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2.2.1 Integrals 1 to 100

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

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 82 356 232 85 151 152 122

N.S.

1 1.00 0.66 2.87 1.87 0.69 1.22 1.23 0.98

time (sec)

N/A 0.253 0.115 0.680 0.272 0.407 0.332 0.410 0.958

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 65 224 196 67 117 116 92

N.S.

1 1.00 0.69 2.38 2.09 0.71 1.24 1.23 0.98

time (sec)

N/A 0.173 0.098 0.653 0.268 0.369 0.218 0.421 0.962

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 45 122 160 48 82 79 62

N.S.

1 1.00 0.70 1.91 2.50 0.75 1.28 1.23 0.97

time (sec)

N/A 0.097 0.074 0.750 0.281 0.419 0.139 0.443 0.922

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 27 53 68 30 46 46 35

N.S.

1 1.00 0.96 1.89 2.43 1.07 1.64 1.64 1.25

time (sec)

N/A 0.016 0.044 0.651 0.269 0.451 0.090 0.451 0.062

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 39 52 97 54 34 47 -1

N.S.

1 1.00 1.39 1.86 3.46 1.93 1.21 1.68 -0.04

time (sec)

N/A 0.108 0.026 0.845 0.342 0.352 2.002 0.421 0.000

Problem 6

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

47 47 59 77 82 76 0 72 -1

N.S.

1 1.00 1.26 1.64 1.74 1.62 0.00 1.53 -0.02

time (sec)

N/A 0.165 0.103 0.852 0.328 0.349 0.000 0.439 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 78 139 66 116 0 134 -1

N.S.

1 1.00 0.89 1.58 0.75 1.32 0.00 1.52 -0.01

time (sec)

N/A 0.200 0.122 0.928 0.350 0.489 0.000 0.411 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 110 205 78 143 0 199 -1

N.S.

1 1.00 0.83 1.55 0.59 1.08 0.00 1.51 -0.01

time (sec)

N/A 0.233 0.206 0.996 0.364 0.342 0.000 0.406 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 140 271 82 161 0 266 -1

N.S.

1 1.00 0.84 1.63 0.49 0.97 0.00 1.60 -0.01

time (sec)

N/A 0.277 0.246 1.023 0.337 0.398 0.000 0.414 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 100 463 329 127 228 236 168

N.S.

1 1.00 0.54 2.52 1.79 0.69 1.24 1.28 0.91

time (sec)

N/A 0.261 0.164 0.622 0.288 0.405 0.367 0.418 0.161

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 87 283 275 95 172 171 125

N.S.

1 1.00 0.65 2.11 2.05 0.71 1.28 1.28 0.93

time (sec)

N/A 0.148 0.124 0.631 0.282 0.360 0.228 0.408 0.923

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 56 147 135 64 112 112 82

N.S.

1 1.00 1.14 3.00 2.76 1.31 2.29 2.29 1.67

time (sec)

N/A 0.034 0.091 0.605 0.283 0.414 0.141 0.392 0.903

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 51 121 175 94 73 113 -1

N.S.

1 1.00 0.82 1.95 2.82 1.52 1.18 1.82 -0.02

time (sec)

N/A 0.137 0.162 0.798 0.348 0.345 2.233 0.418 0.000

Problem 14

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

70 70 62 118 136 122 0 119 -1

N.S.

1 1.00 0.89 1.69 1.94 1.74 0.00 1.70 -0.01

time (sec)

N/A 0.188 0.156 0.763 0.327 0.341 0.000 0.433 0.000

Problem 15

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

121 121 93 181 126 153 0 181 -1

N.S.

1 1.00 0.77 1.50 1.04 1.26 0.00 1.50 -0.01

time (sec)

N/A 0.243 0.235 0.686 0.344 0.370 0.000 0.402 0.000

Problem 16

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

172 172 154 287 117 194 0 285 -1

N.S.

1 1.00 0.90 1.67 0.68 1.13 0.00 1.66 -0.01

time (sec)

N/A 0.300 0.281 0.698 0.340 0.344 0.000 0.424 0.000

Problem 17

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

248 248 206 396 128 231 0 395 -1

N.S.

1 1.00 0.83 1.60 0.52 0.93 0.00 1.59 -0.00

time (sec)

N/A 0.360 0.355 0.704 0.346 0.360 0.000 0.405 0.000

Problem 18

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

219 219 159 442 437 236 0 407 -1

N.S.

1 1.00 0.73 2.02 2.00 1.08 0.00 1.86 -0.00

time (sec)

N/A 0.344 0.400 0.967 0.311 0.366 0.000 0.425 0.000

Problem 19

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

150 150 118 292 328 190 0 256 -1

N.S.

1 1.00 0.79 1.95 2.19 1.27 0.00 1.71 -0.01

time (sec)

N/A 0.247 0.309 0.909 0.319 0.371 0.000 0.406 0.000

Problem 20

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

100 100 89 184 233 156 0 148 -1

N.S.

1 1.00 0.89 1.84 2.33 1.56 0.00 1.48 -0.01

time (sec)

N/A 0.192 0.194 0.875 0.311 0.378 0.000 0.413 0.000

Problem 21

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

68 68 64 114 156 118 0 83 -1

N.S.

1 1.00 0.94 1.68 2.29 1.74 0.00 1.22 -0.01

time (sec)

N/A 0.120 0.093 0.815 0.310 0.386 0.000 0.422 0.000

Problem 22

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

51 51 49 81 57 95 0 56 -1

N.S.

1 1.00 0.96 1.59 1.12 1.86 0.00 1.10 -0.02

time (sec)

N/A 0.054 0.056 0.745 0.299 0.414 0.000 0.423 0.000

Problem 23

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

73 73 63 108 155 123 0 75 -1

N.S.

1 1.00 0.86 1.48 2.12 1.68 0.00 1.03 -0.01

time (sec)

N/A 0.183 0.087 0.721 0.332 0.373 0.000 0.410 0.000

Problem 24

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

113 113 101 172 192 179 0 129 -1

N.S.

1 1.00 0.89 1.52 1.70 1.58 0.00 1.14 -0.01

time (sec)

N/A 0.266 0.244 0.717 0.356 0.443 0.000 0.410 0.000

Problem 25

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

190 190 178 281 242 275 0 248 -1

N.S.

1 1.00 0.94 1.48 1.27 1.45 0.00 1.31 -0.01

time (sec)

N/A 0.345 0.290 0.727 0.376 0.365 0.000 0.402 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

231 231 173 431 406 371 0 2979 -1

N.S.

1 1.00 0.75 1.87 1.76 1.61 0.00 12.90 -0.00

time (sec)

N/A 0.404 0.746 0.987 0.336 0.376 0.000 0.456 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

182 182 156 325 312 333 0 1991 -1

N.S.

1 1.00 0.86 1.79 1.71 1.83 0.00 10.94 -0.01

time (sec)

N/A 0.325 0.626 0.937 0.344 0.417 0.000 0.456 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 115 254 236 274 0 1308 -1

N.S.

1 1.00 0.78 1.73 1.61 1.86 0.00 8.90 -0.01

time (sec)

N/A 0.286 0.496 0.853 0.337 0.362 0.000 0.456 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 97 215 178 200 0 994 -1

N.S.

1 1.00 0.78 1.72 1.42 1.60 0.00 7.95 -0.01

time (sec)

N/A 0.221 0.272 0.738 0.324 0.373 0.000 0.458 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 65 132 81 149 0 615 -1

N.S.

1 1.00 0.92 1.86 1.14 2.10 0.00 8.66 -0.01

time (sec)

N/A 0.084 0.187 0.711 0.317 0.376 0.000 0.441 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

150 150 139 254 227 270 0 1329 -1

N.S.

1 1.00 0.93 1.69 1.51 1.80 0.00 8.86 -0.01

time (sec)

N/A 0.307 0.806 0.714 0.382 0.368 0.000 0.457 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 183 312 0 377 0 3353 -1

N.S.

1 1.00 0.98 1.68 0.00 2.03 0.00 18.03 -0.01

time (sec)

N/A 0.367 0.905 0.737 0.000 0.465 0.000 0.472 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

264 264 236 571 0 566 0 879 -1

N.S.

1 1.00 0.89 2.16 0.00 2.14 0.00 3.33 -0.00

time (sec)

N/A 0.474 0.671 0.914 0.000 0.371 0.000 0.405 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

241 241 153 527 0 475 0 741 -1

N.S.

1 1.00 0.63 2.19 0.00 1.97 0.00 3.07 -0.00

time (sec)

N/A 0.412 0.625 0.752 0.000 0.367 0.000 0.421 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 158 435 0 373 0 529 -1

N.S.

1 1.00 0.89 2.44 0.00 2.10 0.00 2.97 -0.01

time (sec)

N/A 0.282 0.399 0.740 0.000 0.444 0.000 0.411 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 88 276 95 253 0 298 -1

N.S.

1 1.00 0.85 2.65 0.91 2.43 0.00 2.87 -0.01

time (sec)

N/A 0.100 0.398 0.721 0.295 0.342 0.000 0.420 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

262 262 451 488 0 601 0 837 -1

N.S.

1 1.00 1.72 1.86 0.00 2.29 0.00 3.19 -0.00

time (sec)

N/A 0.425 0.866 0.728 0.000 0.407 0.000 0.422 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 541 643 0 762 0 1006 -1

N.S.

1 1.00 1.82 2.16 0.00 2.56 0.00 3.38 -0.00

time (sec)

N/A 0.520 0.977 0.756 0.000 0.430 0.000 0.404 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

377 377 627 760 0 892 0 1169 -1

N.S.

1 1.00 1.66 2.02 0.00 2.37 0.00 3.10 -0.00

time (sec)

N/A 0.634 1.214 0.767 0.000 0.392 0.000 0.429 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 92 447 250 95 168 174 116

N.S.

1 1.00 0.66 3.22 1.80 0.68 1.21 1.25 0.83

time (sec)

N/A 0.184 0.128 0.689 0.263 0.425 0.491 0.422 0.991

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 74 298 214 78 134 138 93

N.S.

1 1.00 0.68 2.73 1.96 0.72 1.23 1.27 0.85

time (sec)

N/A 0.136 0.104 0.661 0.273 0.392 0.308 0.418 0.934

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 57 183 213 60 99 101 70

N.S.

1 1.00 0.72 2.32 2.70 0.76 1.25 1.28 0.89

time (sec)

N/A 0.087 0.092 0.648 0.274 0.374 0.224 0.436 0.975

Problem 43

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

51 51 40 97 86 42 65 70 47

N.S.

1 1.00 0.78 1.90 1.69 0.82 1.27 1.37 0.92

time (sec)

N/A 0.051 0.061 0.651 0.269 0.516 0.127 0.408 0.925

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 55 81 122 73 49 76 -1

N.S.

1 1.00 1.34 1.98 2.98 1.78 1.20 1.85 -0.02

time (sec)

N/A 0.077 0.090 0.911 0.305 0.405 1.936 0.399 0.000

Problem 45

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

42 42 42 81 80 82 0 80 -1

N.S.

1 1.00 1.00 1.93 1.90 1.95 0.00 1.90 -0.02

time (sec)

N/A 0.090 0.075 0.862 0.319 0.465 0.000 0.397 0.000

Problem 46

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

74 74 80 110 90 107 0 109 -1

N.S.

1 1.00 1.08 1.49 1.22 1.45 0.00 1.47 -0.01

time (sec)

N/A 0.127 0.130 0.924 0.345 0.409 0.000 0.421 0.000

Problem 47

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

105 105 95 172 73 127 0 170 -1

N.S.

1 1.00 0.90 1.64 0.70 1.21 0.00 1.62 -0.01

time (sec)

N/A 0.172 0.180 0.933 0.349 0.466 0.000 0.417 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 127 238 76 152 0 237 -1

N.S.

1 1.00 0.85 1.60 0.51 1.02 0.00 1.59 -0.01

time (sec)

N/A 0.219 0.248 0.997 0.325 0.372 0.000 0.413 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 138 738 383 155 286 304 182

N.S.

1 1.00 0.59 3.15 1.64 0.66 1.22 1.30 0.78

time (sec)

N/A 0.266 0.218 0.615 0.282 0.395 0.703 0.413 1.031

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 113 513 353 126 226 239 148

N.S.

1 1.00 0.61 2.79 1.92 0.68 1.23 1.30 0.80

time (sec)

N/A 0.201 0.152 0.609 0.284 0.379 0.471 0.413 0.982

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 85 332 189 98 172 180 114

N.S.

1 1.00 0.62 2.44 1.39 0.72 1.26 1.32 0.84

time (sec)

N/A 0.130 0.117 0.582 0.274 0.388 0.312 0.423 0.118

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 82 226 235 130 121 222 -1

N.S.

1 1.00 0.75 2.05 2.14 1.18 1.10 2.02 -0.01

time (sec)

N/A 0.134 0.259 0.838 0.320 0.419 2.466 0.412 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 95 190 179 127 0 197 -1

N.S.

1 1.00 1.00 2.00 1.88 1.34 0.00 2.07 -0.01

time (sec)

N/A 0.127 0.173 0.879 0.316 0.390 0.000 0.407 0.000

Problem 54

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

114 114 97 188 165 164 0 206 -1

N.S.

1 1.00 0.85 1.65 1.45 1.44 0.00 1.81 -0.01

time (sec)

N/A 0.155 0.272 0.857 0.341 0.357 0.000 0.406 0.000

Problem 55

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

133 133 114 222 135 171 0 236 -1

N.S.

1 1.00 0.86 1.67 1.02 1.29 0.00 1.77 -0.01

time (sec)

N/A 0.183 0.277 0.830 0.328 0.374 0.000 0.419 0.000

Problem 56

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

175 175 124 291 139 194 0 294 -1

N.S.

1 1.00 0.71 1.66 0.79 1.11 0.00 1.68 -0.01

time (sec)

N/A 0.241 0.298 0.789 0.348 0.359 0.000 0.411 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

273 273 274 369 0 605 0 0 -1

N.S.

1 1.00 1.00 1.35 0.00 2.22 0.00 0.00 -0.00

time (sec)

N/A 0.508 0.333 1.171 0.000 0.358 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 210 268 0 502 0 0 -1

N.S.

1 1.00 1.00 1.28 0.00 2.40 0.00 0.00 -0.00

time (sec)

N/A 0.262 0.298 0.987 0.000 0.390 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

226 226 213 259 0 496 0 0 -1

N.S.

1 1.00 0.94 1.15 0.00 2.19 0.00 0.00 -0.00

time (sec)

N/A 0.272 0.211 0.886 0.000 0.369 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 171 200 0 219 0 0 -1

N.S.

1 1.00 0.97 1.13 0.00 1.24 0.00 0.00 -0.01

time (sec)

N/A 0.182 0.148 0.730 0.000 0.390 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

213 213 180 212 0 316 0 0 -1

N.S.

1 1.00 0.85 1.00 0.00 1.48 0.00 0.00 -0.00

time (sec)

N/A 0.190 0.171 0.712 0.000 0.416 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 187 227 0 249 0 0 -1

N.S.

1 1.00 0.95 1.15 0.00 1.26 0.00 0.00 -0.01

time (sec)

N/A 0.271 0.283 0.714 0.000 0.434 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

249 249 243 288 0 599 0 0 -1

N.S.

1 1.00 0.98 1.16 0.00 2.41 0.00 0.00 -0.00

time (sec)

N/A 0.367 0.288 0.721 0.000 0.497 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

270 270 257 330 0 583 0 0 -1

N.S.

1 1.00 0.95 1.22 0.00 2.16 0.00 0.00 -0.00

time (sec)

N/A 0.352 0.422 0.743 0.000 0.386 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

449 449 621 532 0 1179 0 0 -1

N.S.

1 1.00 1.38 1.18 0.00 2.63 0.00 0.00 -0.00

time (sec)

N/A 0.604 1.093 1.144 0.000 0.659 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

431 431 582 495 0 931 0 0 -1

N.S.

1 1.00 1.35 1.15 0.00 2.16 0.00 0.00 -0.00

time (sec)

N/A 0.496 0.495 0.898 0.000 0.453 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

416 416 364 491 0 1162 0 0 -1

N.S.

1 1.00 0.88 1.18 0.00 2.79 0.00 0.00 -0.00

time (sec)

N/A 0.420 0.700 0.832 0.000 0.435 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

239 239 239 291 0 641 0 0 -1

N.S.

1 1.00 1.00 1.22 0.00 2.68 0.00 0.00 -0.00

time (sec)

N/A 0.237 0.402 0.783 0.000 0.521 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

476 476 590 503 0 1162 0 0 -1

N.S.

1 1.00 1.24 1.06 0.00 2.44 0.00 0.00 -0.00

time (sec)

N/A 0.603 0.557 0.731 0.000 0.413 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

435 435 501 546 0 992 0 0 -1

N.S.

1 1.00 1.15 1.26 0.00 2.28 0.00 0.00 -0.00

time (sec)

N/A 0.615 0.845 0.749 0.000 0.489 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

500 500 675 595 0 1310 0 0 -1

N.S.

1 1.00 1.35 1.19 0.00 2.62 0.00 0.00 -0.00

time (sec)

N/A 0.908 0.703 0.784 0.000 0.481 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

476 476 648 820 0 1620 0 0 -1

N.S.

1 1.00 1.36 1.72 0.00 3.40 0.00 0.00 -0.00

time (sec)

N/A 0.749 1.424 1.103 0.000 0.440 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

746 746 932 1064 0 2047 0 0 -1

N.S.

1 1.00 1.25 1.43 0.00 2.74 0.00 0.00 -0.00

time (sec)

N/A 0.822 1.898 0.932 0.000 0.375 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

512 512 637 743 0 1607 0 0 -1

N.S.

1 1.00 1.24 1.45 0.00 3.14 0.00 0.00 -0.00

time (sec)

N/A 0.604 1.352 0.837 0.000 0.575 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

856 856 933 1064 0 2116 0 0 -1

N.S.

1 1.00 1.09 1.24 0.00 2.47 0.00 0.00 -0.00

time (sec)

N/A 0.883 1.775 0.756 0.000 0.391 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

730 730 1046 1090 0 2076 0 0 -1

N.S.

1 1.00 1.43 1.49 0.00 2.84 0.00 0.00 -0.00

time (sec)

N/A 1.260 1.715 0.783 0.000 0.539 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

874 874 1009 1178 0 2346 0 0 -1

N.S.

1 1.00 1.15 1.35 0.00 2.68 0.00 0.00 -0.00

time (sec)

N/A 2.116 1.936 0.790 0.000 0.521 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

791 791 998 1294 0 2363 0 0 -1

N.S.

1 1.00 1.26 1.64 0.00 2.99 0.00 0.00 -0.00

time (sec)

N/A 1.411 2.630 0.820 0.000 0.490 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 100 551 268 105 185 192 152

N.S.

1 1.00 0.65 3.58 1.74 0.68 1.20 1.25 0.99

time (sec)

N/A 0.209 0.132 0.672 0.281 0.423 0.684 0.405 1.046

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 84 389 267 87 151 156 122

N.S.

1 1.00 0.68 3.14 2.15 0.70 1.22 1.26 0.98

time (sec)

N/A 0.158 0.110 0.661 0.277 0.373 0.448 0.413 0.960

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 66 257 196 68 116 119 92

N.S.

1 1.00 0.70 2.73 2.09 0.72 1.23 1.27 0.98

time (sec)

N/A 0.108 0.089 0.660 0.260 0.385 0.300 0.403 0.924

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 49 158 104 53 82 88 65

N.S.

1 1.00 0.74 2.39 1.58 0.80 1.24 1.33 0.98

time (sec)

N/A 0.068 0.074 0.658 0.268 0.418 0.189 0.407 0.098

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 49 113 140 86 66 109 -1

N.S.

1 1.00 0.88 2.02 2.50 1.54 1.18 1.95 -0.02

time (sec)

N/A 0.093 0.147 0.902 0.315 0.347 2.052 0.405 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 55 110 102 90 0 111 -1

N.S.

1 1.00 1.00 2.00 1.85 1.64 0.00 2.02 -0.02

time (sec)

N/A 0.093 0.105 0.925 0.312 0.413 0.000 0.419 0.000

Problem 85

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

69 69 86 114 87 101 0 118 -1

N.S.

1 1.00 1.25 1.65 1.26 1.46 0.00 1.71 -0.01

time (sec)

N/A 0.098 0.115 0.926 0.322 0.362 0.000 0.413 0.000

Problem 86

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

91 91 73 143 95 118 0 141 -1

N.S.

1 1.00 0.80 1.57 1.04 1.30 0.00 1.55 -0.01

time (sec)

N/A 0.150 0.193 0.935 0.329 0.407 0.000 0.402 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 139 818 383 161 284 303 301

N.S.

1 1.00 0.59 3.50 1.64 0.69 1.21 1.29 1.29

time (sec)

N/A 0.277 0.196 0.612 0.267 0.376 0.977 0.405 0.354

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 111 592 243 130 226 244 182

N.S.

1 1.00 0.60 3.18 1.31 0.70 1.22 1.31 0.98

time (sec)

N/A 0.207 0.179 0.618 0.293 0.399 0.690 0.404 0.241

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 108 335 289 161 168 331 -1

N.S.

1 1.00 0.68 2.09 1.81 1.01 1.05 2.07 -0.01

time (sec)

N/A 0.207 0.348 0.864 0.322 0.368 3.193 0.408 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 143 296 235 160 0 308 -1

N.S.

1 1.00 1.00 2.07 1.64 1.12 0.00 2.15 -0.01

time (sec)

N/A 0.197 0.233 0.891 0.327 0.413 0.000 0.408 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 136 265 203 161 0 280 -1

N.S.

1 1.00 0.96 1.88 1.44 1.14 0.00 1.99 -0.01

time (sec)

N/A 0.163 0.226 0.895 0.324 0.361 0.000 0.397 0.000

Problem 92

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

150 150 135 261 188 187 0 279 -1

N.S.

1 1.00 0.90 1.74 1.25 1.25 0.00 1.86 -0.01

time (sec)

N/A 0.208 0.408 0.913 0.329 0.402 0.000 0.407 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 150 292 154 196 0 315 -1

N.S.

1 1.00 0.90 1.75 0.92 1.17 0.00 1.89 -0.01

time (sec)

N/A 0.251 0.359 0.934 0.339 0.372 0.000 0.415 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

373 373 213 925 0 989 0 0 -1

N.S.

1 1.00 0.57 2.48 0.00 2.65 0.00 0.00 -0.00

time (sec)

N/A 0.720 0.370 1.156 0.000 0.433 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

358 358 198 671 0 977 0 0 -1

N.S.

1 1.00 0.55 1.87 0.00 2.73 0.00 0.00 -0.00

time (sec)

N/A 0.476 0.196 1.069 0.000 0.404 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

283 283 170 423 0 500 0 0 -1

N.S.

1 1.00 0.60 1.49 0.00 1.77 0.00 0.00 -0.00

time (sec)

N/A 0.360 0.171 1.014 0.000 0.414 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

345 345 180 280 0 671 0 0 -1

N.S.

1 1.00 0.52 0.81 0.00 1.94 0.00 0.00 -0.00

time (sec)

N/A 0.304 0.168 1.013 0.000 0.441 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

345 345 180 143 0 673 0 0 -1

N.S.

1 1.00 0.52 0.41 0.00 1.95 0.00 0.00 -0.00

time (sec)

N/A 0.300 0.109 1.001 0.000 0.451 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

303 303 186 138 0 530 0 0 -1

N.S.

1 1.00 0.61 0.46 0.00 1.75 0.00 0.00 -0.00

time (sec)

N/A 0.372 0.211 0.992 0.000 0.406 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

381 381 215 187 0 1154 0 0 -1

N.S.

1 1.00 0.56 0.49 0.00 3.03 0.00 0.00 -0.00

time (sec)

N/A 0.442 0.322 1.017 0.000 0.483 0.000 0.000 0.000

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