Equirectangular approximation to distance on a great circle

Time bar (total: 41.2s)

analyze2.4s (5.8%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.8%0.2%0%0%0%0
0%0%99.8%0.2%0%0%0%1
0%0%99.8%0.2%0%0%0%2
0%0%99.8%0.2%0%0%0%3
0%0%99.8%0.2%0%0%0%4
0%0%99.8%0.2%0%0%0%5
0%0%99.8%0.2%0%0%0%6
0%0%99.8%0.2%0%0%0%7
0%0%99.8%0.2%0%0%0%8
0%0%99.8%0.2%0%0%0%9
3.1%3.1%96.6%0.2%0%0%0%10
15.6%15.6%84.2%0.2%0%0%0%11
15.6%15.6%84.2%0.2%0%0%0%12
Compiler

Compiled 38 to 18 computations (52.6% saved)

sample38.6s (93.7%)

Results
3.0s6039×0valid-rival
1.8s5960×0valid-sollya
3.6s2217×1valid-rival
1.3s2177×1valid-sollya
395.0ms79×0exit-sollya
200.0ms40×1exit-sollya
Bogosity

preprocess178.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
631×distribute-lft-neg-out
539×distribute-rgt-neg-out
494×distribute-rgt-in
494×distribute-lft-in
477×unsub-neg
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01591548
14001540
210451524
349171516
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 (neg.f64 R) (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 (neg.f64 phi1) phi2) (-.f64 (neg.f64 phi1) phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 (neg.f64 phi2)) (-.f64 phi1 (neg.f64 phi2))))))
(neg.f64 (*.f64 (neg.f64 R) (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 (neg.f64 phi1) phi2) (-.f64 (neg.f64 phi1) phi2))))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 (neg.f64 phi2)) (-.f64 phi1 (neg.f64 phi2)))))))
(*.f64 lambda1 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 R lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 R lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 lambda2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 R) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 R) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 phi1 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 R phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 R phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 R phi2) (-.f64 R phi2)))))
(*.f64 phi2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 R) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 R) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 R) (-.f64 phi1 R)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda2 lambda1) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda2 lambda1) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 phi1 lambda2) (cos.f64 (/.f64 (+.f64 lambda1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 phi1 lambda2) (cos.f64 (/.f64 (+.f64 lambda1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 lambda1 phi2) (-.f64 lambda1 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 phi2 lambda2) (cos.f64 (/.f64 (+.f64 phi1 lambda1) #s(literal 2 binary64)))) (*.f64 (-.f64 phi2 lambda2) (cos.f64 (/.f64 (+.f64 phi1 lambda1) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 lambda1) (-.f64 phi1 lambda1)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 phi1) (cos.f64 (/.f64 (+.f64 lambda2 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 phi1) (cos.f64 (/.f64 (+.f64 lambda2 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 lambda2 phi2) (-.f64 lambda2 phi2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 phi2) (cos.f64 (/.f64 (+.f64 phi1 lambda2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 phi2) (cos.f64 (/.f64 (+.f64 phi1 lambda2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 lambda2) (-.f64 phi1 lambda2)))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))))) (*.f64 (-.f64 phi2 phi1) (-.f64 phi2 phi1)))))
Outputs
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2)))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2)))
(*.f64 (neg.f64 R) (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2)) (neg.f64 R))
(*.f64 R (neg.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2)) (-.f64 phi1 phi2)))
(*.f64 R (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2))))
(*.f64 R (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (+.f64 lambda1 lambda2))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2)) (-.f64 phi1 phi2)))
(*.f64 R (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2))))
(*.f64 R (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (+.f64 lambda1 lambda2))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 (neg.f64 phi1) phi2) (-.f64 (neg.f64 phi1) phi2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi2 phi1) #s(literal 2 binary64)))) (-.f64 (neg.f64 phi1) phi2)))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi2 phi1) #s(literal 2 binary64)))) (+.f64 phi1 phi2)))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 (neg.f64 phi2)) (-.f64 phi1 (neg.f64 phi2))))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 (neg.f64 phi2))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi1 phi2) #s(literal 2 binary64)))) (+.f64 phi1 phi2)))
(neg.f64 (*.f64 (neg.f64 R) (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2)))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 (neg.f64 lambda1) lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
(*.f64 (neg.f64 R) (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2)) (-.f64 phi1 phi2)))
(*.f64 (neg.f64 R) (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2))))
(*.f64 (neg.f64 R) (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (+.f64 lambda1 lambda2))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 (neg.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
(*.f64 (neg.f64 R) (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2)) (-.f64 phi1 phi2)))
(*.f64 (neg.f64 R) (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 (neg.f64 lambda1) lambda2))))
(*.f64 (neg.f64 R) (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (+.f64 lambda1 lambda2))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 (neg.f64 phi1) phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 (neg.f64 phi1) phi2) (-.f64 (neg.f64 phi1) phi2))))))
(*.f64 R (neg.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi2 phi1) #s(literal 2 binary64)))) (-.f64 (neg.f64 phi1) phi2))))
(*.f64 R (neg.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi2 phi1) #s(literal 2 binary64)))) (+.f64 phi1 phi2))))
(neg.f64 (*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 (neg.f64 phi2)) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 (neg.f64 phi2)) (-.f64 phi1 (neg.f64 phi2)))))))
(*.f64 R (neg.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 (neg.f64 phi2)))))
(*.f64 R (neg.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (-.f64 phi1 phi2) #s(literal 2 binary64)))) (+.f64 phi1 phi2))))
(*.f64 lambda1 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 R lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 R lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 lambda1 (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 R lambda2)) (-.f64 phi1 phi2)))
(*.f64 lambda1 (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 R lambda2))))
(*.f64 lambda2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 R) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 R) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 lambda2 (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 lambda1 R)) (-.f64 phi1 phi2)))
(*.f64 lambda2 (hypot.f64 (-.f64 phi1 phi2) (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))) (-.f64 lambda1 R))))
(*.f64 phi1 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 R phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 R phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 R phi2) (-.f64 R phi2)))))
(*.f64 phi1 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 R phi2) #s(literal 2 binary64)))) (-.f64 R phi2)))
(*.f64 phi2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 R) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 R) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 R) (-.f64 phi1 R)))))
(*.f64 phi2 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 R phi1) #s(literal 2 binary64)))) (-.f64 phi1 R)))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda2 lambda1) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda2 lambda1) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2)))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 phi1 lambda2) (cos.f64 (/.f64 (+.f64 lambda1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 phi1 lambda2) (cos.f64 (/.f64 (+.f64 lambda1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 lambda1 phi2) (-.f64 lambda1 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 phi1 lambda2) (cos.f64 (/.f64 (+.f64 lambda1 phi2) #s(literal 2 binary64)))) (-.f64 lambda1 phi2)))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 phi2 lambda2) (cos.f64 (/.f64 (+.f64 phi1 lambda1) #s(literal 2 binary64)))) (*.f64 (-.f64 phi2 lambda2) (cos.f64 (/.f64 (+.f64 phi1 lambda1) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 lambda1) (-.f64 phi1 lambda1)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 phi2 lambda2) (cos.f64 (/.f64 (+.f64 lambda1 phi1) #s(literal 2 binary64)))) (-.f64 phi1 lambda1)))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 phi1) (cos.f64 (/.f64 (+.f64 lambda2 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 phi1) (cos.f64 (/.f64 (+.f64 lambda2 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 lambda2 phi2) (-.f64 lambda2 phi2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 phi1) (cos.f64 (/.f64 (+.f64 lambda2 phi2) #s(literal 2 binary64)))) (-.f64 lambda2 phi2)))
(*.f64 R (hypot.f64 (-.f64 phi2 lambda2) (*.f64 (-.f64 lambda1 phi1) (cos.f64 (/.f64 (+.f64 lambda2 phi2) #s(literal 2 binary64))))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 phi2) (cos.f64 (/.f64 (+.f64 phi1 lambda2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 phi2) (cos.f64 (/.f64 (+.f64 phi1 lambda2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 lambda2) (-.f64 phi1 lambda2)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 phi2) (cos.f64 (/.f64 (+.f64 lambda2 phi1) #s(literal 2 binary64)))) (-.f64 phi1 lambda2)))
(*.f64 R (hypot.f64 (-.f64 phi1 lambda2) (*.f64 (-.f64 lambda1 phi2) (cos.f64 (/.f64 (+.f64 lambda2 phi1) #s(literal 2 binary64))))))
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))))) (*.f64 (-.f64 phi2 phi1) (-.f64 phi2 phi1)))))
(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (-.f64 phi1 phi2)))
Symmetry

(negabs R)

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 37 to 17 computations (54.1% saved)

eval0.0ms (0%)

Compiler

Compiled 5 to 5 computations (0% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
58.4%
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
Compiler

Compiled 74 to 34 computations (54.1% saved)

simplify5.0ms (0%)

Algorithm
1×egg-herbie
Rules
6×+-commutative
4×sub-neg
4×*-commutative
2×neg-sub0
2×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026136
134136
242136
346136
448136
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
Outputs
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 37 to 17 computations (54.1% saved)

preprocess44.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

(negabs R)

Compiler

Compiled 592 to 272 computations (54.1% saved)

end0.0ms (0%)

Profiling

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