[DRAFT] Implement C optimal discretisation strategy to reduce gradient variance in error budgeting feature

[adlantz]

Opening this PR as a draft just to track changes. As of 5/29 all work is local and hasn't been committed to this fork.

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[nelimee]

@adlantz let me know when I should start reviewing this PR. Ideally, it should be out of draft and with CI passing, but I am fine doing a pre-review if you need one :)