GHC 9.4.6 fails to specialize `recip` from `Fractional` given a fully specific `SPECIALIZE` pragma

[Edit: I've made a mistake and in some of my tests (not the ones that reproduced unsoundness) I've added -fpolymorphic-specialisation as a flag to cabal invocation instead of --ghc-options=-fpolymorphic-specialisation'. When I do the proper --ghc-options, I can't find any recip at all in the emitted Core and so this repro exhibits nothing new. I think it's ripe for closing, since it's full of mistaken claims by me (only some edited out) and since all findings can now be explained by older tickets as follows:

1. This repro shows a case where -fno-polymorphic-specialisation leads to a non-specialized recip (and consequently to 25% slowdown, which is unreliable data, because the code is not specialized enough, so there's an order of magnitude of noise), which is just one more documented performance regression in addition to those mentioned in #23559.
2. This repro shows a case where -fpolymorphic-specialisation leads to unsoundness in GHC >= 9.6, which is again one more case added to what's already in #23559.
3. This repro shows how GHC 9.4.6 doesn't specialize recip as it should, despite SPECIALIZE, which is already fixed for many cases in GHC >= 9.6 (and possibly for this one, can't tell), so we should not focus on 9.4 and it might have been mentioned in some other tickets.
4. With GHC 9.8.1-alpha1 there's no occurrence of recip in the Core emitted with the correct --ghc-options, which proves absolutely nothing, because there's no easy way to discover if recip gets specialized or not in another module from which it's used transitively (#23881). ]

----- Old description below this line

Note that I can't rule out that the unsoundness messes up the specialiser, even though I doubt it. Definitely, the benchmark in question fails at runtime due to the unsoundness.

This specialize pragma

https://github.com/Mikolaj/horde-ad/blob/5393574a36292d133aa92ee2b11a223785a72ad9/src/HordeAd/Core/DualNumber.hs#L165

makes GHC 9.4.6 emit Core for recip below that does not contain any mention of the IsPrimal class. OTOH, in GHC 9.8.1-alpha1, both with and without -fpolymorphic-specialisation I'm getting non-specialized code for this case (lvl298_s1EhY is a (specialized) dictionary for IsPrimal, as can be seen earlier in the Core).

                of
                { D ww_alzs [Dmd=1L] ww1_alzt [Dmd=1L] ww2_alzu [Dmd=1L] ->
                case HordeAd.Core.DualNumber.$w$crecip
                       @GHC.Num.Natural.Natural
                       @(AstRanked PrimalSpan)
                       @Double
                       @0
                       (GHC.Real.$p2RealFrac
                          @(AstRanked PrimalSpan Double 0)
                          (GHC.Float.$p1RealFloat
                             @(AstRanked PrimalSpan Double 0)
                             (HordeAd.Core.TensorADVal.$fIfFNaturalADVal_$s$fRankedTensorAstRanked22
                                @Double
                                @0
                                (HordeAd.Core.Engine.rev4
                                 `cast` (Sym (HordeAd.Core.Types.N:GoodScalar[0] <Double>_N)
                                         :: (HordeAd.Core.Types.GoodScalarConstraint
                                               Double :: Constraint)
                                            ~R# (GoodScalar Double :: Constraint)))
                                $dKnownNat_alqv
                                (ghc-prim:GHC.Classes.$p0(%,%)
                                   @(RealFloat Double)
                                   @(RealFloat (Data.Vector.Storable.Vector Double))
                                   $d(%,%)_alzh)
                                (ghc-prim:GHC.Classes.$p1(%,%)
                                   @(RealFloat Double)
                                   @(RealFloat (Data.Vector.Storable.Vector Double))
                                   $d(%,%)_alzh))))
                       lvl298_s1EhY
                       ww_alzs
                       ww1_alzt
                       ww2_alzu
                of

Repro: check out commit https://github.com/Mikolaj/horde-ad/commit/5393574a36292d133aa92ee2b11a223785a72ad9, uncomment -ddump-stranal in file bench/common/BenchProdTools.hs, run

cabal bench longProdBench --enable-optimization --benchmark-options='-n0 -m prefix "1e7/rev"' -fpolymorphic-specialisation >& log

observe the offending Core (two copies, because -ddump-stranal prints Core twice)

grep -50 HordeAd.Core.DualNumber.\$w\$crecip log