arXiv:2508.05581v1 Announce Type: cross Abstract: Large language models (LLMs) have demonstrated remarkable capabilities for medical question answering and programming, but their potential for generating interpretable computable phenotypes (CPs) is under-explored. In this work, we investigate whether LLMs can generate accurate and concise CPs for six clinical phenotypes of varying complexity, which could be leveraged to enable scalable clinical decision support to improve care for patients with hypertension. In addition to evaluating zero-short performance, we propose and test a synthesize, execute, debug, instruct strategy that uses LLMs to generate and iteratively refine CPs using data-driven feedback. Our results show that LLMs, coupled with iterative learning, can generate interpretable and reasonably accurate programs that approach the performance of state-of-the-art ML methods while requiring significantly fewer training examples.