We proposed a new concept of weak numerical reproducibility and a systematic approach for it with a support of minimal-precision tuning and validation. We expect that the concept of weak numerical reproducibility covers most of the demands for reproducibility in computational sciences. Besides, the minimal-precision computing system can address the demands for accuracy, high-performance, and energy efficient computation as well; ultimately, if it has been realized with new hardware like FPGAs. Although the proposed system is still in development, some of key components are already available, and many of them have been developed by us.