imageReader reads all but two frames of a video

[burkaman]

imageReader reads all but two frames when attempting to read all frames of a video, regardless of the video length. I'm not yet sure which frames are not being read.

OS: NixOS 20.03
ffmpeg version: 3.4.7

Things I would like to try but haven't yet: other OSes, other ffmpeg versions, other video types, and making a short video with numbered frames so I can save the images and see which frames are dropped.

Steps to Reproduce

Make sure you have the following packages installed: ffmpeg-light, JuicyPixels, monad-loops.

1. Make DroppedFrames.hs and add the following:

import Codec.FFmpeg
import Codec.Picture
import Control.Monad.Loops
import Data.Maybe

readAllFrames :: IO Int
readAllFrames = do
 initFFmpeg
 setLogLevel avLogTrace
 (reader, cleanup) <- imageReader (File "pulse.mov") :: IO (IO (Maybe (Image PixelRGB8)), IO ())
 frames <- unfoldM reader
 return $ length frames

2. Generate pulse.mov, either by building the demo application and running with no arguments, or loading /demo/Main.hs in ghci and running testEncode.
3. Run ffmpeg -i pulse.mov -map 0:v:0 -c copy -f null -, and in the second to last line of output you'll see frame= 600, indicating that this video has 600 frames.
4. Load DroppedFrames.hs in ghci and run readAllFrames. The output is 598, indicating imageReader only got 598 frames out of this video.

Here's a gist with the output of ffmpeg and readAllFrames with log level set to trace: https://gist.github.com/burkaman/0bb1e18b6769eed13cdf521c240222c4

[burkaman]

pulse.mov is actually a great test case for this. The default behavior of testEncode writes a 600 frame video of uniform vectors, starting with a frame full of 255s, decreasing by 1 each frame down to 100, increasing back up to 255, then back down again, etc.

When I read back the frames and print out an element of each vector, I see that the 2nd frame is dropped, but the 5th is duplicated, the 9th is dropped, the 12th is duplicated, 16th dropped, 19th duplicated, and it repeats like that every 3 or 4 frames for the entire video. Finally at the end, the 596th is duplicated, and frames 598-600 are dropped. Here's the first 20 frames:

255
253
252
251
251
250
249
248
246
245
244
244
243
242
241
239
238
237
237
236

Here's an updated DroppedFrames.hs to try this yourself:

import Codec.FFmpeg
import Codec.Picture
import Control.Monad.Loops
import Data.Maybe
import qualified Data.Vector.Storable as V

readAllFrames :: IO Int
readAllFrames = do
  initFFmpeg
  (reader, cleanup) <- imageReader (File "pulse.mov") :: IO (IO (Maybe (Image PixelRGB8)), IO ())
  frames <- unfoldM reader
  mapM (putStrLn . show . V.head . imageData) frames
  return $ length frames

Not sure yet why this is happening.

[acowley]

The frame timing things I mentioned that I'm suspicious of are here and a lot of things starting here.

It may be worth instrumenting that code to see what frame times are being used for the pulse example. I can imagine things going wrong in various ways, such as mixing use of rational and floating point times. I don't know exactly what we're doing wrong, but this has always struck me as a real Danger Zone.

[acowley]

Hey @burkaman, did you ever have a chance to dig into this any further?

[burkaman]

Not a lot yet, unfortunately. I did a little bit of light logging around the lines you mentioned and I didn't see anything suspicious yet, but I didn't look very deeply.

I've somewhat convinced myself the problem is in decoding though, not encoding, which is where your suspicious sections are. If I ask ffmpeg to extract all the frames with ffmpeg -i pulse.mov image-%04.png, it gets all 600, and there don't appear to be any deletions or duplicates. I'm wondering if I should try to follow through exactly what ffmpeg does with that command and what ffmpeg-light is doing differently, but maybe that's a bad idea.

This is still on my list, but I haven't managed to devote very much time to it yet.

[gelisam]

I have encountered a similar issue in my gloss-to-flv project, while testing that writing and reading back a video with ffmpeg-light gives back what I started with. Since the encoding is lossy, I don't expect to get exactly the same thing I started with, but I did notice some duplicated frames. Using a tolerance check in order to detect such roundtrip errors automatically, I noticed that roundtrip errors get more common when the fps is increased.

Here is my data. I am encoding a 1 second video at 2 fps up to 300 fps, and I am printing the frame numbers which don't round-trip properly. So the line 2 fps: means that both frames are correct, 35 fps: 35 means that the last frame is incorrect, while 60 fps: 27..60 means that all frames from 27 up are incorrect; possibly because of a single duplicate frame at frame 27, causing all later frames to be off by one.

my data

2 fps:
3 fps:
4 fps:
5 fps:
6 fps:
7 fps:
8 fps:
9 fps:
10 fps:
11 fps:
12 fps:
13 fps:
14 fps:
15 fps:
16 fps:
17 fps:
18 fps:
19 fps:
20 fps:
21 fps:
22 fps:
23 fps:
24 fps:
25 fps:
26 fps:
27 fps:
28 fps:
29 fps:
30 fps:
31 fps:
32 fps:
33 fps:
34 fps:
35 fps: 35
36 fps:
37 fps:
38 fps:
39 fps: 37..39
40 fps:
41 fps: 32..40
42 fps:
43 fps:
44 fps: 43..44
45 fps:
46 fps: 43..46
47 fps: 39..46
48 fps:
49 fps: 25..29,31..48
50 fps:
51 fps: 27..51
52 fps: 42..44,46..51
53 fps:
54 fps: 21..40,42..54
55 fps: 51..54
56 fps:
57 fps: 21..57
58 fps: 36..57
59 fps:
60 fps: 27..60
61 fps: 21..30,32..60
62 fps:
63 fps:
64 fps: 22..64
65 fps: 20..45,47..58,60..63
66 fps: 51..65
67 fps:
68 fps: 27..68
69 fps: 15..67
70 fps: 25..30,32..37,39..44,46..58,60..65,67..69
71 fps:
72 fps: 64..67,69..72
73 fps: 24..73
74 fps: 15..19,21..50,52..54,57,59..65,67..74
75 fps: 21..37,39..52,54..71,73
76 fps: 42..75
77 fps:
78 fps: 37..58,60..78
79 fps: 20..79
80 fps: 17,41..42,50,57,65,73..75
81 fps: 18..40,42..79
82 fps: 32..61,63..81
83 fps:
84 fps: 64..84
85 fps: 28..43,45..60,62..85
86 fps: 17..86
87 fps: 12..83
88 fps: 16..85
89 fps: 24..87
90 fps: 51..58,60..67,69..76,78..85,87..89
91 fps:
92 fps: 43..92
93 fps: 23..47,49..93
94 fps: 16..23,25..94
95 fps: 13..95
96 fps: 13..73,75..82,84..92
97 fps: 17..71,73..94
98 fps: 25..61,64..96
99 fps: 51..56,58..61,63..71,73..91,93..96,98
100 fps:
101 fps: 53..101
102 fps: 27..102
103 fps: 18..103
104 fps: 14..104
105 fps: 11..55,57..99,101..105
106 fps: 11..101
107 fps: 14..103
108 fps: 18..105
109 fps: 27..54,56..107
110 fps: 51..60,62..109
111 fps:
112 fps: 64..112
113 fps: 31..113
114 fps: 21..114
115 fps: 16..59,61..83,85..115
116 fps: 13..116
117 fps: 11..61,63..117
118 fps: 9..83,85..88,90..111
119 fps: 11..113
120 fps: 13..61,63..64,66..67,69..70,72..73,75..76,78..79,81..82,84..115
121 fps: 16..117
122 fps: 21..30,32..119
123 fps: 32..61,63..121
124 fps: 63..123
125 fps:
126 fps: 64..119,121..126
127 fps: 33..64,66..127
128 fps: 22..128
129 fps: 17..129
130 fps: 14..33,35..130
131 fps: 12..131
132 fps: 10..83,85..132
133 fps: 9..133
134 fps: 9..126
135 fps: 10..128
136 fps: 11..129
137 fps: 13..30,32..131
138 fps: 15..99,101..133
139 fps: 19..135
140 fps: 25..73,75..78,80..99,101..106,108..113,115..126,128..137
141 fps: 39..139
142 fps: 84..106,108..141
143 fps:
144 fps: 64..144
145 fps: 35..103,105..132,134..145
146 fps: 24..146
147 fps: 19..147
148 fps: 15..129,131..148
149 fps: 13..149
150 fps: 11..53,55,57..58,60..61,63..64,66..67,70,73,75..115,118,120..121,123..124,126..127,129..130,133,135..150
151 fps: 10..151
152 fps: 9..152
153 fps: 9..153
154 fps: 7..142
155 fps: 8..108,110..139,141..144
156 fps: 8..127,129..146
157 fps: 9..148
158 fps: 10..150
159 fps: 11..152
160 fps: 13..14,16,18..19,21..22,24,27,29..30,32,34,37,39,42,44,46..47,50,52..53,55,59..64,66..80,82..84,87..88,90,93..96,98..100,103..104,106,108..115,117..121,124..131,133..136,139..152
161 fps: 15..156
162 fps: 18..118,120..157
163 fps: 23..159
164 fps: 32..102,104..161
165 fps: 50..51,53..56,58..61,63..84,86..89,91..94,96..109,111..117,119..122,124..127,129..135,137,139..163
166 fps: 126..146,148..154,156,158..165
167 fps:
168 fps: 64..168
169 fps: 37..169
170 fps: 27..95,97..130,132..164,166..170
171 fps: 21..171
172 fps: 17..172
173 fps: 15..89,91..173
174 fps: 13..174
175 fps: 12..91,93..128,131..136,138..143,145..150,153..165,167..175
176 fps: 10..176
177 fps: 10..177
178 fps: 9..178
179 fps: 8..179
180 fps: 8..24,26..33,35..117,119..121,125..150,152..180
181 fps: 7..181
182 fps: 6..166
183 fps: 6..167
184 fps: 7..169
185 fps: 7..171
186 fps: 8..173
187 fps: 8..175
188 fps: 9..66,68..177
189 fps: 10..179
190 fps: 11..117,119..135,137..180
191 fps: 12..95,97..182
192 fps: 13..184
193 fps: 15..186
194 fps: 17..188
195 fps: 21..190
196 fps: 25..51,53..61,63..192
197 fps: 34..98,100..194
198 fps: 50..51,53,55..57,59..61,63..67,69..89,91,93,95..97,99,101,103,105,107,109,111,113,115..117,119..123,125,127,129..148,150..162,164..170,172,175..192,194..196
199 fps: 100..115,117..121,123,125..129,131..133,135..179,181..189,191..198
200 fps:
201 fps: 102..142,144..190,192..201
202 fps: 53..92,94,96..100,102,104,106,108,110,112..153,155..202
203 fps: 35..203
204 fps: 27..204
205 fps: 21..147,149..205
206 fps: 18..206
207 fps: 16..207
208 fps: 14..208
209 fps: 13..209
210 fps: 11..210
211 fps: 11..111,113..211
212 fps: 10..79,81..212
213 fps: 9..106,108..213
214 fps: 9..214
215 fps: 8..161,163..215
216 fps: 8..40,42..148,150..216
217 fps: 7..213,215..217
218 fps: 7..218
219 fps: 7..219
220 fps: 6..115,117..121,124..125,128..220
221 fps: 6..221
222 fps: 6..222
223 fps: 5..199
224 fps: 5..59,61..178,180..201
225 fps: 6..20,22..80,82..85,87..101,103..139,141..148,150..157,159,161..163,165..182,184..203
226 fps: 6..204
227 fps: 6..206
228 fps: 6..208
229 fps: 6..210
230 fps: 7..95,97..212
231 fps: 7..115,117..122,124..213
232 fps: 7..94,96..215
233 fps: 8..217
234 fps: 8..164,166..219
235 fps: 9..221
236 fps: 9..223
237 fps: 10..225
238 fps: 11..227
239 fps: 12..228
240 fps: 13..61,63..64,66..67,69..70,72..73,75..76,78..79,81..82,84..133,135..136,138..139,141..145,147..148,150..151,153..154,156..205,207..217,219..220,222..223,225..226,228..230
241 fps: 14..37,39..232
242 fps: 16..234
243 fps: 18..236
244 fps: 21..183,185..238
245 fps: 26..240
246 fps: 32..184,186..242
247 fps: 42..244
248 fps: 63..134,136..159,161..164,166..174,176..184,186..246
249 fps: 125..139,141..172,174..202,204..237,239..248
250 fps:
251 fps: 127..177,179..251
252 fps: 64..140,142..252
253 fps: 43..253
254 fps: 33..64,67..190,192..193,195..254
255 fps: 26..130,132..255
256 fps: 22..256
257 fps: 19..257
258 fps: 17..258
259 fps: 15..134,136,138..259
260 fps: 14..260
261 fps: 13..261
262 fps: 12..118,120..262
263 fps: 11..138,140..257,259..263
264 fps: 10..148,150..156,158..264
265 fps: 10..265
266 fps: 9..266
267 fps: 9..267
268 fps: 8..268
269 fps: 8..144,146..269
270 fps: 8..43,45..270
271 fps: 7..271
272 fps: 7..209,211..212,214..215,217..272
273 fps: 7..273
274 fps: 7..274
275 fps: 6..242,244,246..275
276 fps: 6..276
277 fps: 6..277
278 fps: 6..278
279 fps: 6..279
280 fps: 6..66,68..126,129,131..132,136..192,195..199,201..262,264..280
281 fps: 6..281
282 fps: 5..79,81..282
283 fps: 5..283
284 fps: 5..284
285 fps: 5..162,164..285
286 fps: 4..245
287 fps: 4..247
288 fps: 4..249
289 fps: 4..251
290 fps: 4..252
291 fps: 4..254
292 fps: 5..256
293 fps: 5..258
294 fps: 5..259
295 fps: 5..261
296 fps: 5..263
297 fps: 5..76,78..265
298 fps: 5..266
299 fps: 5..268
300 fps: 5..22,25,27..28,30..52,54..55,57..58,60..77,82,85..103,105..106,108..109,111..130,133,135..136,138..139,141..158,160,162..163,165..166,168..184,186..187,189..190,192..193,195..211,214,216,219..241,243..244,246..268,270

Here are the things I have noticed in that data.

1. no errors until 35 fps, then 30% of the frame rates have errors until 45 fps, then 60% until 65 fps, 80% until 85 fps, then 90%+ beyond that. So the roundtrip errors increase as the fps increases.
2. no errors for 30 fps, which is surprising because pulse.mov is encoded at 30 fps. I see two important differences between our two experiments: I am using flv instead of mov, and I am rendering the current time as a floating point as black-on-white text instead of varying shades of solid grey. So perhaps the codec makes a difference. For example, maybe pulse.mov is stored in a way which does not store every frame, but instead describes the fact that the color is getting brighter over time. If a codec can save a lot of space at the cost of getting those small off-by-one-shade-of-gray errors @burkaman noticed, that sounds like a worthwhile tradeoff in most situations. Maybe the mov codec can take advantage of this optimization while flv cannot, or maybe the optimization can only be applied to smoothly-animated shades but not rapidly-changing text.
3. no errors at 50 fps, 100 fps, and 200 fps; nor at 125 fps and 250 fps. These round numbers remind me of a similar problem I've just fixed in a similar project, gloss-to-gif, in which roundtrip tests were also failing at some frame rates but succeeding when the frame rate was a round number. The problem there was that the gif format uses an integer number of centiseconds to express the delay between each frame; not every frame rate can be expressed as an exact number of centiseconds per frame, but round frame rates can. I thus solved the problem by converting the frame rate to centiseconds, rounding to an integer number of centiseconds, and using that approximate frame rate instead of the exact one requested by the user. Perhaps the mov and flv formats use a similar encoding under the hood?
4. While in the 60 fps: 27..60 example a single duplicated frame causes all later frames to also be incorrect, not all frame rates lead to such cascading errors. For example, 75 fps: 21..37,39..52,54..71,73 has a few correct frames in the middle of a bunch of incorrect frames. This tells me that ffmpeg-light's time tracking is not getting more and more out of sync with the real time, e.g. as it accumulates more and more rounding errors, instead it is successfully staying in sync, but it is often one frame off. That reminds me of a different problem I was having in gloss-to-gif. After loading the frames from disk, I was representing the animation using a function from Double to Frame. If the frame rate is 10 fps, that function would return the first frame from 0.0 to 0.1, then the second frame from 0.1 to 0.2, etc. When writing the frames back to disk, I was sampling that function at the requested frame rate. For example, at 10 fps I would sample 0.0, 0.1, 0.2, 0.3, etc. But those are exactly the discontinuity points! Since some of those fractional numbers cannot be expressed exactly as a Double, in practice I was sometimes sampling exactly at 0.1, sometimes at 0.1 minus epsilon, and sometimes at 0.1 plus epsilon, thus resulting in being off by one frame quite often. Is ffmpeg-light using a similar setup? My solution was to sample at the middle of the frames, so at 0.05, 0.15, etc.

[gelisam]

A roundtrip failure indicates that the encoding and the decoding don't match, but it doesn't say which of the two directions has the bug.

One advantage of rendering the timestamp over rendering a solid shade of grey is that is is easy to distinguish two frames visually. I took one of the videos exhibiting the glitch, and I compared the frames produced by ffmpeg-light's imageReaderTime to frames displayed by mplayer -fps 1. I did not see any difference, so I conclude that the problem must be somewhere in imageWriter.

[gelisam]

I did not see any difference, so I conclude that the problem must be somewhere in imageWriter.

Wait, that doesn't sound right: @burkaman tried the opposite, using ffmpeg to observe the frame count and then observing that imageReader reads a different number of frames. I'm starting to think there might be more than one bug here, which together explain the results we have observed.

[gelisam]

Turns out the file format matters a lot. If I change nothing except the name of the output file, from "pulse.mov" to "pulse.flv", then imageReader now reads back exactly 600 frames as expected.

[gelisam]

"pulse.gif" also yields 600 frames. I think I will restrict my attention to the gif format for now, since that's the one I am now the most familiar with thanks to my gloss-to-gif project. I re-did my experiment with gif instead of flv, and here is the resulting data. This time I am also including the value of 100/fps in parentheses, in order to check my hypothesis that it is only possible to roundtrip via gif when 100/fps is an integer.

my data

2 fps (50.0):
3 fps (33.333333333333336):
4 fps (25.0):
5 fps (20.0):
6 fps (16.666666666666668):
7 fps (14.285714285714286):
8 fps (12.5):
9 fps (11.11111111111111):
10 fps (10.0):
11 fps (9.090909090909092):
12 fps (8.333333333333334):
13 fps (7.6923076923076925):
14 fps (7.142857142857143):
15 fps (6.666666666666667):12..13,15
16 fps (6.25):13..14
17 fps (5.882352941176471):
18 fps (5.555555555555555):8..10,12..18
19 fps (5.2631578947368425):11..18
20 fps (5.0):
21 fps (4.761904761904762):13..18,20..21
22 fps (4.545454545454546):8..16,18..22
23 fps (4.3478260869565215):7..11,13..21
24 fps (4.166666666666667):14..22
25 fps (4.0):
26 fps (3.8461538461538463):14..19,22..26
27 fps (3.7037037037037037):8..14,17..27
28 fps (3.5714285714285716):6..10,13..17,19,21..28
29 fps (3.4482758620689653):4..14,16..25
30 fps (3.3333333333333335):6..7,9..10,12..13,15..22,25,27
31 fps (3.225806451612903):8..15,17..29
32 fps (3.125):16..17,22,26,29
33 fps (3.0303030303030303):
34 fps (2.9411764705882355):28,30..33
35 fps (2.857142857142857):13..18,20..25,27..31,33,35
36 fps (2.7777777777777777):8..13,15..16,18..24,26..27,29..31,33..36
37 fps (2.7027027027027026):6..9,11..20,22..37
38 fps (2.6315789473684212):5..9,12..32,34..38
39 fps (2.5641025641025643):4..22,24..39
40 fps (2.5):5
41 fps (2.4390243902439024):3..20,22..34
42 fps (2.380952380952381):4..10,12..35
43 fps (2.3255813953488373):4..21,23..37
44 fps (2.272727272727273):7..14,16..39
45 fps (2.2222222222222223):6..10,12,15..27,30..36,38..41
46 fps (2.1739130434782608):7..11,13..34,36..42
47 fps (2.127659574468085):9..22,25..44
48 fps (2.0833333333333335):13..25,29..30,33..40,42..46
49 fps (2.0408163265306123):26..29,31..45,47..48
50 fps (2.0):
51 fps (1.9607843137254901):28..44,46..51
52 fps (1.9230769230769231):14..19,21..32,34..52
53 fps (1.8867924528301887):10..26,28,30..46,48..52
54 fps (1.8518518518518519):8..13,16..26,28..29,31..54
55 fps (1.8181818181818181):6,8..18,20..30,32..36,38,40..42,44..54
56 fps (1.7857142857142858):6..19,21..27,29..31,33..38,40..56
57 fps (1.7543859649122806):5..32,34..57
58 fps (1.7241379310344827):5..14,16,18..58
59 fps (1.694915254237288):4..34,36..59
60 fps (1.6666666666666667):4..9,11..15,18,21..22,24..33,36..37,39..51,54..55,57..60
61 fps (1.639344262295082):4..37,39..61
62 fps (1.6129032258064515):4..15,17..62
63 fps (1.5873015873015872):3..31,33..63
64 fps (1.5625):3..18,20,22..25,27,29..37,39..58,60..62,64
65 fps (1.5384615384615385):3..8,10..25,27..32,34..58,61..65
66 fps (1.5151515151515151):3..29,31..52,54..66
67 fps (1.492537313432836):2..15,17..67
68 fps (1.4705882352941178):2..59,61..68
69 fps (1.4492753623188406):2..69
70 fps (1.4285714285714286):3..24,26..70
71 fps (1.408450704225352):2..71
72 fps (1.3888888888888888):2..72
73 fps (1.36986301369863):2..73
74 fps (1.3513513513513513):2..74
75 fps (1.3333333333333333):2..10,12..13,15..17,19..31,33..34,36..41,43..52,57..58,60..75
76 fps (1.3157894736842106):2..75
77 fps (1.2987012987012987):2..77
78 fps (1.2820512820512822):2..78
79 fps (1.2658227848101267):2..79
80 fps (1.25):2..5,7..65,68..70,72..73,77..78
81 fps (1.2345679012345678):2..81
82 fps (1.2195121951219512):2..55,57..82
83 fps (1.2048192771084338):2..83
84 fps (1.1904761904761905):2..84
85 fps (1.1764705882352942):2..76,78..85
86 fps (1.1627906976744187):2..86
87 fps (1.1494252873563218):2..87
88 fps (1.1363636363636365):2..49,51..88
89 fps (1.1235955056179776):2..89
90 fps (1.1111111111111112):2..40,42..90
91 fps (1.098901098901099):2..22,24..67,69..91
92 fps (1.0869565217391304):2..92
93 fps (1.075268817204301):2..93
94 fps (1.0638297872340425):2..94
95 fps (1.0526315789473684):2..41,43..75,77..90,93..95
96 fps (1.0416666666666667):2..96
97 fps (1.0309278350515463):2..97
98 fps (1.0204081632653061):2..31,33..98
99 fps (1.0101010101010102):2..99
100 fps (1.0):43,45,49..50
101 fps (0.9900990099009901):2..101
102 fps (0.9803921568627451):2..63,65..102
103 fps (0.970873786407767):2..80,82..103
104 fps (0.9615384615384616):2..71,73..104
105 fps (0.9523809523809523):2..29,31..99,101..105
106 fps (0.9433962264150944):2..106
107 fps (0.9345794392523364):2..107
108 fps (0.9259259259259259):2..94,96..108
109 fps (0.9174311926605505):2..59,61..109
110 fps (0.9090909090909091):2..24,26..60,62..108,110
111 fps (0.9009009009009009):2..111
112 fps (0.8928571428571429):2..112
113 fps (0.8849557522123894):2..113
114 fps (0.8771929824561403):2..114
115 fps (0.8695652173913043):2..39,41..102,104..115
116 fps (0.8620689655172413):2..116
117 fps (0.8547008547008547):2..117
118 fps (0.847457627118644):2..118
119 fps (0.8403361344537815):2..119
120 fps (0.8333333333333334):2..16,18..52,54..85,87..88,90..91,93..94,96..120
121 fps (0.8264462809917356):2..121
122 fps (0.819672131147541):2..122
123 fps (0.8130081300813008):2..123
124 fps (0.8064516129032258):2..124
125 fps (0.8):64..66,69,71,74..75
126 fps (0.7936507936507936):2..126
127 fps (0.7874015748031497):2..127
128 fps (0.78125):2..128
129 fps (0.7751937984496124):2..129
130 fps (0.7692307692307693):2..84,86..130
131 fps (0.7633587786259542):2..131
132 fps (0.7575757575757576):2..132
133 fps (0.7518796992481203):2..133
134 fps (0.746268656716418):2..134
135 fps (0.7407407407407407):2..135
136 fps (0.7352941176470589):2..136
137 fps (0.7299270072992701):2..137
138 fps (0.7246376811594203):2..138
139 fps (0.7194244604316546):2..139
140 fps (0.7142857142857143):2..45,47..52,54..140
141 fps (0.7092198581560284):2..141
142 fps (0.704225352112676):2..142
143 fps (0.6993006993006993):2..143
144 fps (0.6944444444444444):2..144
145 fps (0.6896551724137931):2..19,21..145
146 fps (0.684931506849315):2..146
147 fps (0.6802721088435374):2..147
148 fps (0.6756756756756757):2..148
149 fps (0.6711409395973155):2..149
150 fps (0.6666666666666666):2..3,5..12,14..16,18..19,21..22,24..25,27..28,30..45,47..48,50..57,59..61,63..64,66..67,69..70,72..73,75..106,108..109,111..112,114..115,117..118,120..135,137..150
151 fps (0.6622516556291391):2..151
152 fps (0.6578947368421053):2..142,144..152
153 fps (0.6535947712418301):2..153
154 fps (0.6493506493506493):2..154
155 fps (0.6451612903225806):2..155
156 fps (0.6410256410256411):2..156
157 fps (0.6369426751592356):2..157
158 fps (0.6329113924050633):2..158
159 fps (0.6289308176100629):2..134,136..159
160 fps (0.625):3..160
161 fps (0.6211180124223602):2..161
162 fps (0.6172839506172839):2..162
163 fps (0.6134969325153374):2..163
164 fps (0.6097560975609756):2..164
165 fps (0.6060606060606061):2..165
166 fps (0.6024096385542169):2..166
167 fps (0.5988023952095808):2..167
168 fps (0.5952380952380952):2..168
169 fps (0.591715976331361):2..169
170 fps (0.5882352941176471):2..144,146..170
171 fps (0.5847953216374269):2..171
172 fps (0.5813953488372093):2..172
173 fps (0.5780346820809249):2..173
174 fps (0.5747126436781609):2..174
175 fps (0.5714285714285714):2..52,54..59,61..66,68..175
176 fps (0.5681818181818182):2..176
177 fps (0.5649717514124294):2..177
178 fps (0.5617977528089888):2..178
179 fps (0.5586592178770949):2..102,104..179
180 fps (0.5555555555555556):2..76,78..85,87..180
181 fps (0.5524861878453039):2..97,99..181
182 fps (0.5494505494505495):2..182
183 fps (0.546448087431694):2..92,94..183
184 fps (0.5434782608695652):2..184
185 fps (0.5405405405405406):2..185
186 fps (0.5376344086021505):2..186
187 fps (0.5347593582887701):2..187
188 fps (0.5319148936170213):2..188
189 fps (0.5291005291005291):2..189
190 fps (0.5263157894736842):2..14,16..180,182..190
191 fps (0.5235602094240838):2..191
192 fps (0.5208333333333334):2..192
193 fps (0.5181347150259067):2..193
194 fps (0.5154639175257731):2..113,115..194
195 fps (0.5128205128205128):2..101,103..195
196 fps (0.5102040816326531):2..196
197 fps (0.5076142131979695):2..197
198 fps (0.5050505050505051):2..104,106..198
199 fps (0.5025125628140703):2..199
200 fps (0.5):3..4,7,9..11,13..15,17,19,29,31,33,37,39,41..90,93..106,109..110,113..116,119..140,161..200
201 fps (0.4975124378109453):2..201
202 fps (0.49504950495049505):3..202
203 fps (0.49261083743842365):2..203
204 fps (0.49019607843137253):2..204
205 fps (0.4878048780487805):2..205
206 fps (0.4854368932038835):2..206
207 fps (0.4830917874396135):2..207
208 fps (0.4807692307692308):2..208
209 fps (0.4784688995215311):2..209
210 fps (0.47619047619047616):2..151,153..210
211 fps (0.47393364928909953):2..211
212 fps (0.4716981132075472):2..212
213 fps (0.4694835680751174):2..213
214 fps (0.4672897196261682):2..214
215 fps (0.46511627906976744):2..215
216 fps (0.46296296296296297):2..216
217 fps (0.4608294930875576):2..217
218 fps (0.45871559633027525):2..218
219 fps (0.45662100456621):2..219
220 fps (0.45454545454545453):2..10,12..115,117..126,128..220
221 fps (0.45248868778280543):2..221
222 fps (0.45045045045045046):2..222
223 fps (0.4484304932735426):2..223
224 fps (0.44642857142857145):2..224
225 fps (0.4444444444444444):2..18,20..94,96..103,105..169,171..188,190..197,199..225
226 fps (0.4424778761061947):2..226
227 fps (0.44052863436123346):2..227
228 fps (0.43859649122807015):2..228
229 fps (0.4366812227074236):2..177,179..229
230 fps (0.43478260869565216):2..16,18..230
231 fps (0.4329004329004329):2..172,174..231
232 fps (0.43103448275862066):2..232
233 fps (0.4291845493562232):2..167,169..233
234 fps (0.42735042735042733):2..234
235 fps (0.425531914893617):2..235
236 fps (0.423728813559322):2..236
237 fps (0.4219409282700422):2..237
238 fps (0.42016806722689076):2..238
239 fps (0.41841004184100417):2..239
240 fps (0.4166666666666667):2..6,8..18,20..240
241 fps (0.4149377593360996):2..241
242 fps (0.4132231404958678):2..224,226..242
243 fps (0.411522633744856):2..243
244 fps (0.4098360655737705):2..244
245 fps (0.40816326530612246):2..133,135..186,188..245
246 fps (0.4065040650406504):2..246
247 fps (0.4048582995951417):2..247
248 fps (0.4032258064516129):2..248
249 fps (0.40160642570281124):2..249
250 fps (0.4):65,72,75,77,92,97,100..102,107,109..112,115..117,120..122,124..125
251 fps (0.398406374501992):2..222,224..251
252 fps (0.3968253968253968):2..252
253 fps (0.3952569169960474):2..253
254 fps (0.3937007874015748):2..254
255 fps (0.39215686274509803):2..212,214..255
256 fps (0.390625):2..256
257 fps (0.38910505836575876):2..207,209..257
258 fps (0.3875968992248062):2..258
259 fps (0.3861003861003861):2..259
260 fps (0.38461538461538464):2..162,164..175,177..260
261 fps (0.3831417624521073):2..261
262 fps (0.3816793893129771):2..262
263 fps (0.38022813688212925):2..155,157..263
264 fps (0.3787878787878788):2..264
265 fps (0.37735849056603776):2..152,154..265
266 fps (0.37593984962406013):2..266
267 fps (0.37453183520599254):2..149,151..267
268 fps (0.373134328358209):2..268
269 fps (0.37174721189591076):2..146,148..269
270 fps (0.37037037037037035):2..158,160..196,198..270
271 fps (0.36900369003690037):2..143,145..271
272 fps (0.36764705882352944):2..211,213..272
273 fps (0.3663003663003663):2..140,142..273
274 fps (0.36496350364963503):2..274
275 fps (0.36363636363636365):2..137,139..148,150..159,161..171,173..194,196..216,218..275
276 fps (0.36231884057971014):2..276
277 fps (0.36101083032490977):2..277
278 fps (0.3597122302158273):2..278
279 fps (0.35842293906810035):2..279
280 fps (0.35714285714285715):2..280
281 fps (0.35587188612099646):2..281
282 fps (0.3546099290780142):2..282
283 fps (0.35335689045936397):2..283
284 fps (0.352112676056338):2..284
285 fps (0.3508771929824561):2..285
286 fps (0.34965034965034963):2..286
287 fps (0.34843205574912894):2..60,62..287
288 fps (0.3472222222222222):2..288
289 fps (0.3460207612456747):2..289
290 fps (0.3448275862068966):2..290
291 fps (0.3436426116838488):2..291
292 fps (0.3424657534246575):2..292
293 fps (0.3412969283276451):2..293
294 fps (0.3401360544217687):2..294
295 fps (0.3389830508474576):2..295
296 fps (0.33783783783783783):2..296
297 fps (0.3367003367003367):2..297
298 fps (0.33557046979865773):2..298
299 fps (0.33444816053511706):2..299
300 fps (0.3333333333333333):2..18,20..31,33..34,36..37,39..40,42..43,45..46,48..49,51..52,54..55,57..58,60..124,126..127,129..142,144..211,213..214,216..217,219..220,222..223,225..226,228..229,231..232,234..235,237..238,240..251,253..300

My hypothesis looked good for a while, but then the 100 fps case falsified it! I think that means there are at least two bugs. Assuming that the fact that some frame rates are unrepresentable in the target format and that the 100 fps case can be represented in a gif, that 100 fps case should only have one bug (or at least one fewer bug), so I plan to focus on that case next.