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We test equivalences between different realisations of Wilson's renormalisation group by computing the leading, subleading, and anti-symmetric corrections-to-scaling exponents, and the full fixed point potential for the Ising universality class to leading order in a derivative expansion. We discuss our methods with a special emphasis on accuracy and reliability. We establish numerical equivalence of Wilson-Polchinski flows and optimised renormalisation group flows with an unprecedented accuracy in the scaling exponents. Our results are contrasted with high-accuracy findings from Dyson's hierarchical model, where a tiny but systematic difference in all scaling exponents is established. Further applications for our numerical methods are briefly indicated., Comment: 9 pages, 7 figures, comparison and discussion/conclusions sharpened, references added

We give simple expressions for the mean of the max and min bounds of the critical-to-classical crossover functions previously calculated [Bagnuls and Bervillier, Phys. Rev. E 65, 066132 (2002)] within the massive renormalization scheme of the F 4 d (n) model in three dimensions (d = 3) and scalar order parameter (n = 1) of the Ising-like universality class. Our main motivation is to get efficient theoretical expressions to coherently account for many measurements performed in systems where the approach to the critical point is limited but yield data which are still reproducible by the F 4 d (n) model (like in the subclass of one-component fluids).