Average Error: 14.6 → 0.1
Time: 9.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x + 1} \cdot \frac{2 \cdot \left(-\sqrt[3]{1}\right)}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x + 1} \cdot \frac{2 \cdot \left(-\sqrt[3]{1}\right)}{x - 1}
double f(double x) {
        double r148464 = 1.0;
        double r148465 = x;
        double r148466 = r148465 + r148464;
        double r148467 = r148464 / r148466;
        double r148468 = r148465 - r148464;
        double r148469 = r148464 / r148468;
        double r148470 = r148467 - r148469;
        return r148470;
}
↓
double f(double x) {
        double r148471 = 1.0;
        double r148472 = cbrt(r148471);
        double r148473 = r148472 * r148472;
        double r148474 = x;
        double r148475 = r148474 + r148471;
        double r148476 = r148473 / r148475;
        double r148477 = 2.0;
        double r148478 = -r148472;
        double r148479 = r148477 * r148478;
        double r148480 = r148474 - r148471;
        double r148481 = r148479 / r148480;
        double r148482 = r148476 * r148481;
        return r148482;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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Derivation

  1. Initial program 14.6

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  2. Using strategy rm

  3. Applied flip--29.5

    \[\leadsto \frac{1}{x + 1} - \frac{1}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x + 1}}}\]

  4. Applied associate-/r/29.5

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

  5. Applied flip-+14.7

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

  6. Applied associate-/r/14.6

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

  7. Applied distribute-lft-out--14.1

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

  8. Simplified14.1

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

  9. Taylor expanded around 0 0.4

    \[\leadsto \frac{1}{x \cdot x - 1 \cdot 1} \cdot \color{blue}{\left(-2\right)}\]
  10. Using strategy rm

  11. Applied difference-of-squares0.4

    \[\leadsto \frac{1}{\color{blue}{\left(x + 1\right) \cdot \left(x - 1\right)}} \cdot \left(-2\right)\]

  12. Applied add-cube-cbrt0.4

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(x + 1\right) \cdot \left(x - 1\right)} \cdot \left(-2\right)\]

  13. Applied times-frac0.1

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x + 1} \cdot \frac{\sqrt[3]{1}}{x - 1}\right)} \cdot \left(-2\right)\]

  14. Applied associate-*l*0.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x + 1} \cdot \left(\frac{\sqrt[3]{1}}{x - 1} \cdot \left(-2\right)\right)}\]

  15. Simplified0.1

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x + 1} \cdot \color{blue}{\frac{\sqrt[3]{1} \cdot \left(-2\right)}{x - 1}}\]

  16. Final simplification0.1

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x + 1} \cdot \frac{2 \cdot \left(-\sqrt[3]{1}\right)}{x - 1}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))