Average Error: 32.9 → 0
Time: 2.6s
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 r86237 = x;
        double r86238 = r86237 / r86237;
        double r86239 = 1.0;
        double r86240 = r86239 / r86237;
        double r86241 = r86237 * r86237;
        double r86242 = sqrt(r86241);
        double r86243 = r86240 * r86242;
        double r86244 = r86238 - r86243;
        return r86244;
}
↓
double f(double x) {
        double r86245 = 1.0;
        double r86246 = 1.0;
        double r86247 = x;
        double r86248 = fabs(r86247);
        double r86249 = r86246 * r86248;
        double r86250 = r86249 / r86247;
        double r86251 = r86245 - r86250;
        return r86251;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.9
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.9

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

  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 2019294 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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