Average Error: 29.4 → 7.3
Time: 17.6s
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 r3998376 = a;
        double r3998377 = r3998376 * r3998376;
        double r3998378 = b;
        double r3998379 = r3998378 * r3998378;
        double r3998380 = r3998377 - r3998379;
        double r3998381 = r3998380 / r3998377;
        double r3998382 = fabs(r3998381);
        double r3998383 = sqrt(r3998382);
        return r3998383;
}
↓
double f(double a, double b) {
        double r3998384 = 1.0;
        double r3998385 = b;
        double r3998386 = a;
        double r3998387 = r3998385 / r3998386;
        double r3998388 = r3998387 * r3998387;
        double r3998389 = r3998384 - r3998388;
        double r3998390 = fabs(r3998389);
        double r3998391 = sqrt(r3998390);
        return r3998391;
}

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 29.4

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

  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 2019162 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))