Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \sqrt[3]{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \sqrt[3]{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)}
double f(double x) {
        double r5017450 = 1.0;
        double r5017451 = x;
        double r5017452 = r5017451 - r5017450;
        double r5017453 = r5017450 / r5017452;
        double r5017454 = r5017451 + r5017450;
        double r5017455 = r5017451 / r5017454;
        double r5017456 = r5017453 + r5017455;
        return r5017456;
}
↓
double f(double x) {
        double r5017457 = 1.0;
        double r5017458 = x;
        double r5017459 = r5017458 - r5017457;
        double r5017460 = r5017457 / r5017459;
        double r5017461 = r5017458 + r5017457;
        double r5017462 = r5017458 / r5017461;
        double r5017463 = r5017462 * r5017462;
        double r5017464 = r5017462 * r5017463;
        double r5017465 = cbrt(r5017464);
        double r5017466 = r5017460 + r5017465;
        return r5017466;
}

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-cube21.1

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

  4. Applied add-cbrt-cube21.0

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

  5. Applied cbrt-undiv21.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))