Average Error: 32.2 → 0
Time: 4.3s
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 r4923191 = x;
        double r4923192 = r4923191 / r4923191;
        double r4923193 = 1.0;
        double r4923194 = r4923193 / r4923191;
        double r4923195 = r4923191 * r4923191;
        double r4923196 = sqrt(r4923195);
        double r4923197 = r4923194 * r4923196;
        double r4923198 = r4923192 - r4923197;
        return r4923198;
}
↓
double f(double x) {
        double r4923199 = 1.0;
        double r4923200 = x;
        double r4923201 = fabs(r4923200);
        double r4923202 = r4923201 / r4923200;
        double r4923203 = r4923199 - r4923202;
        return r4923203;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.2
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.2

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

  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 2019139 
(FPCore (x)
  :name "sqrt sqr"

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

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