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

\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 r2153663 = lambda1;
        double r2153664 = theta;
        double r2153665 = sin(r2153664);
        double r2153666 = delta;
        double r2153667 = sin(r2153666);
        double r2153668 = r2153665 * r2153667;
        double r2153669 = phi1;
        double r2153670 = cos(r2153669);
        double r2153671 = r2153668 * r2153670;
        double r2153672 = cos(r2153666);
        double r2153673 = sin(r2153669);
        double r2153674 = r2153673 * r2153672;
        double r2153675 = r2153670 * r2153667;
        double r2153676 = cos(r2153664);
        double r2153677 = r2153675 * r2153676;
        double r2153678 = r2153674 + r2153677;
        double r2153679 = asin(r2153678);
        double r2153680 = sin(r2153679);
        double r2153681 = r2153673 * r2153680;
        double r2153682 = r2153672 - r2153681;
        double r2153683 = atan2(r2153671, r2153682);
        double r2153684 = r2153663 + r2153683;
        return r2153684;
}

Reproduce

herbie shell --seed 2019134 +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