Browse 265 equations by domain and cost. Visualize the four boundaries of elementary functions. Explore the FMA staircase. The data behind the claims.
Watch a float sum drift from the exact real: the n·u worst case you can prove vs the √n·u stochastic rounding delivers, plus the cancellation lesson — relative bound dies, absolute holds.
The four walls of ELC
Live MachLib verification status, rained into buckets by the critically-damped spring kernel we proved.
The constructive zero-count bound from MachLib.SingleExpKhovanskii, exposed. Pick an ExpPoly, see how loose `length + Σ deg` is against the real count.
One rung up the tower: zeros of p(eˣ, e^{eˣ}) are provably finite (rolle-only, MachLib), but the explicit constant grows exponentially in the tower degree. Climb the presets and watch the gap.
Gradient descent dynamics on EML expressions
Visualize the elementary closure gap — what EML cannot reach
Operator closure properties of the F16 family
A living system traversing the depth hierarchy in real time
The depth hierarchy as a cosmological structure
The origins of the EML hierarchy from one operator
Barrier functions: EML-∞ over ℝ, resolved over ℂ via T03
World-building stratification across the EML depth bands
Visualize the depth bands of any space
Search 265 equations
The FMA staircase
Probability distributions by EML cost
Open problems