The R-square fitness function is, as expected, based on the standard R-square, which returns the square of the Pearson product moment correlation coefficient.

The Pearson product moment correlation coefficient is a dimensionless index that ranges from -1 to 1 and reflects the extent of a linear relationship between two data sets.

The Pearson product moment correlation coefficient R_i of an individual program i is evaluated by the equation:

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

The fitness f_i of an individual program i is expressed by the equation:

f_i = 1000*R_i*R_i

and therefore 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: