Average Error: 29.1 → 7.5
Time: 8.8s
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 r2357302 = a;
        double r2357303 = r2357302 * r2357302;
        double r2357304 = b;
        double r2357305 = r2357304 * r2357304;
        double r2357306 = r2357303 - r2357305;
        double r2357307 = r2357306 / r2357303;
        double r2357308 = fabs(r2357307);
        double r2357309 = sqrt(r2357308);
        return r2357309;
}
↓
double f(double a, double b) {
        double r2357310 = 1.0;
        double r2357311 = b;
        double r2357312 = a;
        double r2357313 = r2357311 / r2357312;
        double r2357314 = r2357313 * r2357313;
        double r2357315 = r2357310 - r2357314;
        double r2357316 = fabs(r2357315);
        double r2357317 = sqrt(r2357316);
        return r2357317;
}

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. Simplified7.5

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

  3. Final simplification7.5

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

Reproduce

herbie shell --seed 2019129 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))