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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 B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 83 74 87 188 78 88 88 119

N.S.

1 1.02 0.91 1.07 2.32 0.96 1.09 1.09 1.47

time (sec)

N/A 0.243 0.007 0.132 0.204 0.278 0.121 0.413 1.494

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 64 57 67 125 60 68 68 88

N.S.

1 1.05 0.93 1.10 2.05 0.98 1.11 1.11 1.44

time (sec)

N/A 0.218 0.005 0.125 0.192 0.295 0.105 0.277 1.451

Problem 3

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

41 45 40 47 71 42 46 48 57

N.S.

1 1.10 0.98 1.15 1.73 1.02 1.12 1.17 1.39

time (sec)

N/A 0.189 0.004 0.119 0.201 0.289 0.084 0.307 1.389

Problem 4

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

21 26 21 26 31 25 26 31 25

N.S.

1 1.24 1.00 1.24 1.48 1.19 1.24 1.48 1.19

time (sec)

N/A 0.156 0.004 0.080 0.190 0.272 0.070 0.301 0.067

Problem 5

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

15 15 15 22 17 16 12 16 15

N.S.

1 1.00 1.00 1.47 1.13 1.07 0.80 1.07 1.00

time (sec)

N/A 0.159 0.008 0.253 0.263 0.264 0.244 0.302 1.373

Problem 6

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

36 34 36 43 20 47 29 37 36

N.S.

1 0.94 1.00 1.19 0.56 1.31 0.81 1.03 1.00

time (sec)

N/A 0.186 0.010 0.290 0.250 0.281 0.277 0.293 1.357

Problem 7

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

63 58 47 64 21 67 48 58 64

N.S.

1 0.92 0.75 1.02 0.33 1.06 0.76 0.92 1.02

time (sec)

N/A 0.217 0.012 0.282 0.240 0.290 0.273 0.344 1.501

Problem 8

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

85 82 57 87 20 90 71 78 67

N.S.

1 0.96 0.67 1.02 0.24 1.06 0.84 0.92 0.79

time (sec)

N/A 0.252 0.018 0.289 0.249 0.284 0.300 0.316 1.269

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

98 94 75 0 78 0 0 0 96

N.S.

1 0.96 0.77 0.00 0.80 0.00 0.00 0.00 0.98

time (sec)

N/A 0.324 0.011 0.000 0.203 0.000 0.000 0.000 1.320

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

74 71 63 0 65 0 105 0 82

N.S.

1 0.96 0.85 0.00 0.88 0.00 1.42 0.00 1.11

time (sec)

N/A 0.288 0.009 0.000 0.207 0.000 55.014 0.000 1.274

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

50 48 50 0 49 0 90 52 46

N.S.

1 0.96 1.00 0.00 0.98 0.00 1.80 1.04 0.92

time (sec)

N/A 0.246 0.007 0.000 0.193 0.000 0.902 0.307 1.281

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 25 25 0 25 0 63 25 45

N.S.

1 1.00 1.00 0.00 1.00 0.00 2.52 1.00 1.80

time (sec)

N/A 0.218 0.003 0.000 0.192 0.000 0.960 0.354 1.263

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

49 47 58 0 45 0 92 0 67

N.S.

1 0.96 1.18 0.00 0.92 0.00 1.88 0.00 1.37

time (sec)

N/A 0.254 0.068 0.000 0.239 0.000 13.486 0.000 1.290

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 73 72 0 45 0 0 0 113

N.S.

1 0.95 0.94 0.00 0.58 0.00 0.00 0.00 1.47

time (sec)

N/A 0.284 0.063 0.000 0.242 0.000 0.000 0.000 1.309

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

101 99 85 0 45 0 0 0 140

N.S.

1 0.98 0.84 0.00 0.45 0.00 0.00 0.00 1.39

time (sec)

N/A 0.324 0.066 0.000 0.251 0.000 0.000 0.000 1.326

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A C A F B

verified

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

size

45 41 45 0 53 27 54 0 45

N.S.

1 0.91 1.00 0.00 1.18 0.60 1.20 0.00 1.00

time (sec)

N/A 0.201 0.023 0.000 0.086 0.096 3.005 0.000 1.264

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 119 112 525 500 614 495 758 275

N.S.

1 0.91 0.85 4.01 3.82 4.69 3.78 5.79 2.10

time (sec)

N/A 0.307 0.036 1.359 0.210 0.297 0.903 0.339 1.433

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 92 85 322 282 324 294 399 172

N.S.

1 0.93 0.86 3.25 2.85 3.27 2.97 4.03 1.74

time (sec)

N/A 0.259 0.010 0.616 0.218 0.289 0.499 0.307 1.377

Problem 19

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

65 65 59 111 131 140 146 174 94

N.S.

1 1.00 0.91 1.71 2.02 2.15 2.25 2.68 1.45

time (sec)

N/A 0.214 0.007 0.348 0.198 0.297 0.265 0.299 1.297

Problem 20

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

29 29 29 36 40 40 41 45 35

N.S.

1 1.00 1.00 1.24 1.38 1.38 1.41 1.55 1.21

time (sec)

N/A 0.163 0.005 0.221 0.195 0.295 0.143 0.323 1.286

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

63 63 63 309 0 46 0 49 0

N.S.

1 1.00 1.00 4.90 0.00 0.73 0.00 0.78 0.00

time (sec)

N/A 0.252 0.070 0.868 0.000 0.268 0.000 0.297 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

96 94 123 456 0 117 0 286 0

N.S.

1 0.98 1.28 4.75 0.00 1.22 0.00 2.98 0.00

time (sec)

N/A 0.287 0.044 0.979 0.000 0.288 0.000 0.388 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

135 136 144 734 0 263 0 1218 0

N.S.

1 1.01 1.07 5.44 0.00 1.95 0.00 9.02 0.00

time (sec)

N/A 0.353 0.061 1.144 0.000 0.298 0.000 0.412 0.000

Problem 24

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

179 171 152 0 0 0 0 0 0

N.S.

1 0.96 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.459 0.166 0.000 0.000 0.000 0.000 0.000 0.000

Problem 25

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

143 140 127 0 0 0 0 0 0

N.S.

1 0.98 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.399 0.038 0.000 0.000 0.000 0.000 0.000 0.000

Problem 26

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

111 109 106 0 0 0 0 0 0

N.S.

1 0.98 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.336 0.033 0.000 0.000 0.000 0.000 0.000 0.000

Problem 27

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

80 80 80 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 0.290 0.013 0.000 0.000 0.000 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(-2) F F F(-1)

verified

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

size

116 114 139 0 0 0 0 0 0

N.S.

1 0.98 1.20 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.348 0.090 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 F F F(-2) F F F(-1)

verified

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

size

156 158 163 0 0 0 0 0 0

N.S.

1 1.01 1.04 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.418 0.118 0.000 0.000 0.000 0.000 0.000 0.000

Problem 30

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

192 202 203 0 0 0 0 0 0

N.S.

1 1.05 1.06 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.489 0.145 0.000 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

103 103 103 0 0 59 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.57 0.00 0.00 0.00

time (sec)

N/A 0.260 0.077 0.000 0.000 0.115 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 88 88 0 59 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.67 0.00 0.00 0.00 0.00

time (sec)

N/A 0.256 0.057 0.000 0.053 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 26 0 22 0 22 20

N.S.

1 1.00 1.00 1.30 0.00 1.10 0.00 1.10 1.00

time (sec)

N/A 0.246 0.023 1.503 0.000 0.322 0.000 0.324 1.249

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

42 42 42 0 0 27 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.64 0.00 0.00 0.00

time (sec)

N/A 0.299 0.099 0.000 0.000 0.339 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 160 315 589 393 471 568 1209 526

N.S.

1 0.90 1.77 3.31 2.21 2.65 3.19 6.79 2.96

time (sec)

N/A 0.319 0.203 1.615 0.211 0.317 2.168 0.321 1.469

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 136 226 428 284 340 410 770 352

N.S.

1 0.91 1.52 2.87 1.91 2.28 2.75 5.17 2.36

time (sec)

N/A 0.279 0.139 1.074 0.198 0.293 1.164 0.322 0.824

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 112 150 265 187 221 252 424 212

N.S.

1 0.93 1.25 2.21 1.56 1.84 2.10 3.53 1.77

time (sec)

N/A 0.256 0.099 0.853 0.214 0.286 0.665 0.314 0.840

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 88 95 98 102 119 134 183 104

N.S.

1 0.97 1.04 1.08 1.12 1.31 1.47 2.01 1.14

time (sec)

N/A 0.237 0.033 0.352 0.192 0.284 0.388 0.314 0.761

Problem 39

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

29 29 29 36 40 40 41 45 35

N.S.

1 1.00 1.00 1.24 1.38 1.38 1.41 1.55 1.21

time (sec)

N/A 0.163 0.005 0.061 0.200 0.297 0.150 0.311 0.001

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

63 63 62 217 0 0 0 0 0

N.S.

1 1.00 0.98 3.44 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.276 0.011 0.702 0.000 0.000 0.000 0.000 0.000

Problem 41

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 70 57 127 85 95 333 88 84

N.S.

1 0.95 0.77 1.72 1.15 1.28 4.50 1.19 1.14

time (sec)

N/A 0.198 0.046 0.810 0.187 0.299 3.116 0.301 1.325

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 95 83 283 167 274 1945 201 173

N.S.

1 0.85 0.74 2.53 1.49 2.45 17.37 1.79 1.54

time (sec)

N/A 0.263 0.066 1.076 0.199 0.303 13.160 0.333 1.017

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 121 110 455 301 507 0 401 283

N.S.

1 0.86 0.78 3.23 2.13 3.60 0.00 2.84 2.01

time (sec)

N/A 0.288 0.090 1.608 0.210 0.322 0.000 0.313 1.190

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

365 312 360 1343 827 1190 1241 2345 1051

N.S.

1 0.85 0.99 3.68 2.27 3.26 3.40 6.42 2.88

time (sec)

N/A 0.572 0.174 2.201 0.212 0.301 2.349 0.345 1.121

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

287 252 247 850 554 760 774 1315 591

N.S.

1 0.88 0.86 2.96 1.93 2.65 2.70 4.58 2.06

time (sec)

N/A 0.533 0.098 1.477 0.213 0.300 1.226 0.407 0.962

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 186 144 459 314 401 394 583 268

N.S.

1 1.00 0.77 2.47 1.69 2.16 2.12 3.13 1.44

time (sec)

N/A 0.396 0.052 0.612 0.202 0.284 0.690 0.384 0.840

Problem 47

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

65 65 59 111 131 140 146 174 94

N.S.

1 1.00 0.91 1.71 2.02 2.15 2.25 2.68 1.45

time (sec)

N/A 0.217 0.006 0.144 0.203 0.276 0.265 0.357 0.001

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

111 106 194 737 0 0 0 0 0

N.S.

1 0.95 1.75 6.64 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.452 0.111 1.270 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

132 118 126 537 0 0 0 0 0

N.S.

1 0.89 0.95 4.07 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.393 0.057 0.907 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

202 230 204 661 0 0 0 0 0

N.S.

1 1.14 1.01 3.27 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.736 0.123 1.346 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

317 380 302 755 0 0 0 0 0

N.S.

1 1.20 0.95 2.38 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.218 0.214 2.187 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 B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

598 598 475 2719 1687 2802 2594 5182 2133

N.S.

1 1.00 0.79 4.55 2.82 4.69 4.34 8.67 3.57

time (sec)

N/A 0.973 0.266 5.422 0.261 0.376 4.445 0.414 2.359

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

432 432 333 1733 1140 1771 1578 2932 1157

N.S.

1 1.00 0.77 4.01 2.64 4.10 3.65 6.79 2.68

time (sec)

N/A 0.740 0.149 3.551 0.236 0.341 2.407 0.378 1.969

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

265 265 201 906 662 923 836 1321 511

N.S.

1 1.00 0.76 3.42 2.50 3.48 3.15 4.98 1.93

time (sec)

N/A 0.489 0.080 1.740 0.221 0.311 1.270 0.326 1.647

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 92 85 322 282 324 294 399 172

N.S.

1 0.93 0.86 3.25 2.85 3.27 2.97 4.03 1.74

time (sec)

N/A 0.258 0.011 0.257 0.201 0.305 0.499 0.328 0.002

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

158 149 335 1396 0 0 0 0 0

N.S.

1 0.94 2.12 8.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.564 0.184 1.988 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 B C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

190 161 410 1268 0 0 0 0 0

N.S.

1 0.85 2.16 6.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.581 0.246 2.022 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 F F F(-1)

verified

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

size

342 325 620 0 0 0 0 0 0

N.S.

1 0.95 1.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.363 0.474 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 F F F(-1)

verified

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

size

564 584 843 0 0 0 0 0 0

N.S.

1 1.04 1.49 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.525 0.705 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 B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

340 340 258 1493 1163 1756 1372 2488 823

N.S.

1 1.00 0.76 4.39 3.42 5.16 4.04 7.32 2.42

time (sec)

N/A 0.586 0.143 3.524 0.240 0.309 2.313 0.347 1.816

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 119 112 525 500 614 495 758 275

N.S.

1 0.91 0.85 4.01 3.82 4.69 3.78 5.79 2.10

time (sec)

N/A 0.307 0.015 0.589 0.219 0.301 0.900 0.326 0.003

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

205 191 503 2172 0 0 0 0 0

N.S.

1 0.93 2.45 10.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.677 0.175 3.017 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

248 204 531 2156 0 0 0 0 0

N.S.

1 0.82 2.14 8.69 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.709 0.457 3.224 0.000 0.000 0.000 0.000 0.000

Problem 64

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

19 24 19 24 23 22 24 23 23

N.S.

1 1.26 1.00 1.26 1.21 1.16 1.26 1.21 1.21

time (sec)

N/A 0.165 0.005 0.076 0.191 0.275 0.067 0.316 0.070

Problem 65

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

37 41 36 40 27 36 42 44 48

N.S.

1 1.11 0.97 1.08 0.73 0.97 1.14 1.19 1.30

time (sec)

N/A 0.195 0.002 0.117 0.196 0.260 0.085 0.310 1.433

Problem 66

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

55 58 51 55 37 51 63 62 73

N.S.

1 1.05 0.93 1.00 0.67 0.93 1.15 1.13 1.33

time (sec)

N/A 0.219 0.007 0.120 0.190 0.274 0.104 0.330 1.419

Problem 67

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

25 32 25 32 34 30 36 34 31

N.S.

1 1.28 1.00 1.28 1.36 1.20 1.44 1.36 1.24

time (sec)

N/A 0.187 0.007 0.080 0.191 0.276 0.107 0.319 0.083

Problem 68

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

49 53 48 52 38 48 63 65 94

N.S.

1 1.08 0.98 1.06 0.78 0.98 1.29 1.33 1.92

time (sec)

N/A 0.223 0.006 0.139 0.192 0.269 0.135 0.333 1.488

Problem 69

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

73 74 67 71 51 67 95 91 138

N.S.

1 1.01 0.92 0.97 0.70 0.92 1.30 1.25 1.89

time (sec)

N/A 0.248 0.007 0.143 0.196 0.281 0.158 0.315 1.484

Problem 70

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

24 29 24 32 35 32 36 39 29

N.S.

1 1.21 1.00 1.33 1.46 1.33 1.50 1.62 1.21

time (sec)

N/A 0.173 0.006 0.226 0.197 0.285 0.141 0.323 0.070

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 54 102 27 0 0 23

N.S.

1 1.00 1.00 2.25 4.25 1.12 0.00 0.00 0.96

time (sec)

N/A 0.202 0.006 1.079 0.204 0.279 0.000 0.000 1.513

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 0 14 17 0 15

N.S.

1 1.00 1.00 1.07 0.00 0.93 1.13 0.00 1.00

time (sec)

N/A 0.184 0.004 0.173 0.000 0.284 3.014 0.000 0.082

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A F C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 33 20 0 87 0 18

N.S.

1 1.00 1.00 2.06 1.25 0.00 5.44 0.00 1.12

time (sec)

N/A 0.178 0.003 0.099 0.210 0.000 1.483 0.000 0.035

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A F C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 33 20 0 87 0 18

N.S.

1 1.00 1.00 2.06 1.25 0.00 5.44 0.00 1.12

time (sec)

N/A 0.178 0.003 0.107 0.189 0.000 1.472 0.000 0.031

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 9 19 7 10 0 18

N.S.

1 1.00 1.00 1.12 2.38 0.88 1.25 0.00 2.25

time (sec)

N/A 0.149 0.003 0.096 0.195 0.303 1.341 0.000 0.031

Problem 76

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

10 10 10 9 8 8 7 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80

time (sec)

N/A 0.147 0.002 0.132 0.195 0.272 0.041 0.304 1.308

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 17 19 0 60 0 16

N.S.

1 1.00 1.00 0.85 0.95 0.00 3.00 0.00 0.80

time (sec)

N/A 0.191 0.003 0.095 0.197 0.000 1.942 0.000 0.030

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 27 19 20 0 102 0 18

N.S.

1 1.00 1.08 0.76 0.80 0.00 4.08 0.00 0.72

time (sec)

N/A 0.191 0.003 0.117 0.197 0.000 1.967 0.000 0.033

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A F A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 22 40 27 0 94 0 25

N.S.

1 1.00 1.05 1.90 1.29 0.00 4.48 0.00 1.19

time (sec)

N/A 0.189 0.003 0.207 0.224 0.000 1.992 0.000 1.235

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A F A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 22 40 27 0 94 0 25

N.S.

1 1.00 1.05 1.90 1.29 0.00 4.48 0.00 1.19

time (sec)

N/A 0.186 0.003 0.174 0.225 0.000 2.013 0.000 0.075

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 15 26 13 15 0 14

N.S.

1 1.00 1.00 1.07 1.86 0.93 1.07 0.00 1.00

time (sec)

N/A 0.177 0.003 0.179 0.232 0.285 1.844 0.000 0.059

Problem 82

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

17 17 16 15 15 16 14 14 14

N.S.

1 1.00 0.94 0.88 0.88 0.94 0.82 0.82 0.82

time (sec)

N/A 0.155 0.002 0.105 0.189 0.279 0.048 0.312 1.196

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 27 24 26 0 66 0 23

N.S.

1 1.00 1.04 0.92 1.00 0.00 2.54 0.00 0.88

time (sec)

N/A 0.199 0.003 0.217 0.223 0.000 2.717 0.000 1.293

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 34 26 27 0 109 0 25

N.S.

1 1.00 1.10 0.84 0.87 0.00 3.52 0.00 0.81

time (sec)

N/A 0.194 0.003 0.181 0.227 0.000 2.857 0.000 1.263

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

187 164 163 172 131 179 173 342 116

N.S.

1 0.88 0.87 0.92 0.70 0.96 0.93 1.83 0.62

time (sec)

N/A 0.371 0.037 0.444 0.198 0.264 0.765 0.305 1.354

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

177 186 172 483 150 0 0 0 0

N.S.

1 1.05 0.97 2.73 0.85 0.00 0.00 0.00 0.00

time (sec)

N/A 0.762 0.061 0.385 0.206 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

285 285 260 261 215 341 269 626 172

N.S.

1 1.00 0.91 0.92 0.75 1.20 0.94 2.20 0.60

time (sec)

N/A 0.506 0.052 0.831 0.211 0.311 1.374 0.319 1.361

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

299 299 266 9346 0 305 0 582 0

N.S.

1 1.00 0.89 31.26 0.00 1.02 0.00 1.95 0.00

time (sec)

N/A 0.751 0.625 1.542 0.000 0.292 0.000 0.349 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

219 219 197 1889 0 192 0 337 0

N.S.

1 1.00 0.90 8.63 0.00 0.88 0.00 1.54 0.00

time (sec)

N/A 0.572 0.168 1.340 0.000 0.303 0.000 0.341 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

139 139 126 937 0 105 0 159 0

N.S.

1 1.00 0.91 6.74 0.00 0.76 0.00 1.14 0.00

time (sec)

N/A 0.395 0.068 0.962 0.000 0.277 0.000 0.328 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

63 63 63 309 0 46 0 49 0

N.S.

1 1.00 1.00 4.90 0.00 0.73 0.00 0.78 0.00

time (sec)

N/A 0.243 0.010 0.098 0.000 0.278 0.000 0.318 0.000

Problem 92

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

24 24 26 24 26 31 20 26 26

N.S.

1 1.00 1.08 1.00 1.08 1.29 0.83 1.08 1.08

time (sec)

N/A 0.189 0.160 0.045 0.263 0.284 1.183 0.326 1.208

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 26 24 26 55 0 26 26

N.S.

1 1.00 1.08 1.00 1.08 2.29 0.00 1.08 1.08

time (sec)

N/A 0.192 0.354 0.013 0.266 0.317 0.000 0.320 1.237

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

339 585 1674 9517 0 681 0 3473 0

N.S.

1 1.73 4.94 28.07 0.00 2.01 0.00 10.24 0.00

time (sec)

N/A 1.194 0.463 1.702 0.000 0.317 0.000 0.419 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

259 425 1015 5089 0 433 0 2031 0

N.S.

1 1.64 3.92 19.65 0.00 1.67 0.00 7.84 0.00

time (sec)

N/A 0.882 0.251 1.273 0.000 0.307 0.000 0.385 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

177 257 208 2300 0 239 0 973 0

N.S.

1 1.45 1.18 12.99 0.00 1.35 0.00 5.50 0.00

time (sec)

N/A 0.705 0.138 1.008 0.000 0.282 0.000 0.327 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

96 94 123 456 0 117 0 286 0

N.S.

1 0.98 1.28 4.75 0.00 1.22 0.00 2.98 0.00

time (sec)

N/A 0.300 0.030 0.223 0.000 0.263 0.000 0.323 0.000

Problem 98

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

24 24 26 24 188 63 22 26 26

N.S.

1 1.00 1.08 1.00 7.83 2.62 0.92 1.08 1.08

time (sec)

N/A 0.187 0.232 0.015 0.278 0.297 2.767 0.370 1.283

Problem 99

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

24 24 26 24 289 104 24 26 26

N.S.

1 1.00 1.08 1.00 12.04 4.33 1.00 1.08 1.08

time (sec)

N/A 0.188 2.107 0.033 0.290 0.292 11.143 0.338 1.299

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

351 753 351 6545 0 1090 0 8422 0

N.S.

1 2.15 1.00 18.65 0.00 3.11 0.00 23.99 0.00

time (sec)

N/A 1.754 0.794 1.727 0.000 0.311 0.000 0.491 0.000

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