## 6 Results and Discussion
### GEP Model Evaluation  
Model evaluation and its representation between observed and predicted values is illustrated in Figure 4. GEP-based machine learning algorithm is an effective approach to assess the strength parameters of HSC. Model assessment in machine learning is usually done with regression analysis. Regression analysis shows the accuracy of any model with value close to one is an adamant accurate model as represented in Figure 4b. It shows that the regression line of the testing and validation sets is close to 1. Figure 4a,b represent the regression analysis of validation and testing sets with coefficient of determination R\({}^{2}\). This value is greater than 0.8 which depicts the accuracy of the model as 0.91 and 0.90 for the testing (see Figure 4a) and validation (see Figure 4b) sets, respectively. Normalization of gathered data from published literature was also done within the range of zero and one to show the accurateness of data as illustrated in Figure 4c.  
Figure 3: Expression tree of high strength concrete (HSC) using gene expression.  
Statistical measures are used to evaluate the performance of the model by using MAE, RRMSE, RSE, and RMSE as done similarly in a random forest model as shown in Table 8. Low error and higher coefficient give better performance of the model. Most of the errors lies below 5 MPa with an R\({}^{2}\) value greater than 0.8. Thus, it depicts the accuracy of the finalized model. Further analysis is also performed to evaluate the performance of the model by determining the standard deviation (SD) and covariance (COV). The values of SD and COV are determined to be 0.16 and 0.059, respectively.  
The accuracy and performance of the machine learning-based model is evaluated by conducting error distribution between actual targets and predicted values of the testing set as shown in Figure 5. It can be seen that the model predicted the outcome nearly or equal to the experimental values. Moreover, the error distribution of the testing set shows that 86% of the data sample lies below 5 MPa and 13.88% of the data lies in the range of 5 MPa to 8 MPa with 7.47 MPa as maximum error. Thus, the GEP-based model not only gives obstinate accuracy in terms of correlation but also gives the empirical equation  
Figure 4: Model evaluation (**a**) Validation results of data based on GEP; (**b**) testing results of data; (**c**) normalized range of data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **RMSE** & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**RSE**} \\ \hline \multirow{5}{*}{**Fc**} & Validation & Testing & Validation & Testing & Validation & Testing \\ \cline{2-6}  & 1.42 & 1.62 & 0.575 & 0.595 & 0.092 & 0.023 \\ \cline{2-6}  & \multicolumn{2}{c}{**RRMSE**} & \multicolumn{2}{c}{**R**} & \multicolumn{2}{c}{**P(row)**} \\ \cline{2-6}  & Validation & Testing & Validation & Testing & Validation & Testing \\ \cline{2-6}  & 0.0286 & 0.031 & 0.957 & 0.031 & 0.014 & 0.015 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Statistical calculations of the proposed model.  
shown in Equation (9). This equation will help the users to predict the compressive strength of concrete by using hand calculations.