Same answer, four ways to plan the work

One task, four strategies. Watch the LLM calls and the critical-path depth change while the answer stays the same.

Goal: Build a refund summary: the refund window from policy, the warranty on the earbuds made by the company that acquired Acme, and 18% tax on a $250 order.
Four tool calls, one dependency chain (E2 acquirer -> E3 warranty), two independent branches (E1 policy, E4 tax).
LLM calls
5
the cost lever
Critical-path depth
4
sequential rounds
Tool calls
4
same work, always
✓ Final answer (identical for every strategy)
Refund window is 30 days from purchase. The earbuds (made by Globex, which acquired Acme) carry a 2-year limited warranty. Tax on a $250 order at 18% is $45.00.
How we keep it honest: we report LLM calls plus critical-path depth, never wall-clock. "Parallel" means "could run in the same round"; depth is the sequential rounds that real concurrency would shrink.

controller / plan   tools   cost / caution   cheap / win   expensive

The scoreboard

LLM calls is the cost lever; depth is the sequential rounds. Tool calls never change.

Strategy LLM calls Tool calls Crit-path depth

Writing the plan down once cuts LLM calls from 5 (one per hop) to 2 (plan plus synthesize). ReWOO removes every mid-run model call via #E binding. The DAG additionally cuts critical-path depth from 4 to 2: the three independent lookups collapse into one round; only E2 -> E3 chains.