geometry - Tiling rectangles with X pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle

Also in this series: Tiling rectangles with F pentomino plus rectangles

Tiling rectangles with N pentomino plus rectangles

Tiling rectangles with T pentomino plus rectangles

Tiling rectangles with U pentomino plus rectangles

Tiling rectangles with V pentomino plus rectangles

Tiling rectangles with W pentomino plus rectangles

The goal is to tile rectangles as small as possible with the X pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one X-pentomino will tile. Example shown, with the $1\times 1$, you can tile a $3\times 3$ as follows:

Now we don't need to consider $1\times 1$ any longer as we have found the smallest rectangle tilable with copies of X plus copies of $1\times 1$.

I've only found two other solutions. I tagged it 'computer-puzzle' but some people can probably work both of these out by hand.

Answer

I think I've found a smaller one for 1x3:

a 15x10 = 150 solution:

This one has a rather interesting generalization (see the third spoiler block there) for a different pentomino and rectangle size.