Way to find an image inside another image in PHP/GD?

Question

I need a way to find the location of an image inside another image in PHP/gd. For example, locate this image:

inside this image:

I tried to make a function myself to do this, and I WAS successful, but it's very slow, it takes over 50 seconds at 100% CPU for me with the example pictures above, and I'm not sure how to optimize it (if possible) further. So is there some way to do this faster? Preferably, much faster? (For instance Auto Hotkey can do the same operation in <2 seconds on the same computer with this function https://autohotkey.com/docs/commands/ImageSearch.htm )

Edit: I figured I could simply create a copy of the small image by the big image's color indexes with imagecolorexact, this allows 2 things, detect when the small image has a pixel which doesn't exist in the big image, making a match impossible, AND comparing an int(x)===int(x) is much faster than comparing array("red"=>x,"green"=>x,"blue"=>x)==array("red"=>x,"green"=>x,"blue"=>x) - it looks like the speed nearly tripled this way, using 30 seconds before, using 9 seconds now. Still nowhere near the speed of AutoHotKey's though :/

$big = imagecreatefrompng ( 'so_big.png' );
$small = imagecreatefrompng ( 'so_small.png' );
bench ( __LINE__ );
var_dump ( FindImageInImageV2 ( $big, $small) );
bench ( __LINE__ );
die ( "DONED" );
function FindImageInImageV2($big, $small, int $max = PHP_INT_MAX,bool $center=true): array {
    assert ( is_resource ( $small ) );
    assert ( is_resource ( $big ) );
    $ret = array ();
    //think2 ( $big, 'FindImageInImage/big' );
    //think2 ( $small, 'FindImageInImage/small' );
    $smallx = imagesx ( $small );
    $smally = imagesy ( $small );
    $bigx = imagesx ( $big );
    $bigy = imagesy ( $big );
    assert ( $bigx >= $smallx );
    if ($bigx < $smallx) {
        return $ret; // match is impossible
    }
    assert ( $bigy >= $smally );
    if ($bigy < $smally) {
        return $ret; // match is impossible
    }
    $smallcolors = imagecolorstotal ( $small );
    $bigcolors = imagecolorstotal ( $big );
    // assert($smallcolors<$bigcolors);
    if ($smallcolors > $bigcolors) {
        return $ret; // too many colors, match is impossible.
    }
    $smallImageAsColors = array ();
    for($x = 0; $x < $smallx; ++ $x) {
        $smallImageAsColors [$x] = array ();
        for($y = 0; $y < $smally; ++ $y) {
            $tmp = imagecolorsforindex ( $small, imagecolorat ( $small, $x, $y ) );
            //unset ( $tmp ['alpha'] );
            $tmp=imagecolorexact ( $big, $tmp['red'], $tmp['green'],$tmp['blue']);
            if($tmp===-1){
                //small has a color that does not exist in big, match is impossible
                return $ret;
            }
            $smallImageAsColors [$x] [/*$y*/] = $tmp;
        }
    }
    unset ( $x, $y, $tmp );
    for($x = 0; $x < $bigx; ++ $x) {
        if ($bigx < ($x + $smallx)) {//<< todo: can be optimized away.
            break; // too close to the end, no result possible..
        }
        for($y = 0; $y < $bigy; ++ $y) {
            if ($bigy < ($y + $smally)) {//<< todo: can be optimized away.
                continue; // too close to the bottom, no result possible for this $y..
            }
            //$matchFound = true;
            for($i = 0; $i < $smallx; ++ $i) {
                for($ii = 0; $ii < $smally; ++ $ii) {
                    // yelp
                    if($smallImageAsColors [$i][$ii]!==imagecolorat($big,$x+$i,$y+$ii))
                    {
                        //$matchFound=false;
                        //goto outofmatching;//i can micro optimize the jumps more actually... but should i?
                        //goto uglyoptimize;
                        continue 3;
                    }
                }
            }
            //outofmatching:
            //if ($matchFound) {
                $ret [] = array (
                        'x' => ($center?$x+((int)floor($smallx/2)):$x),
                        'y' => ($center?$y+((int)floor($smally/2)):$y)
                );
                if (count ( $ret ) >= $max) {
                    //goto done;
                    return $ret;
                }
            //}
            //uglyoptimize:
        }
    }
    //done:
    return $ret;
}