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autodiff

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

Phase composition vs N (stacked sub-counters)

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.

autodiff — phase composition vs N (v2026.12, median ms) autodiff 8.7× over N 25→200 0.0 685 1371 25 50 100 200 N autodiff — parseTranslationUnit autodiff — SemanticChecking autodiff — generateIR autodiff — frontEndExecute (self) autodiff — specializeModule autodiff — simplifyIR autodiff — linkIR autodiff — unrollLoopsInModule autodiff — legalizeResourceTypes autodiff — legalizeExistentialTypeLayout autodiff — performMandatoryEarlyInlining autodiff — performForceInlining autodiff — linkAndOptimizeIR (self) autodiff — generateOutput (self) autodiff — compileInner (self) phase buckets parseTranslationUnit SemanticChecking generateIR frontEndExecute (self) specializeModule simplifyIR linkIR unrollLoopsInModule legalizeResourceTypes legalizeExistentialTypeLayout performMandatoryEarlyInlining performForceInlining linkAndOptimizeIR (self) emitEntryPointsSourceFromIR generateOutput (self) compileInner (self)

Scaling analysis

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 rangefloor (ms)k (work)fit R²t(Nmin)t(Nmax)top-2×
25–200141.080.98714612692.53×

Growth attribution (N=25 → N=200)

compileInner grows by 1123 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.

buckett@N=25t@N=200Δ msshare× lin∝Nk
simplifyIR19330+31128%2.36×1.39
generateOutput (self)28335+30727%1.55×1.22
specializeModule36285+24922%1.09×1.00
linkAndOptimizeIR (self)11120+10910%1.50×1.18
SemanticChecking3187+565%0.59×0.58

Also growing (below top-5): generateIR (+32 ms, 3%), legalizeExistentialTypeLayout (+26 ms, 2%), legalizeResourceTypes (+25 ms, 2%).

Near-constant (≤2% of growth each): linkIR (3→6 ms), performMandatoryEarlyInlining (1→3 ms), performForceInlining (0→3 ms), parseTranslationUnit (0→1 ms), frontEndExecute (self) (1→1 ms), unrollLoopsInModule (0→1 ms), compileInner (self) (0→0 ms).

Sweep numbers (median ms)

NcompileInnerlinkAndOptimizeIRfrontEndExecute
251467344
5024513355
10050229383
2001269802133