# Mandelbrot viewer performance-cost A/B test

Date: 2026-09-29

## Scope

This A/B test follows the performance-cost audit. Production `index.html` was **not changed**. A is the current production implementation; B variants live under `experiments/ab/variants/` and disable, defer, or gate one candidate operation at a time.

Production SHA-256 before/after testing:

`544820c5024cf6d56e012db6d1bec3ddfcef5d833691b890baa64b26c5c2ee5a`

The existing regression suite passes on production. The combined high-confidence B variant and the individual structural B variants used for gating/lazy allocation also pass the same regression suite; all retain 19 WGSL kernels.

## Measurement limitation

A usable WebGPU backend could not be started in the container (Chromium/SwiftShader/EGL). Therefore this report deliberately separates:

1. **CPU measured time/work**: exact-interior BigInt proof, adaptive-iteration probe, CPU surrogates for strict-cycle and continuation replay.
2. **Exact traffic/residency counts from the production buffer sizes and dispatch extents**: copies, full-frame scans, allocations.
3. **Structural/regression validation**: B variants parse and pass the production regression suite.

No result below is presented as measured GPU frame time unless explicitly stated. Real-device WebGPU p50/p95 remains a follow-up requirement.

## Summary

| Candidate | A/B result | Decision from this test |
|---|---|---|
| Recolor numeric-history copy | B removes 8 B/pixel copy with unchanged numeric field | **Strongly supported** |
| Unread `cpuFrameRgba` retention | B removes 4 B/pixel retained JS data; no reader exists | **Strongly supported** |
| Pre-primary unknown stats after exact interior | B removes one full-frame `fieldMeta` scan; primary path computes stats later | **Strongly supported** |
| Strict direct periodicity-state updates | CPU surrogate median B change **+2.82% slower** | **Do not prioritize for speed** |
| FAST full-screen coverage repair | 36 layout cases + 200 semantic randomized cases: **0 holes** | **Strongly supported**, real GPU A/B still desirable |
| Idle color-auto `colorSource` snapshot | B avoids 12 B/pixel idle snapshot; idle recolor does not consume it | **Strongly supported** |
| Export workspace lifetime | B releases ~24 MiB max workspace after export | **Memory win**, trades for reallocation on next export |
| Exact-interior spatial gate | Fixed corpus proof CPU time reduced ~40% at 1024×768 and ~34% at 2048²; 240 random views: 0 gate false-negatives | **Strongly supported** |
| Conditional numeric-history residency | Budget-scaled 1920×1080 cases had 0–0.6% exact-grid hit rate; native-grid cases 100% | **Supported conditionally**, not blanket removal |
| Lazy export AA samples | 1× export avoids **12 MiB** of four unused AA sample textures across a 3-slot ring | **Strongly supported** |
| Adaptive initial-iteration probe removal | 3/48 survey views selected >350; forcing 350 raised predicted work by **+7.2%, +25.3%, +33.1%** | **Do not remove**; cache/gate instead |
| Continuation restart from n=0 | Resume-state surrogate reduced work **7.6–9.8%**, identical classifications | **Real waste**, but requires state-preserving redesign |
| Deep workspace release after easy frame | Up to ~44.1 MiB standard / ~176.5 MiB high can remain resident | **Memory-lifetime candidate**; real GPU allocation cost unmeasured |

## Results in detail

### 1. Recolor numeric-history copy

Current recolor promotes color history and also copies unchanged `meta/smooth` numeric history. B separates the two responsibilities.

Exact avoided copy per accepted recolor:

- fast cap: 4 MiB
- standard cap: 8 MiB
- high cap: 32 MiB

At 20 Hz color cycling, that corresponds to 80 / 160 / 640 MiB/s of avoidable numeric-history copying at the respective caps. This is a traffic count, not a GPU-time measurement.

Variant: `b01-recolor-no-numeric-copy.html`

### 2. Unread CPU RGBA retention

`cpuFrameRgba` is assigned after CPU fallback rendering but has no subsequent reader in production. B drops the assignment.

Avoided retained JS memory at cap:

- fast: 2 MiB
- standard: 4 MiB
- high: 16 MiB

Variant: `b02-cpu-no-rgba-retention.html`

### 3. Exact-interior pre-primary unknown-stat pass

When exact tile certification only partially covers the frame, production immediately runs a full-frame unknown-stat scan and synchronization before the primary numerical path. The partial-path result is not consumed; the primary path computes the required statistics later.

B removes this pre-primary stats scan while preserving the fully-certified shortcut.

Minimum avoided `fieldMeta` read per pass:

- fast: 2 MiB
- standard: 4 MiB
- high: 16 MiB

This excludes atomics, dispatch overhead, and synchronization cost, so it is a lower bound on removed work.

Variant: `b03-certify-no-preprimary-stats.html`

### 4. Strict direct periodicity-state updates

The strict path does not accept heuristic periodicity, yet production still maintains Brent state. A CPU surrogate compared identical numerical output with and without those state updates.

Across six fixed views, B was not consistently faster: median elapsed change was **+2.82%** (slower), mean +5.47%. One deep case improved by 1.48%, but the result is not robust.

Conclusion: semantically redundant state exists, but this A/B test does **not** justify touching it for performance. GPU register pressure could behave differently; real WebGPU measurement would be needed.

Variant: `b04-strict-no-cycle-state.html`

### 5. FAST coverage repair

Production performs a second full-frame FAST pass intended to fill `reason=0` holes after tiled FAST rendering.

Coverage simulation tested 36 combinations of dimensions, iteration budgets and symmetry modes; all produced **0 holes**. A second semantic randomized test seeded mixed proven/unknown metadata over 200 cases and also found **0 cases with holes**.

Representative work avoided if the repair pass is unnecessary:

- 1365×768: 1,050,624 shader invocations; at least 4,193,280 bytes of metadata reads
- 2731×1536: 4,202,496 invocations; at least 16,779,264 bytes of metadata reads

Variant: `b05-fast-no-coverage-repair.html`

### 6. Idle color-auto snapshot

Starting color cycling while no render is in progress allocates/copies `colorSource`, but idle recolor reads the current numerical field and does not consume that snapshot. Render-time snapshot behavior is preserved in B.

Avoided idle snapshot residency:

- fast: 6 MiB
- standard: 12 MiB
- high: 48 MiB

Variant: `b06-idle-colorauto-no-snapshot.html`

### 7. Export workspace lifetime

The export ring remains allocated after export. With 512-sized slots and ring depth 3, the tested maximum workspace is approximately **24 MiB**. B destroys it in `finally`, reducing post-export residency to zero. The cost is allocation of three slots on a subsequent export.

This is a clear memory trade-off, not a proven speed win.

Variant: `b07-export-release-workspace.html`

### 8. Exact-interior spatial gate

The expensive BigInt tile proof only needs to run when the viewport can intersect the main cardioid or period-2 bulb. B uses a conservative bounding-box gate before tile proof.

The cardioid gate was corrected during the A/B test: the main cardioid reaches `x = 3/8`, so the conservative box is `x ∈ [-3/4, 3/8]`, `y ∈ [-2/3, 2/3]`. The period-2 bulb box is `x ∈ [-5/4, -3/4]`, `y ∈ [-1/4, 1/4]`.

Random validation: 240 views, 160 gate-negative, **0 false negatives** versus the current exact tile proof.

Fixed-corpus aggregate CPU proof time:

- 1024×768: A 41.64 ms → B 25.16 ms, about **39.6% reduction**
- 2048²: A 177.70 ms → B 117.08 ms, about **34.1% reduction**

The largest wins were period-3 views that cannot intersect either analytically certifiable component: about 7–10 ms saved at 1024×768 and 25–30 ms at 2048².

Variant: `b08-exact-interior-spatial-gate.html`

### 9. Conditional numeric-history residency

Exact-grid history reuse requires render-pixel translation to line up exactly with CSS/device motion. A deterministic horizontal-pan survey over offsets -500…500 showed:

| Configuration | Reuse hits | A residency | B policy |
|---|---:|---:|---:|
| 1920×1080 fast → 965×543 | 0.2% | ~4.0 MiB | 0 |
| 1920×1080 standard → 1365×768 | 0.6% | ~8.0 MiB | 0 |
| 1920×1080 high → 2731×1536 | 0% | ~32.0 MiB | 0 |
| 1024×768 native standard | 100% | 6 MiB | keep |
| 1024×768 DPR2 native ratio | 100% | 24 MiB | keep |

B keeps numeric history only for simple reduced render/CSS scale ratios (denominator ≤ 8). This preserves the clearly useful native-grid cases while avoiding permanent allocation where reuse is nearly impossible.

Variant: `b09-conditional-numeric-history.html`

### 10. Lazy export AA sample textures

Production allocates four 512² RGBA8 AA sample textures per export slot even for 1× export, although only 2× AA uses them. Four textures are 4 MiB per slot; with ring depth 3 this is **12 MiB** of unnecessary 1× export allocation.

B creates AA sample textures lazily only for 2× AA. Regression passes.

Variant: `b10-export-aa-samples-lazy.html`

### 11. Adaptive initial-iteration probe

The fixed six-view corpus always selected the base 350 iterations, at a measured probe cost of roughly 1.4–17.4 ms per view. That initially suggested deletion.

A broader deterministic survey of 48 views disproved the blanket-removal hypothesis. Three views (6.25%) selected more than 350. Forcing 350 increased the surrogate work metric by:

- +7.21%
- +33.14%
- +25.25%

Conclusion: **do not delete this probe globally**. Better candidates are caching by nearby view, a cheaper trigger before the full probe, or reducing sample count where confidence is high.

### 12. Continuation replay

Current continuation reconstructs active state from `n=0`; a state-resume surrogate instead kept the base-350 state and continued to 4096. The classifications matched in every tested view.

Work reduction by view: **7.63% to 9.79%**, median about **7.87%**.

This is genuine redundant work, but production perturbation/reference changes complicate state validity. It is a redesign candidate, not a safe line deletion.

## Recommended next actions

### High-confidence changes to consider integrating

1. Separate recolor history promotion from numeric-history copy.
2. Stop retaining unused CPU RGBA output.
3. Remove the partial exact-interior pre-primary stats pass.
4. Remove/disable FAST coverage repair after adding a diagnostic hole counter for one release cycle.
5. Avoid idle color-auto snapshots.
6. Release export workspace after export, subject to acceptable next-export allocation latency.
7. Add the conservative exact-interior spatial gate.
8. Make export AA sample textures lazy.

### Conditional changes

- Allocate numeric history only when exact-grid reuse has realistic geometry.
- Release large deep workspaces after returning to an easy frame or after a memory-pressure/idle policy; do not churn them every frame.

### Do not remove based on this test

- Adaptive initial-iteration probe.
- Strict periodicity state solely for speed; no measurable CPU benefit was established.

### Requires structural work

- Preserve valid continuation state so OPERATION_LIMIT pixels do not replay their first ~350 iterations.

## Reproduction

From project root:

```bash
node tests/regression.mjs
node experiments/ab/ab_test.mjs
node experiments/ab/supplement.mjs
node experiments/ab/variant_check.mjs
```

Raw data:

- `docs/performance-cost-audit/ab/results.json`
- `docs/performance-cost-audit/ab/supplement.json`

All B variants are experimental. Production was not modified by this A/B test.