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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 A A B C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

183 183 153 299 225 355 258 174 -1

N.S.

1 1.00 0.84 1.63 1.23 1.94 1.41 0.95 -0.01

time (sec)

N/A 0.105 0.149 1.358 0.275 0.365 0.264 0.443 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 113 213 140 188 155 133 -1

N.S.

1 1.00 0.92 1.73 1.14 1.53 1.26 1.08 -0.01

time (sec)

N/A 0.071 0.118 1.303 0.261 0.397 0.157 0.429 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

97 97 73 104 85 85 80 84 68

N.S.

1 1.00 0.75 1.07 0.88 0.88 0.82 0.87 0.70

time (sec)

N/A 0.030 0.053 1.927 0.267 0.372 0.099 0.430 0.706

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 176 304 0 0 0 0 -1

N.S.

1 1.00 0.99 1.71 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.197 0.009 3.458 0.000 0.000 0.000 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 92 134 0 1023 0 240 -1

N.S.

1 1.00 1.11 1.61 0.00 12.33 0.00 2.89 -0.01

time (sec)

N/A 0.064 0.069 5.672 0.000 0.388 0.000 0.579 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 190 266 0 3784 0 0 -1

N.S.

1 1.00 1.44 2.02 0.00 28.67 0.00 0.00 -0.01

time (sec)

N/A 0.103 0.130 5.733 0.000 0.454 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 244 624 0 9111 0 0 -1

N.S.

1 1.00 1.25 3.20 0.00 46.72 0.00 0.00 -0.01

time (sec)

N/A 0.200 0.386 6.083 0.000 0.768 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

334 334 191 0 0 560 371 0 -1

N.S.

1 1.00 0.57 0.00 0.00 1.68 1.11 0.00 -0.00

time (sec)

N/A 0.955 0.125 180.000 0.000 0.420 0.385 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 131 0 0 291 223 0 -1

N.S.

1 1.00 0.61 0.00 0.00 1.35 1.04 0.00 -0.00

time (sec)

N/A 0.674 0.101 180.000 0.000 0.351 0.248 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 105 100 0 128 110 0 -1

N.S.

1 1.00 0.86 0.82 0.00 1.05 0.90 0.00 -0.01

time (sec)

N/A 0.428 0.073 3.342 0.000 0.405 0.144 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

272 272 252 0 0 0 0 0 -1

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.301 0.108 1.456 0.000 0.000 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

259 259 848 388 0 0 0 0 -1

N.S.

1 1.00 3.27 1.50 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.403 2.373 6.940 0.000 0.000 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

352 352 936 605 0 0 0 0 -1

N.S.

1 1.00 2.66 1.72 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.479 3.133 7.627 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 193 382 263 526 323 0 -1

N.S.

1 1.00 1.01 2.00 1.38 2.75 1.69 0.00 -0.01

time (sec)

N/A 0.105 0.181 1.645 0.265 0.370 0.301 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 142 262 167 282 197 0 -1

N.S.

1 1.00 1.08 1.98 1.27 2.14 1.49 0.00 -0.01

time (sec)

N/A 0.068 0.133 2.450 0.277 0.373 0.185 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 117 133 101 125 105 124 83

N.S.

1 1.00 1.10 1.25 0.95 1.18 0.99 1.17 0.78

time (sec)

N/A 0.030 0.072 2.095 0.269 0.415 0.108 0.461 1.029

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 183 324 0 0 0 0 -1

N.S.

1 1.00 0.94 1.66 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.185 0.095 2.679 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 121 155 0 1131 0 257 -1

N.S.

1 1.00 1.38 1.76 0.00 12.85 0.00 2.92 -0.01

time (sec)

N/A 0.048 0.139 4.943 0.000 0.413 0.000 0.574 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 184 365 0 4094 0 0 -1

N.S.

1 1.00 1.33 2.64 0.00 29.67 0.00 0.00 -0.01

time (sec)

N/A 0.084 0.274 5.639 0.000 0.492 0.000 0.000 0.000

Problem 20

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

202 202 259 1141 0 9905 0 0 -1

N.S.

1 1.00 1.28 5.65 0.00 49.03 0.00 0.00 -0.00

time (sec)

N/A 0.162 0.700 5.681 0.000 0.790 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

398 398 386 814 0 1187 750 0 -1

N.S.

1 1.00 0.97 2.05 0.00 2.98 1.88 0.00 -0.00

time (sec)

N/A 1.149 0.460 2.490 0.000 0.364 0.513 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

259 259 360 527 0 618 461 0 -1

N.S.

1 1.00 1.39 2.03 0.00 2.39 1.78 0.00 -0.00

time (sec)

N/A 0.761 0.409 1.639 0.000 0.401 0.331 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

150 150 174 240 0 263 240 0 -1

N.S.

1 1.00 1.16 1.60 0.00 1.75 1.60 0.00 -0.01

time (sec)

N/A 0.503 0.190 4.452 0.000 0.427 0.199 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

303 303 285 0 0 0 0 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.322 0.181 0.238 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

279 279 950 556 0 0 0 0 -1

N.S.

1 1.00 3.41 1.99 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.430 3.758 9.337 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

380 380 1099 1174 0 0 0 0 -1

N.S.

1 1.00 2.89 3.09 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.540 5.640 9.194 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

394 394 287 394 0 0 0 0 -1

N.S.

1 1.00 0.73 1.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.880 0.416 10.834 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 A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

245 245 187 254 0 0 0 0 -1

N.S.

1 1.00 0.76 1.04 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.517 0.235 9.183 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 98 120 0 0 0 0 -1

N.S.

1 1.00 0.84 1.03 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.250 0.101 8.141 0.000 0.000 0.000 0.000 0.000

Problem 30

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 0.023 0.160 180.000 0.000 0.000 0.000 0.000 0.000

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

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 0.023 0.292 180.000 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

374 374 530 649 0 0 0 0 -1

N.S.

1 1.00 1.42 1.74 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.520 1.050 9.997 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 A F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

190 190 268 285 0 0 0 0 -1

N.S.

1 1.00 1.41 1.50 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.316 0.544 8.828 0.000 0.000 0.000 0.000 0.000

Problem 34

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 0.021 6.591 180.000 0.000 0.000 0.000 0.000 0.000

Problem 35

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 0.019 142.153 180.000 0.000 0.000 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

82 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 -0.01

time (sec)

N/A 0.264 9.372 180.000 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 A A

verified

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

size

80 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 -0.01

time (sec)

N/A 0.230 0.105 180.000 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 F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 177 0 0 0 0 0 -1

N.S.

1 1.00 1.42 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.057 0.160 180.000 0.000 0.000 0.000 0.000 0.000

Problem 39

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 0.020 0.269 180.000 0.000 0.000 0.000 0.000 0.000

Problem 40

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 0.020 0.591 180.000 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

370 370 216 255 385 250 503 316 -1

N.S.

1 1.00 0.58 0.69 1.04 0.68 1.36 0.85 -0.00

time (sec)

N/A 0.317 0.208 1.572 0.265 0.399 1.476 0.414 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

267 267 154 176 257 179 328 214 -1

N.S.

1 1.00 0.58 0.66 0.96 0.67 1.23 0.80 -0.00

time (sec)

N/A 0.249 0.142 1.644 0.267 0.353 0.710 0.415 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

181 181 103 113 154 121 199 134 -1

N.S.

1 1.00 0.57 0.62 0.85 0.67 1.10 0.74 -0.01

time (sec)

N/A 0.135 0.111 1.665 0.271 0.405 0.332 0.422 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 60 62 74 71 90 70 -1

N.S.

1 1.00 0.71 0.74 0.88 0.85 1.07 0.83 -0.01

time (sec)

N/A 0.049 0.044 1.693 0.272 0.373 0.141 0.410 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

481 481 375 222 0 0 0 0 -1

N.S.

1 1.00 0.78 0.46 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.552 0.269 14.843 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

774 774 687 790 0 0 0 0 -1

N.S.

1 1.00 0.89 1.02 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.812 0.977 100.216 0.000 0.000 0.000 0.000 0.000

Problem 47

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 0.013 1.907 180.000 0.000 0.000 0.000 0.000 0.000

Problem 48

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 0.013 1.357 180.000 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 551 0 0 296 0 82 -1

N.S.

1 1.00 5.74 0.00 0.00 3.08 0.00 0.85 -0.01

time (sec)

N/A 0.119 12.298 180.000 0.000 0.368 0.000 0.427 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 609 0 0 613 0 190 -1

N.S.

1 1.00 3.38 0.00 0.00 3.41 0.00 1.06 -0.01

time (sec)

N/A 0.124 1.788 180.000 0.000 0.404 0.000 0.522 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 655 0 0 1098 0 411 -1

N.S.

1 1.00 2.43 0.00 0.00 4.08 0.00 1.53 -0.00

time (sec)

N/A 0.552 2.517 180.000 0.000 0.452 0.000 0.585 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

369 369 723 0 0 1752 0 876 -1

N.S.

1 1.00 1.96 0.00 0.00 4.75 0.00 2.37 -0.00

time (sec)

N/A 0.704 4.976 180.000 0.000 0.607 0.000 0.717 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

713 713 491 1430 0 0 0 0 -1

N.S.

1 1.00 0.69 2.01 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.957 1.191 7.532 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

479 479 356 1001 0 0 0 0 -1

N.S.

1 1.00 0.74 2.09 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.747 0.710 9.103 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

255 255 251 639 0 0 0 0 -1

N.S.

1 1.00 0.98 2.51 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.363 0.655 7.597 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

785 785 1121 1072 0 0 0 0 -1

N.S.

1 1.00 1.43 1.37 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.302 2.630 6.767 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

918 918 1139 1956 0 0 0 0 -1

N.S.

1 1.00 1.24 2.13 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.441 4.681 10.363 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1029 1029 901 2274 0 0 0 0 -1

N.S.

1 1.00 0.88 2.21 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.271 2.853 8.714 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

725 725 623 1726 0 0 0 0 -1

N.S.

1 1.00 0.86 2.38 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.053 1.811 8.483 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

398 398 432 1176 0 0 0 0 -1

N.S.

1 1.00 1.09 2.95 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.484 1.034 6.847 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A NO TBD TBD TBD TBD TBD TBD

size

1270 0 3068 1965 0 0 0 0 -1

N.S.

1 0.00 2.42 1.55 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.647 9.722 5.962 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1385 1385 1802 3170 0 0 0 0 -1

N.S.

1 1.00 1.30 2.29 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.533 7.222 8.918 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F(-1) F(-2) F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1015 1015 1282 2549 0 0 0 0 -1

N.S.

1 1.00 1.26 2.51 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.306 6.829 11.572 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

568 568 644 1856 0 0 0 0 -1

N.S.

1 1.00 1.13 3.27 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.570 4.193 7.115 0.000 0.000 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1744 1744 6244 4234 0 0 0 0 -1

N.S.

1 1.00 3.58 2.43 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 3.305 15.123 6.301 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

478 478 371 836 0 0 0 0 -1

N.S.

1 1.00 0.78 1.75 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.854 1.154 9.064 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

288 288 284 518 0 0 0 0 -1

N.S.

1 1.00 0.99 1.80 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.576 0.649 9.253 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 B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

136 136 185 248 0 0 0 0 -1

N.S.

1 1.00 1.36 1.82 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.304 0.470 7.950 0.000 0.000 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

365 365 932 754 0 0 0 0 -1

N.S.

1 1.00 2.55 2.07 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.474 1.308 4.184 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

523 523 1115 1978 0 0 0 0 -1

N.S.

1 1.00 2.13 3.78 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.576 4.197 8.476 0.000 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

549 549 353 1238 0 0 0 0 -1

N.S.

1 1.00 0.64 2.26 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.001 1.125 9.006 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

459 459 281 879 0 0 0 0 -1

N.S.

1 1.00 0.61 1.92 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.829 0.617 8.738 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 B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 178 133 499 0 0 0 0 -1

N.S.

1 1.25 0.94 3.51 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.214 0.362 7.118 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

773 773 1203 2484 0 0 0 0 -1

N.S.

1 1.00 1.56 3.21 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.242 8.644 5.722 0.000 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

239 239 204 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.329 0.407 180.000 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

200 200 204 0 0 0 0 0 -1

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.405 0.173 180.000 0.000 0.000 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 219 0 0 0 0 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.450 1.454 180.000 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

75 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 -0.01

time (sec)

N/A 0.433 0.122 180.000 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

774 774 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.847 3.070 180.000 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

600 600 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.633 1.257 180.000 0.000 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 246 0 0 0 0 0 -1

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.234 0.018 180.000 0.000 0.000 0.000 0.000 0.000

Problem 82

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

75 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 -0.01

time (sec)

N/A 0.486 0.214 180.000 0.000 0.000 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 121 285 321 110 255 163 -1

N.S.

1 1.00 0.80 1.88 2.11 0.72 1.68 1.07 -0.01

time (sec)

N/A 0.127 0.107 7.776 0.256 0.367 0.303 0.428 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 101 203 212 91 170 132 -1

N.S.

1 1.00 0.97 1.95 2.04 0.88 1.63 1.27 -0.01

time (sec)

N/A 0.082 0.074 3.301 0.260 0.380 0.171 0.446 0.000

Problem 85

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

90 90 87 113 151 75 104 112 -1

N.S.

1 1.00 0.97 1.26 1.68 0.83 1.16 1.24 -0.01

time (sec)

N/A 0.045 0.048 3.205 0.260 0.368 0.117 0.441 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

41 41 59 36 30 57 46 93 266

N.S.

1 1.00 1.44 0.88 0.73 1.39 1.12 2.27 6.49

time (sec)

N/A 0.011 0.089 0.416 0.252 0.418 0.074 0.429 3.998

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 153 431 0 0 0 0 -1

N.S.

1 1.00 1.17 3.29 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.170 0.010 10.849 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 83 101 0 322 0 73 -1

N.S.

1 1.00 1.30 1.58 0.00 5.03 0.00 1.14 -0.02

time (sec)

N/A 0.058 0.081 4.596 0.000 0.389 0.000 0.435 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 136 201 0 460 0 170 -1

N.S.

1 1.00 1.28 1.90 0.00 4.34 0.00 1.60 -0.01

time (sec)

N/A 0.073 0.192 5.017 0.000 0.400 0.000 0.461 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 162 467 0 566 0 340 -1

N.S.

1 1.00 1.05 3.03 0.00 3.68 0.00 2.21 -0.01

time (sec)

N/A 0.119 0.231 4.970 0.000 0.496 0.000 0.437 0.000

Problem 91

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

92 92 110 0 0 0 0 0 -1

N.S.

1 1.00 1.20 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.098 0.131 180.000 0.000 0.000 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

94 94 111 0 0 0 0 0 -1

N.S.

1 1.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.092 0.078 180.000 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 A B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 103 78 1231 1041 527 846 -1

N.S.

1 1.00 0.76 0.58 9.12 7.71 3.90 6.27 -0.01

time (sec)

N/A 0.057 0.089 3.897 0.283 0.361 0.503 1.060 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 115 144 789 655 394 617 -1

N.S.

1 1.00 0.97 1.21 6.63 5.50 3.31 5.18 -0.01

time (sec)

N/A 0.051 0.088 4.029 0.283 0.377 0.396 0.930 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 71 67 443 352 258 419 -1

N.S.

1 1.00 0.73 0.69 4.57 3.63 2.66 4.32 -0.01

time (sec)

N/A 0.042 0.059 4.082 0.280 0.372 0.259 0.768 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 81 107 207 171 148 245 -1

N.S.

1 1.00 1.08 1.43 2.76 2.28 1.97 3.27 -0.01

time (sec)

N/A 0.026 0.123 3.962 0.266 0.393 0.170 0.630 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

46 46 64 41 35 65 51 100 272

N.S.

1 1.00 1.39 0.89 0.76 1.41 1.11 2.17 5.91

time (sec)

N/A 0.016 0.110 1.160 0.257 0.401 0.216 0.423 3.962

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 69 103 0 0 0 0 -1

N.S.

1 1.00 0.85 1.27 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.104 0.042 8.787 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 78 83 72 168 0 0 -1

N.S.

1 1.00 1.39 1.48 1.29 3.00 0.00 0.00 -0.02

time (sec)

N/A 0.038 0.092 4.029 0.510 0.391 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 55 65 110 210 0 0 -1

N.S.

1 1.00 0.83 0.98 1.67 3.18 0.00 0.00 -0.02

time (sec)

N/A 0.036 0.039 8.156 0.491 0.469 0.000 0.000 0.000

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