To meet the growing demand for high-efficiency optoelectronic devices, it is imperative to accelerate the screening of halide double perovskites (HDPs)—specifically the A2B'B''X6 family—that possess exceptional optoelectronic properties. In this work, we systematically investigate the predictive performance of multiple machine learning and symbolic regression approaches for formation energies (E_f) and band gaps (E_g) based on a dataset comprising 3624 HDPs. All models were implemented within a unified MATLAB framework, including eXtreme Gradient Boosting (MXGBoost), Light Gradient Boosting Machine (MLightGBM), Random Forest, and a Residual Gated Neural Network (RGNN), together with symbolic regression methods GPTIPS and SISSO (mGPTIPS and mSISSO). The machine learning models were trained and evaluated using five-fold cross-validation to ensure robustness and generalization capability. Among all tested algorithms, MXGBoost exhibits the best predictive performance, achieving coefficients of determination (R²) of 0.984 and 0.816 for E_f and E_g on the test sets, respectively. Furthermore, symbolic regression analysis provides explicit mathematical relationships between structural descriptors and target properties, revealing that the electronegativities of X-site anions (χX) and B-site cations (χB″ and χB') play dominant roles in governing both thermodynamic stability and electronic structure. Based on the combined machine learning and symbolic regression framework, two thermodynamically stable direct band gap semiconductors, Na₂HgZnF₆ and Tl₂PbSnF₆, are identified. Subsequent first-principles calculations are carried out to validate their electronic structures, intrinsic defect properties, and optical responses. The results demonstrate that Tl₂PbSnF₆ exhibits more localized charge distributions near the band edges and a significantly reduced concentration of deep-level defects compared with Na₂HgZnF₆, which is beneficial for suppressing nonradiative recombination. In addition, Tl₂PbSnF₆ achieves a high spectroscopic limited maximum efficiency (SLME) of 28.01%, indicating excellent optoelectronic performance. Overall, this study establishes an efficient and interpretable computational framework that integrates machine learning, symbolic regression, and first-principles calculations, providing valuable guidance for the rational design and discovery of high-performance HDPs for optoelectronic applications.