Average Error: 32.1 → 0
Time: 3.9s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{x}\]
double f(double x) {
        double r28526066 = x;
        double r28526067 = r28526066 / r28526066;
        double r28526068 = 1.0;
        double r28526069 = r28526068 / r28526066;
        double r28526070 = r28526066 * r28526066;
        double r28526071 = sqrt(r28526070);
        double r28526072 = r28526069 * r28526071;
        double r28526073 = r28526067 - r28526072;
        return r28526073;
}
↓
double f(double x) {
        double r28526074 = 1.0;
        double r28526075 = x;
        double r28526076 = fabs(r28526075);
        double r28526077 = r28526076 / r28526075;
        double r28526078 = r28526074 - r28526077;
        return r28526078;
}


\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{x}

Error

Bits error versus x

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.1

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

  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 2019102 
(FPCore (x)
  :name "sqrt sqr"

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

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