  We designed a completely automated Maple ($\geqslant 15$) worksheet for
deriving Edgeworth and Cornish-Fisher expansions as well as the acceleration
constant of the bootstrap bias-corrected and accelerated technique. It is valid
for non-parametric or parametric bootstrap, of any (studentized) statistics
that is -a regular enough- function of the mean of an iid sample of an
absolutely continuous distribution.
  This worksheet allowed us to point out one error in the second-order
Cornish-Fisher expansion of the studentized mean stated in Theorem 13.5 by Das
Gupta in [8, p. 194] as well as lay the stress on the influence of the slight
change of the normalizing constant when computing the second-order Edgeworth
and Cornish-Fisher expansions of the t-distribution as stated in Theorem 11.4.2
by Lehman and Romano in [14, p. 460].
  In addition, we successfully applied the worksheet to a complex maximum
likelihood estimator as a first step to derive more accurate confidence
intervals in order to enhance quality controls. The worksheet also features
export of Maple results into R code. In addition, we provide R code to plot
these expansions as well as their increasing rearrangements. All these
supplemental materials are available upon request.
