llm-arithmetic / RESULTS.md
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Results — 2026-08-16 (v2, four models)

Ten arithmetic problems, four Anthropic models, no tools, no MCP, single-shot answers. Expected values computed in code, never by a model.

v1 (2026-08-12) ran only the two ends of the range, claude-opus-5 and claude-haiku-4-5. This run adds claude-sonnet-5 and claude-fable-5 and repeats all four in one sitting, so "same questions, same prompt, same isolation, only the model changed" still holds across the whole table. The v1 headline numbers reproduced: opus 10/10, haiku 3/10.

Note on claude-fable-5: it is the model that ran this session. That does not affect the score, because the ground truth is computed in run.ts and the model never grades itself; it only submits an answer that the script checks.

opus-5 sonnet-5 haiku-4-5 fable-5
answered 10 / 10 10 / 10 10 / 10 10 / 10
exact 10 / 10 9 / 10 3 / 10 9 / 10
within 1% 10 / 10 10 / 10 10 / 10 10 / 10
worst error 0.00% 0.02% 0.145% 0.00%
reasoning tokens (total) 7,771 34,520 58,027 8,274
reasoning tokens (median) 936 3,281 7,051 1,148

"Exact" means the answer differs from the computed value by no more than display rounding (relative error ≤ 1e-6).

Per task

task expected opus-5 sonnet-5 haiku-4-5 fable-5
mrr-0 growth then churn, 36 mo 38,115.31 38,115.31 38,115.31 38,115 (0.001%) 38,115.34
cash-1 revenue vs fixed burn, 60 mo 4,864,506.92 4,864,506.92 4,864,506.96 4,864,544.82 (0.001%) 4,864,506.92
ltv-2 one division 7,800.00 7,800 7,800 7,800 7,800
two-phase-3 growth switches at m6, 60 mo 18,578.75 18,578.75 18,578.73 18,553 (0.139%) 18,578.75
runway-4 stepped burn, month number 5 5 5 5 5
mrr-5 growth then churn, 12 mo 14,887.45 14,887.45 14,887.45 14,887.54 (0.001%) 14,887.46
cash-6 revenue vs fixed burn, 60 mo 5,822,959.30 5,822,959 5,822,959.31 5,831,410 (0.145%) 5,822,959
ltv-7 one division 2,346.84 2,346.84 2,347.37 (0.022%) 2,346.32 (0.022%) 2,346.84
two-phase-8 growth switches at m6, 60 mo 21,262.90 21,262.90 21,262.91 21,271 (0.038%) 21,263
runway-9 stepped burn, month number 11 11 11 11 11

What the numbers say

Nobody refuses and nobody collapses. All four answered every question and every answer landed within 0.145% of the truth, which is already at odds with the shorthand that language models cannot do arithmetic.

"To the cent" is where they separate. Exact matches: opus 10, sonnet 9, fable 9, haiku 3. The difference is drift, not failure. haiku was never wildly wrong, it was slightly wrong seven times out of ten. On cash-6 that slight wrongness is $8,451 off a five-year cash forecast, and nothing in the answer signals it happened. The number simply looks right.

More thinking did not buy accuracy, it went the other way. haiku spent the most reasoning of any model, 58,027 tokens, roughly 7.5x opus's 7,771, and finished last at 3/10. opus was both the most accurate and the cheapest to think. fable landed 9/10 on 8,274 tokens; sonnet landed the same 9/10 but spent 34,520 getting there.

Difficulty concentrates where the rule changes. The growth-switches-at- month-6 problems and the long cash forecasts produced haiku's largest errors. Straight compounding and single divisions were handled cleanly by all four.

Scope

Ten problems, four models, one sitting, single-shot answers. This compares four models on identical tasks. It does not establish a failure rate for any of them, and says nothing about behaviour with tools enabled, which is how anyone would actually run these in production. It measures the model alone, on purpose.