A rational coefficient beside a variable never reaches a fixed point at the safe ceiling
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还没有人认领这个 Issue。
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调研方向
从 ConstantFoldTest.ACoefficientBesideAVariableStallsRatherThanRunsAway 和 RunawayBreadthTest 开始，以复现测得的饱和行为。阅读 issue 中提到的 Rearranges 和 Common 规则，然后确定有理系数正规形或单向规则定向是否合适；完成的要求是得到一个有界且终止的结果，并具备所描述的回归覆盖。
由索引模型根据 Issue 内容生成。
描述
At the safe ceiling (RulesUpTo(Rearranges)), seven of the 3,630 shapes in the growth corpus never
report a fixed point, and they are one family: a rational coefficient beside a variable.
Measured (build 98a9420c, after #1198)
WorkBudget { Steps = 200_000, Time = 30 s }, one input per graph:
| input | fixed point | e-nodes after 30 s | e-nodes after 2 s | extracted |
|---|---|---|---|---|
2 * x * 1/2 |
no | 158 | — | x |
x * 1/2 * 2 |
no | 135 | — | x |
(2 - 0) * x * 1/2 |
no | 159 | 182 | x |
x / x * -x |
no | 583 | 464 | -x |
x / x * x * 1/2 |
no | 249 | 282 | x / 2 |
x / x * x ^ (-2) |
no | 317 | 291 | x ^ (-2) |
1 / (1/2) * x * 1/2 |
no | 159 | 181 | x |
x ^ 2 / x |
no | 145 | 109 | x |
2 ^ (-1) / sqrt(1/2) |
no, step ceiling | 1,565 | 1,072 | sqrt(1/2) |
So this is a stall, not a runaway: the graph barely grows with fifteen times the budget, and
every extraction is right. ConstantFoldTest.ACoefficientBesideAVariableStallsRatherThanRunsAway
pins it in both directions — an entry that starts saturating is to be deleted, and one that grows
past a thousand e-nodes has stopped being a stall.
What it is
The spellings of a coefficient beside a variable — 1/2 * x, x / 2, x * 2 ^ (-1),
2 ^ (-1) * x — are exchanged by Rearranges rules (a-reciprocal-rational-factor-is-a-division,
a-reciprocal-power-is-a-quotient, the quotient and product regrouping rules of Common), and a
fresh spelling keeps appearing at the edge of what has been rewritten, so a pass never comes back
empty. Before #1198 the same rules ran away on constant-only input (2 - 0 + 0 * 2, 54 cases),
because with nothing folding a number the spellings were unbounded; folding rationals on
insertion bounded the family without closing it. RunawayBreadthTest had called these rules
"confluent on plain arithmetic" from three inputs; it now says what was measured.
What would close it, not decided
Either a normal form for a rational coefficient inside the graph — c * x with c a literal,
folded on insertion the way a rational over rationals now is — or an orientation among the
spelling rules so that only one direction fires under saturation. The first is a mechanism; the
second is what the growth ceiling already does for expanding rules and would need a marker for
"rearranges, but one way". Neither is worth doing until something calls the graph on this shape;
Transformation.CanonicalizationOverGraph is offered, not applied.
Found while measuring #746 tier 2 item 4 (PR #1198). Related: the budget overshoot on these
same inputs, filed separately.
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