Average Error: 32.5 → 0
Time: 5.4s
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 r9139633 = x;
        double r9139634 = r9139633 / r9139633;
        double r9139635 = 1.0;
        double r9139636 = r9139635 / r9139633;
        double r9139637 = r9139633 * r9139633;
        double r9139638 = sqrt(r9139637);
        double r9139639 = r9139636 * r9139638;
        double r9139640 = r9139634 - r9139639;
        return r9139640;
}
↓
double f(double x) {
        double r9139641 = 1.0;
        double r9139642 = 1.0;
        double r9139643 = x;
        double r9139644 = fabs(r9139643);
        double r9139645 = r9139642 * r9139644;
        double r9139646 = r9139645 / r9139643;
        double r9139647 = r9139641 - r9139646;
        return r9139647;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  2. Simplified4.7

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied associate-*l/0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))