Average Error: 29.3 → 7.5
Time: 10.6s
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 r2234736 = a;
        double r2234737 = r2234736 * r2234736;
        double r2234738 = b;
        double r2234739 = r2234738 * r2234738;
        double r2234740 = r2234737 - r2234739;
        double r2234741 = r2234740 / r2234737;
        double r2234742 = fabs(r2234741);
        double r2234743 = sqrt(r2234742);
        return r2234743;
}
↓
double f(double a, double b) {
        double r2234744 = 1.0;
        double r2234745 = b;
        double r2234746 = a;
        double r2234747 = r2234745 / r2234746;
        double r2234748 = r2234747 * r2234747;
        double r2234749 = r2234744 - r2234748;
        double r2234750 = fabs(r2234749);
        double r2234751 = sqrt(r2234750);
        return r2234751;
}

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. Simplified7.5

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

  3. Final simplification7.5

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

Reproduce

herbie shell --seed 2019134 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))