Average Error: 32.4 → 0
Time: 1.4s
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 r124995 = x;
        double r124996 = r124995 / r124995;
        double r124997 = 1.0;
        double r124998 = r124997 / r124995;
        double r124999 = r124995 * r124995;
        double r125000 = sqrt(r124999);
        double r125001 = r124998 * r125000;
        double r125002 = r124996 - r125001;
        return r125002;
}
↓
double f(double x) {
        double r125003 = 1.0;
        double r125004 = 1.0;
        double r125005 = x;
        double r125006 = fabs(r125005);
        double r125007 = r125004 * r125006;
        double r125008 = r125007 / r125005;
        double r125009 = -r125008;
        double r125010 = r125003 + r125009;
        return r125010;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.4
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.4

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

  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 2020081 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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