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2.2.2 Integrals 101 to 200

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 101

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

94 94 64 67 83 82 0 105 83

N.S.

1 1.00 0.68 0.71 0.88 0.87 0.00 1.12 0.88

time (sec)

N/A 0.108 0.042 0.407 0.284 1.499 0.000 0.578 0.191

Problem 102

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

61 61 41 45 51 57 0 72 60

N.S.

1 1.00 0.67 0.74 0.84 0.93 0.00 1.18 0.98

time (sec)

N/A 0.013 0.026 0.381 0.286 1.887 0.000 0.475 0.153

Problem 103

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

78 78 84 85 0 159 0 116 99

N.S.

1 1.00 1.08 1.09 0.00 2.04 0.00 1.49 1.27

time (sec)

N/A 0.099 0.082 0.389 0.000 2.443 0.000 0.589 0.498

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 94 135 0 169 0 76 -1

N.S.

1 1.00 0.94 1.35 0.00 1.69 0.00 0.76 -0.01

time (sec)

N/A 0.120 0.100 0.394 0.000 1.390 0.000 0.542 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 106 175 0 198 0 132 -1

N.S.

1 1.00 1.03 1.70 0.00 1.92 0.00 1.28 -0.01

time (sec)

N/A 0.104 0.133 0.399 0.000 1.616 0.000 0.559 0.000

Problem 106

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

223 223 209 328 363 418 0 280 -1

N.S.

1 1.00 0.94 1.47 1.63 1.87 0.00 1.26 -0.00

time (sec)

N/A 0.256 0.352 0.440 0.294 1.541 0.000 0.568 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 191 286 315 369 0 246 -1

N.S.

1 1.00 1.14 1.71 1.89 2.21 0.00 1.47 -0.01

time (sec)

N/A 0.170 0.303 0.388 0.285 2.227 0.000 0.873 0.000

Problem 108

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

148 148 165 244 267 316 0 207 236

N.S.

1 1.00 1.11 1.65 1.80 2.14 0.00 1.40 1.59

time (sec)

N/A 0.129 0.221 0.375 0.296 1.240 0.000 0.650 1.011

Problem 109

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

144 144 149 202 216 275 0 178 -1

N.S.

1 1.00 1.03 1.40 1.50 1.91 0.00 1.24 -0.01

time (sec)

N/A 0.170 0.200 0.373 0.284 1.776 0.000 0.571 0.000

Problem 110

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

137 137 124 162 168 224 0 142 -1

N.S.

1 1.00 0.91 1.18 1.23 1.64 0.00 1.04 -0.01

time (sec)

N/A 0.194 0.180 0.378 0.290 1.109 0.000 0.608 0.000

Problem 111

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

128 128 108 174 148 209 0 126 -1

N.S.

1 1.00 0.84 1.36 1.16 1.63 0.00 0.98 -0.01

time (sec)

N/A 0.176 0.191 0.373 0.298 2.269 0.000 0.614 0.000

Problem 112

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

136 136 112 219 167 189 0 225 -1

N.S.

1 1.00 0.82 1.61 1.23 1.39 0.00 1.65 -0.01

time (sec)

N/A 0.177 0.203 0.380 0.300 1.073 0.000 0.865 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 110 153 177 207 0 254 -1

N.S.

1 1.00 1.06 1.47 1.70 1.99 0.00 2.44 -0.01

time (sec)

N/A 0.161 0.165 0.380 0.285 1.858 0.000 1.201 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 44 48 193 82 0 370 156

N.S.

1 1.00 0.72 0.79 3.16 1.34 0.00 6.07 2.56

time (sec)

N/A 0.113 0.156 0.503 0.287 1.132 0.000 1.866 1.031

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 66 70 241 109 0 430 206

N.S.

1 1.00 0.69 0.73 2.51 1.14 0.00 4.48 2.15

time (sec)

N/A 0.150 0.184 0.378 0.288 1.753 0.000 2.775 1.439

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 89 94 289 134 0 490 256

N.S.

1 1.00 0.67 0.71 2.17 1.01 0.00 3.68 1.92

time (sec)

N/A 0.186 0.226 0.395 0.298 1.501 0.000 2.562 1.925

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 110 118 337 157 0 550 306

N.S.

1 1.00 0.65 0.69 1.98 0.92 0.00 3.24 1.80

time (sec)

N/A 0.217 0.260 0.389 0.287 1.816 0.000 2.740 2.503

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

207 207 132 142 385 181 0 582 356

N.S.

1 1.00 0.64 0.69 1.86 0.87 0.00 2.81 1.72

time (sec)

N/A 0.241 0.320 0.687 0.292 1.609 0.000 5.364 3.210

Problem 119

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

168 168 113 115 150 154 0 175 143

N.S.

1 1.00 0.67 0.68 0.89 0.92 0.00 1.04 0.85

time (sec)

N/A 0.198 0.076 0.392 0.289 1.503 0.000 0.874 0.349

Problem 120

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

131 131 94 91 128 131 0 140 124

N.S.

1 1.00 0.72 0.69 0.98 1.00 0.00 1.07 0.95

time (sec)

N/A 0.163 0.065 0.368 0.297 1.578 0.000 1.062 0.292

Problem 121

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

96 96 70 67 105 106 0 105 103

N.S.

1 1.00 0.73 0.70 1.09 1.10 0.00 1.09 1.07

time (sec)

N/A 0.048 0.048 0.395 0.288 1.588 0.000 1.499 0.255

Problem 122

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

61 61 41 45 80 80 0 72 83

N.S.

1 1.00 0.67 0.74 1.31 1.31 0.00 1.18 1.36

time (sec)

N/A 0.107 0.032 0.363 0.277 1.579 0.000 1.342 0.229

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 108 99 0 206 0 140 -1

N.S.

1 1.00 1.06 0.97 0.00 2.02 0.00 1.37 -0.01

time (sec)

N/A 0.142 0.119 0.360 0.000 1.603 0.000 1.524 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 109 172 0 195 0 115 -1

N.S.

1 1.00 0.82 1.29 0.00 1.47 0.00 0.86 -0.01

time (sec)

N/A 0.150 0.136 0.396 0.000 1.712 0.000 1.191 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 114 213 0 217 0 145 -1

N.S.

1 1.00 0.84 1.58 0.00 1.61 0.00 1.07 -0.01

time (sec)

N/A 0.159 0.154 0.383 0.000 1.448 0.000 0.972 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 132 259 0 250 0 175 -1

N.S.

1 1.00 0.94 1.85 0.00 1.79 0.00 1.25 -0.01

time (sec)

N/A 0.145 0.212 0.399 0.000 1.675 0.000 1.058 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 154 302 0 299 0 214 -1

N.S.

1 1.00 0.87 1.71 0.00 1.69 0.00 1.21 -0.01

time (sec)

N/A 0.180 0.267 0.394 0.000 1.473 0.000 1.250 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

214 214 172 344 0 345 0 234 -1

N.S.

1 1.00 0.80 1.61 0.00 1.61 0.00 1.09 -0.00

time (sec)

N/A 0.226 0.335 0.398 0.000 1.436 0.000 0.943 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

251 251 198 386 0 393 0 294 -1

N.S.

1 1.00 0.79 1.54 0.00 1.57 0.00 1.17 -0.00

time (sec)

N/A 0.258 0.363 0.405 0.000 3.391 0.000 1.214 0.000

Problem 130

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

176 176 147 211 231 275 0 184 -1

N.S.

1 1.00 0.84 1.20 1.31 1.56 0.00 1.05 -0.01

time (sec)

N/A 0.205 0.179 0.394 0.287 2.423 0.000 0.694 0.000

Problem 131

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

139 139 125 169 183 226 0 150 -1

N.S.

1 1.00 0.90 1.22 1.32 1.63 0.00 1.08 -0.01

time (sec)

N/A 0.178 0.147 0.443 0.283 1.414 0.000 0.705 0.000

Problem 132

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

83 83 99 127 134 177 0 112 -1

N.S.

1 1.00 1.19 1.53 1.61 2.13 0.00 1.35 -0.01

time (sec)

N/A 0.112 0.104 0.392 0.288 1.669 0.000 0.616 0.000

Problem 133

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

66 66 82 88 88 131 0 77 89

N.S.

1 1.00 1.24 1.33 1.33 1.98 0.00 1.17 1.35

time (sec)

N/A 0.085 0.063 0.401 0.306 0.925 0.000 0.929 0.814

Problem 134

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

57 57 77 67 56 136 0 66 57

N.S.

1 1.00 1.35 1.18 0.98 2.39 0.00 1.16 1.00

time (sec)

N/A 0.095 0.063 0.384 0.312 1.670 0.000 0.564 0.509

Problem 135

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 43 47 70 38 0 124 39

N.S.

1 1.00 0.70 0.77 1.15 0.62 0.00 2.03 0.64

time (sec)

N/A 0.105 0.075 0.389 0.277 0.908 0.000 0.662 0.197

Problem 136

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

96 96 64 70 119 62 0 180 62

N.S.

1 1.00 0.67 0.73 1.24 0.65 0.00 1.88 0.65

time (sec)

N/A 0.136 0.097 0.378 0.338 1.667 0.000 0.760 0.251

Problem 137

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

133 133 89 94 167 86 0 236 121

N.S.

1 1.00 0.67 0.71 1.26 0.65 0.00 1.77 0.91

time (sec)

N/A 0.167 0.118 0.387 0.406 1.280 0.000 1.081 0.301

Problem 138

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

170 170 110 118 215 110 0 292 156

N.S.

1 1.00 0.65 0.69 1.26 0.65 0.00 1.72 0.92

time (sec)

N/A 0.193 0.141 0.390 0.275 1.740 0.000 1.443 0.322

Problem 139

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

131 131 85 89 106 83 0 130 87

N.S.

1 1.00 0.65 0.68 0.81 0.63 0.00 0.99 0.66

time (sec)

N/A 0.155 0.057 0.373 0.283 1.018 0.000 0.474 0.265

Problem 140

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

94 94 63 65 83 59 0 98 64

N.S.

1 1.00 0.67 0.69 0.88 0.63 0.00 1.04 0.68

time (sec)

N/A 0.116 0.042 0.377 0.285 1.377 0.000 0.515 0.228

Problem 141

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 40 42 50 36 0 67 41

N.S.

1 1.00 0.68 0.71 0.85 0.61 0.00 1.14 0.69

time (sec)

N/A 0.085 0.029 0.372 0.288 0.882 0.000 0.480 0.187

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 73 72 0 138 0 80 -1

N.S.

1 1.00 1.33 1.31 0.00 2.51 0.00 1.45 -0.02

time (sec)

N/A 0.014 0.046 0.372 0.000 1.291 0.000 0.475 0.000

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 86 105 0 152 0 66 -1

N.S.

1 1.00 1.26 1.54 0.00 2.24 0.00 0.97 -0.01

time (sec)

N/A 0.074 0.081 0.523 0.000 1.723 0.000 0.500 0.000

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 104 146 0 199 0 125 -1

N.S.

1 1.00 1.01 1.42 0.00 1.93 0.00 1.21 -0.01

time (sec)

N/A 0.103 0.120 0.445 0.000 1.041 0.000 0.473 0.000

Problem 145

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

184 184 139 166 237 340 0 183 -1

N.S.

1 1.00 0.76 0.90 1.29 1.85 0.00 0.99 -0.01

time (sec)

N/A 0.217 0.192 0.388 0.283 1.063 0.000 0.475 0.000

Problem 146

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

147 147 114 140 187 289 0 145 -1

N.S.

1 1.00 0.78 0.95 1.27 1.97 0.00 0.99 -0.01

time (sec)

N/A 0.180 0.155 0.391 0.281 1.205 0.000 0.465 0.000

Problem 147

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

112 112 90 114 138 230 0 104 -1

N.S.

1 1.00 0.80 1.02 1.23 2.05 0.00 0.93 -0.01

time (sec)

N/A 0.153 0.121 0.395 0.281 2.558 0.000 0.428 0.000

Problem 148

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

67 67 77 75 79 188 0 70 78

N.S.

1 1.00 1.15 1.12 1.18 2.81 0.00 1.04 1.16

time (sec)

N/A 0.109 0.079 0.367 0.287 2.740 0.000 0.439 0.633

Problem 149

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

37 37 37 47 65 49 0 65 53

N.S.

1 1.00 1.00 1.27 1.76 1.32 0.00 1.76 1.43

time (sec)

N/A 0.078 0.067 0.388 0.287 1.862 0.000 0.462 0.181

Problem 150

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

66 66 64 66 112 72 0 189 70

N.S.

1 1.00 0.97 1.00 1.70 1.09 0.00 2.86 1.06

time (sec)

N/A 0.104 0.100 0.387 0.284 1.388 0.000 0.669 0.274

Problem 151

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

101 101 85 94 160 98 0 302 95

N.S.

1 1.00 0.84 0.93 1.58 0.97 0.00 2.99 0.94

time (sec)

N/A 0.140 0.131 0.392 0.288 1.798 0.000 1.258 0.424

Problem 152

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

138 138 108 118 208 121 0 415 173

N.S.

1 1.00 0.78 0.86 1.51 0.88 0.00 3.01 1.25

time (sec)

N/A 0.173 0.158 0.391 0.282 0.997 0.000 2.027 0.559

Problem 153

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

139 139 82 91 82 93 0 145 92

N.S.

1 1.00 0.59 0.65 0.59 0.67 0.00 1.04 0.66

time (sec)

N/A 0.162 0.059 0.385 0.280 1.839 0.000 0.837 0.397

Problem 154

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

104 104 60 66 59 68 0 107 67

N.S.

1 1.00 0.58 0.63 0.57 0.65 0.00 1.03 0.64

time (sec)

N/A 0.131 0.044 0.376 0.287 1.476 0.000 1.392 0.280

Problem 155

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

69 69 35 44 39 45 0 63 44

N.S.

1 1.00 0.51 0.64 0.57 0.65 0.00 0.91 0.64

time (sec)

N/A 0.095 0.030 0.379 0.281 1.563 0.000 1.236 0.210

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 73 79 0 199 0 109 -1

N.S.

1 1.00 1.14 1.23 0.00 3.11 0.00 1.70 -0.02

time (sec)

N/A 0.087 0.067 0.534 0.000 1.655 0.000 0.925 0.000

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 96 130 0 260 0 107 -1

N.S.

1 1.00 0.68 0.92 0.00 1.83 0.00 0.75 -0.01

time (sec)

N/A 0.057 0.110 0.447 0.000 1.635 0.000 0.637 0.000

Problem 158

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

137 137 117 157 0 315 0 149 89

N.S.

1 1.00 0.85 1.15 0.00 2.30 0.00 1.09 0.65

time (sec)

N/A 0.124 0.160 0.397 0.000 1.178 0.000 0.519 1.263

Problem 159

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

39 39 35 28 27 32 46 29 31

N.S.

1 1.00 0.90 0.72 0.69 0.82 1.18 0.74 0.79

time (sec)

N/A 0.014 0.024 0.142 0.268 1.362 1.088 0.464 0.056

Problem 160

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

39 39 35 28 27 32 46 29 31

N.S.

1 1.00 0.90 0.72 0.69 0.82 1.18 0.74 0.79

time (sec)

N/A 0.014 0.026 0.135 0.264 2.259 0.731 0.469 0.106

Problem 161

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

39 39 41 28 27 32 46 29 31

N.S.

1 1.00 1.05 0.72 0.69 0.82 1.18 0.74 0.79

time (sec)

N/A 0.014 0.021 0.126 0.263 2.496 0.472 0.469 0.044

Problem 162

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

39 39 35 28 27 32 37 29 31

N.S.

1 1.00 0.90 0.72 0.69 0.82 0.95 0.74 0.79

time (sec)

N/A 0.015 0.022 0.136 0.267 1.879 1.117 0.452 0.042

Problem 163

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

39 39 35 28 27 32 46 29 31

N.S.

1 1.00 0.90 0.72 0.69 0.82 1.18 0.74 0.79

time (sec)

N/A 0.015 0.019 0.130 0.268 1.748 0.269 0.456 0.044

Problem 164

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

39 39 35 28 27 30 46 29 31

N.S.

1 1.00 0.90 0.72 0.69 0.77 1.18 0.74 0.79

time (sec)

N/A 0.015 0.019 0.128 0.268 1.869 0.317 0.462 0.043

Problem 165

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

37 37 35 28 27 29 44 29 31

N.S.

1 1.00 0.95 0.76 0.73 0.78 1.19 0.78 0.84

time (sec)

N/A 0.015 0.022 0.129 0.266 1.630 0.367 0.569 0.042

Problem 166

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

37 37 35 30 27 29 44 29 31

N.S.

1 1.00 0.95 0.81 0.73 0.78 1.19 0.78 0.84

time (sec)

N/A 0.014 0.024 0.059 0.268 1.929 0.541 0.570 0.103

Problem 167

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 61 52 51 56 80 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.27 0.84 0.81

time (sec)

N/A 0.026 0.036 0.349 0.267 1.871 2.236 0.486 0.130

Problem 168

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 61 52 51 56 80 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.27 0.84 0.81

time (sec)

N/A 0.026 0.034 0.362 0.272 1.605 1.567 0.443 0.050

Problem 169

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 61 52 51 56 80 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.27 0.84 0.81

time (sec)

N/A 0.027 0.033 0.354 0.267 1.548 1.097 0.465 0.048

Problem 170

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 61 52 51 56 66 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.05 0.84 0.81

time (sec)

N/A 0.026 0.032 0.387 0.266 1.682 1.781 0.460 0.049

Problem 171

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 61 52 51 56 80 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.27 0.84 0.81

time (sec)

N/A 0.027 0.032 0.359 0.264 1.744 0.742 0.444 0.048

Problem 172

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 61 52 51 56 80 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.27 0.84 0.81

time (sec)

N/A 0.027 0.032 0.352 0.270 1.627 0.861 0.468 0.048

Problem 173

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 61 52 51 56 80 53 51

N.S.

1 1.00 0.97 0.83 0.81 0.89 1.27 0.84 0.81

time (sec)

N/A 0.029 0.034 0.357 0.263 1.550 1.018 0.428 0.049

Problem 174

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 60 52 51 54 80 53 51

N.S.

1 1.00 0.95 0.83 0.81 0.86 1.27 0.84 0.81

time (sec)

N/A 0.026 0.031 0.350 0.266 1.938 1.316 0.435 0.051

Problem 175

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

85 85 85 76 73 78 114 77 69

N.S.

1 1.00 1.00 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.035 0.072 0.358 0.267 1.828 3.957 0.463 0.102

Problem 176

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

85 85 85 76 73 78 114 77 69

N.S.

1 1.00 1.00 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.034 0.070 0.365 0.266 2.192 2.920 0.441 0.033

Problem 177

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

85 85 97 76 73 78 114 77 69

N.S.

1 1.00 1.14 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.033 0.047 0.363 0.266 1.428 2.192 0.470 0.035

Problem 178

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

85 85 83 76 73 78 95 77 69

N.S.

1 1.00 0.98 0.89 0.86 0.92 1.12 0.91 0.81

time (sec)

N/A 0.034 0.048 0.354 0.321 1.832 2.649 0.428 0.033

Problem 179

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

85 85 83 76 73 78 114 77 69

N.S.

1 1.00 0.98 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.034 0.048 0.365 0.322 1.352 1.627 0.477 0.033

Problem 180

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

85 85 83 76 73 78 114 77 69

N.S.

1 1.00 0.98 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.034 0.043 0.352 0.265 1.691 1.883 0.433 0.033

Problem 181

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

85 85 83 76 73 78 114 77 69

N.S.

1 1.00 0.98 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.033 0.044 0.354 0.274 1.574 2.020 0.464 0.036

Problem 182

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

85 85 83 76 73 78 114 77 69

N.S.

1 1.00 0.98 0.89 0.86 0.92 1.34 0.91 0.81

time (sec)

N/A 0.034 0.041 0.358 0.297 3.025 2.391 0.446 0.033

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

278 278 172 165 237 920 0 298 115

N.S.

1 1.00 0.62 0.59 0.85 3.31 0.00 1.07 0.41

time (sec)

N/A 0.188 0.216 0.446 0.490 2.488 0.000 0.486 0.227

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

276 276 173 164 259 714 0 298 788

N.S.

1 1.00 0.63 0.59 0.94 2.59 0.00 1.08 2.86

time (sec)

N/A 0.173 0.233 0.376 0.493 2.033 0.000 0.441 0.252

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 152 142 214 899 0 264 92

N.S.

1 1.00 0.59 0.55 0.83 3.50 0.00 1.03 0.36

time (sec)

N/A 0.144 0.172 0.417 0.534 2.845 0.000 0.428 0.236

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 150 141 235 660 275 263 789

N.S.

1 1.00 0.59 0.55 0.92 2.59 1.08 1.03 3.09

time (sec)

N/A 0.141 0.171 0.389 0.514 2.486 104.003 0.438 0.275

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 135 124 194 834 303 251 71

N.S.

1 1.00 0.57 0.52 0.82 3.52 1.28 1.06 0.30

time (sec)

N/A 0.124 0.154 0.396 0.520 2.083 38.972 0.442 0.153

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

235 235 134 127 218 645 238 251 739

N.S.

1 1.00 0.57 0.54 0.93 2.74 1.01 1.07 3.14

time (sec)

N/A 0.126 0.151 0.377 0.519 2.515 16.399 0.432 0.292

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

235 235 135 127 194 843 309 251 71

N.S.

1 1.00 0.57 0.54 0.83 3.59 1.31 1.07 0.30

time (sec)

N/A 0.131 0.195 0.410 0.536 2.966 8.918 0.440 0.222

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 136 124 218 653 257 251 811

N.S.

1 1.00 0.57 0.52 0.92 2.76 1.08 1.06 3.42

time (sec)

N/A 0.129 0.201 0.400 0.500 2.938 14.198 0.428 0.301

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 152 140 213 883 258 268 90

N.S.

1 1.00 0.60 0.55 0.84 3.46 1.01 1.05 0.35

time (sec)

N/A 0.145 0.199 0.397 0.532 2.499 71.031 0.510 0.226

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 154 141 247 707 303 257 555

N.S.

1 1.00 0.60 0.55 0.96 2.75 1.18 1.00 2.16

time (sec)

N/A 0.147 0.210 0.397 0.494 2.657 70.478 0.520 0.320

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

276 276 174 158 237 931 0 291 107

N.S.

1 1.00 0.63 0.57 0.86 3.37 0.00 1.05 0.39

time (sec)

N/A 0.167 0.247 0.402 0.512 2.462 0.000 0.472 0.234

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

278 278 176 160 276 734 0 291 563

N.S.

1 1.00 0.63 0.58 0.99 2.64 0.00 1.05 2.03

time (sec)

N/A 0.164 0.250 0.400 0.546 2.716 0.000 0.595 0.351

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

332 332 206 196 298 804 0 335 857

N.S.

1 1.00 0.62 0.59 0.90 2.42 0.00 1.01 2.58

time (sec)

N/A 0.185 0.535 0.553 0.522 2.631 0.000 0.443 0.219

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

310 310 184 171 247 989 0 299 127

N.S.

1 1.00 0.59 0.55 0.80 3.19 0.00 0.96 0.41

time (sec)

N/A 0.165 0.509 0.504 0.493 2.789 0.000 0.434 0.171

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

310 310 183 171 271 748 0 298 823

N.S.

1 1.00 0.59 0.55 0.87 2.41 0.00 0.96 2.65

time (sec)

N/A 0.163 0.509 0.408 0.537 2.041 0.000 0.438 0.259

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

289 289 162 153 223 925 0 283 106

N.S.

1 1.00 0.56 0.53 0.77 3.20 0.00 0.98 0.37

time (sec)

N/A 0.148 0.512 0.413 0.486 1.691 0.000 0.468 0.247

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

289 289 161 152 250 725 0 283 744

N.S.

1 1.00 0.56 0.53 0.87 2.51 0.00 0.98 2.57

time (sec)

N/A 0.150 0.498 0.407 0.529 1.925 0.000 0.450 0.212

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

261 261 152 146 217 912 0 273 91

N.S.

1 1.00 0.58 0.56 0.83 3.49 0.00 1.05 0.35

time (sec)

N/A 0.130 0.469 0.386 0.547 1.900 0.000 0.505 0.229

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