Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]
\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)}
double f(double x) {
        double r3693363 = 1.0;
        double r3693364 = x;
        double r3693365 = r3693364 - r3693363;
        double r3693366 = r3693363 / r3693365;
        double r3693367 = r3693364 + r3693363;
        double r3693368 = r3693364 / r3693367;
        double r3693369 = r3693366 + r3693368;
        return r3693369;
}
↓
double f(double x) {
        double r3693370 = 1.0;
        double r3693371 = x;
        double r3693372 = r3693371 - r3693370;
        double r3693373 = r3693370 / r3693372;
        double r3693374 = r3693371 + r3693370;
        double r3693375 = r3693371 / r3693374;
        double r3693376 = r3693373 + r3693375;
        double r3693377 = r3693376 * r3693376;
        double r3693378 = r3693377 * r3693376;
        double r3693379 = cbrt(r3693378);
        return r3693379;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))