How to create an error image with GIMP

I need to create a quality comparison between two rendering methods by showing the difference of the results akin to figure 6 in [Walter et al. 2005] (p. 5):

(Image copyright by Walter et al. 2005).

I don't exactly understand how to create this effect in such a way that it conforms to the description of 16x error or similar (8x difference etc.). I assume the basis of the idea is to increase the contrast of the difference of the two images to compare. The contrast is increased in a way that conforms to the expression 16x, e.g. by multiplying the values of each channel (RGB) by the factor 16.

However, trying to reproduce the results in the figure above, I found that the curve seems of rather random nature, which might well be due to the lack of understanding the procedure. I used the bottom left and right images, viewed the difference in GIMP and adjusted the value curve of the left one until the difference appeared as dark as possible (indicating the smallest difference). As mentioned before, this curve did not look like it had anything to do with multiplying values by 16.

So, how can I reproduce the results depicted in the figure above in GIMP, and what is the meaning of the term 16x error as used in the paper?