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On-chip learning with compute-in-memory (CIM) paradigm has become popular in machine learning hardware design in the recent years. However, it is hard to achieve high on-chip learning accuracy due to the high nonlinearity in the weight update curve of emerging nonvolatile memory (eNVM) based analog synapse devices. Although digital synapse devices offer good learning accuracy, the row-by-row partial sum accumulation leads to high latency. In this paper, the methods to solve the aforementioned issues are presented with a device-to-algorithm level optimization. For analog synapses, novel hybrid precision synapses with good linearity and more advanced training algorithms are introduced to increase the on-chip learning accuracy. The latency issue for digital synapses can be solved by using parallel partial sum read-out scheme. All these features are included into the recently released MLP + NeuroSimV3.0, which is an in-house developed device-to-system evaluation framework for neuro-inspired accelerators based on CIM paradigm.