Average Error: 31.5 → 0
Time: 8.3s
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 r4398299 = x;
        double r4398300 = r4398299 / r4398299;
        double r4398301 = 1.0;
        double r4398302 = r4398301 / r4398299;
        double r4398303 = r4398299 * r4398299;
        double r4398304 = sqrt(r4398303);
        double r4398305 = r4398302 * r4398304;
        double r4398306 = r4398300 - r4398305;
        return r4398306;
}
↓
double f(double x) {
        double r4398307 = 1.0;
        double r4398308 = x;
        double r4398309 = fabs(r4398308);
        double r4398310 = r4398309 / r4398308;
        double r4398311 = r4398307 - r4398310;
        return r4398311;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.5

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

  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 2019158 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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