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

\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 r13256113 = lambda1;
        double r13256114 = theta;
        double r13256115 = sin(r13256114);
        double r13256116 = delta;
        double r13256117 = sin(r13256116);
        double r13256118 = r13256115 * r13256117;
        double r13256119 = phi1;
        double r13256120 = cos(r13256119);
        double r13256121 = r13256118 * r13256120;
        double r13256122 = cos(r13256116);
        double r13256123 = sin(r13256119);
        double r13256124 = r13256123 * r13256122;
        double r13256125 = r13256120 * r13256117;
        double r13256126 = cos(r13256114);
        double r13256127 = r13256125 * r13256126;
        double r13256128 = r13256124 + r13256127;
        double r13256129 = asin(r13256128);
        double r13256130 = sin(r13256129);
        double r13256131 = r13256123 * r13256130;
        double r13256132 = r13256122 - r13256131;
        double r13256133 = atan2(r13256121, r13256132);
        double r13256134 = r13256113 + r13256133;
        return r13256134;
}

Reproduce

herbie shell --seed 2019124 +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