A large user-defined overload set (`pick`/`pick2`, scalar + vector + two-arg candidates), then `n` call sites with rotating argument types. Every call enumerates all candidates and ranks them by conversion cost to choose the best match — isolating the candidate-ranking cost that scales with overload-set size times call-site count. Scaling null: n scales call sites against a FIXED candidate set; ideal resolution cost is O(n).
bucket: typecheck · mode: module · flags: (none)
compileInner split into phase buckets (named leaves + (self) residuals) stacked across the sweep sizes — the top edge is compileInner, so you can see which phase drives the scaling.
floor-subtracted power-law fit (t − floor) = a·Nk; floor = the minimal workload (fixed per-compile cost), k the global exponent, top-2× the local high-end doubling ratio.
| N range | floor (ms) | k (work) | fit R² | t(Nmin) | t(Nmax) | top-2× |
|---|---|---|---|---|---|---|
| 600–4800 | 10 | 0.95 | 1.000 | 35 | 190 | 1.86× |
compileInner grows by 154 ms across the sweep; the mutually-exclusive phase buckets below partition that growth exactly (no nested-timer double counting). × lin is the same metric as the top-level panels, per bucket: the end point vs a linear expectation anchored to the bucket's share of the minimal floor and fitted on the low-N half — 1.0 = grew exactly linearly, >1 bends up. The super-linearity lives where × lin (and k) are red.
| bucket | t@N=600 | t@N=4800 | Δ ms | share | × lin | ∝Nk |
|---|---|---|---|---|---|---|
| SemanticChecking | 20 | 91 | +71 | 46% | 0.83× | 0.85 |
| generateIR | 9 | 56 | +47 | 31% | 0.93× | 0.94 |
| generateOutput (self) | 4 | 29 | +24 | 16% | 1.16× | 1.16 |
| parseTranslationUnit | 2 | 14 | +12 | 8% | 1.06× | 1.03 |
Near-constant (≤2% of growth each): compileInner (self) (0→0 ms), frontEndExecute (self) (0→0 ms).
| N | compileInner | SemanticChecking | frontEndExecute |
|---|---|---|---|
| 600 | 35 | 20 | 31 |
| 1200 | 58 | 31 | 50 |
| 2400 | 102 | 51 | 87 |
| 4800 | 190 | 91 | 161 |