Quadratic Cost

Adding Up the Turns

Library › Context Problems

1. The Context Window

2. Window Occupancy

3. Growth per Turn

4. Remaining Space

5. Turn Budget

6. Retrieval Footprint

7. Retrieval per Turn

8. Search Rounds

9. Window Sizing

10. Truncation

11. Compaction

12. The Compaction Bill

13. Compacted Retrieval

14. The Compaction Threshold

15. Verbatim Tail

16. Stateless API

17. Retrieval Cost

18. Context Tax

19. Quadratic Cost

20. Cost Forecast

Adding four numbers is easy. Adding a hundred is not, and a conversation does not stop at four. The input goes up by the same step every turn, and a run of numbers like that has an equation: multiply the number of turns by the next number up, halve it, then scale by the step. Work the small case by hand first, then check the equation against what you got. Two numbers decide the total: k, what one turn adds, and n, how many turns there have been. k is fixed by the agent, so shortening its answers drops every total, while n is the conversation itself, and because it appears twice, doubling it does not double the total.

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⬇ Quadratic Cost worksheet (2 pages)

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20. Cost Forecast