Large language models (LLMs) have become a significant workload since their appearance. However, they are also computationally expensive as they have billions of parameters and are trained with massive amounts of data. Thus, recent works have developed dedicated CUDA kernels for LLM training and inference instead of relying on compilergenerated ones, so that hardware resources are as fully utilized as possible. In this work, we explore the possibility of GPU native instruction optimization to further push the CUDA kernels to extreme performance. Contrary to prior works, we adopt an automatic optimization approach by defining a search space of possible GPU native instruction schedules, and then we apply stochastic search to perform optimization. Experiments show that SIP can further improve CUDA kernel throughput by automatically discovering better GPU native instruction schedules and the optimized schedules are tested by 10 million test samples.