Average Error: 32.3 → 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 r2750837 = x;
        double r2750838 = r2750837 / r2750837;
        double r2750839 = 1.0;
        double r2750840 = r2750839 / r2750837;
        double r2750841 = r2750837 * r2750837;
        double r2750842 = sqrt(r2750841);
        double r2750843 = r2750840 * r2750842;
        double r2750844 = r2750838 - r2750843;
        return r2750844;
}
↓
double f(double x) {
        double r2750845 = 1.0;
        double r2750846 = x;
        double r2750847 = fabs(r2750846);
        double r2750848 = r2750847 / r2750846;
        double r2750849 = r2750845 - r2750848;
        return r2750849;
}

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 2019144 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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