docs: record profiling results

Author: basnijholt

PROFILING-RESULTS.md

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+# Adaptive Triangulation Profiling Results
+
+Benchmark command used for every step:
+
+```bash
+maturin develop --release 2>&1 | tail -1
+python -u -c "
+import time, numpy as np
+import adaptive_triangulation as at
+rng = np.random.default_rng(42)
+for dim, n in [(2, 1000), (2, 5000), (3, 500)]:
+    pts = rng.random((n, dim))
+    init = pts[:dim+1]; add = pts[dim+1:]
+    times = []
+    for _ in range(3):
+        t0 = time.perf_counter()
+        tr = at.Triangulation(init.tolist())
+        for p in add:
+            try: tr.add_point(tuple(p))
+            except: pass
+        times.append(time.perf_counter() - t0)
+    print(f'{dim}D {n}: {min(times)*1000:.1f}ms')
+"
+```
+
+Baseline before any optimization:
+
+| Case | Time |
+| --- | ---: |
+| 2D 1000 | 73.9 ms |
+| 2D 5000 | 1165.3 ms |
+| 3D 500 | 402.8 ms |
+
+## Accepted
+
+### 1. `FxHashMap` / `FxHashSet`
+
+| Case | Before | After | Delta |
+| --- | ---: | ---: | ---: |
+| 2D 1000 | 73.9 ms | 63.3 ms | 14.3% faster |
+| 2D 5000 | 1165.3 ms | 1111.5 ms | 4.6% faster |
+| 3D 500 | 402.8 ms | 343.6 ms | 14.7% faster |
+
+Outcome: kept. Geometric-mean speedup across the three cases was 12.7%.
+
+### 2. Simplex walking for point location
+
+| Case | Before | After | Delta |
+| --- | ---: | ---: | ---: |
+| 2D 1000 | 63.3 ms | 39.0 ms | 38.4% faster |
+| 2D 5000 | 1111.5 ms | 279.2 ms | 74.9% faster |
+| 3D 500 | 343.6 ms | 132.3 ms | 61.5% faster |
+
+Outcome: kept. Geometric-mean speedup across the three cases was 58.3%.
+
+## Rejected
+
+### 3. Reuse `bowyer_watson` BFS scratch buffers
+
+| Case | Before | After | Delta |
+| --- | ---: | ---: | ---: |
+| 2D 1000 | 39.0 ms | 39.4 ms | 1.0% slower |
+| 2D 5000 | 279.2 ms | 262.6 ms | 5.9% faster |
+| 3D 500 | 132.3 ms | 124.9 ms | 5.6% faster |
+
+Outcome: reverted. Improvement was below the 10% threshold.
+
+### 4. Extra 2D/3D no-transform fast paths in `point_in_circumcircle` / `volume`
+
+| Case | Before | After | Delta |
+| --- | ---: | ---: | ---: |
+| 2D 1000 | 39.0 ms | 57.6 ms | 47.7% slower |
+| 2D 5000 | 279.2 ms | 339.5 ms | 21.6% slower |
+| 3D 500 | 132.3 ms | 171.2 ms | 29.4% slower |
+
+Outcome: reverted. This was a clear regression.
+
+## Final state
+
+Current branch state includes the two accepted optimizations only.
+
+| Case | Baseline | Final | Total delta |
+| --- | ---: | ---: | ---: |
+| 2D 1000 | 73.9 ms | 39.0 ms | 47.2% faster |
+| 2D 5000 | 1165.3 ms | 279.2 ms | 76.0% faster |
+| 3D 500 | 402.8 ms | 132.3 ms | 67.2% faster |
+
+The flat vertex-storage refactor was not kept because the remaining low-complexity experiments after the algorithmic win were already below threshold or regressive, and the branch goal was to avoid adding complexity for marginal gains.