Because of the ever-increasing execution scale of scientific applications, how to store the extremely large volume of data efficiently is becoming a serious issue. A significant reduction of the scientific data size can effectively mitigate the I/O burden and save considerable storage space. Since lossless compressors suffer from limited compression ratios, error-controlled lossy compressors have been studied for years. Existing error-controlled lossy compressors, however, focus mainly on absolute error bounds, which cannot meet users' diverse demands such as pointwise relative error bounds. Although some of the state-of-the-art lossy compressors support pointwise relative error bound, the compression ratios are generally low because of the limitation in their designs and possible spiky data changes in local data regions. In this work, we propose a novel, efficient approach to perform compression based on the pointwise relative error bound with higher compression ratios than existing solutions provide. Our contribution is threefold. (1) We propose a novel transformation scheme that can transfer the pointwise relative-error-bounded compression problem to an absolute-error-bounded compression issue. We also analyze the practical properties of our transformation scheme both theoretically and experimentally. (2) We implement the proposed technique in two of the most popular absolute-error-bounded lossy compressors, SZ and ZFP. (3) We evaluate our solution using multiple real-world application data across different scientific domains on a supercomputer with up to 4,096 cores and 12 TB of data. Experiments show that our solution achieves over 1.38X dumping and 1.31X loading performance over the second-best lossy compressor, respectively.