Error

Derivation

1. Initial program 14.4

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

3. Applied frac-2neg14.4

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

4. Applied frac-2neg14.4

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

5. Applied frac-sub13.8

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

6. Simplified0.3

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

7. Simplified0.3

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

9. Applied *-commutative0.3

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

10. Applied distribute-rgt1-in0.3

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

11. Applied associate-/r*0.1

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

12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019072 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))