Average Error: 29.5 → 7.5
Time: 33.3s
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 r3265861 = a;
        double r3265862 = r3265861 * r3265861;
        double r3265863 = b;
        double r3265864 = r3265863 * r3265863;
        double r3265865 = r3265862 - r3265864;
        double r3265866 = r3265865 / r3265862;
        double r3265867 = fabs(r3265866);
        double r3265868 = sqrt(r3265867);
        return r3265868;
}
↓
double f(double a, double b) {
        double r3265869 = 1.0;
        double r3265870 = b;
        double r3265871 = a;
        double r3265872 = r3265870 / r3265871;
        double r3265873 = r3265872 * r3265872;
        double r3265874 = r3265869 - r3265873;
        double r3265875 = fabs(r3265874);
        double r3265876 = sqrt(r3265875);
        return r3265876;
}

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 29.5

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

  2. Simplified7.5

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

  3. Final simplification7.5

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

Reproduce

herbie shell --seed 2019149 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))