Average Error: 0.0 → 0.0
Time: 34.2s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\frac{1}{x \cdot x - 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}\right) \cdot \left(\left(\frac{1}{x \cdot x - 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x \cdot x - 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}\right)\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  6. Applied add-cbrt-cube0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 34.2s)Debug logProfile

herbie shell --seed 2018285 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))