Average Error: 32.4 → 0
Time: 6.8s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{x}
double f(double x) {
        double r6161864 = x;
        double r6161865 = r6161864 / r6161864;
        double r6161866 = 1.0;
        double r6161867 = r6161866 / r6161864;
        double r6161868 = r6161864 * r6161864;
        double r6161869 = sqrt(r6161868);
        double r6161870 = r6161867 * r6161869;
        double r6161871 = r6161865 - r6161870;
        return r6161871;
}
↓
double f(double x) {
        double r6161872 = 1.0;
        double r6161873 = x;
        double r6161874 = fabs(r6161873);
        double r6161875 = r6161874 / r6161873;
        double r6161876 = r6161872 - r6161875;
        return r6161876;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.4
Target0
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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "sqrt sqr"

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

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