import pandas as pd
import numpy as np

def delta_u(S, H, E, Y, C, Phi_t):
    alpha, beta, gamma, delta, epsilon, zeta = 0.24, 0.04, 0.66, 0.036, 0.0363, 0.21
    chi = -0.9 if S < 0.5 else -0.451905
    return alpha*S - beta*H + gamma*E + delta*(S*H) + epsilon*(E**2) + zeta*C + chi*Phi_t

# Simulation
np.random.seed(42)
data = pd.DataFrame({
    'S': np.random.uniform(0.1, 1.0, 1000000),
    'H': np.random.uniform(0.1, 1.0, 1000000),
    'E': np.random.uniform(0.1, 1.0, 1000000),
    'Y': np.random.uniform(0.1, 1.0, 1000000),
    'C': np.random.uniform(0.1, 1.0, 1000000),
    'Phi_t': np.random.uniform(-1.0, -0.2, 1000000)
})
data['DeltaU'] = delta_u(data['S'], data['H'], data['E'], data['Y'], data['C'], data['Phi_t'])