Average Error: 29.1 → 7.7
Time: 26.9s
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 r2483202 = a;
        double r2483203 = r2483202 * r2483202;
        double r2483204 = b;
        double r2483205 = r2483204 * r2483204;
        double r2483206 = r2483203 - r2483205;
        double r2483207 = r2483206 / r2483203;
        double r2483208 = fabs(r2483207);
        double r2483209 = sqrt(r2483208);
        return r2483209;
}
↓
double f(double a, double b) {
        double r2483210 = 1.0;
        double r2483211 = b;
        double r2483212 = a;
        double r2483213 = r2483211 / r2483212;
        double r2483214 = r2483213 * r2483213;
        double r2483215 = r2483210 - r2483214;
        double r2483216 = fabs(r2483215);
        double r2483217 = sqrt(r2483216);
        return r2483217;
}

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 29.1

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

  2. Simplified7.7

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

  3. Final simplification7.7

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

Reproduce

herbie shell --seed 2019142 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))