Average Error: 32.3 → 0
Time: 4.4s
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 r7586216 = x;
        double r7586217 = r7586216 / r7586216;
        double r7586218 = 1.0;
        double r7586219 = r7586218 / r7586216;
        double r7586220 = r7586216 * r7586216;
        double r7586221 = sqrt(r7586220);
        double r7586222 = r7586219 * r7586221;
        double r7586223 = r7586217 - r7586222;
        return r7586223;
}
↓
double f(double x) {
        double r7586224 = 1.0;
        double r7586225 = x;
        double r7586226 = fabs(r7586225);
        double r7586227 = r7586226 / r7586225;
        double r7586228 = r7586224 - r7586227;
        return r7586228;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.3
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.3

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

  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 2019119 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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