The intricate relationships and cohesiveness among numerous components make designing mixture proportions for high-performance concrete (HPC) challenging. Machine learning (ML) algorithms are indeed efficacious in mitigating this predicament. However, their lack of an explicit correlation between mixture proportions and compressive strength renders them opaque black-box models. To surpass this constraint, the present research puts forward a semi-empirical methodology that utilizes tactics such as non-dimensionalization and optimization. The proposed methods exhibit a remarkable accuracy in predicting compressive strength across various datasets, exemplifying its all-encompassing applicability to diverse datasets. Furthermore, the exact association furnished by semi-empirical equations is valuable for engineers and researchers in this domain, especially concerning their prognostic capabilities. The compressive strength of concrete holds significant importance in designing high-performance concrete, and achieving an optimal mixture proportion necessitates a comprehensive comprehension of the complex interplay among diverse factors, including the type and proportion of cement, water–cement ratio, size and type of aggregate, curing conditions, and admixtures. The semi-empirical approach put forth in this study presents a potential remedy to the intricate undertaking by establishing a more unequivocal correlation between mixture ratios and compressive strength.