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Modern neuroscience employs in silico experimentation on ever-increasing and more detailed neural networks. The high modelling detail goes hand in hand with the need for high model reproducibility, reusability and transparency. Besides, the size of the models and the long timescales under study mandate the use of a simulation system with high computational performance, so as to provide an acceptable time to result. In this work, we present EDEN (Extensible Dynamics Engine for Networks), a new general-purpose, NeuroML-based neural simulator that achieves both high model flexibility and high computational performance, through an innovative model-analysis and code-generation technique. The simulator runs NeuroML v2 models directly, eliminating the need for users to learn yet another simulator-specific, model-specification language. EDEN's functional correctness and computational performance were assessed through NeuroML models available on the NeuroML-DB and Open Source Brain model repositories. In qualitative experiments, the results produced by EDEN were verified against the established NEURON simulator, for a wide range of models. At the same time, computational-performance benchmarks reveal that EDEN runs up to 2 orders-of-magnitude faster than NEURON on a typical desktop computer, and does so without additional effort from the user. Finally, and without added user effort, EDEN has been built from scratch to scale seamlessly over multiple CPUs and across computer clusters, when available., Comment: 29 pages, 9 figures