n differentiable functions arranged in bounded-depth groups, each group differentiated in both forward and reverse mode, plus a differentiable generic. Stresses the autodiff IR transform (inside linkAndOptimizeIR) and the front-end checking of [Differentiable]. Scales by breadth. Scaling null: n scales group breadth with depth bounded by _GROUP_DEPTH, so ideal autodiff cost is O(n).
bucket: autodiff · mode: target · flags: -target spirv -emit-spirv-directly
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× |
|---|---|---|---|---|---|---|
| 25–200 | 9 | 1.21 | 0.989 | 94 | 1069 | 2.81× |
compileInner grows by 974 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=25 | t@N=200 | Δ ms | share | × lin | ∝Nk |
|---|---|---|---|---|---|---|
| simplifyIR | 13 | 320 | +307 | 31% | 2.78× | 1.54 |
| linkAndOptimizeIR (self) | 23 | 303 | +280 | 29% | 1.67× | 1.25 |
| generateOutput (self) | 23 | 302 | +278 | 29% | 1.59× | 1.27 |
| specializeModule | 6 | 39 | +32 | 3% | 0.87× | 0.87 |
| legalizeExistentialTypeLayout | 1 | 23 | +22 | 2% | 1.86× | 1.35 |
Also growing (below top-5): SemanticChecking (+21 ms, 2%).
Near-constant (≤2% of growth each): legalizeResourceTypes (1→20 ms), generateIR (4→14 ms), performMandatoryEarlyInlining (0→2 ms), linkIR (1→2 ms), performForceInlining (0→1 ms), parseTranslationUnit (0→1 ms), unrollLoopsInModule (0→1 ms), frontEndExecute (self) (0→1 ms), compileInner (self) (0→0 ms).
| N | compileInner | linkAndOptimizeIR | frontEndExecute |
|---|---|---|---|
| 25 | 94 | 47 | 24 |
| 50 | 174 | 95 | 30 |
| 100 | 381 | 228 | 38 |
| 200 | 1069 | 711 | 56 |