Average Error: 0 → 0
Time: 6.6m
Precision: 64
\[\lambda_1 + \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_1 + \cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\]
↓
\[\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right) + \cos \phi_1} + \lambda_1\]
\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 r755871 = lambda1;
        double r755872 = phi2;
        double r755873 = cos(r755872);
        double r755874 = lambda2;
        double r755875 = r755871 - r755874;
        double r755876 = sin(r755875);
        double r755877 = r755873 * r755876;
        double r755878 = phi1;
        double r755879 = cos(r755878);
        double r755880 = cos(r755875);
        double r755881 = r755873 * r755880;
        double r755882 = r755879 + r755881;
        double r755883 = atan2(r755877, r755882);
        double r755884 = r755871 + r755883;
        return r755884;
}
↓
double f(double lambda1, double lambda2, double phi1, double phi2) {
        double r755885 = phi2;
        double r755886 = cos(r755885);
        double r755887 = lambda1;
        double r755888 = lambda2;
        double r755889 = r755887 - r755888;
        double r755890 = sin(r755889);
        double r755891 = r755886 * r755890;
        double r755892 = cos(r755889);
        double r755893 = r755886 * r755892;
        double r755894 = phi1;
        double r755895 = cos(r755894);
        double r755896 = r755893 + r755895;
        double r755897 = atan2(r755891, r755896);
        double r755898 = r755897 + r755887;
        return r755898;
}

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 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 2019138 
(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)))))))