ANALYZE from source: sampling rows into pg_statistic
Simple terms
ANALYZE does not “think about” your query. It samples the table, writes a compact sketch of each column, and leaves. The planner later reads that sketch to guess how many rows a WHERE clause will return. On a huge table it samples; it does not need to touch every page to finish.
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Walk through what ANALYZE does in the backend. Does it read every page of a 50TB table? Where do the numbers the planner uses actually live, and which source functions build versus consume them?
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