Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \left(\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)\]

Error

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Results

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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-cube-cbrt0.0

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

  5. Final simplification0.0

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

Runtime

Time bar (total: 8.1s)Debug logProfile

herbie shell --seed 2018277 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))