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Integrals 1 to 46

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 218 756 936 1085 0 0 190 0

N.S.

1 1.00 0.96 3.33 4.12 4.78 0.00 0.00 0.84 0.00

time (sec)

N/A 0.461 0.080 0.454 0.231 0.136 0.000 0.000 0.203 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 151 440 516 675 0 0 138 0

N.S.

1 1.00 0.96 2.80 3.29 4.30 0.00 0.00 0.88 0.00

time (sec)

N/A 0.365 0.098 0.218 0.199 0.121 0.000 0.000 0.192 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 87 142 0 343 0 0 79 0

N.S.

1 1.00 0.94 1.53 0.00 3.69 0.00 0.00 0.85 0.00

time (sec)

N/A 0.277 0.043 0.085 0.000 0.105 0.000 0.000 0.188 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

18 18 20 18 116 20 22 20 34 22

N.S.

1 1.00 1.11 1.00 6.44 1.11 1.22 1.11 1.89 1.22

time (sec)

N/A 0.206 4.857 0.111 0.298 0.085 0.633 0.198 0.193 15.115

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

18 18 20 18 172 31 46 20 82 22

N.S.

1 1.00 1.11 1.00 9.56 1.72 2.56 1.11 4.56 1.22

time (sec)

N/A 0.203 3.958 0.076 0.340 0.076 2.469 1.469 0.195 15.324

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

371 371 329 1517 3403 1887 0 0 222 0

N.S.

1 1.00 0.89 4.09 9.17 5.09 0.00 0.00 0.60 0.00

time (sec)

N/A 0.730 1.328 0.426 0.447 0.162 0.000 0.000 0.193 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

262 262 232 679 1704 1096 0 0 173 0

N.S.

1 1.00 0.89 2.59 6.50 4.18 0.00 0.00 0.66 0.00

time (sec)

N/A 0.569 1.752 0.277 0.393 0.137 0.000 0.000 0.194 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 123 191 0 525 0 0 118 0

N.S.

1 1.00 0.92 1.43 0.00 3.92 0.00 0.00 0.88 0.00

time (sec)

N/A 0.343 0.732 0.092 0.000 0.109 0.000 0.000 0.192 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 507 37 41 22 70 24

N.S.

1 1.00 1.10 1.00 25.35 1.85 2.05 1.10 3.50 1.20

time (sec)

N/A 0.222 20.926 0.101 0.727 0.081 1.172 1.055 0.195 15.005

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 624 48 76 22 157 24

N.S.

1 1.00 1.10 1.00 31.20 2.40 3.80 1.10 7.85 1.20

time (sec)

N/A 0.222 16.825 0.100 1.026 0.081 2.447 36.676 0.194 14.805

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 216 417 1285 516 0 0 182 0

N.S.

1 1.00 1.42 2.74 8.45 3.39 0.00 0.00 1.20 0.00

time (sec)

N/A 0.540 1.381 0.175 0.255 0.094 0.000 0.000 0.193 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B F F F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

119 119 528 236 377 292 0 0 123 0

N.S.

1 1.00 4.44 1.98 3.17 2.45 0.00 0.00 1.03 0.00

time (sec)

N/A 0.468 6.445 0.140 0.220 0.081 0.000 0.000 0.175 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A F B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 104 53 273 99 0 248 68 79

N.S.

1 1.00 1.55 0.79 4.07 1.48 0.00 3.70 1.01 1.18

time (sec)

N/A 0.304 0.625 0.152 0.116 0.077 0.000 0.224 0.177 15.245

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 391 27 27 22 30 24

N.S.

1 1.00 1.10 1.00 19.55 1.35 1.35 1.10 1.50 1.20

time (sec)

N/A 0.233 6.380 0.079 0.337 0.067 1.095 0.155 0.194 14.783

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 522 51 58 22 58 24

N.S.

1 1.00 1.10 1.00 26.10 2.55 2.90 1.10 2.90 1.20

time (sec)

N/A 0.231 4.770 0.076 0.646 0.068 2.317 0.456 0.202 14.774

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B F F F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

288 288 1447 810 4283 933 0 0 418 0

N.S.

1 1.00 5.02 2.81 14.87 3.24 0.00 0.00 1.45 0.00

time (sec)

N/A 0.931 7.294 0.248 1.086 0.106 0.000 0.000 0.184 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B F F F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

229 229 925 453 1035 493 0 0 246 0

N.S.

1 1.00 4.04 1.98 4.52 2.15 0.00 0.00 1.07 0.00

time (sec)

N/A 0.725 6.760 0.193 0.540 0.091 0.000 0.000 0.181 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A F B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 172 86 1058 183 0 798 112 247

N.S.

1 1.00 1.23 0.61 7.56 1.31 0.00 5.70 0.80 1.76

time (sec)

N/A 0.412 1.368 0.190 0.148 0.085 0.000 0.407 0.181 20.466

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 3956 57 54 22 53 24

N.S.

1 1.00 1.10 1.00 197.80 2.85 2.70 1.10 2.65 1.20

time (sec)

N/A 0.228 9.967 0.102 9.213 0.080 2.373 0.235 0.189 14.894

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 4471 99 105 22 100 24

N.S.

1 1.00 1.10 1.00 223.55 4.95 5.25 1.10 5.00 1.20

time (sec)

N/A 0.230 12.202 0.094 31.443 0.078 9.290 1.001 0.190 15.195

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 22 22 0 22 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.10 1.20

time (sec)

N/A 0.221 0.842 0.121 0.397 0.087 0.000 0.261 0.185 14.767

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

18 18 20 18 124 20 24 20 28 22

N.S.

1 1.00 1.11 1.00 6.89 1.11 1.33 1.11 1.56 1.22

time (sec)

N/A 0.203 8.448 0.068 0.176 0.070 7.613 0.191 0.187 14.767

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 22 22 17 22 140 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 7.00 1.20

time (sec)

N/A 0.225 0.851 0.063 0.308 0.075 2.441 0.133 0.182 14.472

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 365 756 936 1085 0 0 229 0

N.S.

1 1.00 1.61 3.33 4.12 4.78 0.00 0.00 1.01 0.00

time (sec)

N/A 0.440 0.334 0.258 0.235 0.137 0.000 0.000 0.192 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 203 440 516 675 0 0 161 0

N.S.

1 1.00 1.29 2.80 3.29 4.30 0.00 0.00 1.03 0.00

time (sec)

N/A 0.363 0.173 0.181 0.181 0.123 0.000 0.000 0.184 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 104 142 0 343 0 0 93 0

N.S.

1 1.00 1.12 1.53 0.00 3.69 0.00 0.00 1.00 0.00

time (sec)

N/A 0.283 0.010 0.080 0.000 0.106 0.000 0.000 0.171 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

18 18 20 18 116 20 15 20 59 22

N.S.

1 1.00 1.11 1.00 6.44 1.11 0.83 1.11 3.28 1.22

time (sec)

N/A 0.205 0.666 0.069 0.283 0.077 0.795 0.238 0.185 15.086

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

18 18 20 18 172 31 17 20 85 22

N.S.

1 1.00 1.11 1.00 9.56 1.72 0.94 1.11 4.72 1.22

time (sec)

N/A 0.204 1.062 0.059 0.323 0.071 2.936 1.699 0.185 15.407

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

364 364 646 1489 3267 1823 0 0 1395 0

N.S.

1 1.00 1.77 4.09 8.98 5.01 0.00 0.00 3.83 0.00

time (sec)

N/A 0.754 1.670 0.412 0.479 0.169 0.000 0.000 0.209 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B B B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 356 662 1641 1056 0 0 742 0

N.S.

1 1.00 1.39 2.58 6.39 4.11 0.00 0.00 2.89 0.00

time (sec)

N/A 0.572 1.011 0.317 0.266 0.147 0.000 0.000 0.189 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 151 190 0 505 0 0 343 0

N.S.

1 1.00 1.15 1.45 0.00 3.85 0.00 0.00 2.62 0.00

time (sec)

N/A 0.344 0.376 0.103 0.000 0.113 0.000 0.000 0.183 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 501 36 17 22 124 24

N.S.

1 1.00 1.10 1.00 25.05 1.80 0.85 1.10 6.20 1.20

time (sec)

N/A 0.229 39.276 0.148 1.089 0.086 1.205 1.834 0.207 14.711

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 618 47 19 22 172 24

N.S.

1 1.00 1.10 1.00 30.90 2.35 0.95 1.10 8.60 1.20

time (sec)

N/A 0.224 22.007 0.104 1.114 0.080 2.504 56.267 0.188 15.229

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F(-2) B F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD TBD

size

526 526 449 0 0 2309 0 0 616 0

N.S.

1 1.00 0.85 0.00 0.00 4.39 0.00 0.00 1.17 0.00

time (sec)

N/A 1.317 0.988 0.000 0.000 0.294 0.000 0.000 0.195 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F(-2) B F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD TBD

size

394 394 338 0 0 1625 0 0 431 0

N.S.

1 1.00 0.86 0.00 0.00 4.12 0.00 0.00 1.09 0.00

time (sec)

N/A 1.093 0.751 0.000 0.000 0.241 0.000 0.000 0.176 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F(-2) B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 214 516 0 1041 0 0 248 0

N.S.

1 1.00 0.83 2.01 0.00 4.05 0.00 0.00 0.96 0.00

time (sec)

N/A 0.746 0.499 0.152 0.000 0.228 0.000 0.000 0.160 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 298 27 17 22 793 24

N.S.

1 1.00 1.10 1.00 14.90 1.35 0.85 1.10 39.65 1.20

time (sec)

N/A 0.228 1.171 0.091 0.638 0.071 1.188 0.214 0.180 14.775

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 439 51 19 22 2871 24

N.S.

1 1.00 1.10 1.00 21.95 2.55 0.95 1.10 143.55 1.20

time (sec)

N/A 0.228 8.863 0.087 1.006 0.073 2.409 0.571 0.210 14.806

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B F F(-2) B F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD TBD

size

1523 1523 20116 0 0 7008 0 0 0 0

N.S.

1 1.00 13.21 0.00 0.00 4.60 0.00 0.00 0.00 0.00

time (sec)

N/A 3.301 19.830 0.000 0.000 0.491 0.000 0.000 0.403 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B F F(-2) B F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD TBD

size

1117 1117 3365 0 0 4274 0 0 0 0

N.S.

1 1.00 3.01 0.00 0.00 3.83 0.00 0.00 0.00 0.00

time (sec)

N/A 2.505 16.570 0.000 0.000 0.354 0.000 0.000 0.228 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F(-2) B F F F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

582 582 1037 1289 0 2080 0 0 0 0

N.S.

1 1.00 1.78 2.21 0.00 3.57 0.00 0.00 0.00 0.00

time (sec)

N/A 1.374 9.871 0.208 0.000 0.282 0.000 0.000 0.183 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 2279 55 19 22 5490 24

N.S.

1 1.00 1.10 1.00 113.95 2.75 0.95 1.10 274.50 1.20

time (sec)

N/A 0.237 15.680 0.110 11.922 0.087 2.288 0.337 0.280 19.073

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 2918 96 20 22 19510 24

N.S.

1 1.00 1.10 1.00 145.90 4.80 1.00 1.10 975.50 1.20

time (sec)

N/A 0.228 32.978 0.116 37.638 0.107 9.632 2.984 0.361 16.287

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 22 22 0 22 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.10 1.20

time (sec)

N/A 0.225 1.761 0.102 0.502 0.093 0.000 0.294 0.183 15.659

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

18 18 20 18 124 20 17 20 113 22

N.S.

1 1.00 1.11 1.00 6.89 1.11 0.94 1.11 6.28 1.22

time (sec)

N/A 0.204 0.424 0.058 0.174 0.080 5.758 0.164 0.168 15.049

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

20 20 22 20 22 22 17 22 326 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 16.30 1.20

time (sec)

N/A 0.231 0.596 0.068 0.307 0.071 2.669 0.203 0.191 15.291

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