# Question:Why does `simplify` fail to rewrite certain sub-expressions?

## Question:Why does `simplify` fail to rewrite certain sub-expressions?

Maple 2024

As the following worksheet shows,

 >
 > kernelopts('version');
 > Physics:-Version();

 > with(RealDomain):
 > eval(MTM:-det(<    a, b/2, d/2 |    b/2, c, e/2 |    d/2, e/2, f   >), PDETools:-Solve(MTM:-det(<      x**2 + y**2, x1**2 + y1**2, x2**2 + y2**2, x3**2 + y3**2 |      x, x1, x2, x3 |      y, y1, y2, y3 |      1, 1, 1, 1     >) = inner([a, b, c, d, e, f], [x**2, x*y, y**2, x, y, 1]),    {f, e, d, c, b, a}, 'independentof' = {y, x}))/MTM:-det(<   x1, x2, x3 |   y1, y2, y3 |   1, 1, 1  >): simplify(`%`);

 > eval(MTM:-det(<    a, b/2, d/2 |    b/2, c, e/2 |    d/2, e/2, f   >), PDETools:-Solve(MTM:-det(<      x**2 - y**2, x1**2 - y1**2, x2**2 - y2**2, x3**2 - y3**2, x4**2 - y4**2 |      x*y, x1*y1, x2*y2, x3*y3, x4*y4 |      x, x1, x2, x3, x4 |      y, y1, y2, y3, y4 |      1, 1, 1, 1, 1     >) = inner([a, b, c, d, e, f], [x**2, x*y, y**2, x, y, 1]),    {f, e, d, c, b, a}, 'independentof' = {y, x}))/(MTM:-det(<    x2, x3, x4 |     y2, y3, y4 |     1, 1, 1   >)*MTM:-det(<    x3, x4, x1 |     y3, y4, y1 |     1, 1, 1   >)*MTM:-det(<    x4, x1, x2 |     y4, y1, y2 |     1, 1, 1   >)*MTM:-det(<    x1, x2, x3 |     y1, y2, y3 |     1, 1, 1   >)): simplify(`%`);

If I understand correctly, simplify, by default, should try combining every part of an expression with every other to apply a vast range of potential transformations to look at many different forms of it and make progress in picking out the simplest possible one. So, why is `simplify` unable to touch certain sub-expressions when they are encountered at intermediate stages in a computation?