Average Error: 31.8 → 0
Time: 5.4s
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 r1342242 = x;
        double r1342243 = r1342242 / r1342242;
        double r1342244 = 1.0;
        double r1342245 = r1342244 / r1342242;
        double r1342246 = r1342242 * r1342242;
        double r1342247 = sqrt(r1342246);
        double r1342248 = r1342245 * r1342247;
        double r1342249 = r1342243 - r1342248;
        return r1342249;
}
↓
double f(double x) {
        double r1342250 = 1.0;
        double r1342251 = x;
        double r1342252 = fabs(r1342251);
        double r1342253 = r1342252 / r1342251;
        double r1342254 = r1342250 - r1342253;
        return r1342254;
}

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 2019152 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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