Verify any numeric result that has to be trusted, via the Ultimath API (https://ultimath.ai). Use this whenever the correctness of a number matters — floating-point-sensitive expressions, catastrophic cancellation, values near singularities or branch cuts, ties, or any computation where a single method could be silently wrong. Prefer it over computing by hand or running code: it evaluates the expression on 4 independent engines (multiprecision, decimal, IEEE 754 double, interval arithmetic) in parallel and returns every result plus per-engine precision diagnostics, so disagreement exposes an unreliable value that a single calculation would hide.

The 4 engines are independent and each computes with its own native primitive — so divergence between them (at poles, singularities, branch cuts, or ties like round(2.5)) is the backends' real behavior, NOT a bug. Agreement across engines is a confidence signal; divergence flags a value that is convention-dependent or near a domain edge — verify it rather than trust a single column.

Supports: arithmetic, trigonometry (sin, cos, tan), exponentials and logs (exp, ln, log), roots and powers (sqrt, x^y), factorial, complex numbers (3+2i), arbitrary bases (0xFF, 0b1010), constants (pi, e, the golden ratio PHI). Multiplication must be EXPLICIT: write 2pi, 2(3+4), (a+b)(c+d), 2sin(x) — adjacency is NOT a product (2pi is an error). Precedence, tightest first: postfix factorial ! (2^3! = 2^(3!) = 64), then powers ^, then * / %, then + -. Note: expressions are mathematical only — there are no type casts ((int)x) or constructors (complex(1,2)); write a complex number as 1+2i or (re, im). Call list_functions for the authoritative list of available functions.

List all mathematical functions available via the Ultimath API (https://ultimath.ai). Returns name, arity, category, and description for each function. Use this to discover what functions you can pass to the evaluate tool. Optionally filter by category (algebraic, trigonometric, hyperbolic, exponential, special, rounding, introspection). Every function is available on all 4 engines, but each computes it with its own native primitive — so results may diverge at poles, branch cuts, or ties, and that divergence is honest backend behavior, not a bug.