Average Error: 14.6 → 0.5
Time: 30.7s
Precision: 64
Internal Precision: 128
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-2}{(x \cdot \left(x + -1\right) + \left(x + -1\right))_*}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.0

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

  4. Simplified0.5

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

  5. Simplified0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019050 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))