Average Error: 0.0 → 0.0
Time: 7.4s
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 r75948 = 1.0;
        double r75949 = x;
        double r75950 = r75949 - r75948;
        double r75951 = r75948 / r75950;
        double r75952 = r75949 + r75948;
        double r75953 = r75949 / r75952;
        double r75954 = r75951 + r75953;
        return r75954;
}
↓
double f(double x) {
        double r75955 = 1.0;
        double r75956 = x;
        double r75957 = r75956 - r75955;
        double r75958 = r75955 / r75957;
        double r75959 = r75956 + r75955;
        double r75960 = r75956 / r75959;
        double r75961 = r75958 + r75960;
        double r75962 = 3.0;
        double r75963 = pow(r75961, r75962);
        double r75964 = cbrt(r75963);
        return r75964;
}

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))))