Average Error: 31.2 → 8.3
Time: 14.7s
Precision: 64
\[0.0 \le b \le a \le 1\]
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
↓
\[\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}\]
\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 r4124461 = a;
        double r4124462 = r4124461 * r4124461;
        double r4124463 = b;
        double r4124464 = r4124463 * r4124463;
        double r4124465 = r4124462 - r4124464;
        double r4124466 = r4124465 / r4124462;
        double r4124467 = fabs(r4124466);
        double r4124468 = sqrt(r4124467);
        return r4124468;
}
↓
double f(double a, double b) {
        double r4124469 = 1.0;
        double r4124470 = b;
        double r4124471 = a;
        double r4124472 = r4124470 / r4124471;
        double r4124473 = r4124472 * r4124472;
        double r4124474 = r4124469 - r4124473;
        double r4124475 = fabs(r4124474);
        double r4124476 = sqrt(r4124475);
        return r4124476;
}

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 31.2

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

  2. Simplified8.3

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

  3. Final simplification8.3

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))