Adjust scale/proportion of watermark on image

I'm having trouble adjusting the scale of the watermark in the following code(it's zoomed in too much):

<?php
// Load the stamp and the photo to apply the watermark to
$stamp = imagecreatefrompng('https://www.photographresearch.com/simple-shop/watermark.png');
$im = imagecreatefromjpeg('https://www.photographresearch.com/simple-shop/photo.jpg');

// Set the margins for the stamp and get the height/width of the stamp image
$marge_right = -100;
$marge_bottom = -100;
$sx = imagesx($stamp);
$sy = imagesy($stamp);

// Copy the stamp image onto our photo using the margin offsets and the photo 
// width to calculate positioning of the stamp. 
imagecopymerge($im, $stamp, imagesx($im) - $sx - $marge_right, imagesy($im) - $sy - $marge_bottom, 0, 0, imagesx($stamp), imagesy($stamp), 20);


// Output and free memory
header('Content-type: image/png');
imagepng($im);
imagedestroy($im);

?>

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Can someone help me with the math so that the watermark and photo are the same proportions?