Average Error: 32.6 → 0
Time: 1.3s
Precision: binary64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - 1 \cdot \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - 1 \cdot \frac{\left|x\right|}{x}
double code(double x) {
	return ((double) (((double) (x / x)) - ((double) (((double) (1.0 / x)) * ((double) sqrt(((double) (x * x))))))));
}
↓
double code(double x) {
	return ((double) (1.0 - ((double) (1.0 * ((double) (((double) fabs(x)) / x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020184 
(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)))))