Best LLM API for math and multi-step reasoning
Math and reasoning tasks produce long chains of intermediate steps, so output price usually matters more than input price. These are our tracked flagship-tier models, cheapest output rate first.
Math and multi-step reasoning tasks tend to produce long chains of intermediate steps before landing on a final answer — the output is often much larger than the prompt that triggered it. That shifts the cost driver toward the output price rather than the input price. This list filters to flagship-tier models, sorted by output price ascending, since flagship is where providers position their strongest reasoning capability.
We don't benchmark task-specific quality — this shortlist is built from verified price and published context window only. Use it to narrow candidates by cost, then evaluate output quality yourself.
Frequently asked questions
We don't benchmark mathematical accuracy directly, but providers generally position their flagship models — not budget or balanced tiers — as the ones built for harder reasoning. This list reflects that provider positioning, not an independent test we ran.
Reasoning-heavy tasks often generate long intermediate work before the final answer, so the response can run many times longer than the prompt. Since output tokens are billed separately, that shifts more of the bill onto the output rate.
Often, yes — some providers let you cap the reasoning or 'thinking' budget per call, which directly reduces output tokens and cost, sometimes at the expense of accuracy on harder problems. Check the specific model's documentation.