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The increasing demand for improving deep learning model performance has led to a paradigm shift in supporting low-precision computation to harness the robustness of deep learning to errors. Despite the emergence of new low-precision data types and optimization approaches, existing hardware and software have insufficient and inefficient support for those evolving data types, making it challenging to achieve real performance gains through low-precision computing. This paper introduces Ladder, a novel compiler designed to bridge the gap between evolving custom data types and the fixed precision formats supported by current hardware. Leveraging a general type system, tType, and an extended tensor expression, Ladder transforms deep neural network (DNN) computations into optimized computing pipelines with custom data types as the first-class citizen, exposing an optimization space for efficiently handling data storage, accesses, and type conversions. Ladder employs a new set of tensor scheduling primitives and a hardware-aware optimization policy to navigate the complex transformation space, ensuring optimal performance across different memory layers and DNN operators. Our evaluation demonstrates Ladder's capability to systematically support a wide array of low-bit precision custom data types, significantly enhancing the performance of DNN computations on modern accelerators without necessitating hardware modifications. This innovation empowers model designers with the ability to explore data type optimizations and offers hardware vendors a flexible solution to expand their support for diverse precision formats.