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2.2.1 Integrals 1 to 53

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 Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 155 231 153 624 2111 639 721 158

N.S.

1 0.97 1.44 0.96 3.90 13.19 3.99 4.51 0.99

time (sec)

N/A 0.329 3.219 0.343 0.216 0.270 14.402 0.330 2.114

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 108 127 112 410 1164 478 447 111

N.S.

1 0.98 1.15 1.02 3.73 10.58 4.35 4.06 1.01

time (sec)

N/A 0.288 2.254 0.245 0.206 0.254 5.832 0.316 2.045

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 75 100 75 239 557 332 241 72

N.S.

1 1.01 1.35 1.01 3.23 7.53 4.49 3.26 0.97

time (sec)

N/A 0.259 1.508 0.177 0.203 0.267 2.329 0.291 2.006

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 47 65 46 114 197 211 103 41

N.S.

1 1.09 1.51 1.07 2.65 4.58 4.91 2.40 0.95

time (sec)

N/A 0.234 0.494 0.119 0.194 0.262 1.086 0.277 0.125

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 45 47 71 56 488 253 65 37

N.S.

1 0.98 1.02 1.54 1.22 10.61 5.50 1.41 0.80

time (sec)

N/A 0.339 0.080 0.130 0.291 0.280 2.489 0.276 0.122

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 106 97 103 207 1952 0 198 110

N.S.

1 1.19 1.09 1.16 2.33 21.93 0.00 2.22 1.24

time (sec)

N/A 0.277 0.626 0.211 0.320 0.327 0.000 0.293 2.313

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 170 147 156 509 7508 0 409 2719

N.S.

1 1.20 1.04 1.10 3.58 52.87 0.00 2.88 19.15

time (sec)

N/A 0.337 0.349 0.306 0.386 0.382 0.000 0.325 2.712

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 239 203 219 925 20031 0 750 3685

N.S.

1 1.19 1.01 1.09 4.60 99.66 0.00 3.73 18.33

time (sec)

N/A 0.437 0.598 0.485 0.506 0.521 0.000 0.357 2.810

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 27 38 70 34 38 15

N.S.

1 1.00 1.00 1.42 2.00 3.68 1.79 2.00 0.79

time (sec)

N/A 0.279 0.115 0.088 0.283 0.265 0.274 0.268 0.114

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A C B F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 30 4 19 45 0 26 3

N.S.

1 1.00 10.00 1.33 6.33 15.00 0.00 8.67 1.00

time (sec)

N/A 0.223 0.053 0.188 0.277 0.253 0.000 0.284 1.905

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 16 28 15 17 17 0 23 14

N.S.

1 1.14 2.00 1.07 1.21 1.21 0.00 1.64 1.00

time (sec)

N/A 0.237 0.048 0.109 0.279 0.255 0.000 0.291 2.089

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A C B F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 26 51 21 49 279 0 60 20

N.S.

1 1.08 2.12 0.88 2.04 11.62 0.00 2.50 0.83

time (sec)

N/A 0.238 0.102 0.095 0.302 0.282 0.000 0.274 1.946

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 35 49 28 46 211 0 52 27

N.S.

1 1.13 1.58 0.90 1.48 6.81 0.00 1.68 0.87

time (sec)

N/A 0.241 0.087 0.143 0.301 0.259 0.000 0.268 1.917

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C B F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 15 13 14 11 40 0 24 18

N.S.

1 1.15 1.00 1.08 0.85 3.08 0.00 1.85 1.38

time (sec)

N/A 0.233 0.042 0.127 0.280 0.261 0.000 0.271 2.092

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 13 11 12 11 2 0 18 15

N.S.

1 1.18 1.00 1.09 1.00 0.18 0.00 1.64 1.36

time (sec)

N/A 0.228 0.040 0.059 0.276 0.255 0.000 0.283 1.969

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 68 60 253 0 2367 0 0 66

N.S.

1 1.08 0.95 4.02 0.00 37.57 0.00 0.00 1.05

time (sec)

N/A 0.302 0.200 0.211 0.000 0.363 0.000 0.000 3.902

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 89 191 276 0 4877 0 0 0

N.S.

1 1.05 2.25 3.25 0.00 57.38 0.00 0.00 0.00

time (sec)

N/A 0.325 0.836 0.140 0.000 0.434 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 49 44 238 0 1551 0 0 51

N.S.

1 1.11 1.00 5.41 0.00 35.25 0.00 0.00 1.16

time (sec)

N/A 0.265 0.035 0.094 0.000 0.313 0.000 0.000 2.335

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 82 238 0 3455 0 262 0

N.S.

1 1.00 1.37 3.97 0.00 57.58 0.00 4.37 0.00

time (sec)

N/A 0.237 0.329 0.139 0.000 0.369 0.000 0.477 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 61 56 0 0 3479 0 259 0

N.S.

1 1.09 1.00 0.00 0.00 62.12 0.00 4.62 0.00

time (sec)

N/A 0.289 0.038 0.000 0.000 0.380 0.000 0.512 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 48 42 0 0 1539 0 0 0

N.S.

1 1.00 0.88 0.00 0.00 32.06 0.00 0.00 0.00

time (sec)

N/A 0.278 0.101 0.000 0.000 0.324 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 89 86 488 0 4940 0 0 112

N.S.

1 1.09 1.05 5.95 0.00 60.24 0.00 0.00 1.37

time (sec)

N/A 0.317 0.437 0.093 0.000 0.470 0.000 0.000 9.988

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 132 219 529 0 10286 0 0 0

N.S.

1 1.07 1.78 4.30 0.00 83.63 0.00 0.00 0.00

time (sec)

N/A 0.431 0.951 0.098 0.000 0.597 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 70 59 473 0 2362 0 0 64

N.S.

1 1.11 0.94 7.51 0.00 37.49 0.00 0.00 1.02

time (sec)

N/A 0.276 0.164 0.074 0.000 0.373 0.000 0.000 4.154

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 92 111 473 0 5037 0 0 0

N.S.

1 1.05 1.26 5.38 0.00 57.24 0.00 0.00 0.00

time (sec)

N/A 0.284 0.578 0.125 0.000 0.429 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 76 71 0 0 3949 0 470 0

N.S.

1 1.07 1.00 0.00 0.00 55.62 0.00 6.62 0.00

time (sec)

N/A 0.324 0.076 0.000 0.000 0.426 0.000 3.809 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 77 180 0 0 4025 0 0 0

N.S.

1 1.00 2.34 0.00 0.00 52.27 0.00 0.00 0.00

time (sec)

N/A 0.342 0.468 0.000 0.000 0.417 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 60 97 0 683 0 119 68

N.S.

1 1.00 1.94 3.13 0.00 22.03 0.00 3.84 2.19

time (sec)

N/A 0.209 0.120 0.229 0.000 0.261 0.000 0.282 2.038

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 62 142 0 226 0 124 43

N.S.

1 1.00 1.38 3.16 0.00 5.02 0.00 2.76 0.96

time (sec)

N/A 0.227 0.082 0.203 0.000 0.255 0.000 0.302 2.014

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 53 116 158 0 1043 0 265 78

N.S.

1 1.06 2.32 3.16 0.00 20.86 0.00 5.30 1.56

time (sec)

N/A 0.230 0.415 0.103 0.000 0.276 0.000 0.287 2.120

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 70 118 211 0 361 0 285 0

N.S.

1 1.04 1.76 3.15 0.00 5.39 0.00 4.25 0.00

time (sec)

N/A 0.248 0.264 0.107 0.000 0.262 0.000 0.309 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 52 47 129 0 1576 0 0 39

N.S.

1 1.11 1.00 2.74 0.00 33.53 0.00 0.00 0.83

time (sec)

N/A 0.280 0.099 0.117 0.000 0.315 0.000 0.000 2.388

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 134 137 0 3513 0 0 0

N.S.

1 1.00 2.23 2.28 0.00 58.55 0.00 0.00 0.00

time (sec)

N/A 0.297 0.238 0.118 0.000 0.394 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 114 0 1298 0 196 23

N.S.

1 1.00 1.00 3.93 0.00 44.76 0.00 6.76 0.79

time (sec)

N/A 0.255 0.021 0.155 0.000 0.296 0.000 0.419 2.306

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 77 114 0 1357 0 196 25

N.S.

1 1.00 2.48 3.68 0.00 43.77 0.00 6.32 0.81

time (sec)

N/A 0.202 0.137 0.137 0.000 0.298 0.000 0.388 2.223

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 61 56 0 0 3397 0 0 0

N.S.

1 1.09 1.00 0.00 0.00 60.66 0.00 0.00 0.00

time (sec)

N/A 0.292 0.045 0.000 0.000 0.386 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

51 51 127 0 0 1621 0 0 0

N.S.

1 1.00 2.49 0.00 0.00 31.78 0.00 0.00 0.00

time (sec)

N/A 0.287 0.774 0.000 0.000 0.325 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 58 52 287 0 2541 0 359 45

N.S.

1 1.12 1.00 5.52 0.00 48.87 0.00 6.90 0.87

time (sec)

N/A 0.301 0.164 0.097 0.000 0.358 0.000 0.459 2.769

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 109 289 0 2279 0 363 0

N.S.

1 1.00 2.06 5.45 0.00 43.00 0.00 6.85 0.00

time (sec)

N/A 0.294 1.107 0.100 0.000 0.351 0.000 0.459 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 54 41 273 0 2299 0 364 41

N.S.

1 1.10 0.84 5.57 0.00 46.92 0.00 7.43 0.84

time (sec)

N/A 0.278 0.047 0.075 0.000 0.355 0.000 0.471 2.613

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

78 98 70 0 0 6991 0 0 0

N.S.

1 1.26 0.90 0.00 0.00 89.63 0.00 0.00 0.00

time (sec)

N/A 0.345 0.063 0.000 0.000 0.545 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 91 260 0 0 3931 0 540 0

N.S.

1 1.07 3.06 0.00 0.00 46.25 0.00 6.35 0.00

time (sec)

N/A 0.369 7.926 0.000 0.000 0.506 0.000 0.599 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 86 63 435 0 6560 0 951 82

N.S.

1 1.16 0.85 5.88 0.00 88.65 0.00 12.85 1.11

time (sec)

N/A 0.322 0.119 0.105 0.000 0.689 0.000 0.596 4.250

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

88 97 215 454 0 6591 0 952 0

N.S.

1 1.10 2.44 5.16 0.00 74.90 0.00 10.82 0.00

time (sec)

N/A 0.334 7.067 0.104 0.000 0.682 0.000 0.551 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 82 43 420 0 5736 0 909 76

N.S.

1 1.17 0.61 6.00 0.00 81.94 0.00 12.99 1.09

time (sec)

N/A 0.292 0.048 0.081 0.000 0.630 0.000 0.575 4.332

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 142 73 0 0 19199 0 0 0

N.S.

1 1.31 0.68 0.00 0.00 177.77 0.00 0.00 0.00

time (sec)

N/A 0.392 0.072 0.000 0.000 1.242 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 148 1350 0 0 10729 0 1133 0

N.S.

1 1.13 10.31 0.00 0.00 81.90 0.00 8.65 0.00

time (sec)

N/A 0.454 8.544 0.000 0.000 1.296 0.000 0.769 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 62 0 547 0 69 63

N.S.

1 1.00 1.00 2.48 0.00 21.88 0.00 2.76 2.52

time (sec)

N/A 0.199 0.071 0.200 0.000 0.253 0.000 0.265 2.096

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F C B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

27 27 49 66 0 175 0 73 22

N.S.

1 1.00 1.81 2.44 0.00 6.48 0.00 2.70 0.81

time (sec)

N/A 0.202 0.079 0.198 0.000 0.263 0.000 0.267 2.189

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 40 40 41 73 95 102 25 38

N.S.

1 1.05 1.05 1.08 1.92 2.50 2.68 0.66 1.00

time (sec)

N/A 0.317 0.093 0.099 0.289 0.273 0.500 0.263 0.106

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 90 86 116 0 5172 0 0 0

N.S.

1 1.01 0.97 1.30 0.00 58.11 0.00 0.00 0.00

time (sec)

N/A 0.343 0.170 0.815 0.000 0.402 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 43 40 37 0 1290 0 0 0

N.S.

1 1.08 1.00 0.92 0.00 32.25 0.00 0.00 0.00

time (sec)

N/A 0.275 0.021 0.577 0.000 0.406 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 77 73 431 0 3938 0 0 0

N.S.

1 1.04 0.99 5.82 0.00 53.22 0.00 0.00 0.00

time (sec)

N/A 0.316 0.528 0.670 0.000 0.495 0.000 0.000 0.000

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