Average Error: 31.8 → 0
Time: 6.8s
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 r3282210 = x;
        double r3282211 = r3282210 / r3282210;
        double r3282212 = 1.0;
        double r3282213 = r3282212 / r3282210;
        double r3282214 = r3282210 * r3282210;
        double r3282215 = sqrt(r3282214);
        double r3282216 = r3282213 * r3282215;
        double r3282217 = r3282211 - r3282216;
        return r3282217;
}
↓
double f(double x) {
        double r3282218 = 1.0;
        double r3282219 = x;
        double r3282220 = fabs(r3282219);
        double r3282221 = r3282220 / r3282219;
        double r3282222 = r3282218 - r3282221;
        return r3282222;
}

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

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

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