Average Error: 32.4 → 0
Time: 5.0s
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 r1519913 = x;
        double r1519914 = r1519913 / r1519913;
        double r1519915 = 1.0;
        double r1519916 = r1519915 / r1519913;
        double r1519917 = r1519913 * r1519913;
        double r1519918 = sqrt(r1519917);
        double r1519919 = r1519916 * r1519918;
        double r1519920 = r1519914 - r1519919;
        return r1519920;
}
↓
double f(double x) {
        double r1519921 = 1.0;
        double r1519922 = x;
        double r1519923 = fabs(r1519922);
        double r1519924 = r1519923 / r1519922;
        double r1519925 = r1519921 - r1519924;
        return r1519925;
}

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 2019156 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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