Average Error: 29.1 → 7.3
Time: 22.5s
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 r10040011 = a;
        double r10040012 = r10040011 * r10040011;
        double r10040013 = b;
        double r10040014 = r10040013 * r10040013;
        double r10040015 = r10040012 - r10040014;
        double r10040016 = r10040015 / r10040012;
        double r10040017 = fabs(r10040016);
        double r10040018 = sqrt(r10040017);
        return r10040018;
}
↓
double f(double a, double b) {
        double r10040019 = 1.0;
        double r10040020 = b;
        double r10040021 = a;
        double r10040022 = r10040020 / r10040021;
        double r10040023 = r10040022 * r10040022;
        double r10040024 = r10040019 - r10040023;
        double r10040025 = fabs(r10040024);
        double r10040026 = sqrt(r10040025);
        return r10040026;
}

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. Simplified7.3

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

  3. Final simplification7.3

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

Reproduce

herbie shell --seed 2019119 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))