Average Error: 0.0 → 0.0
Time: 6.4s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{1 + x}}\right)}^{3}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{1 + x}}\right)}^{3}}\right)
double f(double x) {
        double r13669 = 2.0;
        double r13670 = 1.0;
        double r13671 = x;
        double r13672 = r13670 - r13671;
        double r13673 = r13670 + r13671;
        double r13674 = r13672 / r13673;
        double r13675 = sqrt(r13674);
        double r13676 = atan(r13675);
        double r13677 = r13669 * r13676;
        return r13677;
}
↓
double f(double x) {
        double r13678 = 2.0;
        double r13679 = 1.0;
        double r13680 = x;
        double r13681 = r13679 - r13680;
        double r13682 = r13679 + r13680;
        double r13683 = r13681 / r13682;
        double r13684 = sqrt(r13683);
        double r13685 = 3.0;
        double r13686 = pow(r13684, r13685);
        double r13687 = cbrt(r13686);
        double r13688 = atan(r13687);
        double r13689 = r13678 * r13688;
        return r13689;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))