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

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 r56389 = R;
        double r56390 = 2.0;
        double r56391 = phi1;
        double r56392 = phi2;
        double r56393 = r56391 - r56392;
        double r56394 = r56393 / r56390;
        double r56395 = sin(r56394);
        double r56396 = pow(r56395, r56390);
        double r56397 = cos(r56391);
        double r56398 = cos(r56392);
        double r56399 = r56397 * r56398;
        double r56400 = lambda1;
        double r56401 = lambda2;
        double r56402 = r56400 - r56401;
        double r56403 = r56402 / r56390;
        double r56404 = sin(r56403);
        double r56405 = r56399 * r56404;
        double r56406 = r56405 * r56404;
        double r56407 = r56396 + r56406;
        double r56408 = sqrt(r56407);
        double r56409 = 1.0;
        double r56410 = r56409 - r56407;
        double r56411 = sqrt(r56410);
        double r56412 = atan2(r56408, r56411);
        double r56413 = r56390 * r56412;
        double r56414 = r56389 * r56413;
        return r56414;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019323 
(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