Average Error: 0.0 → 0.0
Time: 15.4s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{x}{x + 1} + \sqrt[3]{\frac{1}{x - 1} \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right)}\]

Error

Bits error versus x

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019089 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))