Spherical law of cosines

Time bar (total: 14.6s)

analyze660.0ms (4.5%)

Memory
3.4MiB live, 247.3MiB allocated
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 46 to 37 computations (19.6% saved)

sample13.6s (93.3%)

Memory
-0.2MiB live, 3 002.7MiB allocated
Samples
5.1s6 293×1valid-baseline
3.5s6 293×1valid-sollya
2.6s6 293×1valid-rival
380.0ms1 944×0valid-baseline
346.0ms1 944×0valid-rival
252.0ms1 944×0valid-sollya
34.0ms19×2valid-baseline
34.0ms19×2valid-sollya
19.0ms19×2valid-rival
Bogosity

preprocess291.0ms (2%)

Memory
-4.1MiB live, 45.0MiB allocated
Algorithm
1×egg-herbie
Rules
1 840×fma-define
664×fmm-def
626×distribute-lft-in
396×distribute-lft-neg-in
322×neg-mul-1
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01391768
13001768
25461752
39691752
417801752
528971752
632851752
740441752
847051752
954931752
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%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
74.3%
(*.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)

simplify2.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
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)

soundness0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Stop Event
1×fuel
Compiler

Compiled 24 to 17 computations (29.2% saved)

preprocess32.0ms (0.2%)

Memory
1.1MiB live, 32.4MiB allocated
Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

(negabs R)

Compiler

Compiled 384 to 272 computations (29.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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