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1.7 Billion Trees
Every possible EML tree up to 12 nodes. Not one produces sin(x).
Does any finite tree of eml(x, y) = exp(x) − ln(y) equal sin(x)?
Terminals: {1, x}. Every binary tree shape. Every leaf assignment. Every depth up to 12.
The most exhaustive search ever conducted within the EML framework. Every possible composition of eml(x, y) = exp(x) − ln(y) with terminals {1, x} and up to 12 internal nodes was enumerated using Catalan tree shapes and 2ⁿ⁺¹ leaf assignments. The periodic barrier proves no real-valued construction exists at ANY EML depth: every real EML tree defined for large x eventually keeps one sign, and sin(x) never does. Over ℂ, Euler's formula gives sin as the imaginary part of one eml node, given the leaf ix. Search data: monogate-core Rust binary, results/sin_n12.json.