In Section 3.6.4 we saw a few alternative mathematical expressions for the naïve Bayes approximation to the log likelihood ratio of the chance a message is spam or ham. Each suggests a different approach to carrying out the computation. Create alternative versions of compute Freqs () and compute Msg Odds () in Section 3.6 to calculate the log odds. Compare the accuracy of these alternatives to the approach used in Section 3.6. Also consider timing the computation with a call to system. Time () to determine if one approach is much faster or slower than the others