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2.2.1 Integrals 1 to 100

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 F B F(-1) B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

97 97 80 80 0 1574 0 379 83

N.S.

1 1.00 0.82 0.82 0.00 16.23 0.00 3.91 0.86

time (sec)

N/A 0.387 0.388 0.200 0.000 0.282 0.000 0.443 2.364

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

78 74 66 63 0 988 0 224 62

N.S.

1 0.95 0.85 0.81 0.00 12.67 0.00 2.87 0.79

time (sec)

N/A 0.307 0.169 0.155 0.000 0.274 0.000 0.404 2.098

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

75 72 66 62 0 637 0 168 61

N.S.

1 0.96 0.88 0.83 0.00 8.49 0.00 2.24 0.81

time (sec)

N/A 0.301 0.079 0.123 0.000 0.272 0.000 0.341 2.005

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

58 51 52 47 0 594 0 101 41

N.S.

1 0.88 0.90 0.81 0.00 10.24 0.00 1.74 0.71

time (sec)

N/A 0.225 0.043 0.197 0.000 0.276 0.000 0.329 1.919

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

57 51 49 46 0 598 0 0 38

N.S.

1 0.89 0.86 0.81 0.00 10.49 0.00 0.00 0.67

time (sec)

N/A 0.230 0.041 0.184 0.000 0.287 0.000 0.000 1.974

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

78 74 74 65 0 923 0 0 64

N.S.

1 0.95 0.95 0.83 0.00 11.83 0.00 0.00 0.82

time (sec)

N/A 0.312 0.093 0.142 0.000 0.282 0.000 0.000 2.006

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

79 76 78 64 0 1428 0 0 63

N.S.

1 0.96 0.99 0.81 0.00 18.08 0.00 0.00 0.80

time (sec)

N/A 0.306 0.118 0.140 0.000 0.277 0.000 0.000 2.125

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

100 101 90 83 0 2132 0 0 80

N.S.

1 1.01 0.90 0.83 0.00 21.32 0.00 0.00 0.80

time (sec)

N/A 0.406 0.283 0.146 0.000 0.298 0.000 0.000 2.301

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

236 198 193 209 0 292 0 0 249

N.S.

1 0.84 0.82 0.89 0.00 1.24 0.00 0.00 1.06

time (sec)

N/A 0.464 0.319 0.070 0.000 0.300 0.000 0.000 2.425

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

218 177 149 181 0 310 0 0 233

N.S.

1 0.81 0.68 0.83 0.00 1.42 0.00 0.00 1.07

time (sec)

N/A 0.394 0.199 0.108 0.000 0.265 0.000 0.000 2.207

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

132 111 108 109 0 291 0 217 146

N.S.

1 0.84 0.82 0.83 0.00 2.20 0.00 1.64 1.11

time (sec)

N/A 0.329 0.204 0.080 0.000 0.267 0.000 0.425 2.236

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

132 111 98 109 0 1598 0 216 147

N.S.

1 0.84 0.74 0.83 0.00 12.11 0.00 1.64 1.11

time (sec)

N/A 0.320 0.123 0.074 0.000 0.295 0.000 0.387 2.313

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

218 177 177 193 0 356 0 0 197

N.S.

1 0.81 0.81 0.89 0.00 1.63 0.00 0.00 0.90

time (sec)

N/A 0.380 0.254 0.104 0.000 0.261 0.000 0.000 2.074

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

238 200 243 211 0 3348 0 0 165

N.S.

1 0.84 1.02 0.89 0.00 14.07 0.00 0.00 0.69

time (sec)

N/A 0.455 0.401 0.080 0.000 0.332 0.000 0.000 2.110

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

43 43 43 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.208 0.133 0.000 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 48 49 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.214 0.126 0.000 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

57 57 49 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.300 0.111 0.000 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 56 53 97 823 0 90 0

N.S.

1 1.00 0.92 0.87 1.59 13.49 0.00 1.48 0.00

time (sec)

N/A 0.330 0.134 0.145 0.273 0.280 0.000 0.303 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 35 39 45 54 125 0 54 0

N.S.

1 1.13 1.26 1.45 1.74 4.03 0.00 1.74 0.00

time (sec)

N/A 0.257 0.049 0.111 0.263 0.287 0.000 0.278 0.000

Problem 20

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 31 31 52 34 128 0 60 30

N.S.

1 1.00 1.00 1.68 1.10 4.13 0.00 1.94 0.97

time (sec)

N/A 0.247 0.068 0.107 0.269 0.257 0.000 0.294 1.947

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 59 48 79 84 817 0 104 0

N.S.

1 0.91 0.74 1.22 1.29 12.57 0.00 1.60 0.00

time (sec)

N/A 0.328 0.152 0.103 0.266 0.272 0.000 0.305 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

297 187 166 0 0 1994 0 0 0

N.S.

1 0.63 0.56 0.00 0.00 6.71 0.00 0.00 0.00

time (sec)

N/A 0.484 0.357 0.000 0.000 0.294 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

289 182 200 0 0 2037 0 0 0

N.S.

1 0.63 0.69 0.00 0.00 7.05 0.00 0.00 0.00

time (sec)

N/A 0.513 0.151 0.000 0.000 0.315 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

264 167 151 0 0 1618 0 0 0

N.S.

1 0.63 0.57 0.00 0.00 6.13 0.00 0.00 0.00

time (sec)

N/A 0.412 0.117 0.000 0.000 0.283 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

264 165 182 0 0 8338 0 0 0

N.S.

1 0.62 0.69 0.00 0.00 31.58 0.00 0.00 0.00

time (sec)

N/A 0.399 0.248 0.000 0.000 0.408 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 F F(-1)

verified

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

size

289 184 248 0 0 2066 0 0 0

N.S.

1 0.64 0.86 0.00 0.00 7.15 0.00 0.00 0.00

time (sec)

N/A 0.499 0.279 0.000 0.000 0.313 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

309 187 251 0 0 14359 0 0 0

N.S.

1 0.61 0.81 0.00 0.00 46.47 0.00 0.00 0.00

time (sec)

N/A 0.476 0.614 0.000 0.000 0.434 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 55 55 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 0.130 0.000 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 97 82 107 0 2152 0 788 0

N.S.

1 0.72 0.61 0.80 0.00 16.06 0.00 5.88 0.00

time (sec)

N/A 0.452 0.556 0.193 0.000 0.323 0.000 0.582 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 77 63 89 0 633 0 269 0

N.S.

1 0.74 0.61 0.86 0.00 6.09 0.00 2.59 0.00

time (sec)

N/A 0.388 0.094 0.161 0.000 0.289 0.000 0.387 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 77 80 91 0 907 0 0 0

N.S.

1 0.73 0.76 0.87 0.00 8.64 0.00 0.00 0.00

time (sec)

N/A 0.383 0.089 0.170 0.000 0.300 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 99 90 106 0 3022 0 0 0

N.S.

1 0.70 0.64 0.75 0.00 21.43 0.00 0.00 0.00

time (sec)

N/A 0.444 0.217 0.150 0.000 0.338 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 50 43 130 87 1046 151 0 0

N.S.

1 0.68 0.58 1.76 1.18 14.14 2.04 0.00 0.00

time (sec)

N/A 0.327 0.083 0.153 0.276 0.298 68.065 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 38 41 119 34 392 126 0 0

N.S.

1 0.76 0.82 2.38 0.68 7.84 2.52 0.00 0.00

time (sec)

N/A 0.267 0.031 0.154 0.278 0.264 6.192 0.000 0.000

Problem 35

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

31 35 39 192 51 148 0 0 0

N.S.

1 1.13 1.26 6.19 1.65 4.77 0.00 0.00 0.00

time (sec)

N/A 0.260 0.032 0.154 0.273 0.264 0.000 0.000 0.000

Problem 36

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

31 31 31 192 32 187 0 0 0

N.S.

1 1.00 1.00 6.19 1.03 6.03 0.00 0.00 0.00

time (sec)

N/A 0.245 0.034 0.157 0.282 0.255 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 38 40 89 37 287 0 0 0

N.S.

1 0.76 0.80 1.78 0.74 5.74 0.00 0.00 0.00

time (sec)

N/A 0.255 0.072 0.147 0.271 0.262 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 52 51 132 89 1579 0 0 0

N.S.

1 0.65 0.64 1.65 1.11 19.74 0.00 0.00 0.00

time (sec)

N/A 0.333 0.097 0.165 0.269 0.278 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

57 57 53 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.303 0.112 0.000 0.000 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 69 43 77 137 3421 0 77 0

N.S.

1 0.63 0.39 0.70 1.25 31.10 0.00 0.70 0.00

time (sec)

N/A 0.425 0.073 0.156 0.277 0.331 0.000 0.319 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 38 41 55 34 415 0 27 0

N.S.

1 0.76 0.82 1.10 0.68 8.30 0.00 0.54 0.00

time (sec)

N/A 0.257 0.037 0.113 0.272 0.258 0.000 0.269 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 38 40 59 36 422 0 32 0

N.S.

1 0.76 0.80 1.18 0.72 8.44 0.00 0.64 0.00

time (sec)

N/A 0.248 0.066 0.116 0.272 0.275 0.000 0.289 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 71 68 84 155 3473 0 83 0

N.S.

1 0.60 0.58 0.71 1.31 29.43 0.00 0.70 0.00

time (sec)

N/A 0.410 0.253 0.109 0.274 0.319 0.000 0.335 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

353 217 244 0 0 2864 0 0 0

N.S.

1 0.61 0.69 0.00 0.00 8.11 0.00 0.00 0.00

time (sec)

N/A 0.647 2.076 0.000 0.000 0.319 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

291 186 166 0 0 618 0 0 0

N.S.

1 0.64 0.57 0.00 0.00 2.12 0.00 0.00 0.00

time (sec)

N/A 0.511 0.396 0.000 0.000 0.278 0.000 0.000 0.000

Problem 46

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

289 182 200 0 0 288 0 0 0

N.S.

1 0.63 0.69 0.00 0.00 1.00 0.00 0.00 0.00

time (sec)

N/A 0.474 0.182 0.000 0.000 0.272 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

289 184 248 0 0 3316 0 0 0

N.S.

1 0.64 0.86 0.00 0.00 11.47 0.00 0.00 0.00

time (sec)

N/A 0.464 0.154 0.000 0.000 0.332 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

291 184 251 0 0 1159 0 0 0

N.S.

1 0.63 0.86 0.00 0.00 3.98 0.00 0.00 0.00

time (sec)

N/A 0.507 0.302 0.000 0.000 0.278 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

369 221 274 0 0 15579 0 0 0

N.S.

1 0.60 0.74 0.00 0.00 42.22 0.00 0.00 0.00

time (sec)

N/A 0.657 1.745 0.000 0.000 0.539 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

57 57 57 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.304 0.116 0.000 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

63 63 59 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.304 0.130 0.000 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

54 68 54 0 0 0 0 0 0

N.S.

1 1.26 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.297 0.104 0.000 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

60 60 58 0 0 0 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.305 0.115 0.000 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 69 59 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.302 0.139 0.000 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

65 65 61 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.304 0.127 0.000 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

60 60 61 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.305 0.113 0.000 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

54 68 54 0 0 0 0 0 0

N.S.

1 1.26 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 0.105 0.000 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

60 60 58 0 0 0 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.298 0.116 0.000 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

60 60 61 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.306 0.124 0.000 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 69 61 0 0 0 0 0 0

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 0.136 0.000 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 52 94 31 140 448 48 41 88

N.S.

1 1.27 2.29 0.76 3.41 10.93 1.17 1.00 2.15

time (sec)

N/A 0.429 0.270 0.105 0.199 0.255 0.669 0.284 1.868

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 39 84 25 95 273 37 35 60

N.S.

1 1.26 2.71 0.81 3.06 8.81 1.19 1.13 1.94

time (sec)

N/A 0.349 0.198 0.077 0.204 0.244 0.453 0.279 1.902

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 26 61 19 55 142 31 29 36

N.S.

1 1.13 2.65 0.83 2.39 6.17 1.35 1.26 1.57

time (sec)

N/A 0.280 0.161 0.073 0.178 0.244 0.355 0.269 0.047

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 28 13 19 53 22 21 20

N.S.

1 1.00 2.15 1.00 1.46 4.08 1.69 1.62 1.54

time (sec)

N/A 0.213 0.015 0.047 0.184 0.235 0.193 0.286 0.050

Problem 65

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

16 16 14 11 10 26 27 10 14

N.S.

1 1.00 0.88 0.69 0.62 1.62 1.69 0.62 0.88

time (sec)

N/A 0.171 0.115 0.050 0.181 0.244 0.258 0.264 0.061

Problem 66

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

26 31 28 17 16 52 88 18 16

N.S.

1 1.19 1.08 0.65 0.62 2.00 3.38 0.69 0.62

time (sec)

N/A 0.229 0.701 0.074 0.183 0.250 0.484 0.264 0.049

Problem 67

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

36 46 33 23 22 86 182 24 22

N.S.

1 1.28 0.92 0.64 0.61 2.39 5.06 0.67 0.61

time (sec)

N/A 0.301 0.292 0.079 0.185 0.242 0.567 0.277 0.061

Problem 68

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 61 35 29 28 121 299 30 28

N.S.

1 1.33 0.76 0.63 0.61 2.63 6.50 0.65 0.61

time (sec)

N/A 0.383 0.352 0.084 0.186 0.257 0.733 0.274 1.826

Problem 69

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

56 76 41 35 34 159 444 36 34

N.S.

1 1.36 0.73 0.62 0.61 2.84 7.93 0.64 0.61

time (sec)

N/A 0.444 0.496 0.096 0.182 0.265 0.929 0.274 1.865

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 63 47 43 0 438 0 160 44

N.S.

1 1.11 0.82 0.75 0.00 7.68 0.00 2.81 0.77

time (sec)

N/A 0.377 0.848 0.119 0.000 0.263 0.000 0.290 1.941

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 48 39 35 0 259 0 112 54

N.S.

1 1.07 0.87 0.78 0.00 5.76 0.00 2.49 1.20

time (sec)

N/A 0.305 0.705 0.086 0.000 0.265 0.000 0.288 1.880

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 33 27 0 131 0 63 26

N.S.

1 1.00 1.00 0.82 0.00 3.97 0.00 1.91 0.79

time (sec)

N/A 0.238 0.553 0.063 0.000 0.255 0.000 0.278 1.881

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 17 0 50 0 37 16

N.S.

1 1.00 1.00 0.81 0.00 2.38 0.00 1.76 0.76

time (sec)

N/A 0.186 0.418 0.093 0.000 0.255 0.000 0.276 1.909

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 26 27 0 85 0 66 26

N.S.

1 1.00 0.81 0.84 0.00 2.66 0.00 2.06 0.81

time (sec)

N/A 0.242 0.450 0.084 0.000 0.260 0.000 0.286 1.894

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 28 35 0 168 0 113 32

N.S.

1 1.00 0.57 0.71 0.00 3.43 0.00 2.31 0.65

time (sec)

N/A 0.305 0.557 0.077 0.000 0.266 0.000 0.280 1.907

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 66 28 43 0 266 0 161 40

N.S.

1 1.08 0.46 0.70 0.00 4.36 0.00 2.64 0.66

time (sec)

N/A 0.379 0.629 0.075 0.000 0.265 0.000 0.277 1.899

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 146 141 150 348 2748 588 226 244

N.S.

1 1.03 0.99 1.06 2.45 19.35 4.14 1.59 1.72

time (sec)

N/A 0.769 0.852 0.269 0.200 0.275 1.792 0.290 1.975

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 105 109 113 219 1396 444 153 158

N.S.

1 1.04 1.08 1.12 2.17 13.82 4.40 1.51 1.56

time (sec)

N/A 0.538 0.946 0.187 0.188 0.272 1.198 0.288 1.942

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 73 86 87 136 654 333 99 97

N.S.

1 1.06 1.25 1.26 1.97 9.48 4.83 1.43 1.41

time (sec)

N/A 0.387 0.425 0.146 0.188 0.262 0.830 0.290 0.115

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 42 65 59 49 205 209 57 51

N.S.

1 1.11 1.71 1.55 1.29 5.39 5.50 1.50 1.34

time (sec)

N/A 0.265 0.132 0.085 0.193 0.258 0.574 0.280 0.113

Problem 81

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

50 50 64 50 52 62 236 62 55

N.S.

1 1.00 1.28 1.00 1.04 1.24 4.72 1.24 1.10

time (sec)

N/A 0.322 0.112 0.126 0.181 0.249 1.527 0.271 1.894

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 98 100 93 124 426 0 130 104

N.S.

1 1.15 1.18 1.09 1.46 5.01 0.00 1.53 1.22

time (sec)

N/A 0.475 1.585 0.112 0.193 0.264 0.000 0.299 2.005

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 155 134 130 322 1431 0 203 195

N.S.

1 1.20 1.04 1.01 2.50 11.09 0.00 1.57 1.51

time (sec)

N/A 0.694 3.563 0.252 0.202 0.280 0.000 0.289 2.074

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 208 214 163 522 3698 0 303 310

N.S.

1 1.23 1.27 0.96 3.09 21.88 0.00 1.79 1.83

time (sec)

N/A 0.971 6.244 0.349 0.236 0.324 0.000 0.306 2.064

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 53 28 28 49 42 29 22

N.S.

1 1.00 1.71 0.90 0.90 1.58 1.35 0.94 0.71

time (sec)

N/A 0.282 0.045 0.080 0.185 0.266 0.414 0.294 0.047

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 53 28 29 48 42 24 22

N.S.

1 1.00 1.71 0.90 0.94 1.55 1.35 0.77 0.71

time (sec)

N/A 0.287 0.043 0.072 0.179 0.255 0.425 0.258 0.047

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 90 128 63 0 2231 0 0 151

N.S.

1 1.22 1.73 0.85 0.00 30.15 0.00 0.00 2.04

time (sec)

N/A 0.277 6.820 0.217 0.000 0.306 0.000 0.000 2.095

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 85 74 62 0 2307 0 0 242

N.S.

1 1.15 1.00 0.84 0.00 31.18 0.00 0.00 3.27

time (sec)

N/A 0.254 0.175 0.154 0.000 0.316 0.000 0.000 2.149

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 62 42 35 36 93 0 42 34

N.S.

1 1.03 0.70 0.58 0.60 1.55 0.00 0.70 0.57

time (sec)

N/A 0.253 0.238 1.625 0.193 0.244 0.000 0.270 2.046

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 38 36 30 33 60 0 31 29

N.S.

1 1.31 1.24 1.03 1.14 2.07 0.00 1.07 1.00

time (sec)

N/A 0.276 0.233 0.560 0.196 0.250 0.000 0.268 1.928

Problem 91

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

38 40 30 23 22 50 0 30 22

N.S.

1 1.05 0.79 0.61 0.58 1.32 0.00 0.79 0.58

time (sec)

N/A 0.241 0.191 0.267 0.197 0.247 0.000 0.268 1.913

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 27 21 18 17 25 0 19 17

N.S.

1 1.42 1.11 0.95 0.89 1.32 0.00 1.00 0.89

time (sec)

N/A 0.250 0.154 0.141 0.190 0.246 0.000 0.275 1.883

Problem 93

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

10 10 7 7 6 9 0 6 6

N.S.

1 1.00 0.70 0.70 0.60 0.90 0.00 0.60 0.60

time (sec)

N/A 0.187 0.004 0.099 0.188 0.263 0.000 0.262 1.810

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

7 7 10 8 7 18 0 12 11

N.S.

1 1.00 1.43 1.14 1.00 2.57 0.00 1.71 1.57

time (sec)

N/A 0.200 0.010 0.161 0.176 0.247 0.000 0.269 1.858

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 18 21 23 31 77 0 26 29

N.S.

1 2.25 2.62 2.88 3.88 9.62 0.00 3.25 3.62

time (sec)

N/A 0.239 0.322 0.309 0.183 0.255 0.000 0.279 0.081

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 12 11 10 41 55 0 10 16

N.S.

1 1.09 1.00 0.91 3.73 5.00 0.00 0.91 1.45

time (sec)

N/A 0.199 5.085 0.684 0.192 0.241 0.000 0.272 1.856

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 195 156 192 166 1279 0 229 143

N.S.

1 1.26 1.01 1.24 1.07 8.25 0.00 1.48 0.92

time (sec)

N/A 0.490 0.548 5.862 0.198 0.267 0.000 0.276 2.315

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 132 171 172 0 1859 0 163 172

N.S.

1 0.99 1.28 1.28 0.00 13.87 0.00 1.22 1.28

time (sec)

N/A 0.942 1.101 2.014 0.000 0.287 0.000 0.279 2.519

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 118 75 107 83 331 0 114 85

N.S.

1 1.28 0.82 1.16 0.90 3.60 0.00 1.24 0.92

time (sec)

N/A 0.367 0.458 0.611 0.196 0.259 0.000 0.267 2.085

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 75 80 93 0 431 0 72 156

N.S.

1 1.03 1.10 1.27 0.00 5.90 0.00 0.99 2.14

time (sec)

N/A 0.496 0.738 0.266 0.000 0.285 0.000 0.304 2.121

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