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 r91757 = 1.0;
        double r91758 = x;
        double r91759 = r91758 - r91757;
        double r91760 = r91757 / r91759;
        double r91761 = r91758 + r91757;
        double r91762 = r91758 / r91761;
        double r91763 = r91760 + r91762;
        return r91763;
}
↓
double f(double x) {
        double r91764 = 1.0;
        double r91765 = x;
        double r91766 = r91765 - r91764;
        double r91767 = r91764 / r91766;
        double r91768 = r91765 + r91764;
        double r91769 = r91765 / r91768;
        double r91770 = r91767 + r91769;
        double r91771 = 3.0;
        double r91772 = pow(r91770, r91771);
        double r91773 = cbrt(r91772);
        return r91773;
}

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))))