\emph{Large Language Models} (LLMs) are increasingly adopted to optimize source code, offering the promise of faster, more efficient programs without manual tuning. This capability is particularly appealing in the context of sustainable computing, where enhanced performance is often assumed to correspond to reduced energy consumption. However, LLMs themselves are energy- and resource-intensive, raising critical questions about whether their use for code optimization is energetically justified. Prior work mainly focused on runtime performance gains, leaving a gap in our understanding of the broader energy implications of LLM-based code optimization.

In this paper, we report on a systematic, energy-focused evaluation of LLM-based code optimization methods. Relying on $118$ tasks from the EvalPerf benchmark, we assess the trade-offs between code performance, correctness, and energy consumption of multiple optimization methods across multiple families of LLMs. We introduce the \emph{Break-Even Point} (BEP) as a key metric to quantify the number of executions required for an optimized program to outweigh the energy consumed when generating the optimization itself.

Our results show that, while certain configurations achieve substantial speedups and energy reductions, these benefits often demand from hundreds to hundreds of thousands of executions to become energetically profitable. Moreover, the optimization process often yields incorrect or less efficient code. Importantly, we identify a weak negative correlation between performance gains and actual energy savings, challenging assumptions that faster code automatically equates to a smaller energy footprint. This work underscores the necessity of energy-aware optimization strategies. Practitioners should carefully target LLM-based optimization efforts to high-frequency, high-impact workloads, while monitoring energy consumption across the entire life-cycle of development and deployment.