Interpolating every X distance along line in shapely

If I have a shapely multiline object that contains many lines whose total length each is 50km (when traced from the origin), and I want to interpolate along the multiline every X meters (let’s say 100m), returning shapely point objects every 100m, how can I achieve this?

Here is what I have so far, but it only returns one distinct point (when I know it should return several thousand, as tested in ArcMap):

points = []

for x in range(100,50000,100):
    x,y = multiline.interpolate(x).xy
    xy = (x[0],y[0])
    points.append(xy)

trim = list(set(points))

And here is what trim contains:

[(-90.5864707030599, 38.4688716729703)]

If I break the multiline into individual lines, I can get more points (162), but still not the 1000s I should generate:

# breaking out individual lines into shapely line strings
for line in multiline:
    lines_shapes.append(gm.asLineString(line))

points = []

# interpolating points along each line
for line in lines_shapes:
    for x in range(100,50000,100):
        points.append(line.interpolate(100))

point_list = []
for point in points:
    x,y = point.xy
    xy = (x[0],y[0])
    point_list.append(xy)

trim = list(set(point_list))

and trim contains:

[(-90.4766827033434, 38.5972414054466), (-90.5461231698478, 38.5000688058116), (-90.4968889030998, 38.5464768729898), (-90.6189469029766, 38.4718782063951), (-90.513144169767, 38.5129150061034), (-90.5810937033111, 38.5323612724354), (-90.5396967035394, 38.5864442726652), (-90.6868857696619, 38.447798672452), (-90.6213193028429, 38.5146844725911), (-90.509758103553, 38.5536796727591), (-90.476078103521, 38.546296205486), (-90.6427893693333, 38.5555682724382), (-90.6217561026614, 38.5147302723649), (-90.630436369842, 38.5000560723107), (-90.4760629697296, 38.5914768059899), (-90.6849423697939, 38.4566312056467), (-90.6538383698443, 38.4599348058277), (-90.4699029698455, 38.5837950057152), (-90.6694679700701, 38.4474470726055), (-90.6829395031549, 38.4198408724397), (-90.6732927030951, 38.4360894058827), (-90.5866617028747, 38.5332390062557), (-90.6961129028875, 38.4531938061303), (-90.5947731029956, 38.4539120730648), (-90.5142317702794, 38.5249724721824), (-90.5903123694197, 38.5034458725098), (-90.5755567699284, 38.5000690063604), (-90.56752770364, 38.5589170059954), (-90.6271141698824, 38.5430544723665), (-90.6201437702182, 38.4550620064875), (-90.6180047030539, 38.5000570723568), (-90.6589975699812, 38.500065872223), (-90.685946302779, 38.4505508056563), (-90.6840849030951, 38.4547842059075), (-90.6854941029699, 38.4134104059469), (-90.5918703027716, 38.5000662058715), (-90.5471115031927, 38.4808140060424), (-90.463451370184, 38.5525954725834), (-90.6780159694608, 38.4460308724081), (-90.5896267029094, 38.5346980060887), (-90.5807949701111, 38.5325790054973), (-90.7004947695174, 38.4727768728354), (-90.5955769035506, 38.5373834725497), (-90.6569789697031, 38.4542776061077), (-90.6253669031594, 38.521868606032), (-90.6565429028321, 38.4538942062337), (-90.4636589696851, 38.552869806277), (-90.634338969767, 38.546211672811), (-90.4360581033981, 38.5162080059754), (-90.478937169714, 38.604583072231), (-90.6238845029668, 38.5403794056656), (-90.5115069701699, 38.5170084061937), (-90.6607629031848, 38.4788458064697), (-90.6182993029698, 38.4996076730365), (-90.6795531698423, 38.4464060057138), (-90.5715115033526, 38.5319224725247), (-90.6601255698386, 38.4660196727507), (-90.5944027028219, 38.4399328061353), (-90.6658113032484, 38.5630904727274), (-90.657297702926, 38.4486316730944), (-90.6076871697265, 38.5411054058703), (-90.5189131030566, 38.4958198724699), (-90.4633435036991, 38.5571938060298), (-90.4550633700778, 38.5794588057595), (-90.6551231026484, 38.5026692062996), (-90.6304847695558, 38.4814012057819), (-90.6293281694588, 38.5510622058365), (-90.5337045036593, 38.5480590727484), (-90.5636725699325, 38.5031146728847), (-90.5893179035978, 38.5349642063136), (-90.5502847700255, 38.5531414725813), (-90.6577657029242, 38.4673132728702), (-90.6842995029191, 38.45499127301), (-90.596995102941, 38.536759005804), (-90.4590855033927, 38.579707805551), (-90.618116169525, 38.5138608060121), (-90.662823570151, 38.4436198061903), (-90.5324573031614, 38.5290608063917), (-90.4761187699646, 38.5460198060497), (-90.4365065035716, 38.5163978060946), (-90.5993421032549, 38.4517628723399), (-90.6580597695421, 38.4672556730918), (-90.4697125698785, 38.5713498724789), (-90.6246789694582, 38.5225716726252), (-90.5623807028065, 38.539724406037), (-90.5255411029389, 38.5592538722488), (-90.6779729027267, 38.4309624725214), (-90.5757351702413, 38.5712982055281), (-90.4349003036055, 38.5470764060318), (-90.4881969699136, 38.5968882057062), (-90.5654833701608, 38.5641550721791), (-90.6243467697869, 38.5407896062358), (-90.6833993696845, 38.4554192064123), (-90.5125843031225, 38.5353802722622), (-90.4343933036075, 38.5320694055591), (-90.5949243033133, 38.4437996058484), (-90.6531879693487, 38.5465062727268), (-90.4678253704438, 38.5769334060321), (-90.6560765692776, 38.4512860059256), (-90.6705015033411, 38.4387672065226), (-90.4510205703424, 38.5293378056758), (-90.5965189694742, 38.453478006286), (-90.5158851037139, 38.5293438059525), (-90.5153219032826, 38.5000608728918), (-90.571685370183, 38.5322450728324), (-90.5907731028958, 38.5035282063425), (-90.562387970228, 38.5396736725824), (-90.5632127699527, 38.5000698058576), (-90.4351277034801, 38.5467304062636), (-90.6846297033974, 38.4247822729648), (-90.4300920979354, 38.5121736658553), (-90.6077071031996, 38.5414430059705), (-90.700472969951, 38.4725166728872), (-90.6083531698623, 38.5440140058222), (-90.6611483697009, 38.478763472637), (-90.5148001696915, 38.5340326723505), (-90.6261891029441, 38.4987850056043), (-90.6077131034763, 38.5415200724739), (-90.5714903701838, 38.5588274721905), (-90.487086969987, 38.5953794059149), (-90.6309363029674, 38.4813284731115), (-90.4375485030603, 38.5798804061361), (-90.4348689037762, 38.5318386727971), (-90.4636395029601, 38.5528440056267), (-90.5537693695601, 38.5918534726398), (-90.686189369743, 38.45065887269), (-90.5137219032426, 38.5459956061927), (-90.4708333032137, 38.5588582056221), (-90.562663570167, 38.5400910056759), (-90.5898827695735, 38.4573650056716), (-90.6541333699584, 38.4598728056666), (-90.5201981695093, 38.5275174726339), (-90.5279559031418, 38.5197458058049), (-90.4969485029704, 38.5468012728409), (-90.6963449693442, 38.4523242057786), (-90.5869187695849, 38.5329812056987), (-90.7090465028932, 38.4391836726696), (-90.4722723695735, 38.5676876055788), (-90.6076811029, 38.541104472374), (-90.6281757035453, 38.4421816724275), (-90.5341799698291, 38.5482110060135), (-90.5948001033415, 38.494925272764), (-90.5864707030599, 38.4688716729703), (-90.5419337032772, 38.5685326058754), (-90.7019565698392, 38.4481112057488), (-90.6253121695204, 38.521868606032), (-90.5138205031131, 38.5456764727715), (-90.5529913031055, 38.455285806376), (-90.5293321032933, 38.5986526054135), (-90.6309013697018, 38.5463032723585), (-90.4975365696563, 38.6037882720911), (-90.6184813032689, 38.4720362730366), (-90.6781275699308, 38.4462692727899), (-90.5651579702635, 38.4796824727488), (-90.6532305027848, 38.5024180058671), (-90.6545907030978, 38.5581974062657), (-90.5950401027179, 38.4950944055632), (-90.6468105700511, 38.5573522728695), (-90.6698367029009, 38.4476676727061), (-90.4501431701705, 38.5848148728883), (-90.577996903134, 38.503304272455), (-90.6713375697724, 38.545723072942)]

Maybe the problem is in the argument I am passing to interpolate? How do I know what units it expects/is assuming the distance is in?