Average Error: 31.6 → 0
Time: 4.1s
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 r21046224 = x;
        double r21046225 = r21046224 / r21046224;
        double r21046226 = 1.0;
        double r21046227 = r21046226 / r21046224;
        double r21046228 = r21046224 * r21046224;
        double r21046229 = sqrt(r21046228);
        double r21046230 = r21046227 * r21046229;
        double r21046231 = r21046225 - r21046230;
        return r21046231;
}
↓
double f(double x) {
        double r21046232 = 1.0;
        double r21046233 = x;
        double r21046234 = fabs(r21046233);
        double r21046235 = r21046234 / r21046233;
        double r21046236 = r21046232 - r21046235;
        return r21046236;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.6

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

  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 2019120 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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