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

\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 r13110013 = lambda1;
        double r13110014 = theta;
        double r13110015 = sin(r13110014);
        double r13110016 = delta;
        double r13110017 = sin(r13110016);
        double r13110018 = r13110015 * r13110017;
        double r13110019 = phi1;
        double r13110020 = cos(r13110019);
        double r13110021 = r13110018 * r13110020;
        double r13110022 = cos(r13110016);
        double r13110023 = sin(r13110019);
        double r13110024 = r13110023 * r13110022;
        double r13110025 = r13110020 * r13110017;
        double r13110026 = cos(r13110014);
        double r13110027 = r13110025 * r13110026;
        double r13110028 = r13110024 + r13110027;
        double r13110029 = asin(r13110028);
        double r13110030 = sin(r13110029);
        double r13110031 = r13110023 * r13110030;
        double r13110032 = r13110022 - r13110031;
        double r13110033 = atan2(r13110021, r13110032);
        double r13110034 = r13110013 + r13110033;
        return r13110034;
}

Reproduce

herbie shell --seed 2019125 +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