Average Error: 0.0 → 0.0
Time: 2.3s
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 r120415 = 1.0;
        double r120416 = x;
        double r120417 = r120416 - r120415;
        double r120418 = r120415 / r120417;
        double r120419 = r120416 + r120415;
        double r120420 = r120416 / r120419;
        double r120421 = r120418 + r120420;
        return r120421;
}
↓
double f(double x) {
        double r120422 = 1.0;
        double r120423 = x;
        double r120424 = r120423 - r120422;
        double r120425 = r120422 / r120424;
        double r120426 = r120423 + r120422;
        double r120427 = r120423 / r120426;
        double r120428 = r120425 + r120427;
        double r120429 = 3.0;
        double r120430 = pow(r120428, r120429);
        double r120431 = cbrt(r120430);
        return r120431;
}

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 2020064 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))