Average Error: 31.8 → 0
Time: 6.4s
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 r4408837 = x;
        double r4408838 = r4408837 / r4408837;
        double r4408839 = 1.0;
        double r4408840 = r4408839 / r4408837;
        double r4408841 = r4408837 * r4408837;
        double r4408842 = sqrt(r4408841);
        double r4408843 = r4408840 * r4408842;
        double r4408844 = r4408838 - r4408843;
        return r4408844;
}
↓
double f(double x) {
        double r4408845 = 1.0;
        double r4408846 = x;
        double r4408847 = fabs(r4408846);
        double r4408848 = r4408847 / r4408846;
        double r4408849 = r4408845 - r4408848;
        return r4408849;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.8
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.8

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

  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 2019164 
(FPCore (x)
  :name "sqrt sqr"

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

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