\[R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{{\left(\sin \left(\frac{\phi_1 - \phi_2}{2}\right)\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)}}{\sqrt{1 - \left({\left(\sin \left(\frac{\phi_1 - \phi_2}{2}\right)\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right)}}\right)\]

R \cdot \left(2 \cdot \tan^{-1}_* \frac{\sqrt{{\left(\sin \left(\frac{\phi_1 - \phi_2}{2}\right)\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)}}{\sqrt{1 - \left({\left(\sin \left(\frac{\phi_1 - \phi_2}{2}\right)\right)}^{2} + \left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right) \cdot \sin \left(\frac{\lambda_1 - \lambda_2}{2}\right)\right)}}\right)

double f(double R, double lambda1, double lambda2, double phi1, double phi2) {
        double r81179 = R;
        double r81180 = 2.0;
        double r81181 = phi1;
        double r81182 = phi2;
        double r81183 = r81181 - r81182;
        double r81184 = r81183 / r81180;
        double r81185 = sin(r81184);
        double r81186 = pow(r81185, r81180);
        double r81187 = cos(r81181);
        double r81188 = cos(r81182);
        double r81189 = r81187 * r81188;
        double r81190 = lambda1;
        double r81191 = lambda2;
        double r81192 = r81190 - r81191;
        double r81193 = r81192 / r81180;
        double r81194 = sin(r81193);
        double r81195 = r81189 * r81194;
        double r81196 = r81195 * r81194;
        double r81197 = r81186 + r81196;
        double r81198 = sqrt(r81197);
        double r81199 = 1.0;
        double r81200 = r81199 - r81197;
        double r81201 = sqrt(r81200);
        double r81202 = atan2(r81198, r81201);
        double r81203 = r81180 * r81202;
        double r81204 = r81179 * r81203;
        return r81204;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019323 +o rules:numerics
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Distance on a great circle"
  :precision binary64
  (* R (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))))))

Backtrace

get-representation: Unknown representation real		L	C
(unnamed)	/data/pavpan/nightlies/herbie/fix-interface-bugs/src/core/regimes.rkt	65	3
filter	/opt/racket-7.2/collects/racket/private/list.rkt	256	2
infer-splitpoints	/data/pavpan/nightlies/herbie/fix-interface-bugs/src/core/regimes.rkt	34	0
get-final-combination	/data/pavpan/nightlies/herbie/fix-interface-bugs/src/mainloop.rkt	369	0
(unnamed)	/opt/racket-7.2/collects/racket/private/more-scheme.rkt	261	28
run	/opt/racket-7.2/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.2/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.2/collects/racket/private/more-scheme.rkt	261	28