How Does the 'All' Option Affect the Result of Symbolic simplify?

Start with a simple expression

syms alpha beta real
f = cos(beta)-cos(beta)*cos(alpha)^2

f = 

and try to simplify it:

simplify(f)

ans = 

I was expecting the obvious substitution of sin(alpha)^2, but maybe not so obvious to the symbolic engine.

Try 20 steps and return all of the results.

A1 = simplify(f,20,'All',true);

Check the first result

A1(1)

ans = 

Do the same with 1000 steps

A2 = simplify(f,1000,'All',true);
A2(1)

ans = 

I was expecting that the first result, if not the first 20 results, would be the same form both calls to @doc:simplify.

Why does asking for more steps change the result in the first step?

Its looks odd that it takes more than 200 steps to return (arguably?) the simplest result that I suspect most users would be expecting.

simplify(f,200)

ans =