def chao1_var_bias_corrected(singles, doubles):
    """Calculates chao1 variance, bias-corrected.
    
    From EstimateS manual, equation 6.
    """
    s, d = float(singles), float(doubles)
    return s*(s-1)/(2*(d+1)) + (s*(2*s-1)**2)/(4*(d+1)**2) + \
        (s**2 * d * (s-1)**2)/(4*(d+1)**4)