Evaluate a mathematical expression with optional named variables — arithmetic, comparison and logic operators plus functions like sqrt, abs, min, max, sin, cos, log, floor, round, etc. A syntax error, an undefined variable, or a non-finite result is a clean 400. The factorial operator is disabled for safety.

Parse an expression and return the free variables it references, without evaluating it — so an agent can discover which inputs a formula needs before supplying values. A syntax error is a clean 400.