Error

Derivation

1. Initial program 14.7

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

3. Applied *-un-lft-identity14.7

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

4. Applied associate-/r*14.7

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

5. Applied *-un-lft-identity14.7

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

6. Applied *-un-lft-identity14.7

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

7. Applied distribute-lft-out14.7

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

8. Applied associate-/r*14.7

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

9. Applied frac-sub14.2

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

10. Simplified0.4

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
11. Using strategy rm

12. Applied associate-/r*0.1

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

13. Final simplification0.1

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

Reproduce

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