Average Error: 32.4 → 0
Time: 3.9s
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 r3559903 = x;
        double r3559904 = r3559903 / r3559903;
        double r3559905 = 1.0;
        double r3559906 = r3559905 / r3559903;
        double r3559907 = r3559903 * r3559903;
        double r3559908 = sqrt(r3559907);
        double r3559909 = r3559906 * r3559908;
        double r3559910 = r3559904 - r3559909;
        return r3559910;
}
↓
double f(double x) {
        double r3559911 = 1.0;
        double r3559912 = x;
        double r3559913 = fabs(r3559912);
        double r3559914 = r3559913 / r3559912;
        double r3559915 = r3559911 - r3559914;
        return r3559915;
}

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 2019142 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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