Function expectApprox

test/compute-engine/monte-carlo.test.ts:9–21

(
  actual: number,
  expected: number,
  tolerance = TOL,
  absTolerance = ABS_TOL
)

// estimator, never sampling luck. Unseeded, the heavy-tailed semi-infinite
// cases could red-flag any commit's gate at random (observed 2026-08-17:
// ∫_1^∞ 1/x² dx off by 0.63 once, then 3 consecutive passes).
//
// The tolerances still reflect the estimator's statistical accuracy at the
// pinned seeds — with n=1e6, standard error is typically ~1e-3 for
// well-behaved integrands — so they stay meaningful if a seed changes.
const N = 1e6;
const TOL = 0.05; // 5% relative tolerance for most tests
const ABS_TOL = 0.1; // absolute tolerance for values near zero

/** A deterministic uniform-[0,1) stream, seeded per test by a tag string. */
function seededDraw(tag: string): () => number {
  const [lo, hi] = foldSeed(tag);
  let n = 0;
  return () => frameDraw(lo, hi, n++);
}