Claude Haiku 4.5 vs Gemini 2.5 Flash for Math

What Math demands: precise multi-step reasoning, transparent step-by-step tradeoffs with real numbers, strict adherence to structured output (for solutions, proofs, or JSON schemas), long context for multi-page derivations, and faithful, non-hallucinated intermediate steps. The payload includes an external benchmark (MATH Level 5, Epoch AI) but both models have null external scores, so we use our internal proxies. The two task tests present are strategic_analysis and structured_output. On strategic_analysis (the primary proxy for nuanced mathematical reasoning) Claude Haiku 4.5 scores 5 while Gemini 2.5 Flash scores 3; Haiku’s ranking is tied for 1st, Gemini is rank 36 for this dimension. On structured_output both score 4, so neither has a clear advantage for schema compliance. Additional supporting signals: tool_calling (both 5) suggests both models can reliably select and sequence calculation tools; long_context (both 5) indicates either can handle long derivations; faithfulness favors Haiku (5 vs 4) which reduces risk of incorrect assertions in proofs; safety_calibration favors Gemini (4 vs 2), relevant when the system must refuse or cautiously handle problematic prompts. Cost and context window also matter operationally: Haiku costs more (input $1 / output $5 per mTok) with 200k context, Gemini is cheaper (input $0.3 / output $2.5 per mTok) with a larger 1,048,576 token context window.

1. Multi-step contest problems (AIME/USAMO style): Choose Claude Haiku 4.5 — in our testing strategic_analysis is 5 vs 3, so Haiku is more reliable at nuanced tradeoffs, multi-case reasoning, and explaining why a chosen approach is optimal. 2) Automated solution pipelines requiring strict JSON answers (answer + justification fields): Both models are comparable — structured_output 4 vs 4 — so pick either based on cost and operational constraints. 3) Heavy, document-length derivations or chaining many previous steps: Both have long_context 5, but Gemini’s 1,048,576 token window can be advantageous for extremely long contexts; still, Haiku’s stronger strategic reasoning makes it preferable if accuracy of each step matters more than absolute context length. 4) Calculator/tool integration or stepwise numeric checks: Both models score tool_calling 5 in our tests, so either will select and sequence arithmetic tools reliably. 5) Safety-sensitive coursework or systems that must refuse malformed or harmful math prompts: Gemini 2.5 Flash is preferable — safety_calibration 4 vs 2. 6) Cost-sensitive workloads producing long numeric outputs or many API calls: Gemini is materially cheaper (output $2.5 vs $5 per mTok) and will cut runtime cost roughly in half for similar output sizes.

For Math, choose Claude Haiku 4.5 if you need the strongest on-model mathematical reasoning and tradeoff-heavy solutions (strategic_analysis 5 vs 3) and you prioritize faithfulness and stepwise correctness. Choose Gemini 2.5 Flash if you need lower per-token cost (output $2.5 vs $5/mTok), higher safety calibration, better constrained rewriting, or the largest possible context window for extremely long documents.