Average Error: 0.0 → 0.0
Time: 26.0s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1} \cdot \left(x + 1\right) + \log \left(e^{\frac{x}{x + 1}}\right)\]

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 flip--0.0

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

  5. Applied associate-/r/0.0

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

  7. Applied add-log-exp0.0

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

  8. Final simplification0.0

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

Runtime

Time bar (total: 26.0s)Debug logProfile

herbie shell --seed 2018348 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))