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

\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 r1346803 = lambda1;
        double r1346804 = theta;
        double r1346805 = sin(r1346804);
        double r1346806 = delta;
        double r1346807 = sin(r1346806);
        double r1346808 = r1346805 * r1346807;
        double r1346809 = phi1;
        double r1346810 = cos(r1346809);
        double r1346811 = r1346808 * r1346810;
        double r1346812 = cos(r1346806);
        double r1346813 = sin(r1346809);
        double r1346814 = r1346813 * r1346812;
        double r1346815 = r1346810 * r1346807;
        double r1346816 = cos(r1346804);
        double r1346817 = r1346815 * r1346816;
        double r1346818 = r1346814 + r1346817;
        double r1346819 = asin(r1346818);
        double r1346820 = sin(r1346819);
        double r1346821 = r1346813 * r1346820;
        double r1346822 = r1346812 - r1346821;
        double r1346823 = atan2(r1346811, r1346822);
        double r1346824 = r1346803 + r1346823;
        return r1346824;
}

Reproduce

herbie shell --seed 2019138 +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