Average Error: 14.2 → 0.1
Time: 41.1s
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 r4586367 = 1.0;
        double r4586368 = x;
        double r4586369 = r4586368 + r4586367;
        double r4586370 = r4586367 / r4586369;
        double r4586371 = r4586368 - r4586367;
        double r4586372 = r4586367 / r4586371;
        double r4586373 = r4586370 - r4586372;
        return r4586373;
}
↓
double f(double x) {
        double r4586374 = -2.0;
        double r4586375 = x;
        double r4586376 = 1.0;
        double r4586377 = r4586375 + r4586376;
        double r4586378 = r4586374 / r4586377;
        double r4586379 = r4586375 - r4586376;
        double r4586380 = r4586378 / r4586379;
        return r4586380;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.6

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

  4. Simplified13.6

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

  5. Taylor expanded around inf 0.4

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  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 2019151 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))