A natural way to explain neural network responses is by propositional rules. Currently, the state of the art on XAI methods presents local and global algorithms, with local techniques aiming to explain single samples in their neighbourhood. We present here Fidex, a new local algorithm, which we apply to ensembles of neural networks, ensembles of decision trees and support vector machines. The key idea behind Fidex is the precise identification of discriminating hyperplanes. Its computational complexity for a neural network is linear with respect to the product of: the dimensionality of the classification problem; the number of training samples; the maximal number of antecedents per rule; and a constant related to a particular activation function approximating a sigmoid function. Based on Fidex, we formulated a global algorithm named FidexGlo. Essentially, FidexGlo uses Fidex to generate a number of rules equal to the number of samples. Then, a heuristic is deployed to remove as many rules as possible. FidexGlo was applied to four benchmark classification problems, providing competitive results with our previous global rule extraction technique. Fidex and FidexGlo are available at https://github.com/HES-XPLAIN/dimlpfidex.