Average Error: 29.9 → 7.8
Time: 18.8s
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 r2420650 = a;
        double r2420651 = r2420650 * r2420650;
        double r2420652 = b;
        double r2420653 = r2420652 * r2420652;
        double r2420654 = r2420651 - r2420653;
        double r2420655 = r2420654 / r2420651;
        double r2420656 = fabs(r2420655);
        double r2420657 = sqrt(r2420656);
        return r2420657;
}
↓
double f(double a, double b) {
        double r2420658 = 1.0;
        double r2420659 = b;
        double r2420660 = a;
        double r2420661 = r2420659 / r2420660;
        double r2420662 = r2420661 * r2420661;
        double r2420663 = r2420658 - r2420662;
        double r2420664 = fabs(r2420663);
        double r2420665 = sqrt(r2420664);
        return r2420665;
}

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 29.9

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

  2. Simplified7.8

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

  3. Final simplification7.8

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

Reproduce

herbie shell --seed 2019133 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))