Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\sqrt[3]{{\left(\frac{x}{x + 1} + \frac{1}{x - 1}\right)}^{3}}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\sqrt[3]{{\left(\frac{x}{x + 1} + \frac{1}{x - 1}\right)}^{3}}\right)}^{3}}
double f(double x) {
        double r60020 = 1.0;
        double r60021 = x;
        double r60022 = r60021 - r60020;
        double r60023 = r60020 / r60022;
        double r60024 = r60021 + r60020;
        double r60025 = r60021 / r60024;
        double r60026 = r60023 + r60025;
        return r60026;
}
↓
double f(double x) {
        double r60027 = x;
        double r60028 = 1.0;
        double r60029 = r60027 + r60028;
        double r60030 = r60027 / r60029;
        double r60031 = r60027 - r60028;
        double r60032 = r60028 / r60031;
        double r60033 = r60030 + r60032;
        double r60034 = 3.0;
        double r60035 = pow(r60033, r60034);
        double r60036 = cbrt(r60035);
        double r60037 = pow(r60036, r60034);
        double r60038 = cbrt(r60037);
        return r60038;
}

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-cbrt-cube0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

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