Average Error: 0.0 → 0.0
Time: 3.4s
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 r99526 = 1.0;
        double r99527 = x;
        double r99528 = r99527 - r99526;
        double r99529 = r99526 / r99528;
        double r99530 = r99527 + r99526;
        double r99531 = r99527 / r99530;
        double r99532 = r99529 + r99531;
        return r99532;
}
↓
double f(double x) {
        double r99533 = 1.0;
        double r99534 = x;
        double r99535 = r99534 - r99533;
        double r99536 = r99533 / r99535;
        double r99537 = r99534 + r99533;
        double r99538 = r99534 / r99537;
        double r99539 = r99536 + r99538;
        double r99540 = 3.0;
        double r99541 = pow(r99539, r99540);
        double r99542 = cbrt(r99541);
        return r99542;
}

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 2020034 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))