Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\right)}^{3}}
double f(double x) {
        double r133003 = 1.0;
        double r133004 = x;
        double r133005 = r133004 - r133003;
        double r133006 = r133003 / r133005;
        double r133007 = r133004 + r133003;
        double r133008 = r133004 / r133007;
        double r133009 = r133006 + r133008;
        return r133009;
}
↓
double f(double x) {
        double r133010 = 1.0;
        double r133011 = x;
        double r133012 = r133011 - r133010;
        double r133013 = r133010 / r133012;
        double r133014 = r133013 * r133013;
        double r133015 = r133011 + r133010;
        double r133016 = r133011 / r133015;
        double r133017 = r133016 * r133016;
        double r133018 = r133014 - r133017;
        double r133019 = r133013 - r133016;
        double r133020 = r133018 / r133019;
        double r133021 = 3.0;
        double r133022 = pow(r133020, r133021);
        double r133023 = cbrt(r133022);
        return r133023;
}

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 flip-+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))