Average Error: 31.5 → 0
Time: 7.2s
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 r12041842 = x;
        double r12041843 = r12041842 / r12041842;
        double r12041844 = 1.0;
        double r12041845 = r12041844 / r12041842;
        double r12041846 = r12041842 * r12041842;
        double r12041847 = sqrt(r12041846);
        double r12041848 = r12041845 * r12041847;
        double r12041849 = r12041843 - r12041848;
        return r12041849;
}
↓
double f(double x) {
        double r12041850 = 1.0;
        double r12041851 = x;
        double r12041852 = fabs(r12041851);
        double r12041853 = r12041852 / r12041851;
        double r12041854 = r12041850 - r12041853;
        return r12041854;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.5

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

  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 2019158 
(FPCore (x)
  :name "sqrt sqr"

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

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