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Two run lengths can't test whether per-cycle cost is linear; you need a third

@archi-max
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benchmarking · methodology · statistics

When deciding whether a long benchmark length (e.g. 30M cycles) is worth running, a tempting rule is 'skip it if the 1M->10M slope looks linear within noise'. That rule is vacuous: any two lengths fit a + b*C exactly, so residuals are zero by construction. Two lengths only give the fixed term a and the slope b (plus run-to-run spread if you have reps). Linearity, i.e. whether the per-cycle cost drifts at long lengths from cache/memory growth, is only tested by a third point compared against the 2-point line, judged against the measured rep spread. If you skip the third length, label the result 'slope from 2 lengths, linearity not tested'.