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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 B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 94 54 78 129 114 0 130 73

N.S.

1 1.34 0.77 1.11 1.84 1.63 0.00 1.86 1.04

time (sec)

N/A 0.277 0.308 10.949 0.201 0.246 0.000 0.294 2.353

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 40 53 56 111 85 0 85 44

N.S.

1 0.91 1.20 1.27 2.52 1.93 0.00 1.93 1.00

time (sec)

N/A 0.250 0.019 2.915 0.187 0.249 0.000 0.296 2.116

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 58 57 45 62 67 0 92 55

N.S.

1 1.35 1.33 1.05 1.44 1.56 0.00 2.14 1.28

time (sec)

N/A 0.245 0.199 0.842 0.187 0.252 0.000 0.283 2.133

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

24 22 35 25 36 38 0 45 26

N.S.

1 0.92 1.46 1.04 1.50 1.58 0.00 1.88 1.08

time (sec)

N/A 0.220 0.015 1.020 0.197 0.257 0.000 0.269 0.079

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 26 84 36 80 180 0 72 79

N.S.

1 0.96 3.11 1.33 2.96 6.67 0.00 2.67 2.93

time (sec)

N/A 0.223 0.027 1.300 0.201 0.259 0.000 0.273 0.131

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 25 37 44 39 91 0 34 34

N.S.

1 0.93 1.37 1.63 1.44 3.37 0.00 1.26 1.26

time (sec)

N/A 0.244 0.031 3.159 0.201 0.246 0.000 0.278 2.033

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 59 169 70 198 924 0 142 160

N.S.

1 1.09 3.13 1.30 3.67 17.11 0.00 2.63 2.96

time (sec)

N/A 0.256 0.445 6.112 0.207 0.265 0.000 0.287 0.147

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 40 84 73 187 246 0 80 172

N.S.

1 0.89 1.87 1.62 4.16 5.47 0.00 1.78 3.82

time (sec)

N/A 0.248 0.295 11.999 0.198 0.241 0.000 0.284 2.070

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 133 153 109 211 342 0 231 269

N.S.

1 1.17 1.34 0.96 1.85 3.00 0.00 2.03 2.36

time (sec)

N/A 0.375 2.729 13.239 0.207 0.249 0.000 0.305 0.250

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 65 83 69 266 212 0 140 201

N.S.

1 0.90 1.15 0.96 3.69 2.94 0.00 1.94 2.79

time (sec)

N/A 0.289 3.607 27.888 0.204 0.254 0.000 0.294 2.127

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 78 126 90 160 252 0 144 236

N.S.

1 1.07 1.73 1.23 2.19 3.45 0.00 1.97 3.23

time (sec)

N/A 0.294 2.282 20.469 0.203 0.257 0.000 0.291 0.148

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 40 59 43 65 133 0 75 45

N.S.

1 0.89 1.31 0.96 1.44 2.96 0.00 1.67 1.00

time (sec)

N/A 0.241 0.215 11.362 0.186 0.255 0.000 0.286 2.177

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 48 108 72 197 1148 0 139 232

N.S.

1 0.92 2.08 1.38 3.79 22.08 0.00 2.67 4.46

time (sec)

N/A 0.277 3.088 15.116 0.199 0.266 0.000 0.287 2.162

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 45 136 91 140 284 0 111 215

N.S.

1 0.90 2.72 1.82 2.80 5.68 0.00 2.22 4.30

time (sec)

N/A 0.269 4.394 28.010 0.196 0.250 0.000 0.289 2.181

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 116 144 126 354 2930 0 228 316

N.S.

1 1.12 1.38 1.21 3.40 28.17 0.00 2.19 3.04

time (sec)

N/A 0.330 5.079 70.239 0.201 0.280 0.000 0.303 2.192

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 67 151 129 285 408 0 115 115

N.S.

1 0.89 2.01 1.72 3.80 5.44 0.00 1.53 1.53

time (sec)

N/A 0.286 6.648 120.039 0.206 0.253 0.000 0.290 2.155

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 198 651 182 422 727 0 339 686

N.S.

1 1.09 3.58 1.00 2.32 3.99 0.00 1.86 3.77

time (sec)

N/A 0.436 4.737 0.673 0.201 0.262 0.000 0.322 0.339

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 88 119 100 489 403 0 193 348

N.S.

1 0.89 1.20 1.01 4.94 4.07 0.00 1.95 3.52

time (sec)

N/A 0.308 7.117 222.473 0.192 0.255 0.000 0.330 0.294

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 160 480 145 443 595 0 278 592

N.S.

1 1.43 4.29 1.29 3.96 5.31 0.00 2.48 5.29

time (sec)

N/A 0.399 3.724 131.693 0.191 0.257 0.000 0.323 0.205

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 56 93 58 94 276 0 101 288

N.S.

1 0.88 1.45 0.91 1.47 4.31 0.00 1.58 4.50

time (sec)

N/A 0.262 0.318 72.640 0.183 0.259 0.000 0.306 2.145

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 76 134 118 358 3443 0 228 434

N.S.

1 0.92 1.61 1.42 4.31 41.48 0.00 2.75 5.23

time (sec)

N/A 0.305 6.426 143.549 0.190 0.288 0.000 0.296 2.201

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 62 380 148 358 622 0 249 644

N.S.

1 0.89 5.43 2.11 5.11 8.89 0.00 3.56 9.20

time (sec)

N/A 0.288 5.135 241.080 0.187 0.274 0.000 0.313 2.168

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 139 224 192 556 6717 0 341 536

N.S.

1 0.97 1.56 1.33 3.86 46.65 0.00 2.37 3.72

time (sec)

N/A 0.366 9.974 0.404 0.198 0.321 0.000 0.310 2.304

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 93 235 213 664 955 0 355 745

N.S.

1 0.89 2.26 2.05 6.38 9.18 0.00 3.41 7.16

time (sec)

N/A 0.312 4.314 0.849 0.190 0.251 0.000 0.318 2.281

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

117 145 294 327 526 1681 0 0 328

N.S.

1 1.24 2.51 2.79 4.50 14.37 0.00 0.00 2.80

time (sec)

N/A 0.378 3.207 235.072 0.299 0.290 0.000 0.000 3.090

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

71 69 372 170 0 1246 0 0 473

N.S.

1 0.97 5.24 2.39 0.00 17.55 0.00 0.00 6.66

time (sec)

N/A 0.276 3.011 37.000 0.000 0.281 0.000 0.000 2.559

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

75 93 236 148 352 805 0 0 276

N.S.

1 1.24 3.15 1.97 4.69 10.73 0.00 0.00 3.68

time (sec)

N/A 0.301 0.973 8.788 0.283 0.283 0.000 0.000 2.637

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

47 45 328 44 0 595 0 0 42

N.S.

1 0.96 6.98 0.94 0.00 12.66 0.00 0.00 0.89

time (sec)

N/A 0.235 0.989 1.796 0.000 0.268 0.000 0.000 0.127

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 232 65 0 533 0 0 616

N.S.

1 0.98 4.22 1.18 0.00 9.69 0.00 0.00 11.20

time (sec)

N/A 0.258 1.514 1.241 0.000 0.283 0.000 0.000 2.819

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 51 179 120 100 588 0 0 847

N.S.

1 0.96 3.38 2.26 1.89 11.09 0.00 0.00 15.98

time (sec)

N/A 0.256 1.262 0.981 0.284 0.271 0.000 0.000 3.065

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 98 338 111 0 1881 0 0 1586

N.S.

1 1.13 3.89 1.28 0.00 21.62 0.00 0.00 18.23

time (sec)

N/A 0.302 2.979 1.575 0.000 0.320 0.000 0.000 3.631

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

75 77 216 151 195 1753 0 0 248

N.S.

1 1.03 2.88 2.01 2.60 23.37 0.00 0.00 3.31

time (sec)

N/A 0.282 2.931 2.287 0.304 0.280 0.000 0.000 2.835

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

194 220 1330 462 1299 5169 0 0 0

N.S.

1 1.13 6.86 2.38 6.70 26.64 0.00 0.00 0.00

time (sec)

N/A 0.458 14.736 0.231 0.327 0.328 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

114 107 861 264 0 3804 0 0 0

N.S.

1 0.94 7.55 2.32 0.00 33.37 0.00 0.00 0.00

time (sec)

N/A 0.335 6.479 286.110 0.000 0.314 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

131 149 791 325 696 2925 0 0 0

N.S.

1 1.14 6.04 2.48 5.31 22.33 0.00 0.00 0.00

time (sec)

N/A 0.361 11.985 44.871 0.295 0.322 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

84 82 479 70 0 1780 0 0 71

N.S.

1 0.98 5.70 0.83 0.00 21.19 0.00 0.00 0.85

time (sec)

N/A 0.255 3.031 17.108 0.000 0.286 0.000 0.000 2.341

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 106 377 167 0 2376 0 0 0

N.S.

1 1.07 3.81 1.69 0.00 24.00 0.00 0.00 0.00

time (sec)

N/A 0.300 2.152 26.038 0.000 0.320 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

92 92 220 238 262 2407 0 0 0

N.S.

1 1.00 2.39 2.59 2.85 26.16 0.00 0.00 0.00

time (sec)

N/A 0.280 3.870 25.407 0.298 0.324 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

147 156 462 214 0 6878 0 0 0

N.S.

1 1.06 3.14 1.46 0.00 46.79 0.00 0.00 0.00

time (sec)

N/A 0.375 3.738 14.421 0.000 0.381 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

123 126 620 327 430 6143 0 0 0

N.S.

1 1.02 5.04 2.66 3.50 49.94 0.00 0.00 0.00

time (sec)

N/A 0.414 7.419 14.547 0.340 0.339 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

242 269 3457 541 2468 12353 0 0 0

N.S.

1 1.11 14.29 2.24 10.20 51.05 0.00 0.00 0.00

time (sec)

N/A 0.539 31.092 0.229 0.413 0.400 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F(-2) B F(-1) F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

154 152 1364 348 0 8667 0 0 0

N.S.

1 0.99 8.86 2.26 0.00 56.28 0.00 0.00 0.00

time (sec)

N/A 0.481 13.812 0.207 0.000 0.354 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

187 221 2544 1320 1373 9730 0 0 0

N.S.

1 1.18 13.60 7.06 7.34 52.03 0.00 0.00 0.00

time (sec)

N/A 0.447 22.289 0.235 0.366 0.383 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

116 119 1272 84 0 4829 0 0 103

N.S.

1 1.03 10.97 0.72 0.00 41.63 0.00 0.00 0.89

time (sec)

N/A 0.271 11.492 164.165 0.000 0.324 0.000 0.000 2.221

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

154 173 440 291 0 8742 0 0 0

N.S.

1 1.12 2.86 1.89 0.00 56.77 0.00 0.00 0.00

time (sec)

N/A 0.397 4.490 0.265 0.000 0.393 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

126 133 981 819 533 7275 0 0 0

N.S.

1 1.06 7.79 6.50 4.23 57.74 0.00 0.00 0.00

time (sec)

N/A 0.311 8.346 0.258 0.352 0.341 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

213 236 524 350 0 20341 0 0 0

N.S.

1 1.11 2.46 1.64 0.00 95.50 0.00 0.00 0.00

time (sec)

N/A 0.503 5.530 0.247 0.000 0.545 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

165 168 985 1443 782 15161 0 0 0

N.S.

1 1.02 5.97 8.75 4.74 91.88 0.00 0.00 0.00

time (sec)

N/A 0.496 6.336 0.296 0.414 0.440 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 59 45 44 97 61 0 116 50

N.S.

1 0.97 0.74 0.72 1.59 1.00 0.00 1.90 0.82

time (sec)

N/A 0.295 0.139 0.739 0.190 0.267 0.000 0.283 0.116

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 36 50 31 85 41 0 72 34

N.S.

1 1.20 1.67 1.03 2.83 1.37 0.00 2.40 1.13

time (sec)

N/A 0.289 0.009 0.704 0.191 0.263 0.000 0.302 2.008

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 33 27 38 28 60 66 23

N.S.

1 1.00 1.06 0.87 1.23 0.90 1.94 2.13 0.74

time (sec)

N/A 0.215 0.028 0.325 0.191 0.257 5.865 0.286 0.071

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 35 24 28 93 0 36 62

N.S.

1 1.00 1.46 1.00 1.17 3.88 0.00 1.50 2.58

time (sec)

N/A 0.257 0.015 0.357 0.271 0.264 0.000 0.285 1.986

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 48 40 81 321 0 84 124

N.S.

1 1.00 1.20 1.00 2.02 8.02 0.00 2.10 3.10

time (sec)

N/A 0.265 0.010 0.822 0.272 0.257 0.000 0.295 0.124

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 43 39 34 112 158 0 61 61

N.S.

1 1.43 1.30 1.13 3.73 5.27 0.00 2.03 2.03

time (sec)

N/A 0.298 0.014 0.983 0.192 0.250 0.000 0.275 1.984

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 68 93 68 184 1112 0 156 283

N.S.

1 0.97 1.33 0.97 2.63 15.89 0.00 2.23 4.04

time (sec)

N/A 0.378 0.019 1.247 0.274 0.284 0.000 0.284 1.984

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 64 71 56 300 343 0 85 292

N.S.

1 1.28 1.42 1.12 6.00 6.86 0.00 1.70 5.84

time (sec)

N/A 0.310 0.016 1.124 0.194 0.258 0.000 0.302 1.980

Problem 57

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

82 105 58 54 105 78 0 151 66

N.S.

1 1.28 0.71 0.66 1.28 0.95 0.00 1.84 0.80

time (sec)

N/A 0.302 0.315 0.756 0.193 0.256 0.000 0.298 2.006

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 44 72 50 105 414 0 94 114

N.S.

1 0.90 1.47 1.02 2.14 8.45 0.00 1.92 2.33

time (sec)

N/A 0.264 0.065 1.026 0.270 0.265 0.000 0.300 0.151

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 59 52 51 63 80 0 128 65

N.S.

1 1.26 1.11 1.09 1.34 1.70 0.00 2.72 1.38

time (sec)

N/A 0.283 0.239 0.774 0.180 0.257 0.000 0.294 0.147

Problem 60

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

56 57 80 53 101 653 0 112 172

N.S.

1 1.02 1.43 0.95 1.80 11.66 0.00 2.00 3.07

time (sec)

N/A 0.267 0.075 0.997 0.265 0.278 0.000 0.300 2.081

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 100 109 84 201 1372 0 170 303

N.S.

1 1.11 1.21 0.93 2.23 15.24 0.00 1.89 3.37

time (sec)

N/A 0.271 0.050 1.260 0.274 0.266 0.000 0.307 2.044

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 48 93 70 324 404 0 156 452

N.S.

1 0.91 1.75 1.32 6.11 7.62 0.00 2.94 8.53

time (sec)

N/A 0.282 0.051 1.305 0.207 0.243 0.000 0.296 2.031

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 129 187 122 348 2946 0 293 569

N.S.

1 1.01 1.46 0.95 2.72 23.02 0.00 2.29 4.45

time (sec)

N/A 0.314 0.046 1.951 0.298 0.280 0.000 0.307 2.108

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 72 144 102 671 677 0 197 692

N.S.

1 0.90 1.80 1.28 8.39 8.46 0.00 2.46 8.65

time (sec)

N/A 0.295 0.041 1.541 0.208 0.245 0.000 0.287 2.037

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 99 70 93 130 153 0 177 117

N.S.

1 1.18 0.83 1.11 1.55 1.82 0.00 2.11 1.39

time (sec)

N/A 0.316 1.688 1.307 0.205 0.253 0.000 0.311 2.212

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

81 79 483 79 179 1409 0 163 218

N.S.

1 0.98 5.96 0.98 2.21 17.40 0.00 2.01 2.69

time (sec)

N/A 0.295 7.023 2.067 0.282 0.271 0.000 0.315 0.205

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 81 64 77 160 270 0 152 221

N.S.

1 1.12 0.89 1.07 2.22 3.75 0.00 2.11 3.07

time (sec)

N/A 0.295 1.874 1.274 0.195 0.286 0.000 0.306 0.140

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

93 95 575 97 221 1992 0 199 344

N.S.

1 1.02 6.18 1.04 2.38 21.42 0.00 2.14 3.70

time (sec)

N/A 0.310 8.229 1.796 0.274 0.292 0.000 0.315 0.175

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

147 163 1430 138 365 3465 0 310 535

N.S.

1 1.11 9.73 0.94 2.48 23.57 0.00 2.11 3.64

time (sec)

N/A 0.347 10.494 2.122 0.295 0.290 0.000 0.311 2.153

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 66 162 116 695 816 0 302 978

N.S.

1 0.89 2.19 1.57 9.39 11.03 0.00 4.08 13.22

time (sec)

N/A 0.303 3.623 1.782 0.206 0.275 0.000 0.312 2.119

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 195 297 186 556 6114 0 485 931

N.S.

1 0.99 1.52 0.95 2.84 31.19 0.00 2.47 4.75

time (sec)

N/A 0.407 10.734 3.166 0.281 0.311 0.000 0.314 2.240

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 97 238 158 1245 1190 0 360 1333

N.S.

1 0.90 2.20 1.46 11.53 11.02 0.00 3.33 12.34

time (sec)

N/A 0.325 5.156 2.060 0.201 0.270 0.000 0.313 2.172

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 145 95 234 526 1713 0 0 260

N.S.

1 1.24 0.81 2.00 4.50 14.64 0.00 0.00 2.22

time (sec)

N/A 0.375 0.841 1.170 0.313 0.294 0.000 0.000 2.609

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 71 79 209 0 1616 0 0 332

N.S.

1 0.93 1.04 2.75 0.00 21.26 0.00 0.00 4.37

time (sec)

N/A 0.301 0.335 0.850 0.000 0.290 0.000 0.000 2.585

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 93 67 152 352 829 0 0 206

N.S.

1 1.24 0.89 2.03 4.69 11.05 0.00 0.00 2.75

time (sec)

N/A 0.308 0.465 0.651 0.283 0.277 0.000 0.000 2.466

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 50 52 125 0 718 0 0 277

N.S.

1 0.96 1.00 2.40 0.00 13.81 0.00 0.00 5.33

time (sec)

N/A 0.248 0.165 0.548 0.000 0.284 0.000 0.000 2.304

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 80 0 487 0 0 108

N.S.

1 1.00 1.00 2.22 0.00 13.53 0.00 0.00 3.00

time (sec)

N/A 0.225 0.077 0.287 0.000 0.281 0.000 0.000 2.523

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 102 66 411 0 0 125

N.S.

1 1.00 1.00 2.83 1.83 11.42 0.00 0.00 3.47

time (sec)

N/A 0.243 0.040 0.284 0.294 0.263 0.000 0.000 0.546

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 53 194 104 0 526 0 0 307

N.S.

1 0.96 3.53 1.89 0.00 9.56 0.00 0.00 5.58

time (sec)

N/A 0.260 0.815 0.544 0.000 0.295 0.000 0.000 2.470

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 50 182 138 91 645 0 0 166

N.S.

1 0.96 3.50 2.65 1.75 12.40 0.00 0.00 3.19

time (sec)

N/A 0.251 2.068 0.751 0.301 0.282 0.000 0.000 0.458

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 93 213 159 0 1518 0 0 946

N.S.

1 1.08 2.48 1.85 0.00 17.65 0.00 0.00 11.00

time (sec)

N/A 0.290 2.028 1.086 0.000 0.280 0.000 0.000 4.065

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 72 214 183 160 1905 0 0 334

N.S.

1 0.94 2.78 2.38 2.08 24.74 0.00 0.00 4.34

time (sec)

N/A 0.296 3.645 1.450 0.340 0.274 0.000 0.000 2.619

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 117 113 321 0 5842 0 0 0

N.S.

1 0.94 0.90 2.57 0.00 46.74 0.00 0.00 0.00

time (sec)

N/A 0.352 0.956 1.796 0.000 0.330 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 165 103 338 696 3739 0 0 0

N.S.

1 1.15 0.72 2.35 4.83 25.97 0.00 0.00 0.00

time (sec)

N/A 0.400 1.584 1.264 0.314 0.323 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 95 88 237 0 3154 0 0 0

N.S.

1 0.95 0.88 2.37 0.00 31.54 0.00 0.00 0.00

time (sec)

N/A 0.315 0.585 0.932 0.000 0.295 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 80 124 201 0 1856 0 0 0

N.S.

1 0.98 1.51 2.45 0.00 22.63 0.00 0.00 0.00

time (sec)

N/A 0.255 0.335 0.553 0.000 0.278 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 72 187 206 150 1489 0 0 0

N.S.

1 0.97 2.53 2.78 2.03 20.12 0.00 0.00 0.00

time (sec)

N/A 0.261 2.454 0.511 0.313 0.268 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 71 113 181 0 1570 0 0 0

N.S.

1 0.97 1.55 2.48 0.00 21.51 0.00 0.00 0.00

time (sec)

N/A 0.253 0.352 0.544 0.000 0.273 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 81 88 222 165 1569 0 0 0

N.S.

1 0.98 1.06 2.67 1.99 18.90 0.00 0.00 0.00

time (sec)

N/A 0.272 0.198 0.565 0.346 0.285 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 111 282 216 0 2069 0 0 0

N.S.

1 1.10 2.79 2.14 0.00 20.49 0.00 0.00 0.00

time (sec)

N/A 0.305 2.770 1.296 0.000 0.307 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

101 96 229 250 244 2958 0 0 0

N.S.

1 0.95 2.27 2.48 2.42 29.29 0.00 0.00 0.00

time (sec)

N/A 0.336 5.444 1.923 0.356 0.315 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 165 489 271 0 6499 0 0 0

N.S.

1 1.08 3.20 1.77 0.00 42.48 0.00 0.00 0.00

time (sec)

N/A 0.377 5.707 2.889 0.000 0.352 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 244 156 439 1373 11740 0 0 0

N.S.

1 1.20 0.76 2.15 6.73 57.55 0.00 0.00 0.00

time (sec)

N/A 0.509 4.796 3.587 0.367 0.403 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 146 139 335 0 9856 0 0 0

N.S.

1 0.95 0.90 2.18 0.00 64.00 0.00 0.00 0.00

time (sec)

N/A 0.387 2.058 2.288 0.000 0.366 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 152 214 308 0 6806 0 0 0

N.S.

1 1.07 1.51 2.17 0.00 47.93 0.00 0.00 0.00

time (sec)

N/A 0.321 3.211 1.272 0.000 0.345 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

108 113 258 260 353 5109 0 0 0

N.S.

1 1.05 2.39 2.41 3.27 47.31 0.00 0.00 0.00

time (sec)

N/A 0.283 3.957 1.225 0.342 0.321 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 159 294 0 6037 0 0 0

N.S.

1 1.00 1.29 2.39 0.00 49.08 0.00 0.00 0.00

time (sec)

N/A 0.291 0.847 1.277 0.000 0.318 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

125 125 250 310 369 5447 0 0 0

N.S.

1 1.00 2.00 2.48 2.95 43.58 0.00 0.00 0.00

time (sec)

N/A 0.292 5.045 1.295 0.357 0.314 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 111 131 235 0 5006 0 0 0

N.S.

1 1.05 1.24 2.22 0.00 47.23 0.00 0.00 0.00

time (sec)

N/A 0.280 1.364 1.272 0.000 0.315 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 156 125 328 395 5887 0 0 0

N.S.

1 1.08 0.87 2.28 2.74 40.88 0.00 0.00 0.00

time (sec)

N/A 0.330 0.985 1.296 0.408 0.332 0.000 0.000 0.000

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