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Derivation

1. Initial program 14.4

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

3. Applied flip--29.4

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

4. Applied associate-/r/29.5

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

5. Applied flip-+14.4

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

6. Applied associate-/r/14.4

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

7. Applied distribute-lft-out--13.8

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

8. Simplified13.8

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

9. Simplified0.4

   \[\leadsto \frac{1}{-1 + x \cdot x} \cdot \color{blue}{-2}\]
10. Using strategy rm

11. Applied associate-*l/0.4

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

12. Simplified0.4

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

13. Final simplification0.4

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

Runtime

Time bar (total: 14.2s)Debug logProfile

herbie shell --seed 2018286 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))