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Integrals 301 to 398

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 301

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

32 38 32 26 25 27 37 25 22 27

N.S.

1 1.19 1.00 0.81 0.78 0.84 1.16 0.78 0.69 0.84

time (sec)

N/A 0.308 0.036 0.166 0.128 0.086 0.111 0.132 0.189 0.035

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

76 83 49 53 0 95 0 45 128 0

N.S.

1 1.09 0.64 0.70 0.00 1.25 0.00 0.59 1.68 0.00

time (sec)

N/A 0.319 0.331 0.020 0.000 0.125 0.000 0.122 0.177 0.000

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

20 20 20 18 0 14 0 13 15 0

N.S.

1 1.00 1.00 0.90 0.00 0.70 0.00 0.65 0.75 0.00

time (sec)

N/A 0.219 0.451 0.067 0.000 0.070 0.000 0.142 0.207 0.000

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

35 36 18 20 38 19 68 0 19 14

N.S.

1 1.03 0.51 0.57 1.09 0.54 1.94 0.00 0.54 0.40

time (sec)

N/A 0.255 0.272 0.115 0.183 0.078 0.624 0.000 0.183 22.814

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

15 15 111 0 13 16 122 0 21 13

N.S.

1 1.00 7.40 0.00 0.87 1.07 8.13 0.00 1.40 0.87

time (sec)

N/A 0.246 0.313 0.000 0.137 0.100 5.508 0.000 0.173 22.950

Problem 306

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

53 53 28 24 37 24 46 37 23 37

N.S.

1 1.00 0.53 0.45 0.70 0.45 0.87 0.70 0.43 0.70

time (sec)

N/A 0.303 0.025 0.103 0.026 0.065 0.498 0.112 0.200 0.045

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 22 31 26 25 25 27 25 24 25

N.S.

1 0.71 1.00 0.84 0.81 0.81 0.87 0.81 0.77 0.81

time (sec)

N/A 0.298 0.027 0.017 0.038 0.065 0.118 0.132 0.167 22.344

Problem 308

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

11 11 11 10 9 9 8 9 8 9

N.S.

1 1.00 1.00 0.91 0.82 0.82 0.73 0.82 0.73 0.82

time (sec)

N/A 0.227 0.046 0.053 0.029 0.082 0.057 0.113 0.183 23.023

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

6 6 6 5 4 4 5 4 3 4

N.S.

1 1.00 1.00 0.83 0.67 0.67 0.83 0.67 0.50 0.67

time (sec)

N/A 0.214 0.018 0.085 0.146 0.068 0.082 0.102 0.186 0.136

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

20 20 17 14 16 16 0 25 20 16

N.S.

1 1.00 0.85 0.70 0.80 0.80 0.00 1.25 1.00 0.80

time (sec)

N/A 0.240 0.025 0.059 0.113 0.067 0.000 0.115 0.177 23.957

Problem 311

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 17 12 26 11 12 11 11 11

N.S.

1 1.00 1.00 0.71 1.53 0.65 0.71 0.65 0.65 0.65

time (sec)

N/A 0.238 0.003 0.031 0.046 0.065 0.051 0.124 0.181 0.026

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 19 19 12 11 11 15 11 11 12

N.S.

1 1.00 1.00 0.63 0.58 0.58 0.79 0.58 0.58 0.63

time (sec)

N/A 0.241 0.005 0.049 0.034 0.071 0.393 0.135 0.186 0.026

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

41 45 42 28 27 25 37 27 26 27

N.S.

1 1.10 1.02 0.68 0.66 0.61 0.90 0.66 0.63 0.66

time (sec)

N/A 0.268 0.041 0.027 0.139 0.076 1.876 0.131 0.183 0.026

Problem 314

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C A A C A B B

verified

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

size

67 75 86 48 63 65 39 64 107 73

N.S.

1 1.12 1.28 0.72 0.94 0.97 0.58 0.96 1.60 1.09

time (sec)

N/A 0.307 0.084 0.049 0.124 0.077 0.631 0.146 0.179 23.779

Problem 315

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 61 75 49 0 192 162 123 44 0

N.S.

1 1.00 1.23 0.80 0.00 3.15 2.66 2.02 0.72 0.00

time (sec)

N/A 0.313 0.106 0.161 0.000 0.087 1.093 0.124 0.174 0.000

Problem 316

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 65 78 55 0 202 162 131 32 0

N.S.

1 1.00 1.20 0.85 0.00 3.11 2.49 2.02 0.49 0.00

time (sec)

N/A 0.320 0.151 0.165 0.000 0.081 1.125 0.147 0.183 0.000

Problem 317

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

13 23 13 10 21 21 26 22 18 9

N.S.

1 1.77 1.00 0.77 1.62 1.62 2.00 1.69 1.38 0.69

time (sec)

N/A 0.243 0.032 0.121 0.115 0.077 0.112 0.130 0.169 22.675

Problem 318

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

13 23 13 10 21 21 26 22 18 9

N.S.

1 1.77 1.00 0.77 1.62 1.62 2.00 1.69 1.38 0.69

time (sec)

N/A 0.239 0.004 0.104 0.126 0.075 0.143 0.113 0.200 0.027

Problem 319

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 77 72 58 77 122 202 80 155 233

N.S.

1 1.07 1.00 0.81 1.07 1.69 2.81 1.11 2.15 3.24

time (sec)

N/A 0.394 0.110 0.127 0.118 0.077 0.780 0.154 0.177 23.430

Problem 320

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

37 37 23 23 15 22 0 48 14 22

N.S.

1 1.00 0.62 0.62 0.41 0.59 0.00 1.30 0.38 0.59

time (sec)

N/A 0.274 0.022 0.067 0.047 0.067 0.000 0.140 0.172 23.225

Problem 321

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

12 12 41 9 9 17 0 17 23 0

N.S.

1 1.00 3.42 0.75 0.75 1.42 0.00 1.42 1.92 0.00

time (sec)

N/A 0.238 0.010 0.041 0.172 0.071 0.000 0.128 0.206 0.000

Problem 322

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

95 107 71 67 0 74 56 51 73 0

N.S.

1 1.13 0.75 0.71 0.00 0.78 0.59 0.54 0.77 0.00

time (sec)

N/A 0.410 0.197 0.015 0.000 0.779 0.393 0.136 0.178 0.000

Problem 323

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

35 25 28 24 23 21 184 23 19 16

N.S.

1 0.71 0.80 0.69 0.66 0.60 5.26 0.66 0.54 0.46

time (sec)

N/A 0.267 0.026 0.049 0.029 0.096 0.641 0.110 0.183 23.843

Problem 324

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

37 25 30 28 27 22 265 27 19 24

N.S.

1 0.68 0.81 0.76 0.73 0.59 7.16 0.73 0.51 0.65

time (sec)

N/A 0.277 0.025 0.043 0.063 0.081 0.675 0.132 0.193 23.844

Problem 325

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

769 65 44 17 0 0 0 0 103 27

N.S.

1 0.08 0.06 0.02 0.00 0.00 0.00 0.00 0.13 0.04

time (sec)

N/A 0.320 10.027 0.034 0.000 0.000 0.000 0.000 0.226 23.662

Problem 326

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

688 455 40 32 0 0 0 0 11 30

N.S.

1 0.66 0.06 0.05 0.00 0.00 0.00 0.00 0.02 0.04

time (sec)

N/A 0.705 10.018 0.060 0.000 0.000 0.000 0.000 0.247 23.360

Problem 327

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

35 35 40 48 0 38 32 29 32 39

N.S.

1 1.00 1.14 1.37 0.00 1.09 0.91 0.83 0.91 1.11

time (sec)

N/A 0.276 0.157 0.033 0.000 0.103 1.475 0.133 0.182 24.918

Problem 328

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 33 42 48 0 41 42 32 34 40

N.S.

1 0.97 1.24 1.41 0.00 1.21 1.24 0.94 1.00 1.18

time (sec)

N/A 0.269 0.158 0.038 0.000 0.081 1.353 0.139 0.180 23.168

Problem 329

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

21 21 21 16 0 15 56 15 25 22

N.S.

1 1.00 1.00 0.76 0.00 0.71 2.67 0.71 1.19 1.05

time (sec)

N/A 0.279 0.102 0.027 0.000 0.075 0.195 0.135 0.177 23.667

Problem 330

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 64 49 59 0 97 0 105 45 127

N.S.

1 0.98 0.75 0.91 0.00 1.49 0.00 1.62 0.69 1.95

time (sec)

N/A 0.363 0.201 0.128 0.000 0.074 0.000 0.138 0.187 0.160

Problem 331

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 38 50 28 0 41 0 63 37 64

N.S.

1 1.23 1.61 0.90 0.00 1.32 0.00 2.03 1.19 2.06

time (sec)

N/A 0.336 0.238 0.125 0.000 0.071 0.000 0.124 0.176 23.609

Problem 332

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 94 57 46 0 54 58 50 53 0

N.S.

1 1.15 0.70 0.56 0.00 0.66 0.71 0.61 0.65 0.00

time (sec)

N/A 0.358 0.154 0.032 0.000 0.494 0.264 0.120 0.178 0.000

Problem 333

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

74 84 74 56 55 57 155 55 58 95

N.S.

1 1.14 1.00 0.76 0.74 0.77 2.09 0.74 0.78 1.28

time (sec)

N/A 0.566 0.082 0.034 0.157 0.080 2.746 0.118 0.181 0.036

Problem 334

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

115 124 115 81 80 80 221 80 86 130

N.S.

1 1.08 1.00 0.70 0.70 0.70 1.92 0.70 0.75 1.13

time (sec)

N/A 0.642 0.093 0.035 0.109 0.075 3.183 0.144 0.167 0.125

Problem 335

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

92 92 49 108 0 14 0 0 24 40

N.S.

1 1.00 0.53 1.17 0.00 0.15 0.00 0.00 0.26 0.43

time (sec)

N/A 0.341 10.033 0.176 0.000 0.080 0.000 0.000 0.194 24.006

Problem 336

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 22 39 50 40 0 31 16 18

N.S.

1 1.00 1.00 1.77 2.27 1.82 0.00 1.41 0.73 0.82

time (sec)

N/A 0.260 0.049 0.068 0.026 0.070 0.000 0.121 0.180 23.922

Problem 337

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 40 37 26 0 28 25 20

N.S.

1 1.00 1.00 1.67 1.54 1.08 0.00 1.17 1.04 0.83

time (sec)

N/A 0.260 0.037 0.100 0.116 0.083 0.000 0.117 0.186 0.035

Problem 338

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 28 34 39 51 40 0 35 18 24

N.S.

1 1.17 1.42 1.62 2.12 1.67 0.00 1.46 0.75 1.00

time (sec)

N/A 0.261 0.097 0.066 0.033 0.069 0.000 0.122 0.189 0.032

Problem 339

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 37 38 38 32 38 27 20

N.S.

1 1.00 1.00 1.54 1.58 1.58 1.33 1.58 1.12 0.83

time (sec)

N/A 0.273 0.039 0.055 0.035 0.081 1.076 0.121 0.175 0.039

Problem 340

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 27 52 44 35 25 0 35 19 23

N.S.

1 1.00 1.93 1.63 1.30 0.93 0.00 1.30 0.70 0.85

time (sec)

N/A 0.266 0.068 0.097 0.107 0.074 0.000 0.126 0.192 24.229

Problem 341

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 35 49 27 36 37 22 25 40 26

N.S.

1 1.06 1.48 0.82 1.09 1.12 0.67 0.76 1.21 0.79

time (sec)

N/A 0.276 0.123 0.107 0.102 0.071 0.460 0.113 0.186 23.475

Problem 342

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

8 8 40 7 6 18 5 25 15 6

N.S.

1 1.00 5.00 0.88 0.75 2.25 0.62 3.12 1.88 0.75

time (sec)

N/A 0.236 0.052 0.095 0.106 0.080 0.479 0.116 0.188 0.017

Problem 343

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

13 13 11 10 11 18 0 18 14 13

N.S.

1 1.00 0.85 0.77 0.85 1.38 0.00 1.38 1.08 1.00

time (sec)

N/A 0.241 0.027 0.054 0.025 0.075 0.000 0.120 0.183 23.173

Problem 344

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 41 0 33 0 73 57 17

N.S.

1 1.00 1.09 1.86 0.00 1.50 0.00 3.32 2.59 0.77

time (sec)

N/A 0.306 0.076 0.101 0.000 0.073 0.000 0.133 0.179 20.514

Problem 345

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C B A A A A B B

verified

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

size

24 24 39 30 11 13 15 13 12 45

N.S.

1 1.00 1.62 1.25 0.46 0.54 0.62 0.54 0.50 1.88

time (sec)

N/A 0.241 0.029 0.132 0.108 0.116 0.328 0.112 0.188 13.076

Problem 346

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 55 23 27 63 75 59 25 28

N.S.

1 1.00 1.96 0.82 0.96 2.25 2.68 2.11 0.89 1.00

time (sec)

N/A 0.241 0.070 0.082 0.025 0.084 0.335 0.117 0.168 22.017

Problem 347

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 55 23 27 63 75 59 25 28

N.S.

1 1.00 1.96 0.82 0.96 2.25 2.68 2.11 0.89 1.00

time (sec)

N/A 0.255 0.002 0.051 0.030 0.079 0.641 0.111 0.200 23.057

Problem 348

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 55 29 27 63 75 59 25 28

N.S.

1 1.00 1.96 1.04 0.96 2.25 2.68 2.11 0.89 1.00

time (sec)

N/A 0.257 0.002 0.019 0.029 0.092 0.655 0.141 0.188 23.400

Problem 349

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 55 29 27 63 75 59 25 28

N.S.

1 1.00 1.96 1.04 0.96 2.25 2.68 2.11 0.89 1.00

time (sec)

N/A 0.261 0.002 0.017 0.029 0.079 0.708 0.120 0.186 23.599

Problem 350

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 55 29 27 63 75 59 25 28

N.S.

1 1.00 1.96 1.04 0.96 2.25 2.68 2.11 0.89 1.00

time (sec)

N/A 0.259 0.002 0.016 0.029 0.081 0.790 0.131 0.187 23.355

Problem 351

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 55 29 27 63 75 59 25 28

N.S.

1 1.00 1.96 1.04 0.96 2.25 2.68 2.11 0.89 1.00

time (sec)

N/A 0.256 0.002 0.019 0.031 0.082 0.687 0.138 0.179 22.623

Problem 352

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 56 28 36 88 97 76 30 33

N.S.

1 1.00 1.40 0.70 0.90 2.20 2.42 1.90 0.75 0.82

time (sec)

N/A 0.245 0.014 0.079 0.031 0.110 0.339 0.118 0.192 22.583

Problem 353

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 56 28 36 88 97 76 30 33

N.S.

1 1.00 1.40 0.70 0.90 2.20 2.42 1.90 0.75 0.82

time (sec)

N/A 0.271 0.002 0.052 0.026 0.085 0.633 0.132 0.189 23.299

Problem 354

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 56 28 36 88 97 76 30 33

N.S.

1 1.00 1.40 0.70 0.90 2.20 2.42 1.90 0.75 0.82

time (sec)

N/A 0.263 0.002 0.050 0.026 0.076 0.706 0.119 0.185 23.058

Problem 355

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 56 37 36 88 97 76 30 33

N.S.

1 1.00 1.40 0.92 0.90 2.20 2.42 1.90 0.75 0.82

time (sec)

N/A 0.269 0.002 0.020 0.029 0.078 0.675 0.133 0.174 22.647

Problem 356

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 48 51 69 25 28 0 59 26 0

N.S.

1 0.66 0.70 0.95 0.34 0.38 0.00 0.81 0.36 0.00

time (sec)

N/A 0.482 0.069 0.062 0.036 0.081 0.000 0.122 0.167 0.000

Problem 357

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 48 49 67 23 24 0 31 23 0

N.S.

1 0.66 0.67 0.92 0.32 0.33 0.00 0.42 0.32 0.00

time (sec)

N/A 0.354 0.020 0.011 0.037 0.088 0.000 0.130 0.192 0.000

Problem 358

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

64 39 40 61 14 14 0 32 14 39

N.S.

1 0.61 0.62 0.95 0.22 0.22 0.00 0.50 0.22 0.61

time (sec)

N/A 0.478 0.051 0.014 0.033 0.087 0.000 0.138 0.176 22.655

Problem 359

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 47 49 67 18 26 0 0 27 0

N.S.

1 0.65 0.68 0.93 0.25 0.36 0.00 0.00 0.38 0.00

time (sec)

N/A 0.491 0.063 0.018 0.036 0.090 0.000 0.000 0.201 0.000

Problem 360

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 49 48 69 23 26 0 0 24 0

N.S.

1 0.66 0.65 0.93 0.31 0.35 0.00 0.00 0.32 0.00

time (sec)

N/A 0.494 0.065 0.017 0.034 0.105 0.000 0.000 0.195 0.000

Problem 361

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

86 0 110 0 0 74 0 0 84 0

N.S.

1 0.00 1.28 0.00 0.00 0.86 0.00 0.00 0.98 0.00

time (sec)

N/A 0.000 0.883 0.000 0.000 0.468 0.000 0.000 0.476 0.000

Problem 362

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

88 0 91 0 0 0 0 0 25 0

N.S.

1 0.00 1.03 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.000 1.070 0.000 0.000 0.000 0.000 0.000 0.282 0.000

Problem 363

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

78 319 83 214 0 231 0 218 142 649

N.S.

1 4.09 1.06 2.74 0.00 2.96 0.00 2.79 1.82 8.32

time (sec)

N/A 1.316 0.606 1.316 0.000 0.104 0.000 0.229 0.227 23.244

Problem 364

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

126 132 97 430 0 326 0 444 59 0

N.S.

1 1.05 0.77 3.41 0.00 2.59 0.00 3.52 0.47 0.00

time (sec)

N/A 0.546 0.200 0.848 0.000 0.087 0.000 0.180 0.206 0.000

Problem 365

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 96 0 0 62 0 0 56 0

N.S.

1 1.00 4.36 0.00 0.00 2.82 0.00 0.00 2.55 0.00

time (sec)

N/A 0.335 0.404 0.000 0.000 0.483 0.000 0.000 0.247 0.000

Problem 366

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 42 0 0 0 0 0 153 0

N.S.

1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 3.82 0.00

time (sec)

N/A 0.426 1.034 0.000 0.000 0.000 0.000 0.000 0.657 0.000

Problem 367

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

41 41 44 0 0 0 0 0 154 0

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 3.76 0.00

time (sec)

N/A 0.421 1.019 0.000 0.000 0.000 0.000 0.000 0.640 0.000

Problem 368

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

154 187 389 1528 0 0 0 0 186 0

N.S.

1 1.21 2.53 9.92 0.00 0.00 0.00 0.00 1.21 0.00

time (sec)

N/A 0.624 10.620 3.082 0.000 0.000 0.000 0.000 0.236 0.000

Problem 369

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 134 90 1036 0 0 0 0 96 0

N.S.

1 1.21 0.81 9.33 0.00 0.00 0.00 0.00 0.86 0.00

time (sec)

N/A 0.353 20.080 1.433 0.000 0.000 0.000 0.000 0.249 0.000

Problem 370

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

89 83 90 69 0 154 0 164 145 0

N.S.

1 0.93 1.01 0.78 0.00 1.73 0.00 1.84 1.63 0.00

time (sec)

N/A 0.563 0.396 0.568 0.000 0.104 0.000 0.160 0.190 0.000

Problem 371

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 107 0 0 191 0 0 64 0

N.S.

1 1.00 2.33 0.00 0.00 4.15 0.00 0.00 1.39 0.00

time (sec)

N/A 0.991 7.431 0.000 0.000 5.672 0.000 0.000 0.223 0.000

Problem 372

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 47 114 0 0 182 0 0 47 0

N.S.

1 1.02 2.48 0.00 0.00 3.96 0.00 0.00 1.02 0.00

time (sec)

N/A 1.016 6.793 0.000 0.000 5.039 0.000 0.000 0.224 0.000

Problem 373

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 107 0 0 191 0 0 64 0

N.S.

1 1.00 2.33 0.00 0.00 4.15 0.00 0.00 1.39 0.00

time (sec)

N/A 1.707 0.015 0.000 0.000 5.289 0.000 0.000 0.209 0.000

Problem 374

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 47 114 0 0 182 0 0 47 0

N.S.

1 1.02 2.48 0.00 0.00 3.96 0.00 0.00 1.02 0.00

time (sec)

N/A 1.697 0.014 0.000 0.000 4.900 0.000 0.000 0.219 0.000

Problem 375

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 66 27 147 94 96 17 58 22 132

N.S.

1 3.47 1.42 7.74 4.95 5.05 0.89 3.05 1.16 6.95

time (sec)

N/A 3.502 0.446 0.171 0.077 0.093 8.907 0.143 0.192 25.444

Problem 376

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

90 90 180 2501 0 458 0 0 62 0

N.S.

1 1.00 2.00 27.79 0.00 5.09 0.00 0.00 0.69 0.00

time (sec)

N/A 0.343 0.545 11.368 0.000 4.758 0.000 0.000 0.186 0.000

Problem 377

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 425 181 1026 0 289 0 0 85 0

N.S.

1 4.13 1.76 9.96 0.00 2.81 0.00 0.00 0.83 0.00

time (sec)

N/A 1.517 1.674 6.764 0.000 2.678 0.000 0.000 0.181 0.000

Problem 378

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 0 31 32 16 31 73 81 25 31

N.S.

1 0.00 0.91 0.94 0.47 0.91 2.15 2.38 0.74 0.91

time (sec)

N/A 0.000 0.164 0.227 0.111 0.089 17.145 0.146 0.195 23.781

Problem 379

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

32 32 34 32 33 33 0 33 34 33

N.S.

1 1.00 1.06 1.00 1.03 1.03 0.00 1.03 1.06 1.03

time (sec)

N/A 1.910 6.268 0.062 0.093 0.088 0.000 0.184 200.034 23.997

Problem 380

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

verified

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

size

27 27 29 27 29 44 0 0 29 29

N.S.

1 1.00 1.07 1.00 1.07 1.63 0.00 0.00 1.07 1.07

time (sec)

N/A 1.962 5.486 0.061 0.114 0.172 0.000 0.000 200.036 63.469

Problem 381

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

7 7 7 6 5 5 3 5 5 5

N.S.

1 1.00 1.00 0.86 0.71 0.71 0.43 0.71 0.71 0.71

time (sec)

N/A 0.275 0.000 0.028 0.025 0.076 0.017 0.108 0.190 0.018

Problem 382

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

7 7 7 6 5 5 3 5 5 5

N.S.

1 1.00 1.00 0.86 0.71 0.71 0.43 0.71 0.71 0.71

time (sec)

N/A 0.267 0.000 0.027 0.029 0.065 0.019 0.114 0.185 0.024

Problem 383

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 1 1 2 1 1 0 1 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.219 0.000 0.029 0.025 0.068 0.019 0.109 0.165 0.004

Problem 384

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

2 2 2 3 2 2 2 3 2 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.50 1.00 1.00

time (sec)

N/A 0.256 0.000 0.029 0.024 0.076 0.025 0.103 0.187 0.010

Problem 385

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

5 5 5 6 5 5 3 5 5 5

N.S.

1 1.00 1.00 1.20 1.00 1.00 0.60 1.00 1.00 1.00

time (sec)

N/A 0.258 0.000 0.028 0.028 0.074 0.018 0.106 0.174 0.022

Problem 386

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

7 7 7 6 5 5 7 5 5 5

N.S.

1 1.00 1.00 0.86 0.71 0.71 1.00 0.71 0.71 0.71

time (sec)

N/A 0.263 0.000 0.030 0.023 0.073 0.020 0.108 0.172 0.015

Problem 387

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 122 129 85 0 73 0 193 92 549

N.S.

1 2.90 3.07 2.02 0.00 1.74 0.00 4.60 2.19 13.07

time (sec)

N/A 0.643 0.136 0.202 0.000 0.091 0.000 0.145 0.202 0.702

Problem 388

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 122 129 89 0 73 0 193 92 549

N.S.

1 2.90 3.07 2.12 0.00 1.74 0.00 4.60 2.19 13.07

time (sec)

N/A 0.541 0.007 0.145 0.000 0.097 0.000 0.142 0.170 24.444

Problem 389

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 149 129 89 0 73 0 193 92 549

N.S.

1 3.55 3.07 2.12 0.00 1.74 0.00 4.60 2.19 13.07

time (sec)

N/A 0.925 0.114 0.186 0.000 0.083 0.000 0.155 0.192 0.563

Problem 390

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

86 0 86 0 0 113 0 0 134 0

N.S.

1 0.00 1.00 0.00 0.00 1.31 0.00 0.00 1.56 0.00

time (sec)

N/A 0.000 0.255 0.000 0.000 0.089 0.000 0.000 0.178 0.000

Problem 391

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

86 0 86 0 0 113 0 0 133 0

N.S.

1 0.00 1.00 0.00 0.00 1.31 0.00 0.00 1.55 0.00

time (sec)

N/A 0.000 0.215 0.000 0.000 0.099 0.000 0.000 0.189 0.000

Problem 392

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 56 49 63 0 36 0 18 27 0

N.S.

1 0.82 0.72 0.93 0.00 0.53 0.00 0.26 0.40 0.00

time (sec)

N/A 0.766 0.045 0.156 0.000 0.090 0.000 0.111 0.181 0.000

Problem 393

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 56 49 63 0 36 0 18 27 0

N.S.

1 0.82 0.72 0.93 0.00 0.53 0.00 0.26 0.40 0.00

time (sec)

N/A 0.748 0.004 0.041 0.000 0.083 0.000 0.113 0.181 0.000

Problem 394

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 82 70 75 0 74 0 39 59 0

N.S.

1 0.67 0.57 0.61 0.00 0.60 0.00 0.32 0.48 0.00

time (sec)

N/A 0.766 0.052 0.179 0.000 0.086 0.000 0.119 0.187 0.000

Problem 395

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 82 70 75 0 74 0 39 59 0

N.S.

1 0.67 0.57 0.61 0.00 0.60 0.00 0.32 0.48 0.00

time (sec)

N/A 0.745 0.004 0.035 0.000 0.088 0.000 0.120 0.169 0.000

Problem 396

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 70 72 115 0 95 0 0 149 0

N.S.

1 1.00 1.03 1.64 0.00 1.36 0.00 0.00 2.13 0.00

time (sec)

N/A 1.519 0.265 0.198 0.000 0.087 0.000 0.000 0.185 0.000

Problem 397

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

14 27 27 22 0 21 0 0 5 0

N.S.

1 1.93 1.93 1.57 0.00 1.50 0.00 0.00 0.36 0.00

time (sec)

N/A 0.376 0.013 0.125 0.000 0.080 0.000 0.000 0.182 0.000

Problem 398

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 36 35 28 0 41 0 0 10 0

N.S.

1 1.16 1.13 0.90 0.00 1.32 0.00 0.00 0.32 0.00

time (sec)

N/A 0.313 0.027 0.109 0.000 0.074 0.000 0.000 0.168 0.000

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