Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r121414 = 1.0;
        double r121415 = x;
        double r121416 = r121415 - r121414;
        double r121417 = r121414 / r121416;
        double r121418 = r121415 + r121414;
        double r121419 = r121415 / r121418;
        double r121420 = r121417 + r121419;
        return r121420;
}
↓
double f(double x) {
        double r121421 = 1.0;
        double r121422 = x;
        double r121423 = r121422 - r121421;
        double r121424 = r121421 / r121423;
        double r121425 = r121422 + r121421;
        double r121426 = r121422 / r121425;
        double r121427 = r121424 + r121426;
        double r121428 = 3.0;
        double r121429 = pow(r121427, r121428);
        double r121430 = cbrt(r121429);
        return r121430;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))