approximant

This ends up sounding like l, which is technically known as a lateral approximant because the airstream is only through the sides of the tongue.

Don't fool yourself, it ain't that ez, for instance designing a transcendental function approximant with a mathematically proven accuracy.

Technically it’s a retroflex approximant [1] and is found in many places (often not as a separate character or phoneme).

I was trying to decide between a voiced postalveolar affricate d͡ʒ (hard) or voiced palatal approximant j (soft).

Your (2,2) rational approximant will be much more expensive to compute than the polynomial and won't yield the speed gains Goldberg is looking for.

The Padé approximant looks like another interesting candidate to read about.

I tend to go with the alveolar trill, but other options are the alveolar approximant (as you have suggested) and the alveolar tap.

It's a low order approximant of relatavistic mechanics, though.

In that Padé approximant I think you can save a couple multiplications.

One interesting approach for bit-accurate rational approximants is to have a rational approximant get most of the way there while fitting the error of your rational approximant to a polynomial, but I don't think there's a good way to figure out where the computationally-efficient split of the problem is (ie how big to make the rational side and the polynomial side).

But also, the page you've linked to is misleading - it says that Spanish B/V is [b] (bilabial plosive), while in practice it's [β] (bilabial fricative or approximant) in most positions, with [b] as allophone.

When pronouncing an 'r' (alveolar approximant), I, and I think most English speakers, roll the tongue backwards to some degree (although not enough that the point of articulation is the bottom of the tongue).

Rather, they have an R which is a combination of these (tongue straight, sides curled upward; "alveolar approximant").

If you want a less controversial example use the word “one” and consider the voiced labial–velar approximant.

Asian languages have neither the English R (tongue curled backward in mouth, sides curled upward relative to mouth; "retroflex approximant") nor L (tongue straight, sides curled downward; "lateral alveolar approximant").

In my experience most English dialects don't have a better approximant for "voiceless uvular fricative" and so I don't think it's a terrible clwdge.