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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

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

5. Applied flip3-+0.0

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

6. Applied associate-*l/0.0

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

7. Final simplification0.0

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

Runtime

Time bar (total: 22.0s)Debug logProfile

herbie shell --seed 2018355 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))