Spherical law of cosines

Time bar (total: 57.9s)

analyze3.9s (6.8%)

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
0%0%99.8%0.2%0%0%0%10
1.6%1.6%98.2%0.2%0%0%0%11
1.6%1.6%98.2%0.2%0%0%0%12
Compiler

Compiled 25 to 18 computations (28% saved)

sample53.3s (92%)

Results
18.6s6326×1valid-rival
5.7s6164×1valid-sollya
2.7s1914×0valid-rival
401.0ms1904×0valid-sollya
810.0ms162×1exit-sollya
101.0ms16×2valid-rival
31.0ms12×2valid-sollya
50.0ms10×0exit-sollya
20.0ms4×2exit-sollya
Bogosity

preprocess579.0ms (1%)

Algorithm
1×egg-herbie
Rules
1840×fma-define
664×fma-neg
625×distribute-lft-in
395×distribute-lft-neg-in
374×unsub-neg
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01391768
13001768
25461752
39691752
417771752
528941752
632821752
740401752
847011752
954921752
1061381752
1164271752
1266211752
1375221752
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (neg.f64 R))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2)))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 (neg.f64 phi1)) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 (neg.f64 phi1)) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 (neg.f64 phi2))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 (neg.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (neg.f64 R)))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2))))) R))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2)))))) R))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 (neg.f64 phi1)) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 (neg.f64 phi1)) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 (neg.f64 phi2))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 (neg.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2))))) R))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 R lambda2))))) lambda1)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R))))) lambda2)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 R) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 R) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) phi1)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 R)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 R)) (cos.f64 (-.f64 lambda1 lambda2))))) phi2)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 (-.f64 phi1 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda1)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda1)) (cos.f64 (-.f64 phi2 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda2) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 phi1))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi2) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
Outputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
(*.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
(*.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (neg.f64 R))
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (neg.f64 R))
(*.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (neg.f64 R))
(*.f64 R (neg.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 (+.f64 lambda1 lambda2))))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (+.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2)))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 (+.f64 lambda1 lambda2))))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (+.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 (neg.f64 phi1)) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 (neg.f64 phi1)) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (neg.f64 (sin.f64 phi1)) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2))))))
(*.f64 R (acos.f64 (-.f64 (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 (neg.f64 phi2))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 (neg.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (neg.f64 (sin.f64 phi1)) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2))))))
(*.f64 R (acos.f64 (-.f64 (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (neg.f64 R)))
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
(*.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2))))) R))
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)))))) (neg.f64 R))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 (+.f64 lambda1 lambda2))))))))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (+.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2)))))) R))
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)))))) (neg.f64 R))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 (+.f64 lambda1 lambda2))))))))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (+.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 (neg.f64 phi1)) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 (neg.f64 phi1)) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R))
(*.f64 (acos.f64 (fma.f64 (neg.f64 (sin.f64 phi1)) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (neg.f64 R))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2))))))
(*.f64 R (neg.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2)))))))
(*.f64 R (neg.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2)))))))
(*.f64 R (neg.f64 (acos.f64 (-.f64 (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
(neg.f64 (*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 (neg.f64 phi2))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 (neg.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2))))) R))
(*.f64 (acos.f64 (fma.f64 (neg.f64 (sin.f64 phi1)) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (neg.f64 R))
(*.f64 (neg.f64 R) (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2))))))
(*.f64 R (neg.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2)))))))
(*.f64 R (neg.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))) (*.f64 (sin.f64 phi1) (neg.f64 (sin.f64 phi2)))))))
(*.f64 R (neg.f64 (acos.f64 (-.f64 (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 R lambda2))))) lambda1)
(*.f64 lambda1 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 R lambda2)))))))
(*.f64 lambda1 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 R lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R))))) lambda2)
(*.f64 lambda2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R))))))
(*.f64 lambda2 (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 lambda2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 R)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 R) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 R) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) phi1)
(*.f64 phi1 (acos.f64 (fma.f64 (sin.f64 R) (sin.f64 phi2) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 R))))))
(*.f64 phi1 (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 R) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 R))))))
(*.f64 phi1 (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 R) (*.f64 (cos.f64 R) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))
(*.f64 phi1 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi2) (cos.f64 R)) (*.f64 (sin.f64 phi2) (sin.f64 R)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 R)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 R)) (cos.f64 (-.f64 lambda1 lambda2))))) phi2)
(*.f64 phi2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 R) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 R))))))
(*.f64 phi2 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 R)) (*.f64 (sin.f64 phi1) (sin.f64 R)))))
(*.f64 phi2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 R) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 R))))))
(*.f64 phi2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 R) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda2 lambda1)) (cos.f64 R))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
(*.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 (-.f64 phi1 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 phi2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda1) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 lambda1)) (cos.f64 (-.f64 phi1 lambda2))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda1) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 (-.f64 lambda2 phi1)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 phi1)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda1)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda1)) (cos.f64 (-.f64 phi2 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 lambda1) (cos.f64 (-.f64 phi2 lambda2)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda2) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 phi1))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi1))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi2) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi1)) (*.f64 (sin.f64 phi2) (sin.f64 lambda2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 lambda2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 lambda2) (cos.f64 (-.f64 lambda1 phi2)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 lambda2)))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 phi2))) (*.f64 (sin.f64 phi1) (sin.f64 lambda2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi2) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
(*.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
Symmetry

(negabs R)

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 24 to 17 computations (29.2% saved)

eval0.0ms (0%)

Compiler

Compiled 5 to 5 computations (0% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
73.2%
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify45.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02682
13382
23882
34082
44182
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
Outputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 24 to 17 computations (29.2% saved)

preprocess98.0ms (0.2%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

(negabs R)

Compiler

Compiled 384 to 272 computations (29.2% saved)

end0.0ms (0%)

Profiling

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