Average Error: 32.3 → 0
Time: 5.8s
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 r2015968 = x;
        double r2015969 = r2015968 / r2015968;
        double r2015970 = 1.0;
        double r2015971 = r2015970 / r2015968;
        double r2015972 = r2015968 * r2015968;
        double r2015973 = sqrt(r2015972);
        double r2015974 = r2015971 * r2015973;
        double r2015975 = r2015969 - r2015974;
        return r2015975;
}
↓
double f(double x) {
        double r2015976 = 1.0;
        double r2015977 = x;
        double r2015978 = fabs(r2015977);
        double r2015979 = r2015978 / r2015977;
        double r2015980 = r2015976 - r2015979;
        return r2015980;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.3
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.3

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

  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 2019154 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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