## 3 Results and Discussion  
Two datasets for the generation and testing the GP and FNNs were applied. The first (Test 1) has 5700 samples with similar input ranges for training and evaluation; the second (Test 2) included a total of 160 datapoints in different input ranges from those used for training. The two models used energy consumption as output, while the inputs were intensity, red light component, blue light component, green light component, white light component, pulsed Frequency, and duty Cycle.  
We normalized the first dataset to get its variables on the same scale. Table 3 presents the slopes and offsets for normalization. Subsequently, the most relevant inputs in Test 1 were selected if Spearman's \(p\) value < 0.05 and \(\rho\geq\) 0.05, which implied a weak correlation with 95% reliability [59]. Table 4 shows the correlation coefficients obtained using the inputs indicated in bold. After that, we split Test 1 as follows: 80% for the training and 20% for testing; meanwhile, Test 2 was also applied for testing in both models.  
All the training stages for the GP and FNN models of this work were performed without parallel computing on a computer with Microsoft Windows 10.0.19041 Pro OS, Intel Core(tm) i7-6700 CPU with 3.40 GHz, 16 GB RAM, and NVIDIA GeForce GTX 970 graphic card.  
The GP training parameters selected with cross-validation were: S\({}_{P}\) = 200, S\({}_{T}\) = 20, and P\({}_{M}\) = 8%, for a limit of N\({}_{G}\) = 5000 generations. We avoided overfitting by selecting the complexity parameters (number of operations per parentheses and the number of parentheses) with 10-fold cross-validation in the training set. The best parameters obtained were 16 operators and 2 parentheses, with a cross-validation MAE of 3.0649, after testing 1\(-\)20 operators and 1\(-\)2 parentheses.  
The GP model in the Equation (11) omitted input three (green light component), according to [PERSON]'s correlations in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Variables** & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) & \(x_{6}\) & \(x_{7}\) \\ \hline \(\rho\) & **0.9109** & **0.2039** & \(-\)0.0219 & **0.2908** & **0.3064** & **0.0891** & **0.0620** \\ \(p_{value}\) & **0** & **0** & 0.0990 & **0** & **0** & **0** & **0** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Input variables selected based on Spearman’s coefficients.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Variables** & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) & \(x_{6}\) & \(x_{7}\) & \(y\) \\ \hline Slopes & 135.0 & 175.75 & 61.05 & 129.5 & 185.0 & 1000.0 & 90.0 & 34.10 \\ Offsets & 50.0 & 0 & 0 & 0 & 0 & 0 & 0.0 & 20.60 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Slope and Offset normalization coefficients per variable.  
\[g(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7})=\frac{\frac{\sin(x_{1})}{3}-2\cos(x_{1 })-\cos(x_{6})\sin(x_{5})^{7}-x_{2}\cos(x_{7})+{x_{6}}^{5}+8^{x_{5}}+6}{x_{6}+ \cos(x_{2})-\sin(x_{4})+\cos(x_{7})\sin(x_{7})+\frac{7}{\sin(x_{1})}-\frac{x_{7 }\sin(x_{4})}{3}-9x_{4}\cos(x_{7})\sin(x_{4})+7} \tag{11}\]  
We selected the complexity parameters of the FNNs model with 10-fold cross-validation obtaining three layers and 10 neurons per layer after testing 1-5 layers and 1-10 neurons, with a cross-validated MSE of 0.8666, and took 21,829.51 s or 6.06 h.