Average Error: 0.0 → 0.0
Time: 25.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\log \left(e^{\frac{1}{x - 1}}\right) + \frac{x}{x + 1}\right)\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\log \left(e^{\frac{1}{x - 1}}\right) + \frac{x}{x + 1}\right)\right)}
double f(double x) {
        double r16388362 = 1.0;
        double r16388363 = x;
        double r16388364 = r16388363 - r16388362;
        double r16388365 = r16388362 / r16388364;
        double r16388366 = r16388363 + r16388362;
        double r16388367 = r16388363 / r16388366;
        double r16388368 = r16388365 + r16388367;
        return r16388368;
}
↓
double f(double x) {
        double r16388369 = 1.0;
        double r16388370 = x;
        double r16388371 = r16388370 - r16388369;
        double r16388372 = r16388369 / r16388371;
        double r16388373 = r16388370 + r16388369;
        double r16388374 = r16388370 / r16388373;
        double r16388375 = r16388372 + r16388374;
        double r16388376 = exp(r16388372);
        double r16388377 = log(r16388376);
        double r16388378 = r16388377 + r16388374;
        double r16388379 = r16388375 * r16388378;
        double r16388380 = r16388375 * r16388379;
        double r16388381 = cbrt(r16388380);
        return r16388381;
}

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. Using strategy rm

  5. Applied add-log-exp0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))