Workflow search pays for complete quality observations, whose execution cost changes as reusable prefixes accumulate. AgentUCT uses an economic model of the remaining evaluation cost to guide UCT selection while backing up raw quality. Query-prefix accounting connects the search decisions to reusable execution state. For finite fixed-reward trees with bounded adaptive cold-cost estimates and successful persistent caching, we prove an $O(\log T)$ bound on cumulative quality regret over $T$ complete evaluations. Across five paired seeds, AgentUCT achieves 69.57% test F1 versus 68.01% for UCT at a 32M weighted-token budget on a retrospective HotpotQA panel. On GSM8K, it reaches 93.07% mean accuracy at the first budget, compared with 92.60% for UCT and 91.60% for AFlow. Single-factor RAG controls show that online prices and historical continuations improve the selected workflows at equal retained evaluation counts.

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