?P3

P3[ψ]

FreeLieFormatting[False]

P3[ψ]

ψs[x,y,y]

ASeries$43[2]

?ASeries$43

?ASeries$14

?ASeries$24

?LieMorphism$23

?ASeries$27

?LieSeries$26

ψ

?LieSeries$13

?FreeLie`Private`solver$4248

ψ1=LS[{LW@x,LW@y}, ψ1s]

Timing[P3[ψ1][9]]

P3[ψ_]:=Module[{pd},
pd=τ[LW[y],ψ];
pd + LieMorphism[{LW[x]->LW[y],LW[y]->0}]@pd - LieMorphism[{LW[x]->LW[x]+LW[y],LW[y]->0}]@pd-2(Subscript[R, {x,y}])[ψ]
]

Timing[P3[ψ1[9]]]