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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 F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 104 154 159 215 131 0 145 176

N.S.

1 0.99 1.47 1.51 2.05 1.25 0.00 1.38 1.68

time (sec)

N/A 0.385 5.132 6.241 0.242 0.286 0.000 0.337 18.912

Problem 2

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

86 86 144 111 133 117 0 128 146

N.S.

1 1.00 1.67 1.29 1.55 1.36 0.00 1.49 1.70

time (sec)

N/A 0.351 1.289 3.683 0.238 0.290 0.000 0.325 17.219

Problem 3

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

61 56 132 98 108 103 0 111 114

N.S.

1 0.92 2.16 1.61 1.77 1.69 0.00 1.82 1.87

time (sec)

N/A 0.296 0.571 4.149 0.213 0.275 0.000 0.311 15.641

Problem 4

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 38 38 58 68 67 0 55 77

N.S.

1 1.00 1.00 1.53 1.79 1.76 0.00 1.45 2.03

time (sec)

N/A 0.323 0.031 1.509 0.214 0.292 0.000 0.284 14.542

Problem 5

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

42 42 77 50 101 66 0 60 31

N.S.

1 1.00 1.83 1.19 2.40 1.57 0.00 1.43 0.74

time (sec)

N/A 0.293 0.202 0.745 0.220 0.268 0.000 0.297 13.764

Problem 6

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

36 36 23 21 97 51 0 20 20

N.S.

1 1.00 0.64 0.58 2.69 1.42 0.00 0.56 0.56

time (sec)

N/A 0.236 0.222 0.802 0.220 0.273 0.000 0.303 13.524

Problem 7

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

76 76 43 36 117 78 0 37 35

N.S.

1 1.00 0.57 0.47 1.54 1.03 0.00 0.49 0.46

time (sec)

N/A 0.386 0.399 0.832 0.232 0.258 0.000 0.316 14.247

Problem 8

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

116 120 55 49 177 104 0 51 61

N.S.

1 1.03 0.47 0.42 1.53 0.90 0.00 0.44 0.53

time (sec)

N/A 0.543 3.953 0.915 0.233 0.264 0.000 0.322 14.117

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

158 164 65 62 197 128 0 65 106

N.S.

1 1.04 0.41 0.39 1.25 0.81 0.00 0.41 0.67

time (sec)

N/A 0.723 5.136 0.899 0.220 0.263 0.000 0.362 13.796

Problem 10

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

171 157 102 209 368 177 0 197 251

N.S.

1 0.92 0.60 1.22 2.15 1.04 0.00 1.15 1.47

time (sec)

N/A 0.483 1.320 8.879 0.207 0.286 0.000 0.417 17.751

Problem 11

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

150 139 91 195 321 161 0 178 219

N.S.

1 0.93 0.61 1.30 2.14 1.07 0.00 1.19 1.46

time (sec)

N/A 0.444 0.893 6.697 0.215 0.294 0.000 0.363 17.241

Problem 12

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

94 81 82 143 227 145 0 159 187

N.S.

1 0.86 0.87 1.52 2.41 1.54 0.00 1.69 1.99

time (sec)

N/A 0.344 0.450 6.147 0.211 0.288 0.000 0.365 18.310

Problem 13

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

73 67 80 79 150 99 0 87 155

N.S.

1 0.92 1.10 1.08 2.05 1.36 0.00 1.19 2.12

time (sec)

N/A 0.440 0.038 2.635 0.212 0.274 0.000 0.321 16.965

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

61 56 45 96 108 103 0 111 113

N.S.

1 0.92 0.74 1.57 1.77 1.69 0.00 1.82 1.85

time (sec)

N/A 0.298 0.088 4.211 0.202 0.262 0.000 0.305 15.884

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 69 65 82 225 108 0 100 77

N.S.

1 0.93 0.88 1.11 3.04 1.46 0.00 1.35 1.04

time (sec)

N/A 0.471 0.586 0.933 0.207 0.276 0.000 0.310 13.771

Problem 16

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

89 89 109 65 201 128 0 84 63

N.S.

1 1.00 1.22 0.73 2.26 1.44 0.00 0.94 0.71

time (sec)

N/A 0.481 0.208 1.003 0.208 0.277 0.000 0.326 13.786

Problem 17

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

38 38 25 23 189 83 0 22 22

N.S.

1 1.00 0.66 0.61 4.97 2.18 0.00 0.58 0.58

time (sec)

N/A 0.261 0.140 0.876 0.216 0.279 0.000 0.325 13.543

Problem 18

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

80 80 47 38 270 114 0 41 37

N.S.

1 1.00 0.59 0.48 3.38 1.42 0.00 0.51 0.46

time (sec)

N/A 0.430 0.570 0.879 0.215 0.261 0.000 0.352 14.421

Problem 19

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

121 126 59 51 269 140 0 57 67

N.S.

1 1.04 0.49 0.42 2.22 1.16 0.00 0.47 0.55

time (sec)

N/A 0.622 0.772 1.002 0.225 0.258 0.000 0.373 14.170

Problem 20

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

163 172 69 64 389 168 0 73 108

N.S.

1 1.06 0.42 0.39 2.39 1.03 0.00 0.45 0.66

time (sec)

N/A 0.844 1.255 1.011 0.224 0.275 0.000 0.406 14.261

Problem 21

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

227 208 122 253 443 209 0 235 316

N.S.

1 0.92 0.54 1.11 1.95 0.92 0.00 1.04 1.39

time (sec)

N/A 0.543 3.241 9.323 0.227 0.295 0.000 0.419 17.264

Problem 22

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

206 190 111 239 408 193 0 216 284

N.S.

1 0.92 0.54 1.16 1.98 0.94 0.00 1.05 1.38

time (sec)

N/A 0.506 2.200 8.284 0.207 0.293 0.000 0.439 16.929

Problem 23

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

121 104 102 176 368 177 0 197 252

N.S.

1 0.86 0.84 1.45 3.04 1.46 0.00 1.63 2.08

time (sec)

N/A 0.370 0.917 8.492 0.213 0.284 0.000 0.398 16.854

Problem 24

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

100 94 125 142 244 115 0 103 220

N.S.

1 0.94 1.25 1.42 2.44 1.15 0.00 1.03 2.20

time (sec)

N/A 0.538 0.043 3.906 0.232 0.306 0.000 0.369 16.504

Problem 25

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

94 81 81 143 227 145 0 159 188

N.S.

1 0.86 0.86 1.52 2.41 1.54 0.00 1.69 2.00

time (sec)

N/A 0.339 0.494 6.603 0.217 0.271 0.000 0.361 17.534

Problem 26

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

86 86 70 111 133 117 0 128 146

N.S.

1 1.00 0.81 1.29 1.55 1.36 0.00 1.49 1.70

time (sec)

N/A 0.344 0.404 4.161 0.208 0.288 0.000 0.334 16.369

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 98 65 106 387 125 0 118 105

N.S.

1 0.98 0.65 1.06 3.87 1.25 0.00 1.18 1.05

time (sec)

N/A 0.610 0.574 1.111 0.207 0.279 0.000 0.338 14.682

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 117 65 97 349 165 0 116 93

N.S.

1 0.98 0.55 0.82 2.93 1.39 0.00 0.97 0.78

time (sec)

N/A 0.699 0.659 1.145 0.226 0.257 0.000 0.363 13.372

Problem 29

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

132 135 139 78 309 176 0 102 78

N.S.

1 1.02 1.05 0.59 2.34 1.33 0.00 0.77 0.59

time (sec)

N/A 0.694 0.215 1.077 0.225 0.266 0.000 0.368 13.101

Problem 30

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

38 38 25 23 356 111 0 22 22

N.S.

1 1.00 0.66 0.61 9.37 2.92 0.00 0.58 0.58

time (sec)

N/A 0.251 0.111 0.939 0.225 0.262 0.000 0.349 12.855

Problem 31

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

80 80 47 38 357 140 0 41 37

N.S.

1 1.00 0.59 0.48 4.46 1.75 0.00 0.51 0.46

time (sec)

N/A 0.429 0.350 1.045 0.233 0.262 0.000 0.406 12.926

Problem 32

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

121 126 59 51 518 168 0 57 67

N.S.

1 1.04 0.49 0.42 4.28 1.39 0.00 0.47 0.55

time (sec)

N/A 0.603 0.750 1.012 0.222 0.263 0.000 0.418 13.323

Problem 33

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

162 172 69 64 517 194 0 73 108

N.S.

1 1.06 0.43 0.40 3.19 1.20 0.00 0.45 0.67

time (sec)

N/A 0.846 5.005 1.167 0.242 0.262 0.000 0.503 13.230

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 116 53 138 591 153 0 132 112

N.S.

1 0.96 0.44 1.14 4.88 1.26 0.00 1.09 0.93

time (sec)

N/A 0.447 0.991 1.303 0.209 0.286 0.000 0.338 13.273

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 98 53 106 386 140 0 116 96

N.S.

1 0.98 0.53 1.06 3.86 1.40 0.00 1.16 0.96

time (sec)

N/A 0.632 0.478 1.104 0.199 0.270 0.000 0.326 13.594

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 70 62 80 224 119 0 97 77

N.S.

1 0.95 0.84 1.08 3.03 1.61 0.00 1.31 1.04

time (sec)

N/A 0.483 0.437 0.963 0.231 0.287 0.000 0.302 13.121

Problem 37

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

41 41 77 47 101 70 0 58 31

N.S.

1 1.00 1.88 1.15 2.46 1.71 0.00 1.41 0.76

time (sec)

N/A 0.294 0.153 0.796 0.197 0.269 0.000 0.287 13.267

Problem 38

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

16 16 16 17 18 18 0 18 18

N.S.

1 1.00 1.00 1.06 1.12 1.12 0.00 1.12 1.12

time (sec)

N/A 0.313 0.022 0.994 0.193 0.255 0.000 0.285 12.919

Problem 39

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

59 51 53 48 77 50 0 56 50

N.S.

1 0.86 0.90 0.81 1.31 0.85 0.00 0.95 0.85

time (sec)

N/A 0.340 0.461 0.787 0.196 0.286 0.000 0.294 13.096

Problem 40

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

78 74 61 59 97 74 0 69 63

N.S.

1 0.95 0.78 0.76 1.24 0.95 0.00 0.88 0.81

time (sec)

N/A 0.398 0.526 0.933 0.204 0.251 0.000 0.317 13.093

Problem 41

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

120 109 79 74 117 102 0 82 83

N.S.

1 0.91 0.66 0.62 0.98 0.85 0.00 0.68 0.69

time (sec)

N/A 0.466 1.526 0.888 0.209 0.256 0.000 0.330 13.438

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 162 75 155 765 210 0 156 170

N.S.

1 0.99 0.46 0.95 4.66 1.28 0.00 0.95 1.04

time (sec)

N/A 0.660 2.917 1.450 0.230 0.274 0.000 0.406 12.939

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 146 75 125 531 197 0 140 136

N.S.

1 0.97 0.50 0.83 3.54 1.31 0.00 0.93 0.91

time (sec)

N/A 0.879 1.964 1.267 0.212 0.291 0.000 0.349 12.991

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 118 75 95 341 178 0 121 104

N.S.

1 0.99 0.63 0.80 2.87 1.50 0.00 1.02 0.87

time (sec)

N/A 0.717 0.455 1.118 0.214 0.269 0.000 0.346 13.039

Problem 45

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

88 88 109 65 196 138 0 89 46

N.S.

1 1.00 1.24 0.74 2.23 1.57 0.00 1.01 0.52

time (sec)

N/A 0.494 0.156 0.827 0.219 0.280 0.000 0.311 13.037

Problem 46

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

36 36 23 21 94 53 0 20 20

N.S.

1 1.00 0.64 0.58 2.61 1.47 0.00 0.56 0.56

time (sec)

N/A 0.233 0.059 0.785 0.203 0.270 0.000 0.286 12.844

Problem 47

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

59 51 59 48 76 49 0 69 61

N.S.

1 0.86 1.00 0.81 1.29 0.83 0.00 1.17 1.03

time (sec)

N/A 0.339 0.707 0.728 0.210 0.266 0.000 0.304 12.871

Problem 48

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 32 33 28 31 50 0 31 28

N.S.

1 0.84 0.87 0.74 0.82 1.32 0.00 0.82 0.74

time (sec)

N/A 0.348 0.041 1.026 0.186 0.256 0.000 0.318 12.991

Problem 49

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

80 69 79 74 121 109 0 96 76

N.S.

1 0.86 0.99 0.92 1.51 1.36 0.00 1.20 0.95

time (sec)

N/A 0.356 0.828 0.665 0.202 0.282 0.000 0.327 13.465

Problem 50

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

98 90 89 87 140 120 0 109 89

N.S.

1 0.92 0.91 0.89 1.43 1.22 0.00 1.11 0.91

time (sec)

N/A 0.401 1.690 0.670 0.200 0.253 0.000 0.346 14.314

Problem 51

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

141 129 99 100 161 163 0 122 102

N.S.

1 0.91 0.70 0.71 1.14 1.16 0.00 0.87 0.72

time (sec)

N/A 0.469 3.868 0.851 0.214 0.269 0.000 0.391 15.563

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 210 75 168 935 263 0 176 193

N.S.

1 0.98 0.35 0.78 4.35 1.22 0.00 0.82 0.90

time (sec)

N/A 0.891 5.144 1.056 0.260 0.270 0.000 0.460 12.969

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 194 75 136 680 250 0 159 159

N.S.

1 1.01 0.39 0.70 3.52 1.30 0.00 0.82 0.82

time (sec)

N/A 1.144 3.394 0.984 0.214 0.288 0.000 0.412 12.956

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 166 75 108 470 231 0 141 126

N.S.

1 1.01 0.46 0.66 2.87 1.41 0.00 0.86 0.77

time (sec)

N/A 0.967 0.926 0.885 0.223 0.297 0.000 0.373 13.038

Problem 55

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

131 134 139 76 304 192 0 109 61

N.S.

1 1.02 1.06 0.58 2.32 1.47 0.00 0.83 0.47

time (sec)

N/A 0.702 0.187 0.725 0.211 0.272 0.000 0.355 13.042

Problem 56

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

38 38 25 23 185 82 0 22 22

N.S.

1 1.00 0.66 0.61 4.87 2.16 0.00 0.58 0.58

time (sec)

N/A 0.259 0.085 0.723 0.200 0.257 0.000 0.336 13.005

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

76 76 43 36 115 79 0 37 35

N.S.

1 1.00 0.57 0.47 1.51 1.04 0.00 0.49 0.46

time (sec)

N/A 0.385 0.196 0.659 0.204 0.262 0.000 0.320 13.132

Problem 58

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

78 74 67 59 95 76 0 87 74

N.S.

1 0.95 0.86 0.76 1.22 0.97 0.00 1.12 0.95

time (sec)

N/A 0.388 0.488 0.713 0.213 0.259 0.000 0.343 12.950

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

80 69 79 74 120 109 0 103 111

N.S.

1 0.86 0.99 0.92 1.50 1.36 0.00 1.29 1.39

time (sec)

N/A 0.348 0.733 0.703 0.205 0.258 0.000 0.359 13.239

Problem 60

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

59 41 50 41 41 76 0 41 38

N.S.

1 0.69 0.85 0.69 0.69 1.29 0.00 0.69 0.64

time (sec)

N/A 0.362 0.062 1.078 0.210 0.273 0.000 0.367 13.393

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

99 81 99 99 159 163 0 128 129

N.S.

1 0.82 1.00 1.00 1.61 1.65 0.00 1.29 1.30

time (sec)

N/A 0.366 3.107 0.789 0.199 0.263 0.000 0.401 14.146

Problem 62

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

120 110 109 110 181 190 0 142 109

N.S.

1 0.92 0.91 0.92 1.51 1.58 0.00 1.18 0.91

time (sec)

N/A 0.438 5.142 0.787 0.208 0.278 0.000 0.418 14.424

Problem 63

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

162 145 119 121 200 217 0 155 120

N.S.

1 0.90 0.73 0.75 1.23 1.34 0.00 0.96 0.74

time (sec)

N/A 0.495 5.141 0.889 0.216 0.253 0.000 0.426 14.679

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 171 70 77 0 119 0 107 483

N.S.

1 1.05 0.43 0.47 0.00 0.73 0.00 0.66 2.96

time (sec)

N/A 0.793 2.276 7.670 0.000 0.274 0.000 0.840 20.552

Problem 65

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

122 126 60 67 0 105 0 83 384

N.S.

1 1.03 0.49 0.55 0.00 0.86 0.00 0.68 3.15

time (sec)

N/A 0.601 0.678 7.285 0.000 0.275 0.000 0.829 17.242

Problem 66

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

81 81 50 55 0 82 0 56 120

N.S.

1 1.00 0.62 0.68 0.00 1.01 0.00 0.69 1.48

time (sec)

N/A 0.419 0.416 4.587 0.000 0.270 0.000 0.697 17.059

Problem 67

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

39 39 38 42 0 65 0 31 87

N.S.

1 1.00 0.97 1.08 0.00 1.67 0.00 0.79 2.23

time (sec)

N/A 0.249 0.170 3.961 0.000 0.264 0.000 0.664 14.442

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 78 80 0 272 0 61 0

N.S.

1 1.00 1.01 1.04 0.00 3.53 0.00 0.79 0.00

time (sec)

N/A 0.383 0.253 3.635 0.000 0.329 0.000 0.953 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 81 178 0 342 0 72 0

N.S.

1 1.00 1.07 2.34 0.00 4.50 0.00 0.95 0.00

time (sec)

N/A 0.382 0.777 4.181 0.000 0.339 0.000 1.004 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 117 60 269 0 405 0 104 0

N.S.

1 1.04 0.53 2.38 0.00 3.58 0.00 0.92 0.00

time (sec)

N/A 0.526 0.479 4.186 0.000 0.346 0.000 1.176 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 179 88 79 0 147 0 109 606

N.S.

1 1.05 0.51 0.46 0.00 0.86 0.00 0.64 3.54

time (sec)

N/A 0.953 2.477 16.900 0.000 0.288 0.000 1.019 25.263

Problem 72

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

128 132 78 69 0 131 0 85 503

N.S.

1 1.03 0.61 0.54 0.00 1.02 0.00 0.66 3.93

time (sec)

N/A 0.746 1.662 15.644 0.000 0.268 0.000 0.833 20.220

Problem 73

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

85 85 66 57 0 105 0 58 384

N.S.

1 1.00 0.78 0.67 0.00 1.24 0.00 0.68 4.52

time (sec)

N/A 0.496 1.458 5.524 0.000 0.277 0.000 0.875 17.148

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 55 46 0 84 0 33 93

N.S.

1 1.00 1.34 1.12 0.00 2.05 0.00 0.80 2.27

time (sec)

N/A 0.282 0.602 4.711 0.000 0.273 0.000 0.757 17.857

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 123 107 108 0 343 0 82 0

N.S.

1 1.05 0.91 0.92 0.00 2.93 0.00 0.70 0.00

time (sec)

N/A 0.610 0.563 4.243 0.000 0.316 0.000 1.061 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 126 64 120 0 372 0 109 0

N.S.

1 1.12 0.57 1.06 0.00 3.29 0.00 0.96 0.00

time (sec)

N/A 0.620 0.423 4.841 0.000 0.314 0.000 1.230 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 127 150 228 0 429 0 106 0

N.S.

1 1.09 1.28 1.95 0.00 3.67 0.00 0.91 0.00

time (sec)

N/A 0.622 1.133 4.581 0.000 0.327 0.000 1.299 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 168 64 320 0 517 0 139 0

N.S.

1 1.02 0.39 1.95 0.00 3.15 0.00 0.85 0.00

time (sec)

N/A 0.776 0.614 5.486 0.000 0.345 0.000 1.114 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 179 88 79 0 163 0 109 710

N.S.

1 1.05 0.51 0.46 0.00 0.95 0.00 0.64 4.15

time (sec)

N/A 0.941 3.768 41.034 0.000 0.290 0.000 1.064 27.136

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 132 78 69 0 147 0 85 607

N.S.

1 1.03 0.61 0.54 0.00 1.15 0.00 0.66 4.74

time (sec)

N/A 0.719 1.034 38.804 0.000 0.271 0.000 1.033 25.004

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 66 57 0 119 0 58 471

N.S.

1 1.00 0.78 0.67 0.00 1.40 0.00 0.68 5.54

time (sec)

N/A 0.483 0.679 6.830 0.000 0.276 0.000 0.862 21.874

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 55 46 0 97 0 33 375

N.S.

1 1.00 1.34 1.12 0.00 2.37 0.00 0.80 9.15

time (sec)

N/A 0.295 0.774 5.636 0.000 0.263 0.000 0.823 17.156

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 168 119 125 0 377 0 111 0

N.S.

1 1.02 0.73 0.76 0.00 2.30 0.00 0.68 0.00

time (sec)

N/A 0.840 0.844 6.383 0.000 0.344 0.000 1.177 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 171 64 141 0 432 0 124 0

N.S.

1 1.02 0.38 0.84 0.00 2.57 0.00 0.74 0.00

time (sec)

N/A 0.852 0.595 7.095 0.000 0.331 0.000 1.033 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 176 64 223 0 441 0 133 0

N.S.

1 1.01 0.37 1.28 0.00 2.53 0.00 0.76 0.00

time (sec)

N/A 0.853 0.615 6.293 0.000 0.318 0.000 1.138 0.000

Problem 86

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

142 142 72 81 163 88 0 108 164

N.S.

1 1.00 0.51 0.57 1.15 0.62 0.00 0.76 1.15

time (sec)

N/A 0.692 0.850 5.281 0.316 0.266 0.000 0.830 17.983

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

108 107 62 71 137 77 0 84 125

N.S.

1 0.99 0.57 0.66 1.27 0.71 0.00 0.78 1.16

time (sec)

N/A 0.566 0.535 5.040 0.298 0.280 0.000 0.797 15.559

Problem 88

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

72 72 50 57 110 50 0 60 77

N.S.

1 1.00 0.69 0.79 1.53 0.69 0.00 0.83 1.07

time (sec)

N/A 0.443 0.312 2.822 0.300 0.267 0.000 0.702 13.685

Problem 89

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

39 39 29 28 84 45 0 59 40

N.S.

1 1.00 0.74 0.72 2.15 1.15 0.00 1.51 1.03

time (sec)

N/A 0.297 0.114 3.295 0.303 0.275 0.000 0.627 13.157

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 52 112 0 269 0 64 0

N.S.

1 1.00 0.58 1.26 0.00 3.02 0.00 0.72 0.00

time (sec)

N/A 0.456 0.292 3.001 0.000 0.324 0.000 0.437 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 124 58 192 0 329 0 97 0

N.S.

1 1.02 0.48 1.57 0.00 2.70 0.00 0.80 0.00

time (sec)

N/A 0.601 0.528 3.100 0.000 0.321 0.000 0.497 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 160 58 268 0 401 0 128 0

N.S.

1 1.03 0.37 1.72 0.00 2.57 0.00 0.82 0.00

time (sec)

N/A 0.770 0.586 3.310 0.000 0.324 0.000 0.544 0.000

Problem 93

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

155 155 72 89 188 103 0 121 188

N.S.

1 1.00 0.46 0.57 1.21 0.66 0.00 0.78 1.21

time (sec)

N/A 0.866 1.505 12.579 0.305 0.270 0.000 0.930 17.736

Problem 94

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

123 122 64 79 163 82 0 99 136

N.S.

1 0.99 0.52 0.64 1.33 0.67 0.00 0.80 1.11

time (sec)

N/A 0.700 0.899 12.524 0.319 0.269 0.000 0.808 17.268

Problem 95

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

89 88 54 53 110 72 0 60 134

N.S.

1 0.99 0.61 0.60 1.24 0.81 0.00 0.67 1.51

time (sec)

N/A 0.529 0.359 3.375 0.309 0.263 0.000 0.703 16.881

Problem 96

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

41 41 55 44 109 60 0 62 94

N.S.

1 1.00 1.34 1.07 2.66 1.46 0.00 1.51 2.29

time (sec)

N/A 0.310 0.118 3.705 0.315 0.267 0.000 0.648 17.175

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 137 60 184 0 331 0 93 0

N.S.

1 0.99 0.43 1.33 0.00 2.40 0.00 0.67 0.00

time (sec)

N/A 0.722 0.318 3.503 0.000 0.317 0.000 0.571 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 172 64 200 0 369 0 129 0

N.S.

1 1.02 0.38 1.18 0.00 2.18 0.00 0.76 0.00

time (sec)

N/A 0.886 0.488 3.612 0.000 0.334 0.000 0.517 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

203 208 64 281 0 487 0 160 0

N.S.

1 1.02 0.32 1.38 0.00 2.40 0.00 0.79 0.00

time (sec)

N/A 1.036 0.798 3.350 0.000 0.334 0.000 0.555 0.000

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

169 172 74 91 214 109 0 126 492

N.S.

1 1.02 0.44 0.54 1.27 0.64 0.00 0.75 2.91

time (sec)

N/A 0.954 0.911 36.524 0.324 0.284 0.000 1.024 22.304

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