The variable is not irrational, it is floating-point, so it isn't even real. (the square-root of 2 is irrational though, and thus cannot be accurately represented by it)
Just use more digits for your literal, and the round-trip conversion will work. An IEEE double-precision floating-point value needs 17 significant decimal digits to safely represent it, not 14.
Let's see what happens when we take the number 1 and uptick it in the least significant bit. (The '0x' means the numeral is hexadecimal. That makes it easier for me to control the bits for this example.):
x = 0x1.0000000000001
> print(x == 1)
false
> print(('%.16g'):format(x))
1
> print(('%.17g'):format(x))
1.0000000000000002