Give the cost model a name, so a caller can pick one instead of writing one (#746 v2.0)

[Rafael-SOWNet]

#746 v2.0 asks for "a cost model that is comparable across domains and is data, so callers can supply their own (smallest tree, fewest radicals, numerically stablest, most readable to a student)".

Half of it already existed

MathS.Settings.ComplexityCriteria has always been a Setting<Func<Entity, double>>, and its own documentation carries a worked example of ranking by fewest divisions. Measured, it does exactly what it says:

a / b + b / c                 default
(a * c + b ^ 2) / (b * c)     ranking by fewest divisions

Worth stating plainly before adding anything, because the roadmap item reads as though none of it were built.

What was missing: a criterion could not be named

Two callers wanting the smallest tree each wrote the same lambda, neither could record which one produced an answer, and nothing could list the alternatives.

using var _ = MathS.Settings.ComplexityCriteria.Set(CostModel.FewestDivisions.Cost);

CostModel is a name, a description and the function, with Default, SmallestTree, FewestDivisions and FewestRadicals in All.

CostModel.Default is the function the setting already used — moved, not copied, with ComplexityCriteria now initialising from it. A copy would have passed every test here and drifted later, so the test asserts the rate is equal, not merely that the same candidate wins.

Every model counts nodes a little, even the ones about something else

A criterion counting only its own feature ties constantly, and a tie goes to whichever candidate the search generated first — an accident rather than a preference. That is the same trap #205 hit, where two forms of 1 / (sqrt(3) + 5) rated equal. The node term is small enough not to overturn the feature and large enough to order what the feature cannot separate.

Two things measured rather than assumed — both of which I had wrong first

• The default prefers the rationalised form of 1 / (sqrt(3) + 5), 17 against 19. But a hand-written (sqrt(3) - 5) / (-22) costs 21, worse than either, because the negative denominator is itself weighted. The form to compare against is the one Simplify actually produces.
• The models' disagreement is on a / b + b / c: default 24 against 33 for the combined form, fewest-divisions 2.007 against 1.011 the other way. The radical pair's node counts tie at 7, so that pair demonstrates a weighting difference, not a disagreement — it gets its own test saying so.

Measured

Suite 7225 passed / 0 failed, 16 new. No behaviour changes — the default is the same function and the suite's answers are unmoved. PublicApi.txt records the type; the new file gets a per-file header year in .editorconfig, following the convention documented there.

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