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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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 50 41 40 40 46 40 40

N.S.

1 1.00 1.00 0.82 0.80 0.80 0.92 0.80 0.80

time (sec)

N/A 0.209 0.016 0.021 0.179 0.233 0.017 0.297 0.016

Problem 2

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

69 69 69 58 57 57 65 61 59

N.S.

1 1.00 1.00 0.84 0.83 0.83 0.94 0.88 0.86

time (sec)

N/A 0.225 0.022 0.067 0.180 0.239 0.018 0.361 0.019

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

88 88 88 75 74 74 83 82 78

N.S.

1 1.00 1.00 0.85 0.84 0.84 0.94 0.93 0.89

time (sec)

N/A 0.253 0.031 0.141 0.182 0.232 0.018 0.290 7.853

Problem 4

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

105 105 105 90 89 89 102 103 95

N.S.

1 1.00 1.00 0.86 0.85 0.85 0.97 0.98 0.90

time (sec)

N/A 0.295 0.031 0.234 0.191 0.237 0.019 0.366 7.905

Problem 5

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

122 122 122 105 104 104 121 124 112

N.S.

1 1.00 1.00 0.86 0.85 0.85 0.99 1.02 0.92

time (sec)

N/A 0.319 0.032 1.908 0.189 0.246 0.020 0.294 0.048

Problem 6

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

112 112 97 95 94 94 116 100 94

N.S.

1 1.00 0.87 0.85 0.84 0.84 1.04 0.89 0.84

time (sec)

N/A 0.327 0.039 0.099 0.182 0.243 0.024 0.369 0.047

Problem 7

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

154 154 154 139 138 138 165 151 138

N.S.

1 1.00 1.00 0.90 0.90 0.90 1.07 0.98 0.90

time (sec)

N/A 0.352 0.038 0.133 0.202 0.237 0.033 0.306 7.852

Problem 8

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

196 196 196 183 182 182 209 202 182

N.S.

1 1.00 1.00 0.93 0.93 0.93 1.07 1.03 0.93

time (sec)

N/A 0.421 0.044 0.151 0.186 0.250 0.031 0.378 7.879

Problem 9

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

234 234 234 219 218 218 258 253 220

N.S.

1 1.00 1.00 0.94 0.93 0.93 1.10 1.08 0.94

time (sec)

N/A 0.491 0.061 0.232 0.195 0.242 0.033 0.319 0.083

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

45 50 50 50 43 43 515 47 51

N.S.

1 1.11 1.11 1.11 0.96 0.96 11.44 1.04 1.13

time (sec)

N/A 0.239 0.017 0.050 0.181 0.262 1.809 0.287 7.813

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

51 55 58 62 51 51 2195 55 63

N.S.

1 1.08 1.14 1.22 1.00 1.00 43.04 1.08 1.24

time (sec)

N/A 0.265 0.022 0.058 0.203 0.289 95.810 0.364 7.763

Problem 12

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

57 62 68 74 61 61 0 65 75

N.S.

1 1.09 1.19 1.30 1.07 1.07 0.00 1.14 1.32

time (sec)

N/A 0.292 0.027 0.069 0.194 0.416 0.000 0.301 7.797

Problem 13

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

64 69 81 89 72 72 0 76 90

N.S.

1 1.08 1.27 1.39 1.12 1.12 0.00 1.19 1.41

time (sec)

N/A 0.395 0.035 0.084 0.203 1.139 0.000 0.311 7.904

Problem 14

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

76 78 98 107 88 88 0 92 108

N.S.

1 1.03 1.29 1.41 1.16 1.16 0.00 1.21 1.42

time (sec)

N/A 0.488 0.045 0.091 0.196 4.998 0.000 0.299 8.146

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 95 98 68 65 65 923 65 118

N.S.

1 1.03 1.07 0.74 0.71 0.71 10.03 0.71 1.28

time (sec)

N/A 0.330 0.169 0.122 0.260 0.267 1.662 0.304 0.128

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 108 121 82 75 75 3589 75 159

N.S.

1 1.04 1.16 0.79 0.72 0.72 34.51 0.72 1.53

time (sec)

N/A 0.344 0.110 0.226 0.274 0.289 65.868 0.297 7.978

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 133 150 90 83 83 0 83 199

N.S.

1 1.05 1.18 0.71 0.65 0.65 0.00 0.65 1.57

time (sec)

N/A 0.436 0.363 0.267 0.263 0.409 0.000 0.300 8.105

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 138 165 99 92 92 0 92 1209

N.S.

1 1.01 1.21 0.73 0.68 0.68 0.00 0.68 8.89

time (sec)

N/A 0.424 0.471 0.386 0.277 1.119 0.000 0.318 11.144

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 150 187 117 106 106 0 106 1509

N.S.

1 0.99 1.24 0.77 0.70 0.70 0.00 0.70 9.99

time (sec)

N/A 0.487 0.472 0.457 0.275 4.389 0.000 0.304 12.662

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 190 194 43 0 398481 0 1342 1308

N.S.

1 1.01 1.03 0.23 0.00 2108.37 0.00 7.10 6.92

time (sec)

N/A 0.386 0.172 0.084 0.000 3.158 0.000 1.399 8.363

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 211 234 48 0 723401 0 1714 3942

N.S.

1 1.00 1.11 0.23 0.00 3428.44 0.00 8.12 18.68

time (sec)

N/A 0.428 0.136 0.070 0.000 18.016 0.000 1.287 8.641

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 248 280 53 0 2136355 0 3270 15179

N.S.

1 1.01 1.14 0.22 0.00 8719.82 0.00 13.35 61.96

time (sec)

N/A 0.481 0.181 0.067 0.000 249.076 0.000 1.331 8.942

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

290 293 383 78 0 0 0 5199 5981

N.S.

1 1.01 1.32 0.27 0.00 0.00 0.00 17.93 20.62

time (sec)

N/A 0.897 0.308 0.102 0.000 0.000 0.000 1.470 8.465

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

321 321 441 99 0 0 0 5941 11383

N.S.

1 1.00 1.37 0.31 0.00 0.00 0.00 18.51 35.46

time (sec)

N/A 0.789 0.392 0.096 0.000 0.000 0.000 1.547 8.741

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

545 545 816 246 0 0 0 11830 49150

N.S.

1 1.00 1.50 0.45 0.00 0.00 0.00 21.71 90.18

time (sec)

N/A 2.995 0.729 0.762 0.000 0.000 0.000 2.097 10.688

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 105 90 83 83 169 604 87 84

N.S.

1 1.12 0.96 0.88 0.88 1.80 6.43 0.93 0.89

time (sec)

N/A 0.317 0.038 0.081 0.180 0.278 2.041 0.298 0.053

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 126 112 105 106 217 0 109 107

N.S.

1 1.10 0.97 0.91 0.92 1.89 0.00 0.95 0.93

time (sec)

N/A 0.374 0.054 0.088 0.194 0.315 0.000 0.315 0.060

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 147 134 125 127 262 0 130 128

N.S.

1 1.07 0.97 0.91 0.92 1.90 0.00 0.94 0.93

time (sec)

N/A 0.424 0.039 0.102 0.194 0.486 0.000 0.295 7.876

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 159 159 143 145 304 0 152 146

N.S.

1 1.06 1.06 0.95 0.97 2.03 0.00 1.01 0.97

time (sec)

N/A 0.488 0.049 0.103 0.193 1.405 0.000 0.302 7.980

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 167 185 161 163 346 0 173 164

N.S.

1 1.03 1.14 0.99 1.01 2.14 0.00 1.07 1.01

time (sec)

N/A 0.559 0.059 0.123 0.198 6.239 0.000 0.306 0.347

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 149 146 124 96 154 952 96 149

N.S.

1 1.06 1.04 0.89 0.69 1.10 6.80 0.69 1.06

time (sec)

N/A 0.389 0.351 0.153 0.283 0.277 2.014 0.303 0.145

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 178 186 154 120 212 4106 124 201

N.S.

1 1.08 1.13 0.93 0.73 1.28 24.88 0.75 1.22

time (sec)

N/A 0.447 0.282 0.268 0.280 0.301 81.025 0.324 0.180

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 193 200 172 135 239 0 138 237

N.S.

1 1.08 1.12 0.96 0.75 1.34 0.00 0.77 1.32

time (sec)

N/A 0.489 0.267 0.276 0.274 0.464 0.000 0.331 8.138

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 201 234 196 143 255 0 151 1547

N.S.

1 1.07 1.25 1.05 0.76 1.36 0.00 0.81 8.27

time (sec)

N/A 0.510 0.387 0.412 0.278 1.101 0.000 0.415 3.309

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 208 243 214 155 279 0 165 1894

N.S.

1 1.07 1.25 1.10 0.80 1.44 0.00 0.85 9.76

time (sec)

N/A 0.577 0.388 0.506 0.294 4.866 0.000 0.298 13.239

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

330 316 341 209 0 1678440 0 3426 2382

N.S.

1 0.96 1.03 0.63 0.00 5086.18 0.00 10.38 7.22

time (sec)

N/A 0.617 0.503 0.247 0.000 235.031 0.000 1.345 8.365

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

368 356 398 232 0 0 0 5156 4707

N.S.

1 0.97 1.08 0.63 0.00 0.00 0.00 14.01 12.79

time (sec)

N/A 0.668 0.720 0.260 0.000 0.000 0.000 1.737 8.403

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

386 376 421 252 0 0 0 5573 7373

N.S.

1 0.97 1.09 0.65 0.00 0.00 0.00 14.44 19.10

time (sec)

N/A 0.662 0.741 0.279 0.000 0.000 0.000 1.787 8.609

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

439 429 489 274 0 0 0 7495 13024

N.S.

1 0.98 1.11 0.62 0.00 0.00 0.00 17.07 29.67

time (sec)

N/A 0.824 1.093 0.154 0.000 0.000 0.000 1.730 8.795

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

468 460 524 304 0 0 0 7962 18449

N.S.

1 0.98 1.12 0.65 0.00 0.00 0.00 17.01 39.42

time (sec)

N/A 0.825 1.211 0.154 0.000 0.000 0.000 1.908 9.411

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

770 788 935 506 0 0 0 20159 82785

N.S.

1 1.02 1.21 0.66 0.00 0.00 0.00 26.18 107.51

time (sec)

N/A 4.258 3.220 1.013 0.000 0.000 0.000 3.934 22.902

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 160 128 107 121 307 668 115 118

N.S.

1 1.12 0.90 0.75 0.85 2.15 4.67 0.80 0.83

time (sec)

N/A 0.398 0.068 0.090 0.189 0.291 2.230 0.313 0.053

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 193 161 139 155 389 0 149 151

N.S.

1 1.10 0.92 0.79 0.89 2.22 0.00 0.85 0.86

time (sec)

N/A 0.495 0.088 0.117 0.201 0.316 0.000 0.320 0.063

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 224 193 169 188 470 0 182 182

N.S.

1 1.10 0.95 0.83 0.92 2.30 0.00 0.89 0.89

time (sec)

N/A 0.571 0.062 0.109 0.194 0.505 0.000 0.310 7.862

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 244 231 193 214 544 0 216 209

N.S.

1 1.09 1.03 0.86 0.96 2.43 0.00 0.96 0.93

time (sec)

N/A 0.630 0.087 0.124 0.197 1.450 0.000 0.364 0.151

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 242 261 217 238 616 0 249 233

N.S.

1 1.01 1.09 0.91 1.00 2.58 0.00 1.04 0.97

time (sec)

N/A 0.679 0.085 0.131 0.189 6.601 0.000 0.282 0.372

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 201 186 158 137 278 1103 125 185

N.S.

1 1.09 1.01 0.85 0.74 1.50 5.96 0.68 1.00

time (sec)

N/A 0.479 0.530 0.183 0.274 0.294 2.187 0.287 0.153

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 240 235 202 173 384 4496 165 249

N.S.

1 1.08 1.05 0.91 0.78 1.72 20.16 0.74 1.12

time (sec)

N/A 0.556 0.390 0.277 0.286 0.309 138.761 0.325 7.974

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 260 259 232 200 435 0 192 295

N.S.

1 1.07 1.07 0.95 0.82 1.79 0.00 0.79 1.21

time (sec)

N/A 0.614 0.435 0.304 0.272 0.487 0.000 0.307 8.066

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

263 280 303 262 217 485 0 222 1611

N.S.

1 1.06 1.15 1.00 0.83 1.84 0.00 0.84 6.13

time (sec)

N/A 0.659 0.568 0.432 0.284 1.221 0.000 0.307 3.443

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

269 285 325 292 229 521 0 249 1963

N.S.

1 1.06 1.21 1.09 0.85 1.94 0.00 0.93 7.30

time (sec)

N/A 0.717 0.580 0.505 0.281 5.488 0.000 0.295 12.838

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

474 491 488 499 0 0 0 3389 4225

N.S.

1 1.04 1.03 1.05 0.00 0.00 0.00 7.15 8.91

time (sec)

N/A 0.854 1.137 0.528 0.000 0.000 0.000 3.107 8.771

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

621 605 625 607 0 0 0 5284 8689

N.S.

1 0.97 1.01 0.98 0.00 0.00 0.00 8.51 13.99

time (sec)

N/A 1.071 1.929 0.648 0.000 0.000 0.000 2.444 9.384

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

646 627 661 644 0 0 0 5619 13431

N.S.

1 0.97 1.02 1.00 0.00 0.00 0.00 8.70 20.79

time (sec)

N/A 1.020 2.357 0.579 0.000 0.000 0.000 2.552 10.415

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

679 692 739 724 0 0 0 6854 23811

N.S.

1 1.02 1.09 1.07 0.00 0.00 0.00 10.09 35.07

time (sec)

N/A 1.403 3.899 0.240 0.000 0.000 0.000 3.094 10.961

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

728 732 821 795 0 0 0 7340 36653

N.S.

1 1.01 1.13 1.09 0.00 0.00 0.00 10.08 50.35

time (sec)

N/A 1.373 5.350 0.296 0.000 0.000 0.000 3.383 12.374

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1150 1172 1590 1167 0 0 0 22429 114377

N.S.

1 1.02 1.38 1.01 0.00 0.00 0.00 19.50 99.46

time (sec)

N/A 2.874 6.849 1.392 0.000 0.000 0.000 3.501 32.044

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

645 653 775 422 0 0 0 16214 53538

N.S.

1 1.01 1.20 0.65 0.00 0.00 0.00 25.14 83.00

time (sec)

N/A 1.516 2.474 0.583 0.000 0.000 0.000 3.249 13.368

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1177 1236 1649 1182 0 0 0 29142 97905

N.S.

1 1.05 1.40 1.00 0.00 0.00 0.00 24.76 83.18

time (sec)

N/A 3.032 6.801 1.140 0.000 0.000 0.000 4.868 27.137

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

416 416 416 412 418 418 503 463 398

N.S.

1 1.00 1.00 0.99 1.00 1.00 1.21 1.11 0.96

time (sec)

N/A 0.912 0.078 28.809 0.190 0.258 0.053 0.304 0.298

Problem 61

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

259 259 259 259 251 251 309 285 246

N.S.

1 1.00 1.00 1.00 0.97 0.97 1.19 1.10 0.95

time (sec)

N/A 0.604 0.035 27.405 0.191 0.270 0.041 0.298 8.113

Problem 62

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

154 154 154 141 138 138 165 151 138

N.S.

1 1.00 1.00 0.92 0.90 0.90 1.07 0.98 0.90

time (sec)

N/A 0.364 0.027 0.134 0.186 0.276 0.027 0.387 0.069

Problem 63

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

20 20 20 17 16 16 15 16 16

N.S.

1 1.00 1.00 0.85 0.80 0.80 0.75 0.80 0.80

time (sec)

N/A 0.198 0.004 0.025 0.187 0.258 0.028 0.619 0.016

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 211 234 48 0 723401 0 1616 3942

N.S.

1 1.00 1.11 0.23 0.00 3428.44 0.00 7.66 18.68

time (sec)

N/A 0.480 0.143 0.063 0.000 18.527 0.000 1.225 0.637

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

368 356 398 232 0 0 0 5159 4707

N.S.

1 0.97 1.08 0.63 0.00 0.00 0.00 14.02 12.79

time (sec)

N/A 0.711 0.738 0.243 0.000 0.000 0.000 2.825 8.620

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

621 605 625 607 0 0 0 5280 8689

N.S.

1 0.97 1.01 0.98 0.00 0.00 0.00 8.50 13.99

time (sec)

N/A 1.108 2.034 0.558 0.000 0.000 0.000 1.596 9.343

Problem 67

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

4 4 4 5 4 4 3 5 4

N.S.

1 1.00 1.00 1.25 1.00 1.00 0.75 1.25 1.00

time (sec)

N/A 0.150 0.002 0.025 0.183 0.269 0.024 0.279 0.012

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

14 14 16 15 14 14 12 15 14

N.S.

1 1.00 1.14 1.07 1.00 1.00 0.86 1.07 1.00

time (sec)

N/A 0.184 0.017 0.033 0.197 0.262 0.057 0.315 7.856

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

31 31 30 28 27 27 26 28 27

N.S.

1 1.00 0.97 0.90 0.87 0.87 0.84 0.90 0.87

time (sec)

N/A 0.221 0.023 0.034 0.181 0.262 0.077 0.306 0.022

Problem 70

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

51 51 45 45 43 43 41 47 44

N.S.

1 1.00 0.88 0.88 0.84 0.84 0.80 0.92 0.86

time (sec)

N/A 0.281 0.022 0.039 0.191 0.261 0.082 0.299 0.022

Problem 71

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

68 68 68 65 62 62 63 72 64

N.S.

1 1.00 1.00 0.96 0.91 0.91 0.93 1.06 0.94

time (sec)

N/A 0.318 0.023 0.042 0.188 0.244 0.099 0.298 0.020

Problem 72

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

92 92 92 88 84 84 88 103 87

N.S.

1 1.00 1.00 0.96 0.91 0.91 0.96 1.12 0.95

time (sec)

N/A 0.347 0.042 0.045 0.183 0.251 0.126 0.295 0.023

Problem 73

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

11 11 11 12 11 11 8 13 8

N.S.

1 1.00 1.00 1.09 1.00 1.00 0.73 1.18 0.73

time (sec)

N/A 0.176 0.045 0.032 0.189 0.254 0.044 0.309 0.051

Problem 74

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

22 22 23 24 22 22 29 24 22

N.S.

1 1.00 1.05 1.09 1.00 1.00 1.32 1.09 1.00

time (sec)

N/A 0.199 0.016 0.038 0.181 0.247 0.165 0.290 7.893

Problem 75

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

29 29 30 31 29 29 44 31 29

N.S.

1 1.00 1.03 1.07 1.00 1.00 1.52 1.07 1.00

time (sec)

N/A 0.240 0.042 0.044 0.179 0.239 0.301 0.304 0.043

Problem 76

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

47 47 44 47 45 45 66 47 45

N.S.

1 1.00 0.94 1.00 0.96 0.96 1.40 1.00 0.96

time (sec)

N/A 0.271 0.070 0.052 0.189 0.253 0.480 0.302 0.039

Problem 77

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

66 66 67 65 62 62 94 67 63

N.S.

1 1.00 1.02 0.98 0.94 0.94 1.42 1.02 0.95

time (sec)

N/A 0.298 0.039 0.056 0.191 0.256 0.850 0.308 0.043

Problem 78

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

90 90 91 88 84 84 122 95 86

N.S.

1 1.00 1.01 0.98 0.93 0.93 1.36 1.06 0.96

time (sec)

N/A 0.330 0.029 0.061 0.179 0.249 1.394 0.299 0.051

Problem 79

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

29 29 29 20 19 19 19 22 19

N.S.

1 1.00 1.00 0.69 0.66 0.66 0.66 0.76 0.66

time (sec)

N/A 0.196 0.007 0.038 0.190 0.251 0.063 0.285 0.041

Problem 80

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

42 42 39 38 32 32 304 35 38

N.S.

1 1.00 0.93 0.90 0.76 0.76 7.24 0.83 0.90

time (sec)

N/A 0.228 0.014 0.046 0.178 0.261 1.109 0.274 7.785

Problem 81

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

47 47 44 47 37 37 716 40 47

N.S.

1 1.00 0.94 1.00 0.79 0.79 15.23 0.85 1.00

time (sec)

N/A 0.255 0.017 0.056 0.186 0.250 7.753 0.306 0.066

Problem 82

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

57 57 55 59 47 47 1389 50 59

N.S.

1 1.00 0.96 1.04 0.82 0.82 24.37 0.88 1.04

time (sec)

N/A 0.271 0.031 0.059 0.189 0.268 54.944 0.301 7.872

Problem 83

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

74 74 71 78 62 62 0 65 78

N.S.

1 1.00 0.96 1.05 0.84 0.84 0.00 0.88 1.05

time (sec)

N/A 0.304 0.028 0.073 0.188 0.284 0.000 0.286 8.034

Problem 84

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

96 96 91 99 82 82 0 87 99

N.S.

1 1.00 0.95 1.03 0.85 0.85 0.00 0.91 1.03

time (sec)

N/A 0.348 0.034 0.076 0.184 0.315 0.000 0.302 7.928

Problem 85

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

46 46 42 33 32 45 34 36 32

N.S.

1 1.00 0.91 0.72 0.70 0.98 0.74 0.78 0.70

time (sec)

N/A 0.232 0.017 0.060 0.186 0.266 0.138 0.293 0.030

Problem 86

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

71 71 66 64 57 93 1188 61 64

N.S.

1 1.00 0.93 0.90 0.80 1.31 16.73 0.86 0.90

time (sec)

N/A 0.308 0.034 0.069 0.183 0.279 7.105 0.299 7.948

Problem 87

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

82 82 77 79 68 116 0 72 79

N.S.

1 1.00 0.94 0.96 0.83 1.41 0.00 0.88 0.96

time (sec)

N/A 0.341 0.043 0.076 0.193 0.340 0.000 0.301 7.902

Problem 88

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

95 95 90 94 81 141 0 85 94

N.S.

1 1.00 0.95 0.99 0.85 1.48 0.00 0.89 0.99

time (sec)

N/A 0.368 0.041 0.083 0.184 0.722 0.000 0.286 7.943

Problem 89

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

106 106 102 109 92 164 0 96 108

N.S.

1 1.00 0.96 1.03 0.87 1.55 0.00 0.91 1.02

time (sec)

N/A 0.394 0.045 0.098 0.181 3.260 0.000 0.291 8.113

Problem 90

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

122 122 118 127 108 200 0 112 127

N.S.

1 1.00 0.97 1.04 0.89 1.64 0.00 0.92 1.04

time (sec)

N/A 0.445 0.050 0.116 0.190 19.688 0.000 0.297 8.369

Problem 91

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

56 55 48 40 42 72 46 46 42

N.S.

1 0.98 0.86 0.71 0.75 1.29 0.82 0.82 0.75

time (sec)

N/A 0.222 0.019 0.064 0.192 0.254 0.149 0.313 0.027

Problem 92

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

89 94 80 78 75 153 1255 79 79

N.S.

1 1.06 0.90 0.88 0.84 1.72 14.10 0.89 0.89

time (sec)

N/A 0.438 0.035 0.073 0.197 0.270 6.979 0.290 0.057

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 110 97 96 91 191 0 95 97

N.S.

1 1.05 0.92 0.91 0.87 1.82 0.00 0.90 0.92

time (sec)

N/A 0.526 0.055 0.081 0.186 0.340 0.000 0.304 0.077

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 114 114 107 229 0 111 115

N.S.

1 1.00 0.97 0.97 0.91 1.96 0.00 0.95 0.98

time (sec)

N/A 0.485 0.043 0.100 0.186 0.725 0.000 0.300 7.978

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 136 132 123 267 0 127 133

N.S.

1 1.00 1.04 1.01 0.94 2.04 0.00 0.97 1.02

time (sec)

N/A 0.518 0.060 0.124 0.187 3.518 0.000 0.290 8.236

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 147 153 150 139 305 0 143 151

N.S.

1 1.00 1.04 1.02 0.95 2.07 0.00 0.97 1.03

time (sec)

N/A 0.554 0.063 0.125 0.197 21.463 0.000 0.297 8.666

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 60 47 52 103 53 56 52

N.S.

1 1.00 0.88 0.69 0.76 1.51 0.78 0.82 0.76

time (sec)

N/A 0.251 0.021 0.067 0.187 0.251 0.157 0.295 0.026

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 105 97 92 88 211 1034 92 90

N.S.

1 1.00 0.92 0.88 0.84 2.01 9.85 0.88 0.86

time (sec)

N/A 0.339 0.060 0.077 0.191 0.279 5.457 0.300 0.058

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 122 121 113 108 267 0 112 113

N.S.

1 1.00 0.99 0.93 0.89 2.19 0.00 0.92 0.93

time (sec)

N/A 0.370 0.042 0.080 0.198 0.361 0.000 0.285 7.901

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 141 144 134 126 321 0 130 131

N.S.

1 1.00 1.02 0.95 0.89 2.28 0.00 0.92 0.93

time (sec)

N/A 0.402 0.052 0.088 0.188 0.777 0.000 0.288 8.211

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