Average Error: 30.9 → 7.9
Time: 11.4s
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 r3232072 = a;
        double r3232073 = r3232072 * r3232072;
        double r3232074 = b;
        double r3232075 = r3232074 * r3232074;
        double r3232076 = r3232073 - r3232075;
        double r3232077 = r3232076 / r3232073;
        double r3232078 = fabs(r3232077);
        double r3232079 = sqrt(r3232078);
        return r3232079;
}
↓
double f(double a, double b) {
        double r3232080 = 1.0;
        double r3232081 = b;
        double r3232082 = a;
        double r3232083 = r3232081 / r3232082;
        double r3232084 = r3232083 * r3232083;
        double r3232085 = r3232080 - r3232084;
        double r3232086 = fabs(r3232085);
        double r3232087 = sqrt(r3232086);
        return r3232087;
}

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 30.9

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

  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 2019171 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))