Error

Derivation

1. Initial program 0.0

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

3. Applied flip--0.0

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

4. Applied associate-/r/0.0

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

5. Applied fma-def0.0

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

6. Simplified0.0

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

8. Applied add-cbrt-cube0.0

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

9. Final simplification0.0

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

Runtime

Time bar (total: 17.3s)Debug logProfile

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