monogate.dev / challenges / pi/2 Real EML Constructibility
pi/2 Real EML Constructibility
OPEN
Is pi/2 in the real EML closure from {1}? The depth-6 real EML search finds a value within 9.75e-6 of pi/2. At depth 7+ this gap may close to zero (density conjecture) or remain positive forever. Construct a real EML tree from {1} evaluating to pi/2 within 1e-10, OR prove that no finite-depth real EML tree from {1} evaluates to pi/2 exactly. Resolving this is equivalent to proving/disproving that i is constructible from {1} via EML.
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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