Optimization of calculation speed with distance estimation

I was just working with the distance estimation algorithms and also created a few for some of my own fractals.
The idea came up that it might be possible to significantly increase the calculation speed using a distance estimation method, especially when high anti-aliasing is used.
The distance is particularly accurate when you are near the boundary. You could, for example, use a 9x9 anti-aliasing near the 1-pixel boundary and reduce it to 1:1 or 2:1 (for the orbit edges) for all other pixels. Depending on the fractal, this could bring enormous speed improvements.

The distance does not need to be calculated perfectly, a distance limit is sufficient. It would be used in a pixel-accurate variant that takes zoom and resolution into account.

The only downside is likely that perturbation may no longer work, as the final calculation requires both z and dz.

To achieve this, the formula would need access to this level of the program. It would need to be possible to tell UF during the first calculation whether it is a pixel with high or low anti-aliasing requirements.

Not all formulas can work with the distance calculation method that Mandelbrot uses, but many are compatible, and I think Mandelbrot is one of the favorites for many. An expert could derive a distance calculation for their favorite formula.

(One more note: The distance formula I found in the parameters of UF is incorrect. There should be at least a correct formula available for Mandelbrot as a first example.)

In case something more.

The distance algo can render pixel exact boundaries.
And for optimization you can use a distance for 2 3 pixels, and only render this area with high anti aliasing.

I needs only a mechanism so that the script can report back.
(There could be a extra mechanism for this... a Distance: section(?))

The same is possible for inside, what could be a big benefit, if you can exclude pixels to be rendered completely. There is a inside distance algo too.

Here without anti aliasing.

The high precision zone must not be so big.
And just imagine the speed gain... in deep zoom.....