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

\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 r9598987 = lambda1;
        double r9598988 = theta;
        double r9598989 = sin(r9598988);
        double r9598990 = delta;
        double r9598991 = sin(r9598990);
        double r9598992 = r9598989 * r9598991;
        double r9598993 = phi1;
        double r9598994 = cos(r9598993);
        double r9598995 = r9598992 * r9598994;
        double r9598996 = cos(r9598990);
        double r9598997 = sin(r9598993);
        double r9598998 = r9598997 * r9598996;
        double r9598999 = r9598994 * r9598991;
        double r9599000 = cos(r9598988);
        double r9599001 = r9598999 * r9599000;
        double r9599002 = r9598998 + r9599001;
        double r9599003 = asin(r9599002);
        double r9599004 = sin(r9599003);
        double r9599005 = r9598997 * r9599004;
        double r9599006 = r9598996 - r9599005;
        double r9599007 = atan2(r9598995, r9599006);
        double r9599008 = r9598987 + r9599007;
        return r9599008;
}

Reproduce

herbie shell --seed 2019107 +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