Average Error: 46.7 → 17.6
Time: 9.0s
Precision: 64
Internal Precision: 128
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[0\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original46.7
Target26.1
Herbie17.6
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 46.7

    \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]

  2. Taylor expanded around 0 17.6

    \[\leadsto \color{blue}{0}\]

  3. Final simplification17.6

    \[\leadsto 0\]

Runtime

Time bar (total: 9.0s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0) 2 0)

  (- (/ x x) (* (/ 1 x) (sqrt (* x x)))))