Average Error: 29.2 → 7.5
Time: 18.0s
Precision: 64
\[0 \le b \le a \le 1\]
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
↓
\[\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}\]
\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}
↓
\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}
double f(double a, double b) {
        double r2859364 = a;
        double r2859365 = r2859364 * r2859364;
        double r2859366 = b;
        double r2859367 = r2859366 * r2859366;
        double r2859368 = r2859365 - r2859367;
        double r2859369 = r2859368 / r2859365;
        double r2859370 = fabs(r2859369);
        double r2859371 = sqrt(r2859370);
        return r2859371;
}
↓
double f(double a, double b) {
        double r2859372 = 1.0;
        double r2859373 = b;
        double r2859374 = a;
        double r2859375 = r2859373 / r2859374;
        double r2859376 = r2859375 * r2859375;
        double r2859377 = r2859372 - r2859376;
        double r2859378 = fabs(r2859377);
        double r2859379 = sqrt(r2859378);
        return r2859379;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.2

    \[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]

  2. Simplified7.5

    \[\leadsto \color{blue}{\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}}\]

  3. Final simplification7.5

    \[\leadsto \sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))