Compacting is itself a call to the model, and it is billed like any other. The model reads the whole window to write the summary, system prompt included, and that is the input. Then it writes the summary one token at a time, and that is the output, priced several times higher. So a summary that is a quarter the size of the history is nowhere near a quarter of the bill.
Paid members: the worksheet and its printable PDF are below ↓