Two costs compound at once
The fixed overhead — system prompt plus tool schemas — is paid on every iteration. The accumulated history grows with every step, because each tool result and each thought is resent on the next call.
Together they produce a cost curve that a per-request estimate misses by a factor of three to ten. The table shows where the money actually goes, iteration by iteration.
What to change
The overhead line is usually the largest single item and the easiest to cut: trim tool descriptions and move conditional instructions into skills. Caching it drops it to roughly a tenth, which the checkbox models.
The iteration count multiplies everything. An agent that cannot finish in four passes rarely finishes in ten either — it just costs more to fail. Lower the ceiling, then investigate why anything was reaching it.