4.1.13 - ##xE^ and /xE^ vs BEAF and FGH

Here I will analyse ##xE^ compared to fgh and beaf....
Name hhxec and sxec bxec BEAF approximation
(climbing)
FGH
blasphemorgulusE100{#,#,1,2}100{X,X,1,2} & 100φ(1,0,0,0)
grangol-carta-blasphemorgulusE100{#,#,1,2}100#100φ(1,0,0,0)+1
blasphemorgulus-by-deuteronE100{#,#,1,2}100{#,#,1,2}100φ(1,0,0,0)*2
blasphemorgulus-by-hyperionE100{#,#,1,2}*#100{X,X,1,2}+1 & 100ωφ(1,0,0,0)+1
deutero-blasphemorgulusE100{#,#,1,2}*{#,#,1,2}100{X,X,1,2}*2 & 100ωφ(1,0,0,0)*2
blasphemorgulfactE100{#,#,1,2}^#100{X,X,1,2}*X & 100ωωφ(1,0,0,0)+1
dutetrated-blasphemorgulusE100{#,#,1,2}^{#,#,1,2}100{X,X,1,2}^2 & 100ωωφ(1,0,0,0)*2
terrible blasphemorgulusE100{#,#,1,2}^^#100{X,X,1,2}^^X & 100εφ(1,0,0,0)+1
territerated blasphemorgulusE100{#,#,1,2}^^#>#100{X,X,1,2}^^(X+1) & 100εφ(1,0,0,0)+ω
terrisquared blasphemorgulusE100{#,#,1,2}^^##100{X,X,1,2}^^X^2 & 100ζφ(1,0,0,0)+1
terricubed blasphemorgulusE100{#,#,1,2}^^###100{X,X,1,2}^^X^3 & 100ηφ(1,0,0,0)+1
territoped blasphemorgulusE100{#,#,1,2}^^#^#100{X,X,1,2}^^X^X & 100φ(ω,φ(1,0,0,0)+1)
dupentated-blasphemorgulusE100{#,#,1,2}^^{#,#,1,2}100{X,X,1,2}^^^2 & 100Γφ(1,0,0,0)+1[2]
horrible blasphemorgulusE100{#,#,1,2}^^^#100{X,X,1,2}^^^X & 100Γφ(1,0,0,0)+1
horrendous blasphemorgulusE100{#,#,1,2}^^^^#100{X,X,1,2}^^^^X & 100φ(2,0,φ(1,0,0,0)+1)
heptorrendous blasphemorgulusE100{{#,#,1,2},#,5}100{{X,X,1,2},X,5} & 100φ(3,0,φ(1,0,0,0)+1)
ogdorrendous blasphemorgulusE100{{#,#,1,2},#,6}100{{X,X,1,2},X,6} & 100φ(4,0,φ(1,0,0,0)+1)
ennorrendous blasphemorgulusE100{{#,#,1,2},#,7}100{{X,X,1,2},X,7} & 100φ(5,0,φ(1,0,0,0)+1)
dekorrendous blasphemorgulusE100{{#,#,1,2},#,8}100{{X,X,1,2},X,8} & 100φ(6,0,φ(1,0,0,0)+1)
goliahblasphemorgulusE100{{#,#,1,2},#,10}100{{X,X,1,2},X,10} & 100φ(8,0,φ(1,0,0,0)+1)
golliblasphemorgulusE100{{#,#,1,2},#,50}100{{X,X,1,2},X,50} & 100φ(48,0,φ(1,0,0,0)+1)
godsgoblasphemorgulusE100{{#,#,1,2},#,#}100{{X,X,1,2},X,X} & 100φ(ω,0,φ(1,0,0,0)+1)
ohmygosh-ohmygosh-ohmygoooblasphemorgulusE100{{#,#,1,2},#,{#,#,#}}100{{X,X,1,2},X,{X,X,X}} & 100φ(φ(ω,0,0),0,φ(1,0,0,0)+1)
ohmygosh-ohmygosh-ohmygosh-ohmygoooblasphemorgulusE100{{#,#,1,2},#,{#,#,{#,#,#}}}100{{X,X,1,2},X,{X,X,{X,X,X}}} & 100φ(φ(φ(ω,0,0),0,0),0,φ(1,0,0,0)+1)
blasphemorgublasphemorgulusE100({#,#,1,2}){{#,99,1,2}}#100
blasphemormygosh-blasphemormygoshE100({#,#,1,2}){{#,#,1,2}}({#,#,1,2})100
blasphemormygosh-blasphemormygosh-blasphemormygoshE100({#,#,1,2}){{#,#,1,2}}({#,#,1,2}){{#,#,1,2}}({#,#,1,2})100
tweilasphemorgueE100{{#,#,1,2},#,1,2}100φ(1,0,0,1)
frielasphemorgueE100{{{#,#,1,2},#,1,2},#,1,2}100φ(1,0,0,2)
fiorilasphemorgueE100{#,#+1,1,2}4E100{#,#>4,1,2}100φ(1,0,0,3)
finnasphemorgueE100{#,#+1,1,2}5E100{#,#>5,1,2}100φ(1,0,0,4)
sexasphemorgueE100{#,#+1,1,2}6E100{#,#>6,1,2}100φ(1,0,0,5)
sjournalasphemorgueE100{#,#+1,1,2}7E100{#,#>7,1,2}100φ(1,0,0,6)
attalasphemorgueE100{#,#+1,1,2}8E100{#,#>8,1,2}100φ(1,0,0,7)
neiulasphemorgueE100{#,#+1,1,2}9E100{#,#>9,1,2}100φ(1,0,0,8)
tenasphemorgueE100{#,#+1,1,2}10E100{#,#>10,1,2}100φ(1,0,0,9)
hundrelasphemorgue
/ blasphemorguliterator
E100{#,#+1,1,2}100E100#{{1}}#>#100{X,X+1,1,2} & 100φ(1,0,0,ω)
hundrelasphemorgulated-hundrelasphemorgue
/ blasphemorgulditerator
E100{{#,#+1,1,2},#+1,1,2}100E100#{{1}}#>(#+#)100φ(1,0,0,ω*2)
hundrelasphemorgulated-hundrelasphemorgulated-hundrelasphemorgue
/ blasphemorgultriterator
E100{{{#,#+1,1,2},#+1,1,2},#+1,1,2}100E100#{{1}}#>(#+#+#)100φ(1,0,0,ω*3)
ludicriss /
blasphemorgulgriditerator
E100&(1)100E100#{{1}}#>##100φ(1,0,0,ω2)
ludicube /
blasphemorgulcubiculator
E100&(#)100E100#{{1}}#>###100φ(1,0,0,ω3)
luditess /
blasphemorgulquarticulator
E100&(##)100E100#{{1}}#>####100φ(1,0,0,ω4)
blasphemorgulspatialatorE100&(#^#)98E100#{{1}}#>#^#100φ(1,0,0,ωω)[100]
luditopeE100&(#^#)100E100#{{1}}#>#^#102φ(1,0,0,ωω)[102]
blasphemorbid[STNO]~E100&({#,#,#})100E100#{{1}}#>#{#}#100{X,X+2,1,2} & 100φ(1,0,0,φ(ω,0,0))
E100&({#,#,#})100~E100#{{1}}#>#{#}#100
blasphemortrid[STNO]~E100&({#,#,{#,#,#}})100E100#{{1}}#>#{#{#}#}#100{X,X+3,1,2} & 100φ(1,0,0,φ(φ(ω,0,0),0,0))
E100&({#,#,{#,#,#}})100~E100#{{1}}#>#{#{#}#}#100
blasphemortetrid[STNO]~E100&({#,#,{#,#,{#,#,#}}})100E100#{{1}}#>#{#{#{#}#}#}#100{X,X+4,1,2} & 100φ(1,0,0,φ(φ(φ(ω,0,0),0,0),0,0))
E100&({#,#,{#,#,{#,#,#}}})100~E100#{{1}}#>#{#{#{#}#}#}#100
blasphemorputrid[STNO]~E100&({#,#,1,2})5E100#{{1}}#>#{{1}}#5{X,X+5,1,2} & 100φ(1,0,0,φ(1,0,0,0))[4]
blasphemorhexid[STNO]~E100&({#,#,1,2})6E100#{{1}}#>#{{1}}#6{X,X+6,1,2} & 100φ(1,0,0,φ(1,0,0,0))[5]
blasphemorheptid[STNO]~E100&({#,#,1,2})7E100#{{1}}#>#{{1}}#7{X,X+7,1,2} & 100φ(1,0,0,φ(1,0,0,0))[6]
blasphemorogdid[STNO]~E100&({#,#,1,2})8E100#{{1}}#>#{{1}}#8{X,X+8,1,2} & 100φ(1,0,0,φ(1,0,0,0))[7]
blasphemorennid[STNO]~E100&({#,#,1,2})9E100#{{1}}#>#{{1}}#9{X,X+9,1,2} & 100φ(1,0,0,φ(1,0,0,0))[8]
blasphemordecrepid[STNO]~E100&({#,#,1,2})10E100#{{1}}#>#{{1}}#10{X,X+10,1,2} & 100φ(1,0,0,φ(1,0,0,0))[9]
dustaculated-blasphemorgulus
/ blasphemorgudubbus
~E100&({#,#,1,2})100E100#{{1}}#>#{{1}}#100{X,2X,1,2} & 100φ(1,0,0,φ(1,0,0,0))[99]
tristaculated-blasphemorgulus
/ blasphemorgutrebbus
~E100&(&({#,#,1,2}))100E100#{{1}}#>#{{1}}#>#{{1}}#100{X,3X,1,2} & 100φ(1,0,0,φ(1,0,0,φ(1,0,0,0)))
tetrastaculated-blasphemorgulus
/ blasphemorguquabbus
~E100&(&(&({#,#,1,2})))100E100#{{1}}#>#{{1}}#>#{{1}}#>#{{1}}#100{X,4X,1,2} & 100φ(1,0,0,φ(1,0,0,φ(1,0,0,φ(1,0,0,0))))
pentastaculated-blasphemorgulus~E100#*^#4E100#{{1}}##5{X,5X,1,2} & 100φ(1,0,1,0)[4]
hexastaculated-blasphemorgulus~E100#*^#5E100#{{1}}##6{X,6X,1,2} & 100φ(1,0,1,0)[5]
heptastaculated-blasphemorgulus~E100#*^#6E100#{{1}}##7{X,7X,1,2} & 100φ(1,0,1,0)[6]
ogdastaculated-blasphemorgulus~E100#*^#7E100#{{1}}##8{X,8X,1,2} & 100φ(1,0,1,0)[7]
ennastaculated-blasphemorgulus~E100#*^#8E100#{{1}}##9{X,9X,1,2} & 100φ(1,0,1,0)[8]
dekastaculated-blasphemorgulus~E100#*^#9E100#{{1}}##10{X,10X,1,2} & 100φ(1,0,1,0)[9]
blasphemorgulcross~E100#*^#99E100#{{1}}##100{X,X2,1,2} & 100φ(1,0,1,0)
agoraphobia~E100#*^#100~E100#{{1}}##101
blasphemorgulcubor~E100#*^^#100E100#{{1}}###100{X,X3,1,2} & 100φ(1,0,2,0)
acrophobia[STNO] /
astralthrathoth
E100#*^^#100~E100#{{1}}###100
blasphemorgulteron~E100#*^^##100E100#{{1}}####100{X,X4,1,2} & 100φ(1,0,3,0)
megalophobia[STNO]E100#*^^##100~E100#{{1}}####100
blasphemorgulpeton~E100#*^^###100E100#{{1}}#####100{X,X5,1,2} & 100φ(1,0,4,0)
arithmophobia[STNO]E100#*^^###100~E100#{{1}}#####100
...
blasphemorgultope
/ ecstasulus[STNO]
~E100#*^^#^#98E100#{{1}}#^#100{X,XX,1,2} & 100φ(1,0,ω,0)
blasphemorgulthoth[XEAR]~E100#*^^#^^#100E100#{{1}}#^^#100{X,X^^X,1,2} & 100φ(1,0,ε0,0)
blasphemorgulthul[XEAR]~E100#*^^#^^^#100E100#{{1}}#^^^#100{X,X^^^X,1,2} & 100φ(1,0,γ0,0)
blasphemorgulhexacthul[XEAR]~E100#*^^#^^^^#100E100#{{1}}#^^^^#100{X,X^^^^X,1,2} & 100φ(1,0,φ(2,0,0),0)
blasphemarxitri[XEAR]~E100#*^^{#,#,1,2}100E100#{{1}}#{{1}}#100{X,3,2,2} & 100φ(1,0,φ(1,0,0,0),0)
blasphemarxitet[XEAR]~E100#*^^#*^^{#,#,1,2}100E100#{{1}}#{{1}}#{{1}}#100{X,4,2,2} & 100φ(1,0,φ(1,0,φ(1,0,0,0),0),0)
blasphemorgulhenus[GOBL]~E100#*^^^#100E100#{{2}}#100{X,X,2,2} & 100φ(1,1,0,0)
blasphemorguldius[GOBL]~E100#*^^^^#100E100#{{3}}#100{X,X,3,2} & 100φ(1,2,0,0)
blasphemorgultris~E100#*^^^^^#100E100#{{4}}#100{X,X,4,2} & 100φ(1,3,0,0)
deusus-godsgodgogle[XEAR]~E100*{#,#,#}98E100#{{#}}#100{X,X,X,2} & 100φ(1,ω,0,0)
sacriligulus[STNO] /
blasphemorguldeus /
trilasphemorgulus [Douglas Shamlin Jr.]
~E100*{#,#,1,2}100E100#{{{1}}}#100{X,X,1,3} & 100φ(2,0,0,0)
treusus-godsgodgogle[XEAR]~E100**{#,#,#}98E100#{{{#}}}#100{X,X,X,3} & 100φ(2,ω,0,0)
hereticulus[STNO] /
blasphemorgultruce /
quadlasphemorgulus [Douglas Shamlin Jr.]
~E100**{#,#,1,2}100E100#{{{{1}}}}#100{X,X,1,4} & 100φ(3,0,0,0)
quadeusus-godsgodgogle[XEAR]~E100***{#,#,#}98E100#{{{{#}}}}#100{X,X,X,4} & 100φ(3,ω,0,0)
apostatulus[STNO] /
blasphemorgulquad /
quinlasphemorgulus [Douglas Shamlin Jr.]
~E100***{#,#,1,2}100E100#{{{{{1}}}}}#100{X,X,1,5} & 100φ(4,0,0,0)
blasphemorgulquid /
sexlasphemorgulus [Douglas Shamlin Jr.]
~E100****{#,#,1,2}100E100#{{{{{{1}}}}}}#100{X,X,1,6} & 100φ(5,0,0,0)
blasphemorgulsid /
seplasphemorgulus [Douglas Shamlin Jr.]
~E100*****{#,#,1,2}100E100#{{{{{{{1}}}}}}}#100{X,X,1,7} & 100φ(6,0,0,0)
blasphemorgulseptuce /
oclasphemorgulus [Douglas Shamlin Jr.]
~E100******{#,#,1,2}100E100#{{{{{{{{1}}}}}}}}#100{X,X,1,8} & 100φ(7,0,0,0)
blasphemorguloctuce /
nonlasphemorgulus [Douglas Shamlin Jr.]
~E100*******{#,#,1,2}100E100#{{{{{{{{{1}}}}}}}}}#100{X,X,1,9} & 100φ(8,0,0,0)
blasphemorgulnonuce /
declasphemorgulus [Douglas Shamlin Jr.]
~E100********{#,#,1,2}100E100#{{{{{{{{{{1}}}}}}}}}}#100{X,X,1,10} & 100φ(9,0,0,0)
thohtothihlith[STNO]~E100*(98){#,#,1,2}100E100{#,#,1,100}100{X,X,1,100} & 100φ(99,0,0,0)
General Gogulus
/tetrentriculus[STNO]
~E100*(99){#,#,#}100E100{#,#,#,100}100{X,X,X,100} & 100φ(99,ω,0,0)
gorgonghoulgog~E100*(#){#,#,1,2}100E100{#,#,1,102}100{X,X,1,102} & 100φ(101,0,0,0)
pentemorgulus[Douglas Shamlin Jr.]~E100*(*(*(...99 *s... (99)...))){#,#,#}100E100{#,#,1,1,2}100{X,100,1,1,2} & 100φ(1,0,0,0,0)
transmorgrifihgh~E100#/^#100~E100{#,#,1,1,2}101{X,101,1,1,2} & 100
TO BE CONTINUED

Bibliography & Sources

Thanks to the following sources for providing the information:
[XEC5] Extended Cascading-E Part V
[STNO] Structor Numbers
[XEAR] ExE Arithmonyms
[GOBL] Googology Wiki | Blasphemorgulus regiment

4.1.12: Solidus-Extended Cascading-E and beyond!!!!