Type any number. The compass searches its expression library — combinations of e, π, φ, √2, lemniscate ϖ, Catalan's G — and returns the closest matches.
e, π, φ, √2, √3, √5, the lemniscate ϖ, Catalan's G, γ — using small-integer arithmetic, simple unary ops (square, cube, reciprocal, sqrt, factorial, log, sin/cos/tan/arctan), and pairs combined by +, −, ·, ÷. Then for your target, it sorts by absolute distance. Hits within 10⁻⁴ with short expressions are suggestive; hits within 10⁻⁶ are worth a second look; hits within 10⁻⁹ with short expressions are genuine candidate identities. Most "remarkable" coincidences are not (Ramanujan's e^(π√163) is the famous exception). The compass tells you which class your number lives in.