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 r14745058 = x;
        double r14745059 = r14745058 / r14745058;
        double r14745060 = 1.0;
        double r14745061 = r14745060 / r14745058;
        double r14745062 = r14745058 * r14745058;
        double r14745063 = sqrt(r14745062);
        double r14745064 = r14745061 * r14745063;
        double r14745065 = r14745059 - r14745064;
        return r14745065;
}
↓
double f(double x) {
        double r14745066 = 1.0;
        double r14745067 = x;
        double r14745068 = fabs(r14745067);
        double r14745069 = r14745068 / r14745067;
        double r14745070 = r14745066 - r14745069;
        return r14745070;
}

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 2019104 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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