Average Error: 0.0 → 0.0
Time: 1.8m
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\frac{\left(\left(\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}{x - 1}\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{1 + x} \cdot \frac{x}{1 + x}\right)\right) \cdot \left(\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}{x - 1}\right)}{\left(\left(\frac{1}{x - 1} - \frac{x}{1 + x}\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x} - \frac{x}{1 + x} \cdot \frac{1}{x - 1}\right)\right)\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x} - \frac{x}{1 + x} \cdot \frac{1}{x - 1}\right)\right)}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\frac{\left(\left(\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}{x - 1}\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{1 + x} \cdot \frac{x}{1 + x}\right)\right) \cdot \left(\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}{x - 1}\right)}{\left(\left(\frac{1}{x - 1} - \frac{x}{1 + x}\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x} - \frac{x}{1 + x} \cdot \frac{1}{x - 1}\right)\right)\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x} - \frac{x}{1 + x} \cdot \frac{1}{x - 1}\right)\right)}}
double f(double x) {
        double r24463620 = 1.0;
        double r24463621 = x;
        double r24463622 = r24463621 - r24463620;
        double r24463623 = r24463620 / r24463622;
        double r24463624 = r24463621 + r24463620;
        double r24463625 = r24463621 / r24463624;
        double r24463626 = r24463623 + r24463625;
        return r24463626;
}
↓
double f(double x) {
        double r24463627 = x;
        double r24463628 = 1.0;
        double r24463629 = r24463628 + r24463627;
        double r24463630 = r24463627 / r24463629;
        double r24463631 = r24463630 * r24463630;
        double r24463632 = r24463630 * r24463631;
        double r24463633 = r24463627 - r24463628;
        double r24463634 = r24463628 / r24463633;
        double r24463635 = r24463634 * r24463634;
        double r24463636 = r24463635 / r24463633;
        double r24463637 = r24463632 + r24463636;
        double r24463638 = r24463635 - r24463631;
        double r24463639 = r24463637 * r24463638;
        double r24463640 = r24463639 * r24463637;
        double r24463641 = r24463634 - r24463630;
        double r24463642 = r24463630 * r24463634;
        double r24463643 = r24463631 - r24463642;
        double r24463644 = r24463635 + r24463643;
        double r24463645 = r24463641 * r24463644;
        double r24463646 = r24463645 * r24463644;
        double r24463647 = r24463640 / r24463646;
        double r24463648 = cbrt(r24463647);
        return r24463648;
}

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. Using strategy rm

  5. Applied flip3-+0.0

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

  6. Applied flip3-+0.0

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

  7. Applied flip-+0.0

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

  8. Applied frac-times0.0

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

  9. Applied frac-times0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))