Average Error: 14.5 → 0.1
Time: 15.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[-\frac{\frac{1}{x + 1}}{x - 1} \cdot 2\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
-\frac{\frac{1}{x + 1}}{x - 1} \cdot 2
double f(double x) {
        double r5152737 = 1.0;
        double r5152738 = x;
        double r5152739 = r5152738 + r5152737;
        double r5152740 = r5152737 / r5152739;
        double r5152741 = r5152738 - r5152737;
        double r5152742 = r5152737 / r5152741;
        double r5152743 = r5152740 - r5152742;
        return r5152743;
}
↓
double f(double x) {
        double r5152744 = 1.0;
        double r5152745 = x;
        double r5152746 = r5152745 + r5152744;
        double r5152747 = r5152744 / r5152746;
        double r5152748 = r5152745 - r5152744;
        double r5152749 = r5152747 / r5152748;
        double r5152750 = 2.0;
        double r5152751 = r5152749 * r5152750;
        double r5152752 = -r5152751;
        return r5152752;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied flip--29.2

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

  4. Applied associate-/r/29.3

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

  5. Applied flip-+14.5

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

  6. Applied associate-/r/14.5

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

  7. Applied distribute-lft-out--13.9

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

  8. Taylor expanded around 0 0.4

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

  10. Applied difference-of-squares0.4

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

  11. Applied associate-/r*0.1

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

  12. Final simplification0.1

    \[\leadsto -\frac{\frac{1}{x + 1}}{x - 1} \cdot 2\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))