Climate change has become trending news due to its serious impacts on Earth. Initiatives are being taken to lessen the impact of climate change and mitigate it. Among the different initiatives, researchers are aiming to find suitable alternatives for cement. This study is a humble effort to effectively utilize industrial- and agricultural-waste-based pozzolanic materials in concrete to make it economical and environmentally friendly. For this purpose, a ternary blend of binders (i.e., cement, fly ash, and rice husk ash) was employed in concrete. Different variables such as the quantity of different binders, fine and coarse aggregates, water, superplasticizer, and the age of the samples were considered to study their influence on the compressive strength of the ternary blended concrete using gene expression programming (GEP) and artificial neural networking (ANN). The performance of these two models was evaluated using R2, RMSE, and a comparison of regression slopes. It was observed that the GEP model with 100 chromosomes, a head size of 10, and five genes resulted in an optimum GEP model, as apparent from its high R2 value of 0.80 and 0.70 in the TR and TS phase, respectively. However, the ANN model performed better than the GEP model, as evident from its higher R2 value of 0.94 and 0.88 in the TR and TS phase, respectively. Similarly, lower values of RMSE and MAE were observed for the ANN model in comparison to the GEP model. The regression slope analysis revealed that the predicted values obtained from the ANN model were in good agreement with the experimental values, as shown by its higher R2 value (0.89) compared with that of the GEP model (R2 = 0.80). Subsequently, parametric analysis of the ANN model revealed that the addition of pozzolanic materials enhanced the compressive strength of the ternary blended concrete samples. Additionally, we observed that the compressive strength of the ternary blended concrete samples increased rapidly within the first 28 days of casting.