ocaml: phase 5.1 euler9.ml baseline (Project Euler #9, abc = 31875000)

Find the unique Pythagorean triple with a + b + c = 1000 and
return their product.

The naive triple loop timed out under host contention (10-minute
cap exceeded with ~333 * 999 ~= 333k inner iterations of complex
checks). Rewritten with algebraic reduction:

  a + b + c = 1000  AND  a^2 + b^2 = c^2
  =>  b = (500000 - 1000 * a) / (1000 - a)

so only the outer a-loop is needed (333 iterations). Single-pass
form:

  for a = 1 to 333 do
    let num = 500000 - 1000 * a in
    let den = 1000 - a in
    if num mod den = 0 then begin
      let b = num / den in
      if b > a then
        let c = 1000 - a - b in
        if c > b then result := a * b * c
    end
  done

Triple (200, 375, 425), product 31875000.

103 baseline programs total.

lib/ocaml/baseline/euler9.ml

@@ -0,0 +1,17 @@
+let euler9 () =
+  let result = ref 0 in
+  for a = 1 to 333 do
+    let num = 500000 - 1000 * a in
+    let den = 1000 - a in
+    if num mod den = 0 then begin
+      let b = num / den in
+      if b > a then
+        let c = 1000 - a - b in
+        if c > b then result := a * b * c
+    end
+  done;
+  !result
+
+;;
+
+euler9 ()

lib/ocaml/baseline/expected.json

@@ -27,6 +27,7 @@
   "euler1.ml": 233168,
   "euler2.ml": 4613732,
   "euler6.ml": 25164150,
+  "euler9.ml": 31875000,
   "expr_eval.ml": 16,
   "expr_simp.ml": 22,
   "factorial.ml": 3628800,

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — euler9.ml baseline (Project Euler #9, abc
+  product for the unique Pythagorean triple with a+b+c=1000 →
+  31875000). Naive triple loop times out under contention (10-min
+  cap); rewritten with algebraic reduction
+  `b = (500000 - 1000a) / (1000 - a)` so only one loop is needed.
+  Triple is (200, 375, 425). 103 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler6.ml baseline (Project Euler #6, square
   of sum minus sum of squares for 1..100 = 25164150). Single for-loop
   threading two refs; (sum 1..100)^2 - sum(i^2 for 1..100) = 5050^2