Average Error: 0.0 → 0.0
Time: 1.7s
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 r132954 = 1.0;
        double r132955 = x;
        double r132956 = r132955 - r132954;
        double r132957 = r132954 / r132956;
        double r132958 = r132955 + r132954;
        double r132959 = r132955 / r132958;
        double r132960 = r132957 + r132959;
        return r132960;
}
↓
double f(double x) {
        double r132961 = 1.0;
        double r132962 = x;
        double r132963 = r132962 - r132961;
        double r132964 = r132961 / r132963;
        double r132965 = r132962 + r132961;
        double r132966 = r132962 / r132965;
        double r132967 = r132964 + r132966;
        double r132968 = 3.0;
        double r132969 = pow(r132967, r132968);
        double r132970 = cbrt(r132969);
        return r132970;
}

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 2020027 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))