Average Error: 0.0 → 0.0
Time: 11.7s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
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 r23921 = 2.0;
        double r23922 = 1.0;
        double r23923 = x;
        double r23924 = r23922 - r23923;
        double r23925 = r23922 + r23923;
        double r23926 = r23924 / r23925;
        double r23927 = sqrt(r23926);
        double r23928 = atan(r23927);
        double r23929 = r23921 * r23928;
        return r23929;
}
↓
double f(double x) {
        double r23930 = 2.0;
        double r23931 = 1.0;
        double r23932 = x;
        double r23933 = r23931 - r23932;
        double r23934 = r23931 + r23932;
        double r23935 = r23933 / r23934;
        double r23936 = sqrt(r23935);
        double r23937 = atan(r23936);
        double r23938 = r23930 * r23937;
        return r23938;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))