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

\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 r12514271 = lambda1;
        double r12514272 = theta;
        double r12514273 = sin(r12514272);
        double r12514274 = delta;
        double r12514275 = sin(r12514274);
        double r12514276 = r12514273 * r12514275;
        double r12514277 = phi1;
        double r12514278 = cos(r12514277);
        double r12514279 = r12514276 * r12514278;
        double r12514280 = cos(r12514274);
        double r12514281 = sin(r12514277);
        double r12514282 = r12514281 * r12514280;
        double r12514283 = r12514278 * r12514275;
        double r12514284 = cos(r12514272);
        double r12514285 = r12514283 * r12514284;
        double r12514286 = r12514282 + r12514285;
        double r12514287 = asin(r12514286);
        double r12514288 = sin(r12514287);
        double r12514289 = r12514281 * r12514288;
        double r12514290 = r12514280 - r12514289;
        double r12514291 = atan2(r12514279, r12514290);
        double r12514292 = r12514271 + r12514291;
        return r12514292;
}

Reproduce

herbie shell --seed 2019119 +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