Average Error: 0.0 → 0.0
Time: 6.6s
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 r16078 = 2.0;
        double r16079 = 1.0;
        double r16080 = x;
        double r16081 = r16079 - r16080;
        double r16082 = r16079 + r16080;
        double r16083 = r16081 / r16082;
        double r16084 = sqrt(r16083);
        double r16085 = atan(r16084);
        double r16086 = r16078 * r16085;
        return r16086;
}
↓
double f(double x) {
        double r16087 = 2.0;
        double r16088 = 1.0;
        double r16089 = x;
        double r16090 = r16088 - r16089;
        double r16091 = r16089 + r16088;
        double r16092 = r16090 / r16091;
        double r16093 = sqrt(r16092);
        double r16094 = 3.0;
        double r16095 = pow(r16093, r16094);
        double r16096 = cbrt(r16095);
        double r16097 = atan(r16096);
        double r16098 = r16087 * r16097;
        return r16098;
}

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 2019350 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))