Average Error: 32.8 → 0
Time: 1.1s
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 r160367 = x;
        double r160368 = r160367 / r160367;
        double r160369 = 1.0;
        double r160370 = r160369 / r160367;
        double r160371 = r160367 * r160367;
        double r160372 = sqrt(r160371);
        double r160373 = r160370 * r160372;
        double r160374 = r160368 - r160373;
        return r160374;
}
↓
double f(double x) {
        double r160375 = 1.0;
        double r160376 = 1.0;
        double r160377 = x;
        double r160378 = fabs(r160377);
        double r160379 = r160376 * r160378;
        double r160380 = r160379 / r160377;
        double r160381 = -r160380;
        double r160382 = r160375 + r160381;
        return r160382;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.8
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.8

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

  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 2020033 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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