Average Error: 29.0 → 7.6
Time: 14.5s
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 r1490097 = a;
        double r1490098 = r1490097 * r1490097;
        double r1490099 = b;
        double r1490100 = r1490099 * r1490099;
        double r1490101 = r1490098 - r1490100;
        double r1490102 = r1490101 / r1490098;
        double r1490103 = fabs(r1490102);
        double r1490104 = sqrt(r1490103);
        return r1490104;
}
↓
double f(double a, double b) {
        double r1490105 = 1.0;
        double r1490106 = b;
        double r1490107 = a;
        double r1490108 = r1490106 / r1490107;
        double r1490109 = r1490108 * r1490108;
        double r1490110 = r1490105 - r1490109;
        double r1490111 = fabs(r1490110);
        double r1490112 = sqrt(r1490111);
        return r1490112;
}

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. Simplified7.6

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

  3. Final simplification7.6

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

Reproduce

herbie shell --seed 2019151 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0 b a 1)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))