Average Error: 39.2 → 34.5
Time: 13.1s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	return ((double) (R * ((double) sqrt(((double) (((double) (((double) (((double) (lambda1 - lambda2)) * ((double) cos(((double) (((double) (phi1 + phi2)) / 2.0)))))) * ((double) (((double) (lambda1 - lambda2)) * ((double) cos(((double) (((double) (phi1 + phi2)) / 2.0)))))))) + ((double) (((double) (phi1 - phi2)) * ((double) (phi1 - phi2))))))))));
}

↓
double code(double R, double lambda1, double lambda2, double phi1, double phi2) {
	double VAR;
	if ((phi1 <= -5.1932364225039894e-40)) {
		VAR = ((double) (R * ((double) (phi2 - phi1))));
	} else {
		double VAR_1;
		if (((phi1 <= 8.893889606600523e-137) || !(phi1 <= 2.1628661069747332e-23))) {
			VAR_1 = ((double) (R * ((double) sqrt(((double) (((double) (((double) (lambda1 - lambda2)) * ((double) (((double) (lambda1 - lambda2)) * ((double) (((double) cos(((double) (((double) (phi1 + phi2)) / 2.0)))) * ((double) cos(((double) (((double) (phi1 + phi2)) / 2.0)))))))))) + ((double) (((double) (phi1 - phi2)) * ((double) (phi1 - phi2))))))))));
		} else {
			VAR_1 = ((double) (R * ((double) (((double) sqrt(((double) (((double) (((double) (lambda1 - lambda2)) * ((double) (((double) (((double) (lambda1 - lambda2)) * ((double) (1.0 + ((double) cos(((double) (((double) (((double) (phi1 + phi2)) / 2.0)) * 2.0)))))))) * ((double) (((double) (phi1 * phi1)) + ((double) (phi2 * ((double) (phi1 + phi2)))))))))) + ((double) (2.0 * ((double) (((double) (phi1 - phi2)) * ((double) (((double) pow(phi1, 3.0)) - ((double) pow(phi2, 3.0)))))))))))) / ((double) sqrt(((double) (2.0 * ((double) (((double) (phi1 * phi1)) + ((double) (phi2 * ((double) (phi1 + phi2))))))))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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. Split input into 3 regimes
  2. if  phi1  < -5.1932364225039894e-40
    1. Initial program 46.2
      \[\]
    2. Simplified46.2
      \[\leadsto \]
    3. Taylor expanded around 0 28.6
      \[\leadsto \]
    if -5.1932364225039894e-40 <  phi1  < 8.8938896066005225e-137 or 2.16286610697473319e-23 <  phi1 
    1. Initial program 37.4
      \[\]
    2. Simplified37.4
      \[\leadsto \]
    if 8.8938896066005225e-137 <  phi1  < 2.16286610697473319e-23
    1. Initial program 30.7
      \[\]
    2. Simplified30.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied flip3--34.5
      \[\leadsto \]
    5. Applied associate-*r/37.5
      \[\leadsto \]
    6. Applied cos-mult37.5
      \[\leadsto \]
    7. Applied associate-*r/37.5
      \[\leadsto \]
    8. Applied associate-*r/37.6
      \[\leadsto \]
    9. Applied frac-add38.7
      \[\leadsto \]
    10. Applied sqrt-div38.8
      \[\leadsto \]
    11. Simplified32.7
      \[\leadsto \]
    12. Simplified32.7
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification34.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Equirectangular approximation to distance on a great circle"
  :precision binary64
  (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))