The same 8 summaries, combined three ways

The same 8 summaries, combined three ways

Each row is one of the 10 heaviest keys; each column is one order of combining the same 8 per-shard summaries. Where the three columns differ, the count a query returns depends on nothing but the shape of the merge tree — 37 of the keys on this plate. The truth column is the exact count over the union and is what all three are estimating.

Drawn at 700 × 438, wide on the page. Everything above is what merge-shape returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

5 essays call merge-shape. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.