Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{x + 1}}\right)}^{3}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{x + 1}}\right)}^{3}}\right)
double f(double x) {
        double r12924 = 2.0;
        double r12925 = 1.0;
        double r12926 = x;
        double r12927 = r12925 - r12926;
        double r12928 = r12925 + r12926;
        double r12929 = r12927 / r12928;
        double r12930 = sqrt(r12929);
        double r12931 = atan(r12930);
        double r12932 = r12924 * r12931;
        return r12932;
}
↓
double f(double x) {
        double r12933 = 2.0;
        double r12934 = 1.0;
        double r12935 = x;
        double r12936 = r12934 - r12935;
        double r12937 = r12935 + r12934;
        double r12938 = r12936 / r12937;
        double r12939 = sqrt(r12938);
        double r12940 = 3.0;
        double r12941 = pow(r12939, r12940);
        double r12942 = cbrt(r12941);
        double r12943 = atan(r12942);
        double r12944 = r12933 * r12943;
        return r12944;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 2 \cdot \tan^{-1} \color{blue}{\left(\sqrt[3]{\left(\sqrt{\frac{1 - x}{1 + x}} \cdot \sqrt{\frac{1 - x}{1 + x}}\right) \cdot \sqrt{\frac{1 - x}{1 + x}}}\right)}\]

  4. Simplified0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt[3]{\color{blue}{{\left(\sqrt{\frac{1 - x}{x + 1}}\right)}^{3}}}\right)\]

  5. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{x + 1}}\right)}^{3}}\right)\]

Reproduce

herbie shell --seed 2020021 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))