Large language models (LLMs) have shown strong abilities in writing and revising programs, yet many program-synthesis benchmarks still evaluate programs in symbolic or digital environments. We introduce compositional machine design, a physically grounded form of program synthesis where machines are written as programs that compose standardized parts, and success is determined by simulated physical behavior. To study this problem, we present BesiegeField, a testbed built on the machine-building game Besiege. In BesiegeField, LLM agents generate machine programs from textual functional demands, execute the resulting machines in simulation, and receive rewards and state feedback. We benchmark LLM agents across representative machine-design tasks under single-agent generation, iterative editing, and hierarchical workflows. Strong models recover task-relevant structures and sometimes achieve nontrivial physical performance, but often struggle with spatially precise assembly, mechanism-level planning, and translating feedback into useful structural edits. We further finetune Qwen2.5-14B, an open-source LLM, with reinforcement learning from simulation-derived rewards. We find that, under a fixed generation budget, RL improves the best machine discovered. We additionally evaluate human performance to provide a reference point for task difficulty. These results establish compositional machine design as a testbed for studying LLM agents that synthesize executable machine programs and improve them through physical feedback.

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