Average Error: 0.0 → 0.0
Time: 4.1s
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 r144644 = 1.0;
        double r144645 = x;
        double r144646 = r144645 - r144644;
        double r144647 = r144644 / r144646;
        double r144648 = r144645 + r144644;
        double r144649 = r144645 / r144648;
        double r144650 = r144647 + r144649;
        return r144650;
}
↓
double f(double x) {
        double r144651 = 1.0;
        double r144652 = x;
        double r144653 = r144652 - r144651;
        double r144654 = r144651 / r144653;
        double r144655 = r144652 + r144651;
        double r144656 = r144652 / r144655;
        double r144657 = r144654 + r144656;
        double r144658 = 3.0;
        double r144659 = pow(r144657, r144658);
        double r144660 = cbrt(r144659);
        return r144660;
}

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 2020003 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))