confrac,matrix function 2.

I don't know why you are confused. What you are doing the whole time is calculating approximations. With different substitutions you get different aproximation-functions. This is especially true as you compare a linear substitution to a nonlinear one. Your 1/x substitution has quite some advantages, though.

While I can see no reason why someone would do that I find it strange and have no suitable explanation for tha fact that applying confrac a second time makes the approximation that bad.