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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 499 182 233 141 0 145 176

N.S.

1 1.00 4.75 1.73 2.22 1.34 0.00 1.38 1.68

time (sec)

N/A 0.140 1.706 0.270 0.273 3.048 0.000 0.573 6.644

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 887 111 144 126 0 128 146

N.S.

1 1.00 10.31 1.29 1.67 1.47 0.00 1.49 1.70

time (sec)

N/A 0.110 6.491 0.212 0.265 2.843 0.000 0.557 5.197

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 313 98 117 111 0 111 114

N.S.

1 1.00 5.13 1.61 1.92 1.82 0.00 1.82 1.87

time (sec)

N/A 0.070 0.735 0.188 0.265 3.328 0.000 0.577 3.810

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 58 74 73 0 55 77

N.S.

1 1.00 1.00 1.53 1.95 1.92 0.00 1.45 2.03

time (sec)

N/A 0.032 0.028 0.139 0.275 2.900 0.000 0.525 2.238

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 77 50 109 72 0 60 31

N.S.

1 1.00 1.83 1.19 2.60 1.71 0.00 1.43 0.74

time (sec)

N/A 0.037 0.084 0.130 0.271 2.500 0.000 0.569 1.846

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 50 21 105 55 0 20 20

N.S.

1 1.00 1.39 0.58 2.92 1.53 0.00 0.56 0.56

time (sec)

N/A 0.033 0.251 0.138 0.283 2.385 0.000 0.470 2.060

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 87 37 127 84 0 37 35

N.S.

1 1.00 1.14 0.49 1.67 1.11 0.00 0.49 0.46

time (sec)

N/A 0.070 0.345 0.154 0.287 3.273 0.000 0.490 1.710

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 113 50 193 112 0 51 61

N.S.

1 1.00 0.97 0.43 1.66 0.97 0.00 0.44 0.53

time (sec)

N/A 0.109 0.407 0.167 0.279 4.040 0.000 0.707 1.746

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 139 63 215 138 0 65 106

N.S.

1 1.00 0.88 0.40 1.36 0.87 0.00 0.41 0.67

time (sec)

N/A 0.149 0.366 0.193 0.275 3.370 0.000 0.791 1.843

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 102 299 398 189 0 197 251

N.S.

1 1.00 0.60 1.75 2.33 1.11 0.00 1.15 1.47

time (sec)

N/A 0.207 1.875 0.352 0.283 2.547 0.000 0.824 5.760

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

150 150 91 255 347 172 0 178 219

N.S.

1 1.00 0.61 1.70 2.31 1.15 0.00 1.19 1.46

time (sec)

N/A 0.176 1.403 0.307 0.276 2.866 0.000 0.611 5.608

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 82 192 245 155 0 159 187

N.S.

1 1.00 0.87 2.04 2.61 1.65 0.00 1.69 1.99

time (sec)

N/A 0.110 0.766 0.270 0.302 2.373 0.000 0.741 6.503

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 51 117 162 106 0 87 155

N.S.

1 1.00 0.70 1.60 2.22 1.45 0.00 1.19 2.12

time (sec)

N/A 0.078 0.155 0.193 0.274 3.763 0.000 0.570 5.213

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 45 96 117 111 0 111 113

N.S.

1 1.00 0.74 1.57 1.92 1.82 0.00 1.82 1.85

time (sec)

N/A 0.073 0.119 0.192 0.263 2.496 0.000 0.552 3.786

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 220 82 243 118 0 100 77

N.S.

1 1.00 2.97 1.11 3.28 1.59 0.00 1.35 1.04

time (sec)

N/A 0.071 1.885 0.155 0.279 2.164 0.000 0.661 1.907

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 109 67 217 138 0 84 63

N.S.

1 1.00 1.22 0.75 2.44 1.55 0.00 0.94 0.71

time (sec)

N/A 0.092 0.088 0.161 0.277 2.611 0.000 0.637 1.779

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 25 23 205 89 0 22 22

N.S.

1 1.00 0.66 0.61 5.39 2.34 0.00 0.58 0.58

time (sec)

N/A 0.055 0.125 0.178 0.284 2.496 0.000 0.540 1.643

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 115 39 294 122 0 41 37

N.S.

1 1.00 1.44 0.49 3.68 1.52 0.00 0.51 0.46

time (sec)

N/A 0.109 0.450 0.183 0.310 1.742 0.000 0.582 1.621

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 141 52 293 150 0 57 67

N.S.

1 1.00 1.17 0.43 2.42 1.24 0.00 0.47 0.55

time (sec)

N/A 0.166 0.435 0.214 0.307 3.232 0.000 0.604 1.631

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 167 65 425 180 0 73 108

N.S.

1 1.00 1.02 0.40 2.61 1.10 0.00 0.45 0.66

time (sec)

N/A 0.224 0.660 0.221 0.311 2.582 0.000 0.647 1.691

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 122 345 480 223 0 235 316

N.S.

1 1.00 0.54 1.52 2.11 0.98 0.00 1.04 1.39

time (sec)

N/A 0.255 3.262 0.350 0.282 2.480 0.000 0.634 5.579

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 111 322 442 206 0 216 284

N.S.

1 1.00 0.54 1.56 2.15 1.00 0.00 1.05 1.38

time (sec)

N/A 0.224 2.295 0.389 0.296 2.563 0.000 0.664 5.518

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 102 302 398 189 0 197 252

N.S.

1 1.00 0.84 2.50 3.29 1.56 0.00 1.63 2.08

time (sec)

N/A 0.128 1.667 0.364 0.295 3.046 0.000 0.605 5.707

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 60 180 264 123 0 103 220

N.S.

1 1.00 0.60 1.80 2.64 1.23 0.00 1.03 2.20

time (sec)

N/A 0.099 0.251 0.243 0.280 3.063 0.000 0.606 5.560

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 81 192 245 155 0 159 188

N.S.

1 1.00 0.86 2.04 2.61 1.65 0.00 1.69 2.00

time (sec)

N/A 0.113 0.831 0.271 0.287 3.071 0.000 0.601 6.265

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 70 111 144 126 0 128 146

N.S.

1 1.00 0.81 1.29 1.67 1.47 0.00 1.49 1.70

time (sec)

N/A 0.113 0.611 0.210 0.296 3.699 0.000 0.490 4.792

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 287 112 419 136 0 118 105

N.S.

1 1.00 2.87 1.12 4.19 1.36 0.00 1.18 1.05

time (sec)

N/A 0.094 2.644 0.174 0.280 2.629 0.000 0.552 3.172

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 402 97 377 179 0 116 93

N.S.

1 1.00 3.38 0.82 3.17 1.50 0.00 0.97 0.78

time (sec)

N/A 0.128 3.546 0.167 0.279 3.241 0.000 0.545 2.043

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 139 78 335 190 0 102 78

N.S.

1 1.00 1.05 0.59 2.54 1.44 0.00 0.77 0.59

time (sec)

N/A 0.154 0.125 0.206 0.307 2.338 0.000 0.517 1.778

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 25 23 388 119 0 22 22

N.S.

1 1.00 0.66 0.61 10.21 3.13 0.00 0.58 0.58

time (sec)

N/A 0.052 0.159 0.196 0.320 2.409 0.000 0.654 1.811

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 141 39 389 150 0 41 37

N.S.

1 1.00 1.76 0.49 4.86 1.88 0.00 0.51 0.46

time (sec)

N/A 0.109 0.407 0.225 0.300 2.202 0.000 0.624 1.621

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 167 52 566 180 0 57 67

N.S.

1 1.00 1.38 0.43 4.68 1.49 0.00 0.47 0.55

time (sec)

N/A 0.164 0.705 0.201 0.303 2.614 0.000 0.821 1.859

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 193 65 565 208 0 73 108

N.S.

1 1.00 1.19 0.40 3.49 1.28 0.00 0.45 0.67

time (sec)

N/A 0.224 0.606 0.234 0.321 4.696 0.000 0.692 1.716

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 1036 140 641 165 0 132 112

N.S.

1 1.00 8.56 1.16 5.30 1.36 0.00 1.09 0.93

time (sec)

N/A 0.120 6.454 0.187 0.295 3.270 0.000 0.556 1.854

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 287 110 418 151 0 116 96

N.S.

1 1.00 2.87 1.10 4.18 1.51 0.00 1.16 0.96

time (sec)

N/A 0.097 2.628 0.175 0.286 2.716 0.000 0.562 1.660

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 220 80 242 129 0 97 77

N.S.

1 1.00 2.97 1.08 3.27 1.74 0.00 1.31 1.04

time (sec)

N/A 0.073 1.672 0.139 0.291 2.820 0.000 0.562 1.636

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 77 48 109 76 0 58 31

N.S.

1 1.00 1.88 1.17 2.66 1.85 0.00 1.41 0.76

time (sec)

N/A 0.039 0.070 0.149 0.271 3.176 0.000 0.642 1.577

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 19 19 19 0 18 18

N.S.

1 1.00 1.00 1.19 1.19 1.19 0.00 1.12 1.12

time (sec)

N/A 0.064 0.030 0.123 0.270 3.248 0.000 0.546 1.556

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 81 48 83 54 0 56 50

N.S.

1 1.00 1.37 0.81 1.41 0.92 0.00 0.95 0.85

time (sec)

N/A 0.106 0.500 0.142 0.281 1.797 0.000 0.810 1.642

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 107 61 105 80 0 69 63

N.S.

1 1.00 1.37 0.78 1.35 1.03 0.00 0.88 0.81

time (sec)

N/A 0.136 0.845 0.165 0.270 3.277 0.000 0.723 1.722

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 145 74 127 110 0 82 83

N.S.

1 1.00 1.21 0.62 1.06 0.92 0.00 0.68 0.69

time (sec)

N/A 0.172 0.918 0.164 0.295 3.026 0.000 0.578 2.131

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 380 155 829 226 0 156 170

N.S.

1 1.00 2.32 0.95 5.05 1.38 0.00 0.95 1.04

time (sec)

N/A 0.183 1.204 0.228 0.293 3.983 0.000 0.666 1.734

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

150 150 349 125 575 212 0 140 136

N.S.

1 1.00 2.33 0.83 3.83 1.41 0.00 0.93 0.91

time (sec)

N/A 0.152 2.004 0.198 0.292 3.481 0.000 0.687 1.681

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 485 95 369 192 0 121 104

N.S.

1 1.00 4.08 0.80 3.10 1.61 0.00 1.02 0.87

time (sec)

N/A 0.134 4.378 0.175 0.281 3.364 0.000 0.610 1.649

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 109 65 212 148 0 89 46

N.S.

1 1.00 1.24 0.74 2.41 1.68 0.00 1.01 0.52

time (sec)

N/A 0.093 0.093 0.171 0.283 2.713 0.000 0.560 1.612

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 23 21 102 57 0 20 20

N.S.

1 1.00 0.64 0.58 2.83 1.58 0.00 0.56 0.56

time (sec)

N/A 0.035 0.090 0.155 0.275 3.412 0.000 0.598 1.567

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 83 48 82 53 0 69 61

N.S.

1 1.00 1.41 0.81 1.39 0.90 0.00 1.17 1.03

time (sec)

N/A 0.103 0.594 0.145 0.279 2.824 0.000 0.534 1.618

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 33 66 33 53 0 31 28

N.S.

1 1.00 0.87 1.74 0.87 1.39 0.00 0.82 0.74

time (sec)

N/A 0.074 0.052 0.207 0.281 2.394 0.000 0.540 1.565

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 147 76 131 117 0 96 76

N.S.

1 1.00 1.84 0.95 1.64 1.46 0.00 1.20 0.95

time (sec)

N/A 0.110 0.987 0.170 0.297 2.846 0.000 0.498 2.009

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 179 87 152 129 0 109 89

N.S.

1 1.00 1.83 0.89 1.55 1.32 0.00 1.11 0.91

time (sec)

N/A 0.146 0.935 0.193 0.308 2.052 0.000 0.513 2.668

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 211 102 175 175 0 122 102

N.S.

1 1.00 1.50 0.72 1.24 1.24 0.00 0.87 0.72

time (sec)

N/A 0.185 1.253 0.191 0.291 2.114 0.000 0.566 4.237

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 406 168 1015 283 0 176 193

N.S.

1 1.00 1.89 0.78 4.72 1.32 0.00 0.82 0.90

time (sec)

N/A 0.247 2.124 0.212 0.309 2.336 0.000 0.647 1.653

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 380 136 738 269 0 159 159

N.S.

1 1.00 1.97 0.70 3.82 1.39 0.00 0.82 0.82

time (sec)

N/A 0.215 1.307 0.223 0.301 2.227 0.000 0.659 1.642

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 826 108 510 249 0 141 126

N.S.

1 1.00 5.04 0.66 3.11 1.52 0.00 0.86 0.77

time (sec)

N/A 0.188 6.335 0.200 0.289 2.389 0.000 0.605 1.629

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 139 76 330 206 0 109 61

N.S.

1 1.00 1.06 0.58 2.52 1.57 0.00 0.83 0.47

time (sec)

N/A 0.151 0.124 0.195 0.283 3.267 0.000 0.585 1.646

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 25 23 201 88 0 22 22

N.S.

1 1.00 0.66 0.61 5.29 2.32 0.00 0.58 0.58

time (sec)

N/A 0.051 0.108 0.167 0.284 2.391 0.000 0.647 1.593

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 87 37 125 85 0 37 35

N.S.

1 1.00 1.14 0.49 1.64 1.12 0.00 0.49 0.46

time (sec)

N/A 0.070 0.347 0.180 0.291 2.570 0.000 0.566 1.576

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 109 61 103 82 0 87 74

N.S.

1 1.00 1.40 0.78 1.32 1.05 0.00 1.12 0.95

time (sec)

N/A 0.140 0.798 0.147 0.276 2.688 0.000 0.528 1.624

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 147 76 130 117 0 103 111

N.S.

1 1.00 1.84 0.95 1.62 1.46 0.00 1.29 1.39

time (sec)

N/A 0.109 0.795 0.166 0.290 4.183 0.000 0.640 1.708

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 50 95 44 81 0 41 38

N.S.

1 1.00 0.85 1.61 0.75 1.37 0.00 0.69 0.64

time (sec)

N/A 0.083 0.069 0.220 0.316 4.666 0.000 0.577 1.628

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 211 102 173 175 0 128 129

N.S.

1 1.00 2.13 1.03 1.75 1.77 0.00 1.29 1.30

time (sec)

N/A 0.113 1.256 0.191 0.284 3.690 0.000 0.664 2.536

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 257 115 197 204 0 142 109

N.S.

1 1.00 2.14 0.96 1.64 1.70 0.00 1.18 0.91

time (sec)

N/A 0.161 1.503 0.192 0.321 3.671 0.000 0.736 2.882

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 289 128 218 233 0 155 120

N.S.

1 1.00 1.78 0.79 1.35 1.44 0.00 0.96 0.74

time (sec)

N/A 0.194 2.112 0.191 0.278 4.143 0.000 0.683 3.107

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 86 83 0 128 0 107 483

N.S.

1 1.00 0.53 0.51 0.00 0.79 0.00 0.66 2.96

time (sec)

N/A 0.195 0.852 2.042 0.000 3.437 0.000 1.029 9.131

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 76 73 0 113 0 83 384

N.S.

1 1.00 0.62 0.60 0.00 0.93 0.00 0.68 3.15

time (sec)

N/A 0.142 0.470 2.322 0.000 3.766 0.000 1.078 6.004

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 64 63 0 89 0 56 120

N.S.

1 1.00 0.79 0.78 0.00 1.10 0.00 0.69 1.48

time (sec)

N/A 0.094 0.264 2.413 0.000 2.887 0.000 0.878 5.364

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 51 53 0 71 0 31 87

N.S.

1 1.00 1.31 1.36 0.00 1.82 0.00 0.79 2.23

time (sec)

N/A 0.043 0.181 2.308 0.000 3.310 0.000 0.802 2.749

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 132 85 0 294 0 61 -1

N.S.

1 1.00 1.71 1.10 0.00 3.82 0.00 0.79 -0.01

time (sec)

N/A 0.078 0.636 2.181 0.000 3.536 0.000 1.134 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 246 164 0 370 0 72 -1

N.S.

1 1.00 3.24 2.16 0.00 4.87 0.00 0.95 -0.01

time (sec)

N/A 0.080 1.122 2.254 0.000 3.567 0.000 1.107 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 309 308 0 439 0 104 -1

N.S.

1 1.00 2.73 2.73 0.00 3.88 0.00 0.92 -0.01

time (sec)

N/A 0.112 1.131 1.964 0.000 4.371 0.000 1.232 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 88 85 0 157 0 109 606

N.S.

1 1.00 0.51 0.50 0.00 0.92 0.00 0.64 3.54

time (sec)

N/A 0.310 1.662 2.467 0.000 4.051 0.000 1.129 14.397

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 78 75 0 140 0 85 503

N.S.

1 1.00 0.61 0.59 0.00 1.09 0.00 0.66 3.93

time (sec)

N/A 0.229 1.265 2.193 0.000 4.129 0.000 1.006 7.990

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 66 65 0 113 0 58 384

N.S.

1 1.00 0.78 0.76 0.00 1.33 0.00 0.68 4.52

time (sec)

N/A 0.145 0.780 2.319 0.000 3.877 0.000 1.027 6.139

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 55 55 0 91 0 33 93

N.S.

1 1.00 1.34 1.34 0.00 2.22 0.00 0.80 2.27

time (sec)

N/A 0.067 0.460 2.197 0.000 2.429 0.000 0.955 5.725

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 123 173 145 0 371 0 82 -1

N.S.

1 1.05 1.48 1.24 0.00 3.17 0.00 0.70 -0.01

time (sec)

N/A 0.159 0.920 2.238 0.000 3.205 0.000 1.170 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 124 184 144 0 400 0 109 -1

N.S.

1 1.10 1.63 1.27 0.00 3.54 0.00 0.96 -0.01

time (sec)

N/A 0.161 1.453 2.401 0.000 2.865 0.000 2.569 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 130 359 230 0 463 0 106 -1

N.S.

1 1.11 3.07 1.97 0.00 3.96 0.00 0.91 -0.01

time (sec)

N/A 0.159 2.486 2.427 0.000 3.238 0.000 1.391 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 398 402 0 557 0 139 -1

N.S.

1 1.00 2.43 2.45 0.00 3.40 0.00 0.85 -0.01

time (sec)

N/A 0.196 5.745 2.481 0.000 3.640 0.000 1.257 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 88 85 0 174 0 109 710

N.S.

1 1.00 0.51 0.50 0.00 1.02 0.00 0.64 4.15

time (sec)

N/A 0.303 2.554 2.397 0.000 2.683 0.000 1.261 14.671

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 78 75 0 157 0 85 607

N.S.

1 1.00 0.61 0.59 0.00 1.23 0.00 0.66 4.74

time (sec)

N/A 0.219 1.563 2.458 0.000 2.342 0.000 1.182 13.711

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 66 65 0 128 0 58 471

N.S.

1 1.00 0.78 0.76 0.00 1.51 0.00 0.68 5.54

time (sec)

N/A 0.141 1.044 2.299 0.000 3.230 0.000 0.983 9.194

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 55 55 0 105 0 33 375

N.S.

1 1.00 1.34 1.34 0.00 2.56 0.00 0.80 9.15

time (sec)

N/A 0.065 0.738 2.308 0.000 2.993 0.000 1.004 5.616

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 185 206 0 407 0 111 -1

N.S.

1 1.00 1.13 1.26 0.00 2.48 0.00 0.68 -0.01

time (sec)

N/A 0.228 1.548 2.326 0.000 4.108 0.000 2.097 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 324 157 0 466 0 124 -1

N.S.

1 1.00 1.93 0.93 0.00 2.77 0.00 0.74 -0.01

time (sec)

N/A 0.232 2.940 2.369 0.000 3.673 0.000 1.176 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F(-1) A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 263 206 0 475 0 133 -1

N.S.

1 1.00 1.51 1.18 0.00 2.73 0.00 0.76 -0.01

time (sec)

N/A 0.244 4.590 2.520 0.000 3.433 0.000 1.183 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 86 83 175 95 0 108 164

N.S.

1 1.00 0.61 0.58 1.23 0.67 0.00 0.76 1.15

time (sec)

N/A 0.160 0.771 2.323 0.506 2.735 0.000 0.960 6.331

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 74 73 147 83 0 84 125

N.S.

1 1.00 0.69 0.68 1.36 0.77 0.00 0.78 1.16

time (sec)

N/A 0.132 0.430 2.046 0.533 2.672 0.000 0.891 4.229

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 54 63 118 54 0 60 77

N.S.

1 1.00 0.75 0.88 1.64 0.75 0.00 0.83 1.07

time (sec)

N/A 0.105 0.245 2.462 0.518 3.719 0.000 0.813 2.367

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 29 43 90 49 0 59 40

N.S.

1 1.00 0.74 1.10 2.31 1.26 0.00 1.51 1.03

time (sec)

N/A 0.072 0.142 2.549 0.525 3.388 0.000 0.772 1.770

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 155 107 0 291 0 64 -1

N.S.

1 1.00 1.74 1.20 0.00 3.27 0.00 0.72 -0.01

time (sec)

N/A 0.113 0.501 2.290 0.000 3.776 0.000 0.585 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 183 266 0 357 0 97 -1

N.S.

1 1.00 1.50 2.18 0.00 2.93 0.00 0.80 -0.01

time (sec)

N/A 0.148 1.407 2.231 0.000 4.091 0.000 0.627 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 306 471 0 435 0 128 -1

N.S.

1 1.00 1.96 3.02 0.00 2.79 0.00 0.82 -0.01

time (sec)

N/A 0.180 3.009 2.264 0.000 3.205 0.000 0.680 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 84 85 202 111 0 121 188

N.S.

1 1.00 0.54 0.55 1.30 0.72 0.00 0.78 1.21

time (sec)

N/A 0.223 0.932 2.213 0.506 2.812 0.000 1.039 6.017

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 68 75 175 88 0 99 136

N.S.

1 1.00 0.55 0.61 1.42 0.72 0.00 0.80 1.11

time (sec)

N/A 0.193 0.416 2.210 0.508 2.741 0.000 0.935 5.542

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 60 53 118 78 0 60 134

N.S.

1 1.00 0.67 0.60 1.33 0.88 0.00 0.67 1.51

time (sec)

N/A 0.153 0.259 2.461 0.509 4.022 0.000 0.805 5.233

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 55 53 117 65 0 62 94

N.S.

1 1.00 1.34 1.29 2.85 1.59 0.00 1.51 2.29

time (sec)

N/A 0.070 0.155 2.493 0.529 3.114 0.000 0.763 5.295

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 259 131 0 359 0 93 -1

N.S.

1 1.00 1.88 0.95 0.00 2.60 0.00 0.67 -0.01

time (sec)

N/A 0.196 2.159 2.295 0.000 3.377 0.000 0.702 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 365 320 0 399 0 129 -1

N.S.

1 1.00 2.16 1.89 0.00 2.36 0.00 0.76 -0.01

time (sec)

N/A 0.243 1.392 2.460 0.000 4.569 0.000 0.677 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 434 551 0 527 0 160 -1

N.S.

1 1.00 2.14 2.71 0.00 2.60 0.00 0.79 -0.00

time (sec)

N/A 0.271 2.412 2.420 0.000 3.958 0.000 0.692 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 78 85 230 117 0 126 492

N.S.

1 1.00 0.46 0.50 1.36 0.69 0.00 0.75 2.91

time (sec)

N/A 0.276 0.623 2.656 0.525 1.976 0.000 1.106 10.238

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