Average Error: 30.6 → 7.9
Time: 12.4s
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 r2842525 = a;
        double r2842526 = r2842525 * r2842525;
        double r2842527 = b;
        double r2842528 = r2842527 * r2842527;
        double r2842529 = r2842526 - r2842528;
        double r2842530 = r2842529 / r2842526;
        double r2842531 = fabs(r2842530);
        double r2842532 = sqrt(r2842531);
        return r2842532;
}
↓
double f(double a, double b) {
        double r2842533 = 1.0;
        double r2842534 = b;
        double r2842535 = a;
        double r2842536 = r2842534 / r2842535;
        double r2842537 = r2842536 * r2842536;
        double r2842538 = r2842533 - r2842537;
        double r2842539 = fabs(r2842538);
        double r2842540 = sqrt(r2842539);
        return r2842540;
}

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 30.6

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

  2. Simplified7.9

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

  3. Final simplification7.9

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

Reproduce

herbie shell --seed 2019192 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))