Average Error: 31.8 → 0
Time: 2.7s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{1 \cdot \left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{1 \cdot \left|x\right|}{x}
double f(double x) {
        double r84780 = x;
        double r84781 = r84780 / r84780;
        double r84782 = 1.0;
        double r84783 = r84782 / r84780;
        double r84784 = r84780 * r84780;
        double r84785 = sqrt(r84784);
        double r84786 = r84783 * r84785;
        double r84787 = r84781 - r84786;
        return r84787;
}
↓
double f(double x) {
        double r84788 = 1.0;
        double r84789 = 1.0;
        double r84790 = x;
        double r84791 = fabs(r84790);
        double r84792 = r84789 * r84791;
        double r84793 = r84792 / r84790;
        double r84794 = r84788 - r84793;
        return r84794;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.8
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 31.8

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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