-sollya
3.0ms27×3exit-sollya
1.0ms11×2exit-sollya
1.0ms11×1exit-sollya
Sollya Eval
PtRival-outSollya-intervalSollya-pointstatusSollya statusRival itersollya-timecheck
(-4.0882757475079983e+133)#f(+nan.0 +nan.0)+nan.0invalidexit00.147688#f
(-2.0731661649507578e+70)#f(+nan.0 +nan.0)+nan.0invalidexit00.097296#f
(1.821121736701989e+280)#f(+nan.0 +nan.0)+nan.0invalidexit00.08690300000000001#f
(-5.564075622828722e-165)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.112115#f
(7.950372488250906e+260)#f(+nan.0 +nan.0)+nan.0invalidexit00.107855#f
(2.3058815943531302e-129)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.088163#f
(-1.6087679658626147e-33)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.127978#f
(2.0013434346453506e+40)#f(+nan.0 +nan.0)+nan.0invalidexit00.08107099999999999#f
(-4.421905025959751e+177)#f(+nan.0 +nan.0)+nan.0invalidexit00.114472#f
(4.796476324577501e+32)#f(+nan.0 +nan.0)+nan.0invalidexit00.122137#f
(-3.839362314831252e-295)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.126329#f
(6.122795020004721e-181)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.13077799999999998#f
(3.0239479512979892e+175)#f(+nan.0 +nan.0)+nan.0invalidexit00.12222599999999999#f
(-3.6818031352613685e+37)#f(+nan.0 +nan.0)+nan.0invalidexit00.13848300000000002#f
(-9.471720349190048e+300)#f(+nan.0 +nan.0)+nan.0invalidexit00.088097#f
(-9.093998126397027e+234)#f(+nan.0 +nan.0)+nan.0invalidexit00.135691#f
(1.6267649201942786e-165)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.11776400000000001#f
(-1.5832469314938154e-17)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.08829#f
(2.657710581458784e+97)#f(+nan.0 +nan.0)+nan.0invalidexit00.111387#f
(3.064894499909781e+236)#f(+nan.0 +nan.0)+nan.0invalidexit00.131457#f
(-7.053933819996793e+170)#f(+nan.0 +nan.0)+nan.0invalidexit00.109018#f
(-3.8626234764402556e+219)#f(+nan.0 +nan.0)+nan.0invalidexit00.087676#f
(-3.892416929189718e-70)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.154529#f
(-4.473526617405156e+215)#f(+nan.0 +nan.0)+nan.0invalidexit00.114225#f
(-3.5450382531808485e+69)#f(+nan.0 +nan.0)+nan.0invalidexit00.12929000000000002#f
(-9.299243671503967e-262)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.12012300000000001#f
(1.3086946235551407e+215)#f(+nan.0 +nan.0)+nan.0invalidexit00.055119#f
(5.1612842866134266e+228)#f(+nan.0 +nan.0)+nan.0invalidexit00.085437#f
(2.870212773327758e+244)#f(+nan.0 +nan.0)+nan.0invalidexit00.122677#f
(4.095640826434674e+185)#f(+nan.0 +nan.0)+nan.0invalidexit00.11025599999999999#f
(-6.126506676498498e+255)#f(+nan.0 +nan.0)+nan.0invalidexit00.091287#f
(-3163.9317415139394)#f(+nan.0 +nan.0)+nan.0invalidexit00.09629700000000001#f
(-8.465871418127989e-123)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.131215#f
(1.4448911613551451e+267)#f(+nan.0 +nan.0)+nan.0invalidexit00.127603#f
(6.175763333928271e+93)#f(+nan.0 +nan.0)+nan.0invalidexit00.105381#f
(-2.436443667970667e+203)#f(+nan.0 +nan.0)+nan.0invalidexit00.090105#f
(4.252762074249847e+263)#f(+nan.0 +nan.0)+nan.0invalidexit00.08537#f
(4.081711331062092e-263)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.104542#f
(8.10701345959679e+297)#f(+nan.0 +nan.0)+nan.0invalidexit00.089691#f
(254363876.5341204)#f(+nan.0 +nan.0)+nan.0invalidexit00.097772#f
(1.728402066101224e+41)#f(+nan.0 +nan.0)+nan.0invalidexit00.12178#f
(-7.922532335889991e-246)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.124659#f
(-1.5068287345511204e+233)#f(+nan.0 +nan.0)+nan.0invalidexit00.135652#f
(4.145692711652061e-200)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.119327#f
(-4.607508408026144e+166)#f(+nan.0 +nan.0)+nan.0invalidexit00.11757000000000001#f
(-1.0450040513079687e+58)#f(+nan.0 +nan.0)+nan.0invalidexit00.109284#f
(7.452310827048563e+93)#f(+nan.0 +nan.0)+nan.0invalidexit00.059126000000000005#f
(4.200155731779063e+70)#f(+nan.0 +nan.0)+nan.0invalidexit00.125407#f
(7.392103841695203e-48)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.102004#f
(1.6809831367580324e+247)#f(+nan.0 +nan.0)+nan.0invalidexit00.058359999999999995#f
(2.9288901311427373e+150)#f(+nan.0 +nan.0)+nan.0invalidexit00.11966199999999999#f
(-2.217247681370031e-144)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.12758299999999997#f
(-9.122058071050936e+291)#f(+nan.0 +nan.0)+nan.0invalidexit00.059604#f
(-1046335476852566100.0)#f(+nan.0 +nan.0)+nan.0invalidexit00.098247#f
(4.5468017659860553e-299)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.067704#f
(1.0650527693768576e-118)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.119574#f
(-6.2771236694271605e-264)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.06601#f
(1.356337542603042e+270)#f(+nan.0 +nan.0)+nan.0invalidexit00.12544#f
(6.0334589586338665e+88)#f(+nan.0 +nan.0)+nan.0invalidexit00.131689#f
(-4.6024650243026865e-230)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.13727699999999998#f
(1.9506929465817524e-54)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.060305#f
(-1.1037123592128641e-213)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.120368#f
(-6.359517535548266e+124)#f(+nan.0 +nan.0)+nan.0invalidexit00.12615700000000002#f
(-2.4882906017903597e+231)#f(+nan.0 +nan.0)+nan.0invalidexit00.088777#f
(6.232879852982152e-194)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.116759#f
(2.7815740491067996e-89)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.122464#f
(-5.9500099756422185e-291)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.107642#f
(2.7489082461538025e+53)#f(+nan.0 +nan.0)+nan.0invalidexit00.111806#f
(9.003490835986774e+80)#f(+nan.0 +nan.0)+nan.0invalidexit00.106263#f
(-3.281969686427321e+239)#f(+nan.0 +nan.0)+nan.0invalidexit00.110944#f
(2.169982865798581e+303)#f(+nan.0 +nan.0)+nan.0invalidexit00.053553#f
(8.535082154706885e-119)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.12746#f
(-2.625100179270543e+160)#f(+nan.0 +nan.0)+nan.0invalidexit00.08519800000000001#f
(5.0871421506048416e+35)#f(+nan.0 +nan.0)+nan.0invalidexit00.12534499999999998#f
(8.911843239471942e-128)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.12290200000000001#f
(-5.902655928097003e+172)#f(+nan.0 +nan.0)+nan.0invalidexit00.085301#f
(7.018628781851679e+124)#f(+nan.0 +nan.0)+nan.0invalidexit00.087274#f
(4.335256629042642e+239)#f(+nan.0 +nan.0)+nan.0invalidexit00.12533#f
(1.1327580454866005e+180)#f(+nan.0 +nan.0)+nan.0invalidexit00.10917#f
(4.902204825501046e-232)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.117587#f
(-1.0677116222743206e-92)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.11157399999999999#f
(3.61645774732606e+178)#f(+nan.0 +nan.0)+nan.0invalidexit00.11344499999999999#f
(9.772386254202398e+297)#f(+nan.0 +nan.0)+nan.0invalidexit00.109161#f
(-5.978187290816706e+163)#f(+nan.0 +nan.0)+nan.0invalidexit00.093385#f
(2.1471820341055805e+253)#f(+nan.0 +nan.0)+nan.0invalidexit00.12762099999999998#f
(2.3692547321159184e+242)#f(+nan.0 +nan.0)+nan.0invalidexit00.066412#f
(-3.07977298039538e+268)#f(+nan.0 +nan.0)+nan.0invalidexit00.09046900000000001#f
(2.7544399290773436e-272)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.11835#f
(-1.0823943015835095e+88)#f(+nan.0 +nan.0)+nan.0invalidexit00.10778700000000001#f
(-1.7536148814288473e-20)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.091559#f
(-4.861091381858138e-37)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.109071#f
(9.445289360926386e-140)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.162931#f
(-8.005625397052334e-303)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.117927#f
(-21400944110481250.0)#f(+nan.0 +nan.0)+nan.0invalidexit00.13974699999999998#f
(7.307414408655564e+123)#f(+nan.0 +nan.0)+nan.0invalidexit00.12413300000000001#f
(-3.894730476443268e-18)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.116757#f
(-7.621080810906841e+180)#f(+nan.0 +nan.0)+nan.0invalidexit00.12457399999999999#f
(3.1481050942625623e-176)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.11037200000000001#f
(4.484411445337435e-226)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.133538#f
(3.6209056948080254e+158)#f(+nan.0 +nan.0)+nan.0invalidexit00.109006#f
(-8.49171661085995e-220)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.064293#f
(5.892481787129736e-252)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.132968#f
(2.1892144579644843e+117)#f(+nan.0 +nan.0)+nan.0invalidexit00.124465#f
(-1.2028794480295752e+79)#f(+nan.0 +nan.0)+nan.0invalidexit00.103144#f
(8.594325003743321e-66)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.12103900000000001#f
(3.625778506965928e+215)#f(+nan.0 +nan.0)+nan.0invalidexit00.12236899999999999#f
(-1.4779931382167413e+207)#f(+nan.0 +nan.0)+nan.0invalidexit00.130916#f
(3.890750103796304e+66)#f(+nan.0 +nan.0)+nan.0invalidexit00.05817#f
(2.579626167619924e-48)3.141592653589793(+nan.0 +nan.0)+nan.0validexit10.12479799999999999#f
(-1.737742019377996e-300)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.06172300000000001#f
(1.1136981342541097e+130)#f(+nan.0 +nan.0)+nan.0invalidexit00.118916#f
(6.633275218498859e+298)#f(+nan.0 +nan.0)+nan.0invalidexit00.125539#f
(2.58472427917989e+241)#f(+nan.0 +nan.0)+nan.0invalidexit00.057111#f
(-2.7969015402227663e+121)#f(+nan.0 +nan.0)+nan.0invalidexit00.113355#f
(-2.1761299395545184e+218)#f(+nan.0 +nan.0)+nan.0invalidexit00.20302499999999998#f
(5.281353127954048e+208)#f(+nan.0 +nan.0)+nan.0invalidexit00.123031#f
(-1.625735318241207e+50)#f(+nan.0 +nan.0)+nan.0invalidexit00.107978#f
(26.555884564726362)#f(+nan.0 +nan.0)+nan.0invalidexit00.096562#f
(4.842590276790161e-210)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.10037#f
(9.889848458125675e+73)#f(+nan.0 +nan.0)+nan.0invalidexit00.119858#f
(-8.305427151139969e-191)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.09418699999999999#f
(-4.122091892366067e-252)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.127198#f
(-4.281138991483191e+163)#f(+nan.0 +nan.0)+nan.0invalidexit00.132628#f
(-5.120568410179896e+123)#f(+nan.0 +nan.0)+nan.0invalidexit00.08747899999999999#f
(3.742385367882932e-304)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.0916#f
(8.71812802122346e+258)#f(+nan.0 +nan.0)+nan.0invalidexit00.091732#f
(-1.9361379173789867e-259)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.093992#f
(5.539793923680985e-212)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.093472#f
(2.0628856650490613e+33)#f(+nan.0 +nan.0)+nan.0invalidexit00.053519#f
(-3.46540493450569e-240)3.141592653589793(+nan.0 +nan.0)+nan.0validexit30.05974#f
(4.068796170638335e+179)#f(+nan.0 +nan.0)+nan.0invalidexit00.055595#f
(-2.2165225298863628e-91)3.141592653589793(+nan.0 +nan.0)+nan.0validexit20.084695#f
Sollya timings
Total time spent in Sollya 1.7s
Bogosity

preprocess522.0ms (0.6%)

Algorithm
egg-herbie
Rules
586×fma-neg
504×sub-neg
432×fma-define
359×unsub-neg
342×distribute-lft-neg-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
022200
169200
2188184
3652184
42521184
55095184
66375184
77330184
Stop Event
node limit
Calls
Call 1
Inputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64))))
(neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64)))))
Outputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64))))
(neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64)))))
(neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (fma.f64 v v #s(literal -1 binary64)))))
(neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64)))))
(neg.f64 (acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64)))))
Symmetry

(abs v)

Compiler

Compiled 15 to 9 computations (40% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune3.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.0%
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
Compiler

Compiled 30 to 18 computations (40% saved)

simplify8.0ms (0%)

Algorithm
egg-herbie
Rules
12×neg-mul-1
10×unsub-neg
*-commutative
+-commutative
distribute-lft-neg-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01453
12753
24153
35553
47453
510153
610953
711153
Stop Event
saturated
Calls
Call 1
Inputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
Outputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))

soundness1.0ms (0%)

Stop Event
fuel
Compiler

Compiled 15 to 10 computations (33.3% saved)

preprocess127.0ms (0.1%)

Remove

(abs v)

Compiler

Compiled 120 to 78 computations (35% saved)

end0.0ms (0%)

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