\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
double f(double x) {
        double r40969 = 2.0;
        double r40970 = 1.0;
        double r40971 = x;
        double r40972 = r40970 - r40971;
        double r40973 = r40970 + r40971;
        double r40974 = r40972 / r40973;
        double r40975 = sqrt(r40974);
        double r40976 = atan(r40975);
        double r40977 = r40969 * r40976;
        return r40977;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019173 
(FPCore (x)
  :name "arccos"
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

Backtrace

hash-ref: no value found for key key: #<enode 347(347)>LC
for-loop/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt1972
extractor-extract/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt1960
for-loop/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt352
(unnamed)/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt260
simplify!/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt2170
run-iter!/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3200
for-loop/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3544
run-improve43/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3390
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128
run/opt/racket-7.0/share/pkgs/profile-lib/main.rkt392
profile-thunk16/opt/racket-7.0/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128