Average Error: 32.4 → 0
Time: 1.8s
Precision: 64
Internal precision: 128
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
⬇
\[1 - \frac{\left|x\right|}{x}\]

Error

Bits error versus x

Target

Original32.4
Comparison0
Herbie0
\[ \begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Derivation

  1. Initial program 32.4

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

  2. Applied simplify 0

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

Runtime

Time bar (total: 1.8s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(4121501433 828962133 1135886690 4164430413 2050040402 982866809)'
(FPCore (x)
  :name "sqrt sqr"

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

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