Average Error: 30.6 → 7.7
Time: 39.0s
Precision: 64
\[0.0 \le b \le a \le 1\]
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
↓
\[\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}\]
\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 r4512661 = a;
        double r4512662 = r4512661 * r4512661;
        double r4512663 = b;
        double r4512664 = r4512663 * r4512663;
        double r4512665 = r4512662 - r4512664;
        double r4512666 = r4512665 / r4512662;
        double r4512667 = fabs(r4512666);
        double r4512668 = sqrt(r4512667);
        return r4512668;
}
↓
double f(double a, double b) {
        double r4512669 = 1.0;
        double r4512670 = b;
        double r4512671 = a;
        double r4512672 = r4512670 / r4512671;
        double r4512673 = r4512672 * r4512672;
        double r4512674 = r4512669 - r4512673;
        double r4512675 = fabs(r4512674);
        double r4512676 = sqrt(r4512675);
        return r4512676;
}

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 30.6

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

  2. Simplified7.7

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

  3. Final simplification7.7

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

Reproduce

herbie shell --seed 2019168 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))