Here is another view of how the second mode can improve the fit. This graph is mapping Sydney Harbor tide data to SOI (blue dots). The Eureqa optimizer definitely wants to smooth over 12 months (to get rid of annual and biannual fluctuations in tide gauge readings). It also subtracts out a background of 37 months via a smoothing average (sma) to remove trends and longer scale fluctuations. That gives a fit of size complexity = 15.
But to fill in details it adds in a modulated sine wave to increase the size complexity to 60.