Average Error: 30.5 → 8.0
Time: 45.2s
Precision: 64
\[0.0 \le b \le a \le 1.0\]
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
↓
\[\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}\]
\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 r3263032 = a;
        double r3263033 = r3263032 * r3263032;
        double r3263034 = b;
        double r3263035 = r3263034 * r3263034;
        double r3263036 = r3263033 - r3263035;
        double r3263037 = r3263036 / r3263033;
        double r3263038 = fabs(r3263037);
        double r3263039 = sqrt(r3263038);
        return r3263039;
}
↓
double f(double a, double b) {
        double r3263040 = 1.0;
        double r3263041 = b;
        double r3263042 = a;
        double r3263043 = r3263041 / r3263042;
        double r3263044 = r3263043 * r3263043;
        double r3263045 = r3263040 - r3263044;
        double r3263046 = fabs(r3263045);
        double r3263047 = sqrt(r3263046);
        return r3263047;
}

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 30.5

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

  2. Simplified8.0

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

  3. Final simplification8.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))