I've been looking into ∃∀-solvers for program synthesis as well as SyGuS tools lately. Unfortunately I'm not very impressed.
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But my ad-hoc tree search for gen programs for bit permutations using ROT, GREV, and EXT/DEP works really well: http://nbviewer.jupyter.org/url/svn.clifford.at/handicraft/2017/permsyn/data.ipynb …pic.twitter.com/gP1Exkubgj
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Not a superoptimizer, but (most of) the generated programs are reasonably good. The "simple" version of my algo takes ~2 ms on my machine.
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I'm sure that can be further optimized by at least an order of magnitude. I did not optimize my code for performance at all..
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