Average Error: 14.4 → 14.4
Time: 868.0ms
Precision: binary64
Cost: 13504
\[0 \leq b \land b \leq a \land a \leq 1\]
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
↓
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}
↓
\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}
(FPCore (a b)
 :precision binary64
 (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))
↓
(FPCore (a b)
 :precision binary64
 (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))
double code(double a, double b) {
	return sqrt(fabs(((a * a) - (b * b)) / (a * a)));
}
↓
double code(double a, double b) {
	return sqrt(fabs(((a * a) - (b * b)) / (a * a)));
}

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 14.4

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

Reproduce

herbie shell --seed 2021042 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :precision binary64
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))