Average Error: 0.0 → 0.0
Time: 1.1m
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\sqrt[3]{\left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right) \cdot \left(\left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right)\right)} + \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  3. Applied flip3-+0.0

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

  5. Applied add-cbrt-cube0.0

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

  6. Final simplification0.0

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018304 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))