Average Error: 16.7 → 4.0
Time: 30.1s
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) exp(((double) log(((double) log(((double) exp(((double) acos(((double) (((double) (((double) sin(phi1)) * ((double) sin(phi2)))) + ((double) (((double) cos(phi1)) * ((double) (((double) cos(phi2)) * ((double) (((double) (((double) cos(lambda1)) * ((double) cos(lambda2)))) + ((double) (((double) sin(lambda1)) * ((double) sin(lambda2)))))))))))))))))))))) * 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 16.7
    \[\]
  2. Simplified16.7
    \[\leadsto \]
  3. Using strategy rm
  4. Applied cos-diff4.0
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-exp-log4.0
    \[\leadsto \]
  7. Using strategy rm
  8. Applied add-log-exp4.0
    \[\leadsto \]
  9. Final simplification4.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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))