Average Error: 14.6 → 0.1
Time: 12.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r5371686 = 1.0;
        double r5371687 = x;
        double r5371688 = r5371687 + r5371686;
        double r5371689 = r5371686 / r5371688;
        double r5371690 = r5371687 - r5371686;
        double r5371691 = r5371686 / r5371690;
        double r5371692 = r5371689 - r5371691;
        return r5371692;
}
↓
double f(double x) {
        double r5371693 = -2.0;
        double r5371694 = x;
        double r5371695 = 1.0;
        double r5371696 = r5371694 + r5371695;
        double r5371697 = r5371693 / r5371696;
        double r5371698 = r5371694 - r5371695;
        double r5371699 = r5371697 / r5371698;
        return r5371699;
}

Error

Bits error versus x

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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 frac-sub14.1

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

  4. Simplified14.0

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

  5. Taylor expanded around 0 0.3

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))