$e-1$ has EML complexity at most 2

Proved

EmlComplexity.attains_e_sub_one

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

elementary-functionseml-complexityexpression-complexity

The constant $e - 1$ is the value of a valid closed EML tree with two nodes: $\mathrm{eml}(1, \mathrm{eml}(1,1)) = e - \ln e = e - 1$ .

Preamble

import Definitions.Def_EmlComplexity

Formal statement

namespace EmlComplexity
theorem attains_e_sub_one : Attains (Real.exp 1 - 1) 2 := 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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e−1e-1e−1 has EML complexity at most 2

$e-1$ has EML complexity at most 2