$1/2$ has EML complexity at most 17

Proved

EmlComplexity.attains_half

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

elementary-functionseml-complexityexpression-complexity

The constant $1/2$ is the value of a valid closed EML tree with seventeen nodes: $\exp(-\ln 2)$ , where $\ln 2$ is built as $e - \ln(\exp(e - \ln 2))$ from the nine-node tree for $2$ .

Preamble

import Definitions.Def_EmlComplexity

Formal statement

namespace EmlComplexity
theorem attains_half : Attains ((1 / 2 : ℝ)) 17 := 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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1/21/21/2 has EML complexity at most 17

$1/2$ has EML complexity at most 17