Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r101778 = 1.0;
        double r101779 = x;
        double r101780 = r101779 - r101778;
        double r101781 = r101778 / r101780;
        double r101782 = r101779 + r101778;
        double r101783 = r101779 / r101782;
        double r101784 = r101781 + r101783;
        return r101784;
}
↓
double f(double x) {
        double r101785 = 1.0;
        double r101786 = x;
        double r101787 = r101786 - r101785;
        double r101788 = r101785 / r101787;
        double r101789 = r101786 + r101785;
        double r101790 = r101786 / r101789;
        double r101791 = 3.0;
        double r101792 = pow(r101790, r101791);
        double r101793 = cbrt(r101792);
        double r101794 = r101788 + r101793;
        return r101794;
}

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-cube20.9

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

  4. Applied add-cbrt-cube21.5

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

  5. Applied cbrt-undiv21.5

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))