Chinese idioms (成语, Chengyu) are concise four-character expressions steeped in history and culture, whose literal translations often fail to capture their full meaning.This complexity makes them challenging for language models to interpret and use correctly.Existing benchmarks focus on narrow tasks-multiplechoice cloze tests, isolated translation, or simple paraphrasing.We introduce CHENGYU-BENCH, a comprehensive benchmark featuring three tasks: (1) Evaluative Connotation, classifying idioms as positive or negative; (2) Appropriateness, detecting incorrect idiom usage in context; and (3) Open Cloze, filling blanks in longer passages without options.CHENGYU-BENCH comprises 2,937 human-verified examples covering 1,765 common idioms sourced from diverse corpora.We evaluate leading LLMs and find they achieve over 95% accuracy on Evaluative Connotation, but only ~85% on Appropriateness and ~40% top-1 accuracy on Open Cloze.Error analysis reveals that most mistakes arise from fundamental misunderstandings of idiom meanings.CHENGYU-BENCH demonstrates that while LLMs can reliably gauge idiom sentiment, they still struggle to grasp the cultural and contextual nuances essential for proper usage.The benchmark and source code are available at: https: //github.com/sofyc/ChengyuBench.

Test-time reasoning algorithms such as chain-of-thought, self-consistency, and MCTS enhance LLM problem-solving but can wastefully generate many tokens without improving accuracy. At the same time, we observe that these algorithms exhibit answer stabilization: their intermediate solutions often cease to change after a certain point, and further investment of compute does not change their final answer. To quantify this phenomenon, we introduce Certaindex, an algorithm-agnostic metric measuring this evolving stability, signaling when further computation is unlikely to alter the final result. Certaindex is lightweight, can accelerate reasoning program inference via early exit, and further enables dynamic token allocation, gang scheduling, and many opportunities when integrated with real-world LLM serving systems. To quantify real-world benefits, we built Certaindex as a scheduler into Dynasor, our reasoning-aware LLM serving system, and demonstrate up to 50\% compute savings and 3.3$\times$ higher throughput in real workloads with no accuracy drop. Our code is available at https://github.com/hao-ai-lab/Dynasor.git