Awhile back (http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2009/09/msg00280.html)there was some discussion of automatically transforming a*b.transpose()*c into the equivalent (and faster) a*b.dot(c).

A quick test 3.0.3 shows the latter expression being appreciably faster than the former at -O3 using the (admittedly lousy) benchmark

    Eigen::Vector3d a, b, c, d;

    for (unsigned long i = 0; i < 1000000; ++i) {
        grvy_timer_begin("Outer");
        a.setRandom();
        b.setRandom();
        c.setRandom();
        d = a*b.transpose()*c;
        grvy_timer_end("Outer");

        grvy_timer_begin("Dot");
        a.setRandom();
        b.setRandom();
        c.setRandom();
        d = a*b.dot(c);
        grvy_timer_end("Dot");
    }

Very, very low priority.  Just wanted to capture it as an issue.

- Rhys