Average Error: 21.1 → 21.1
Time: 18.1s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{x}{x + 1} + \sqrt[3]{\frac{1}{x - 1}} \cdot \left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right)\]

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 21.1

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

  3. Applied add-cube-cbrt21.1

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

  5. Applied *-commutative21.1

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

  6. Final simplification21.1

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

Runtime

Time bar (total: 18.1s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))