Average Error: 32.5 → 0
Time: 3.9s
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 r5640584 = x;
        double r5640585 = r5640584 / r5640584;
        double r5640586 = 1.0;
        double r5640587 = r5640586 / r5640584;
        double r5640588 = r5640584 * r5640584;
        double r5640589 = sqrt(r5640588);
        double r5640590 = r5640587 * r5640589;
        double r5640591 = r5640585 - r5640590;
        return r5640591;
}
↓
double f(double x) {
        double r5640592 = 1.0;
        double r5640593 = x;
        double r5640594 = fabs(r5640593);
        double r5640595 = 1.0;
        double r5640596 = r5640593 / r5640595;
        double r5640597 = r5640594 / r5640596;
        double r5640598 = r5640592 - r5640597;
        return r5640598;
}

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)))))