Average Error: 32.1 → 0
Time: 1.8s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)
double f(double x) {
        double r159845 = x;
        double r159846 = r159845 / r159845;
        double r159847 = 1.0;
        double r159848 = r159847 / r159845;
        double r159849 = r159845 * r159845;
        double r159850 = sqrt(r159849);
        double r159851 = r159848 * r159850;
        double r159852 = r159846 - r159851;
        return r159852;
}
↓
double f(double x) {
        double r159853 = 1.0;
        double r159854 = 1.0;
        double r159855 = x;
        double r159856 = fabs(r159855);
        double r159857 = r159854 * r159856;
        double r159858 = r159857 / r159855;
        double r159859 = -r159858;
        double r159860 = r159853 + r159859;
        return r159860;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.1

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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