Average Error: 31.9 → 0
Time: 3.9s
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 r2726173 = x;
        double r2726174 = r2726173 / r2726173;
        double r2726175 = 1.0;
        double r2726176 = r2726175 / r2726173;
        double r2726177 = r2726173 * r2726173;
        double r2726178 = sqrt(r2726177);
        double r2726179 = r2726176 * r2726178;
        double r2726180 = r2726174 - r2726179;
        return r2726180;
}
↓
double f(double x) {
        double r2726181 = 1.0;
        double r2726182 = x;
        double r2726183 = fabs(r2726182);
        double r2726184 = r2726183 / r2726182;
        double r2726185 = r2726181 - r2726184;
        return r2726185;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.9
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.9

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

  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 2019143 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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