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\[\lambda_1 + \tan^{-1}_* \frac{\left(\sin theta \cdot \sin delta\right) \cdot \cos \phi_1}{\cos delta - \sin \phi_1 \cdot \sin \left(\sin^{-1} \left(\sin \phi_1 \cdot \cos delta + \left(\cos \phi_1 \cdot \sin delta\right) \cdot \cos theta\right)\right)}\]
\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 r9183549 = lambda1;
        double r9183550 = theta;
        double r9183551 = sin(r9183550);
        double r9183552 = delta;
        double r9183553 = sin(r9183552);
        double r9183554 = r9183551 * r9183553;
        double r9183555 = phi1;
        double r9183556 = cos(r9183555);
        double r9183557 = r9183554 * r9183556;
        double r9183558 = cos(r9183552);
        double r9183559 = sin(r9183555);
        double r9183560 = r9183559 * r9183558;
        double r9183561 = r9183556 * r9183553;
        double r9183562 = cos(r9183550);
        double r9183563 = r9183561 * r9183562;
        double r9183564 = r9183560 + r9183563;
        double r9183565 = asin(r9183564);
        double r9183566 = sin(r9183565);
        double r9183567 = r9183559 * r9183566;
        double r9183568 = r9183558 - r9183567;
        double r9183569 = atan2(r9183557, r9183568);
        double r9183570 = r9183549 + r9183569;
        return r9183570;
}

Reproduce

herbie shell --seed 2019104 +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))))))))))