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

\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 r2951287 = lambda1;
        double r2951288 = theta;
        double r2951289 = sin(r2951288);
        double r2951290 = delta;
        double r2951291 = sin(r2951290);
        double r2951292 = r2951289 * r2951291;
        double r2951293 = phi1;
        double r2951294 = cos(r2951293);
        double r2951295 = r2951292 * r2951294;
        double r2951296 = cos(r2951290);
        double r2951297 = sin(r2951293);
        double r2951298 = r2951297 * r2951296;
        double r2951299 = r2951294 * r2951291;
        double r2951300 = cos(r2951288);
        double r2951301 = r2951299 * r2951300;
        double r2951302 = r2951298 + r2951301;
        double r2951303 = asin(r2951302);
        double r2951304 = sin(r2951303);
        double r2951305 = r2951297 * r2951304;
        double r2951306 = r2951296 - r2951305;
        double r2951307 = atan2(r2951295, r2951306);
        double r2951308 = r2951287 + r2951307;
        return r2951308;
}

Reproduce

herbie shell --seed 2019133 +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