The following two expressions are the same when checked numerically.

`fun1[x_, y_] = 1/4 (Sqrt[(1 - y)/( 4 + y (-4 + (1 - 2 x)^2 y))] (2 - y + Sqrt[ 4 + y (-4 + (1 - 2 x)^2 y)]) - 2 ((-1 + 2 x) y + Sqrt[ 4 + y (-4 + (1 - 2 x)^2 y)]) Sqrt[-(((-1 + y) (-2 + y + Sqrt[ 4 + y (-4 + (1 - 2 x)^2 y)])^2)/(4 - 4 y + ((-1 + 2 x) y + Sqrt[ 4 + y (-4 + (1 - 2 x)^2 y)])^2)^2)]); fun2[x_, y_] = Sqrt[1 - y]/2; `

However, *Mathematica* is not able to reduce `fun1[x,y]`

to `fun2[x,y]`

, with `Simplify`

of `FullSimplify`

. Is there any way of doing this simplification? Also note that $ 0\le x \le 1$ and $ 0\le y\le 1$ .