Average Error: 31.2 → 8.3
Time: 14.0s
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 r1896618 = a;
        double r1896619 = r1896618 * r1896618;
        double r1896620 = b;
        double r1896621 = r1896620 * r1896620;
        double r1896622 = r1896619 - r1896621;
        double r1896623 = r1896622 / r1896619;
        double r1896624 = fabs(r1896623);
        double r1896625 = sqrt(r1896624);
        return r1896625;
}
↓
double f(double a, double b) {
        double r1896626 = 1.0;
        double r1896627 = b;
        double r1896628 = a;
        double r1896629 = r1896627 / r1896628;
        double r1896630 = r1896629 * r1896629;
        double r1896631 = r1896626 - r1896630;
        double r1896632 = fabs(r1896631);
        double r1896633 = sqrt(r1896632);
        return r1896633;
}

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)))))