Average Error: 0.0 → 0.0
Time: 12.0s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1}} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1}} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r76027 = 1.0;
        double r76028 = x;
        double r76029 = r76028 - r76027;
        double r76030 = r76027 / r76029;
        double r76031 = r76028 + r76027;
        double r76032 = r76028 / r76031;
        double r76033 = r76030 + r76032;
        return r76033;
}
↓
double f(double x) {
        double r76034 = 1.0;
        double r76035 = x;
        double r76036 = r76035 - r76034;
        double r76037 = r76034 / r76036;
        double r76038 = cbrt(r76037);
        double r76039 = r76038 * r76038;
        double r76040 = r76039 * r76038;
        double r76041 = r76035 + r76034;
        double r76042 = r76035 / r76041;
        double r76043 = r76040 + r76042;
        double r76044 = 3.0;
        double r76045 = pow(r76043, r76044);
        double r76046 = cbrt(r76045);
        return r76046;
}

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

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))