Average Error: 29.0 → 7.5
Time: 21.4s
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 r2900013 = a;
        double r2900014 = r2900013 * r2900013;
        double r2900015 = b;
        double r2900016 = r2900015 * r2900015;
        double r2900017 = r2900014 - r2900016;
        double r2900018 = r2900017 / r2900014;
        double r2900019 = fabs(r2900018);
        double r2900020 = sqrt(r2900019);
        return r2900020;
}
↓
double f(double a, double b) {
        double r2900021 = 1.0;
        double r2900022 = b;
        double r2900023 = a;
        double r2900024 = r2900022 / r2900023;
        double r2900025 = r2900024 * r2900024;
        double r2900026 = r2900021 - r2900025;
        double r2900027 = fabs(r2900026);
        double r2900028 = sqrt(r2900027);
        return r2900028;
}

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 29.0

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

  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 2019141 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))