Error

Derivation

1. Initial program 13.9

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

3. Applied flip--28.6

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

4. Applied associate-/r/28.7

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

5. Applied flip-+13.9

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

6. Applied associate-/r/13.9

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

7. Applied distribute-lft-out--13.3

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

8. Simplified13.3

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

9. Simplified0.3

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

10. Final simplification0.3

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))

Details

Time bar (total: 27.5s)Debug log