Average Error: 0.0 → 0.0
Time: 2.4s
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 r7829 = 2.0;
        double r7830 = 1.0;
        double r7831 = x;
        double r7832 = r7830 - r7831;
        double r7833 = r7830 + r7831;
        double r7834 = r7832 / r7833;
        double r7835 = sqrt(r7834);
        double r7836 = atan(r7835);
        double r7837 = r7829 * r7836;
        return r7837;
}
↓
double f(double x) {
        double r7838 = 2.0;
        double r7839 = 1.0;
        double r7840 = x;
        double r7841 = r7839 - r7840;
        double r7842 = r7840 + r7839;
        double r7843 = r7841 / r7842;
        double r7844 = sqrt(r7843);
        double r7845 = 3.0;
        double r7846 = pow(r7844, r7845);
        double r7847 = cbrt(r7846);
        double r7848 = atan(r7847);
        double r7849 = r7838 * r7848;
        return r7849;
}

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 2020047 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))