fix: replace the erfc approximation with libm, for free

#41 asked whether the Numerical Recipes `erfcc` approximation — 1.2e-7
relative, and the binding accuracy constraint on the whole crate — was
worth replacing, given it sits in the inference hot loop. It is, and it
costs nothing.

Measured, against an independent incomplete-gamma reference:

    range        previous (NR)        libm
    [-3, 0]            7.95e-8     2.15e-14
    [0, 0.5]           8.69e-8     4.70e-14
    [0.5, 2]           9.38e-8     1.24e-12
    [2, 6]             1.04e-7     5.20e-14
    [6, 26]            1.07e-7     1.75e-13

    erfc(0)          1.00000003          1.0  (exactly)
    |erfc(z)+erfc(-z)-2|  6.00e-8     2.22e-16

Performance, on `benches/batch.rs`: change [-3.34% +2.26%], p = 0.89 —
no change detected.

That result is counterintuitive, because libm's erfc is 1.65x slower
when swept uniformly over [-2.5, 2.5]. The sweep was the wrong input
distribution. Capturing the arguments inference actually passes:

    |x|<0.5    96.16%
    0.5-0.84    2.05%
    0.84-1.25   1.24%
    1.25-2      0.54%
    2-6         0.00%

98% fall below 0.84375, which is exactly where FDLIBM skips the
exponential entirely — while the NR form always pays for one. On the
real trace libm is the faster of the two (3.23 vs 3.78 ns/call).

An ad-hoc `Instant` harness reported a 16% end-to-end speedup; that was
an artifact of its own setup allocating and leaking per run, and
criterion's verdict of "no change" is the one to believe.

What it bought:

- `compute_margin` against exact quantiles: 8.4e-8 -> 1.7e-16.
- `cdf(mu, mu, sigma)` is now exactly 0.5; it was 1.5e-8 out.
- `sf + cdf` sums to one within a ULP, from 3e-8.
- `erfcx`'s two branches now agree to round-off across the crossover
  rather than to 1e-7, so the log-space evidence path and the linear one
  are consistent.
- Ten test tolerances tightened from 1e-6 to 1e-13..1e-15, and the
  prediction floor is now the integrator's rather than `cdf`'s.

Five goldens moved, by 2.4e-9 to 6e-7 — the magnitude of the removed
error, and `test_env_ttt`'s mu still rounds to the same six decimals.
Re-recorded with more digits so future drift stays visible. Verified as
movement toward truth per the goldens policy: every value now derives
from a primitive checked against an independent reference and satisfying
the exact identities, which the previous one did not.

Adds `libm` — zero transitive dependencies, rust-lang maintained.

Closes #41

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ

src/predict.rs

@@ -33,17 +33,23 @@ pub(crate) const MAX_TEAMS_FOR_DISTRIBUTION: usize = 6;
 
 /// Relative tolerance for the first-place integrals.
 ///
-/// Tightening past this buys nothing: the underlying `cdf` is a rational
-/// approximation with fractional error ~1.2e-7, which contributes ~6e-9 to a
-/// finished probability and dominates any further quadrature refinement.
+/// The adaptive integrator reaches the exact two-team closed form to ~1e-15 at
+/// this tolerance, which is round-off for a probability. `cdf` is no longer the
+/// limit — it went to ~1 ULP when `erfc` moved to `libm` — so this is the
+/// integrator's own floor.
 const WIN_TOLERANCE: f64 = 1e-8;
 
 /// Nodes for the ranking grid, and the floor below which a grid is pointless.
 ///
-/// The recursion converges as O(h^2). Measured against the exact two-team
-/// closed form, 2_048 nodes leave ~1.2e-6 of discretisation error while 8_192
-/// reach ~1e-7 — at which point the residual is the `cdf` rational
-/// approximation (~2.4e-8), not the grid, and refining further buys nothing.
+/// The recursion converges as O(h^2), so this trades nodes against accuracy
+/// directly. Measured against the exact two-team closed form, 2_048 nodes leave
+/// ~1.2e-6 of discretisation error and 8_192 reach ~1e-7.
+///
+/// Unlike the adaptive path there is no approximation floor underneath this any
+/// more — `cdf` is accurate to ~1 ULP since `erfc` moved to `libm` — so the
+/// error here is purely the grid, and a caller who needs more can only get it
+/// by paying for more nodes. 8_192 is the accuracy/cost point chosen, not a
+/// point where refining stops helping.
 const MIN_GRID_POINTS: usize = 8_192;
 const MAX_GRID_POINTS: usize = 262_144;
 
@@ -523,7 +529,7 @@ mod tests {
             let got = win_probabilities(&perf, &flat(2, eps));
             let (wa, wb) = closed_form_two(perf[0], perf[1], eps);
             assert!(
-                (got[0] - wa).abs() < 1e-7 && (got[1] - wb).abs() < 1e-7,
+                (got[0] - wa).abs() < 1e-12 && (got[1] - wb).abs() < 1e-12,
                 "mu=({ma},{mb}) sigma=({sa},{sb}) eps={eps}: got {got:?}, want [{wa}, {wb}]"
             );
         }