Average Error: 0.0 → 0.0
Time: 6.1s
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 r124448 = 1.0;
        double r124449 = x;
        double r124450 = r124449 - r124448;
        double r124451 = r124448 / r124450;
        double r124452 = r124449 + r124448;
        double r124453 = r124449 / r124452;
        double r124454 = r124451 + r124453;
        return r124454;
}
↓
double f(double x) {
        double r124455 = 1.0;
        double r124456 = x;
        double r124457 = r124456 - r124455;
        double r124458 = r124455 / r124457;
        double r124459 = r124456 + r124455;
        double r124460 = r124456 / r124459;
        double r124461 = r124458 + r124460;
        double r124462 = 3.0;
        double r124463 = pow(r124461, r124462);
        double r124464 = cbrt(r124463);
        return r124464;
}

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 2019179 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))