Function that maps the "pureness" of a rational number? By pureness I mean a number that shows how much the numerator and denominator are small.
E.g. $\frac{1}{1}$ is purest, $\frac{1}{2}$ is less pure (but the same as $\frac{2}{1}$), $\frac{2}{3}$ is less pure than the previous examples, $\frac{53}{41}$ is worse, .... $\pi$ isn't pure at all (as well as e...).

$f(\frac{a}{b})=\frac{1}{|a|+|b|}$
For the following conditions on $x$, $f(x)$ is either zero or not defined:


*

*$x$ irrational

*$x=0$


Higher output values implies high purity.
