Average Error: 17.0 → 3.8
Time: 20.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return ((double) (((double) acos(((double) (((double) (((double) sin(phi1)) * ((double) sin(phi2)))) + ((double) (((double) (((double) cos(phi1)) * ((double) cos(phi2)))) * ((double) cos(((double) (lambda1 - lambda2)))))))))) * R));
}

↓
double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return ((double) (((double) acos(((double) (((double) (((double) sin(phi1)) * ((double) sin(phi2)))) + ((double) (((double) (((double) cos(lambda1)) * ((double) (((double) cos(lambda2)) * ((double) (((double) cos(phi1)) * ((double) cos(phi2)))))))) + ((double) cbrt(((double) pow(((double) (((double) cos(phi1)) * ((double) (((double) (((double) cos(phi2)) * ((double) sin(lambda2)))) * ((double) sin(lambda1)))))), 3.0)))))))))) * R));
}

Error
Bits error versus R
Bits error versus lambda1
Bits error versus lambda2
Bits error versus phi1
Bits error versus phi2
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 17.0
    \[\]
  2. Using strategy rm
  3. Applied cos-diff3.7
    \[\leadsto \]
  4. Applied distribute-lft-in3.7
    \[\leadsto \]
  5. Simplified3.7
    \[\leadsto \]
  6. Simplified3.7
    \[\leadsto \]
  7. Using strategy rm
  8. Applied add-cbrt-cube3.7
    \[\leadsto \]
  9. Applied add-cbrt-cube3.7
    \[\leadsto \]
  10. Applied cbrt-unprod3.7
    \[\leadsto \]
  11. Applied add-cbrt-cube3.8
    \[\leadsto \]
  12. Applied cbrt-unprod3.8
    \[\leadsto \]
  13. Applied add-cbrt-cube3.8
    \[\leadsto \]
  14. Applied cbrt-unprod3.8
    \[\leadsto \]
  15. Simplified3.8
    \[\leadsto \]
  16. Final simplification3.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Spherical law of cosines"
  :precision binary64
  (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R))