Average Error: 32.5 → 0
Time: 4.1s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{\frac{x}{1}}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{\frac{x}{1}}
double f(double x) {
        double r5408246 = x;
        double r5408247 = r5408246 / r5408246;
        double r5408248 = 1.0;
        double r5408249 = r5408248 / r5408246;
        double r5408250 = r5408246 * r5408246;
        double r5408251 = sqrt(r5408250);
        double r5408252 = r5408249 * r5408251;
        double r5408253 = r5408247 - r5408252;
        return r5408253;
}
↓
double f(double x) {
        double r5408254 = 1.0;
        double r5408255 = x;
        double r5408256 = fabs(r5408255);
        double r5408257 = 1.0;
        double r5408258 = r5408255 / r5408257;
        double r5408259 = r5408256 / r5408258;
        double r5408260 = r5408254 - r5408259;
        return r5408260;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))