ΔE 26.9, loose: different enough that you should pick on purpose. Crimson Magenta is much more saturated, warmer than Amethyst Alchemy.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 27). Crimson Magenta is much more saturated, warmer than Amethyst Alchemy.
The same difference applies the other way round: Amethyst Alchemy is much more muted, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Amethyst Alchemy on the colour wheel See Crimson Magenta on the colour wheel
All matches: Amethyst Alchemy equivalents · Crimson Magenta equivalents