Reason Wide, Not Deep: Amortizing the Reasoning Premium into Distilled Skills

Reasoning modes of language models outperform their non-reasoning counterparts on multi-step agentic tasks, but pay a 3--6$\times$ premium in output tokens on \emph{every} episode --- much of it spent re-deriving procedures that are shared across episodes of the same domain. We show this recurring cost can be \emph{amortized}: a coding agent analyses a small corpus of existing trajectories from a training split and compiles a compact natural-language \emph{skill} that is injected into the non-reasoning model's system prompt. Across four agentic benchmarks (ALFWorld, $\tau^2$-bench telecom and retail, and SSB-Verified), skills recover 55\%--100\%+ of the reasoning gap for GPT 5.4 Mini on held-out tasks --- exceeding the reasoning mode outright on two of four --- while emitting 2.7--6$\times$ fewer output tokens and zero reasoning tokens. Notably, reasoning traces are not a prerequisite: skills distilled from non-reasoning trajectories alone remain competitive with skills distilled from paired reasoning/non-reasoning corpora, with domain-dependent differences between the two sources. We interpret these results through a search lens: test-time reasoning is \emph{deep} search inside a single episode, re-paid at every deployment, while corpus distillation is \emph{wide} search across episodes, paid once. The two recover overlapping procedural knowledge.