Find the coordinates of the minimum bounding rectangle enclosing two rectangles

Given the coordinates of the top left corners of two rectangles (x1, y1), (x2, y2), their respective widths and heights (w1, h1), (w2, h2) (They may or may not overlap). How do I find the coordinates of the top left corner (x3, y3) and the width and height (w3, h3) of the minimum bounding rectangle that encloses the 2 given rectangles. The widths and heights of the two rectangles are always parallel to the xy axis respectively. x increases from left to right and y increases from top to bottom.

For example, if
x1 = 2, y1 = -1, w1 = 3, h1 = 6
x2 = -1, y2 = 3, w2 = 8, h2 = 3
then
x3 = -1, y3 = -1, w3 = 8, h3 = 7

I can only find x3 and y3 but not w3 and h3.
x3 = min(x1, x2), y3 = min(y1, y2)

One way to define an axis-aligned rectangle is to list its four coordinates (xmin, xmax, ymin, ymax).

If you have two rectangles:

R1 (xmin1, xmax1, ymin1, ymax1)
R2 (xmin2, xmax2, ymin2, ymax2)

Then the minimum axis-aligned bounding rectangle is of course given by coordinates:

R (min(xmin1,xmin2), max(xmax1,xmax2), min(ymin1,ymin2), max(ymax1,ymax2))

You can switch easily between the (xmin, xmax, ymin, ymax) and the (xtopleft, ytopleft, width, height) representations:

(xmin, xmax, ymin, ymax) = (xtopleft, ytopleft, xtopleft+width, ytopleft+height)
(xtopleft, ytopleft, width, height) = (xmin, ymin, xmax-xmin, ymax-ymin)