Average Error: 32.6 → 0
Time: 2.7s
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 r78472 = x;
        double r78473 = r78472 / r78472;
        double r78474 = 1.0;
        double r78475 = r78474 / r78472;
        double r78476 = r78472 * r78472;
        double r78477 = sqrt(r78476);
        double r78478 = r78475 * r78477;
        double r78479 = r78473 - r78478;
        return r78479;
}
↓
double f(double x) {
        double r78480 = 1.0;
        double r78481 = 1.0;
        double r78482 = x;
        double r78483 = fabs(r78482);
        double r78484 = r78481 * r78483;
        double r78485 = r78484 / r78482;
        double r78486 = r78480 - r78485;
        return r78486;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  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 2019298 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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