Original:
37 points.

Polygon with values 0..1 and simplified with 1.0 / 2048.0
Result:
MULTIPOLYGON(((0.561648 1,1 1,1 0,0.468083 0,0.52758 0.00800554,0.599683 0.0280924,0.601611 0.265374,0.622693 0.316765,0.69507 0.357497,0.695623 0.429711,0.655111 0.502298,0.696467 0.543147,0.840712 0.593546,0.882583 0.66546,0.852357 0.748213,0.84264 0.789567,0.832667 0.841202,0.740538 0.873004,0.617349 0.905045,0.566576 0.977697,0.561648 1)),((0 0.801979,0.0308575 0.786234,0.0705513 0.631135,0.141616 0.527248,0.233985 0.505872,0.264777 0.526263,0.336631 0.505009,0.356603 0.422321,0.355803 0.350038,0.375252 0.205364,0.415206 0.0709182,0.45479 0,0 0,0 0.801979)))
35 points.

Same values but multiplied by 2047.0 and simplified with 1.0
Result:
MULTIPOLYGON(((1149.69 2047,2047 2047,2047 0,958.166 0,1079.96 16.3873,1227.55 57.5051,1231.5 543.221,1274.65 648.418,1422.81 731.796,1423.94 879.618,1341.01 1028.2,1425.67 1111.82,1720.94 1214.99,1806.65 1362.2,1744.77 1531.59,1724.88 1616.24,1704.47 1721.94,1515.88 1787.04,1263.71 1852.63,1159.78 2001.35,1149.69 2047)),((0 1641.65,63.1653 1609.42,144.419 1291.93,289.888 1079.28,478.967 1035.52,541.999 1077.26,689.084 1033.75,729.966 864.491,728.329 716.528,768.141 420.38,849.927 145.17,930.955 0,0 0,0 1641.65)))
35 points.