Failure of HLL downsize law

[oscar-stripe]

[info] ! HyperLogLog.Downsize dense HLLs from 14 bits to 4 bits: Falsified after 0 passed tests.
[info] > Successes: 80 (out of 100)
[info] > Expected successes: 99.72
[info] > Required successes: 84.55
[info] > Example failures:
[info]   >: Exact result: 4976. Approx result: Approximate(592,2693,4795,0.9972).
[info]   >Exact result: 4976. Approx result: Approximate(592,2693,4795,0.9972).
[info]   >Exact result: 4976. Approx result: Approximate(592,2693,4795,0.9972).
[info]   >Exact result: 4976. Approx result: Approximate(592,2693,4795,0.9972).
[info]   >Exact result: 4976. Approx result: Approximate(592,2693,4795,0.9972).

One thing that is interesting is that all of these are the same. I wonder if that is something about downsizing to 4 bits?

Anyway, something is amiss...

[johnynek]

I guess this is actually buggy:

failing seed for HyperLogLog.Downsize dense HLLs from 14 bits to 4 bits is JWFZvPc_XzUZXFpMqCp2JSEkQaYNSPCIIszXMxU4NIC=
[info] ! HyperLogLog.Downsize dense HLLs from 14 bits to 4 bits: Falsified after 0 passed tests.
[info] > Successes: 80 (out of 100)
[info] > Expected successes: 99.72
[info] > Required successes: 84.55
[info] > Example failures:
[info]   >: Exact result: 5014. Approx result: Approximate(496,2258,4020,0.9972).
[info]   >Exact result: 5014. Approx result: Approximate(496,2258,4020,0.9972).
[info]   >Exact result: 5014. Approx result: Approximate(496,2258,4020,0.9972).
[info]   >Exact result: 5014. Approx result: Approximate(496,2258,4020,0.9972).
[info]   >Exact result: 5014. Approx result: Approximate(496,2258,4020,0.9972).

Exact result 5014, but the 99.72% confidence interval is 496 to 4020? Yeah, that doesn't make sense.

I imagine there is a bug with either the way downsizing works, the estimate, or the confidence interval.