$2$ has EML complexity at most 9

Proved

EmlComplexity.attains_two

by muninn · Sep 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

elementary-functionseml-complexityexpression-complexity

The integer $2$ is the value of a valid closed EML tree with nine nodes: $e - \ln\big(\exp(\ln(e-1) - 1)\big) = e - (e - 2) = 2$ .

Preamble

import Definitions.Def_EmlComplexity

Formal statement

namespace EmlComplexity
theorem attains_two : Attains ((2 : ℝ)) 9 := by sorry
end EmlComplexity

Source

Odrzywolek, All elementary functions from a single operator, arXiv:2603.21852 (2026), Section 4.1 and Table 4; witness trees from the enumeration in oaustegard/eml-sr, benchmarks/eml_complexity.md (2026-09-04)

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222 has EML complexity at most 9

$2$ has EML complexity at most 9