Average Error: 32.2 → 0
Time: 5.6s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right| \cdot 1}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right| \cdot 1}{x}
double f(double x) {
        double r3874994 = x;
        double r3874995 = r3874994 / r3874994;
        double r3874996 = 1.0;
        double r3874997 = r3874996 / r3874994;
        double r3874998 = r3874994 * r3874994;
        double r3874999 = sqrt(r3874998);
        double r3875000 = r3874997 * r3874999;
        double r3875001 = r3874995 - r3875000;
        return r3875001;
}
↓
double f(double x) {
        double r3875002 = 1.0;
        double r3875003 = x;
        double r3875004 = fabs(r3875003);
        double r3875005 = 1.0;
        double r3875006 = r3875004 * r3875005;
        double r3875007 = r3875006 / r3875003;
        double r3875008 = r3875002 - r3875007;
        return r3875008;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 32.2

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

  2. Simplified4.9

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

  4. Applied associate-*l/0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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