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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 A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 111 130 96 89 279 74 -1

N.S.

1 1.00 0.84 0.98 0.73 0.67 2.11 0.56 -0.01

time (sec)

N/A 0.048 0.147 0.091 0.489 2.519 2.900 1.629 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 158 215 163 128 830 117 -1

N.S.

1 1.00 0.79 1.07 0.81 0.64 4.13 0.58 -0.00

time (sec)

N/A 0.096 0.223 0.073 0.510 2.584 25.940 2.406 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 147 184 140 118 775 106 -1

N.S.

1 1.00 0.85 1.07 0.81 0.69 4.51 0.62 -0.01

time (sec)

N/A 0.066 0.209 0.092 0.496 2.324 25.547 1.933 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 136 153 117 108 653 96 -1

N.S.

1 1.00 0.86 0.96 0.74 0.68 4.11 0.60 -0.01

time (sec)

N/A 0.061 0.220 0.059 0.472 2.171 8.134 1.532 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 125 126 94 98 580 84 -1

N.S.

1 1.00 1.08 1.09 0.81 0.84 5.00 0.72 -0.01

time (sec)

N/A 0.021 0.202 0.050 0.478 2.445 8.117 1.614 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 125 126 94 98 580 84 -1

N.S.

1 1.00 1.08 1.09 0.81 0.84 5.00 0.72 -0.01

time (sec)

N/A 0.021 0.002 0.000 0.476 1.903 8.099 2.517 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 140 157 122 102 469 99 107

N.S.

1 1.00 1.24 1.39 1.08 0.90 4.15 0.88 0.95

time (sec)

N/A 0.060 0.318 0.063 0.494 2.109 10.469 2.789 2.904

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 143 188 128 122 386 157 114

N.S.

1 1.00 1.22 1.61 1.09 1.04 3.30 1.34 0.97

time (sec)

N/A 0.058 0.295 0.085 0.487 1.864 3.690 1.425 3.513

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 141 219 151 125 461 211 120

N.S.

1 1.00 1.17 1.81 1.25 1.03 3.81 1.74 0.99

time (sec)

N/A 0.059 0.420 0.079 0.504 2.302 4.262 1.602 3.735

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 139 250 173 121 457 256 -1

N.S.

1 1.00 1.16 2.08 1.44 1.01 3.81 2.13 -0.01

time (sec)

N/A 0.058 0.379 0.073 0.488 2.568 3.772 1.021 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 141 281 197 112 541 288 -1

N.S.

1 1.00 1.19 2.38 1.67 0.95 4.58 2.44 -0.01

time (sec)

N/A 0.059 0.395 0.066 0.517 2.165 4.954 0.858 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 151 166 146 93 774 366 93

N.S.

1 1.00 1.40 1.54 1.35 0.86 7.17 3.39 0.86

time (sec)

N/A 0.040 0.408 0.077 0.483 2.946 4.808 0.926 4.264

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 126 198 169 103 918 425 118

N.S.

1 1.00 0.88 1.38 1.18 0.72 6.42 2.97 0.83

time (sec)

N/A 0.060 0.415 0.064 0.483 2.357 8.963 1.012 4.660

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 132 225 192 113 1037 492 192

N.S.

1 1.00 0.77 1.31 1.12 0.66 6.03 2.86 1.12

time (sec)

N/A 0.077 0.495 0.085 0.495 2.499 9.762 1.073 5.334

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 148 256 215 123 1159 425 212

N.S.

1 1.00 0.74 1.27 1.07 0.61 5.77 2.11 1.05

time (sec)

N/A 0.099 0.518 0.083 0.495 2.992 26.955 1.024 6.044

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 92 107 75 68 177 54 112

N.S.

1 1.00 0.89 1.04 0.73 0.66 1.72 0.52 1.09

time (sec)

N/A 0.034 0.137 0.062 0.494 2.349 2.114 1.283 3.138

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 79 103 72 85 163 68 87

N.S.

1 1.00 1.08 1.41 0.99 1.16 2.23 0.93 1.19

time (sec)

N/A 0.026 0.203 0.063 0.485 2.341 4.061 1.075 2.956

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 59 120 80 98 231 0 55

N.S.

1 1.00 1.02 2.07 1.38 1.69 3.98 0.00 0.95

time (sec)

N/A 0.016 0.234 0.061 0.269 1.955 3.749 0.000 2.590

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 149 251 286 259 2004 0 -1

N.S.

1 1.00 0.93 1.56 1.78 1.61 12.45 0.00 -0.01

time (sec)

N/A 0.089 0.443 0.109 0.490 2.384 26.015 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 136 220 255 245 1821 0 -1

N.S.

1 1.00 0.93 1.50 1.73 1.67 12.39 0.00 -0.01

time (sec)

N/A 0.075 0.397 0.082 0.555 2.466 22.823 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 124 189 230 230 1739 0 -1

N.S.

1 1.00 1.02 1.55 1.89 1.89 14.25 0.00 -0.01

time (sec)

N/A 0.055 0.384 0.062 0.498 1.981 26.932 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 82 208 145 159 418 0 78

N.S.

1 1.00 0.98 2.48 1.73 1.89 4.98 0.00 0.93

time (sec)

N/A 0.031 0.305 0.053 0.267 2.198 23.407 0.000 2.701

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 82 178 122 160 337 0 78

N.S.

1 1.00 0.91 1.98 1.36 1.78 3.74 0.00 0.87

time (sec)

N/A 0.026 0.294 0.068 0.278 3.890 7.449 0.000 2.659

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 82 147 102 161 513 0 78

N.S.

1 1.00 0.87 1.56 1.09 1.71 5.46 0.00 0.83

time (sec)

N/A 0.028 0.313 0.066 0.274 4.242 7.487 0.000 2.615

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 82 120 79 160 432 0 78

N.S.

1 1.00 0.99 1.45 0.95 1.93 5.20 0.00 0.94

time (sec)

N/A 0.015 0.286 0.061 0.269 3.040 7.095 0.000 2.621

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 82 90 75 161 604 0 78

N.S.

1 1.00 1.02 1.12 0.94 2.01 7.55 0.00 0.98

time (sec)

N/A 0.012 0.008 0.054 0.270 2.947 8.106 0.000 2.584

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 118 182 153 231 2378 0 127

N.S.

1 1.00 1.01 1.56 1.31 1.97 20.32 0.00 1.09

time (sec)

N/A 0.064 0.447 0.056 0.277 2.965 15.357 0.000 3.079

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 134 213 182 254 2404 0 141

N.S.

1 1.00 0.88 1.39 1.19 1.66 15.71 0.00 0.92

time (sec)

N/A 0.083 0.421 0.079 0.270 2.722 12.669 0.000 3.305

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 147 244 206 270 2691 0 181

N.S.

1 1.00 0.80 1.33 1.12 1.47 14.62 0.00 0.98

time (sec)

N/A 0.103 0.480 0.092 0.271 2.381 15.771 0.000 3.428

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 104 173 123 221 903 0 164

N.S.

1 1.00 0.86 1.43 1.02 1.83 7.46 0.00 1.36

time (sec)

N/A 0.034 0.392 0.071 0.282 3.224 7.367 0.000 2.690

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 126 199 144 281 1401 0 202

N.S.

1 1.00 0.85 1.34 0.97 1.90 9.47 0.00 1.36

time (sec)

N/A 0.040 0.484 0.058 0.358 4.176 15.585 0.000 2.737

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 71 90 63 66 119 70 84

N.S.

1 1.00 1.31 1.67 1.17 1.22 2.20 1.30 1.56

time (sec)

N/A 0.022 0.197 0.111 0.507 2.041 3.530 0.760 0.088

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

173 173 125 295 142 98 558 84 -1

N.S.

1 1.00 0.72 1.71 0.82 0.57 3.23 0.49 -0.01

time (sec)

N/A 0.145 0.225 0.065 0.487 2.701 11.071 0.639 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 114 222 119 88 357 73 -1

N.S.

1 1.00 0.79 1.54 0.83 0.61 2.48 0.51 -0.01

time (sec)

N/A 0.115 0.205 0.075 0.479 1.865 3.850 1.155 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 103 202 96 78 386 63 -1

N.S.

1 1.00 0.90 1.76 0.83 0.68 3.36 0.55 -0.01

time (sec)

N/A 0.090 0.205 0.057 0.489 3.111 4.592 0.937 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 89 133 72 67 218 49 -1

N.S.

1 1.00 1.07 1.60 0.87 0.81 2.63 0.59 -0.01

time (sec)

N/A 0.054 0.163 0.056 0.485 3.220 2.416 1.143 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 78 113 50 57 269 40 -1

N.S.

1 1.00 0.94 1.36 0.60 0.69 3.24 0.48 -0.01

time (sec)

N/A 0.017 0.028 0.068 0.471 3.400 2.149 1.050 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 102 91 61 69 184 65 -1

N.S.

1 1.00 1.55 1.38 0.92 1.05 2.79 0.98 -0.02

time (sec)

N/A 0.073 0.192 0.067 0.480 3.220 2.884 0.812 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 102 93 65 77 207 107 -1

N.S.

1 1.00 1.50 1.37 0.96 1.13 3.04 1.57 -0.01

time (sec)

N/A 0.073 0.207 0.075 0.479 3.208 1.789 1.050 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 116 139 80 61 214 166 -1

N.S.

1 1.00 1.45 1.74 1.00 0.76 2.68 2.08 -0.01

time (sec)

N/A 0.072 0.253 0.066 0.483 2.547 2.835 0.805 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 86 151 103 71 303 237 -1

N.S.

1 1.00 0.80 1.41 0.96 0.66 2.83 2.21 -0.01

time (sec)

N/A 0.086 0.259 0.068 0.481 1.792 2.622 0.832 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 104 229 126 83 449 299 -1

N.S.

1 1.00 0.74 1.64 0.90 0.59 3.21 2.14 -0.01

time (sec)

N/A 0.105 0.294 0.069 0.486 2.064 4.868 1.483 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 115 240 149 93 510 363 -1

N.S.

1 1.00 0.68 1.42 0.88 0.55 3.02 2.15 -0.01

time (sec)

N/A 0.122 0.342 0.087 0.480 1.819 4.443 1.570 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 126 303 255 177 0 0 -1

N.S.

1 1.00 0.88 2.12 1.78 1.24 0.00 0.00 -0.01

time (sec)

N/A 0.169 0.407 0.078 0.502 2.049 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 113 324 273 162 0 0 -1

N.S.

1 1.00 0.93 2.68 2.26 1.34 0.00 0.00 -0.01

time (sec)

N/A 0.134 0.400 0.064 0.491 2.106 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 70 261 142 109 0 0 66

N.S.

1 1.00 0.72 2.69 1.46 1.12 0.00 0.00 0.68

time (sec)

N/A 0.112 0.323 0.070 0.275 2.061 0.000 0.000 2.893

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 70 282 120 110 0 0 67

N.S.

1 1.00 0.80 3.24 1.38 1.26 0.00 0.00 0.77

time (sec)

N/A 0.074 0.339 0.057 0.303 1.687 0.000 0.000 2.865

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 69 173 100 110 0 0 65

N.S.

1 1.00 0.78 1.94 1.12 1.24 0.00 0.00 0.73

time (sec)

N/A 0.021 0.303 0.058 0.273 2.346 0.000 0.000 2.862

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 70 193 73 111 0 0 66

N.S.

1 1.00 0.91 2.51 0.95 1.44 0.00 0.00 0.86

time (sec)

N/A 0.013 0.011 0.058 0.272 1.662 0.000 0.000 2.814

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 107 202 150 163 0 0 -1

N.S.

1 1.00 0.91 1.73 1.28 1.39 0.00 0.00 -0.01

time (sec)

N/A 0.100 0.465 0.070 0.271 2.331 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 123 288 180 186 0 0 -1

N.S.

1 1.00 0.85 1.99 1.24 1.28 0.00 0.00 -0.01

time (sec)

N/A 0.170 0.455 0.087 0.273 2.084 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

182 182 136 361 203 202 0 0 -1

N.S.

1 1.00 0.75 1.98 1.12 1.11 0.00 0.00 -0.01

time (sec)

N/A 0.226 0.482 0.085 0.268 1.671 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 147 381 226 212 0 0 -1

N.S.

1 1.00 0.70 1.82 1.08 1.01 0.00 0.00 -0.00

time (sec)

N/A 0.297 0.536 0.093 0.274 1.864 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 58 71 70 50 73 34 36

N.S.

1 1.00 0.72 0.88 0.86 0.62 0.90 0.42 0.44

time (sec)

N/A 0.057 0.126 0.112 0.481 1.181 0.257 1.121 2.501

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 53 57 56 45 60 30 31

N.S.

1 1.00 0.84 0.90 0.89 0.71 0.95 0.48 0.49

time (sec)

N/A 0.048 0.119 0.079 0.485 1.771 0.174 1.034 0.029

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 46 41 40 38 37 21 22

N.S.

1 1.00 1.12 1.00 0.98 0.93 0.90 0.51 0.54

time (sec)

N/A 0.029 0.089 0.063 0.487 1.861 0.110 0.912 0.029

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 41 29 28 33 27 19 21

N.S.

1 1.00 1.02 0.72 0.70 0.82 0.68 0.48 0.52

time (sec)

N/A 0.007 0.101 0.070 0.481 1.594 0.076 0.765 0.030

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 52 29 41 46 31 34 32

N.S.

1 1.00 1.62 0.91 1.28 1.44 0.97 1.06 1.00

time (sec)

N/A 0.037 0.087 0.122 0.477 1.955 3.020 0.882 0.047

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 57 30 42 53 51 55 35

N.S.

1 1.00 1.73 0.91 1.27 1.61 1.55 1.67 1.06

time (sec)

N/A 0.037 0.087 0.120 0.486 1.730 2.247 0.802 0.079

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 48 42 54 43 116 91 47

N.S.

1 1.00 0.94 0.82 1.06 0.84 2.27 1.78 0.92

time (sec)

N/A 0.039 0.087 0.100 0.485 2.008 3.561 1.368 2.487

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 47 56 68 48 128 125 67

N.S.

1 1.00 0.70 0.84 1.01 0.72 1.91 1.87 1.00

time (sec)

N/A 0.047 0.090 0.089 0.479 1.878 4.147 1.731 0.032

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 58 70 82 53 223 163 77

N.S.

1 1.00 0.65 0.79 0.92 0.60 2.51 1.83 0.87

time (sec)

N/A 0.053 0.105 0.082 0.479 2.742 6.423 1.701 0.032

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 63 84 96 58 201 199 90

N.S.

1 1.00 0.59 0.79 0.90 0.54 1.88 1.86 0.84

time (sec)

N/A 0.066 0.106 0.078 0.477 2.815 7.268 1.052 0.036

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 127 324 150 105 544 287 -1

N.S.

1 1.00 0.95 2.42 1.12 0.78 4.06 2.14 -0.01

time (sec)

N/A 0.134 0.443 0.071 0.517 1.899 5.220 1.080 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

310 310 210 610 251 179 0 170 -1

N.S.

1 1.00 0.68 1.97 0.81 0.58 0.00 0.55 -0.00

time (sec)

N/A 0.296 0.544 0.091 0.495 2.003 0.000 1.219 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

281 281 199 548 228 169 0 160 -1

N.S.

1 1.00 0.71 1.95 0.81 0.60 0.00 0.57 -0.00

time (sec)

N/A 0.250 0.426 0.064 0.505 2.418 0.000 1.197 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

252 252 188 486 205 159 0 149 -1

N.S.

1 1.00 0.75 1.93 0.81 0.63 0.00 0.59 -0.00

time (sec)

N/A 0.222 0.440 0.069 0.505 3.705 0.000 1.252 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 177 424 182 149 1681 139 -1

N.S.

1 1.00 0.79 1.90 0.82 0.67 7.54 0.62 -0.00

time (sec)

N/A 0.190 0.391 0.069 0.493 1.403 138.751 1.349 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

230 230 166 366 159 139 1554 128 -1

N.S.

1 1.00 0.72 1.59 0.69 0.60 6.76 0.56 -0.00

time (sec)

N/A 0.075 0.412 0.062 0.491 1.859 137.531 1.061 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 155 304 130 129 1284 117 -1

N.S.

1 1.00 0.82 1.62 0.69 0.69 6.83 0.62 -0.01

time (sec)

N/A 0.049 0.367 0.071 0.493 1.180 29.382 1.329 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 184 353 200 142 1263 143 -1

N.S.

1 1.00 0.97 1.86 1.05 0.75 6.65 0.75 -0.01

time (sec)

N/A 0.192 0.552 0.084 0.479 1.392 39.162 1.173 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 187 357 212 161 1057 199 -1

N.S.

1 1.00 0.97 1.85 1.10 0.83 5.48 1.03 -0.01

time (sec)

N/A 0.195 0.534 0.097 0.492 2.317 11.820 1.361 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

207 207 189 474 214 167 1059 256 -1

N.S.

1 1.00 0.91 2.29 1.03 0.81 5.12 1.24 -0.00

time (sec)

N/A 0.193 0.627 0.068 0.493 2.931 12.362 1.534 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 189 536 211 167 911 314 -1

N.S.

1 1.00 0.90 2.55 1.00 0.80 4.34 1.50 -0.00

time (sec)

N/A 0.195 0.597 0.091 0.485 1.940 7.738 1.310 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 187 598 233 168 1028 365 -1

N.S.

1 1.00 0.89 2.86 1.11 0.80 4.92 1.75 -0.00

time (sec)

N/A 0.191 0.654 0.069 0.558 1.476 9.473 1.382 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

216 216 189 660 259 168 1178 425 -1

N.S.

1 1.00 0.88 3.06 1.20 0.78 5.45 1.97 -0.00

time (sec)

N/A 0.186 0.694 0.072 0.483 1.640 8.129 1.629 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

214 214 192 722 282 167 1397 476 -1

N.S.

1 1.00 0.90 3.37 1.32 0.78 6.53 2.22 -0.00

time (sec)

N/A 0.187 0.714 0.074 0.485 1.600 12.696 1.114 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 188 580 303 161 1513 505 -1

N.S.

1 1.00 0.91 2.82 1.47 0.78 7.34 2.45 -0.00

time (sec)

N/A 0.188 0.726 0.076 0.522 1.800 12.947 0.663 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

204 204 185 640 327 152 1719 529 -1

N.S.

1 1.00 0.91 3.14 1.60 0.75 8.43 2.59 -0.00

time (sec)

N/A 0.184 0.801 0.082 0.499 3.652 31.668 0.740 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 156 504 230 133 1889 618 -1

N.S.

1 1.00 0.83 2.70 1.23 0.71 10.10 3.30 -0.01

time (sec)

N/A 0.159 0.709 0.104 0.492 2.543 34.480 0.712 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 167 568 253 143 2159 677 -1

N.S.

1 1.00 0.74 2.52 1.12 0.64 9.60 3.01 -0.00

time (sec)

N/A 0.178 0.785 0.132 0.492 3.457 143.030 0.577 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

254 254 175 626 276 153 2397 744 -1

N.S.

1 1.00 0.69 2.46 1.09 0.60 9.44 2.93 -0.00

time (sec)

N/A 0.204 0.837 0.177 0.486 2.640 154.534 0.567 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 123 450 284 181 0 214 -1

N.S.

1 1.00 0.71 2.59 1.63 1.04 0.00 1.23 -0.01

time (sec)

N/A 0.242 0.470 0.078 0.499 3.054 0.000 0.785 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 108 438 299 167 0 193 -1

N.S.

1 1.00 0.76 3.08 2.11 1.18 0.00 1.36 -0.01

time (sec)

N/A 0.194 0.385 0.072 0.485 3.044 0.000 0.690 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 95 377 273 152 0 170 -1

N.S.

1 1.00 0.81 3.19 2.31 1.29 0.00 1.44 -0.01

time (sec)

N/A 0.134 0.389 0.077 0.496 2.978 0.000 0.710 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 53 365 143 100 0 98 49

N.S.

1 1.00 0.57 3.92 1.54 1.08 0.00 1.05 0.53

time (sec)

N/A 0.078 0.318 0.058 0.287 3.630 0.000 0.687 2.690

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 50 308 119 98 0 128 46

N.S.

1 1.00 0.58 3.58 1.38 1.14 0.00 1.49 0.53

time (sec)

N/A 0.022 0.299 0.068 0.266 3.428 0.000 1.223 2.656

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 53 246 96 102 0 158 49

N.S.

1 1.00 0.51 2.39 0.93 0.99 0.00 1.53 0.48

time (sec)

N/A 0.029 0.009 0.065 0.268 2.513 0.000 0.988 2.657

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 89 305 148 153 0 195 -1

N.S.

1 1.00 0.78 2.68 1.30 1.34 0.00 1.71 -0.01

time (sec)

N/A 0.102 0.474 0.070 0.264 2.765 0.000 0.851 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 105 309 177 176 0 287 -1

N.S.

1 1.00 0.72 2.13 1.22 1.21 0.00 1.98 -0.01

time (sec)

N/A 0.182 0.434 0.084 0.280 3.413 0.000 0.721 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

182 182 118 436 201 192 0 353 -1

N.S.

1 1.00 0.65 2.40 1.10 1.05 0.00 1.94 -0.01

time (sec)

N/A 0.224 0.486 0.078 0.276 2.335 0.000 0.713 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 111 296 115 89 0 77 -1

N.S.

1 1.00 0.76 2.01 0.78 0.61 0.00 0.52 -0.01

time (sec)

N/A 0.088 0.161 0.072 0.552 2.803 0.000 0.669 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 100 243 93 78 0 66 -1

N.S.

1 1.00 0.85 2.06 0.79 0.66 0.00 0.56 -0.01

time (sec)

N/A 0.062 0.157 0.082 0.494 2.466 0.000 0.659 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 89 157 71 69 0 54 -1

N.S.

1 1.00 1.03 1.83 0.83 0.80 0.00 0.63 -0.01

time (sec)

N/A 0.071 0.134 0.066 0.474 5.373 0.000 1.368 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 77 135 52 57 0 43 -1

N.S.

1 1.00 1.24 2.18 0.84 0.92 0.00 0.69 -0.02

time (sec)

N/A 0.023 0.125 0.060 0.478 5.397 0.000 1.493 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 63 78 29 48 0 31 -1

N.S.

1 1.00 1.37 1.70 0.63 1.04 0.00 0.67 -0.02

time (sec)

N/A 0.010 0.111 0.069 0.491 4.628 0.000 2.337 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 81 141 55 51 0 48 -1

N.S.

1 1.00 1.76 3.07 1.20 1.11 0.00 1.04 -0.02

time (sec)

N/A 0.035 0.123 0.068 0.480 2.141 0.000 1.777 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 98 228 0 49 0 102 -1

N.S.

1 1.00 1.92 4.47 0.00 0.96 0.00 2.00 -0.02

time (sec)

N/A 0.035 0.170 0.061 0.000 2.338 0.000 1.334 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 75 326 0 61 0 172 -1

N.S.

1 1.00 0.91 3.98 0.00 0.74 0.00 2.10 -0.01

time (sec)

N/A 0.048 0.173 0.068 0.000 3.537 0.000 1.319 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 131 351 0 72 0 239 -1

N.S.

1 1.00 1.15 3.08 0.00 0.63 0.00 2.10 -0.01

time (sec)

N/A 0.068 0.246 0.082 0.000 4.270 0.000 1.197 0.000

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