Reducing the energy consumption of software systems though optimizations techniques such as genetic improvement is gaining interest. However, efficient and effective improvement of software systems requires a better understanding of the code-change search space. One important choice practitioners have is whether to preserve the system’s original output or permit approximation with each scenario having its own search space characteristics. When output preservation is a hard constraint, we report that the maximum energy reduction achievable by the modification operators is 2.69% (0.76% on average). By contrast, this figure increases dramatically to 95.60% (33.90% on average) when approximation is permitted, indicating the critical importance of approximate output quality assessment for code optimization. We investigate synergy, a phenomenon that occurs when simultaneously applied source code modifications produce an effect greater than their individual sum. Our results reveal that 12.0% of all joint code modifications produced such a synergistic effect though 38.5% produce an antagonistic interaction in which simultaneously applied modifications are less effective than when applied individually. This highlights the need for more advanced search-based approaches.