Average Error: 0.0 → 0.0
Time: 10.3s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\right) \cdot \left(\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\right)\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\left(\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\right) \cdot \left(\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\right)\right)}
double f(double x) {
        double r6181317 = 1.0;
        double r6181318 = x;
        double r6181319 = r6181318 - r6181317;
        double r6181320 = r6181317 / r6181319;
        double r6181321 = r6181318 + r6181317;
        double r6181322 = r6181318 / r6181321;
        double r6181323 = r6181320 + r6181322;
        return r6181323;
}
↓
double f(double x) {
        double r6181324 = 1.0;
        double r6181325 = x;
        double r6181326 = r6181325 - r6181324;
        double r6181327 = r6181324 / r6181326;
        double r6181328 = r6181325 + r6181324;
        double r6181329 = r6181328 / r6181325;
        double r6181330 = r6181324 / r6181329;
        double r6181331 = r6181327 + r6181330;
        double r6181332 = r6181331 * r6181331;
        double r6181333 = r6181331 * r6181332;
        double r6181334 = cbrt(r6181333);
        return r6181334;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied clear-num0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\frac{1}{\frac{x + 1}{x}}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))