Average Error: 32.5 → 0
Time: 6.7s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - 1 \cdot \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - 1 \cdot \frac{\left|x\right|}{x}
double f(double x) {
        double r9175161 = x;
        double r9175162 = r9175161 / r9175161;
        double r9175163 = 1.0;
        double r9175164 = r9175163 / r9175161;
        double r9175165 = r9175161 * r9175161;
        double r9175166 = sqrt(r9175165);
        double r9175167 = r9175164 * r9175166;
        double r9175168 = r9175162 - r9175167;
        return r9175168;
}
↓
double f(double x) {
        double r9175169 = 1.0;
        double r9175170 = 1.0;
        double r9175171 = x;
        double r9175172 = fabs(r9175171);
        double r9175173 = r9175172 / r9175171;
        double r9175174 = r9175170 * r9175173;
        double r9175175 = r9175169 - r9175174;
        return r9175175;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  2. Simplified4.7

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied div-inv4.7

    \[\leadsto 1 - \color{blue}{\left(1 \cdot \frac{1}{x}\right)} \cdot \left|x\right|\]

  5. Applied associate-*l*4.7

    \[\leadsto 1 - \color{blue}{1 \cdot \left(\frac{1}{x} \cdot \left|x\right|\right)}\]

  6. Simplified0

    \[\leadsto 1 - 1 \cdot \color{blue}{\frac{\left|x\right|}{x}}\]

  7. Final simplification0

    \[\leadsto 1 - 1 \cdot \frac{\left|x\right|}{x}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))