Learned indexes, which use machine learning models to replace traditional index structures, have shown promising results in recent studies. However, existing learned indexes exhibit a performance gap between synthetic and real-world datasets, making them far from practical indexes. In this paper, we identify that ignoring the importance of data partitioning during model training is the main reason for this problem. Thus, we explicitly apply data partitioning to index construction and propose a new efficient and updatable cache-aware RMI framework, called CARMI. Specifically, we introduce entropy as a metric to quantify and characterize the effectiveness of data partitioning of tree nodes in learned indexes and propose a novel cost model, laying a new theoretical foundation for future research. Then, based on our novel cost model, CARMI can automatically determine tree structures and model types under various datasets and workloads by a hybrid construction algorithm without any manual tuning. Furthermore, since memory accesses limit the performance of RMIs, a new cache-aware design is also applied in CARMI, which makes full use of the characteristics of the CPU cache to effectively reduce the number of memory accesses. Our experimental study shows that CARMI performs better than baselines, achieving an average of 2.2x/1.9x speedup compared to B+ Tree/ALEX, while using only about 0.77x memory space of B+ Tree. On the SOSD platform, CARMI outperforms all baselines, with an average speedup of 1.2x over the nearest competitor RMI, which has been carefully tuned for each dataset in advance.