(a) if the current x is lower than the previous x:
    (a.1) if the current x has been seen before, discard the current point
    (a.2) else discard the previous point.
(b) elsif the current x is identical to the prev. x (due to a.1 on prev.iteration)
    (b.1) discard previous point

##</code><code>##

#! perl -slw
use strict;

printf "%s", scalar <DATA>;
my @points = map[ split ' ', $_ ], <DATA>;

my @modified;
my %xseen;

push @modified, shift @points;
$xseen{$modified[-1][0]} = undef;

while ( @points ) {
    if ( $points[0][0] < $modified[-1][0] ) {
        if ( exists( $xseen{$points[0][0]} )) {
            shift @points;
            next;
        }
        else {
            pop @modified;
        }
    }
    elsif ( $points[0][0] eq $modified[-1][0] ) {
        pop @modified;
    }
    push @modified, shift @points;
    $xseen{$modified[-1][0]} = undef;
}

print join ' ', @$_ for @modified;

##</code><code>##

0.0036759 0.4018006     0.0036759 0.4018006
0.0036962 0.4074616     0.0036962 0.4074616
0.0037064 0.4216399     0.0037064 0.4216399
0.0037166 0.4438854     0.0037166 0.4438854
0.0037268 0.4628417     0.0037268 0.4628417
0.0037370 0.4894152     0.0037370 0.4894152
0.0037471 0.4952320     0.0037471 0.4952320
0.0037675 0.4979326     0.0037675 0.4979326
0.0037879 0.5014988     0.0037879 0.5014988
0.0038082 0.5057747     0.0038082 0.5057747
0.0038184 0.5166984     0.0038184 0.5558402
0.0038286 0.5613627     0.0038286 0.5613627
0.0038388 0.6026338     0.0038388 0.6026338
0.0038490 0.6257104
0.0038693 0.6709805     0.0038693 0.6709805
0.0038795 0.6808655     0.0038795 0.6808655
0.0038897 0.6866130     0.0038897 0.6866130
0.0039202 0.6981425     0.0039202 0.6981425
0.0039406 0.7057251     0.0039406 0.7057251
0.0039508 0.7161121
0.0039610 0.7216518     0.0039610 0.7216518
0.0039712 0.7433434     0.0039712 0.7433434
0.0039813 0.7577987
0.0039915 0.7713018     0.0039915 0.7713018
0.0040017 0.7981869     0.0040017 0.7981869
0.0040119 0.8014242     0.0040119 0.8014242
0.0040221 0.8264223     0.0040221 0.8264223
0.0040526 0.8290191     0.0040526 0.8290191
0.0040628 0.8323083     0.0040628 0.8323083
0.0040933 0.8361688     0.0040933 0.8361688
0.0041035 0.8409814     0.0041035 0.8409814
0.0041137 0.8527880
0.0041239 0.8591068     0.0041239 0.8591068
0.0041341 0.864785 
0.0041443 0.8760895     0.0041443 0.8760895