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A recently published method for solving the neutrino evolution equation withconstant matter density is further refined and used to lay out an exactalgorithm for computing oscillation probabilities, which is moderately fasterthan previous methods when looping through neutrinos of different energies. Inparticular, the three examples of $\overset{\scriptscriptstyle{(-)}}{\nu}_e$survival, $\overset{\scriptscriptstyle{(-)}}{\nu}_\mu$ survival and$\overset{\scriptscriptstyle{(-)}}{\nu}_e$ appearance probabilities are writtenin terms of mixing angles, mass differences and matter electron density. Aprogram based on this new method is found to be roughly twice as fast as, andin agreement with, the leading GLoBES package. Furthermore, the behaviour ofall relevant effective parameters is sketched out in terms of a range ofneutrino energies, or matter electron densities. For instance, the$\overset{\scriptscriptstyle{(-)}}{\nu}_e$ survival probability in constantmatter density is found to have no dependence on the mixing angle $\theta_{23}$or the CP-violating phase $\delta_{13}$.

Fast Exact Algorithm for Neutrino Oscillation in Constant Matter Density