Error

Try it out

Derivation

1. Initial program 0.0

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

2. Initial simplification0.0

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

4. Applied add-log-exp0.0

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

5. Applied add-log-exp0.0

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

6. Applied sum-log0.0

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

7. Simplified0.0

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

9. Applied add-sqr-sqrt0.0

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

10. Final simplification0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{1}{x - 1} + \frac{x}{x + 1}}} \cdot \sqrt{e^{\frac{1}{x - 1} + \frac{x}{x + 1}}}\right)\]

Runtime

Time bar (total: 8.6s)Debug logProfile

herbie shell --seed 2018286 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))