monogate.dev / challenges / EML-4 Exact Separation
EML-4 Exact Separation
OPEN
Find a function f in C[0.2, 3.0] that is provably EML-3 (floor F(3) < 1e-8) but NOT EML-2 (floor F(2) >= 1e-8). The census confirms x^2 is EML-3 with F(2)=1.7e-8, F(3)=9.3e-21. Extend this to a FORMAL proof (not just numerical evidence) that x^2 is not in the EML-2 closure. Equivalently: prove that no depth-2 EML atom combination can approximate x^2 to arbitrary precision on [0.2, 3.0].
Grammar
Allowed
eml(x, y) = exp(x) − ln(y) — the single operator
Terminal: constant 1
Terminal: variable x (for function challenges)
Compositions: any finite binary tree over the above
Forbidden
ln(0) — undefined, throws RangeError
Math.sin, Math.cos, Math.PI, or any Math.* shortcut
Any function outside the EML grammar
Extended-reals convention (ln(0) = −∞) — not this grammar
Under extended-reals grammar (pveierland/eml-eval), i is solved at K=75. This challenge is the strict grammar variant where ln(0) throws.
Leaderboard — 0 valid constructions
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