Average Error: 14.4 → 0.1
Time: 19.2s
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 r4119861 = 1.0;
        double r4119862 = x;
        double r4119863 = r4119862 + r4119861;
        double r4119864 = r4119861 / r4119863;
        double r4119865 = r4119862 - r4119861;
        double r4119866 = r4119861 / r4119865;
        double r4119867 = r4119864 - r4119866;
        return r4119867;
}
↓
double f(double x) {
        double r4119868 = -2.0;
        double r4119869 = x;
        double r4119870 = 1.0;
        double r4119871 = r4119869 + r4119870;
        double r4119872 = r4119868 / r4119871;
        double r4119873 = r4119869 - r4119870;
        double r4119874 = r4119872 / r4119873;
        return r4119874;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.7

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied difference-of-sqr--10.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019138 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))