pre-step gate: prestep='none'|'progress' (default bit-identical), refuse the similarity step BEFORE spending an evaluation when it promises less progress than bisection — two lengths already in hand, no new constant; R1-R4 pinned by tests/test_prestep_gate.py (6 green); the gate grid writes to its OWN sweep_gate.json

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

simroot/pure.py

@@ -413,7 +413,7 @@ def _local_order(x2, f2, x1, f1, x0, f0):
 
 def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
               guard="step", stats=None, budget_factor=2.0,
-              budget_extra=None, endowment=1.0, space="x"):
+              budget_extra=None, endowment=1.0, space="x", prestep="none"):
     """The pure similarity root finder.
 
     similarity : key into PURE_SIMS
@@ -467,6 +467,8 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
         raise ValueError(f"unknown scale {scale!r}")
     if space not in SPACES:
         raise ValueError(f"unknown space {space!r}")
+    if prestep not in ("none", "progress"):
+        raise ValueError(f"unknown prestep {prestep!r}")
     if space == "log" and scale not in ("derived", "derived3"):
         # u-space needs a slope; with a chosen or bracket scale there is none to
         # transform, and computing something anyway would hide that (PREREG §3a).
@@ -494,8 +496,10 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
         sg = _Safeguard(guard, abs(B - A), xtol, budget_factor, budget_extra)
         sg.credit = endowment
         forced = 0
+        pre_refused = 0
         if stats is not None:
             stats['forced'] = 0
+            stats['pre_refused'] = 0
 
         while abs(B - A) > xtol:
             if sg.bisect_before_step(abs(B - A)):
@@ -592,7 +596,22 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
                     x_new = 0.5 * (A + B)
                 else:
                     step = None
-                    if space == "log":
+                    if prestep == "progress":
+                        # PRE-STEP GATE (PREREG 2026-09-21).  Measured cause of our cost:
+                        # the safeguard REPAIRS 77.5% of evaluations after the fact, while
+                        # Chandrupatla REFUSES its model on 72% of steps for free and
+                        # halves instead - 2.310 halvings per evaluation against our 1.422.
+                        # Our step never leaves the bracket (0 <= S <= 1), so the question
+                        # is not overshoot but PROGRESS: if the similarity step promises
+                        # less than bisection would remove, spend the same single
+                        # evaluation on the midpoint instead.  Two lengths already in hand
+                        # are compared; there is no threshold and no new constant.
+                        cand = (1.0 - S(abs(fx) / sc)) * (far - x)
+                        half = 0.5 * (A + B) - x
+                        if abs(cand) < abs(half):
+                            step = half
+                            pre_refused += 1
+                    if step is None and space == "log":
                         # c = the bracket end with the smaller |f| (the side the
                         # root is nearer); s = xtol, fixed by derivation in
                         # PREREG amendment 1, never chosen.  Falls back to the
@@ -624,7 +643,7 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
                 if x_new == x or x_new == x_prev:
                     # the bracket can no longer be split in floating point
                     if stats is not None:
-                        stats['forced'] = forced
+                        stats['forced'] = forced; stats['pre_refused'] = pre_refused
                     return x_new, g.n, abs(B - A) <= xtol
 
             w_before = abs(B - A)
@@ -636,7 +655,7 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
             x, fx = x_new, fnew
             if fnew == 0.0:
                 if stats is not None:
-                    stats['forced'] = forced
+                    stats['forced'] = forced; stats['pre_refused'] = pre_refused
                 return x_new, g.n, True
             if FA * fnew < 0.0:
                 B, FB = x_new, fnew
@@ -645,9 +664,9 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
             if guard == "credit":
                 sg.note_shrink(w_before, abs(B - A))
         if stats is not None:
-            stats['forced'] = forced
+            stats['forced'] = forced; stats['pre_refused'] = pre_refused
         return 0.5 * (A + B), g.n, True
     except _Budget:
         if stats is not None:
-            stats['forced'] = forced
+            stats['forced'] = forced; stats['pre_refused'] = pre_refused
         return x, g.n, False