Average Error: 14.4 → 0.4
Time: 2.1s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{1 \cdot \left(\left(-1\right) - 1\right)}{x \cdot x - 1 \cdot 1}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.8

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020181 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))