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Equation 8 · Part 1 · The Real Economics of Shipping a Model to a Device

Symbol Q^*_distill

Qdistill∗=600/0.0018≈333,000Q^{*}_{\mathrm{distill}} = 600 / 0.0018 \approx 333{,}000
Qdistill∗Q^{*}_{\mathrm{distill}}

What this part means

Qd∗Q^*_distill is part of the quantity the equation computes from the expression on the right.

Its job in the formula

Qd∗Q^*_distill is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…consistent with how frontier and compact API tiers are typically priced relative to each other, that a teacher-class model costs $0.002 per query to serve and a well-distilled student costs $0.0002 — a tenfold gap. Then Qdistill∗Q^{*}_{\mathrm{distill}} = 600 / 0.0018 ≈\approx 333{,}000 queries. Any production feature serving that many requests clears the investment in days, sometimes hours. This is the arithmetic reason distillation has become the default route to a deployable small model rather than a research curiosity:…

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