It turns out that BrowserUK's approach was an order of magnitude quicker than the other approaches presented here. I took the liberty of coding up Sundialsvc4's suggestion of buffering a few hundred thousand lines worth of data before printing them out to a file. I used array refs since there was no reason to use hash refs.

I used a Powershell script to time the different approaches.

echo 'BrowserUK 1024' > bench.txt
Measure-Command { .\buk.bat } >> bench.txt
echo 'BrowserUK 2048' >> bench.txt
Measure-Command { .\buk2048.bat } >> bench.txt
echo 'Sundial approach by Lotus1' >> bench.txt
Measure-Command { perl sundial.pl test.csv > dialout.csv} >> bench.txt
echo spacebar >> bench.txt
Measure-Command { .\sed -n "s/^\([^\t]*\t\)[^\t]*\t\([^\t]*\t\)[^\t]*\
+t[^\t]*\t\([^\t]*\)\t.*/\2\1\3/p" test.csv > spaceout.csv} >> bench.t
+xt
echo 'kenosis/choroba' >> bench.txt
Measure-Command { perl kc.pl test.csv > kcout.csv} >> bench.txt
echo 'mildside -- wrong order but testing anyway' >> bench.txt
Measure-Command { .\cut '-f1,3,6' test.csv > cutout.csv} >> bench.txt
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Here are the results using a 1Gb test file on an idle server with 16 cores and 8Gb RAM: update: (Windows Server 2008 R2)

BrowserUK 1024
Minutes           : 1
Seconds           : 54
Milliseconds      : 103
Ticks             : 1141033211

BrowserUK 2048
Minutes           : 1
Seconds           : 55
Milliseconds      : 124
Ticks             : 1151241665

Sundial approach by Lotus1
Minutes           : 21
Seconds           : 53
Milliseconds      : 28
Ticks             : 13130283183

spacebar
Minutes           : 21
Seconds           : 24
Milliseconds      : 215
Ticks             : 12842154788

kenosis/choroba
Minutes           : 22
Seconds           : 4
Milliseconds      : 865
Ticks             : 13248658887

mildside -- wrong order but testing anyway
Minutes           : 22
Seconds           : 19
Milliseconds      : 295
Ticks             : 13392954883
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Here is the sundialsvc4 approach that I put together for the test:

#! perl -sw
use strict;

my $count = 0;
my @lines;
while( <> ) {
    $count++;
    my @f = ( split /\t/, $_, 7 )[ 0, 2, 5 ];
    push @lines, \@f;
    
    if( $count >= 300000 ) {  #size of buffer
        $count = 0;
        print_buffer( \@lines );
    }
}
print_buffer( \@lines );

sub print_buffer {
    my ($aref) = @_;
    foreach (@$aref) {
        print join( "\t", @$_ ) . "\n";
    }
    splice( @$aref );
}
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Here is the Kenosis/choroba approach.

#! perl -sw
use strict;

#kenosis/choroba approach

while( <> ) {
    print join( "\t", ( split /\t/, $_, 7 )[ 0, 2, 5 ]), "\n";
}
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Great job there Lotus1.

I'm curious about the use of splice to clear the array in your code, as below:

    splice( @$aref );

I would probably have used the below:

    @$aref = ();

Is splice faster or better in some other way?

Thanks. I started with assigning the empty array but I had a bug somewhere so I stuck the splice in and got it working. I think I forgot the '@' in the first try but put it in with splice. I don't know which is faster but it is only called a handful of times in this approach anyway.

taking care that I/O doesn’t sneak up on you from the backside in the form of virtual-memory paging.

You and your hobby horses. Virtual memory limits don't enter into it.

When running, those two programs I posted use 2.7 MB and 3.2 MB respectively when using the 256 times larger read size than standard that I suggest. Even if I increase that 10-fold to 10MB each -- which slows the processing down -- they use a whole 12 MB & 16 MB. The programmer that runs my heating system could handle that.

I’m personally not sure that threads would help here

I'm not sure that standing on one leg whilst drinking blood from a freshly decapitated chicken would help; so I don;t mention it.

And your instincts prejudiced guessing is wrong!

Approximately 2/3rds of the throughput gains from my posted solution come exactly because the CPU intensive part of the processing -- the spliting and joining of the records -- can run flat out (100% utilisation) on one CPU, whilst the first thread doing the Input is instantly ready to respond to the completion of each read because it isn't having to perform any CPU intensive processing on each record.

push it onto an array (of hashrefs).

The input is a stream; the output is a stream; What on earth do you need an array of hashrefs for?

I suspect that you will be astonished at what just-this does for the program.

No. I can pretty much call it without trying it. It will run 3 to 5 times slower than a simple:

perl -F"\t" -anle"print join chr(9), @F[2,0,5]" in.tsv > out.tsv
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That is, instead of taking the OPs 5+ hours to run it will take closer to 24 hours.

Why? You'll never know unless you try it. And you won't do that.

(And even if you get someone else to do it for you, you won't post the results, because it will show your 'advice' to be nothing more than groundless guessing.)