# Baseline numbers captured before T0 changes
# Hardware: lrrr.local / Apple M5 Pro
# Date: 2026-04-24

Batch::iteration          29.840 µs
Gaussian::add            219.58 ps
Gaussian::sub            219.41 ps
Gaussian::mul              1.568 ns   ← hot path; target ≥1.5× improvement
Gaussian::div              1.572 ns   ← hot path; target ≥1.5× improvement
Gaussian::pi             262.89 ps
Gaussian::tau            262.47 ps
Gaussian::pi_tau_combined 219.40 ps

# After T0 (2026-04-24, same hardware)

Batch::iteration           21.253 µs   (1.40× — below 3× target; see post-mortem)
Gaussian::add             218.62 ps    (1.00× — unchanged, Add/Sub use moment form)
Gaussian::sub             220.15 ps    (1.00×)
Gaussian::mul             218.69 ps    (7.17× — nat-param: now two f64 adds, no sqrt)
Gaussian::div             218.64 ps    (7.19× — nat-param: now two f64 subs, no sqrt)
Gaussian::pi              263.19 ps    (1.00× — now a field read, same cost)
Gaussian::tau             263.51 ps    (1.00× — now a field read, same cost)
Gaussian::pi_tau_combined 219.13 ps    (1.00×)

# Post-mortem: Batch::iteration 1.40× vs. 3× target
#
# Root cause: the bench has 100 tiny 2-team events. Each event still allocates
# ~10 Vecs per iteration (down from ~18). The arena covers teams/diffs/ties/margins
# (was 4 Vecs, now 0 new allocs) but the following remain:
#   - within_priors() returns Vec<Vec<Player<D>>>: 3 Vecs per event (300 total)
#   - event.outputs() returns Vec<f64>: 1 Vec per event (100 total)
#   - sort_perm() allocates 2 scratch Vecs: 200 total
#   - Game::likelihoods = collect() allocates Vec<Vec<Gaussian>>: 4 Vecs (400 total)
# Total remaining: ~1000 allocs per iteration call vs. ~1800 before (44% reduction).
#
# The HashMap → dense Vec win (target 2–4×) benefits the History-level forward/backward
# sweep, NOT Batch::iteration in isolation — so this bench doesn't show it.
#
# To hit ≥3× on Batch::iteration:
#   - Arena-ify sort_perm (use a stack-fixed array for small n_teams)
#   - Pass a within_priors output buffer through the arena
#   - Make Game::likelihoods write into an arena slice rather than allocating
# These land in T1 (factor graph) when we redesign Game's internals.