from mpmath import mp

# Use 50 decimal digits of precision
mp.dps = 50

# Print with 10 digits of precision
out_prec = 10

def func(x):
    return mp.e - x * x * mp.exp(x)

def inv_func(y, sign, k):
    return 2 * mp.lambertw(sign * mp.sqrt(mp.e - y) / 2, k=k)

r = mp.mpf('.1')
for i in range(-25, 15):
    x = i * r
    y = func(x)

    # Determine which square root and branch of the Lambert W
    # function we need to get back the x we started with
    if x < -2:
        sign, k = -1, -1
    elif -2 <= x < 0:
        sign, k = -1, 0
    else:
        sign, k = 1, 0

    xx = inv_func(y, sign, k)
    print(x, mp.nstr(y, n=out_prec), mp.nstr(xx, n=out_prec))

-2.5 2.205250587 -2.5
-2.4 2.195746418 -2.4
-2.3 2.187912545 -2.3
-2.2 2.181994542 -2.2
-2.1 2.17824898 -2.1
-2.0 2.176940696 -2.0
-1.9 2.178339113 -1.9
-1.8 2.182713431 -1.8
-1.7 2.190326444 -1.7
-1.6 2.201426742 -1.6
-1.5 2.216238968 -1.5
-1.4 2.234951779 -1.4
-1.3 2.257703098 -1.3
-1.2 2.284562163 -1.2
-1.1 2.315507817 -1.1
-1.0 2.350402387 -1.0
-0.9 2.388960404 -0.9
-0.8 2.430711291 -0.8
-0.7 2.47495503 -0.7
-0.6 2.520709639 -0.6
-0.5 2.566649164 -0.5
-0.4 2.611030621 -0.4
-0.3 2.651608189 -0.3
-0.2 2.685532598 -0.2
-0.1 2.709233454 -0.1
0.0 2.718281828 0.0
0.1 2.707230119 0.1
0.2 2.669425718 0.2
0.3 2.596794536 0.3
0.4 2.479589877 0.4
0.5 2.306101511 0.5
0.6 2.06231906 0.6
0.7 1.731543002 0.7
0.8 1.293935634 0.8
0.9 0.7260033084 0.9
1.0 0.0 1.0
1.1 -0.9167590605 1.1
1.2 -2.06268654 1.2
1.3 -3.48282954 1.3
1.4 -5.229910107 1.4