Average Error: 32.4 → 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 r128375 = x;
        double r128376 = r128375 / r128375;
        double r128377 = 1.0;
        double r128378 = r128377 / r128375;
        double r128379 = r128375 * r128375;
        double r128380 = sqrt(r128379);
        double r128381 = r128378 * r128380;
        double r128382 = r128376 - r128381;
        return r128382;
}
↓
double f(double x) {
        double r128383 = 1.0;
        double r128384 = 1.0;
        double r128385 = x;
        double r128386 = fabs(r128385);
        double r128387 = r128384 * r128386;
        double r128388 = r128387 / r128385;
        double r128389 = r128383 - r128388;
        return r128389;
}

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

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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