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A rational coefficient beside a variable never reaches a fixed point at the safe ceiling

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Evaluación

Dificultad
5/5
Tiempo estimado
Más de una semana
Aptitud para principiantes
35/100
Tipo de issue
Error
Claridad
Bastante claro
Estado de actividad
Activo
Stack tecnológico
csharp
Área
backend

Línea de trabajo

Comienza con ConstantFoldTest.ACoefficientBesideAVariableStallsRatherThanRunsAway y RunawayBreadthTest para reproducir el comportamiento de saturación medido. Lee las reglas Rearranges y Common mencionadas en la issue y determina después si es apropiada una forma normal con coeficientes racionales o una orientación unidireccional de las reglas; el trabajo estará terminado cuando haya un resultado acotado y terminante con la cobertura de regresión descrita.

Escrito por el modelo de indexación a partir del texto del issue.

Descripción

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.

Lenguaje dominante
C#
Estrellas
831
Forks
79
Merge medio
2 h 22 min
PR fusionados (30 d)
507

Preparar el entorno

Primeros pasos

  1. Lee el issue completo y luego la guía de contribución del proyecto.
  2. Comenta en el issue que vas a ocuparte — evita que dos personas hagan lo mismo.
  3. Haz un fork del repositorio y trabaja en una rama.
  4. Abre un pull request que haga referencia al número del issue.

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