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Derivation

1. Initial program 0.0

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

3. Applied add-cbrt-cube0.0

   \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right) \cdot \frac{1}{x - 1}}} + \frac{x}{x + 1}\]

4. Applied simplify0.0

   \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{x - 1}}{\left(x - 1\right) \cdot \left(x - 1\right)}}} + \frac{x}{x + 1}\]
5. Using strategy rm

6. Applied flip--0.0

   \[\leadsto \sqrt[3]{\frac{\frac{1}{x - 1}}{\left(x - 1\right) \cdot \color{blue}{\frac{x \cdot x - 1 \cdot 1}{x + 1}}}} + \frac{x}{x + 1}\]

7. Applied associate-*r/0.0

   \[\leadsto \sqrt[3]{\frac{\frac{1}{x - 1}}{\color{blue}{\frac{\left(x - 1\right) \cdot \left(x \cdot x - 1 \cdot 1\right)}{x + 1}}}} + \frac{x}{x + 1}\]

8. Applied associate-/r/0.0

   \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{x - 1}}{\left(x - 1\right) \cdot \left(x \cdot x - 1 \cdot 1\right)} \cdot \left(x + 1\right)}} + \frac{x}{x + 1}\]

9. Applied cbrt-prod0.0

   \[\leadsto \color{blue}{\sqrt[3]{\frac{\frac{1}{x - 1}}{\left(x - 1\right) \cdot \left(x \cdot x - 1 \cdot 1\right)}} \cdot \sqrt[3]{x + 1}} + \frac{x}{x + 1}\]

10. Applied simplify0.0

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\frac{\frac{1}{x - 1}}{x \cdot x - 1}}{x - 1}}} \cdot \sqrt[3]{x + 1} + \frac{x}{x + 1}\]

Runtime

Time bar (total: 3.3m)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))