ΔE 15.9, loose: different enough that you should pick on purpose. Garnet Purple is noticeably darker, more muted, cooler than Purple Alchemy.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Garnet Purple is noticeably darker, more muted, cooler than Purple Alchemy.
The same difference applies the other way round: Purple Alchemy is noticeably lighter, more saturated, warmer.
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 Purple Alchemy on the colour wheel See Garnet Purple on the colour wheel
All matches: Purple Alchemy equivalents · Garnet Purple equivalents