Average Error: 0.0 → 0.0
Time: 2.6s
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 r122977 = 1.0;
        double r122978 = x;
        double r122979 = r122978 - r122977;
        double r122980 = r122977 / r122979;
        double r122981 = r122978 + r122977;
        double r122982 = r122978 / r122981;
        double r122983 = r122980 + r122982;
        return r122983;
}
↓
double f(double x) {
        double r122984 = 1.0;
        double r122985 = x;
        double r122986 = r122985 - r122984;
        double r122987 = r122984 / r122986;
        double r122988 = r122985 + r122984;
        double r122989 = r122985 / r122988;
        double r122990 = r122987 + r122989;
        double r122991 = 3.0;
        double r122992 = pow(r122990, r122991);
        double r122993 = cbrt(r122992);
        return r122993;
}

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 2019362 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))