for all-integer comparison you have to use int64_t

do not derive the inequality by hand, use Maxima:

rot(c,s) := matrix([c,-s],[s,c]);
/* D: sqrt(a^2+b^2); */
ma: rot(e/D, sqrt(D^2-e^2)/D);
mb: rot(b/D, a/D);
dd: (ma.mb.[a,-b])[1][1],ratsimp;

load(ineq)$
assume(D>0)$ assume(a>0)$ assume(b>0)$ assume(d>0)$ assume(e>0)$
ne: d >= dd;
ne: (ne * D^2)-2*a*b*e,ratsimp;