Average Error: 0.0 → 0.0
Time: 3.3s
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 r137451 = 1.0;
        double r137452 = x;
        double r137453 = r137452 - r137451;
        double r137454 = r137451 / r137453;
        double r137455 = r137452 + r137451;
        double r137456 = r137452 / r137455;
        double r137457 = r137454 + r137456;
        return r137457;
}
↓
double f(double x) {
        double r137458 = 1.0;
        double r137459 = x;
        double r137460 = r137459 - r137458;
        double r137461 = r137458 / r137460;
        double r137462 = r137459 + r137458;
        double r137463 = r137459 / r137462;
        double r137464 = r137461 + r137463;
        double r137465 = 3.0;
        double r137466 = pow(r137464, r137465);
        double r137467 = cbrt(r137466);
        return r137467;
}

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 2020081 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))