Add perf test for #15304

The test max memory usage improves dramatically with the fixes to
memory usage in demand analyser from #15455

3 files changed, 778 insertions, 0 deletions

diff --git a/testsuite/tests/perf/compiler/T15304.hs b/testsuite/tests/perf/compiler/T15304.hs
new file mode 100644
index 0000000000..e09faacdb3
--- /dev/null
+++ b/testsuite/tests/perf/compiler/T15304.hs
@@ -0,0 +1,764 @@
+{-# LANGUAGE GADTSyntax #-}
+{-# LANGUAGE ViewPatterns #-}
+{-# OPTIONS_GHC -fno-warn-type-defaults #-}
+
+
+
+--------------------------------------------------------------------------------------------
+-- |
+-- Copyright   :  (C) 2018 Nathan Waivio
+-- License     :  BSD3
+-- Maintainer  :  Nathan Waivio <nathan.waivio@gmail.com>
+-- Stability   :  Stable
+-- Portability :  unportable
+--
+-- Library implementing standard functions for the <https://en.wikipedia.org/wiki/Algebra_of_physical_space Algebra of Physical Space> Cl(3,0)
+--
+---------------------------------------------------------------------------------------------
+
+
+module T15304 where
+
+
+
+data Cl3 where
+  R   :: !Double -> Cl3 -- Real Scalar Sub-algebra (G0)
+  V3  :: !Double -> !Double -> !Double -> Cl3 -- Vectors (G1)
+  BV  :: !Double -> !Double -> !Double -> Cl3 -- Bivectors (G2)
+  I   :: !Double -> Cl3 -- Trivector Imaginary Pseudo-Scalar (G3)
+  PV  :: !Double -> !Double -> !Double -> !Double -> Cl3 -- Paravector (G0 + G1)
+  H   :: !Double -> !Double -> !Double -> !Double -> Cl3 -- Quaternion Even Sub-algebra (G0 + G2)
+  C   :: !Double -> !Double -> Cl3 -- Complex Sub-algebra (G0 + G3)
+  BPV :: !Double -> !Double -> !Double -> !Double -> !Double -> !Double -> Cl3 -- Biparavector (G1 + G2)
+  ODD :: !Double -> !Double -> !Double -> !Double -> Cl3 -- Odd (G1 + G3)
+  TPV :: !Double -> !Double -> !Double -> !Double -> Cl3 -- Triparavector (G2 + G3)
+  APS :: !Double -> !Double -> !Double -> !Double -> !Double -> !Double -> !Double -> !Double -> Cl3 -- Algebra of Physical Space (G0 + G1 + G2 + G3)
+
+
+instance Num Cl3 where
+  (R a0) + (R b0) = R (a0 + b0)
+
+  (R a0) + (V3 b1 b2 b3) = PV a0 b1 b2 b3
+  (R a0) + (BV b23 b31 b12) = H a0 b23 b31 b12
+  (R a0) + (I b123) = C a0 b123
+  (R a0) + (PV b0 b1 b2 b3) = PV (a0 + b0) b1 b2 b3
+  (R a0) + (H b0 b23 b31 b12) = H (a0 + b0) b23 b31 b12
+  (R a0) + (C b0 b123) = C (a0 + b0) b123
+  (R a0) + (BPV b1 b2 b3 b23 b31 b12) = APS a0 b1 b2 b3 b23 b31 b12 0
+  (R a0) + (ODD b1 b2 b3 b123) = APS a0 b1 b2 b3 0 0 0 b123
+  (R a0) + (TPV b23 b31 b12 b123) = APS a0 0 0 0 b23 b31 b12 b123
+  (R a0) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0 + b0) b1 b2 b3 b23 b31 b12 b123
+
+  (V3 a1 a2 a3) + (R b0) = PV b0 a1 a2 a3
+  (BV a23 a31 a12) + (R b0) = H b0 a23 a31 a12
+  (I a123) + (R b0) = C b0 a123
+  (PV a0 a1 a2 a3) + (R b0) = PV (a0 + b0) a1 a2 a3
+  (H a0 a23 a31 a12) + (R b0) = H (a0 + b0) a23 a31 a12
+  (C a0 a123) + (R b0) = C (a0 + b0) a123
+  (BPV a1 a2 a3 a23 a31 a12) + (R b0) = APS b0 a1 a2 a3 a23 a31 a12 0
+  (ODD a1 a2 a3 a123) + (R b0) = APS b0 a1 a2 a3 0 0 0 a123
+  (TPV a23 a31 a12 a123) + (R b0) = APS b0 0 0 0 a23 a31 a12 a123
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (R b0) = APS (a0 + b0) a1 a2 a3 a23 a31 a12 a123
+
+  (V3 a1 a2 a3) + (V3 b1 b2 b3) = V3 (a1 + b1) (a2 + b2) (a3 + b3)
+
+  (V3 a1 a2 a3) + (BV b23 b31 b12) = BPV a1 a2 a3 b23 b31 b12
+  (V3 a1 a2 a3) + (I b123) = ODD a1 a2 a3 b123
+  (V3 a1 a2 a3) + (PV b0 b1 b2 b3) = PV b0 (a1 + b1) (a2 + b2) (a3 + b3)
+  (V3 a1 a2 a3) + (H b0 b23 b31 b12) = APS b0 a1 a2 a3 b23 b31 b12 0
+  (V3 a1 a2 a3) + (C b0 b123) = APS b0 a1 a2 a3 0 0 0 b123
+  (V3 a1 a2 a3) + (BPV b1 b2 b3 b23 b31 b12) = BPV (a1 + b1) (a2 + b2) (a3 + b3) b23 b31 b12
+  (V3 a1 a2 a3) + (ODD b1 b2 b3 b123) = ODD (a1 + b1) (a2 + b2) (a3 + b3) b123
+  (V3 a1 a2 a3) + (TPV b23 b31 b12 b123) = APS 0 a1 a2 a3 b23 b31 b12 b123
+  (V3 a1 a2 a3) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS b0 (a1 + b1) (a2 + b2) (a3 + b3) b23 b31 b12 b123
+
+  (BV a23 a31 a12) + (V3 b1 b2 b3) = BPV b1 b2 b3 a23 a31 a12
+  (I a123) + (V3 b1 b2 b3) = ODD b1 b2 b3 a123
+  (PV a0 a1 a2 a3) + (V3 b1 b2 b3) = PV a0 (a1 + b1) (a2 + b2) (a3 + b3)
+  (H a0 a23 a31 a12) + (V3 b1 b2 b3) = APS a0 b1 b2 b3 a23 a31 a12 0
+  (C a0 a123) + (V3 b1 b2 b3) = APS a0 b1 b2 b3 0 0 0 a123
+  (BPV a1 a2 a3 a23 a31 a12) + (V3 b1 b2 b3) = BPV (a1 + b1) (a2 + b2) (a3 + b3) a23 a31 a12
+  (ODD a1 a2 a3 a123) + (V3 b1 b2 b3) = ODD (a1 + b1) (a2 + b2) (a3 + b3) a123
+  (TPV a23 a31 a12 a123) + (V3 b1 b2 b3) = APS 0 b1 b2 b3 a23 a31 a12 a123
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (V3 b1 b2 b3) = APS a0 (a1 + b1) (a2 + b2) (a3 + b3) a23 a31 a12 a123
+
+  (BV a23 a31 a12) + (BV b23 b31 b12) = BV (a23 + b23) (a31 + b31) (a12 + b12)
+
+  (BV a23 a31 a12) + (I b123) = TPV a23 a31 a12 b123
+  (BV a23 a31 a12) + (PV b0 b1 b2 b3) = APS b0 b1 b2 b3 a23 a31 a12 0
+  (BV a23 a31 a12) + (H b0 b23 b31 b12) = H b0 (a23 + b23) (a31 + b31) (a12 + b12)
+  (BV a23 a31 a12) + (C b0 b123) = APS b0 0 0 0 a23 a31 a12 b123
+  (BV a23 a31 a12) + (BPV b1 b2 b3 b23 b31 b12) = BPV b1 b2 b3 (a23 + b23) (a31 + b31) (a12 + b12)
+  (BV a23 a31 a12) + (ODD b1 b2 b3 b123) = APS 0 b1 b2 b3 a23 a31 a12 b123
+  (BV a23 a31 a12) + (TPV b23 b31 b12 b123) = TPV (a23 + b23) (a31 + b31) (a12 + b12) b123
+  (BV a23 a31 a12) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS b0 b1 b2 b3 (a23 + b23) (a31 + b31) (a12 + b12) b123
+
+  (I a123) + (BV b23 b31 b12) = TPV b23 b31 b12 a123
+  (PV a0 a1 a2 a3) + (BV b23 b31 b12) = APS a0 a1 a2 a3 b23 b31 b12 0
+  (H a0 a23 a31 a12) + (BV b23 b31 b12) = H a0 (a23 + b23) (a31 + b31) (a12 + b12)
+  (C a0 a123) + (BV b23 b31 b12) = APS a0 0 0 0 b23 b31 b12 a123
+  (BPV a1 a2 a3 a23 a31 a12) + (BV b23 b31 b12) = BPV a1 a2 a3 (a23 + b23) (a31 + b31) (a12 + b12)
+  (ODD a1 a2 a3 a123) + (BV b23 b31 b12) = APS 0 a1 a2 a3 b23 b31 b12 a123
+  (TPV a23 a31 a12 a123) + (BV b23 b31 b12) = TPV (a23 + b23) (a31 + b31) (a12 + b12) a123
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (BV b23 b31 b12) = APS a0 a1 a2 a3 (a23 + b23) (a31 + b31) (a12 + b12) a123
+
+  (I a123) + (I b123) = I (a123 + b123)
+
+  (I a123) + (PV b0 b1 b2 b3) = APS b0 b1 b2 b3 0 0 0 a123
+  (I a123) + (H b0 b23 b31 b12) = APS b0 0 0 0 b23 b31 b12 a123
+  (I a123) + (C b0 b123) = C b0 (a123 + b123)
+  (I a123) + (BPV b1 b2 b3 b23 b31 b12) = APS 0 b1 b2 b3 b23 b31 b12 a123
+  (I a123) + (ODD b1 b2 b3 b123) = ODD b1 b2 b3 (a123 + b123)
+  (I a123) + (TPV b23 b31 b12 b123) = TPV b23 b31 b12 (a123 + b123)
+  (I a123) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS b0 b1 b2 b3 b23 b31 b12 (a123 + b123)
+
+  (PV a0 a1 a2 a3) + (I b123) = APS a0 a1 a2 a3 0 0 0 b123
+  (H a0 a23 a31 a12) + (I b123) = APS a0 0 0 0 a23 a31 a12 b123
+  (C a0 a123) + (I b123) = C a0 (a123 + b123)
+  (BPV a1 a2 a3 a23 a31 a12) + (I b123) = APS 0 a1 a2 a3 a23 a31 a12 b123
+  (ODD a1 a2 a3 a123) + (I b123) = ODD a1 a2 a3 (a123 + b123)
+  (TPV a23 a31 a12 a123) + (I b123) = TPV a23 a31 a12 (a123 + b123)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (I b123) = APS a0 a1 a2 a3 a23 a31 a12 (a123 + b123)
+
+  (PV a0 a1 a2 a3) + (PV b0 b1 b2 b3) = PV (a0 + b0) (a1 + b1) (a2 + b2) (a3 + b3)
+
+  (PV a0 a1 a2 a3) + (H b0 b23 b31 b12) = APS (a0 + b0) a1 a2 a3 b23 b31 b12 0
+  (PV a0 a1 a2 a3) + (C b0 b123) = APS (a0 + b0) a1 a2 a3 0 0 0 b123
+  (PV a0 a1 a2 a3) + (BPV b1 b2 b3 b23 b31 b12) = APS a0 (a1 + b1) (a2 + b2) (a3 + b3) b23 b31 b12 0
+  (PV a0 a1 a2 a3) + (ODD b1 b2 b3 b123) = APS a0 (a1 + b1) (a2 + b2) (a3 + b3) 0 0 0 b123
+  (PV a0 a1 a2 a3) + (TPV b23 b31 b12 b123) = APS a0 a1 a2 a3 b23 b31 b12 b123
+  (PV a0 a1 a2 a3) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0 + b0) (a1 + b1) (a2 + b2) (a3 + b3) b23 b31 b12 b123
+
+  (H a0 a23 a31 a12) + (PV b0 b1 b2 b3) = APS (a0 + b0) b1 b2 b3 a23 a31 a12 0
+  (C a0 a123) + (PV b0 b1 b2 b3) = APS (a0 + b0) b1 b2 b3 0 0 0 a123
+  (BPV a1 a2 a3 a23 a31 a12) + (PV b0 b1 b2 b3) = APS b0 (a1 + b1) (a2 + b2) (a3 + b3) a23 a31 a12 0
+  (ODD a1 a2 a3 a123) + (PV b0 b1 b2 b3) = APS b0 (a1 + b1) (a2 + b2) (a3 + b3) 0 0 0 a123
+  (TPV a23 a31 a12 a123) + (PV b0 b1 b2 b3) = APS b0 b1 b2 b3 a23 a31 a12 a123
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (PV b0 b1 b2 b3) = APS (a0 + b0) (a1 + b1) (a2 + b2) (a3 + b3) a23 a31 a12 a123
+
+  (H a0 a23 a31 a12) + (H b0 b23 b31 b12) = H (a0 + b0) (a23 + b23) (a31 + b31) (a12 + b12)
+
+  (H a0 a23 a31 a12) + (C b0 b123) = APS (a0 + b0) 0 0 0 a23 a31 a12 b123
+  (H a0 a23 a31 a12) + (BPV b1 b2 b3 b23 b31 b12) = APS a0 b1 b2 b3 (a23 + b23) (a31 + b31) (a12 + b12) 0
+  (H a0 a23 a31 a12) + (ODD b1 b2 b3 b123) = APS a0 b1 b2 b3 a23 a31 a12 b123
+  (H a0 a23 a31 a12) + (TPV b23 b31 b12 b123) = APS a0 0 0 0 (a23 + b23) (a31 + b31) (a12 + b12) b123
+  (H a0 a23 a31 a12) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0 + b0) b1 b2 b3 (a23 + b23) (a31 + b31) (a12 + b12) b123
+
+  (C a0 a123) + (H b0 b23 b31 b12) = APS (a0 + b0) 0 0 0 b23 b31 b12 a123
+  (BPV a1 a2 a3 a23 a31 a12) + (H b0 b23 b31 b12) = APS b0 a1 a2 a3 (a23 + b23) (a31 + b31) (a12 + b12) 0
+  (ODD a1 a2 a3 a123) + (H b0 b23 b31 b12) = APS b0 a1 a2 a3 b23 b31 b12 a123
+  (TPV a23 a31 a12 a123) + (H b0 b23 b31 b12) = APS b0 0 0 0 (a23 + b23) (a31 + b31) (a12 + b12) a123
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (H b0 b23 b31 b12) = APS (a0 + b0) a1 a2 a3 (a23 + b23) (a31 + b31) (a12 + b12) a123
+
+  (C a0 a123) + (C b0 b123) = C (a0 + b0) (a123 + b123)
+
+  (C a0 a123) + (BPV b1 b2 b3 b23 b31 b12) = APS a0 b1 b2 b3 b23 b31 b12 a123
+  (C a0 a123) + (ODD b1 b2 b3 b123) = APS a0 b1 b2 b3 0 0 0 (a123 + b123)
+  (C a0 a123) + (TPV b23 b31 b12 b123) = APS a0 0 0 0 b23 b31 b12 (a123 + b123)
+  (C a0 a123) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0 + b0) b1 b2 b3 b23 b31 b12 (a123 + b123)
+
+  (BPV a1 a2 a3 a23 a31 a12) + (C b0 b123) = APS b0 a1 a2 a3 a23 a31 a12 b123
+  (ODD a1 a2 a3 a123) + (C b0 b123) = APS b0 a1 a2 a3 0 0 0 (a123 + b123)
+  (TPV a23 a31 a12 a123) + (C b0 b123) = APS b0 0 0 0 a23 a31 a12 (a123 + b123)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (C b0 b123) = APS (a0 + b0) a1 a2 a3 a23 a31 a12 (a123 + b123)
+
+  (BPV a1 a2 a3 a23 a31 a12) + (BPV b1 b2 b3 b23 b31 b12) = BPV (a1 + b1) (a2 + b2) (a3 + b3) (a23 + b23) (a31 + b31) (a12 + b12)
+
+  (BPV a1 a2 a3 a23 a31 a12) + (ODD b1 b2 b3 b123) = APS 0 (a1 + b1) (a2 + b2) (a3 + b3) a23 a31 a12 b123
+  (BPV a1 a2 a3 a23 a31 a12) + (TPV b23 b31 b12 b123) = APS 0 a1 a2 a3 (a23 + b23) (a31 + b31) (a12 + b12) b123
+  (BPV a1 a2 a3 a23 a31 a12) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS b0 (a1 + b1) (a2 + b2) (a3 + b3) (a23 + b23) (a31 + b31) (a12 + b12) b123
+
+  (ODD a1 a2 a3 a123) + (BPV b1 b2 b3 b23 b31 b12) = APS 0 (a1 + b1) (a2 + b2) (a3 + b3) b23 b31 b12 a123
+  (TPV a23 a31 a12 a123) + (BPV b1 b2 b3 b23 b31 b12) = APS 0 b1 b2 b3 (a23 + b23) (a31 + b31) (a12 + b12) a123
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (BPV b1 b2 b3 b23 b31 b12) = APS a0 (a1 + b1) (a2 + b2) (a3 + b3) (a23 + b23) (a31 + b31) (a12 + b12) a123
+
+  (ODD a1 a2 a3 a123) + (ODD b1 b2 b3 b123) = ODD (a1 + b1) (a2 + b2) (a3 + b3) (a123 + b123)
+
+  (ODD a1 a2 a3 a123) + (TPV b23 b31 b12 b123) = APS 0 a1 a2 a3 b23 b31 b12 (a123 + b123)
+  (ODD a1 a2 a3 a123) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS b0 (a1 + b1) (a2 + b2) (a3 + b3) b23 b31 b12 (a123 + b123)
+
+  (TPV a23 a31 a12 a123) + (ODD b1 b2 b3 b123) = APS 0 b1 b2 b3 a23 a31 a12 (a123 + b123)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (ODD b1 b2 b3 b123) = APS a0 (a1 + b1) (a2 + b2) (a3 + b3) a23 a31 a12 (a123 + b123)
+
+  (TPV a23 a31 a12 a123) + (TPV b23 b31 b12 b123) = TPV (a23 + b23) (a31 + b31) (a12 + b12) (a123 + b123)
+
+  (TPV a23 a31 a12 a123) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS b0 b1 b2 b3 (a23 + b23) (a31 + b31) (a12 + b12) (a123 + b123)
+
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (TPV b23 b31 b12 b123) = APS a0 a1 a2 a3 (a23 + b23) (a31 + b31) (a12 + b12) (a123 + b123)
+
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) + (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0 + b0)
+                                                                                (a1 + b1) (a2 + b2) (a3 + b3)
+                                                                                (a23 + b23) (a31 + b31) (a12 + b12)
+                                                                                (a123 + b123)
+
+  -- | Multiplication Instance implementing a Geometric Product
+  (R a0) * (R b0) = R (a0*b0)
+
+  (R a0) * (V3 b1 b2 b3) = V3 (a0*b1) (a0*b2) (a0*b3)
+  (R a0) * (BV b23 b31 b12) = BV (a0*b23) (a0*b31) (a0*b12)
+  (R a0) * (I b123) = I (a0*b123)
+  (R a0) * (PV b0 b1 b2 b3) = PV (a0*b0)
+                                 (a0*b1) (a0*b2) (a0*b3)
+  (R a0) * (H b0 b23 b31 b12) = H (a0*b0)
+                                  (a0*b23) (a0*b31) (a0*b12)
+  (R a0) * (C b0 b123) = C (a0*b0)
+                           (a0*b123)
+  (R a0) * (BPV b1 b2 b3 b23 b31 b12) = BPV (a0*b1) (a0*b2) (a0*b3)
+                                            (a0*b23) (a0*b31) (a0*b12)
+  (R a0) * (ODD b1 b2 b3 b123) = ODD (a0*b1) (a0*b2) (a0*b3)
+                                     (a0*b123)
+  (R a0) * (TPV b23 b31 b12 b123) = TPV (a0*b23) (a0*b31) (a0*b12)
+                                        (a0*b123)
+  (R a0) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0*b0)
+                                                    (a0*b1) (a0*b2) (a0*b3)
+                                                    (a0*b23) (a0*b31) (a0*b12)
+                                                    (a0*b123)
+
+  (V3 a1 a2 a3) * (R b0) = V3 (a1*b0) (a2*b0) (a3*b0)
+  (BV a23 a31 a12) * (R b0) = BV (a23*b0) (a31*b0) (a12*b0)
+  (I a123) * (R b0) = I (a123*b0)
+  (PV a0 a1 a2 a3) * (R b0) = PV (a0*b0)
+                                 (a1*b0) (a2*b0) (a3*b0)
+  (H a0 a23 a31 a12) * (R b0) = H (a0*b0)
+                                  (a23*b0) (a31*b0) (a12*b0)
+  (C a0 a123) * (R b0) = C (a0*b0)
+                           (a123*b0)
+  (BPV a1 a2 a3 a23 a31 a12) * (R b0) = BPV (a1*b0) (a2*b0) (a3*b0)
+                                            (a23*b0) (a31*b0) (a12*b0)
+  (ODD a1 a2 a3 a123) * (R b0) = ODD (a1*b0) (a2*b0) (a3*b0)
+                                     (a123*b0)
+  (TPV a23 a31 a12 a123) * (R b0) = TPV (a23*b0) (a31*b0) (a12*b0)
+                                        (a123*b0)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (R b0) = APS (a0*b0)
+                                                    (a1*b0) (a2*b0) (a3*b0)
+                                                    (a23*b0) (a31*b0) (a12*b0)
+                                                    (a123*b0)
+
+  (V3 a1 a2 a3) * (V3 b1 b2 b3) = H (a1*b1 + a2*b2 + a3*b3)
+                                    (a2*b3 - a3*b2) (a3*b1 - a1*b3) (a1*b2 - a2*b1)
+
+  (V3 a1 a2 a3) * (BV b23 b31 b12) = ODD (a3*b31 - a2*b12) (a1*b12 - a3*b23) (a2*b23 - a1*b31)
+                                         (a1*b23 + a2*b31 + a3*b12)
+  (V3 a1 a2 a3) * (I b123) = BV (a1*b123) (a2*b123) (a3*b123)
+  (V3 a1 a2 a3) * (PV b0 b1 b2 b3) = APS (a1*b1 + a2*b2 + a3*b3)
+                                         (a1*b0) (a2*b0) (a3*b0)
+                                         (a2*b3 - a3*b2) (a3*b1 - a1*b3) (a1*b2 - a2*b1)
+                                         0
+  (V3 a1 a2 a3) * (H b0 b23 b31 b12) = ODD (a1*b0 - a2*b12 + a3*b31) (a2*b0 + a1*b12 - a3*b23) (a3*b0 - a1*b31 + a2*b23)
+                                           (a1*b23 + a2*b31 + a3*b12)
+  (V3 a1 a2 a3) * (C b0 b123) = BPV (a1*b0) (a2*b0) (a3*b0)
+                                    (a1*b123) (a2*b123) (a3*b123)
+  (V3 a1 a2 a3) * (BPV b1 b2 b3 b23 b31 b12) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                   (a3*b31 - a2*b12) (a1*b12 - a3*b23) (a2*b23 - a1*b31)
+                                                   (a2*b3 - a3*b2) (a3*b1 - a1*b3) (a1*b2 - a2*b1)
+                                                   (a1*b23 + a2*b31 + a3*b12)
+  (V3 a1 a2 a3) * (ODD b1 b2 b3 b123) = H (a1*b1 + a2*b2 + a3*b3)
+                                          (a1*b123 + a2*b3 - a3*b2) (a2*b123 - a1*b3 + a3*b1) (a3*b123 + a1*b2 - a2*b1)
+  (V3 a1 a2 a3) * (TPV b23 b31 b12 b123) = APS 0
+                                               (a3*b31 - a2*b12) (a1*b12 - a3*b23) (a2*b23 - a1*b31)
+                                               (a1*b123) (a2*b123) (a3*b123)
+                                               (a1*b23 + a2*b31 + a3*b12)
+  (V3 a1 a2 a3) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                           (a1*b0 - a2*b12 + a3*b31) (a2*b0 + a1*b12 - a3*b23) (a3*b0 - a1*b31 + a2*b23)
+                                                           (a1*b123 + a2*b3 - a3*b2) (a3*b1 - a1*b3 + a2*b123) (a1*b2 - a2*b1 + a3*b123)
+                                                           (a1*b23 + a2*b31 + a3*b12)
+
+  (BV a23 a31 a12) * (V3 b1 b2 b3) = ODD (a12*b2  - a31*b3) (a23*b3 - a12*b1) (a31*b1  - a23*b2)
+                                         (a23*b1  + a31*b2  + a12*b3)
+  (I a123) * (V3 b1 b2 b3) = BV (a123*b1) (a123*b2) (a123*b3)
+  (PV a0 a1 a2 a3) * (V3 b1 b2 b3) = APS (a1*b1 + a2*b2 + a3*b3)
+                                         (a0*b1) (a0*b2) (a0*b3)
+                                         (a2*b3 - a3*b2) (a3*b1 - a1*b3) (a1*b2 - a2*b1)
+                                         0
+  (H a0 a23 a31 a12) * (V3 b1 b2 b3) = ODD (a0*b1 + a12*b2 - a31*b3) (a0*b2 - a12*b1 + a23*b3) (a0*b3 + a31*b1 - a23*b2)
+                                           (a23*b1 + a31*b2 + a12*b3)
+  (C a0 a123) * (V3 b1 b2 b3) = BPV (a0*b1) (a0*b2) (a0*b3)
+                                    (a123*b1) (a123*b2) (a123*b3)
+  (BPV a1 a2 a3 a23 a31 a12) * (V3 b1 b2 b3) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                   (a12*b2 - a31*b3) (a23*b3 - a12*b1) (a31*b1 - a23*b2)
+                                                   (a2*b3 - a3*b2) (a3*b1 - a1*b3) (a1*b2 - a2*b1)
+                                                   (a23*b1 + a31*b2 + a12*b3)
+  (ODD a1 a2 a3 a123) * (V3 b1 b2 b3) = H (a1*b1 + a2*b2 + a3*b3)
+                                          (a123*b1 + a2*b3 - a3*b2) (a123*b2 - a1*b3 + a3*b1) (a123*b3 + a1*b2 - a2*b1)
+  (TPV a23 a31 a12 a123) * (V3 b1 b2 b3) = APS 0
+                                               (a12*b2 - a31*b3) (a23*b3 - a12*b1) (a31*b1 - a23*b2)
+                                               (a123*b1) (a123*b2) (a123*b3)
+                                               (a23*b1 + a31*b2 + a12*b3)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (V3 b1 b2 b3) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                           (a0*b1 + a12*b2 - a31*b3) (a0*b2 - a12*b1 + a23*b3) (a0*b3 + a31*b1 - a23*b2)
+                                                           (a123*b1 + a2*b3 - a3*b2) (a3*b1 - a1*b3 + a123*b2) (a1*b2 - a2*b1 + a123*b3)
+                                                           (a23*b1 + a31*b2 + a12*b3)
+
+  (BV a23 a31 a12) * (BV b23 b31 b12) = H (negate $ a23*b23 + a31*b31 + a12*b12)
+                                          (a12*b31 - a31*b12) (a23*b12 - a12*b23) (a31*b23 - a23*b31)
+
+  (BV a23 a31 a12) * (I b123) = V3 (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+  (BV a23 a31 a12) * (PV b0 b1 b2 b3) = APS 0
+                                            (a12*b2 - a31*b3) (a23*b3 - a12*b1) (a31*b1 - a23*b2)
+                                            (a23*b0) (a31*b0) (a12*b0)
+                                            (a23*b1 + a31*b2 + a12*b3)
+  (BV a23 a31 a12) * (H b0 b23 b31 b12) = H (negate $ a23*b23 + a31*b31 + a12*b12)
+                                            (a23*b0 - a31*b12 + a12*b31) (a31*b0 + a23*b12 - a12*b23) (a12*b0 - a23*b31 + a31*b23)
+  (BV a23 a31 a12) * (C b0 b123) = BPV (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                       (a23*b0) (a31*b0) (a12*b0)
+  (BV a23 a31 a12) * (BPV b1 b2 b3 b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                      (a12*b2 - a31*b3) (a23*b3 - a12*b1) (a31*b1 - a23*b2)
+                                                      (a12*b31 - a31*b12) (a23*b12 - a12*b23) (a31*b23 - a23*b31)
+                                                      (a23*b1 + a31*b2 + a12*b3)
+  (BV a23 a31 a12) * (ODD b1 b2 b3 b123) = ODD (a12*b2 - a31*b3 - a23*b123) (a23*b3 - a12*b1 - a31*b123) (a31*b1 - a23*b2 - a12*b123)
+                                               (a23*b1 + a31*b2 + a12*b3)
+  (BV a23 a31 a12) * (TPV b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                  (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                                  (a12*b31 - a31*b12) (a23*b12 - a12*b23) (a31*b23 - a23*b31)
+                                                  0
+  (BV a23 a31 a12) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                              (a12*b2 - a31*b3 - a23*b123) (a23*b3 - a31*b123 - a12*b1) (a31*b1 - a23*b2 - a12*b123)
+                                                              (a23*b0 - a31*b12 + a12*b31) (a31*b0 + a23*b12 - a12*b23) (a12*b0 - a23*b31 + a31*b23)
+                                                              (a23*b1 + a31*b2 + a12*b3)
+
+  (I a123) * (BV b23 b31 b12) = V3 (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+  (PV a0 a1 a2 a3) * (BV b23 b31 b12) = APS 0
+                                            (a3*b31 - a2*b12) (a1*b12 - a3*b23) (a2*b23 - a1*b31)
+                                            (a0*b23) (a0*b31) (a0*b12)
+                                            (a1*b23 + a2*b31 + a3*b12)
+  (H a0 a23 a31 a12) * (BV b23 b31 b12) = H (negate $ a23*b23 + a31*b31 + a12*b12)
+                                            (a0*b23 - a31*b12 + a12*b31) (a0*b31 + a23*b12 - a12*b23) (a0*b12 - a23*b31 + a31*b23)
+  (C a0 a123) * (BV b23 b31 b12) = BPV (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                       (a0*b23) (a0*b31) (a0*b12)
+  (BPV a1 a2 a3 a23 a31 a12) * (BV b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                      (a3*b31 - a2*b12) (a1*b12 - a3*b23) (a2*b23 - a1*b31)
+                                                      (a12*b31 - a31*b12) (a23*b12 - a12*b23) (a31*b23 - a23*b31)
+                                                      (a1*b23 + a2*b31 + a3*b12)
+  (ODD a1 a2 a3 a123) * (BV b23 b31 b12) = ODD (negate $ a123*b23 + a2*b12 - a3*b31)
+                                               (negate $ a123*b31 - a1*b12 + a3*b23)
+                                               (negate $ a123*b12 + a1*b31 - a2*b23)
+                                               (a1*b23 + a2*b31 + a3*b12)
+  (TPV a23 a31 a12 a123) * (BV b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                  (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                                  (negate $ a31*b12 - a12*b31) (negate $ a12*b23 - a23*b12) (negate $ a23*b31 - a31*b23)
+                                                  0
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (BV b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                              (a3*b31 - a123*b23 - a2*b12) (a1*b12 - a3*b23 - a123*b31) (a2*b23 - a123*b12 - a1*b31)
+                                                              (a0*b23 - a31*b12 + a12*b31) (a0*b31 + a23*b12 - a12*b23) (a0*b12 - a23*b31 + a31*b23)
+                                                              (a1*b23 + a2*b31 + a3*b12)
+
+  (I a123) * (I b123) = R (negate $ a123*b123)
+
+  (I a123) * (PV b0 b1 b2 b3) = TPV (a123*b1) (a123*b2) (a123*b3)
+                                    (a123*b0)
+  (I a123) * (H b0 b23 b31 b12) = ODD (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                      (a123*b0)
+  (I a123) * (C b0 b123) = C (negate $ a123*b123)
+                             (a123*b0)
+  (I a123) * (BPV b1 b2 b3 b23 b31 b12) = BPV (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                              (a123*b1) (a123*b2) (a123*b3)
+  (I a123) * (ODD b1 b2 b3 b123) = H (negate $ a123*b123)
+                                     (a123*b1) (a123*b2) (a123*b3)
+  (I a123) * (TPV b23 b31 b12 b123) = PV (negate $ a123*b123)
+                                         (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+  (I a123) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (negate $ a123*b123)
+                                                      (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                                      (a123*b1) (a123*b2) (a123*b3)
+                                                      (a123*b0)
+
+  (PV a0 a1 a2 a3) * (I b123) = TPV (a1*b123) (a2*b123) (a3*b123)
+                                    (a0*b123)
+  (H a0 a23 a31 a12) * (I b123) = ODD (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                      (a0*b123)
+  (C a0 a123) * (I b123) = C (negate $ a123*b123)
+                             (a0*b123)
+  (BPV a1 a2 a3 a23 a31 a12) * (I b123) = BPV (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                              (a1*b123) (a2*b123) (a3*b123)
+  (ODD a1 a2 a3 a123) * (I b123) = H (negate $ a123*b123)
+                                     (a1*b123) (a2*b123) (a3*b123)
+  (TPV a23 a31 a12 a123) * (I b123) = PV (negate $ a123*b123)
+                                         (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (I b123) = APS (negate $ a123*b123)
+                                                      (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                                      (a1*b123) (a2*b123) (a3*b123)
+                                                      (a0*b123)
+
+
+  (PV a0 a1 a2 a3) * (PV b0 b1 b2 b3) = APS (a0*b0 + a1*b1 + a2*b2 + a3*b3)
+                                            (a0*b1 + a1*b0) (a0*b2 + a2*b0) (a0*b3 + a3*b0)
+                                            (a2*b3 - a3*b2) (a3*b1 - a1*b3) (a1*b2 - a2*b1)
+                                            0
+
+  (PV a0 a1 a2 a3) * (H b0 b23 b31 b12) = APS (a0*b0)
+                                              (a1*b0 - a2*b12 + a3*b31) (a2*b0 + a1*b12 - a3*b23) (a3*b0 - a1*b31 + a2*b23)
+                                              (a0*b23) (a0*b31) (a0*b12)
+                                              (a1*b23 + a2*b31 + a3*b12)
+  (PV a0 a1 a2 a3) * (C b0 b123) = APS (a0*b0)
+                                       (a1*b0) (a2*b0) (a3*b0)
+                                       (a1*b123) (a2*b123) (a3*b123)
+                                       (a0*b123)
+  (PV a0 a1 a2 a3) * (BPV b1 b2 b3 b23 b31 b12) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                      (a0*b1 - a2*b12 + a3*b31) (a0*b2 + a1*b12 - a3*b23) (a0*b3 - a1*b31 + a2*b23)
+                                                      (a0*b23 + a2*b3 - a3*b2) (a0*b31 - a1*b3 + a3*b1) (a0*b12 + a1*b2 - a2*b1)
+                                                      (a1*b23 + a2*b31 + a3*b12)
+  (PV a0 a1 a2 a3) * (ODD b1 b2 b3 b123) = APS (a1*b1 + a2*b2 + a3*b3)
+                                               (a0*b1) (a0*b2) (a0*b3)
+                                               (a1*b123 + a2*b3 - a3*b2) (a2*b123 - a1*b3 + a3*b1) (a3*b123 + a1*b2 - a2*b1)
+                                               (a0*b123)
+  (PV a0 a1 a2 a3) * (TPV b23 b31 b12 b123) = APS 0
+                                                  (a3*b31 - a2*b12) (a1*b12 - a3*b23) (a2*b23 - a1*b31)
+                                                  (a0*b23 + a1*b123) (a0*b31 + a2*b123) (a0*b12 + a3*b123)
+                                                  (a0*b123 + a1*b23 + a2*b31 + a3*b12)
+  (PV a0 a1 a2 a3) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0*b0 + a1*b1 + a2*b2 + a3*b3)
+                                                              (a0*b1 + a1*b0 - a2*b12 + a3*b31)
+                                                              (a0*b2 + a2*b0 + a1*b12 - a3*b23)
+                                                              (a0*b3 + a3*b0 - a1*b31 + a2*b23)
+                                                              (a0*b23 + a1*b123 + a2*b3 - a3*b2)
+                                                              (a0*b31 - a1*b3 + a3*b1 + a2*b123)
+                                                              (a0*b12 + a1*b2 - a2*b1 + a3*b123)
+                                                              (a0*b123 + a1*b23 + a2*b31 + a3*b12)
+
+  (H a0 a23 a31 a12) * (PV b0 b1 b2 b3) = APS (a0*b0)
+                                              (a0*b1 + a12*b2 - a31*b3) (a0*b2 - a12*b1 + a23*b3) (a0*b3 + a31*b1 - a23*b2)
+                                              (a23*b0) (a31*b0) (a12*b0)
+                                              (a23*b1 + a31*b2 + a12*b3)
+  (C a0 a123) * (PV b0 b1 b2 b3) = APS (a0*b0)
+                                       (a0*b1) (a0*b2) (a0*b3)
+                                       (a123*b1) (a123*b2) (a123*b3)
+                                       (a123*b0)
+  (BPV a1 a2 a3 a23 a31 a12) * (PV b0 b1 b2 b3) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                      (a1*b0 + a12*b2 - a31*b3) (a2*b0 - a12*b1 + a23*b3) (a3*b0 + a31*b1 - a23*b2)
+                                                      (a23*b0 + a2*b3 - a3*b2) (a31*b0 - a1*b3 + a3*b1) (a12*b0 + a1*b2 - a2*b1)
+                                                      (a23*b1 + a31*b2 + a12*b3)
+  (ODD a1 a2 a3 a123) * (PV b0 b1 b2 b3) = APS (a1*b1 + a2*b2 + a3*b3)
+                                               (a1*b0) (a2*b0) (a3*b0)
+                                               (a123*b1 + a2*b3 - a3*b2)
+                                               (a123*b2 - a1*b3 + a3*b1)
+                                               (a123*b3 + a1*b2 - a2*b1)
+                                               (a123*b0)
+  (TPV a23 a31 a12 a123) * (PV b0 b1 b2 b3) = APS 0
+                                                  (a12*b2 - a31*b3) (a23*b3 - a12*b1) (a31*b1 - a23*b2)
+                                                  (a23*b0 + a123*b1) (a31*b0 + a123*b2) (a12*b0 + a123*b3)
+                                                  (a123*b0 + a23*b1 + a31*b2 + a12*b3)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (PV b0 b1 b2 b3) = APS (a0*b0 + a1*b1 + a2*b2 + a3*b3)
+                                                              (a0*b1 + a1*b0 + a12*b2 - a31*b3)
+                                                              (a0*b2 + a2*b0 - a12*b1 + a23*b3)
+                                                              (a0*b3 + a3*b0 + a31*b1 - a23*b2)
+                                                              (a23*b0 + a123*b1 + a2*b3 - a3*b2)
+                                                              (a31*b0 - a1*b3 + a3*b1 + a123*b2)
+                                                              (a12*b0 + a1*b2 - a2*b1 + a123*b3)
+                                                              (a123*b0 + a23*b1 + a31*b2 + a12*b3)
+
+  (H a0 a23 a31 a12) * (H b0 b23 b31 b12) = H (a0*b0 - a23*b23 - a31*b31 - a12*b12)
+                                              (a0*b23 + a23*b0 - a31*b12 + a12*b31)
+                                              (a0*b31 + a31*b0 + a23*b12 - a12*b23)
+                                              (a0*b12 + a12*b0 - a23*b31 + a31*b23)
+
+  (H a0 a23 a31 a12) * (C b0 b123) = APS (a0*b0)
+                                         (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                         (a23*b0) (a31*b0) (a12*b0)
+                                         (a0*b123)
+  (H a0 a23 a31 a12) * (BPV b1 b2 b3 b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                        (a0*b1 + a12*b2 - a31*b3) (a0*b2 - a12*b1 + a23*b3) (a0*b3 + a31*b1 - a23*b2)
+                                                        (a0*b23 - a31*b12 + a12*b31) (a0*b31 + a23*b12 - a12*b23) (a0*b12 - a23*b31 + a31*b23)
+                                                        (a23*b1 + a31*b2  + a12*b3)
+  (H a0 a23 a31 a12) * (ODD b1 b2 b3 b123) = ODD (a0*b1 + a12*b2 - a31*b3 - a23*b123)
+                                                 (a0*b2 - a12*b1 + a23*b3 - a31*b123)
+                                                 (a0*b3 + a31*b1 - a23*b2 - a12*b123)
+                                                 (a0*b123 + a23*b1 + a31*b2 + a12*b3)
+  (H a0 a23 a31 a12) * (TPV b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                    (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                                    (a0*b23 - a31*b12 + a12*b31) (a0*b31 + a23*b12 - a12*b23) (a0*b12 - a23*b31 + a31*b23)
+                                                    (a0*b123)
+  (H a0 a23 a31 a12) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0*b0 - a23*b23 - a31*b31 - a12*b12)
+                                                                (a0*b1 + a12*b2 - a31*b3 - a23*b123)
+                                                                (a0*b2 - a12*b1 + a23*b3 - a31*b123)
+                                                                (a0*b3 + a31*b1 - a23*b2 - a12*b123)
+                                                                (a0*b23 + a23*b0 - a31*b12 + a12*b31)
+                                                                (a0*b31 + a31*b0 + a23*b12 - a12*b23)
+                                                                (a0*b12 + a12*b0 - a23*b31 + a31*b23)
+                                                                (a0*b123 + a23*b1 + a31*b2 + a12*b3)
+
+  (C a0 a123) * (H b0 b23 b31 b12) = APS (a0*b0)
+                                         (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                         (a0*b23) (a0*b31) (a0*b12)
+                                         (a123*b0)
+  (BPV a1 a2 a3 a23 a31 a12) * (H b0 b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                        (a1*b0 - a2*b12 + a3*b31) (a2*b0 + a1*b12 - a3*b23) (a3*b0 - a1*b31 + a2*b23)
+                                                        (a23*b0 - a31*b12 + a12*b31) (a31*b0 + a23*b12 - a12*b23) (a12*b0 - a23*b31 + a31*b23)
+                                                        (a1*b23 + a2*b31 + a3*b12)
+  (ODD a1 a2 a3 a123) * (H b0 b23 b31 b12) = ODD (a1*b0 - a2*b12 + a3*b31 - a123*b23)
+                                                 (a2*b0 + a1*b12 - a3*b23 - a123*b31)
+                                                 (a3*b0 - a1*b31 + a2*b23 - a123*b12)
+                                                 (a123*b0 + a1*b23 + a2*b31 + a3*b12)
+  (TPV a23 a31 a12 a123) * (H b0 b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                    (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                                    (a23*b0 - a31*b12 + a12*b31) (a31*b0 + a23*b12 - a12*b23) (a12*b0 - a23*b31 + a31*b23)
+                                                    (a123*b0)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (H b0 b23 b31 b12) = APS (a0*b0 - a23*b23 - a31*b31 - a12*b12)
+                                                                (a1*b0 - a2*b12 + a3*b31 - a123*b23)
+                                                                (a2*b0 + a1*b12 - a3*b23 - a123*b31)
+                                                                (a3*b0 - a1*b31 + a2*b23 - a123*b12)
+                                                                (a0*b23 + a23*b0 - a31*b12 + a12*b31)
+                                                                (a0*b31 + a31*b0 + a23*b12 - a12*b23)
+                                                                (a0*b12 + a12*b0 - a23*b31 + a31*b23)
+                                                                (a123*b0 + a1*b23 + a2*b31 + a3*b12)
+
+  (C a0 a123) * (C b0 b123) = C (a0*b0 - a123*b123)
+                                (a0*b123 + a123*b0)
+
+  (C a0 a123) * (BPV b1 b2 b3 b23 b31 b12) = BPV (a0*b1 - a123*b23) (a0*b2 - a123*b31) (a0*b3 - a123*b12)
+                                                 (a0*b23 + a123*b1) (a0*b31 + a123*b2) (a0*b12 + a123*b3)
+  (C a0 a123) * (ODD b1 b2 b3 b123) = APS (negate $ a123*b123)
+                                          (a0*b1) (a0*b2) (a0*b3)
+                                          (a123*b1) (a123*b2) (a123*b3)
+                                          (a0*b123)
+  (C a0 a123) * (TPV b23 b31 b12 b123) = APS (negate $ a123*b123)
+                                             (negate $ a123*b23) (negate $ a123*b31) (negate $ a123*b12)
+                                             (a0*b23) (a0*b31) (a0*b12)
+                                             (a0*b123)
+  (C a0 a123) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0*b0 - a123*b123)
+                                                         (a0*b1 - a123*b23) (a0*b2 - a123*b31) (a0*b3 - a123*b12)
+                                                         (a0*b23 + a123*b1) (a0*b31 + a123*b2) (a0*b12 + a123*b3)
+                                                         (a0*b123 + a123*b0)
+
+  (BPV a1 a2 a3 a23 a31 a12) * (C b0 b123) = BPV (a1*b0 - a23*b123) (a2*b0 - a31*b123) (a3*b0 - a12*b123)
+                                                 (a23*b0 + a1*b123) (a31*b0 + a2*b123) (a12*b0 + a3*b123)
+  (ODD a1 a2 a3 a123) * (C b0 b123) = APS (negate $ a123*b123)
+                                          (a1*b0) (a2*b0) (a3*b0)
+                                          (a1*b123) (a2*b123) (a3*b123)
+                                          (a123*b0)
+  (TPV a23 a31 a12 a123) * (C b0 b123) = APS (negate $ a123*b123)
+                                             (negate $ a23*b123) (negate $ a31*b123) (negate $ a12*b123)
+                                             (a23*b0) (a31*b0) (a12*b0)
+                                             (a123*b0)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (C b0 b123) = APS (a0*b0 - a123*b123)
+                                                         (a1*b0 - a23*b123) (a2*b0 - a31*b123) (a3*b0 - a12*b123)
+                                                         (a23*b0 + a1*b123) (a31*b0 + a2*b123) (a12*b0 + a3*b123)
+                                                         (a0*b123 + a123*b0)
+
+  (BPV a1 a2 a3 a23 a31 a12) * (BPV b1 b2 b3 b23 b31 b12) = APS (a1*b1 + a2*b2 + a3*b3 - a23*b23 - a31*b31 - a12*b12)
+                                                                (a12*b2 - a2*b12 + a3*b31 - a31*b3)
+                                                                (a1*b12 - a12*b1 - a3*b23 + a23*b3)
+                                                                (a31*b1 - a1*b31 + a2*b23 - a23*b2)
+                                                                (a2*b3 - a3*b2 - a31*b12 + a12*b31)
+                                                                (a3*b1 - a1*b3 + a23*b12 - a12*b23)
+                                                                (a1*b2 - a2*b1 - a23*b31 + a31*b23)
+                                                                (a1*b23 + a23*b1 + a2*b31 + a31*b2 + a3*b12 + a12*b3)
+
+  (BPV a1 a2 a3 a23 a31 a12) * (ODD b1 b2 b3 b123) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                         (a12*b2 - a31*b3 - a23*b123) (a23*b3 - a12*b1 - a31*b123) (a31*b1 - a23*b2 - a12*b123)
+                                                         (a1*b123 + a2*b3 - a3*b2) (a2*b123 - a1*b3 + a3*b1) (a3*b123 + a1*b2 - a2*b1)
+                                                         (a23*b1 + a31*b2 + a12*b3)
+  (BPV a1 a2 a3 a23 a31 a12) * (TPV b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                            (a3*b31 - a2*b12 - a23*b123) (a1*b12 - a3*b23 - a31*b123) (a2*b23 - a1*b31 - a12*b123)
+                                                            (a1*b123 - a31*b12 + a12*b31) (a2*b123 + a23*b12 - a12*b23) (a3*b123 - a23*b31 + a31*b23)
+                                                            (a1*b23 + a2*b31 + a3*b12)
+  (BPV a1 a2 a3 a23 a31 a12) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a1*b1 + a2*b2 + a3*b3 - a23*b23 - a31*b31 - a12*b12)
+                                                                        (a1*b0 - a2*b12 + a12*b2 + a3*b31 - a31*b3 - a23*b123)
+                                                                        (a2*b0 + a1*b12 - a12*b1 - a3*b23 + a23*b3 - a31*b123)
+                                                                        (a3*b0 - a1*b31 + a31*b1 + a2*b23 - a23*b2 - a12*b123)
+                                                                        (a23*b0 + a1*b123 + a2*b3 - a3*b2 - a31*b12 + a12*b31)
+                                                                        (a31*b0 - a1*b3 + a3*b1 + a2*b123 + a23*b12 - a12*b23)
+                                                                        (a12*b0 + a1*b2 - a2*b1 + a3*b123 - a23*b31 + a31*b23)
+                                                                        (a1*b23 + a23*b1 + a2*b31 + a31*b2 + a3*b12 + a12*b3)
+
+  (ODD a1 a2 a3 a123) * (BPV b1 b2 b3 b23 b31 b12) = APS (a1*b1 + a2*b2 + a3*b3)
+                                                         (a3*b31 - a2*b12 - a123*b23) (a1*b12 - a3*b23 - a123*b31) (a2*b23 - a1*b31 - a123*b12)
+                                                         (a123*b1 + a2*b3 - a3*b2) (a123*b2 - a1*b3 + a3*b1) (a123*b3 + a1*b2 - a2*b1)
+                                                         (a1*b23 + a2*b31 + a3*b12)
+  (TPV a23 a31 a12 a123) * (BPV b1 b2 b3 b23 b31 b12) = APS (negate $ a23*b23 + a31*b31 + a12*b12)
+                                                            (a12*b2 - a31*b3 - a123*b23) (a23*b3 - a12*b1 - a123*b31) (a31*b1 - a23*b2 - a123*b12)
+                                                            (a123*b1 - a31*b12 + a12*b31) (a123*b2 + a23*b12 - a12*b23) (a123*b3 - a23*b31 + a31*b23)
+                                                            (a23*b1 + a31*b2 + a12*b3)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (BPV b1 b2 b3 b23 b31 b12) = APS (a1*b1 + a2*b2 + a3*b3 - a23*b23 - a31*b31 - a12*b12)
+                                                                        (a0*b1 - a2*b12 + a12*b2 + a3*b31 - a31*b3 - a123*b23)
+                                                                        (a0*b2 + a1*b12 - a12*b1 - a3*b23 + a23*b3 - a123*b31)
+                                                                        (a0*b3 - a1*b31 + a31*b1 + a2*b23 - a23*b2 - a123*b12)
+                                                                        (a0*b23 + a123*b1 + a2*b3 - a3*b2 - a31*b12 + a12*b31)
+                                                                        (a0*b31 - a1*b3 + a3*b1 + a123*b2 + a23*b12 - a12*b23)
+                                                                        (a0*b12 + a1*b2 - a2*b1 + a123*b3 - a23*b31 + a31*b23)
+                                                                        (a1*b23 + a23*b1 + a2*b31 + a31*b2 + a3*b12 + a12*b3)
+
+  (ODD a1 a2 a3 a123) * (ODD b1 b2 b3 b123) = H (a1*b1 + a2*b2 + a3*b3 - a123*b123)
+                                                (a1*b123 + a123*b1 + a2*b3 - a3*b2)
+                                                (a2*b123 + a123*b2 - a1*b3 + a3*b1)
+                                                (a3*b123 + a123*b3 + a1*b2 - a2*b1)
+
+  (ODD a1 a2 a3 a123) * (TPV b23 b31 b12 b123) = APS (negate $ a123*b123)
+                                                     (a3*b31 - a2*b12 - a123*b23) (a1*b12 - a3*b23 - a123*b31) (a2*b23 - a1*b31 - a123*b12)
+                                                     (a1*b123) (a2*b123) (a3*b123)
+                                                     (a1*b23 + a2*b31 + a3*b12)
+  (ODD a1 a2 a3 a123) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a1*b1 + a2*b2 + a3*b3 - a123*b123)
+                                                                 (a1*b0 - a2*b12 + a3*b31 - a123*b23)
+                                                                 (a2*b0 + a1*b12 - a3*b23 - a123*b31)
+                                                                 (a3*b0 - a1*b31 + a2*b23 - a123*b12)
+                                                                 (a1*b123 + a123*b1 + a2*b3 - a3*b2)
+                                                                 (a2*b123 + a123*b2 - a1*b3 + a3*b1)
+                                                                 (a3*b123 + a123*b3 + a1*b2 - a2*b1)
+                                                                 (a123*b0 + a1*b23 + a2*b31 + a3*b12)
+
+  (TPV a23 a31 a12 a123) * (ODD b1 b2 b3 b123) = APS (negate $ a123*b123)
+                                                     (a12*b2 - a31*b3 - a23*b123) (a23*b3 - a12*b1 - a31*b123) (a31*b1 - a23*b2 - a12*b123)
+                                                     (a123*b1) (a123*b2) (a123*b3)
+                                                     (a23*b1 + a31*b2 + a12*b3)
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (ODD b1 b2 b3 b123) = APS (a1*b1 + a2*b2 + a3*b3 - a123*b123)
+                                                                 (a0*b1 + a12*b2 - a31*b3 - a23*b123)
+                                                                 (a0*b2 - a12*b1 + a23*b3 - a31*b123)
+                                                                 (a0*b3 + a31*b1 - a23*b2 - a12*b123)
+                                                                 (a1*b123 + a123*b1 + a2*b3 - a3*b2)
+                                                                 (a2*b123 + a123*b2 - a1*b3 + a3*b1)
+                                                                 (a3*b123 + a123*b3 + a1*b2 - a2*b1)
+                                                                 (a0*b123 + a23*b1 + a31*b2 + a12*b3)
+
+  (TPV a23 a31 a12 a123) * (TPV b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12 + a123*b123)
+                                                        (negate $ a23*b123 + a123*b23) (negate $ a31*b123 + a123*b31) (negate $ a12*b123 + a123*b12)
+                                                        (a12*b31 - a31*b12) (a23*b12 - a12*b23) (a31*b23 - a23*b31)
+                                                        0
+
+  (TPV a23 a31 a12 a123) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12 + a123*b123)
+                                                                    (a12*b2 - a31*b3 - a23*b123 - a123*b23)
+                                                                    (a23*b3 - a12*b1 - a31*b123 - a123*b31)
+                                                                    (a31*b1 - a23*b2 - a12*b123 - a123*b12)
+                                                                    (a23*b0 + a123*b1 - a31*b12 + a12*b31)
+                                                                    (a31*b0 + a123*b2 + a23*b12 - a12*b23)
+                                                                    (a12*b0 + a123*b3 - a23*b31 + a31*b23)
+                                                                    (a123*b0 + a23*b1 + a31*b2 + a12*b3)
+
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (TPV b23 b31 b12 b123) = APS (negate $ a23*b23 + a31*b31 + a12*b12 + a123*b123)
+                                                                    (a3*b31 - a2*b12 - a23*b123 - a123*b23)
+                                                                    (a1*b12 - a3*b23 - a31*b123 - a123*b31)
+                                                                    (a2*b23 - a1*b31 - a12*b123 - a123*b12)
+                                                                    (a0*b23 + a1*b123 - a31*b12 + a12*b31)
+                                                                    (a0*b31 + a2*b123 + a23*b12 - a12*b23)
+                                                                    (a0*b12 + a3*b123 - a23*b31 + a31*b23)
+                                                                    (a0*b123 + a1*b23 + a2*b31 + a3*b12)
+
+  (APS a0 a1 a2 a3 a23 a31 a12 a123) * (APS b0 b1 b2 b3 b23 b31 b12 b123) = APS (a0*b0 + a1*b1 + a2*b2 + a3*b3 - a23*b23 - a31*b31 - a12*b12 - a123*b123)
+                                                                                (a0*b1 + a1*b0 - a2*b12 + a12*b2 + a3*b31 - a31*b3 - a23*b123 - a123*b23)
+                                                                                (a0*b2 + a2*b0 + a1*b12 - a12*b1 - a3*b23 + a23*b3 - a31*b123 - a123*b31)
+                                                                                (a0*b3 + a3*b0 - a1*b31 + a31*b1 + a2*b23 - a23*b2 - a12*b123 - a123*b12)
+                                                                                (a0*b23 + a23*b0 + a1*b123 + a123*b1 + a2*b3 - a3*b2 - a31*b12 + a12*b31)
+                                                                                (a0*b31 + a31*b0 - a1*b3 + a3*b1 + a2*b123 + a123*b2 + a23*b12 - a12*b23)
+                                                                                (a0*b12 + a12*b0 + a1*b2 - a2*b1 + a3*b123 + a123*b3 - a23*b31 + a31*b23)
+                                                                                (a0*b123 + a123*b0 + a1*b23 + a23*b1 + a2*b31 + a31*b2 + a3*b12 + a12*b3)
+
+
+  -- |'abs' is the spectral norm aka the spectral radius
+  -- it is the largest singular value. This function may need to be fiddled with
+  -- to make the math a bit safer wrt overflows.  This makes use of the largest
+  -- singular value, if the smallest singular value is zero then the element is not
+  -- invertable, we can see here that R, C, V3, BV, and H are all invertable.
+  abs (R a0) = R (abs a0) -- absolute value of a real number
+  abs (V3 a1 a2 a3) = R (sqrt (a1^2 + a2^2 + a3^2)) -- magnitude of a vector
+  abs (BV a23 a31 a12) = R (sqrt (a23^2 + a31^2 + a12^2)) -- magnitude of a bivector
+  abs (I a123) = R (abs a123) -- magnitude of a Imaginary number
+  abs (PV a0 a1 a2 a3) = R (sqrt (a0^2 + a1^2 + a2^2 + a3^2 + 2 * abs a0 * sqrt (a1^2 + a2^2 + a3^2)))
+  abs (H a0 a23 a31 a12) = R (sqrt (a0^2 + a23^2 + a31^2 + a12^2)) -- largest singular value
+  abs (C a0 a123) = R (sqrt (a0^2 + a123^2)) -- magnitude of a complex number
+  abs (BPV a1 a2 a3 a23 a31 a12) = R (sqrt (a1^2 + a23^2 + a2^2 + a31^2 + a3^2 + a12^2 +
+                                             2 * sqrt ((a1*a31 - a2*a23)^2 + (a1*a12 - a3*a23)^2 + (a2*a12 - a3*a31)^2)))
+  abs (ODD a1 a2 a3 a123) = R (sqrt (a1^2 + a2^2 + a3^2 + a123^2))
+  abs (TPV a23 a31 a12 a123) = R (sqrt (a23^2 + a31^2 + a12^2 + a123^2 + 2 * abs a123 * sqrt (a23^2 + a31^2 + a12^2)))
+  abs (APS a0 a1 a2 a3 a23 a31 a12 a123) = R (sqrt (a0^2 + a1^2 + a2^2 + a3^2 + a23^2 + a31^2 + a12^2 + a123^2 +
+                                                    2 * sqrt ((a0*a1 + a123*a23)^2 + (a0*a2 + a123*a31)^2 + (a0*a3 + a123*a12)^2 +
+                                                              (a2*a12 - a3*a31)^2 + (a3*a23 - a1*a12)^2 + (a1*a31 - a2*a23)^2)))
+
+
+  -- |'signum' satisfies the Law "abs x * signum x == x"
+  -- kind of cool: signum of a vector is the unit vector.
+  signum cliffor = let (R mag) = abs cliffor in cliffor * R (recip mag)
+
+
+  -- |'fromInteger'
+  fromInteger int = R (fromInteger int)
+
+
+  -- |'negate' simply distributes into the grade components
+  negate x = x
+
+instance Fractional Cl3 where
+
+instance Floating Cl3 where
+  pi = R pi
+
+  --
+  exp (C a0 a123) =
+    let expa0 = exp a0
+    in C (expa0 * cos a123) (expa0 * sin a123)
+  exp cliffor = reduce $! spectraldcmp exp cliffor
+
+  --
+  log (C a0 a123) = C (log (sqrt (a0^2 + a123^2))) (atan2 a123 a0)
+  log cliffor = reduce $! spectraldcmp log cliffor
+
+  --
+  sqrt (C a0 a123) = C u (if a123 < 0 then -v else v)
+                       where (u,v) = if a0 < 0 then (v',u') else (u',v')
+                             v'    = abs a123 / (u'*2)
+                             u'    = sqrt ((sqrt (a0^2 + a123^2) + abs a0) / 2)
+  sqrt cliffor = reduce $! spectraldcmp sqrt cliffor
+
+  --
+  sin (C a0 a123) = C (sin a0 * cosh a123) (cos a0 * sinh a123)
+  sin cliffor = reduce $! spectraldcmp sin cliffor
+
+  --
+  cos (C a0 a123) = C (cos a0 * cosh a123) (negate $ sin a0 * sinh a123)
+  cos cliffor = reduce $! spectraldcmp cos cliffor
+
+  --
+  tan (C a0 a123) = C (sinx*coshy) (cosx*sinhy) / C (cosx*coshy) (negate $ sinx*sinhy)
+                       where sinx  = sin a0
+                             cosx  = cos a0
+                             sinhy = sinh a123
+                             coshy = cosh a123
+  tan cliffor = reduce $! spectraldcmp tan cliffor
+
+  --
+  asin (C a0 a123) = C a123' (-a0')
+                       where  (C a0' a123') = log (C (-a123) a0 + sqrt (1 - C a0 a123 * C a0 a123)) -- check this
+  asin cliffor = reduce $! spectraldcmp asin cliffor
+
+  --
+  acos (C a0 a123) = C a123'' (-a0'')
+               where (C a0'' a123'') = log (C a0 a123 + C (-a123') a0')  -- check this
+                     (C a0' a123')   = sqrt (1 - C a0 a123 * C a0 a123)  -- check this
+  acos cliffor = reduce $! spectraldcmp acos cliffor
+
+  --
+  atan (C a0 a123) = C a123' (-a0')
+                       where (C a0' a123') = log (C (1-a123) a0 / sqrt (1 + C a0 a123 * C a0 a123))  -- check this
+  atan cliffor = reduce $! spectraldcmp atan cliffor
+
+  --
+  sinh (C a0 a123) = C (cos a123 * sinh a0) (sin a123 * cosh a0)
+  sinh cliffor = reduce $! spectraldcmp sinh cliffor
+
+  --
+  cosh (C a0 a123) = C (cos a123 * cosh a0) (sin a123 * sinh a0)
+  cosh cliffor = reduce $! spectraldcmp cosh cliffor
+
+  --
+  tanh (C a0 a123) = C (cosy*sinhx) (siny*coshx) / C (cosy*coshx) (siny*sinhx)
+                        where siny  = sin a123
+                              cosy  = cos a123
+                              sinhx = sinh a0
+                              coshx = cosh a0
+  tanh cliffor = reduce $! spectraldcmp tanh cliffor
+
+
+
+
+--
+
+spectraldcmp ::  (Cl3 -> Cl3) -> Cl3 -> Cl3
+spectraldcmp function cliffor =
+  let (eig1,eig2) = projEigs cliffor
+  in function eig1 * cliffor + function eig2 * cliffor
+
+
+
+projEigs :: Cl3 -> (Cl3,Cl3)
+projEigs cliffor =
+  let eig1 = 2 * (cliffor * cliffor * cliffor)
+  in (eig1,eig1)
+
+reduce :: Cl3 -> Cl3
+reduce r@R{} = r
+reduce aps@APS{} = aps
diff --git a/testsuite/tests/perf/compiler/T15304.stderr b/testsuite/tests/perf/compiler/T15304.stderr
new file mode 100644
index 0000000000..0f33758144
--- /dev/null
+++ b/testsuite/tests/perf/compiler/T15304.stderr
@@ -0,0 +1,10 @@
+
+T15304.hs:675:10: warning: [-Wmissing-methods (in -Wdefault)]
+    • No explicit implementation for
+        ‘fromRational’ and (either ‘recip’ or ‘/’)
+    • In the instance declaration for ‘Fractional Cl3’
+
+T15304.hs:677:10: warning: [-Wmissing-methods (in -Wdefault)]
+    • No explicit implementation for
+        ‘asinh’, ‘acosh’, and ‘atanh’
+    • In the instance declaration for ‘Floating Cl3’
diff --git a/testsuite/tests/perf/compiler/all.T b/testsuite/tests/perf/compiler/all.T
index 651c9a2128..d0d7bb9e6b 100644
--- a/testsuite/tests/perf/compiler/all.T
+++ b/testsuite/tests/perf/compiler/all.T
@@ -456,3 +456,7 @@ test ('T9198',
 test('T11545',
      [ normal ],
      compile, ['-O +RTS -M50M -RTS'])
+
+test('T15304',
+     [ collect_compiler_stats('all', 10) ],
+     compile, ['-O'])