$-1$ has EML complexity at most 8

Proved

EmlComplexity.attains_neg_one

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

elementary-functionseml-complexityexpression-complexity

The constant $-1$ is the value of a valid closed EML tree with eight nodes: $\exp(\ln(e-1)) - \ln(e^{e}) = (e - 1) - e$ .

Preamble

import Definitions.Def_EmlComplexity

Formal statement

namespace EmlComplexity
theorem attains_neg_one : Attains ((-1 : ℝ)) 8 := 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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−1-1−1 has EML complexity at most 8

$-1$ has EML complexity at most 8