Improved and better tested:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];
use Math::Random::MT qw[ rand srand ];

sub xrand {
    my( $x, $y ) = @_;
    my $lo = $x / $y;
    my $hi = $x * $y;
    if( rand() < 0.5 ) {
        my $root = sqrt( $hi - $x );
        my $rv = rand( $root )**2 + $x;
        return $rv;
    }
    else {
        my $diff = $x - $lo;
        my $root = sqrt( $diff );
        my $rv = ( $diff - rand( $root )**2 ) + $lo;
        return $rv;
    }
}

our $T //= 1000;
our $X //= 10;
our $Y //= 2;
my $min = $X / $Y;
my $max = $X * $Y;

my( $loCount, $exactX, $hiCount ) = (0) x 3;
my  %dist;
for ( 1 .. $T ) {
    my $rand = xrand( $X, $Y );
    die 'Out of range' unless $rand >= $min and $rand <= $max;
    if( $rand < $X ) {
        ++$loCount;
    }
    elsif( $rand > $X ) {
        ++$hiCount;
    }
    else {
        ++$exactX;
    }
    ++$dist{ int( $rand *10 ) / 10 };
}

pp \%dist;

printf "After $T samples %f%% < %f%% < %f%%\n",
    $loCount * 100 / $T, $exactX *100 / $T, $hiCount * 100 / $T;
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