Error

Derivation

1. Initial program 14.7

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

3. Applied frac-2neg14.7

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

4. Applied frac-2neg14.7

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

5. Applied frac-sub14.2

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

6. Simplified0.4

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

7. Simplified0.4

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

8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))