In R, the procedure `density` gives a kernel density
estimator (KDE) of data. 

In order to get a suitable histogram
of the very heavy tailed Cauchy distribution, it is
usually necessary to disregard more than a few values in the tails of the sample.

Then in order show the actual Cauchy density curve (black
below), it is necessary to adjust the density by dividing
by the proportion of the sample plotted in the histogram.

Also, to get a the best KDE (dotted red) you may need to use parameter
`adj` tp adjust the default bandwidth. (I used the default.) Of course, the histogram would be 'smoother' if it had fewer bins; the KDE is made entirely without
reference to the histogram.

By adjusting the proportion of the sample plotted, the bandwidth of the KDE, and the sample size, you may be able to improve on
my plot below. But the agreement of the density function and the KDE in the the plot below is roughly typical
for samples of size 500 to 1000.

[![enter image description here][2]][2]

R code for figure:

    k = diff(pt(c(-4,4),1))
    set.seed(2022)
    w = rt(1000, 1)        # whole sample, size 1000
    y = w[x > -4 & w < 4]  # 861 plotted points
    length(y)
    [1] 861

    hist(y, prob=T, ylim=c(0,.4), br=50, col="skyblue2")
     curve(dt(x,1)/k, add=T, lwd=2)
     lines(density(y), col="red", lwd=2, lty="dotted")

 


  [1]: https://i.sstatic.net/0lb9M.png
  [2]: https://i.sstatic.net/FJ9PC.png