Average Error: 32.6 → 0
Time: 4.7s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - 1 \cdot \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - 1 \cdot \frac{\left|x\right|}{x}
double f(double x) {
        double r96637 = x;
        double r96638 = r96637 / r96637;
        double r96639 = 1.0;
        double r96640 = r96639 / r96637;
        double r96641 = r96637 * r96637;
        double r96642 = sqrt(r96641);
        double r96643 = r96640 * r96642;
        double r96644 = r96638 - r96643;
        return r96644;
}
↓
double f(double x) {
        double r96645 = 1.0;
        double r96646 = 1.0;
        double r96647 = x;
        double r96648 = fabs(r96647);
        double r96649 = r96648 / r96647;
        double r96650 = r96646 * r96649;
        double r96651 = r96645 - r96650;
        return r96651;
}

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. Simplified5.0

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied div-inv5.0

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

  5. Applied associate-*l*5.0

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

  6. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2 0.0)

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