ISAX heterogeneous processors integrate cores that share a common base ISA, with certain cores offering extension ISAs (e.g., vector extension) to accelerate computation. ISAX balances performance and energy efficiency while facilitating the reuse of existing software ecosystems. RISC-V, which adopts the ISAX architecture, has gained extensive attention in both industry and academia. Binary translation via binary rewriting enables transparent ISAX heterogeneous computing by translating extension instructions when migrating a program to cores without extension support. However, current binary rewriting methods still struggle to achieve both high performance and correctness.