Average Error: 29.0 → 7.5
Time: 23.0s
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 r2601291 = a;
        double r2601292 = r2601291 * r2601291;
        double r2601293 = b;
        double r2601294 = r2601293 * r2601293;
        double r2601295 = r2601292 - r2601294;
        double r2601296 = r2601295 / r2601292;
        double r2601297 = fabs(r2601296);
        double r2601298 = sqrt(r2601297);
        return r2601298;
}
↓
double f(double a, double b) {
        double r2601299 = 1.0;
        double r2601300 = b;
        double r2601301 = a;
        double r2601302 = r2601300 / r2601301;
        double r2601303 = r2601302 * r2601302;
        double r2601304 = r2601299 - r2601303;
        double r2601305 = fabs(r2601304);
        double r2601306 = sqrt(r2601305);
        return r2601306;
}

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 29.0

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

  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 2019144 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))