proof (proof_412)

Race #554

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Official speed 74.80 wpm (69.14 seconds elapsed during race)
Without ending ping 75.04 wpm (219 ms delay sending score to TypeRacer’s server)
Timerless 75.39 wpm (326 ms elapsed before first character typed; 68.60 seconds elapsed during race)
Timerless minus one 75.22 wpm, ignoring the first character typed
Race Start October 10, 2023 5:12:49pm UTC
Race Finish October 10, 2023 5:13:59pm UTC
Outcome No win (3 of 5)
Opponents 1. koppix (83.05 wpm)
Accuracy 98.1%
Points 87.27
Text #4940061 (Length: 431 characters)

The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous. See how they make the solution of difference equations into child's play. Then see how the theory of functions of a complex variable gives, virtually by inspection, the approximate size of the solution. The interplay between the two channels is vitally important for the appreciation of the music.
Characters typed The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continouuous. See how they make the solution of fdifference equaitions into child's play . Then see how the theory of functions of a occomplex cavariable gives, vurtirtually by inspection, the approximate size of the solution. The itnernterplay between the two channels is vitally important for the appreciation of the music.
Timing
Character T h e f u l l b e a u t y o f t h e s u
Milliseconds 326 246 82 97 108 108 161 138 88 106 95 153 175 126 114 138 110 100 82 126 90 101 73 143 408
Character b j e c t o f g e n e r a t i n g f u n c t
Milliseconds 215 204 90 107 243 72 148 89 91 341 382 164 100 180 232 167 105 149 84 118 184 148 184 114 177
Character i o n s e m e r g e s o n l y f r o m t u
Milliseconds 73 53 152 85 123 209 131 104 138 179 191 162 80 121 135 128 153 86 200 172 96 95 106 215 84
Character n i n g i n o n b o t h c h a n n e l s :
Milliseconds 182 138 108 96 97 205 146 101 91 111 80 399 158 121 121 85 194 81 112 100 147 107 110 149 282
Character t h e d i s c r e t e a n d t h e c o n
Milliseconds 136 207 71 111 62 151 61 125 132 265 115 244 144 151 157 137 43 163 107 111 56 138 117 105 149
Character t i n o u -u -o u o u s . S e e h o w t h e y
Milliseconds 95 102 140 132 174 554 135 372 213 275 503 355 141 381 230 144 88 130 139 76 109 95 106 75 92
Character m a k e t h e s o l u t i o n o f f -f d
Milliseconds 86 141 95 112 87 94 271 131 69 90 144 60 171 190 93 181 125 149 99 116 88 89 135 335 144
Character i f f e r e n c e e q u a i -i t i o n s i n t
Milliseconds 83 268 132 125 116 113 179 71 104 353 126 525 385 144 211 358 191 91 144 156 100 98 144 127 83
Character o c h i l d ' s p l a y - . T h e n s e
Milliseconds 126 90 280 102 114 118 212 129 198 80 213 208 128 147 325 325 277 127 327 151 106 108 98 159 138
Character e h o w t h e t h e o r y o f f u n c t
Milliseconds 114 60 167 143 67 112 112 71 111 98 123 71 140 11 232 81 161 133 102 100 125 148 178 51 218
Character i o n s o f a o c -c -o c o m p l e x c a -a
Milliseconds 102 43 176 94 97 148 135 123 119 94 140 82 448 173 239 68 184 114 198 195 304 219 226 131 286
Character -c v a r i a b l e g i v e s , v u r t -t -r -u i
Milliseconds 152 89 136 89 141 128 106 200 113 84 251 153 157 154 177 119 98 346 196 118 209 250 137 319 187
Character r t u a l l y b y i n s p e c t i o n , t h
Milliseconds 151 189 134 132 144 127 193 63 151 187 106 208 123 105 167 80 152 185 102 22 171 190 70 190 118
Character e a p p r o x i m a t e s i z e o f t h e
Milliseconds 101 91 125 82 140 123 85 457 227 227 83 146 173 66 195 71 413 259 95 126 96 120 237 36 147
Character s o l u t i o n . T h e i t n e r -r -e -n -t n
Milliseconds 77 143 53 157 199 134 124 107 188 190 80 341 170 137 58 135 174 11 176 105 293 280 145 131 314
Character t e r p l a y b e t w e e n t h e t w o c
Milliseconds 89 207 187 234 174 141 155 122 201 94 150 145 56 139 175 62 236 134 52 128 124 327 113 132 176
Character h a n n e l s i s v i t a l l y i m p o r t
Milliseconds 92 101 109 129 102 104 81 107 110 127 89 143 166 108 130 108 105 186 62 190 152 122 64 98 163
Character a n t f o r t h e a p p r e c i a t i o n
Milliseconds 114 189 97 155 71 125 109 154 88 129 146 182 146 256 142 81 98 178 415 218 135 57 90 132 150
Character o f t h e m u s i c .
Milliseconds 186 99 145 104 90 106 65 162 203 88 87 152 105
WPM Timing
Seconds WPM
1.38 78.1
2.77 86.77
4.15 83.88
5.53 78.1
6.91 78.1
8.3 80.99
9.68 81.82
11.06 82.44
12.45 82.92
13.83 83.3
15.21 84.41
16.59 83.16
17.98 85.44
19.36 79.96
20.74 76.94
22.13 77.01
23.51 78.61
24.89 79.54
26.27 78.55
27.66 78.1
29.04 75.62
30.42 76.13
31.81 76.21
33.19 74.48
34.57 74.63
35.96 76.43
37.34 76.81
38.72 77.48
40.1 76
41.49 74.63
42.87 74.74
44.25 74.3
45.64 72.31
47.02 72.74
48.4 73.39
49.78 73.76
51.17 73.41
52.55 73.53
53.93 73.87
55.32 73.98
56.7 72.38
58.08 72.11
59.46 72.45
60.85 72.77
62.23 73.47
63.61 73.95
65 74.4
66.38 74.3
67.76 74.38
69.14 74.8