If we round the value up (⌈r · b⌉), we get a number that is equal or greater than aideal; if it’s greater, the difference between the two values will be less than 1. In other words, we can write the following inequality:
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Expectedly, two DBs are significantly worse at inserting larger documents, but performance is again very close - slight edge for Postgres with 2213 inserts per second vs 2171 for Mongo.