Average Error: 32.7 → 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 r61369 = x;
        double r61370 = r61369 / r61369;
        double r61371 = 1.0;
        double r61372 = r61371 / r61369;
        double r61373 = r61369 * r61369;
        double r61374 = sqrt(r61373);
        double r61375 = r61372 * r61374;
        double r61376 = r61370 - r61375;
        return r61376;
}
↓
double f(double x) {
        double r61377 = 1.0;
        double r61378 = 1.0;
        double r61379 = x;
        double r61380 = fabs(r61379);
        double r61381 = r61378 * r61380;
        double r61382 = r61381 / r61379;
        double r61383 = r61377 - r61382;
        return r61383;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.7
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.7

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

  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 2019291 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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