Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\left(\sqrt[3]{\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}}\right) \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}}\]

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 clear-num0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\frac{1}{\frac{x + 1}{x}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019093 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))