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

\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 r2284881 = lambda1;
        double r2284882 = theta;
        double r2284883 = sin(r2284882);
        double r2284884 = delta;
        double r2284885 = sin(r2284884);
        double r2284886 = r2284883 * r2284885;
        double r2284887 = phi1;
        double r2284888 = cos(r2284887);
        double r2284889 = r2284886 * r2284888;
        double r2284890 = cos(r2284884);
        double r2284891 = sin(r2284887);
        double r2284892 = r2284891 * r2284890;
        double r2284893 = r2284888 * r2284885;
        double r2284894 = cos(r2284882);
        double r2284895 = r2284893 * r2284894;
        double r2284896 = r2284892 + r2284895;
        double r2284897 = asin(r2284896);
        double r2284898 = sin(r2284897);
        double r2284899 = r2284891 * r2284898;
        double r2284900 = r2284890 - r2284899;
        double r2284901 = atan2(r2284889, r2284900);
        double r2284902 = r2284881 + r2284901;
        return r2284902;
}

Reproduce

herbie shell --seed 2019141 +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