Average Error: 32.5 → 0
Time: 1.9s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)
double f(double x) {
        double r127986 = x;
        double r127987 = r127986 / r127986;
        double r127988 = 1.0;
        double r127989 = r127988 / r127986;
        double r127990 = r127986 * r127986;
        double r127991 = sqrt(r127990);
        double r127992 = r127989 * r127991;
        double r127993 = r127987 - r127992;
        return r127993;
}
↓
double f(double x) {
        double r127994 = 1.0;
        double r127995 = 1.0;
        double r127996 = x;
        double r127997 = fabs(r127996);
        double r127998 = r127995 * r127997;
        double r127999 = r127998 / r127996;
        double r128000 = -r127999;
        double r128001 = r127994 + r128000;
        return r128001;
}

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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019318 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2 0.0)

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