import numpy as np
import matplotlib.pyplot as plt

def exp2lin(x):
    # convert exponential values to linear ones
    epsilon = 1 - np.fabs(x).min()
    return np.sign(x) * np.log10( epsilon + np.fabs(x) )

X = np.linspace(-3,3,1000)
Y = np.concatenate([-np.logspace(3,-0.01,500), np.logspace(-0.01,3,500)])
Y_hat = exp2lin(Y)
#plt.scatter(X, Y, s=1, color="blue")
plt.scatter(X, Y_hat, s=1, color="green")
plt.show()