Average Error: 32.4 → 0
Time: 4.2s
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 r90106 = x;
        double r90107 = r90106 / r90106;
        double r90108 = 1.0;
        double r90109 = r90108 / r90106;
        double r90110 = r90106 * r90106;
        double r90111 = sqrt(r90110);
        double r90112 = r90109 * r90111;
        double r90113 = r90107 - r90112;
        return r90113;
}
↓
double f(double x) {
        double r90114 = 1.0;
        double r90115 = 1.0;
        double r90116 = x;
        double r90117 = fabs(r90116);
        double r90118 = r90115 * r90117;
        double r90119 = r90118 / r90116;
        double r90120 = r90114 - r90119;
        return r90120;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.4
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.4

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

  2. Simplified4.8

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  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 2019235 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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