Average Error: 0 → 0
Time: 8.1m
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 r4426721 = lambda1;
        double r4426722 = phi2;
        double r4426723 = cos(r4426722);
        double r4426724 = lambda2;
        double r4426725 = r4426721 - r4426724;
        double r4426726 = sin(r4426725);
        double r4426727 = r4426723 * r4426726;
        double r4426728 = phi1;
        double r4426729 = cos(r4426728);
        double r4426730 = cos(r4426725);
        double r4426731 = r4426723 * r4426730;
        double r4426732 = r4426729 + r4426731;
        double r4426733 = atan2(r4426727, r4426732);
        double r4426734 = r4426721 + r4426733;
        return r4426734;
}
↓
double f(double lambda1, double lambda2, double phi1, double phi2) {
        double r4426735 = phi2;
        double r4426736 = cos(r4426735);
        double r4426737 = lambda1;
        double r4426738 = lambda2;
        double r4426739 = r4426737 - r4426738;
        double r4426740 = sin(r4426739);
        double r4426741 = r4426736 * r4426740;
        double r4426742 = cos(r4426739);
        double r4426743 = r4426736 * r4426742;
        double r4426744 = phi1;
        double r4426745 = cos(r4426744);
        double r4426746 = r4426743 + r4426745;
        double r4426747 = atan2(r4426741, r4426746);
        double r4426748 = r4426747 + r4426737;
        return r4426748;
}

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 2019125 
(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)))))))