Average Error: 32.2 → 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 r3116158 = x;
        double r3116159 = r3116158 / r3116158;
        double r3116160 = 1.0;
        double r3116161 = r3116160 / r3116158;
        double r3116162 = r3116158 * r3116158;
        double r3116163 = sqrt(r3116162);
        double r3116164 = r3116161 * r3116163;
        double r3116165 = r3116159 - r3116164;
        return r3116165;
}
↓
double f(double x) {
        double r3116166 = 1.0;
        double r3116167 = x;
        double r3116168 = fabs(r3116167);
        double r3116169 = r3116168 / r3116167;
        double r3116170 = r3116166 - r3116169;
        return r3116170;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.2
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.2

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

  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 2019139 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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