Average Error: 28.2 → 7.3
Time: 13.1s
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 r1206882 = a;
        double r1206883 = r1206882 * r1206882;
        double r1206884 = b;
        double r1206885 = r1206884 * r1206884;
        double r1206886 = r1206883 - r1206885;
        double r1206887 = r1206886 / r1206883;
        double r1206888 = fabs(r1206887);
        double r1206889 = sqrt(r1206888);
        return r1206889;
}
↓
double f(double a, double b) {
        double r1206890 = 1.0;
        double r1206891 = b;
        double r1206892 = a;
        double r1206893 = r1206891 / r1206892;
        double r1206894 = r1206893 * r1206893;
        double r1206895 = r1206890 - r1206894;
        double r1206896 = fabs(r1206895);
        double r1206897 = sqrt(r1206896);
        return r1206897;
}

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 28.2

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

  2. Simplified7.3

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

  3. Final simplification7.3

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

Reproduce

herbie shell --seed 2019155 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))