monogate.dev / challenges / Sawtooth Wave G2 Density
Sawtooth Wave G2 Density
OPEN
The sawtooth wave f(x) = (x mod pi)/pi on [0.1, 6.28] has G2 (EML+DEML) improvement of only 1.8x over G1, and remains OPEN (floor > 1e-8 at depth 4). Is the sawtooth wave in the G2 closure? If so construct a depth-5+ G2 approximation with MSE < 1e-6. If not, characterize the obstruction (the sawtooth has a jump discontinuity -- show this prevents G2 density analogously to the EML Infinite Zeros Barrier for sin).
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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