CMYK to RGB

[diuming]

I try to convert CMYK to RGB with the following formula.
R = 255 × (1-C) × (1-K)
G = 255 × (1-M) × (1-K)
B = 255 × (1-Y) × (1-K)

Convert CMYK(0, 100, 100, 80) to RGB that I get RGB(51, 0, 0).

I try to use pdf-lib to draw rectangle with CMYK(0, 1.0, 1.0, 0.8) color and generate pdf.
I found the rectangle RGB color is RGB(59, 8, 3) and It's better than RGB(51, 0, 0).

The pdf-lib look not use icc-profile and pdf file not embedded icc-profile create by pdf-lib.

I'm looking for a formula or a approach to convert CMYK(0, 100, 100, 80) to RGB(59, 8, 3), because RGB(59, 8, 3) is correct color and may color systems converting result are RGB(59, 8, 3).

I don't have any idea and give me advice please.