WEBVTT

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When does preparation repay its cost?

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A reusable representation can take time to build before it answers a query.

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We will compare total time for the same queries and the same output,

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using an explicitly hypothetical example. You will learn to include the build cost,

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locate equality, and distinguish it from the first strict improvement.

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Assume direct evaluation takes three milliseconds per query.

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The prepared method costs one hundred twenty
milliseconds to build and half a millisecond per query.

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Both return the same single Boolean answer for each input.

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These numbers illustrate a method; they are not measurements of this repository.

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Let N be the number of queries. Direct evaluation costs three N milliseconds.

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The prepared path costs one hundred twenty plus half N.

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The build cost is paid once only if the prepared artifact can actually be reused across those queries.

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Set the two costs equal.

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Subtract half N from both sides, giving two and a half N equals one hundred twenty.

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Divide to obtain

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Divide to obtain forty-eight queries.

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At exactly forty-eight, both paths take

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At exactly forty-eight, both paths take one hundred forty-four milliseconds under our assumptions.

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At ten queries, direct evaluation takes thirty milliseconds,
while preparation plus queries takes one hundred twenty-five.

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At one hundred queries, direct takes three hundred and prepared takes one hundred seventy.

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The preferable path changes with reuse, even though each prepared query is faster.

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A real experiment must say whether parsing, compilation,
caches, conversion, and final output are included.

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Use the same inputs, verify results first, and report
repeated measurements with host and software details.

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A warm cached run and a cold run answer different questions.

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In our hypothetical model, equality occurs at forty-eight queries.

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What is the smallest whole number of queries for which the prepared method is strictly faster?

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Calculate both totals there rather than rounding the equality point into a claimed win.

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At forty-nine queries, the direct total is

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At forty-nine queries, the direct total is one hundred forty-seven milliseconds.

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The prepared total is

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The prepared total is one hundred forty-four and a half.

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That is the first whole-query count with a strict improvement in this model.

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Different build or query costs would change the crossover.