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

\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 r2137656 = lambda1;
        double r2137657 = theta;
        double r2137658 = sin(r2137657);
        double r2137659 = delta;
        double r2137660 = sin(r2137659);
        double r2137661 = r2137658 * r2137660;
        double r2137662 = phi1;
        double r2137663 = cos(r2137662);
        double r2137664 = r2137661 * r2137663;
        double r2137665 = cos(r2137659);
        double r2137666 = sin(r2137662);
        double r2137667 = r2137666 * r2137665;
        double r2137668 = r2137663 * r2137660;
        double r2137669 = cos(r2137657);
        double r2137670 = r2137668 * r2137669;
        double r2137671 = r2137667 + r2137670;
        double r2137672 = asin(r2137671);
        double r2137673 = sin(r2137672);
        double r2137674 = r2137666 * r2137673;
        double r2137675 = r2137665 - r2137674;
        double r2137676 = atan2(r2137664, r2137675);
        double r2137677 = r2137656 + r2137676;
        return r2137677;
}

Reproduce

herbie shell --seed 2019129 +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