Current approaches for clinical information extraction are inefficient in terms of computational costs and memory consumption, hindering their application to process large-scale electronic health records (EHRs). We propose an efficient end-to-end model, the Joint-NERRE-Fourier (JNRF), to jointly learn the tasks of named entity recognition and relation extraction for documents of variable length. The architecture uses positional encoding and unitary batch sizes to process variable length documents and uses a weight-shared Fourier network layer for low-complexity token mixing. Finally, we reach the theoretical computational complexity lower bound for relation extraction using a selective pooling strategy and distance-aware attention weights with trainable polynomial distance functions. We evaluated the JNRF architecture using the 2018 N2C2 ADE benchmark to jointly extract medication-related entities and relations in variable-length EHR summaries. JNRF outperforms rolling window BERT with selective pooling by 0.42%, while being twice as fast to train. Compared to state-of-the-art BiLSTM-CRF architectures on the N2C2 ADE benchmark, results show that the proposed approach trains 22 times faster and reduces GPU memory consumption by 1.75 folds, with a reasonable performance tradeoff of 90%, without the use of external tools, hand-crafted rules or post-processing. Given the significant carbon footprint of deep learning models and the current energy crises, these methods could support efficient and cleaner information extraction in EHRs and other types of large-scale document databases