Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r97436 = 1.0;
        double r97437 = x;
        double r97438 = r97437 - r97436;
        double r97439 = r97436 / r97438;
        double r97440 = r97437 + r97436;
        double r97441 = r97437 / r97440;
        double r97442 = r97439 + r97441;
        return r97442;
}
↓
double f(double x) {
        double r97443 = 1.0;
        double r97444 = x;
        double r97445 = r97444 - r97443;
        double r97446 = r97443 / r97445;
        double r97447 = r97444 + r97443;
        double r97448 = r97444 / r97447;
        double r97449 = 3.0;
        double r97450 = pow(r97448, r97449);
        double r97451 = cbrt(r97450);
        double r97452 = r97446 + r97451;
        return r97452;
}

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-cube20.3

    \[\leadsto \frac{1}{x - 1} + \frac{x}{\color{blue}{\sqrt[3]{\left(\left(x + 1\right) \cdot \left(x + 1\right)\right) \cdot \left(x + 1\right)}}}\]

  4. Applied add-cbrt-cube20.9

    \[\leadsto \frac{1}{x - 1} + \frac{\color{blue}{\sqrt[3]{\left(x \cdot x\right) \cdot x}}}{\sqrt[3]{\left(\left(x + 1\right) \cdot \left(x + 1\right)\right) \cdot \left(x + 1\right)}}\]

  5. Applied cbrt-undiv20.9

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\sqrt[3]{\frac{\left(x \cdot x\right) \cdot x}{\left(\left(x + 1\right) \cdot \left(x + 1\right)\right) \cdot \left(x + 1\right)}}}\]

  6. Simplified0.0

    \[\leadsto \frac{1}{x - 1} + \sqrt[3]{\color{blue}{{\left(\frac{x}{x + 1}\right)}^{3}}}\]

  7. Final simplification0.0

    \[\leadsto \frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))