Average Error: 0.0 → 0.0
Time: 3.9s
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 r101038 = 1.0;
        double r101039 = x;
        double r101040 = r101039 - r101038;
        double r101041 = r101038 / r101040;
        double r101042 = r101039 + r101038;
        double r101043 = r101039 / r101042;
        double r101044 = r101041 + r101043;
        return r101044;
}
↓
double f(double x) {
        double r101045 = 1.0;
        double r101046 = x;
        double r101047 = r101046 - r101045;
        double r101048 = r101045 / r101047;
        double r101049 = r101048 * r101048;
        double r101050 = r101046 + r101045;
        double r101051 = r101046 / r101050;
        double r101052 = r101051 * r101051;
        double r101053 = r101049 - r101052;
        double r101054 = r101048 - r101051;
        double r101055 = r101053 / r101054;
        double r101056 = 3.0;
        double r101057 = pow(r101055, r101056);
        double r101058 = cbrt(r101057);
        return r101058;
}

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))))