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

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Paul
Paul 2025-10-14，2:24
编辑： Paul 2025-10-14，2:28
Ran in:
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 = 

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