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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 B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 76 547 326 169 311 324 215

N.S.

1 1.00 0.84 6.01 3.58 1.86 3.42 3.56 2.36

time (sec)

N/A 0.085 0.180 0.300 0.278 0.351 0.364 0.431 0.452

Problem 2

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

70 70 61 308 222 109 202 204 143

N.S.

1 1.00 0.87 4.40 3.17 1.56 2.89 2.91 2.04

time (sec)

N/A 0.056 0.112 0.303 0.268 0.338 0.251 0.441 0.142

Problem 3

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 44 147 134 62 112 112 82

N.S.

1 1.00 0.90 3.00 2.73 1.27 2.29 2.29 1.67

time (sec)

N/A 0.034 0.088 0.303 0.275 0.405 0.181 0.414 0.120

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 29 46 46 35

N.S.

1 1.00 0.96 1.89 2.43 1.04 1.64 1.64 1.25

time (sec)

N/A 0.014 0.053 0.424 0.261 0.372 0.087 0.411 0.096

Problem 5

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 82 57 94 0 57 -1

N.S.

1 1.00 0.96 1.61 1.12 1.84 0.00 1.12 -0.02

time (sec)

N/A 0.077 0.057 0.365 0.295 0.333 0.000 0.409 0.000

Problem 6

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 65 133 80 148 0 615 -1

N.S.

1 1.00 0.92 1.87 1.13 2.08 0.00 8.66 -0.01

time (sec)

N/A 0.093 0.151 0.378 0.299 0.371 0.000 0.447 0.000

Problem 7

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 88 277 94 254 0 301 -1

N.S.

1 1.00 0.85 2.66 0.90 2.44 0.00 2.89 -0.01

time (sec)

N/A 0.125 0.376 0.388 0.317 0.369 0.000 0.415 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 132 910 382 312 660 374 334

N.S.

1 1.00 0.81 5.62 2.36 1.93 4.07 2.31 2.06

time (sec)

N/A 0.076 0.363 0.442 0.320 0.371 0.700 0.450 0.693

Problem 9

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

134 134 104 523 263 209 456 243 229

N.S.

1 1.00 0.78 3.90 1.96 1.56 3.40 1.81 1.71

time (sec)

N/A 0.050 0.250 0.372 0.283 0.351 0.384 0.430 0.376

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 75 262 165 123 264 136 127

N.S.

1 1.00 0.79 2.76 1.74 1.29 2.78 1.43 1.34

time (sec)

N/A 0.043 0.185 0.368 0.267 0.337 0.240 0.441 0.181

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 52 103 88 64 126 63 60

N.S.

1 1.00 0.95 1.87 1.60 1.16 2.29 1.15 1.09

time (sec)

N/A 0.018 0.127 0.418 0.263 0.350 0.147 0.438 0.093

Problem 12

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

78 78 66 97 72 104 0 68 -1

N.S.

1 1.00 0.85 1.24 0.92 1.33 0.00 0.87 -0.01

time (sec)

N/A 0.113 0.083 3.020 0.293 0.336 0.000 0.447 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 75 152 88 166 0 574 -1

N.S.

1 1.00 0.93 1.88 1.09 2.05 0.00 7.09 -0.01

time (sec)

N/A 0.108 0.291 3.308 0.318 0.391 0.000 0.483 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 102 299 99 280 0 330 -1

N.S.

1 1.00 0.91 2.67 0.88 2.50 0.00 2.95 -0.01

time (sec)

N/A 0.136 0.616 3.328 0.322 0.357 0.000 0.425 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 123 555 110 411 0 537 -1

N.S.

1 1.00 0.76 3.43 0.68 2.54 0.00 3.31 -0.01

time (sec)

N/A 0.130 0.611 3.246 0.308 0.358 0.000 0.422 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 150 1266 639 528 772 654 532

N.S.

1 1.00 0.67 5.63 2.84 2.35 3.43 2.91 2.36

time (sec)

N/A 0.250 0.621 0.493 0.301 0.370 0.810 0.449 0.547

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 127 710 435 345 495 414 364

N.S.

1 1.00 0.73 4.06 2.49 1.97 2.83 2.37 2.08

time (sec)

N/A 0.161 0.618 0.427 0.303 0.351 0.530 0.407 0.349

Problem 18

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

123 123 86 343 269 199 284 230 184

N.S.

1 1.00 0.70 2.79 2.19 1.62 2.31 1.87 1.50

time (sec)

N/A 0.093 0.244 0.421 0.282 0.351 0.383 0.413 0.408

Problem 19

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

75 75 59 125 141 97 126 98 79

N.S.

1 1.00 0.79 1.67 1.88 1.29 1.68 1.31 1.05

time (sec)

N/A 0.044 0.143 0.464 0.276 0.387 0.203 0.435 0.162

Problem 20

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

121 121 102 166 117 188 0 113 -1

N.S.

1 1.00 0.84 1.37 0.97 1.55 0.00 0.93 -0.01

time (sec)

N/A 0.192 0.162 1.604 0.322 0.376 0.000 0.417 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 160 271 145 301 0 1076 -1

N.S.

1 1.00 1.10 1.87 1.00 2.08 0.00 7.42 -0.01

time (sec)

N/A 0.193 0.817 1.620 0.337 0.340 0.000 0.475 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 220 562 145 529 0 601 -1

N.S.

1 1.00 1.20 3.05 0.79 2.88 0.00 3.27 -0.01

time (sec)

N/A 0.303 0.539 1.642 0.343 0.334 0.000 0.423 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 296 541 333 396 0 0 -1

N.S.

1 1.00 1.99 3.63 2.23 2.66 0.00 0.00 -0.01

time (sec)

N/A 0.099 2.052 0.880 0.345 0.356 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 170 306 195 242 0 0 -1

N.S.

1 1.00 1.72 3.09 1.97 2.44 0.00 0.00 -0.01

time (sec)

N/A 0.063 1.587 0.772 0.327 0.339 0.000 0.000 0.000

Problem 25

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

50 50 174 60 0 119 0 0 -1

N.S.

1 1.00 3.48 1.20 0.00 2.38 0.00 0.00 -0.02

time (sec)

N/A 0.029 0.059 0.507 0.000 0.335 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.015 9.354 180.000 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.015 9.265 180.000 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 133 473 320 1159 0 0 -1

N.S.

1 1.00 1.29 4.59 3.11 11.25 0.00 0.00 -0.01

time (sec)

N/A 0.146 1.360 0.940 0.413 0.351 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 198 240 0 623 0 0 -1

N.S.

1 1.00 2.68 3.24 0.00 8.42 0.00 0.00 -0.01

time (sec)

N/A 0.102 3.680 0.826 0.000 0.412 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 52 56 91 166 0 80 49

N.S.

1 1.00 1.79 1.93 3.14 5.72 0.00 2.76 1.69

time (sec)

N/A 0.021 0.088 0.470 0.273 0.350 0.000 0.435 0.077

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.029 15.084 180.000 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.026 15.624 180.000 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

256 256 398 876 605 4008 0 0 -1

N.S.

1 1.00 1.55 3.42 2.36 15.66 0.00 0.00 -0.00

time (sec)

N/A 0.195 5.980 1.069 0.420 0.412 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 375 444 393 2218 0 0 -1

N.S.

1 1.00 2.44 2.88 2.55 14.40 0.00 0.00 -0.01

time (sec)

N/A 0.119 8.802 0.947 0.410 0.367 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 313 197 0 1026 0 0 -1

N.S.

1 1.00 3.40 2.14 0.00 11.15 0.00 0.00 -0.01

time (sec)

N/A 0.058 1.688 0.691 0.000 0.353 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.033 52.153 180.000 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.026 55.688 180.000 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 108 0 308 521 0 232 -1

N.S.

1 1.00 0.63 0.00 1.80 3.05 0.00 1.36 -0.01

time (sec)

N/A 0.261 0.040 180.000 0.278 0.352 0.000 0.471 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 106 0 268 385 0 202 -1

N.S.

1 1.00 0.73 0.00 1.84 2.64 0.00 1.38 -0.01

time (sec)

N/A 0.168 0.068 180.000 0.273 0.353 0.000 0.488 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 104 0 230 301 0 168 -1

N.S.

1 1.00 0.85 0.00 1.87 2.45 0.00 1.37 -0.01

time (sec)

N/A 0.126 0.063 180.000 0.283 0.359 0.000 0.451 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 104 0 181 122 0 90 -1

N.S.

1 1.00 1.00 0.00 1.74 1.17 0.00 0.87 -0.01

time (sec)

N/A 0.091 0.024 180.000 0.282 0.374 0.000 0.436 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 120 0 103 339 0 0 -1

N.S.

1 1.00 1.02 0.00 0.87 2.87 0.00 0.00 -0.01

time (sec)

N/A 0.135 0.107 180.000 0.261 0.379 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 161 0 114 532 0 0 -1

N.S.

1 1.00 1.08 0.00 0.77 3.57 0.00 0.00 -0.01

time (sec)

N/A 0.171 0.529 180.000 0.343 0.395 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 168 0 114 855 0 0 -1

N.S.

1 1.00 0.97 0.00 0.66 4.91 0.00 0.00 -0.01

time (sec)

N/A 0.221 0.381 180.000 0.353 0.374 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

239 239 190 0 281 1001 0 0 -1

N.S.

1 1.00 0.79 0.00 1.18 4.19 0.00 0.00 -0.00

time (sec)

N/A 0.310 4.511 180.000 0.479 0.359 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 163 0 239 755 0 0 -1

N.S.

1 1.00 0.77 0.00 1.13 3.58 0.00 0.00 -0.00

time (sec)

N/A 0.224 1.558 180.000 0.492 0.624 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 129 0 189 590 0 0 -1

N.S.

1 1.00 0.78 0.00 1.14 3.55 0.00 0.00 -0.01

time (sec)

N/A 0.202 0.407 180.000 0.476 0.434 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 142 0 107 155 0 115 -1

N.S.

1 1.00 1.02 0.00 0.77 1.12 0.00 0.83 -0.01

time (sec)

N/A 0.156 0.081 180.000 0.478 0.462 0.000 0.534 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 570 0 116 571 0 0 -1

N.S.

1 1.00 4.01 0.00 0.82 4.02 0.00 0.00 -0.01

time (sec)

N/A 0.166 3.199 180.000 0.346 0.433 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 156 0 118 864 0 0 -1

N.S.

1 1.00 0.90 0.00 0.68 4.97 0.00 0.00 -0.01

time (sec)

N/A 0.226 0.795 180.000 0.344 0.541 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

220 220 825 0 118 1352 0 0 -1

N.S.

1 1.00 3.75 0.00 0.54 6.15 0.00 0.00 -0.00

time (sec)

N/A 0.222 6.082 180.000 0.330 0.463 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

251 251 222 0 118 1827 0 0 -1

N.S.

1 1.00 0.88 0.00 0.47 7.28 0.00 0.00 -0.00

time (sec)

N/A 0.283 0.369 180.000 0.326 0.407 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

381 381 243 0 513 2090 0 0 -1

N.S.

1 1.00 0.64 0.00 1.35 5.49 0.00 0.00 -0.00

time (sec)

N/A 0.798 6.676 180.000 0.506 0.462 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

325 325 243 0 430 1543 0 0 -1

N.S.

1 1.00 0.75 0.00 1.32 4.75 0.00 0.00 -0.00

time (sec)

N/A 0.612 2.702 180.000 0.483 0.440 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

275 275 209 0 333 1216 0 0 -1

N.S.

1 1.00 0.76 0.00 1.21 4.42 0.00 0.00 -0.00

time (sec)

N/A 0.382 0.207 180.000 0.482 0.381 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

228 228 191 0 178 252 0 0 -1

N.S.

1 1.00 0.84 0.00 0.78 1.11 0.00 0.00 -0.00

time (sec)

N/A 0.288 0.131 180.000 0.494 0.353 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

246 246 574 0 197 1346 0 0 -1

N.S.

1 1.00 2.33 0.00 0.80 5.47 0.00 0.00 -0.00

time (sec)

N/A 0.325 8.422 180.000 0.370 0.355 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 253 0 196 2059 0 0 -1

N.S.

1 1.00 0.91 0.00 0.71 7.43 0.00 0.00 -0.00

time (sec)

N/A 0.516 2.002 180.000 0.361 0.373 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

331 331 3211 0 197 3286 0 0 -1

N.S.

1 1.00 9.70 0.00 0.60 9.93 0.00 0.00 -0.00

time (sec)

N/A 0.575 14.151 180.000 0.357 0.469 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 50 132 175 189 133 146 -1

N.S.

1 1.00 0.45 1.19 1.58 1.70 1.20 1.32 -0.01

time (sec)

N/A 0.111 0.011 0.237 0.262 0.340 13.772 0.437 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 49 120 149 137 99 108 -1

N.S.

1 1.00 0.53 1.30 1.62 1.49 1.08 1.17 -0.01

time (sec)

N/A 0.078 0.012 0.196 0.290 0.581 1.019 0.420 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 47 71 116 58 70 61 -1

N.S.

1 1.00 0.61 0.92 1.51 0.75 0.91 0.79 -0.01

time (sec)

N/A 0.051 0.007 0.196 0.274 0.416 0.565 0.447 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 49 120 74 137 94 0 -1

N.S.

1 1.00 0.56 1.38 0.85 1.57 1.08 0.00 -0.01

time (sec)

N/A 0.079 0.015 0.198 0.269 0.442 1.989 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 84 132 57 178 129 0 -1

N.S.

1 1.00 0.74 1.16 0.50 1.56 1.13 0.00 -0.01

time (sec)

N/A 0.104 0.055 0.198 0.315 0.414 15.711 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.020 23.349 180.000 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.020 15.644 180.000 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F(-2) A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

63 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.071 5.432 0.129 0.000 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 17 0 0 0 0 0 38

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 1.90

time (sec)

N/A 0.036 0.078 1.747 0.000 0.000 0.000 0.000 0.174

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 22 0 0 108 0 0 40

N.S.

1 1.00 0.92 0.00 0.00 4.50 0.00 0.00 1.67

time (sec)

N/A 0.038 0.043 1.652 0.000 0.347 0.000 0.000 0.153

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 33 0 0 0 0 0 111

N.S.

1 1.00 0.70 0.00 0.00 0.00 0.00 0.00 2.36

time (sec)

N/A 0.052 0.077 1.813 0.000 0.000 0.000 0.000 0.291

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 68 0 0 0 0 0 -1

N.S.

1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.080 0.848 1.678 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.031 2.010 180.000 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 206 0 161 340 0 0 -1

N.S.

1 1.00 0.87 0.00 0.68 1.43 0.00 0.00 -0.00

time (sec)

N/A 0.225 0.144 180.000 0.082 0.089 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 131 0 102 241 0 0 -1

N.S.

1 1.00 0.91 0.00 0.71 1.67 0.00 0.00 -0.01

time (sec)

N/A 0.140 0.123 180.000 0.070 0.085 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 101 0 79 168 0 0 -1

N.S.

1 1.00 0.92 0.00 0.72 1.53 0.00 0.00 -0.01

time (sec)

N/A 0.061 0.044 180.000 0.060 0.086 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.015 5.970 180.000 0.000 0.000 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.024 2.439 180.000 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 54 73 55 86 0 0 -1

N.S.

1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 -0.02

time (sec)

N/A 0.051 0.020 0.171 0.075 0.080 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 53 73 55 86 0 0 -1

N.S.

1 1.00 0.90 1.24 0.93 1.46 0.00 0.00 -0.02

time (sec)

N/A 0.051 0.016 0.173 0.079 0.088 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 54 73 55 86 0 0 -1

N.S.

1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 -0.02

time (sec)

N/A 0.049 0.017 0.161 0.087 0.080 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 53 73 55 78 0 0 -1

N.S.

1 1.00 0.90 1.24 0.93 1.32 0.00 0.00 -0.02

time (sec)

N/A 0.047 0.014 0.155 0.077 0.106 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 49 67 43 78 0 0 -1

N.S.

1 1.00 1.00 1.37 0.88 1.59 0.00 0.00 -0.02

time (sec)

N/A 0.048 0.017 0.181 0.083 0.082 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 51 67 55 86 0 0 -1

N.S.

1 1.00 0.93 1.22 1.00 1.56 0.00 0.00 -0.02

time (sec)

N/A 0.049 0.015 0.187 0.094 0.085 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 54 71 55 86 0 0 -1

N.S.

1 1.00 0.92 1.20 0.93 1.46 0.00 0.00 -0.02

time (sec)

N/A 0.050 0.017 0.168 0.093 0.083 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 79 0 71 136 0 0 -1

N.S.

1 1.00 0.92 0.00 0.83 1.58 0.00 0.00 -0.01

time (sec)

N/A 0.114 0.101 0.285 0.082 0.089 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 78 0 71 136 0 0 -1

N.S.

1 1.00 0.92 0.00 0.84 1.60 0.00 0.00 -0.01

time (sec)

N/A 0.095 0.100 0.225 0.075 0.138 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 79 0 71 136 0 0 -1

N.S.

1 1.00 0.92 0.00 0.83 1.58 0.00 0.00 -0.01

time (sec)

N/A 0.102 0.093 0.228 0.074 0.136 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 76 0 71 122 0 0 -1

N.S.

1 1.00 0.89 0.00 0.84 1.44 0.00 0.00 -0.01

time (sec)

N/A 0.090 0.080 0.215 0.081 0.088 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 63 0 55 117 0 0 -1

N.S.

1 1.00 0.88 0.00 0.76 1.62 0.00 0.00 -0.01

time (sec)

N/A 0.087 0.065 0.284 0.094 0.087 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 72 0 0 136 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 1.64 0.00 0.00 -0.01

time (sec)

N/A 0.095 0.088 0.287 0.000 0.084 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 77 0 0 136 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 1.62 0.00 0.00 -0.01

time (sec)

N/A 0.098 0.082 0.286 0.000 0.102 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 17 0 0 0 0 0 -1

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.075 0.059 1.598 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 17 0 0 0 0 0 -1

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.078 0.084 1.587 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 45 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.086 0.094 1.566 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 63 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.150 0.103 1.587 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 128 494 248 287 517 262 196

N.S.

1 1.00 1.31 5.04 2.53 2.93 5.28 2.67 2.00

time (sec)

N/A 0.099 0.293 0.441 0.294 0.345 0.443 0.456 0.383

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 88 249 149 175 314 150 118

N.S.

1 1.00 1.19 3.36 2.01 2.36 4.24 2.03 1.59

time (sec)

N/A 0.071 0.254 0.368 0.269 0.373 0.281 0.440 0.246

Problem 98

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

50 50 48 96 70 84 162 69 56

N.S.

1 1.00 0.96 1.92 1.40 1.68 3.24 1.38 1.12

time (sec)

N/A 0.034 0.077 0.380 0.263 0.345 0.197 0.434 0.123

Problem 99

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 60 96 73 81 0 69 -1

N.S.

1 1.00 0.86 1.37 1.04 1.16 0.00 0.99 -0.01

time (sec)

N/A 0.116 0.174 0.543 0.320 0.357 0.000 0.417 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 83 153 90 139 0 630 -1

N.S.

1 1.00 0.87 1.61 0.95 1.46 0.00 6.63 -0.01

time (sec)

N/A 0.131 0.280 0.502 0.307 0.375 0.000 0.447 0.000

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