Average Error: 32.1 → 0
Time: 4.0s
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 r28094766 = x;
        double r28094767 = r28094766 / r28094766;
        double r28094768 = 1.0;
        double r28094769 = r28094768 / r28094766;
        double r28094770 = r28094766 * r28094766;
        double r28094771 = sqrt(r28094770);
        double r28094772 = r28094769 * r28094771;
        double r28094773 = r28094767 - r28094772;
        return r28094773;
}
↓
double f(double x) {
        double r28094774 = 1.0;
        double r28094775 = x;
        double r28094776 = fabs(r28094775);
        double r28094777 = r28094776 / r28094775;
        double r28094778 = r28094774 - r28094777;
        return r28094778;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.1

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

  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 2019125 
(FPCore (x)
  :name "sqrt sqr"

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

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