Traceless Busy Beaver
Score: \$ A(255, 2) - 1 = (2 \uparrow^{253} 5) - 4 \$

+&lt;+&lt;&lt;++&gt;-[-[&lt;+&gt;&gt;[-&lt;[-&gt;+&lt;]+&gt;&gt;]+&lt;-]&gt;[&gt;]+[&lt;]+&lt;]&gt;[-&gt;]


\$ A \$ here is the Péter-Ackermann formulation of the Ackermann function, while the other score expression uses Knuth up-arrow notation. The 35-byte main loop [-[&lt;+&gt;&gt;[-&lt;[-&gt;+&lt;]+&gt;&gt;]+&lt;-]&gt;[&gt;]+[&lt;]+&lt;] can be used to compute \$ A(m,n) \$ by placing on the tape the values 1 - m, m, 1 &lt;n times&gt; and entering the loop with the pointer on the m cell. After the loop terminates, the nonzero tape contents are \$ A(m,n) \$ ones starting immediately to the right of the pointer.

I used the following Python program for modeling the behavior of the program:

def a(M, N):
    assert M &gt; 0
    m = [-M + 1, M]
    n = N
    while m[-1]:
        while m[-1] &gt; 1:
            m[-1] -= 1
            m[-2] += 1
            while n:
                m.insert(-1, 1)
                n -= 1
            n = 1
        n += 2
        m.pop()
    return n