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SQLITE_ENABLE_STAT4 triggers failures in analyze3.test
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> ...SETI program analyzing data streams looking for alien signals. Literally millions of computers...

I certainly commend the vision!

Any problem could be solved, possibly much better, when throwing near infinite resources at it [Any other Factorio players here? :)], but what Engineers have to always be keenly aware of, is the Value proposition.

The reward of finding one more obscure test-case that isn't covered by the existing set, to uncover a possible problem for a compile-mutation with prevalence factor of 1 in Millions-Billions (unpronounceable figures as others demonstrated), is quite low. I'm not trying to down-play it, let's regard it as an important problem, but the point here is the incidence-level, not problem severity.

I'd say the best thing to do is what is being done - i.e:  
"Programmers of Earth, please compile SQLite any ways you like, and if you find a combination that fails any test in any new release, please report it, we will add it to the test set."

Fast, efficient, Zero-added energy, solves all encountered problems as fast, with the one very minor disadvantage: The problem has to actually be "encountered" first.

I say "minor disadvantage", because while this might be an inadequate philosophy when building a control system for a Nuclear power-plant, in programming, most software do go through quite a lot of testing and verification, and time for this is allocated to every project's budget. Saving those few, who use a truly unique compile-set, about a Day's worth (that's the typical turn-around time) would gain you no more than a mild "Thanks hey."  They typically have other bigger problems.

Hardly worth extra effort, never mind SETI-level effort.

Still, perhaps a public script or small app that does nothing but run your compiles, run the tests, then in the even of failure, send your compile-options, System info plus the failure-detail to a small web API or such where the SQLite people can examine it.

Currently this is pretty much what the forum does with the slight deficit that some people might not send in their failures (or not adequately detail them), we only see the ones who do. But then they may as readily choose not to run the script/app.

I honestly doubt there is much improvement to be had over the current.