Error

Derivation

1. Initial program 0.0

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

3. Applied *-un-lft-identity0.0

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

4. Applied associate-/l*0.0

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

5. Taylor expanded around -inf 0.0

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

6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019100 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))