Thinking Costs Tokens: When More Structure is Worth the Price

Reasoning-specialized models like OpenAI's 5.1 and DeepSeek-V3.2 allocate substantial inference compute to extended chain-of-thought (CoT) traces, yet reasoning tokens incur significant costs. How do different reasoning modalities of code, natural language, hybrid, or none do perform under token constraints? We introduce a framework that constrains models to reason exclusively through code, comments, both, or neither, then systematically ablates token budgets to 10%, 30%, 50%, and 70% of optimal. We evaluate four frontier models (GPT-5.1, Gemini 3 Flash, DeepSeek-V3.2, Grok 4.1) across mathematical benchmarks (AIME, GSM8K, HMMT). Our findings reveal: (1) truncated reasoning can hurt as DeepSeek-V3.2 achieves 53% with no reasoning but only 17% with truncated CoT at 50% budget; (2) code degrades gracefully as Gemini's comments collapse to 0% while code maintains 43-47%; (3) hybrid reasoning underperforms single modalities; (4) robustness is model-dependent as Grok maintains 80-90% at 30% budget where OpenAI and DeepSeek collapse to 7-27%. These results suggest incomplete reasoning chains actively mislead models, with implications for deploying reasoning-specialized systems under resource constraints.

Standard evaluation of large language models assumes stable model rankings across inference conditions. We challenge this assumption by varying the token generation budget, i.e., the maximum tokens a model may produce, across seven levels (64--4,096), evaluating four models on three reasoning benchmarks (56,476 inferences). We report four findings: (i) 3--19% of items exhibit non-monotone behavior (accuracy decreasing with more budget), even after controlling for truncation, and this phenomenon is model-specific (cross-model overlap: 6--14%). (ii) Model rankings reverse across budgets on all benchmarks ($p {<} 0.01$, McNemar). (iii) Oracle analysis reveals model complementarity up to $+27.8$pp, most pronounced at constrained budgets. (iv) A budget-aware router captures 14.1% of the oracle gap cross-domain; budget features help within-domain ($+1.6$ to $+5.7$pp) but are domain-specific and hurt transfer ($-1.2$pp). These results argue for budget-conditioned evaluation protocols.

Accuracy-only benchmarking of reasoning-capable large language models misses a central deployment question: when do extended thinking tokens earn their cost? We introduce the Token Economy Score (TES), a marginal benchmarking metric that measures the accuracy gain of a reasoning model over a non-reasoning baseline, normalized by the generated-token multiplier. We define paired and approximated TES variants for model families with reasoning toggles and frontier models without direct non-reasoning counterparts. We then conduct an empirical benchmarking analysis across 151 model-benchmark evaluation runs on seven benchmarks spanning mathematics, code generation, science reasoning, instruction following, expert knowledge, knowledge recall, and research-level physics. The analysis examines three deployment-facing dimensions: which task structures yield positive marginal reasoning efficiency, how increasing reasoning effort changes TES within model families, and how deployment context changes economic viability. Results show that task structure predicts reasoning efficiency better than nominal difficulty: sequential inferencechain tasks such as AIME 2025 and LiveCodeBench show high TES, while knowledge-recall tasks such as MMLU-Pro show low TES despite their difficulty. We also find systematic diminishing returns at higher reasoning effort levels, including cases where additional thinking reduces accuracy. Finally, Reasoning Cost Share (RCS) shows that inference spend is often dominated by internal thinking, while Deployment Cost Multiplier (DCM) shows how on-premises deployment can change the economics of otherwise costly reasoning workloads. These findings support a benchmarking-driven model-selection rule: enable reasoning selectively by task type, effort level, and deployment context rather than treating it as a universally beneficial mode.