Simplification of exponential and trigonometric expression

Hello,

I know that the function q(x,a,phi,r,theta,psi) defined as

define(Wvac(x,p), 1/(%pi) * exp(-(x^2+p^2)))$
define(Wsq(x,p), Wvac(exp(-r)*(cos(theta/2)*x + sin(theta/2)*p), 
exp(r)*(-sin(theta/2)*x + cos(theta/2)*p)))$
define(Wsqd(x,p), Wsq(x-a*cos(phi),p-a*sin(phi)))$
define(W(x,p), Wsqd(cos(psi)*x-sin(psi)*p,sin(psi)*x+cos(psi)*p))$
assume(A<0)$
F : integrate(1/(%pi)*exp(A*p^2+B*p+C), p, minf, inf)$
l : makelist(coeff(expand(log(%pi*W(x,p))),p,n),n,0,2)$
define(q(x,a,phi,r,theta,psi), (trigreduce(trigexpand(subst([A = l[3], B 
= l[2], C = l[1]], F)))));

is equivalent to the function p(x,a,phi,r,theta,psi) defined as

xavg(a,psi,phi) := a*cos(psi-phi)$
sigma2(r,theta,psi) := 
%e^((-2)*r)*cos(psi-theta/2)^2+%e^(2*r)*sin(psi-theta/2)^2$
define(p(x,a,phi,r,theta,psi), sqrt(2/(%pi*sigma2(r,theta,psi))) * 
exp(-2*(x-xavg(a,psi,phi))^2/sigma2(r,theta,psi)));

but I am not able to simplify q to the form of p. Can you help me?

Thank you,

Michele