e-boost通过自适应剪枝与初始化求解，实现高效且精准的表达式提取。

E-graphs have attracted growing interest in many fields, particularly in logic synthesis and formal verification. E-graph extraction is a challenging NP-hard combinatorial optimization problem. It requires identifying optimal terms from exponentially many equivalent expressions, serving as the primary performance bottleneck in e-graph based optimization tasks. However, traditional extraction methods face a critical trade-off: heuristic approaches offer speed but sacrifice optimality, while exact methods provide optimal solutions but face prohibitive computational costs on practical problems. We present e-boost, a novel framework that bridges this gap through three key innovations: (1) parallelized heuristic extraction that leverages weak data dependence to compute DAG costs concurrently, enabling efficient multi-threaded performance without sacrificing extraction quality; (2) adaptive search space pruning that employs a parameterized threshold mechanism to retain only promising candidates, dramatically reducing the solution space while preserving near-optimal solutions; and (3) initialized exact solving that formulates the reduced problem as an Integer Linear Program with warm-start capabilities, guiding solvers toward high-quality solutions faster. Across the diverse benchmarks in formal verification and logic synthesis fields, e-boost demonstrates 558x runtime speedup over traditional exact approaches (ILP) and 19.04% performance improvement over the state-of-the-art extraction framework (SmoothE). In realistic logic synthesis tasks, e-boost produces 7.6% and 8.1% area improvements compared to conventional synthesis tools with two different technology mapping libraries. e-boost is available at https://github.com/Yu-Maryland/e-boost.