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2.2.1 Integrals 1 to 61

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 142 91 200 170 216 0 0 0

N.S.

1 1.63 1.05 2.30 1.95 2.48 0.00 0.00 0.00

time (sec)

N/A 0.667 0.016 0.296 0.201 0.265 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 106 66 166 138 168 0 0 0

N.S.

1 1.68 1.05 2.63 2.19 2.67 0.00 0.00 0.00

time (sec)

N/A 0.509 0.014 0.251 0.207 0.277 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 71 47 122 98 112 0 0 0

N.S.

1 1.58 1.04 2.71 2.18 2.49 0.00 0.00 0.00

time (sec)

N/A 0.349 0.010 0.268 0.192 0.264 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

10 10 12 10 35 12 8 12 12

N.S.

1 1.00 1.20 1.00 3.50 1.20 0.80 1.20 1.20

time (sec)

N/A 0.199 13.895 0.045 0.410 0.260 0.472 0.280 1.879

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

10 10 12 10 46 12 10 12 12

N.S.

1 1.00 1.20 1.00 4.60 1.20 1.00 1.20 1.20

time (sec)

N/A 0.205 23.107 0.052 0.324 0.244 0.446 0.284 1.895

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 131 222 198 146 632 0 0 0

N.S.

1 1.51 2.55 2.28 1.68 7.26 0.00 0.00 0.00

time (sec)

N/A 0.641 1.089 0.110 0.258 0.264 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 96 117 156 108 453 0 0 0

N.S.

1 1.48 1.80 2.40 1.66 6.97 0.00 0.00 0.00

time (sec)

N/A 0.468 1.577 0.115 0.268 0.263 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 35 46 54 115 189 190 98 48

N.S.

1 1.13 1.48 1.74 3.71 6.10 6.13 3.16 1.55

time (sec)

N/A 0.261 0.170 0.112 0.234 0.258 0.678 0.293 1.890

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

12 12 14 12 69 14 10 14 14

N.S.

1 1.00 1.17 1.00 5.75 1.17 0.83 1.17 1.17

time (sec)

N/A 0.215 25.940 0.045 0.291 0.245 0.520 0.292 1.907

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

12 12 14 12 91 14 12 14 14

N.S.

1 1.00 1.17 1.00 7.58 1.17 1.00 1.17 1.17

time (sec)

N/A 0.213 25.753 0.049 0.291 0.253 0.487 0.292 1.865

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 266 422 375 302 1985 0 0 0

N.S.

1 1.49 2.36 2.09 1.69 11.09 0.00 0.00 0.00

time (sec)

N/A 1.447 3.708 0.171 0.246 0.313 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 168 314 246 226 1467 0 0 0

N.S.

1 1.47 2.75 2.16 1.98 12.87 0.00 0.00 0.00

time (sec)

N/A 0.949 3.542 0.163 0.254 0.275 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 112 131 164 149 975 0 0 0

N.S.

1 1.37 1.60 2.00 1.82 11.89 0.00 0.00 0.00

time (sec)

N/A 0.524 1.532 0.135 0.237 0.324 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

12 12 14 12 144 14 10 14 14

N.S.

1 1.00 1.17 1.00 12.00 1.17 0.83 1.17 1.17

time (sec)

N/A 0.210 21.674 0.059 0.309 0.260 0.597 0.309 1.809

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

12 12 14 12 175 14 12 14 14

N.S.

1 1.00 1.17 1.00 14.58 1.17 1.00 1.17 1.17

time (sec)

N/A 0.215 15.902 0.059 0.299 0.242 0.542 0.302 1.816

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 179 244 165 183 304 864 188 223

N.S.

1 1.06 1.44 0.98 1.08 1.80 5.11 1.11 1.32

time (sec)

N/A 0.690 0.929 0.385 0.262 0.261 0.763 0.290 2.164

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 127 169 103 124 192 522 119 186

N.S.

1 1.04 1.39 0.84 1.02 1.57 4.28 0.98 1.52

time (sec)

N/A 0.491 0.590 0.314 0.246 0.269 0.634 0.278 1.974

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 78 81 46 72 101 250 62 76

N.S.

1 1.05 1.09 0.62 0.97 1.36 3.38 0.84 1.03

time (sec)

N/A 0.322 0.707 0.191 0.215 0.255 0.542 0.286 1.945

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 122 61 48 75 0 48 0

N.S.

1 1.00 0.78 0.39 0.31 0.48 0.00 0.31 0.00

time (sec)

N/A 0.747 0.631 0.342 0.334 0.243 0.000 0.286 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 168 206 91 56 216 0 321 0

N.S.

1 1.06 1.30 0.57 0.35 1.36 0.00 2.02 0.00

time (sec)

N/A 0.741 0.929 0.364 0.474 0.280 0.000 0.313 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 219 265 210 68 342 0 175 0

N.S.

1 1.04 1.26 1.00 0.32 1.62 0.00 0.83 0.00

time (sec)

N/A 0.955 1.232 0.400 0.650 0.259 0.000 0.294 0.000

Problem 22

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

230 230 420 273 297 571 2193 368 266

N.S.

1 1.00 1.83 1.19 1.29 2.48 9.53 1.60 1.16

time (sec)

N/A 0.528 2.909 0.496 0.501 0.254 1.060 0.298 2.057

Problem 23

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

170 170 207 163 191 359 1353 217 164

N.S.

1 1.00 1.22 0.96 1.12 2.11 7.96 1.28 0.96

time (sec)

N/A 0.430 2.308 0.435 0.406 0.274 0.885 0.293 1.944

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 133 114 74 107 190 700 103 88

N.S.

1 1.00 0.86 0.56 0.80 1.43 5.26 0.77 0.66

time (sec)

N/A 0.386 1.459 0.377 0.321 0.250 0.798 0.275 1.907

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

297 297 199 106 81 137 0 77 0

N.S.

1 1.00 0.67 0.36 0.27 0.46 0.00 0.26 0.00

time (sec)

N/A 1.047 1.127 0.335 0.698 0.263 0.000 0.282 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

420 420 442 164 100 615 0 585 0

N.S.

1 1.00 1.05 0.39 0.24 1.46 0.00 1.39 0.00

time (sec)

N/A 1.121 2.391 0.391 1.322 0.265 0.000 0.329 0.000

Problem 27

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

336 336 615 379 406 844 3918 548 374

N.S.

1 1.00 1.83 1.13 1.21 2.51 11.66 1.63 1.11

time (sec)

N/A 0.690 4.566 0.584 1.640 0.277 1.466 0.296 2.167

Problem 28

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

246 246 371 223 254 532 2443 315 234

N.S.

1 1.00 1.51 0.91 1.03 2.16 9.93 1.28 0.95

time (sec)

N/A 0.518 3.166 0.523 1.149 0.259 1.205 0.284 2.141

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 182 185 102 138 286 1287 142 127

N.S.

1 0.99 1.01 0.56 0.75 1.56 7.03 0.78 0.69

time (sec)

N/A 0.487 1.756 0.430 0.675 0.262 1.110 0.304 2.012

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

437 437 312 151 114 195 0 104 0

N.S.

1 1.00 0.71 0.35 0.26 0.45 0.00 0.24 0.00

time (sec)

N/A 2.028 1.319 0.374 2.288 0.254 0.000 0.289 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

692 692 796 239 140 1162 0 841 0

N.S.

1 1.00 1.15 0.35 0.20 1.68 0.00 1.22 0.00

time (sec)

N/A 2.223 3.767 0.471 5.164 0.262 0.000 0.324 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 122 37 44 22 22

N.S.

1 1.00 1.10 1.00 6.10 1.85 2.20 1.10 1.10

time (sec)

N/A 0.217 41.615 0.066 0.389 0.244 4.418 0.329 2.154

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

18 18 20 18 68 20 24 20 20

N.S.

1 1.00 1.11 1.00 3.78 1.11 1.33 1.11 1.11

time (sec)

N/A 0.213 20.068 0.056 0.292 0.261 2.784 0.303 2.148

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 88 115 0 0 148 0 0 0

N.S.

1 1.00 1.31 0.00 0.00 1.68 0.00 0.00 0.00

time (sec)

N/A 0.334 1.200 0.000 0.000 0.079 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

152 152 162 0 0 248 0 0 0

N.S.

1 1.00 1.07 0.00 0.00 1.63 0.00 0.00 0.00

time (sec)

N/A 0.425 1.734 0.000 0.000 0.086 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

223 223 228 0 0 345 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 1.55 0.00 0.00 0.00

time (sec)

N/A 0.529 1.974 0.000 0.000 0.091 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 133 249 766 419 488 0 0 0

N.S.

1 1.00 1.87 5.76 3.15 3.67 0.00 0.00 0.00

time (sec)

N/A 0.477 0.355 0.416 0.258 0.262 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 149 465 240 303 0 0 0

N.S.

1 1.00 1.48 4.60 2.38 3.00 0.00 0.00 0.00

time (sec)

N/A 0.423 0.213 0.364 0.257 0.259 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 87 201 0 156 0 0 0

N.S.

1 1.00 1.16 2.68 0.00 2.08 0.00 0.00 0.00

time (sec)

N/A 0.337 0.055 0.186 0.000 0.260 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

18 18 20 18 78 20 15 20 20

N.S.

1 1.00 1.11 1.00 4.33 1.11 0.83 1.11 1.11

time (sec)

N/A 0.214 5.728 0.058 0.257 0.259 0.960 0.275 1.970

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

18 18 20 18 131 31 17 20 20

N.S.

1 1.00 1.11 1.00 7.28 1.72 0.94 1.11 1.11

time (sec)

N/A 0.209 31.405 0.058 0.271 0.252 3.172 0.356 2.039

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

271 271 843 1425 781 3239 0 0 0

N.S.

1 1.00 3.11 5.26 2.88 11.95 0.00 0.00 0.00

time (sec)

N/A 0.809 4.907 0.524 0.279 0.316 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 209 473 825 494 1854 0 0 0

N.S.

1 1.00 2.26 3.95 2.36 8.87 0.00 0.00 0.00

time (sec)

N/A 0.661 6.924 0.461 0.267 0.288 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 127 218 318 244 851 0 0 0

N.S.

1 1.00 1.72 2.50 1.92 6.70 0.00 0.00 0.00

time (sec)

N/A 0.426 7.225 0.392 0.260 0.263 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 226 36 17 22 22

N.S.

1 1.00 1.10 1.00 11.30 1.80 0.85 1.10 1.10

time (sec)

N/A 0.232 42.155 0.173 0.400 0.253 1.491 0.325 2.195

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 375 47 19 22 22

N.S.

1 1.00 1.10 1.00 18.75 2.35 0.95 1.10 1.10

time (sec)

N/A 0.227 34.097 0.177 0.450 0.257 2.495 0.464 2.453

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

556 556 2043 2823 1531 11137 0 0 0

N.S.

1 1.00 3.67 5.08 2.75 20.03 0.00 0.00 0.00

time (sec)

N/A 1.426 8.913 0.776 0.303 0.388 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

401 392 585 1586 997 6356 0 0 0

N.S.

1 0.98 1.46 3.96 2.49 15.85 0.00 0.00 0.00

time (sec)

N/A 1.044 7.466 0.629 0.282 0.337 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 259 318 651 528 2907 0 0 0

N.S.

1 0.99 1.22 2.49 2.02 11.14 0.00 0.00 0.00

time (sec)

N/A 0.640 8.176 0.490 0.268 0.296 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 644 52 17 22 22

N.S.

1 1.00 1.10 1.00 32.20 2.60 0.85 1.10 1.10

time (sec)

N/A 0.236 48.149 0.342 0.746 0.265 1.982 0.415 2.069

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 1144 63 19 22 22

N.S.

1 1.00 1.10 1.00 57.20 3.15 0.95 1.10 1.10

time (sec)

N/A 0.234 56.003 0.318 0.952 0.265 3.207 0.796 2.163

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 200 247 1158 521 730 0 0 0

N.S.

1 0.95 1.18 5.51 2.48 3.48 0.00 0.00 0.00

time (sec)

N/A 0.965 1.530 0.448 0.323 0.277 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 155 200 735 332 492 0 0 0

N.S.

1 0.99 1.28 4.71 2.13 3.15 0.00 0.00 0.00

time (sec)

N/A 0.761 1.081 0.414 0.290 0.273 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 112 152 357 0 300 0 0 0

N.S.

1 1.04 1.41 3.31 0.00 2.78 0.00 0.00 0.00

time (sec)

N/A 0.496 1.041 0.359 0.000 0.277 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 117 27 17 22 22

N.S.

1 1.00 1.10 1.00 5.85 1.35 0.85 1.10 1.10

time (sec)

N/A 0.239 7.377 0.068 0.345 0.243 1.179 0.280 1.907

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 202 51 19 22 22

N.S.

1 1.00 1.10 1.00 10.10 2.55 0.95 1.10 1.10

time (sec)

N/A 0.238 13.540 0.073 0.509 0.249 1.970 0.368 2.114

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

638 638 659 2444 1056 6171 0 0 0

N.S.

1 1.00 1.03 3.83 1.66 9.67 0.00 0.00 0.00

time (sec)

N/A 2.444 7.975 0.581 0.533 0.360 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

475 475 519 1238 751 3702 0 0 0

N.S.

1 1.00 1.09 2.61 1.58 7.79 0.00 0.00 0.00

time (sec)

N/A 1.931 5.060 0.501 0.511 0.316 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 214 244 524 0 1797 0 0 0

N.S.

1 1.09 1.24 2.67 0.00 9.17 0.00 0.00 0.00

time (sec)

N/A 0.817 3.873 0.445 0.000 0.310 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 472 55 19 22 22

N.S.

1 1.00 1.10 1.00 23.60 2.75 0.95 1.10 1.10

time (sec)

N/A 0.241 41.450 0.073 1.101 0.261 1.827 0.311 2.272

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

20 20 22 20 789 96 20 22 22

N.S.

1 1.00 1.10 1.00 39.45 4.80 1.00 1.10 1.10

time (sec)

N/A 0.245 39.171 0.071 2.157 0.274 3.323 0.511 2.714

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