Average Error: 0.0 → 0.0
Time: 6.5s
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 r83811 = 1.0;
        double r83812 = x;
        double r83813 = r83812 - r83811;
        double r83814 = r83811 / r83813;
        double r83815 = r83812 + r83811;
        double r83816 = r83812 / r83815;
        double r83817 = r83814 + r83816;
        return r83817;
}
↓
double f(double x) {
        double r83818 = 1.0;
        double r83819 = x;
        double r83820 = r83819 - r83818;
        double r83821 = r83818 / r83820;
        double r83822 = r83819 + r83818;
        double r83823 = r83819 / r83822;
        double r83824 = r83821 + r83823;
        double r83825 = 3.0;
        double r83826 = pow(r83824, r83825);
        double r83827 = cbrt(r83826);
        return r83827;
}

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 2019322 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))