It certainly took long enough, but after an hour or so of hunting I finally tracked down the formula that the ImageMagick color converter uses to convert CMYK colors into RGB. I rewrote it a little to make the expression more illuminating:

for a CMYK color point \((c,m,y,k)\) and RGB color point \((r,g,b)\). The tricky part to locate was the constant \(Q_R\), and a related constant \(Q_S\), which ImageMagick calls QuantumRange and QuantumScale respectively.

• \(Q_R\) is the range that each of the color values can take on, so if each of your channels (red, green, blue, cyan, magenta, yellow, black) is given by a number from 0–255, for example, \(Q_R\) would be 255.
• \(Q_S\) is actually just the reciprocal of \(Q_R\). I suspect they give it a different name only because floating-point division is pretty inefficient so it saves some CPU cycles to precompute \(1/Q_R\).

If anyone wants to track it down themselves, the algorithm is in the ConvertCMYKToRGB function in the ImageMagick source code (line 1327 of colorspace.c) and the constants are defined in magick-type.h (QuantumRange) and image-private.h (QuantumScale).