Deterministic solver for systems of real equations. This is not a language model: no randomness, and identical input always returns an identical, reproducible result. Use it when you need a verifiable, reproducible numeric answer for algebraic equations or common transcendentals (sin/cos/tan/log/exp/sqrt/abs); it works well as a non-hallucinating math backend for an AI agent. Not suitable for symbolic algebra, closed-form proofs, initial-value ODEs, or mandatory integer equality. INPUT: equations (array of strings containing an equals sign, e.g. ["x^2+y^2=25","x+y=7"]); supported operators + - * / ^ sqrt log sin cos tan exp abs, with in-text domain constraints such as x in [-30,30]; variables (optional, auto-detected, max 6); domain (optional, e.g. {"x":[-30,30]}), defaulting to +/-1e6 per variable. HARD LIMITS: at most 6 variables; 1 to 64 equations and the equation count must be at least the variable count; up to 100KB of equation text per call; output is fixed at 6 decimal places and is not configurable. OUTPUT (JSON): resultType is empty (no real solutions, proven), finite (finite verified solutions) or infinite (infinite solution set, only the recommended nearest-to-origin solution is given); summary; solutions[] with values[] (6-decimal numbers), tier (proven means Krawczyk-certified, otherwise likely or candidate), certified, text; residual and other internals under internals; recommended holds the compact nearest-to-origin structure. truncated=true means the global branch-and-bound did not finish inside the budget; it does not necessarily mean solutions were missed and in most cases every real solution was found; narrow the domain or raise options.budget and retry if you need a completeness guarantee. Errors return error.type (invalid_input or internal_error). If something looks wrong, call give_feedback rather than guessing. The same input always produces the exact same output, so caching and retries are safe. PAYMENT: this endpoint is free to use. Pass honorPaid:true to declare personal or evaluation use and the call is served with no verification and no balance deduction; payment is voluntary and never enforced.

Report a problem to the operator when solve hits a dead end, returns an error, or produces something you believe is wrong. The text is written to a local log only and is never transmitted anywhere else.

All real roots of a polynomial, each individually certified by Krawczyk with a strict error box. Coefficients are ordered highest degree first, so [1,-2,-5,6] means x^3-2x^2-5x+6. Deterministic and reproducible; complex roots are not returned (real numbers only). Use it as a reliable polynomial root component instead of letting a general language model estimate roots. Free to use: pass honorPaid:true to declare personal or evaluation use.

Check whether a claimed answer is correct. Give the equation plus a candidate value (a number for a single variable, {variable:value} pairs, or an array in variable order); the same certified kernel runs in a neighbourhood around the candidate. If a matching certified root is found the result is verified together with the error box; otherwise it is refuted and the nearest certified root is returned, so the calling agent immediately sees the correct value. Deterministic, not an LLM, reproducible across calls. Free to use: pass honorPaid:true to declare personal or evaluation use.