Average Error: 0 → 0
Time: 7.7m
Precision: 64
\[\lambda_1 + \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_1 + \cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\]
↓
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right) + \cos \phi_1} + \lambda_1\]
double f(double lambda1, double lambda2, double phi1, double phi2) {
        double r5205999 = lambda1;
        double r5206000 = phi2;
        double r5206001 = cos(r5206000);
        double r5206002 = lambda2;
        double r5206003 = r5205999 - r5206002;
        double r5206004 = sin(r5206003);
        double r5206005 = r5206001 * r5206004;
        double r5206006 = phi1;
        double r5206007 = cos(r5206006);
        double r5206008 = cos(r5206003);
        double r5206009 = r5206001 * r5206008;
        double r5206010 = r5206007 + r5206009;
        double r5206011 = atan2(r5206005, r5206010);
        double r5206012 = r5205999 + r5206011;
        return r5206012;
}
↓
double f(double lambda1, double lambda2, double phi1, double phi2) {
        double r5206013 = phi2;
        double r5206014 = cos(r5206013);
        double r5206015 = lambda1;
        double r5206016 = lambda2;
        double r5206017 = r5206015 - r5206016;
        double r5206018 = sin(r5206017);
        double r5206019 = r5206014 * r5206018;
        double r5206020 = cos(r5206017);
        double r5206021 = r5206014 * r5206020;
        double r5206022 = phi1;
        double r5206023 = cos(r5206022);
        double r5206024 = r5206021 + r5206023;
        double r5206025 = atan2(r5206019, r5206024);
        double r5206026 = r5206025 + r5206015;
        return r5206026;
}


\lambda_1 + \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_1 + \cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right)}
↓
\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right) + \cos \phi_1} + \lambda_1

Error

Bits error versus lambda1

Bits error versus lambda2

Bits error versus phi1

Bits error versus phi2

Derivation

  1. Initial program 0

    \[\lambda_1 + \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_1 + \cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\]

  2. Final simplification0

    \[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right) + \cos \phi_1} + \lambda_1\]

Reproduce

herbie shell --seed 2019101 
(FPCore (lambda1 lambda2 phi1 phi2)
  :name "Midpoint on a great circle"
  (+ lambda1 (atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))))