The growth corpus reaches 194 rules instead of 84 (#825)

[Rafael-SOWNet]

A declaration is only checked if the corpus makes the rule fire. The arithmetic grammar reached 84
of the 324, and six whole sets — trigonometry, booleans, sets, comparisons and both factorial ones
— were never exercised at all. A declaration on any of their rules was being checked by a test that
never ran it.

	before	after
rules that fire	84	194
declared rules actually checked	18	59
rules the corpus cannot reach	240	130

Three changes

A rule is tried at every node, not only at the root. A rule matches where its shape sits, and
asking only about whole corpus expressions left most of them never firing.

Shapes the generated grammar does not build, supplied on top of it the way
MatchedRulesAgreeWithTheSwitchTest already supplies its own: the trigonometric identities and the
arguments the multiple-angle rules want, logarithms, factorials both ways round, the boolean laws,
set operations, and the polynomial shapes the division, gcd and factorisation sets match.

The comparison set, which was the largest block still out of reach. Its rules key on zero or a
number being on the left of the operator, on both sides being the same thing, and on a negative
factor or divisor standing beside a zero — none of which an arithmetic grammar produces, because it
builds comparisons only in the form a person would write:

0 > x        x >= x        x / (-2) > 0        (-2) * x <= 0

over all five comparison operators. With those, De Morgan in both directions rather than one, the
trigonometric reciprocal pairs (cosec(x) * sin(x), cotan(arccotan(x)) — shapes rules exist for
and nothing built), logarithms in and of reciprocal bases, and the differences and products that
contain their own operand a second time.

Both counts are asserted, so the check cannot quietly stop being exercised.

Nothing it newly reaches contradicts a declaration

Worth stating rather than assuming: this coverage is exactly where an untested claim would have been
hiding, and the one false declaration this test found when it was written (#1158) was found the same
way — by making a rule fire that nothing had made fire before. All 59 declarations that now run
survive it.

No growth changes here

This alters nothing that runs. The undeclared rules it newly exercises are the measured evidence for
declaring them, which is #1161 and its successors — Saturation.RulesUpTo builds its set as the
rules up to Rearranges, so those declarations do change which rules equality saturation fires.

Verification

Full suite 9552 passed, 0 failed, 14 skipped.

Part of #825.