Average Error: 0.1 → 0.2
Time: 18.7s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return ((double) (lambda1 + ((double) atan2(((double) (((double) (((double) sin(theta)) * ((double) sin(delta)))) * ((double) cos(phi1)))), ((double) (((double) cos(delta)) - ((double) (((double) sin(phi1)) * ((double) sin(((double) asin(((double) (((double) (((double) sin(phi1)) * ((double) cos(delta)))) + ((double) (((double) (((double) cos(phi1)) * ((double) sin(delta)))) * ((double) cos(theta))))))))))))))))));
}

↓
double code(double lambda1, double phi1, double phi2, double delta, double theta) {
	return ((double) (lambda1 + ((double) atan2(((double) (((double) (((double) sin(theta)) * ((double) sin(delta)))) * ((double) cos(phi1)))), ((double) (((double) (((double) (((double) pow(((double) cos(delta)), 6.0)) - ((double) (((double) pow(((double) (((double) (((double) cos(delta)) * ((double) sin(phi1)))) + ((double) (((double) cos(phi1)) * ((double) (((double) sin(delta)) * ((double) cos(theta)))))))), 6.0)) * ((double) pow(((double) sin(phi1)), 6.0)))))) / ((double) (((double) pow(((double) cos(delta)), 3.0)) + ((double) (((double) pow(((double) (((double) (((double) cos(delta)) * ((double) sin(phi1)))) + ((double) (((double) cos(phi1)) * ((double) (((double) sin(delta)) * ((double) cos(theta)))))))), 3.0)) * ((double) pow(((double) sin(phi1)), 3.0)))))))) / ((double) (((double) (((double) cos(delta)) * ((double) cos(delta)))) + ((double) (((double) sin(phi1)) * ((double) (((double) sin(((double) asin(((double) (((double) (((double) cos(delta)) * ((double) sin(phi1)))) + ((double) (((double) cos(phi1)) * ((double) (((double) sin(delta)) * ((double) cos(theta)))))))))))) * ((double) (((double) cos(delta)) + ((double) (((double) sin(phi1)) * ((double) sin(((double) asin(((double) (((double) (((double) cos(delta)) * ((double) sin(phi1)))) + ((double) (((double) cos(phi1)) * ((double) (((double) sin(delta)) * ((double) cos(theta))))))))))))))))))))))))))));
}

Error
Bits error versus lambda1
Bits error versus phi1
Bits error versus phi2
Bits error versus delta
Bits error versus theta
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 0.1
    \[\]
  2. Using strategy rm
  3. Applied flip3--0.1
    \[\leadsto \]
  4. Simplified0.2
    \[\leadsto \]
  5. Simplified0.2
    \[\leadsto \]
  6. Taylor expanded around inf 0.1
    \[\leadsto \]
  7. Simplified0.1
    \[\leadsto \]
  8. Using strategy rm
  9. Applied flip--0.2
    \[\leadsto \]
  10. Simplified0.2
    \[\leadsto \]
  11. Simplified0.2
    \[\leadsto \]
  12. Final simplification0.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (lambda1 phi1 phi2 delta theta)
  :name "Destination given bearing on a great circle"
  :precision binary64
  (+ lambda1 (atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))