Eccentricity of an ellipse

Time bar (total: 36.6s)

analyze22.0ms (0.1%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%37.5%62.5%0%0%0%0
0%0%37.5%62.5%0%0%0%1
0%0%18.7%81.3%0%0%0%2
0%0%9.4%90.6%0%0%0%3
0%0%9.4%90.6%0%0%0%4
0%0%7%93%0%0%0%5
20%1.2%4.7%94.1%0%0%0%6
25%1.2%3.5%95.3%0%0%0%7
40%1.8%2.6%95.6%0%0%0%8
51.9%2%1.9%96%0%0%0%9
64.7%2.4%1.3%96.3%0%0%0%10
72.9%2.6%1%96.5%0%0%0%11
80.2%2.7%0.7%96.6%0%0%0%12
Compiler

Compiled 26 to 15 computations (42.3% saved)

sample36.1s (98.7%)

Results
4.1s8256×0valid
531.0ms8222×0valid-sollya
426.0ms774×0precondition
21.0ms34×0exit-sollya
Sollya Eval
PtRival-outSollya-intervalSollya-pointstatusSollya statusRival itersollya-timecheck
(1.6529468362809845e-29 4.0868415371191154e-227)1.0(1.0 1.0)+nan.0validexit00.21038400000000002#f
(2.6870068903747376e-135 7.831763393413308e-172)1.0(1.0 1.0)+nan.0validexit00.220325#f
(2.7653374874655388e-145 1.4246182855957214e-152)0.9999999999999987(0.9999999999999987 0.9999999999999987)+nan.0validexit00.214456#f
(6.165058118849083e-78 6.091597216946175e-198)1.0(1.0 1.0)+nan.0validexit00.22202300000000003#f
(2.856074732003167e-237 1.229794168828763e-288)1.0(1.0 1.0)+nan.0validexit00.231901#f
(1.1604697049577352e-58 8.392048584956033e-90)1.0(1.0 1.0)+nan.0validexit00.184547#f
(1.1017046243613422e-199 2.866438276015876e-248)1.0(1.0 1.0)+nan.0validexit00.21012599999999998#f
(9.640007238214675e-182 4.045663400036988e-213)1.0(1.0 1.0)+nan.0validexit00.224748#f
(5.037987913893202e-91 1.663414871779597e-304)1.0(+nan.0 +nan.0)+nan.0validexit05.0#f
(1.956396899414292e-226 1.313270966376458e-264)1.0(1.0 1.0)+nan.0validexit00.22145199999999998#f
(6.724346700491296e-22 6.952087551340759e-36)1.0(1.0 1.0)+nan.0validexit00.169381#f
(1.2853386936220203e-214 2.1751742459243684e-243)1.0(1.0 1.0)+nan.0validexit00.134028#f
(1.873762566725337e-263 9.366990024391928e-296)1.0(1.0 1.0)+nan.0validexit00.26190399999999997#f
(9.735378947455714e-62 2.44817297515304e-66)0.9999999996838097(+nan.0 +nan.0)+nan.0validexit05.0#f
(7.159944569742945e-34 5.6122782306681615e-188)1.0(1.0 1.0)+nan.0validexit00.169569#f
(3.704631783781295e-250 6.139066098380983e-294)1.0(1.0 1.0)+nan.0validexit00.206674#f
(6.358173878964242e-36 5.172718366554619e-249)1.0(1.0 1.0)+nan.0validexit00.210553#f
(6.510151684422602e-95 3.822350580026498e-212)1.0(1.0 1.0)+nan.0validexit00.127323#f
(2.7546728434975015e-113 1.6077500985298114e-225)1.0(1.0 1.0)+nan.0validexit00.218906#f
(1.6142043480136778e-98 9.465130552951852e-224)1.0(1.0 1.0)+nan.0validexit00.226726#f
(8.173077688622755e-16 1.7116177567067548e-161)1.0(1.0 1.0)+nan.0validexit00.209369#f
(1.340053689416582e-29 1.0785887885603784e-230)1.0(1.0 1.0)+nan.0validexit00.219243#f
(6.6415903768372255e-52 3.314019583405144e-155)1.0(1.0 1.0)+nan.0validexit00.233215#f
(1.587748892534755e-42 6.725428764098075e-245)1.0(1.0 1.0)+nan.0validexit00.22065200000000001#f
(2.53995699671892e-39 1.348065423749568e-220)1.0(1.0 1.0)+nan.0validexit00.169758#f
(6.308983053639205e-273 3.449416428265873e-305)1.0(1.0 1.0)+nan.0validexit00.108158#f
(5.705828503971078e-284 4.2637490881243754e-290)0.9999999999997208(0.9999999999997208 0.9999999999997208)+nan.0validexit00.175365#f
(3.239671709765879e-36 1.7124853078242944e-307)1.0(+nan.0 +nan.0)+nan.0validexit05.0#f
(4.089017583161326e-177 2.7550820635336e-185)1.0(1.0 1.0)+nan.0validexit00.21461#f
(1.3468376021684489e-149 1.7228988430965292e-211)1.0(1.0 1.0)+nan.0validexit00.219761#f
(5.071088726514521e-28 8.276097287418314e-176)1.0(1.0 1.0)+nan.0validexit00.20741400000000002#f
(1.3034510819773973e-272 1.1775298442471864e-277)0.999999999959194(0.999999999959194 0.999999999959194)+nan.0validexit00.218039#f
(3.3782551893863774e-77 3.701201880528106e-239)1.0(1.0 1.0)+nan.0validexit00.201608#f
(9.564646457213063e-266 1.1235655402559139e-283)1.0(1.0 1.0)+nan.0validexit00.11244299999999999#f
Sollya timings
Total time spent in Sollya 553.0ms
Bogosity

preprocess212.0ms (0.6%)

Algorithm
egg-herbie
Rules
707×times-frac
477×div-sub
450×fma-neg
318×fabs-mul
295×associate-*l/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032407
1106323
2390295
32599295
47059295
Stop Event
node limit
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a))))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (*.f64 b b))))
Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 b (/.f64 b (*.f64 a a))))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 b (/.f64 b (*.f64 a a))))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 b (/.f64 b (*.f64 a a))))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 b (/.f64 b (*.f64 a a))))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a))))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))))
(neg.f64 (sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 b (/.f64 b (*.f64 a a)))))))
(neg.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a)))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))))
(neg.f64 (sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 b (/.f64 b (*.f64 a a)))))))
(neg.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (*.f64 b b))))
(sqrt.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 a b) (/.f64 a b)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 a b) (/.f64 a b) #s(literal -1 binary64))))
(sqrt.f64 (fabs.f64 (fma.f64 a (/.f64 a (*.f64 b b)) #s(literal -1 binary64))))
Symmetry

(abs a)

(abs b)

Compiler

Compiled 15 to 8 computations (46.7% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune127.0ms (0.3%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
79.2%
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Rules
sub-neg
+-commutative
*-commutative
neg-sub0
neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01457
12257
23557
34957
46057
56657
66957
Stop Event
saturated
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (/.f64 (fabs.f64 (-.f64 (*.f64 a a) (*.f64 b b))) (*.f64 a a)))

soundness1.0ms (0%)

Stop Event
fuel
Compiler

Compiled 15 to 8 computations (46.7% saved)

preprocess121.0ms (0.3%)

Remove

(abs b)

(abs a)

Compiler

Compiled 180 to 96 computations (46.7% saved)

end0.0ms (0%)

Profiling

Loading profile data...