Average Error: 32.5 → 0
Time: 4.0s
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 r3113191 = x;
        double r3113192 = r3113191 / r3113191;
        double r3113193 = 1.0;
        double r3113194 = r3113193 / r3113191;
        double r3113195 = r3113191 * r3113191;
        double r3113196 = sqrt(r3113195);
        double r3113197 = r3113194 * r3113196;
        double r3113198 = r3113192 - r3113197;
        return r3113198;
}
↓
double f(double x) {
        double r3113199 = 1.0;
        double r3113200 = x;
        double r3113201 = fabs(r3113200);
        double r3113202 = r3113201 / r3113200;
        double r3113203 = r3113199 - r3113202;
        return r3113203;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  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 2019146 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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