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

\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 r1385616 = lambda1;
        double r1385617 = theta;
        double r1385618 = sin(r1385617);
        double r1385619 = delta;
        double r1385620 = sin(r1385619);
        double r1385621 = r1385618 * r1385620;
        double r1385622 = phi1;
        double r1385623 = cos(r1385622);
        double r1385624 = r1385621 * r1385623;
        double r1385625 = cos(r1385619);
        double r1385626 = sin(r1385622);
        double r1385627 = r1385626 * r1385625;
        double r1385628 = r1385623 * r1385620;
        double r1385629 = cos(r1385617);
        double r1385630 = r1385628 * r1385629;
        double r1385631 = r1385627 + r1385630;
        double r1385632 = asin(r1385631);
        double r1385633 = sin(r1385632);
        double r1385634 = r1385626 * r1385633;
        double r1385635 = r1385625 - r1385634;
        double r1385636 = atan2(r1385624, r1385635);
        double r1385637 = r1385616 + r1385636;
        return r1385637;
}

Reproduce

herbie shell --seed 2019135 +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