Average Error: 32.6 → 0
Time: 697.0ms
Precision: 64
Internal precision: 1408
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
⬇
\[1 - \frac{\left|x\right|}{x}\]

Error

Bits error versus x

Target

Original32.6
Comparison0
Herbie0
\[ \begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Derivation

  1. Initial program 32.6

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

  2. Applied simplify 0

    \[\leadsto \color{blue}{1 - \frac{\left|x\right|}{x}}\]
  3. Removed slow pow expressions

Runtime

Time bar (total: 697.0ms) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (x)
  :name "sqrt sqr"

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

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