Failure rate against state, medians of 48-value groups

Failure rate against state, medians of 48-value groups

A run "fails" when its estimate of 12,000 distinct keys is out by more than 15%. Each point counts the failures in 240 runs of a design that takes the median of g independent estimators, g from 1 to 9, each holding 48 hashes. The vertical axis is logarithmic, so the straight fall is an exponential: at one estimator 67 of the 240 runs miss, and at 9 it is 3. The median is wrong only when half the groups are wrong, which is a coin-flip tail rather than a variance — and that is where every δ in this field comes from.

Drawn at 690 × 400, wide on the page. Everything above is what tail-sharpening returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

1 essay calls tail-sharpening. 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.