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

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

double f(double lambda1, double phi1, double __attribute__((unused)) phi2, double delta, double theta) {
        double r5865745 = lambda1;
        double r5865746 = theta;
        double r5865747 = sin(r5865746);
        double r5865748 = delta;
        double r5865749 = sin(r5865748);
        double r5865750 = r5865747 * r5865749;
        double r5865751 = phi1;
        double r5865752 = cos(r5865751);
        double r5865753 = r5865750 * r5865752;
        double r5865754 = cos(r5865748);
        double r5865755 = sin(r5865751);
        double r5865756 = r5865755 * r5865754;
        double r5865757 = r5865752 * r5865749;
        double r5865758 = cos(r5865746);
        double r5865759 = r5865757 * r5865758;
        double r5865760 = r5865756 + r5865759;
        double r5865761 = asin(r5865760);
        double r5865762 = sin(r5865761);
        double r5865763 = r5865755 * r5865762;
        double r5865764 = r5865754 - r5865763;
        double r5865765 = atan2(r5865753, r5865764);
        double r5865766 = r5865745 + r5865765;
        return r5865766;
}

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (lambda1 phi1 phi2 delta theta)
  :name "Destination given bearing on a great circle"
  (+ lambda1 (atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

Timeout in 10.0m

Reproduce