Local optima and global optimum distribution

<p>We understand the reviewer's concern regarding the distribution of local optima and global optimum. Here we address these concerns via the following two additional results, which were not presented in the main text.</p> <ul> <li><strong>Figure 1, local optima distribution: </strong>This plot presents exactly the analysis that the reviewer suggested on LLVM-W1. Specifically, for all local optima configurations in this landscape, we count the percentage of the on/off (note that all options considered in LLVM are binary) of each option, and plot them in a stacked bar chart. From the results, we can clearly see that for all options, nearly 50% times each option is on/off. This then further consolidates our finding that local optima are uniformly distributed across the landscape.&nbsp;</li> <li><strong>Figure 2, gobal optimum distribution: </strong>This plot visually depicts the distribution of the global optimum (purple star) of each workload of LLVM in the entire landscape. This is achieved by using UMAP dimensionality reduction to project each configurations to a 2D space. From the plot, we can see that the global optimum of each workload tends to be far from each other.&nbsp; <ul> <li>While this provides a qualitative intuition, we also report strict numerical distances here. The average distance for global optimum of different workloads in LLVM, SQLite and Apache is $9.44 \pm 2.48$, $12.54 \pm 3.67$, and $9.64 \pm 2.14$, respectively. These distances are relatively lower than the respective radius of each landscape, but are still considerably high for a direct transfer.&nbsp;</li> </ul> </li> </ul> <p>We sincerely hope these additional results can address the reviewer's concern.&nbsp;</p>