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2.2.1 Integrals 1 to 91

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(-2) A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 80 67 39 0 39 51 53 49

N.S.

1 1.03 0.86 0.50 0.00 0.50 0.65 0.68 0.63

time (sec)

N/A 0.248 0.105 35.648 0.000 0.249 0.118 0.326 4.707

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 31 51 31 0 26 37 71 59

N.S.

1 1.07 1.76 1.07 0.00 0.90 1.28 2.45 2.03

time (sec)

N/A 0.398 0.050 4.868 0.000 0.246 0.120 0.328 4.634

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 39 19 0 25 31 41 35

N.S.

1 1.04 0.78 0.38 0.00 0.50 0.62 0.82 0.70

time (sec)

N/A 0.234 0.110 2.675 0.000 0.252 0.103 0.296 4.175

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 23 33 18 0 14 17 33 39

N.S.

1 1.21 1.74 0.95 0.00 0.74 0.89 1.74 2.05

time (sec)

N/A 0.334 0.030 1.169 0.000 0.252 0.082 0.311 4.906

Problem 5

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

16 18 31 21 28 25 0 20 20

N.S.

1 1.12 1.94 1.31 1.75 1.56 0.00 1.25 1.25

time (sec)

N/A 0.336 0.035 1.186 0.211 0.258 0.000 0.307 4.250

Problem 6

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

18 19 15 20 17 25 0 18 19

N.S.

1 1.06 0.83 1.11 0.94 1.39 0.00 1.00 1.06

time (sec)

N/A 0.213 0.039 2.969 0.220 0.257 0.000 0.325 4.675

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 26 75 42 59 73 0 46 41

N.S.

1 1.08 3.12 1.75 2.46 3.04 0.00 1.92 1.71

time (sec)

N/A 0.384 0.042 5.619 0.200 0.264 0.000 0.329 4.742

Problem 8

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

19 19 29 15 12 36 0 12 13

N.S.

1 1.00 1.53 0.79 0.63 1.89 0.00 0.63 0.68

time (sec)

N/A 0.215 0.042 7.676 0.219 0.243 0.000 0.311 4.286

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 139 58 83 123 0 62 57

N.S.

1 1.00 3.48 1.45 2.08 3.08 0.00 1.55 1.42

time (sec)

N/A 0.417 0.044 131.157 0.207 0.254 0.000 0.330 5.001

Problem 10

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

37 37 41 28 24 54 0 24 27

N.S.

1 1.00 1.11 0.76 0.65 1.46 0.00 0.65 0.73

time (sec)

N/A 0.228 0.041 0.274 0.186 0.244 0.000 0.302 4.410

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 103 80 91 97 0 10412 121

N.S.

1 1.00 1.02 0.79 0.90 0.96 0.00 103.09 1.20

time (sec)

N/A 0.290 0.092 3.127 0.205 0.270 0.000 1.730 5.219

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 95 82 73 87 74 0 976 155

N.S.

1 1.14 0.99 0.88 1.05 0.89 0.00 11.76 1.87

time (sec)

N/A 0.352 0.095 1.734 0.296 0.275 0.000 0.535 4.446

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 69 71 60 70 74 0 4486 87

N.S.

1 1.00 1.03 0.87 1.01 1.07 0.00 65.01 1.26

time (sec)

N/A 0.274 0.028 1.351 0.225 0.274 0.000 1.005 4.715

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 59 56 52 52 47 0 373 50

N.S.

1 1.20 1.14 1.06 1.06 0.96 0.00 7.61 1.02

time (sec)

N/A 0.273 0.052 0.586 0.292 0.266 0.000 0.376 4.281

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 48 40 46 49 0 1020 53

N.S.

1 1.00 1.30 1.08 1.24 1.32 0.00 27.57 1.43

time (sec)

N/A 0.225 0.021 0.385 0.220 0.269 0.000 0.424 4.218

Problem 16

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

26 26 52 40 46 58 0 49 86

N.S.

1 1.00 2.00 1.54 1.77 2.23 0.00 1.88 3.31

time (sec)

N/A 0.217 0.021 0.454 0.203 0.276 0.000 0.346 4.515

Problem 17

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

25 23 38 26 25 62 0 35 25

N.S.

1 0.92 1.52 1.04 1.00 2.48 0.00 1.40 1.00

time (sec)

N/A 0.258 0.029 0.426 0.209 0.258 0.000 0.356 4.174

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 107 68 83 142 0 118 149

N.S.

1 1.00 1.78 1.13 1.38 2.37 0.00 1.97 2.48

time (sec)

N/A 0.268 0.030 1.352 0.204 0.282 0.000 0.366 4.883

Problem 19

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

57 49 78 46 50 122 0 62 49

N.S.

1 0.86 1.37 0.81 0.88 2.14 0.00 1.09 0.86

time (sec)

N/A 0.271 0.032 1.965 0.205 0.265 0.000 0.367 4.180

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 98 151 90 123 213 0 177 211

N.S.

1 1.00 1.54 0.92 1.26 2.17 0.00 1.81 2.15

time (sec)

N/A 0.305 0.096 3.683 0.207 0.278 0.000 0.392 4.631

Problem 21

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

87 73 116 66 72 174 0 84 70

N.S.

1 0.84 1.33 0.76 0.83 2.00 0.00 0.97 0.80

time (sec)

N/A 0.291 0.040 5.391 0.202 0.267 0.000 0.390 4.566

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 171 250 140 128 137 0 5604 127

N.S.

1 1.51 2.21 1.24 1.13 1.21 0.00 49.59 1.12

time (sec)

N/A 0.468 3.122 1.872 0.297 0.274 0.000 2.742 4.151

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 122 152 113 104 126 0 32694 174

N.S.

1 1.00 1.25 0.93 0.85 1.03 0.00 267.98 1.43

time (sec)

N/A 0.365 1.639 2.102 0.198 0.272 0.000 16.946 7.452

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 101 162 109 82 101 0 981 75

N.S.

1 1.33 2.13 1.43 1.08 1.33 0.00 12.91 0.99

time (sec)

N/A 0.297 2.701 1.171 0.293 0.264 0.000 0.619 4.624

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 111 83 67 90 0 2405 93

N.S.

1 1.00 1.63 1.22 0.99 1.32 0.00 35.37 1.37

time (sec)

N/A 0.290 0.855 1.121 0.259 0.277 0.000 1.076 4.795

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 97 56 60 102 0 74 125

N.S.

1 1.00 2.26 1.30 1.40 2.37 0.00 1.72 2.91

time (sec)

N/A 0.250 1.152 0.592 0.298 0.287 0.000 0.447 4.387

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 40 91 38 39 96 0 51 44

N.S.

1 0.95 2.17 0.90 0.93 2.29 0.00 1.21 1.05

time (sec)

N/A 0.238 1.396 1.908 0.356 0.265 0.000 0.458 4.562

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 250 101 122 230 0 172 292

N.S.

1 1.00 2.63 1.06 1.28 2.42 0.00 1.81 3.07

time (sec)

N/A 0.325 2.783 1.808 0.228 0.309 0.000 0.508 4.160

Problem 29

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

79 73 127 80 69 174 0 91 72

N.S.

1 0.92 1.61 1.01 0.87 2.20 0.00 1.15 0.91

time (sec)

N/A 0.271 2.754 3.493 0.213 0.271 0.000 0.491 4.665

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 165 994 145 187 333 0 269 378

N.S.

1 1.00 6.02 0.88 1.13 2.02 0.00 1.63 2.29

time (sec)

N/A 0.404 7.247 6.330 0.214 0.301 0.000 0.505 4.219

Problem 31

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

122 112 114 119 104 240 0 131 107

N.S.

1 0.92 0.93 0.98 0.85 1.97 0.00 1.07 0.88

time (sec)

N/A 0.309 2.820 12.763 0.232 0.273 0.000 0.502 4.951

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 205 771 184 173 188 0 66584 291

N.S.

1 1.00 3.76 0.90 0.84 0.92 0.00 324.80 1.42

time (sec)

N/A 0.457 7.288 2.718 0.217 0.276 0.000 147.410 7.567

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 125 203 163 113 149 0 2370 151

N.S.

1 1.21 1.97 1.58 1.10 1.45 0.00 23.01 1.47

time (sec)

N/A 0.323 4.787 1.759 0.518 0.272 0.000 1.178 4.679

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 133 637 144 128 144 0 12476 193

N.S.

1 1.00 4.79 1.08 0.96 1.08 0.00 93.80 1.45

time (sec)

N/A 0.352 6.788 1.467 0.361 0.273 0.000 8.347 6.429

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 86 241 107 111 148 0 144 278

N.S.

1 1.00 2.80 1.24 1.29 1.72 0.00 1.67 3.23

time (sec)

N/A 0.300 3.873 0.551 0.280 0.300 0.000 0.679 5.636

Problem 36

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

64 59 126 55 56 127 0 70 62

N.S.

1 0.92 1.97 0.86 0.88 1.98 0.00 1.09 0.97

time (sec)

N/A 0.247 2.520 2.518 0.202 0.276 0.000 0.708 4.165

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 141 897 140 171 299 0 304 581

N.S.

1 1.00 6.36 0.99 1.21 2.12 0.00 2.16 4.12

time (sec)

N/A 0.364 7.383 4.121 0.218 0.319 0.000 0.747 5.204

Problem 38

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

113 104 212 106 98 237 0 133 103

N.S.

1 0.92 1.88 0.94 0.87 2.10 0.00 1.18 0.91

time (sec)

N/A 0.293 4.193 6.966 0.213 0.281 0.000 0.695 4.287

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 229 1229 198 250 427 0 373 698

N.S.

1 1.00 5.37 0.86 1.09 1.86 0.00 1.63 3.05

time (sec)

N/A 0.480 7.635 10.945 0.223 0.363 0.000 0.758 5.465

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 154 515 165 142 343 0 189 146

N.S.

1 0.92 3.08 0.99 0.85 2.05 0.00 1.13 0.87

time (sec)

N/A 0.352 3.550 19.516 0.403 0.283 0.000 0.767 4.318

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

275 275 1017 267 218 224 0 0 319

N.S.

1 1.00 3.70 0.97 0.79 0.81 0.00 0.00 1.16

time (sec)

N/A 0.549 7.867 4.709 0.313 0.286 0.000 0.000 8.568

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 157 263 250 154 186 0 3651 161

N.S.

1 1.13 1.89 1.80 1.11 1.34 0.00 26.27 1.16

time (sec)

N/A 0.350 6.311 3.530 0.701 0.269 0.000 2.567 4.979

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 180 383 217 166 176 0 19074 268

N.S.

1 1.00 2.13 1.21 0.92 0.98 0.00 105.97 1.49

time (sec)

N/A 0.418 6.406 3.035 0.211 0.298 0.000 11.223 8.146

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 352 170 139 175 0 193 496

N.S.

1 1.00 2.98 1.44 1.18 1.48 0.00 1.64 4.20

time (sec)

N/A 0.346 6.852 1.374 0.209 0.323 0.000 1.035 6.075

Problem 45

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

83 75 162 79 72 159 0 86 81

N.S.

1 0.90 1.95 0.95 0.87 1.92 0.00 1.04 0.98

time (sec)

N/A 0.262 3.302 3.400 0.224 0.279 0.000 1.119 4.119

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 1128 157 188 346 0 300 670

N.S.

1 1.00 7.01 0.98 1.17 2.15 0.00 1.86 4.16

time (sec)

N/A 0.398 8.039 6.386 0.213 0.335 0.000 1.065 5.099

Problem 47

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

137 125 188 133 120 267 0 161 132

N.S.

1 0.91 1.37 0.97 0.88 1.95 0.00 1.18 0.96

time (sec)

N/A 0.322 5.981 11.767 0.364 0.279 0.000 1.159 4.780

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

274 274 1491 241 304 547 0 479 857

N.S.

1 1.00 5.44 0.88 1.11 2.00 0.00 1.75 3.13

time (sec)

N/A 0.529 8.071 17.346 0.410 0.398 0.000 1.093 4.898

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 178 233 218 171 386 0 235 181

N.S.

1 0.92 1.20 1.12 0.88 1.99 0.00 1.21 0.93

time (sec)

N/A 0.381 6.102 25.775 0.564 0.294 0.000 1.175 4.620

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

402 402 660 327 387 697 0 647 990

N.S.

1 1.00 1.64 0.81 0.96 1.73 0.00 1.61 2.46

time (sec)

N/A 0.649 8.994 50.856 0.236 0.416 0.000 1.153 4.700

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

274 251 289 358 658 370 0 464 683

N.S.

1 0.92 1.05 1.31 2.40 1.35 0.00 1.69 2.49

time (sec)

N/A 1.309 3.796 9.862 0.311 0.307 0.000 0.452 8.297

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 241 249 208 280 216 0 334 313

N.S.

1 1.53 1.58 1.32 1.77 1.37 0.00 2.11 1.98

time (sec)

N/A 0.586 4.171 4.691 0.301 0.284 0.000 0.404 5.202

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 166 139 202 364 261 0 241 324

N.S.

1 0.99 0.83 1.20 2.17 1.55 0.00 1.43 1.93

time (sec)

N/A 0.902 1.798 2.096 0.295 0.293 0.000 0.465 7.206

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 146 170 122 144 122 0 184 147

N.S.

1 1.55 1.81 1.30 1.53 1.30 0.00 1.96 1.56

time (sec)

N/A 0.366 0.873 1.153 0.300 0.270 0.000 0.389 5.008

Problem 55

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

90 90 79 101 141 185 0 118 110

N.S.

1 1.00 0.88 1.12 1.57 2.06 0.00 1.31 1.22

time (sec)

N/A 0.518 0.460 0.698 0.479 0.285 0.000 0.430 4.450

Problem 56

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

66 66 75 63 107 183 0 94 174

N.S.

1 1.00 1.14 0.95 1.62 2.77 0.00 1.42 2.64

time (sec)

N/A 0.398 0.352 0.750 0.516 0.309 0.000 0.432 4.913

Problem 57

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

50 49 47 48 47 95 0 60 39

N.S.

1 0.98 0.94 0.96 0.94 1.90 0.00 1.20 0.78

time (sec)

N/A 0.260 0.534 0.787 0.206 0.273 0.000 0.422 4.231

Problem 58

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

122 122 179 140 215 270 0 209 764

N.S.

1 1.00 1.47 1.15 1.76 2.21 0.00 1.71 6.26

time (sec)

N/A 0.564 1.306 1.507 0.305 0.313 0.000 0.497 5.554

Problem 59

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

108 103 95 96 97 208 0 144 102

N.S.

1 0.95 0.88 0.89 0.90 1.93 0.00 1.33 0.94

time (sec)

N/A 0.313 2.944 1.425 0.229 0.277 0.000 0.399 4.362

Problem 60

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

169 160 150 165 168 385 0 251 167

N.S.

1 0.95 0.89 0.98 0.99 2.28 0.00 1.49 0.99

time (sec)

N/A 0.375 6.166 4.075 0.210 0.287 0.000 0.437 5.689

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

297 405 664 383 799 619 0 735 757

N.S.

1 1.36 2.24 1.29 2.69 2.08 0.00 2.47 2.55

time (sec)

N/A 1.522 6.724 33.908 0.316 0.340 0.000 0.545 6.106

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

217 304 392 269 507 444 0 513 481

N.S.

1 1.40 1.81 1.24 2.34 2.05 0.00 2.36 2.22

time (sec)

N/A 0.984 4.469 9.209 0.657 0.312 0.000 0.534 5.821

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 207 246 171 293 292 0 263 255

N.S.

1 1.40 1.66 1.16 1.98 1.97 0.00 1.78 1.72

time (sec)

N/A 0.586 3.747 2.489 0.526 0.279 0.000 0.510 4.788

Problem 64

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

72 67 109 67 74 293 0 74 79

N.S.

1 0.93 1.51 0.93 1.03 4.07 0.00 1.03 1.10

time (sec)

N/A 0.270 0.873 0.964 0.203 0.283 0.000 0.454 5.084

Problem 65

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

140 131 244 127 144 442 0 203 150

N.S.

1 0.94 1.74 0.91 1.03 3.16 0.00 1.45 1.07

time (sec)

N/A 0.348 4.103 1.725 0.204 0.290 0.000 0.505 4.314

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 206 589 205 225 787 0 332 237

N.S.

1 0.94 2.69 0.94 1.03 3.59 0.00 1.52 1.08

time (sec)

N/A 0.446 7.713 2.484 0.223 0.317 0.000 0.494 5.993

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

382 498 746 466 1088 932 0 923 1068

N.S.

1 1.30 1.95 1.22 2.85 2.44 0.00 2.42 2.80

time (sec)

N/A 2.191 6.717 70.944 0.341 0.377 0.000 0.686 6.858

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

285 378 521 331 744 705 0 588 717

N.S.

1 1.33 1.83 1.16 2.61 2.47 0.00 2.06 2.52

time (sec)

N/A 1.402 6.503 20.582 0.547 0.338 0.000 0.682 6.090

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

206 270 316 236 463 526 0 482 433

N.S.

1 1.31 1.53 1.15 2.25 2.55 0.00 2.34 2.10

time (sec)

N/A 0.796 4.212 5.726 0.446 0.301 0.000 0.636 5.518

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 86 241 85 108 565 0 113 99

N.S.

1 0.91 2.54 0.89 1.14 5.95 0.00 1.19 1.04

time (sec)

N/A 0.281 4.194 1.467 0.568 0.280 0.000 0.568 4.867

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 165 456 158 192 811 0 237 200

N.S.

1 0.93 2.56 0.89 1.08 4.56 0.00 1.33 1.12

time (sec)

N/A 0.383 6.671 2.467 0.233 0.298 0.000 0.600 5.051

Problem 72

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

265 248 494 246 281 1018 0 382 297

N.S.

1 0.94 1.86 0.93 1.06 3.84 0.00 1.44 1.12

time (sec)

N/A 0.482 6.951 4.388 0.252 0.306 0.000 0.687 5.836

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

366 464 590 425 997 1053 0 902 962

N.S.

1 1.27 1.61 1.16 2.72 2.88 0.00 2.46 2.63

time (sec)

N/A 2.000 5.757 55.089 0.421 0.374 0.000 0.908 7.612

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

264 329 395 288 662 802 0 642 597

N.S.

1 1.25 1.50 1.09 2.51 3.04 0.00 2.43 2.26

time (sec)

N/A 0.982 3.952 17.837 0.342 0.329 0.000 0.828 5.610

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 103 259 103 140 874 0 129 131

N.S.

1 0.89 2.23 0.89 1.21 7.53 0.00 1.11 1.13

time (sec)

N/A 0.294 3.276 2.236 0.392 0.297 0.000 0.674 5.324

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 188 528 184 228 1235 0 222 232

N.S.

1 0.92 2.58 0.90 1.11 6.02 0.00 1.08 1.13

time (sec)

N/A 0.407 2.879 4.263 0.403 0.317 0.000 0.702 5.642

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

300 279 673 280 325 1536 0 428 337

N.S.

1 0.93 2.24 0.93 1.08 5.12 0.00 1.43 1.12

time (sec)

N/A 0.542 3.101 7.964 0.650 0.366 0.000 0.761 6.834

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 41 26 50 55 0 44 38

N.S.

1 1.00 1.58 1.00 1.92 2.12 0.00 1.69 1.46

time (sec)

N/A 0.301 0.120 0.373 0.293 0.259 0.000 0.364 4.558

Problem 79

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

229 229 205 0 0 0 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.727 2.756 0.000 0.000 0.000 0.000 0.000 0.000

Problem 80

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

179 179 166 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 0.488 1.274 0.000 0.000 0.000 0.000 0.000 0.000

Problem 81

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

109 109 109 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 0.361 0.337 0.000 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

765 580 0 0 0 0 0 0 0

N.S.

1 0.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.415 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 83

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

21 21 23 21 23 23 20 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10

time (sec)

N/A 2.847 6.546 1.297 2.514 0.298 54.374 0.717 8.005

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

435 476 910 0 0 0 0 0 0

N.S.

1 1.09 2.09 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.898 6.810 0.000 0.000 0.000 0.000 0.000 0.000

Problem 85

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

276 281 270 0 0 0 0 0 0

N.S.

1 1.02 0.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.480 1.329 0.000 0.000 0.000 0.000 0.000 0.000

Problem 86

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 48 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 0.227 6.136 0.000 0.000 0.000 0.000 0.000 0.000

Problem 87

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

140 147 78 0 0 0 0 0 0

N.S.

1 1.05 0.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 7.965 0.000 0.000 0.000 0.000 0.000 0.000

Problem 88

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

21 21 23 21 23 32 0 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.52 0.00 1.10 1.10

time (sec)

N/A 2.367 4.963 3.144 4.326 0.243 0.000 1.344 7.380

Problem 89

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

19 19 21 19 21 21 19 21 21

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.00 1.11 1.11

time (sec)

N/A 1.311 2.767 0.568 1.577 0.236 4.717 1.209 5.479

Problem 90

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

19 19 21 19 21 21 19 21 23

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.00 1.11 1.21

time (sec)

N/A 0.823 4.425 1.531 1.487 0.238 3.695 0.857 4.562

Problem 91

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

21 21 23 21 23 23 20 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10

time (sec)

N/A 2.114 23.126 1.567 2.959 0.246 34.947 1.238 6.322

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