Average Error: 32.6 → 0
Time: 4.5s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{\frac{x}{1}}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{\frac{x}{1}}
double f(double x) {
        double r172581 = x;
        double r172582 = r172581 / r172581;
        double r172583 = 1.0;
        double r172584 = r172583 / r172581;
        double r172585 = r172581 * r172581;
        double r172586 = sqrt(r172585);
        double r172587 = r172584 * r172586;
        double r172588 = r172582 - r172587;
        return r172588;
}
↓
double f(double x) {
        double r172589 = 1.0;
        double r172590 = x;
        double r172591 = fabs(r172590);
        double r172592 = 1.0;
        double r172593 = r172590 / r172592;
        double r172594 = r172591 / r172593;
        double r172595 = r172589 - r172594;
        return r172595;
}

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. Simplified4.9

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

  4. Applied *-un-lft-identity4.9

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

  5. Applied *-un-lft-identity4.9

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

  6. Applied times-frac4.9

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

  7. Applied associate-*l*4.9

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

  8. Simplified0

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

  9. Final simplification0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "sqrt sqr"

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

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