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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 126 86 85 113 94 279 109 246

N.S.

1 0.96 0.66 0.65 0.86 0.72 2.13 0.83 1.88

time (sec)

N/A 0.637 0.286 6.763 0.253 0.275 0.279 0.277 2.357

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 116 77 64 90 76 226 86 212

N.S.

1 1.07 0.71 0.59 0.83 0.70 2.09 0.80 1.96

time (sec)

N/A 0.439 0.162 4.573 0.234 0.263 0.178 0.278 1.948

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 92 59 51 67 56 121 64 67

N.S.

1 1.14 0.73 0.63 0.83 0.69 1.49 0.79 0.83

time (sec)

N/A 0.329 0.120 3.626 0.218 0.263 0.120 0.267 1.021

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

58 62 52 65 63 63 0 99 115

N.S.

1 1.07 0.90 1.12 1.09 1.09 0.00 1.71 1.98

time (sec)

N/A 0.500 0.067 2.970 0.269 0.277 0.000 0.287 1.305

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 54 49 59 86 0 117 91

N.S.

1 1.00 1.29 1.17 1.40 2.05 0.00 2.79 2.17

time (sec)

N/A 0.457 0.013 4.398 0.218 0.292 0.000 0.301 1.227

Problem 6

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

58 62 67 74 95 101 0 105 128

N.S.

1 1.07 1.16 1.28 1.64 1.74 0.00 1.81 2.21

time (sec)

N/A 0.519 0.016 5.785 0.236 0.283 0.000 0.298 1.144

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

86 92 56 88 107 107 0 156 129

N.S.

1 1.07 0.65 1.02 1.24 1.24 0.00 1.81 1.50

time (sec)

N/A 0.633 0.183 7.229 0.203 0.286 0.000 0.303 2.906

Problem 8

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

117 120 75 118 152 129 0 188 166

N.S.

1 1.03 0.64 1.01 1.30 1.10 0.00 1.61 1.42

time (sec)

N/A 0.752 0.286 8.477 0.221 0.278 0.000 0.309 3.495

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 193 123 108 204 126 592 158 315

N.S.

1 0.99 0.63 0.56 1.05 0.65 3.05 0.81 1.62

time (sec)

N/A 1.175 0.309 7.616 0.267 0.268 0.390 0.286 2.638

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 172 97 88 156 106 350 129 277

N.S.

1 1.06 0.60 0.54 0.96 0.65 2.15 0.79 1.70

time (sec)

N/A 0.780 0.204 6.123 0.247 0.277 0.271 0.272 2.348

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 122 73 71 132 86 309 103 117

N.S.

1 0.99 0.59 0.58 1.07 0.70 2.51 0.84 0.95

time (sec)

N/A 0.442 0.353 5.125 0.203 0.266 0.183 0.294 1.086

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 104 109 86 107 95 0 179 159

N.S.

1 1.08 1.14 0.90 1.11 0.99 0.00 1.86 1.66

time (sec)

N/A 0.874 1.505 4.136 0.228 0.302 0.000 0.290 1.215

Problem 13

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

112 117 109 96 101 116 0 143 152

N.S.

1 1.04 0.97 0.86 0.90 1.04 0.00 1.28 1.36

time (sec)

N/A 0.971 1.633 4.176 0.276 0.276 0.000 0.292 1.105

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 116 293 113 142 129 0 152 154

N.S.

1 1.04 2.62 1.01 1.27 1.15 0.00 1.36 1.38

time (sec)

N/A 0.960 2.792 5.858 0.266 0.280 0.000 0.302 1.114

Problem 15

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

110 118 61 119 138 131 0 187 184

N.S.

1 1.07 0.55 1.08 1.25 1.19 0.00 1.70 1.67

time (sec)

N/A 0.959 0.806 7.715 0.221 0.272 0.000 0.317 1.223

Problem 16

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

147 161 157 164 234 141 0 212 185

N.S.

1 1.10 1.07 1.12 1.59 0.96 0.00 1.44 1.26

time (sec)

N/A 1.136 0.604 7.987 0.232 0.281 0.000 0.327 3.630

Problem 17

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

178 187 186 182 218 161 0 246 222

N.S.

1 1.05 1.04 1.02 1.22 0.90 0.00 1.38 1.25

time (sec)

N/A 1.309 0.828 10.447 0.259 0.266 0.000 0.327 3.657

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 238 145 123 284 146 750 185 353

N.S.

1 1.00 0.61 0.52 1.20 0.62 3.16 0.78 1.49

time (sec)

N/A 1.479 0.404 9.163 0.252 0.266 0.555 0.313 2.451

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 189 123 106 239 126 646 158 315

N.S.

1 1.01 0.65 0.56 1.27 0.67 3.44 0.84 1.68

time (sec)

N/A 0.837 0.246 7.278 0.236 0.277 0.423 0.289 2.585

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 140 97 91 190 106 422 131 277

N.S.

1 0.95 0.66 0.61 1.28 0.72 2.85 0.89 1.87

time (sec)

N/A 0.491 0.428 6.536 0.216 0.273 0.299 0.292 2.229

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 150 124 103 163 112 0 213 195

N.S.

1 1.02 0.84 0.70 1.11 0.76 0.00 1.45 1.33

time (sec)

N/A 1.166 1.608 5.819 0.216 0.286 0.000 0.297 1.289

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 152 298 128 137 138 0 210 189

N.S.

1 1.05 2.06 0.88 0.94 0.95 0.00 1.45 1.30

time (sec)

N/A 1.189 2.707 6.854 0.217 0.282 0.000 0.307 1.146

Problem 23

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

160 153 214 152 175 148 0 230 207

N.S.

1 0.96 1.34 0.95 1.09 0.92 0.00 1.44 1.29

time (sec)

N/A 1.251 3.870 6.735 0.218 0.283 0.000 0.315 1.139

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 162 475 149 177 151 0 219 199

N.S.

1 1.04 3.04 0.96 1.13 0.97 0.00 1.40 1.28

time (sec)

N/A 1.316 8.244 8.356 0.222 0.283 0.000 0.317 1.240

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 172 160 186 257 151 0 222 231

N.S.

1 1.02 0.95 1.10 1.52 0.89 0.00 1.31 1.37

time (sec)

N/A 1.296 1.237 8.150 0.232 0.304 0.000 0.321 1.311

Problem 26

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

194 210 195 211 292 161 0 246 224

N.S.

1 1.08 1.01 1.09 1.51 0.83 0.00 1.27 1.15

time (sec)

N/A 1.522 1.710 10.397 0.228 0.266 0.000 0.334 3.656

Problem 27

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

225 236 242 247 382 181 0 280 262

N.S.

1 1.05 1.08 1.10 1.70 0.80 0.00 1.24 1.16

time (sec)

N/A 1.705 2.598 11.855 0.232 0.286 0.000 0.337 3.076

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

279 289 167 142 393 166 1149 211 391

N.S.

1 1.04 0.60 0.51 1.41 0.59 4.12 0.76 1.40

time (sec)

N/A 1.912 0.561 10.954 0.217 0.287 0.774 0.336 1.537

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 213 145 123 319 146 799 185 353

N.S.

1 0.97 0.66 0.56 1.46 0.67 3.65 0.84 1.61

time (sec)

N/A 0.885 0.334 7.914 0.221 0.285 0.552 0.300 1.536

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 164 119 106 273 126 707 158 316

N.S.

1 0.92 0.66 0.59 1.53 0.70 3.95 0.88 1.77

time (sec)

N/A 0.526 0.557 7.902 0.225 0.271 0.408 0.299 1.571

Problem 31

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

177 188 147 120 222 138 0 248 202

N.S.

1 1.06 0.83 0.68 1.25 0.78 0.00 1.40 1.14

time (sec)

N/A 1.443 2.559 5.744 0.307 0.284 0.000 0.311 0.964

Problem 32

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

181 197 338 144 194 158 0 244 234

N.S.

1 1.09 1.87 0.80 1.07 0.87 0.00 1.35 1.29

time (sec)

N/A 1.530 5.512 6.296 0.264 0.302 0.000 0.344 0.670

Problem 33

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

186 196 370 179 211 171 0 248 244

N.S.

1 1.05 1.99 0.96 1.13 0.92 0.00 1.33 1.31

time (sec)

N/A 1.560 9.271 8.048 0.239 0.287 0.000 0.347 0.693

Problem 34

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

198 202 386 190 211 170 0 248 252

N.S.

1 1.02 1.95 0.96 1.07 0.86 0.00 1.25 1.27

time (sec)

N/A 1.608 10.339 8.243 0.249 0.285 0.000 0.331 0.694

Problem 35

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

200 215 350 209 296 171 0 253 246

N.S.

1 1.08 1.75 1.04 1.48 0.86 0.00 1.26 1.23

time (sec)

N/A 1.673 7.360 9.554 0.251 0.283 0.000 0.331 1.033

Problem 36

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

207 218 194 233 315 177 0 257 277

N.S.

1 1.05 0.94 1.13 1.52 0.86 0.00 1.24 1.34

time (sec)

N/A 1.619 5.092 10.959 0.260 0.309 0.000 0.337 1.218

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 250 243 246 456 181 0 280 262

N.S.

1 1.08 1.05 1.06 1.97 0.78 0.00 1.21 1.13

time (sec)

N/A 1.899 5.114 12.014 0.259 0.273 0.000 0.350 3.990

Problem 38

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

263 283 280 284 462 201 0 314 301

N.S.

1 1.08 1.06 1.08 1.76 0.76 0.00 1.19 1.14

time (sec)

N/A 2.134 5.118 14.404 0.223 0.300 0.000 0.337 3.970

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 136 283 91 351 113 1795 180 153

N.S.

1 0.87 1.81 0.58 2.25 0.72 11.51 1.15 0.98

time (sec)

N/A 0.685 1.559 2.015 0.295 0.269 1.821 0.266 1.140

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 108 225 73 269 97 1163 152 114

N.S.

1 0.87 1.81 0.59 2.17 0.78 9.38 1.23 0.92

time (sec)

N/A 0.562 1.271 1.637 0.317 0.268 1.163 0.267 1.074

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 97 159 56 184 77 665 96 83

N.S.

1 0.99 1.62 0.57 1.88 0.79 6.79 0.98 0.85

time (sec)

N/A 0.374 0.819 1.733 0.310 0.263 0.761 0.261 1.024

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 50 108 37 117 53 202 74 59

N.S.

1 1.04 2.25 0.77 2.44 1.10 4.21 1.54 1.23

time (sec)

N/A 0.379 0.457 1.594 0.329 0.261 0.537 0.258 1.055

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 49 114 59 125 88 0 80 101

N.S.

1 1.02 2.38 1.23 2.60 1.83 0.00 1.67 2.10

time (sec)

N/A 0.406 0.822 2.112 0.296 0.268 0.000 0.272 1.304

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 62 229 85 144 109 0 101 72

N.S.

1 1.02 3.75 1.39 2.36 1.79 0.00 1.66 1.18

time (sec)

N/A 0.517 1.782 2.669 0.250 0.279 0.000 0.279 1.221

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 98 284 120 239 152 0 130 106

N.S.

1 0.93 2.70 1.14 2.28 1.45 0.00 1.24 1.01

time (sec)

N/A 0.659 2.654 2.303 0.251 0.278 0.000 0.299 1.184

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 118 765 170 325 172 0 185 150

N.S.

1 0.89 5.75 1.28 2.44 1.29 0.00 1.39 1.13

time (sec)

N/A 0.689 7.013 2.319 0.254 0.292 0.000 0.289 1.433

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 181 399 120 415 167 2161 220 220

N.S.

1 0.95 2.09 0.63 2.17 0.87 11.31 1.15 1.15

time (sec)

N/A 0.961 2.094 2.262 0.320 0.265 4.241 0.275 1.163

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 159 341 100 325 148 1426 191 181

N.S.

1 0.98 2.09 0.61 1.99 0.91 8.75 1.17 1.11

time (sec)

N/A 0.871 1.805 1.740 0.428 0.276 2.690 0.279 1.112

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 147 273 85 236 134 845 137 134

N.S.

1 1.04 1.94 0.60 1.67 0.95 5.99 0.97 0.95

time (sec)

N/A 0.640 1.451 1.746 0.312 0.263 1.614 0.270 1.061

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 93 195 69 165 102 335 114 97

N.S.

1 1.03 2.17 0.77 1.83 1.13 3.72 1.27 1.08

time (sec)

N/A 0.701 1.043 1.958 0.307 0.255 1.025 0.264 1.030

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 69 141 47 119 91 104 84 64

N.S.

1 1.05 2.14 0.71 1.80 1.38 1.58 1.27 0.97

time (sec)

N/A 0.415 0.544 1.514 0.318 0.278 0.622 0.270 1.107

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 78 166 73 146 132 0 112 77

N.S.

1 1.01 2.16 0.95 1.90 1.71 0.00 1.45 1.00

time (sec)

N/A 0.514 1.079 2.529 0.278 0.270 0.000 0.278 1.193

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 98 288 118 191 167 0 142 113

N.S.

1 1.08 3.16 1.30 2.10 1.84 0.00 1.56 1.24

time (sec)

N/A 0.746 1.549 2.411 0.261 0.273 0.000 0.301 1.214

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 145 484 156 288 222 0 171 144

N.S.

1 0.99 3.32 1.07 1.97 1.52 0.00 1.17 0.99

time (sec)

N/A 0.945 2.972 2.566 0.225 0.276 0.000 0.317 1.084

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 169 594 196 379 237 0 225 197

N.S.

1 0.98 3.45 1.14 2.20 1.38 0.00 1.31 1.15

time (sec)

N/A 1.054 4.109 2.637 0.240 0.290 0.000 0.292 1.136

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 214 463 118 365 201 1586 228 229

N.S.

1 0.99 2.14 0.55 1.69 0.93 7.34 1.06 1.06

time (sec)

N/A 1.191 2.537 2.106 0.306 0.267 5.509 0.300 1.091

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 202 393 102 276 184 967 174 184

N.S.

1 1.07 2.08 0.54 1.46 0.97 5.12 0.92 0.97

time (sec)

N/A 0.935 2.134 1.718 0.312 0.276 3.572 0.283 1.043

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 145 283 85 205 149 422 151 153

N.S.

1 1.07 2.08 0.62 1.51 1.10 3.10 1.11 1.12

time (sec)

N/A 1.078 1.822 1.813 0.297 0.265 2.175 0.281 1.089

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 123 227 65 140 137 128 104 116

N.S.

1 1.08 1.99 0.57 1.23 1.20 1.12 0.91 1.02

time (sec)

N/A 0.789 1.141 1.769 0.288 0.294 1.295 0.273 1.157

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 100 129 58 134 89 136 89 69

N.S.

1 1.02 1.32 0.59 1.37 0.91 1.39 0.91 0.70

time (sec)

N/A 0.457 0.579 1.513 0.213 0.268 0.944 0.300 1.186

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

115 125 203 87 167 184 0 131 114

N.S.

1 1.09 1.77 0.76 1.45 1.60 0.00 1.14 0.99

time (sec)

N/A 0.768 1.427 2.556 0.213 0.269 0.000 0.295 1.206

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 145 457 135 233 222 0 178 150

N.S.

1 1.12 3.54 1.05 1.81 1.72 0.00 1.38 1.16

time (sec)

N/A 1.077 5.677 2.401 0.219 0.270 0.000 0.294 1.099

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 199 597 175 330 289 0 207 195

N.S.

1 1.04 3.11 0.91 1.72 1.51 0.00 1.08 1.02

time (sec)

N/A 1.319 4.169 2.568 0.225 0.284 0.000 0.309 1.054

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 223 723 213 421 306 0 261 246

N.S.

1 0.99 3.21 0.95 1.87 1.36 0.00 1.16 1.09

time (sec)

N/A 1.380 5.781 2.699 0.290 0.296 0.000 0.339 1.045

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 245 513 118 318 234 1086 207 245

N.S.

1 1.10 2.30 0.53 1.43 1.05 4.87 0.93 1.10

time (sec)

N/A 1.233 5.733 2.092 0.364 0.281 7.600 0.294 1.083

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 193 371 102 246 193 462 184 192

N.S.

1 1.11 2.13 0.59 1.41 1.11 2.66 1.06 1.10

time (sec)

N/A 1.388 5.911 1.841 0.390 0.279 4.822 0.294 1.124

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 171 315 87 201 179 192 154 162

N.S.

1 1.12 2.07 0.57 1.32 1.18 1.26 1.01 1.07

time (sec)

N/A 1.115 4.807 1.661 0.367 0.278 2.876 0.285 1.135

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 149 179 76 175 124 182 117 84

N.S.

1 1.08 1.30 0.55 1.27 0.90 1.32 0.85 0.61

time (sec)

N/A 0.852 2.229 2.107 0.284 0.253 2.096 0.307 1.104

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 135 159 78 175 123 178 117 87

N.S.

1 0.99 1.17 0.57 1.29 0.90 1.31 0.86 0.64

time (sec)

N/A 0.582 2.214 1.783 0.223 0.271 1.603 0.282 1.194

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 165 245 111 228 237 0 182 156

N.S.

1 1.14 1.69 0.77 1.57 1.63 0.00 1.26 1.08

time (sec)

N/A 1.022 3.081 2.210 0.220 0.302 0.000 0.300 1.198

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 184 680 155 274 277 0 212 204

N.S.

1 1.14 4.22 0.96 1.70 1.72 0.00 1.32 1.27

time (sec)

N/A 1.402 7.635 3.011 0.240 0.288 0.000 0.347 1.092

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 239 784 192 372 354 0 241 260

N.S.

1 1.07 3.50 0.86 1.66 1.58 0.00 1.08 1.16

time (sec)

N/A 1.673 8.736 2.625 0.247 0.274 0.000 0.323 1.069

Problem 73

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

257 267 361 230 461 372 0 295 303

N.S.

1 1.04 1.40 0.89 1.79 1.45 0.00 1.15 1.18

time (sec)

N/A 1.778 4.312 2.582 0.235 0.274 0.000 0.321 1.101

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 234 114 135 160 110 0 208 0

N.S.

1 1.05 0.51 0.61 0.72 0.49 0.00 0.93 0.00

time (sec)

N/A 1.195 0.615 4.816 0.427 0.279 0.000 1.091 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 193 92 116 131 93 0 166 0

N.S.

1 1.07 0.51 0.64 0.73 0.52 0.00 0.92 0.00

time (sec)

N/A 0.984 0.273 5.117 0.396 0.268 0.000 0.546 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 155 74 97 103 75 0 132 0

N.S.

1 1.13 0.54 0.71 0.75 0.55 0.00 0.96 0.00

time (sec)

N/A 0.839 0.163 4.960 0.389 0.266 0.000 0.360 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 106 58 78 72 59 0 93 0

N.S.

1 1.12 0.61 0.82 0.76 0.62 0.00 0.98 0.00

time (sec)

N/A 0.469 0.086 4.457 0.387 0.270 0.000 0.290 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 104 82 242 37 139 0 114 0

N.S.

1 1.08 0.85 2.52 0.39 1.45 0.00 1.19 0.00

time (sec)

N/A 0.589 0.107 7.426 0.368 0.291 0.000 0.315 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 105 91 428 731 155 0 128 0

N.S.

1 1.12 0.97 4.55 7.78 1.65 0.00 1.36 0.00

time (sec)

N/A 0.636 0.155 7.780 0.406 0.300 0.000 0.319 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 114 103 735 2643 173 0 149 0

N.S.

1 1.04 0.94 6.68 24.03 1.57 0.00 1.35 0.00

time (sec)

N/A 0.669 0.264 9.684 3.125 0.294 0.000 0.310 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 156 123 1102 3088 191 0 244 0

N.S.

1 1.02 0.80 7.20 20.18 1.25 0.00 1.59 0.00

time (sec)

N/A 0.836 0.543 9.887 0.575 0.309 0.000 0.365 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 197 150 1447 0 208 0 292 0

N.S.

1 1.01 0.77 7.38 0.00 1.06 0.00 1.49 0.00

time (sec)

N/A 1.034 0.924 11.106 0.000 0.304 0.000 0.352 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 245 115 137 170 119 0 218 0

N.S.

1 1.09 0.51 0.61 0.76 0.53 0.00 0.97 0.00

time (sec)

N/A 1.354 0.505 4.712 0.478 0.280 0.000 1.871 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 191 93 118 138 100 0 178 0

N.S.

1 1.10 0.53 0.68 0.79 0.57 0.00 1.02 0.00

time (sec)

N/A 1.025 0.312 5.068 0.443 0.276 0.000 0.771 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 140 75 108 108 81 0 138 0

N.S.

1 1.06 0.57 0.82 0.82 0.61 0.00 1.05 0.00

time (sec)

N/A 0.601 0.173 4.746 0.427 0.257 0.000 0.409 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 139 95 282 54 161 0 165 0

N.S.

1 1.05 0.71 2.12 0.41 1.21 0.00 1.24 0.00

time (sec)

N/A 0.844 0.221 7.868 0.409 0.285 0.000 0.515 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 149 106 445 1354 174 0 157 0

N.S.

1 1.10 0.78 3.27 9.96 1.28 0.00 1.15 0.00

time (sec)

N/A 0.923 0.236 6.998 0.595 0.288 0.000 0.537 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 156 118 769 2025 189 0 177 0

N.S.

1 1.06 0.80 5.23 13.78 1.29 0.00 1.20 0.00

time (sec)

N/A 0.968 0.398 9.007 0.495 0.340 0.000 0.548 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 165 124 1105 6857 196 0 252 0

N.S.

1 1.06 0.80 7.13 44.24 1.26 0.00 1.63 0.00

time (sec)

N/A 0.999 0.606 10.385 167.208 0.300 0.000 0.497 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

200 205 152 1447 6985 212 0 301 0

N.S.

1 1.02 0.76 7.24 34.92 1.06 0.00 1.50 0.00

time (sec)

N/A 1.204 1.037 10.107 1.249 0.322 0.000 0.561 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

245 249 174 1785 0 232 0 352 0

N.S.

1 1.02 0.71 7.29 0.00 0.95 0.00 1.44 0.00

time (sec)

N/A 1.399 1.513 10.768 0.000 0.318 0.000 0.568 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

273 295 138 156 223 151 0 282 0

N.S.

1 1.08 0.51 0.57 0.82 0.55 0.00 1.03 0.00

time (sec)

N/A 1.742 0.782 34.310 0.491 0.265 0.000 6.912 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 225 117 137 189 129 0 238 0

N.S.

1 1.07 0.55 0.65 0.90 0.61 0.00 1.13 0.00

time (sec)

N/A 1.156 0.501 12.986 0.440 0.280 0.000 2.426 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 174 95 118 155 110 0 191 0

N.S.

1 1.03 0.56 0.70 0.92 0.65 0.00 1.13 0.00

time (sec)

N/A 0.711 0.333 6.311 0.457 0.296 0.000 0.928 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 181 115 334 78 192 0 229 0

N.S.

1 1.06 0.68 1.96 0.46 1.13 0.00 1.35 0.00

time (sec)

N/A 1.143 0.380 14.133 0.406 0.282 0.000 1.390 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 191 127 507 8175 204 0 217 0

N.S.

1 1.10 0.73 2.93 47.25 1.18 0.00 1.25 0.00

time (sec)

N/A 1.214 0.422 17.890 0.733 0.287 0.000 1.428 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 198 137 802 3668 214 0 214 0

N.S.

1 1.08 0.74 4.36 19.93 1.16 0.00 1.16 0.00

time (sec)

N/A 1.264 0.555 62.574 3.438 0.309 0.000 1.510 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 205 142 1161 12441 220 0 293 0

N.S.

1 1.07 0.74 6.05 64.80 1.15 0.00 1.53 0.00

time (sec)

N/A 1.334 0.768 190.715 1.065 0.316 0.000 1.488 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

200 215 153 1650 0 226 0 322 0

N.S.

1 1.08 0.76 8.25 0.00 1.13 0.00 1.61 0.00

time (sec)

N/A 1.365 1.131 3.954 0.000 0.313 0.000 1.316 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 258 176 1975 13407 246 0 376 0

N.S.

1 1.05 0.72 8.06 54.72 1.00 0.00 1.53 0.00

time (sec)

N/A 1.584 1.362 4.453 4.160 0.318 0.000 1.460 0.000

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