Average Error: 0.0 → 0.0
Time: 7.6s
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 r104353 = 1.0;
        double r104354 = x;
        double r104355 = r104354 - r104353;
        double r104356 = r104353 / r104355;
        double r104357 = r104354 + r104353;
        double r104358 = r104354 / r104357;
        double r104359 = r104356 + r104358;
        return r104359;
}
↓
double f(double x) {
        double r104360 = 1.0;
        double r104361 = x;
        double r104362 = r104361 - r104360;
        double r104363 = r104360 / r104362;
        double r104364 = r104361 + r104360;
        double r104365 = r104361 / r104364;
        double r104366 = r104363 + r104365;
        double r104367 = 3.0;
        double r104368 = pow(r104366, r104367);
        double r104369 = cbrt(r104368);
        return r104369;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))