More Than a Score: Probing the Impact of Prompt Specificity on LLM Code Generation

State-of-the-art Large Language Models (LLMs) achieve high pass@1 on general benchmarks like HumanEval but underperform on specialized suites such as ParEval. Is this due to LLMs missing domain knowledge or insufficient prompt detail is given? To answer this, we introduce PartialOrderEval, which augments any code generation benchmark with a partial order of prompts from minimal to maximally detailed. Applying it to HumanEval and both serial and OpenMP subsets of ParEval, we measure how pass@1 scales with prompt specificity. Our experiments with Llama-3.x and Qwen2.5-Coder demonstrate varying degrees of prompt sensitivity across different tasks, and a qualitative analysis highlights explicit I/O specifications, edge-case handling, and stepwise breakdowns as the key drivers of prompt detail improvement.