Claude Haiku 4.5 vs Claude Opus 4.6 for Math

What Math demands: precise stepwise reasoning, reliable symbolic manipulation, adherence to structured output, sustained multi-step context, and the ability to refuse or flag invalid/problematic requests. Because an authoritative external math benchmark is normally primary, we checked for that signal — the top-level math_level_5 entry in the payload is present but has no scores, so it cannot decide the race. Supplementary external measures included in the payload favor Opus: SWE-bench Verified 78.7% and AIME 2025 94.4% (Epoch AI). Internally, both models tie at 5/5 for strategic_analysis, tool_calling, faithfulness, and long_context — all crucial for math. Opus wins where creative_problem_solving (5 vs 4) and safety_calibration (5 vs 2) matter (e.g., open-ended olympiad problems and safe handling of adversarial prompts). Haiku's strengths — 5/5 faithfulness, 5/5 tool_calling, and lower cost — make it an efficient option for high-throughput calculation, but lacks the external math bench signals present for Opus.

1. Contest-style olympiad problems (AIME-level): Opus 4.6 is preferable — it scores 94.4% on AIME 2025 (Epoch AI) in the payload and 5/5 creative_problem_solving in our tests, so it handles non-obvious multi-step insight better than Haiku (4/5). 2) Real-code/math integration or long derivations: Opus offers a 1,000,000-token context window and 128,000 max output tokens vs Haiku's 200,000 / 64,000, letting Opus manage very long proofs or workbook-length transcripts. 3) High-volume, cost-sensitive numeric tasks: Haiku 4.5 costs far less (input/output per mTok 1/5) than Opus (5/25) and still scores 5/5 on tool_calling and faithfulness, so it is efficient for routine symbolic evaluation, batch question answering, and applications that trade a small drop in creative insight for much lower cost. 4) Safety-sensitive classroom or automated grading: Opus has 5/5 safety_calibration vs Haiku's 2/5 in our tests, making Opus safer at refusing malformed or unsafe requests and preferable where correct refusal behavior matters. 5) Classification/routing of problem types: Haiku edges Opus on classification (4 vs 3), so for rapid triage of problem types Haiku may be slightly more consistent in our tests.

For Math, choose Claude Haiku 4.5 if you need an efficient, lower-cost model for high-throughput calculations, routine symbolic steps, or classification/triage (input/output cost per mTok 1/5 vs Opus 5/25) and you can accept a small loss in creative insight and safety calibration. Choose Claude Opus 4.6 if you need the strongest math performance in this payload — Opus has external support (SWE-bench Verified 78.7% and AIME 2025 94.4% per Epoch AI), higher creative_problem_solving (5 vs 4), better safety calibration (5 vs 2), and much larger context and output capacity for long proofs and contest-style problems.