Asymptote B

Average Error: 0.0 → 0.0

Time: 11.5s

Precision: 64

Math

\[\frac{1}{x - 1} + \frac{x}{x + 1}\]

↓

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

C

double f(double x) {
        double r17159861 = 1.0;
        double r17159862 = x;
        double r17159863 = r17159862 - r17159861;
        double r17159864 = r17159861 / r17159863;
        double r17159865 = r17159862 + r17159861;
        double r17159866 = r17159862 / r17159865;
        double r17159867 = r17159864 + r17159866;
        return r17159867;
}

↓

double f(double x) {
        double r17159868 = 1.0;
        double r17159869 = x;
        double r17159870 = r17159869 - r17159868;
        double r17159871 = r17159868 / r17159870;
        double r17159872 = r17159869 + r17159868;
        double r17159873 = r17159869 / r17159872;
        double r17159874 = r17159871 + r17159873;
        double r17159875 = r17159874 * r17159874;
        double r17159876 = r17159875 * r17159874;
        double r17159877 = cbrt(r17159876);
        return r17159877;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

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

3. Applied add-cbrt-cube 0.0

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

4. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019107 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))