Average Error: 13.0 → 0.3
Time: 22.8s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double lambda1, double lambda2, double phi1, double phi2) {
	return ((double) atan2(((double) (((double) sin(((double) (lambda1 - lambda2)))) * ((double) cos(phi2)))), ((double) (((double) (((double) cos(phi1)) * ((double) sin(phi2)))) - ((double) (((double) (((double) sin(phi1)) * ((double) cos(phi2)))) * ((double) cos(((double) (lambda1 - lambda2))))))))));
}

↓
double code(double lambda1, double lambda2, double phi1, double phi2) {
	return ((double) atan2(((double) (((double) (((double) (((double) sin(lambda1)) * ((double) cos(lambda2)))) - ((double) (((double) cos(lambda1)) * ((double) sin(lambda2)))))) * ((double) cos(phi2)))), ((double) (((double) (((double) cos(phi1)) * ((double) sin(phi2)))) - ((double) (((double) cos(phi2)) * ((double) (((double) cbrt(((double) (((double) (((double) cos(lambda2)) * ((double) cos(lambda1)))) + ((double) (((double) sin(lambda1)) * ((double) sin(lambda2)))))))) * ((double) (((double) sin(phi1)) * ((double) (((double) cbrt(((double) (((double) (((double) cos(lambda2)) * ((double) cos(lambda1)))) + ((double) (((double) sin(lambda1)) * ((double) sin(lambda2)))))))) * ((double) cbrt(((double) (((double) (((double) cos(lambda2)) * ((double) cos(lambda1)))) + ((double) (((double) sin(lambda1)) * ((double) sin(lambda2))))))))))))))))))));
}

Error
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 13.0
    \[\]
  2. Simplified13.0
    \[\leadsto \]
  3. Using strategy rm
  4. Applied sin-diff6.6
    \[\leadsto \]
  5. Using strategy rm
  6. Applied cos-diff0.2
    \[\leadsto \]
  7. Using strategy rm
  8. Applied add-cube-cbrt0.3
    \[\leadsto \]
  9. Applied associate-*r*0.3
    \[\leadsto \]
  10. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (lambda1 lambda2 phi1 phi2)
  :name "Bearing on a great circle"
  :precision binary64
  (atan2 (* (sin (- lambda1 lambda2)) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))))