$-3$ has EML complexity at most 20

Proved

EmlComplexity.attains_neg_three

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

elementary-functionseml-complexityexpression-complexity

The integer $-3$ is the value of a valid closed EML tree with twenty nodes: $\exp(\ln(e^{e} - 3)) - \ln(\exp(e^{e}))$ , where $e^{e} - 3$ is reached by three subtractions of $1$ from $e^{e}$ .

Preamble

import Definitions.Def_EmlComplexity

Formal statement

namespace EmlComplexity
theorem attains_neg_three : Attains ((-3 : ℝ)) 20 := 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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−3-3−3 has EML complexity at most 20

$-3$ has EML complexity at most 20