Equation 2 · Part 1 · AI Inference Economics in Practice: An Advanced Technical Guide
Symbol r
What this part means
r is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
r is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol r→Article meaning
The passage around this formula
That convergence on roughly one tenth of base input for a cache read — independently verified today across all three platforms [ 2 , 6 , 10 ] — supports a design rule. Let w be the write-price multiplier for the chosen retention window and r 0.1 the read-price multiplier. For a prefix served identically R times within that window — the first serving is the write, the remaining R-1 are reads — caching beats never caching once
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value guide →
See this notation across published equations →
Sources cited in the article section
- [5] Prompt Caching ↗
- [2] Prompt Caching ↗
- [9] Context Caching ↗
- [6] Pricing ↗
- [10] Gemini Developer API Pricing ↗
These citations provide research context; check each source for the exact claim it supports.