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I decided to test the delta DE method even further and figured that the most "regular" object that would show errors most obviously would be a high magnification of the quaternionic Mandy for z^2+c - so here it is rendered at 640*480 exactly as you see it (it's a png).

Magnification: *2.1582312 e12
DE "solid" value: 1 e-13
delta distance: 1.25 e-14

As you can see it's obviously stretching the limits of "double" accuracy - in particular the real axis is scalloped and the rim of the "horn" is markedly uneven.

Anyone with a fast PC and some spare time is invited to have a go at rendering this one with UF's extended precision set to "always" just to compare the result with this render - if you're interested let me know and I'll send you the formula and the parameter file (though be warned on my 3GHz P4HT it took over an hour with extended precision set to "never").



http://www.fractalforums.com/gallery/?sa=view;id=1015

Here's the analytical DE version:



http://www.fractalforums.com/gallery/?sa=view;id=1019

As you can see the analytical method smooths the surface detail so aliasing is reduced but the surface detail (rings) is less obvious.
Edit: For instance in the Delta DE version you can see that the "horn" opens out slightly close to the edge, a detail that's missing from the analytical version.
This took just under 8 minutes @640*480.

For those interested, in the above renders my maxiter parameter was set high at 400 to ensure "solid" was based purely on the distance threshold rather than on the maxiter value - in actual fact the maximum iteration count attained in the delta DE version was 62 and the maximum attained in the analytical DE version was 58.