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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 A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 77 74 84 92 62 105 118 90

N.S.

1 0.89 0.85 0.97 1.06 0.71 1.21 1.36 1.03

time (sec)

N/A 0.248 0.044 0.444 0.200 0.292 0.704 0.326 5.922

Problem 2

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

87 96 57 62 63 62 172 107 226

N.S.

1 1.10 0.66 0.71 0.72 0.71 1.98 1.23 2.60

time (sec)

N/A 0.426 0.167 0.641 0.186 0.302 0.508 0.321 10.114

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

64 57 60 63 70 51 83 88 68

N.S.

1 0.89 0.94 0.98 1.09 0.80 1.30 1.38 1.06

time (sec)

N/A 0.247 0.021 0.289 0.182 0.325 0.357 0.328 0.057

Problem 4

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

65 70 62 52 48 51 124 77 165

N.S.

1 1.08 0.95 0.80 0.74 0.78 1.91 1.18 2.54

time (sec)

N/A 0.338 0.095 0.546 0.185 0.317 0.230 0.306 9.799

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

45 41 44 46 48 39 60 48 46

N.S.

1 0.91 0.98 1.02 1.07 0.87 1.33 1.07 1.02

time (sec)

N/A 0.230 0.018 0.240 0.187 0.274 0.165 0.311 0.070

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

43 44 46 41 37 37 71 47 103

N.S.

1 1.02 1.07 0.95 0.86 0.86 1.65 1.09 2.40

time (sec)

N/A 0.262 0.074 0.244 0.187 0.287 0.133 0.307 8.900

Problem 7

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

22 22 39 23 20 25 34 25 20

N.S.

1 1.00 1.77 1.05 0.91 1.14 1.55 1.14 0.91

time (sec)

N/A 0.190 0.024 0.136 0.187 0.267 0.081 0.295 0.053

Problem 8

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

17 18 26 16 15 17 0 37 15

N.S.

1 1.06 1.53 0.94 0.88 1.00 0.00 2.18 0.88

time (sec)

N/A 0.193 0.018 0.267 0.182 0.293 0.000 0.303 0.054

Problem 9

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

23 23 23 20 23 40 0 19 19

N.S.

1 1.00 1.00 0.87 1.00 1.74 0.00 0.83 0.83

time (sec)

N/A 0.257 0.023 0.461 0.187 0.270 0.000 0.334 6.047

Problem 10

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

39 42 52 50 42 67 0 54 30

N.S.

1 1.08 1.33 1.28 1.08 1.72 0.00 1.38 0.77

time (sec)

N/A 0.248 0.022 0.534 0.186 0.329 0.000 0.311 0.076

Problem 11

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

44 44 41 38 35 52 0 66 63

N.S.

1 1.00 0.93 0.86 0.80 1.18 0.00 1.50 1.43

time (sec)

N/A 0.285 0.052 0.523 0.179 0.275 0.000 0.350 6.041

Problem 12

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

84 81 74 63 86 136 0 92 71

N.S.

1 0.96 0.88 0.75 1.02 1.62 0.00 1.10 0.85

time (sec)

N/A 0.271 0.024 0.717 0.188 0.312 0.000 0.328 6.079

Problem 13

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

126 131 171 89 115 85 398 123 461

N.S.

1 1.04 1.36 0.71 0.91 0.67 3.16 0.98 3.66

time (sec)

N/A 0.585 1.046 0.844 0.190 0.332 0.716 0.407 8.801

Problem 14

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

67 60 58 73 95 71 158 117 92

N.S.

1 0.90 0.87 1.09 1.42 1.06 2.36 1.75 1.37

time (sec)

N/A 0.254 0.070 0.431 0.192 0.362 0.475 0.377 5.927

Problem 15

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

102 105 151 76 89 72 287 106 349

N.S.

1 1.03 1.48 0.75 0.87 0.71 2.81 1.04 3.42

time (sec)

N/A 0.476 0.388 0.665 0.187 0.294 0.391 0.359 8.609

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

45 41 46 48 56 58 107 56 53

N.S.

1 0.91 1.02 1.07 1.24 1.29 2.38 1.24 1.18

time (sec)

N/A 0.240 0.063 0.296 0.183 0.290 0.235 0.352 0.073

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

78 79 131 56 65 59 180 72 237

N.S.

1 1.01 1.68 0.72 0.83 0.76 2.31 0.92 3.04

time (sec)

N/A 0.390 0.204 0.329 0.185 0.285 0.188 0.323 8.429

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 47 21 20 44 53 20 32

N.S.

1 1.00 2.14 0.95 0.91 2.00 2.41 0.91 1.45

time (sec)

N/A 0.198 0.020 0.192 0.194 0.299 0.114 0.302 5.817

Problem 19

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

34 30 29 44 30 32 0 91 26

N.S.

1 0.88 0.85 1.29 0.88 0.94 0.00 2.68 0.76

time (sec)

N/A 0.232 0.019 0.299 0.181 0.293 0.000 0.318 0.074

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 39 75 30 47 74 0 33 28

N.S.

1 1.03 1.97 0.79 1.24 1.95 0.00 0.87 0.74

time (sec)

N/A 0.297 0.046 0.467 0.269 0.302 0.000 0.309 6.035

Problem 21

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

20 20 19 31 18 19 0 30 18

N.S.

1 1.00 0.95 1.55 0.90 0.95 0.00 1.50 0.90

time (sec)

N/A 0.207 0.026 0.435 0.185 0.353 0.000 0.347 5.889

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 60 58 38 52 97 0 54 81

N.S.

1 0.95 0.92 0.60 0.83 1.54 0.00 0.86 1.29

time (sec)

N/A 0.342 0.011 0.494 0.186 0.319 0.000 0.356 6.082

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 62 56 100 71 125 0 77 58

N.S.

1 0.97 0.88 1.56 1.11 1.95 0.00 1.20 0.91

time (sec)

N/A 0.262 0.053 0.603 0.183 0.298 0.000 0.341 5.863

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 61 82 63 77 85 0 106 156

N.S.

1 0.95 1.28 0.98 1.20 1.33 0.00 1.66 2.44

time (sec)

N/A 0.314 0.011 0.601 0.190 0.279 0.000 0.336 6.264

Problem 25

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

109 101 85 160 108 203 0 119 94

N.S.

1 0.93 0.78 1.47 0.99 1.86 0.00 1.09 0.86

time (sec)

N/A 0.295 0.100 0.786 0.188 0.305 0.000 0.333 6.048

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 73 110 86 98 115 0 171 276

N.S.

1 0.89 1.34 1.05 1.20 1.40 0.00 2.09 3.37

time (sec)

N/A 0.322 0.020 0.731 0.186 0.291 0.000 0.342 6.552

Problem 27

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

154 165 181 111 141 98 439 157 501

N.S.

1 1.07 1.18 0.72 0.92 0.64 2.85 1.02 3.25

time (sec)

N/A 0.724 1.300 1.025 0.197 0.307 0.980 0.445 9.013

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 60 58 85 108 85 196 134 106

N.S.

1 0.90 0.87 1.27 1.61 1.27 2.93 2.00 1.58

time (sec)

N/A 0.253 0.065 0.594 0.181 0.324 0.675 0.394 5.978

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

130 139 161 85 115 85 335 123 389

N.S.

1 1.07 1.24 0.65 0.88 0.65 2.58 0.95 2.99

time (sec)

N/A 0.624 0.517 0.747 0.184 0.325 0.543 0.370 8.457

Problem 30

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

45 41 43 68 82 72 146 82 80

N.S.

1 0.91 0.96 1.51 1.82 1.60 3.24 1.82 1.78

time (sec)

N/A 0.233 0.109 0.400 0.183 0.295 0.357 0.375 6.002

Problem 31

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

106 113 141 67 91 72 226 89 277

N.S.

1 1.07 1.33 0.63 0.86 0.68 2.13 0.84 2.61

time (sec)

N/A 0.507 0.303 0.395 0.187 0.299 0.269 0.332 8.391

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 65 21 20 57 70 20 53

N.S.

1 1.00 2.95 0.95 0.91 2.59 3.18 0.91 2.41

time (sec)

N/A 0.198 0.021 0.257 0.183 0.285 0.178 0.298 0.069

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

52 49 41 58 43 45 0 128 36

N.S.

1 0.94 0.79 1.12 0.83 0.87 0.00 2.46 0.69

time (sec)

N/A 0.228 0.024 0.401 0.189 0.347 0.000 0.330 0.061

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 59 55 54 68 101 0 91 138

N.S.

1 1.18 1.10 1.08 1.36 2.02 0.00 1.82 2.76

time (sec)

N/A 0.415 0.025 0.664 0.273 0.301 0.000 0.340 6.235

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 36 59 72 33 51 0 92 35

N.S.

1 0.90 1.48 1.80 0.82 1.28 0.00 2.30 0.88

time (sec)

N/A 0.241 0.034 0.525 0.187 0.306 0.000 0.345 6.039

Problem 36

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

31 31 28 37 78 99 0 38 55

N.S.

1 1.00 0.90 1.19 2.52 3.19 0.00 1.23 1.77

time (sec)

N/A 0.292 0.019 0.665 0.191 0.281 0.000 0.337 6.036

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 28 32 28 30 0 63 18

N.S.

1 1.00 1.22 1.39 1.22 1.30 0.00 2.74 0.78

time (sec)

N/A 0.213 0.018 0.490 0.182 0.279 0.000 0.393 0.082

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 94 110 55 103 149 0 86 135

N.S.

1 1.02 1.20 0.60 1.12 1.62 0.00 0.93 1.47

time (sec)

N/A 0.437 0.011 0.726 0.193 0.322 0.000 0.325 6.274

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 82 67 125 96 185 0 90 81

N.S.

1 0.94 0.77 1.44 1.10 2.13 0.00 1.03 0.93

time (sec)

N/A 0.282 0.078 0.700 0.188 0.324 0.000 0.344 5.964

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 92 134 84 122 112 0 138 228

N.S.

1 0.93 1.35 0.85 1.23 1.13 0.00 1.39 2.30

time (sec)

N/A 0.428 0.013 0.907 0.212 0.272 0.000 0.343 6.361

Problem 41

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

67 60 58 135 173 149 558 219 134

N.S.

1 0.90 0.87 2.01 2.58 2.22 8.33 3.27 2.00

time (sec)

N/A 0.269 0.282 2.356 0.179 0.323 3.633 0.433 0.226

Problem 42

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

286 309 211 142 339 150 1280 208 684

N.S.

1 1.08 0.74 0.50 1.19 0.52 4.48 0.73 2.39

time (sec)

N/A 1.568 2.003 2.210 0.214 0.337 2.809 0.444 9.075

Problem 43

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

45 41 43 108 134 136 422 134 132

N.S.

1 0.91 0.96 2.40 2.98 3.02 9.38 2.98 2.93

time (sec)

N/A 0.252 0.667 1.418 0.186 0.313 2.051 0.382 0.128

Problem 44

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

262 283 191 122 319 137 1018 174 572

N.S.

1 1.08 0.73 0.47 1.22 0.52 3.89 0.66 2.18

time (sec)

N/A 1.395 0.956 1.230 0.199 0.318 1.440 0.460 8.411

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 147 21 20 122 148 20 118

N.S.

1 1.00 6.68 0.95 0.91 5.55 6.73 0.91 5.36

time (sec)

N/A 0.199 0.056 0.858 0.178 0.302 0.970 0.364 0.125

Problem 46

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

162 139 95 113 109 114 0 288 109

N.S.

1 0.86 0.59 0.70 0.67 0.70 0.00 1.78 0.67

time (sec)

N/A 0.295 0.119 0.959 0.184 0.307 0.000 0.353 5.459

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 225 55 111 331 231 0 231 513

N.S.

1 1.12 0.27 0.55 1.65 1.15 0.00 1.15 2.55

time (sec)

N/A 1.189 0.041 3.773 0.275 0.328 0.000 0.360 10.497

Problem 48

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

121 108 111 128 97 130 0 275 97

N.S.

1 0.89 0.92 1.06 0.80 1.07 0.00 2.27 0.80

time (sec)

N/A 0.289 0.165 1.076 0.189 0.293 0.000 0.384 6.016

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 201 59 166 311 247 0 200 437

N.S.

1 1.12 0.33 0.93 1.74 1.38 0.00 1.12 2.44

time (sec)

N/A 1.005 0.039 2.497 0.279 0.333 0.000 0.453 11.277

Problem 50

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

110 100 73 150 95 139 0 243 96

N.S.

1 0.91 0.66 1.36 0.86 1.26 0.00 2.21 0.87

time (sec)

N/A 0.288 0.297 1.024 0.184 0.370 0.000 0.418 5.894

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 74 141 67 258 50 1355 114 107

N.S.

1 1.01 1.93 0.92 3.53 0.68 18.56 1.56 1.47

time (sec)

N/A 0.361 0.543 0.427 0.271 0.344 11.908 0.307 9.962

Problem 52

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

47 43 46 45 47 37 530 47 54

N.S.

1 0.91 0.98 0.96 1.00 0.79 11.28 1.00 1.15

time (sec)

N/A 0.249 0.070 0.249 0.192 0.359 6.870 0.325 6.014

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 48 119 43 156 37 558 75 66

N.S.

1 0.98 2.43 0.88 3.18 0.76 11.39 1.53 1.35

time (sec)

N/A 0.278 0.183 0.315 0.271 0.374 3.678 0.367 8.590

Problem 54

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

32 23 24 25 25 25 158 25 22

N.S.

1 0.72 0.75 0.78 0.78 0.78 4.94 0.78 0.69

time (sec)

N/A 0.217 0.022 0.157 0.187 0.289 1.863 0.356 5.890

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 97 19 52 17 88 34 29

N.S.

1 1.00 5.11 1.00 2.74 0.89 4.63 1.79 1.53

time (sec)

N/A 0.211 0.079 0.240 0.267 0.303 0.999 0.327 6.051

Problem 56

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

16 18 16 19 18 16 24 19 16

N.S.

1 1.12 1.00 1.19 1.12 1.00 1.50 1.19 1.00

time (sec)

N/A 0.199 0.005 0.118 0.181 0.287 0.247 0.289 0.058

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

37 39 30 43 47 58 0 58 33

N.S.

1 1.05 0.81 1.16 1.27 1.57 0.00 1.57 0.89

time (sec)

N/A 0.245 0.021 0.311 0.187 0.321 0.000 0.385 0.085

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 45 51 129 49 0 67 71

N.S.

1 1.00 1.07 1.21 3.07 1.17 0.00 1.60 1.69

time (sec)

N/A 0.290 0.037 0.355 0.188 0.293 0.000 0.314 6.254

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

77 80 75 67 91 125 0 96 74

N.S.

1 1.04 0.97 0.87 1.18 1.62 0.00 1.25 0.96

time (sec)

N/A 0.281 0.058 0.549 0.185 0.343 0.000 0.316 6.120

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 59 66 74 294 75 0 119 125

N.S.

1 0.95 1.06 1.19 4.74 1.21 0.00 1.92 2.02

time (sec)

N/A 0.321 0.072 0.587 0.194 0.352 0.000 0.305 7.425

Problem 61

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

120 119 97 91 130 147 0 116 115

N.S.

1 0.99 0.81 0.76 1.08 1.22 0.00 0.97 0.96

time (sec)

N/A 0.308 0.100 0.955 0.196 0.292 0.000 0.324 0.173

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 113 151 78 393 60 2531 179 172

N.S.

1 1.09 1.45 0.75 3.78 0.58 24.34 1.72 1.65

time (sec)

N/A 0.514 0.758 0.488 0.283 0.315 56.716 0.324 10.061

Problem 63

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

47 43 46 46 47 47 1037 47 54

N.S.

1 0.91 0.98 0.98 1.00 1.00 22.06 1.00 1.15

time (sec)

N/A 0.244 0.115 0.398 0.190 0.276 35.372 0.442 5.995

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 87 131 56 267 50 1243 127 65

N.S.

1 1.09 1.64 0.70 3.34 0.62 15.54 1.59 0.81

time (sec)

N/A 0.406 0.322 0.505 0.291 0.302 22.326 0.433 6.007

Problem 65

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

23 23 34 19 35 37 394 35 32

N.S.

1 1.00 1.48 0.83 1.52 1.61 17.13 1.52 1.39

time (sec)

N/A 0.216 0.048 0.293 0.204 0.285 12.827 0.329 5.983

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 58 109 34 140 35 403 73 32

N.S.

1 1.04 1.95 0.61 2.50 0.62 7.20 1.30 0.57

time (sec)

N/A 0.328 0.116 0.428 0.277 0.302 7.325 0.312 6.129

Problem 67

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

32 31 26 28 30 27 150 54 27

N.S.

1 0.97 0.81 0.88 0.94 0.84 4.69 1.69 0.84

time (sec)

N/A 0.235 0.024 0.286 0.202 0.395 0.511 0.399 0.073

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 104 30 56 61 95 33 28

N.S.

1 1.00 3.06 0.88 1.65 1.79 2.79 0.97 0.82

time (sec)

N/A 0.221 0.116 0.357 0.283 0.295 2.106 0.298 5.946

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

21 20 18 21 20 21 32 20 18

N.S.

1 0.95 0.86 1.00 0.95 1.00 1.52 0.95 0.86

time (sec)

N/A 0.200 0.020 0.183 0.193 0.284 0.411 0.303 0.061

Problem 70

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

60 58 38 55 72 105 0 71 60

N.S.

1 0.97 0.63 0.92 1.20 1.75 0.00 1.18 1.00

time (sec)

N/A 0.256 0.068 0.493 0.193 0.296 0.000 0.300 6.061

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 75 53 63 204 79 0 93 156

N.S.

1 1.06 0.75 0.89 2.87 1.11 0.00 1.31 2.20

time (sec)

N/A 0.435 0.055 0.556 0.207 0.271 0.000 0.317 6.166

Problem 72

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

104 99 85 79 108 178 0 106 93

N.S.

1 0.95 0.82 0.76 1.04 1.71 0.00 1.02 0.89

time (sec)

N/A 0.294 0.084 0.872 0.197 0.302 0.000 0.322 0.112

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 94 78 86 396 103 0 145 276

N.S.

1 1.01 0.84 0.92 4.26 1.11 0.00 1.56 2.97

time (sec)

N/A 0.474 0.046 0.951 0.198 0.275 0.000 0.311 6.742

Problem 74

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

146 138 137 103 167 198 0 126 151

N.S.

1 0.95 0.94 0.71 1.14 1.36 0.00 0.86 1.03

time (sec)

N/A 0.320 0.222 1.379 0.191 0.371 0.000 0.329 0.237

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 112 141 67 310 60 1717 140 81

N.S.

1 1.09 1.37 0.65 3.01 0.58 16.67 1.36 0.79

time (sec)

N/A 0.500 0.714 0.454 0.284 0.286 90.802 0.328 6.055

Problem 76

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

23 23 44 19 45 45 654 45 53

N.S.

1 1.00 1.91 0.83 1.96 1.96 28.43 1.96 2.30

time (sec)

N/A 0.217 0.112 0.253 0.182 0.276 58.420 0.350 6.242

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 82 121 45 184 45 690 88 57

N.S.

1 1.06 1.57 0.58 2.39 0.58 8.96 1.14 0.74

time (sec)

N/A 0.404 0.273 0.548 0.273 0.274 37.033 0.321 6.168

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 38 38 41 36 564 115 36

N.S.

1 1.00 0.76 0.76 0.82 0.72 11.28 2.30 0.72

time (sec)

N/A 0.239 0.043 0.430 0.188 0.283 23.005 0.323 5.907

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 53 59 54 139 78 478 80 69

N.S.

1 1.08 1.20 1.10 2.84 1.59 9.76 1.63 1.41

time (sec)

N/A 0.332 0.035 0.492 0.273 0.375 13.892 0.319 6.410

Problem 80

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

39 36 58 32 37 41 299 35 36

N.S.

1 0.92 1.49 0.82 0.95 1.05 7.67 0.90 0.92

time (sec)

N/A 0.245 0.045 0.352 0.182 0.283 0.596 0.439 5.931

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 28 36 99 95 153 36 53

N.S.

1 1.00 1.04 1.33 3.67 3.52 5.67 1.33 1.96

time (sec)

N/A 0.223 0.017 0.444 0.202 0.298 4.436 0.307 6.044

Problem 82

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

22 22 20 21 20 36 51 20 18

N.S.

1 1.00 0.91 0.95 0.91 1.64 2.32 0.91 0.82

time (sec)

N/A 0.205 0.020 0.257 0.179 0.278 0.540 0.305 5.908

Problem 83

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

82 77 61 67 98 154 0 81 83

N.S.

1 0.94 0.74 0.82 1.20 1.88 0.00 0.99 1.01

time (sec)

N/A 0.275 0.060 0.646 0.191 0.347 0.000 0.304 6.062

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 108 63 74 310 106 0 119 228

N.S.

1 1.09 0.64 0.75 3.13 1.07 0.00 1.20 2.30

time (sec)

N/A 0.560 0.068 0.813 0.209 0.270 0.000 0.317 6.574

Problem 85

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

126 118 95 91 146 228 0 116 129

N.S.

1 0.94 0.75 0.72 1.16 1.81 0.00 0.92 1.02

time (sec)

N/A 0.306 0.109 1.176 0.186 0.304 0.000 0.478 0.203

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 129 85 97 482 130 0 171 167

N.S.

1 1.05 0.69 0.79 3.92 1.06 0.00 1.39 1.36

time (sec)

N/A 0.621 0.086 1.297 0.221 0.287 0.000 0.330 7.094

Problem 87

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

171 157 145 115 188 248 0 136 173

N.S.

1 0.92 0.85 0.67 1.10 1.45 0.00 0.80 1.01

time (sec)

N/A 0.336 0.333 1.961 0.196 0.366 0.000 0.340 0.286

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 142 275 100 295 244 0 99 91

N.S.

1 1.12 2.17 0.79 2.32 1.92 0.00 0.78 0.72

time (sec)

N/A 0.624 6.064 0.705 0.285 0.301 0.000 0.483 9.358

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 35 28 58 74 82 2006 68 64

N.S.

1 0.97 0.78 1.61 2.06 2.28 55.72 1.89 1.78

time (sec)

N/A 0.224 0.059 0.654 0.210 0.274 9.838 0.393 0.080

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 36 107 375 239 0 125 118

N.S.

1 1.00 0.62 1.84 6.47 4.12 0.00 2.16 2.03

time (sec)

N/A 0.321 0.060 0.893 0.203 0.287 0.000 0.392 8.122

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 57 58 43 93 100 1120 137 54

N.S.

1 0.88 0.89 0.66 1.43 1.54 17.23 2.11 0.83

time (sec)

N/A 0.255 0.076 0.794 0.188 0.340 9.265 0.383 5.932

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 128 58 107 461 291 2470 151 140

N.S.

1 1.08 0.49 0.91 3.91 2.47 20.93 1.28 1.19

time (sec)

N/A 0.580 0.060 1.116 0.203 0.285 164.635 0.563 9.038

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 41 43 33 96 105 493 28 28

N.S.

1 0.91 0.96 0.73 2.13 2.33 10.96 0.62 0.62

time (sec)

N/A 0.243 0.108 0.965 0.196 0.285 9.749 0.373 0.118

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 198 78 107 547 339 3405 177 162

N.S.

1 1.08 0.43 0.58 2.99 1.85 18.61 0.97 0.89

time (sec)

N/A 0.895 0.111 1.299 0.211 0.303 84.940 0.392 9.979

Problem 95

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

22 22 20 21 20 108 128 20 18

N.S.

1 1.00 0.91 0.95 0.91 4.91 5.82 0.91 0.82

time (sec)

N/A 0.197 0.041 1.227 0.189 0.318 9.463 0.355 6.135

Problem 96

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

194 172 122 127 213 374 0 131 198

N.S.

1 0.89 0.63 0.65 1.10 1.93 0.00 0.68 1.02

time (sec)

N/A 0.326 0.532 2.625 0.184 0.316 0.000 0.365 0.392

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 273 113 132 740 225 0 249 233

N.S.

1 1.11 0.46 0.54 3.02 0.92 0.00 1.02 0.95

time (sec)

N/A 1.427 0.259 4.016 0.221 0.298 0.000 0.537 10.094

Problem 98

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

238 213 175 151 248 446 0 166 231

N.S.

1 0.89 0.74 0.63 1.04 1.87 0.00 0.70 0.97

time (sec)

N/A 0.384 1.126 5.512 0.206 0.355 0.000 0.394 0.597

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

279 304 125 143 866 249 0 301 277

N.S.

1 1.09 0.45 0.51 3.10 0.89 0.00 1.08 0.99

time (sec)

N/A 1.522 0.315 6.420 0.235 0.320 0.000 0.427 11.476

Problem 100

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

284 252 195 175 305 466 0 186 290

N.S.

1 0.89 0.69 0.62 1.07 1.64 0.00 0.65 1.02

time (sec)

N/A 0.462 1.694 7.944 0.197 0.397 0.000 0.447 0.990

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