Average Error: 16.0 → 15.5
Time: 25.8s
Precision: 64
Internal Precision: 128
\[\frac{x}{x \cdot x + 1}\]
↓
\[\left(x + {x}^{5}\right) - {x}^{3}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.0
Target16.1
Herbie15.5
\[\frac{1}{x + \frac{1}{x}}\]

Derivation

  1. Initial program 16.0

    \[\frac{x}{x \cdot x + 1}\]

  2. Taylor expanded around 0 15.5

    \[\leadsto \color{blue}{\left(x + {x}^{5}\right) - {x}^{3}}\]

  3. Final simplification15.5

    \[\leadsto \left(x + {x}^{5}\right) - {x}^{3}\]

Runtime

Time bar (total: 25.8s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (x)
  :name "x / (x^2 + 1)"

  :herbie-target
  (/ 1 (+ x (/ 1 x)))

  (/ x (+ (* x x) 1)))