where P_(ij) is the value predicted by the individual program i for fitness case j (out of n fitness cases or sample cases); and T_j is the target value for fitness case j.

For a perfect fit, P_(ij) = T_j and E_i = 0. So, the rMSE index ranges from 0 to infinity, with 0 corresponding to the ideal.

As it stands, E_i can not be used directly as fitness since, for fitness proportionate selection, the value of fitness must increase with efficiency.

Thus, for evaluating the fitness f_i of an individual program i, the following equation is used:

which obviously ranges from 0 to 1000, with 1000 corresponding to the ideal.

Its counterpart with parsimony pressure, uses this fitness measure f_i as raw fitness rf_i and complements it with a parsimony term.

Thus, in this case, raw maximum fitness rf_max = 1000. And the overall fitness fpp_i (that is, fitness with parsimony pressure) is evaluated by the formula:

where S_i is the size of the program, S_max and S_min represent, respectively, maximum and minimum program sizes and are evaluated by the formulas:

S_max = G (h + t)

S_min = G

where G is the number of genes, and h and t are the head and tail sizes (note that, for simplicity, the linking function was not taken into account). Thus, when rf_i = rf_max and S_i = S_min (highly improbable, though, as this can only happen for very simple functions as this means that all the sub-ETs are composed of just one node), fpp_i = fpp_max, with fpp_max evaluated by the formula: