Average Error: 0.0 → 0.0
Time: 6.2s
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 r66445 = 1.0;
        double r66446 = x;
        double r66447 = r66446 - r66445;
        double r66448 = r66445 / r66447;
        double r66449 = r66446 + r66445;
        double r66450 = r66446 / r66449;
        double r66451 = r66448 + r66450;
        return r66451;
}
↓
double f(double x) {
        double r66452 = 1.0;
        double r66453 = x;
        double r66454 = r66453 - r66452;
        double r66455 = r66452 / r66454;
        double r66456 = r66453 + r66452;
        double r66457 = r66453 / r66456;
        double r66458 = r66455 + r66457;
        double r66459 = 3.0;
        double r66460 = pow(r66458, r66459);
        double r66461 = cbrt(r66460);
        return r66461;
}

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 2019323 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))