monogate.dev / challenges / sin(x)
sin(x)
PROVED IMPOSSIBLE
Construct sin(x) as a pure EML tree using only constant {1} under strict principal-branch ln where ln(0) throws.
Result
Proved impossible by T01 (Infinite Zeros Barrier). Every depth-k real EML tree has at most 2^k zeros on any compact interval. sin(x) has infinitely many zeros, so no finite-depth EML tree can equal sin(x) exactly.
ProofT01
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
#
Author
Nodes
Depth
Date
No valid constructions yet. Be the first.