Average Error: 32.5 → 0
Time: 1.8s
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 r146077 = x;
        double r146078 = r146077 / r146077;
        double r146079 = 1.0;
        double r146080 = r146079 / r146077;
        double r146081 = r146077 * r146077;
        double r146082 = sqrt(r146081);
        double r146083 = r146080 * r146082;
        double r146084 = r146078 - r146083;
        return r146084;
}
↓
double f(double x) {
        double r146085 = 1.0;
        double r146086 = 1.0;
        double r146087 = x;
        double r146088 = fabs(r146087);
        double r146089 = r146086 * r146088;
        double r146090 = r146089 / r146087;
        double r146091 = -r146090;
        double r146092 = r146085 + r146091;
        return r146092;
}

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 2019322 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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