Average Error: 32.2 → 0
Time: 6.1s
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 r3376249 = x;
        double r3376250 = r3376249 / r3376249;
        double r3376251 = 1.0;
        double r3376252 = r3376251 / r3376249;
        double r3376253 = r3376249 * r3376249;
        double r3376254 = sqrt(r3376253);
        double r3376255 = r3376252 * r3376254;
        double r3376256 = r3376250 - r3376255;
        return r3376256;
}
↓
double f(double x) {
        double r3376257 = 1.0;
        double r3376258 = x;
        double r3376259 = fabs(r3376258);
        double r3376260 = 1.0;
        double r3376261 = r3376259 * r3376260;
        double r3376262 = r3376261 / r3376258;
        double r3376263 = r3376257 - r3376262;
        return r3376263;
}

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)))))