We can see on figure 2 the comparison between exact values and Karlin's approximations. The conservative design of the approximations seems to be successful except for very short unsignificant sequences. While the approximations are rather close to perfection for sequences with more than 2 000 amino-acids, the smaller the sequence is, the worse the approximations get. This is obviously consistent with the asymptotic nature of Karlin's formula but seems to indicate that these approximations are not reliable for 99.5% of the sequence in the database (protein of length < 2 000).