Average Error: 32.1 → 0
Time: 2.3s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{1 \cdot \left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{1 \cdot \left|x\right|}{x}
double f(double x) {
        double r95001 = x;
        double r95002 = r95001 / r95001;
        double r95003 = 1.0;
        double r95004 = r95003 / r95001;
        double r95005 = r95001 * r95001;
        double r95006 = sqrt(r95005);
        double r95007 = r95004 * r95006;
        double r95008 = r95002 - r95007;
        return r95008;
}
↓
double f(double x) {
        double r95009 = 1.0;
        double r95010 = 1.0;
        double r95011 = x;
        double r95012 = fabs(r95011);
        double r95013 = r95010 * r95012;
        double r95014 = r95013 / r95011;
        double r95015 = r95009 - r95014;
        return r95015;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.1

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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