sqrt sqr

Average Error: 32.6 → 0

Time: 1.1s

Precision: 64

Math

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

↓

\[1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)\]

Error

Bits error versus x

Target

Original	32.6
Target	0
Herbie	0

\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

1. Initial program 32.6

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

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2020126 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))