To see how long different parts of a curl request take, you can use curl -w.

Create a file, curl-timing.txt with the following:

     time_namelookup:  %{time_namelookup}s\n
        time_connect:  %{time_connect}s\n
     time_appconnect:  %{time_appconnect}s\n
    time_pretransfer:  %{time_pretransfer}s\n
       time_redirect:  %{time_redirect}s\n
  time_starttransfer:  %{time_starttransfer}s\n
          time_total:  %{time_total}s\n

Then, run your curl request as normal, but insert -w '@curl-format.txt', i.e.:

curl -w '@curl-format.txt' -o /dev/null -s -L ''

The output looks like:

     time_namelookup:  0.008203s
        time_connect:  0.036324s
     time_appconnect:  0.108840s
    time_pretransfer:  0.108922s
       time_redirect:  0.000000s
  time_starttransfer:  0.173767s
          time_total:  0.175557s