Average Error: 29.3 → 7.9
Time: 18.3s
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 r2739334 = a;
        double r2739335 = r2739334 * r2739334;
        double r2739336 = b;
        double r2739337 = r2739336 * r2739336;
        double r2739338 = r2739335 - r2739337;
        double r2739339 = r2739338 / r2739335;
        double r2739340 = fabs(r2739339);
        double r2739341 = sqrt(r2739340);
        return r2739341;
}
↓
double f(double a, double b) {
        double r2739342 = 1.0;
        double r2739343 = b;
        double r2739344 = a;
        double r2739345 = r2739343 / r2739344;
        double r2739346 = r2739345 * r2739345;
        double r2739347 = r2739342 - r2739346;
        double r2739348 = fabs(r2739347);
        double r2739349 = sqrt(r2739348);
        return r2739349;
}

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 29.3

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

  2. Simplified7.9

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

  3. Final simplification7.9

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))