This is not an issue of precision. It is the property of the function itself. Consider a function
and choose two numbers 
, 
They have a difference of 
. But if I apply the function
, 
I get a difference of 
on their output. As you can see, there is nothing I can do to improve the 'precision'. This is already the exact output of the function.
and choose two numbers , They have a difference of . But if I apply the function, I get a difference of on their output. As you can see, there is nothing I can do to improve the 'precision'. This is already the exact output of the function.I can define an arbitrary function to further magnify this effect: 
.
.
