\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]

2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)

double f(double x) {
        double r8005 = 2.0;
        double r8006 = 1.0;
        double r8007 = x;
        double r8008 = r8006 - r8007;
        double r8009 = r8006 + r8007;
        double r8010 = r8008 / r8009;
        double r8011 = sqrt(r8010);
        double r8012 = atan(r8011);
        double r8013 = r8005 * r8012;
        return r8013;
}

Reproduce

Please include this information when filing a bug report:

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

Backtrace

atab-pick-alt: contract violation expected: alt? given: '(#<alt (λ (x) (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))>) in: the range of the #:picking-func argument of (-> alt-table? #:only-fresh boolean? #:picking-func (-> (listof alt?) alt?) (values alt? alt-table?)) contract from: /data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt blaming: /data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt (assuming the contract is correct) at: /data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt:13.3		L	C
raise-blame-error16	/opt/racket-7.0/collects/racket/contract/private/blame.rkt	347	0
(unnamed)	/data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt	59	0
(unnamed)	/opt/racket-7.0/collects/racket/contract/private/arrow-val-first.rkt	388	18
choose-best-alt!	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	110	0
run-iter!	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	319	0
for-loop	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	353	4
run-improve43	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	338	0
(unnamed)	/opt/racket-7.0/collects/racket/private/more-scheme.rkt	261	28
run	/opt/racket-7.0/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.0/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.0/collects/racket/private/more-scheme.rkt	261	28