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 | 10 | 1.01 | 0.994 | 136 | 1032 | 2.26× |
compileInner grows by 896 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 |
|---|---|---|---|---|---|---|
| generateOutput (self) | 26 | 307 | +280 | 31% | 1.48× | 1.21 |
| specializeModule | 37 | 295 | +257 | 29% | 1.06× | 0.99 |
| simplifyIR | 13 | 133 | +120 | 13% | 1.34× | 1.11 |
| linkAndOptimizeIR (self) | 11 | 93 | +83 | 9% | 1.19× | 1.07 |
| SemanticChecking | 29 | 88 | +59 | 7% | 0.60× | 0.60 |
Also growing (below top-5): generateIR (+33 ms, 4%), legalizeExistentialTypeLayout (+26 ms, 3%), legalizeResourceTypes (+25 ms, 3%).
Near-constant (≤2% of growth each): linkIR (3→6 ms), performMandatoryEarlyInlining (1→5 ms), performForceInlining (0→3 ms), compileInner (self) (0→1 ms), unrollLoopsInModule (0→1 ms), parseTranslationUnit (0→1 ms), frontEndExecute (self) (0→1 ms).
| N | compileInner | linkAndOptimizeIR | frontEndExecute |
|---|---|---|---|
| 25 | 136 | 68 | 41 |
| 50 | 234 | 125 | 55 |
| 100 | 457 | 256 | 81 |
| 200 | 1032 | 589 | 135 |