Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\right)}^{3}}
double f(double x) {
        double r78485 = 1.0;
        double r78486 = x;
        double r78487 = r78486 - r78485;
        double r78488 = r78485 / r78487;
        double r78489 = r78486 + r78485;
        double r78490 = r78486 / r78489;
        double r78491 = r78488 + r78490;
        return r78491;
}
↓
double f(double x) {
        double r78492 = 1.0;
        double r78493 = x;
        double r78494 = r78493 - r78492;
        double r78495 = r78492 / r78494;
        double r78496 = r78493 + r78492;
        double r78497 = r78493 / r78496;
        double r78498 = 3.0;
        double r78499 = pow(r78497, r78498);
        double r78500 = cbrt(r78499);
        double r78501 = r78495 + r78500;
        double r78502 = pow(r78501, r78498);
        double r78503 = cbrt(r78502);
        return r78503;
}

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. Using strategy rm

  6. Applied add-cbrt-cube21.0

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

  7. Applied add-cbrt-cube21.6

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

  8. Applied cbrt-undiv21.6

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))