Average Error: 31.7 → 0
Time: 3.8s
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 r2335773 = x;
        double r2335774 = r2335773 / r2335773;
        double r2335775 = 1.0;
        double r2335776 = r2335775 / r2335773;
        double r2335777 = r2335773 * r2335773;
        double r2335778 = sqrt(r2335777);
        double r2335779 = r2335776 * r2335778;
        double r2335780 = r2335774 - r2335779;
        return r2335780;
}
↓
double f(double x) {
        double r2335781 = 1.0;
        double r2335782 = x;
        double r2335783 = fabs(r2335782);
        double r2335784 = r2335783 / r2335782;
        double r2335785 = r2335781 - r2335784;
        return r2335785;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.7
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.7

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

  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 2019149 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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