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Integrals 1 to 91

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 Reduce Mupad

grade

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

verified

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

size

125 125 143 0 0 256 0 0 23 0

N.S.

1 1.00 1.14 0.00 0.00 2.05 0.00 0.00 0.18 0.00

time (sec)

N/A 0.403 0.181 0.000 0.000 0.105 0.000 0.000 0.246 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 77 92 0 0 184 0 0 23 0

N.S.

1 1.00 1.19 0.00 0.00 2.39 0.00 0.00 0.30 0.00

time (sec)

N/A 0.267 0.127 0.000 0.000 0.132 0.000 0.000 0.207 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

26 26 26 23 22 33 39 28 25 42

N.S.

1 1.00 1.00 0.88 0.85 1.27 1.50 1.08 0.96 1.62

time (sec)

N/A 0.201 0.014 0.184 0.031 0.094 0.610 0.120 0.198 2.158

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 36 18 14 18 21 20

N.S.

1 1.00 1.12 1.00 2.25 1.12 0.88 1.12 1.31 1.25

time (sec)

N/A 0.188 2.878 0.026 0.134 0.093 1.605 0.127 0.202 2.416

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 38 18 15 18 29 20

N.S.

1 1.00 1.12 1.00 2.38 1.12 0.94 1.12 1.81 1.25

time (sec)

N/A 0.193 3.567 0.028 0.149 0.092 0.744 0.144 0.228 2.563

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 38 21 15 18 23 20

N.S.

1 1.00 1.12 1.00 2.38 1.31 0.94 1.12 1.44 1.25

time (sec)

N/A 0.189 3.477 0.024 0.133 0.105 1.072 0.168 0.205 2.342

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 38 21 15 18 23 20

N.S.

1 1.00 1.12 1.00 2.38 1.31 0.94 1.12 1.44 1.25

time (sec)

N/A 0.188 3.052 0.026 0.137 0.093 0.696 0.131 0.218 2.340

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 38 18 15 18 25 20

N.S.

1 1.00 1.12 1.00 2.38 1.12 0.94 1.12 1.56 1.25

time (sec)

N/A 0.188 2.965 0.024 0.138 0.071 0.627 0.182 0.271 2.449

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 38 18 15 18 29 20

N.S.

1 1.00 1.12 1.00 2.38 1.12 0.94 1.12 1.81 1.25

time (sec)

N/A 0.189 3.236 0.028 0.144 0.071 1.055 0.238 0.194 2.469

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

217 213 320 0 0 1198 0 0 544 0

N.S.

1 0.98 1.47 0.00 0.00 5.52 0.00 0.00 2.51 0.00

time (sec)

N/A 0.850 1.752 0.000 0.000 0.125 0.000 0.000 0.213 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 118 324 0 0 782 0 0 299 0

N.S.

1 0.99 2.72 0.00 0.00 6.57 0.00 0.00 2.51 0.00

time (sec)

N/A 0.633 1.234 0.000 0.000 0.105 0.000 0.000 0.218 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

44 43 43 41 46 194 0 55 107 77

N.S.

1 0.98 0.98 0.93 1.05 4.41 0.00 1.25 2.43 1.75

time (sec)

N/A 0.597 0.086 0.306 0.035 0.086 0.000 0.123 0.208 0.116

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 86 36 15 20 45 22

N.S.

1 1.00 1.11 1.00 4.78 2.00 0.83 1.11 2.50 1.22

time (sec)

N/A 0.331 20.949 0.083 0.282 0.085 6.971 0.167 0.208 2.553

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 87 36 17 20 195 22

N.S.

1 1.00 1.11 1.00 4.83 2.00 0.94 1.11 10.83 1.22

time (sec)

N/A 0.308 7.507 0.079 0.244 0.071 1.019 0.205 0.204 2.649

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 79 42 17 20 829 22

N.S.

1 1.00 1.11 1.00 4.39 2.33 0.94 1.11 46.06 1.22

time (sec)

N/A 0.260 7.312 0.079 0.249 0.088 1.510 0.662 0.226 2.426

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 72 42 17 20 586 22

N.S.

1 1.00 1.11 1.00 4.00 2.33 0.94 1.11 32.56 1.22

time (sec)

N/A 0.266 6.242 0.075 0.250 0.074 0.954 0.563 0.245 2.320

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 87 36 17 20 50 22

N.S.

1 1.00 1.11 1.00 4.83 2.00 0.94 1.11 2.78 1.22

time (sec)

N/A 0.206 7.061 0.075 0.245 0.085 0.872 0.687 0.211 2.578

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 87 36 17 20 56 22

N.S.

1 1.00 1.11 1.00 4.83 2.00 0.94 1.11 3.11 1.22

time (sec)

N/A 0.227 7.062 0.076 0.297 0.079 1.457 0.950 0.220 2.543

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B F A B B

verified

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

size

90 104 90 62 182 1918 0 146 329 395

N.S.

1 1.16 1.00 0.69 2.02 21.31 0.00 1.62 3.66 4.39

time (sec)

N/A 0.507 0.067 1.036 0.132 0.083 0.000 0.134 0.201 0.106

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

349 350 272 0 0 731 0 0 87 0

N.S.

1 1.00 0.78 0.00 0.00 2.09 0.00 0.00 0.25 0.00

time (sec)

N/A 1.145 0.499 0.000 0.000 0.104 0.000 0.000 0.253 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

241 235 187 0 0 536 0 0 87 0

N.S.

1 0.98 0.78 0.00 0.00 2.22 0.00 0.00 0.36 0.00

time (sec)

N/A 0.768 0.254 0.000 0.000 0.114 0.000 0.000 0.223 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 67 67 90 0 304 0 61 77 171

N.S.

1 1.02 1.02 1.36 0.00 4.61 0.00 0.92 1.17 2.59

time (sec)

N/A 0.370 0.167 0.139 0.000 0.113 0.000 0.121 0.218 0.202

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 58 19 15 20 57 22

N.S.

1 1.00 1.11 1.00 3.22 1.06 0.83 1.11 3.17 1.22

time (sec)

N/A 0.203 1.896 0.049 0.120 0.080 1.091 0.184 0.206 2.327

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 66 23 17 20 100 22

N.S.

1 1.00 1.11 1.00 3.67 1.28 0.94 1.11 5.56 1.22

time (sec)

N/A 0.239 2.633 0.051 0.124 0.077 0.923 0.235 0.231 2.454

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 59 20 15 20 58 22

N.S.

1 1.00 1.11 1.00 3.28 1.11 0.83 1.11 3.22 1.22

time (sec)

N/A 0.319 2.475 0.046 0.132 0.082 0.547 0.137 0.244 2.327

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 59 20 15 20 58 22

N.S.

1 1.00 1.11 1.00 3.28 1.11 0.83 1.11 3.22 1.22

time (sec)

N/A 0.342 2.135 0.046 0.137 0.074 0.447 0.134 0.228 2.395

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 66 23 17 20 100 22

N.S.

1 1.00 1.11 1.00 3.67 1.28 0.94 1.11 5.56 1.22

time (sec)

N/A 0.339 2.116 0.046 0.147 0.078 0.828 0.134 0.240 2.349

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 66 23 17 20 100 22

N.S.

1 1.00 1.11 1.00 3.67 1.28 0.94 1.11 5.56 1.22

time (sec)

N/A 0.338 2.101 0.048 0.133 0.073 1.068 0.134 0.233 2.478

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

994 990 1565 0 0 3918 0 0 38 0

N.S.

1 1.00 1.57 0.00 0.00 3.94 0.00 0.00 0.04 0.00

time (sec)

N/A 3.064 4.191 0.000 0.000 0.160 0.000 0.000 0.217 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

555 546 654 0 0 2473 0 0 38 0

N.S.

1 0.98 1.18 0.00 0.00 4.46 0.00 0.00 0.07 0.00

time (sec)

N/A 1.362 3.331 0.000 0.000 0.137 0.000 0.000 0.217 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 146 220 177 0 1314 0 148 0 316

N.S.

1 1.19 1.79 1.44 0.00 10.68 0.00 1.20 0.00 2.57

time (sec)

N/A 0.774 0.556 0.204 0.000 0.117 0.000 0.133 0.229 2.970

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 249 38 17 20 341 22

N.S.

1 1.00 1.11 1.00 13.83 2.11 0.94 1.11 18.94 1.22

time (sec)

N/A 0.279 35.474 0.062 0.282 0.075 1.843 0.852 0.261 2.977

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 319 44 19 3 2679 22

N.S.

1 1.00 1.11 1.00 17.72 2.44 1.06 0.17 148.83 1.22

time (sec)

N/A 0.285 17.706 0.058 0.281 0.081 1.543 1.289 0.327 3.076

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 312 38 17 20 38 22

N.S.

1 1.00 1.11 1.00 17.33 2.11 0.94 1.11 2.11 1.22

time (sec)

N/A 0.291 14.258 0.057 0.282 0.096 1.002 0.217 0.248 2.658

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 300 38 17 20 38 22

N.S.

1 1.00 1.11 1.00 16.67 2.11 0.94 1.11 2.11 1.22

time (sec)

N/A 0.301 12.923 0.055 0.290 0.087 0.740 0.246 0.223 2.584

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 318 44 19 20 290 22

N.S.

1 1.00 1.11 1.00 17.67 2.44 1.06 1.11 16.11 1.22

time (sec)

N/A 0.329 16.680 0.056 0.283 0.085 1.646 0.228 0.255 2.788

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 320 44 19 20 321 22

N.S.

1 1.00 1.11 1.00 17.78 2.44 1.06 1.11 17.83 1.22

time (sec)

N/A 0.335 16.630 0.058 0.285 0.081 2.048 0.239 0.275 2.846

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

6 6 6 7 12 28 0 12 20 12

N.S.

1 1.00 1.00 1.17 2.00 4.67 0.00 2.00 3.33 2.00

time (sec)

N/A 0.390 0.016 0.082 0.036 0.068 0.000 0.129 0.234 2.261

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

426 426 415 0 0 0 0 0 22 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.05 0.00

time (sec)

N/A 0.955 0.407 0.000 0.000 0.000 0.000 0.000 0.259 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

310 310 311 0 0 0 0 0 22 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.07 0.00

time (sec)

N/A 0.565 0.318 0.000 0.000 0.000 0.000 0.000 0.232 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

194 194 207 0 0 0 0 0 20 0

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 0.10 0.00

time (sec)

N/A 0.402 0.270 0.000 0.000 0.000 0.000 0.000 0.219 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 36 18 15 18 20 20

N.S.

1 1.00 1.11 0.89 2.00 1.00 0.83 1.00 1.11 1.11

time (sec)

N/A 0.185 7.118 0.069 0.321 0.085 2.423 0.130 0.212 2.409

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 42 18 17 18 24 20

N.S.

1 1.00 1.11 0.89 2.33 1.00 0.94 1.00 1.33 1.11

time (sec)

N/A 0.189 6.677 0.068 0.293 0.081 1.565 0.148 0.237 2.486

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

677 683 748 0 0 0 0 0 0 0

N.S.

1 1.01 1.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.133 5.298 0.000 0.000 0.000 0.000 0.000 0.258 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

497 499 582 0 0 0 0 0 1182 0

N.S.

1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 2.38 0.00

time (sec)

N/A 0.993 4.477 0.000 0.000 0.000 0.000 0.000 0.256 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

319 321 466 0 0 0 0 0 718 0

N.S.

1 1.01 1.46 0.00 0.00 0.00 0.00 0.00 2.25 0.00

time (sec)

N/A 1.076 3.614 0.000 0.000 0.000 0.000 0.000 0.250 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 86 36 17 20 43 22

N.S.

1 1.00 1.10 0.90 4.30 1.80 0.85 1.00 2.15 1.10

time (sec)

N/A 0.293 58.725 0.205 0.396 0.082 11.923 0.196 0.202 2.749

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 110 36 19 20 179 22

N.S.

1 1.00 1.10 0.90 5.50 1.80 0.95 1.00 8.95 1.10

time (sec)

N/A 0.285 22.994 0.200 0.433 0.079 2.512 0.299 0.217 2.707

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

961 962 721 0 0 0 0 0 82 0

N.S.

1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 2.163 0.727 0.000 0.000 0.000 0.000 0.000 0.229 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

721 722 547 0 0 0 0 0 82 0

N.S.

1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 0.11 0.00

time (sec)

N/A 1.422 0.513 0.000 0.000 0.000 0.000 0.000 0.239 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

481 482 373 0 0 0 0 0 78 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 1.161 0.419 0.000 0.000 0.000 0.000 0.000 0.241 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 58 19 17 20 56 22

N.S.

1 1.00 1.10 0.90 2.90 0.95 0.85 1.00 2.80 1.10

time (sec)

N/A 0.228 3.484 0.128 0.326 0.081 2.535 0.165 0.239 2.413

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 66 23 19 20 95 22

N.S.

1 1.00 1.10 0.90 3.30 1.15 0.95 1.00 4.75 1.10

time (sec)

N/A 0.259 5.764 0.129 0.404 0.082 2.785 0.255 0.231 2.383

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

2851 2850 2961 0 0 0 0 0 0 0

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 5.522 8.553 0.000 0.000 0.000 0.000 0.000 0.561 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

2123 2122 2173 0 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.326 6.221 0.000 0.000 0.000 0.000 0.000 0.417 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1395 1394 1393 0 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.904 8.295 0.000 0.000 0.000 0.000 0.000 0.355 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 253 38 19 20 325 22

N.S.

1 1.00 1.10 0.90 12.65 1.90 0.95 1.00 16.25 1.10

time (sec)

N/A 0.201 115.054 0.151 0.890 0.112 4.571 1.097 0.246 2.720

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 324 44 20 3 6527 22

N.S.

1 1.00 1.10 0.90 16.20 2.20 1.00 0.15 326.35 1.10

time (sec)

N/A 0.205 57.917 0.150 1.050 0.095 8.071 1.383 0.484 2.839

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

254 254 288 0 0 0 0 0 24 0

N.S.

1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 0.496 0.359 0.000 0.000 0.000 0.000 0.000 0.235 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

140 140 172 0 0 0 0 0 21 0

N.S.

1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.333 0.560 0.000 0.000 0.000 0.000 0.000 0.208 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

26 26 26 23 22 33 37 29 23 43

N.S.

1 1.00 1.00 0.88 0.85 1.27 1.42 1.12 0.88 1.65

time (sec)

N/A 0.252 0.033 0.122 0.028 0.098 0.479 0.113 0.238 2.424

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 16 42 25 19 18 30 20

N.S.

1 1.00 1.10 0.80 2.10 1.25 0.95 0.90 1.50 1.00

time (sec)

N/A 0.277 8.489 0.068 0.309 0.081 1.076 0.126 0.218 2.683

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 16 42 25 19 18 36 20

N.S.

1 1.00 1.10 0.80 2.10 1.25 0.95 0.90 1.80 1.00

time (sec)

N/A 0.246 9.491 0.066 0.318 0.081 5.579 0.144 0.245 2.600

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

407 407 496 0 0 0 0 0 950 0

N.S.

1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 2.33 0.00

time (sec)

N/A 1.336 3.739 0.000 0.000 0.000 0.000 0.000 0.287 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 229 344 0 0 0 0 0 492 0

N.S.

1 1.00 1.50 0.00 0.00 0.00 0.00 0.00 2.15 0.00

time (sec)

N/A 0.965 2.084 0.000 0.000 0.000 0.000 0.000 0.222 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

47 47 47 42 48 194 0 55 99 77

N.S.

1 1.00 1.00 0.89 1.02 4.13 0.00 1.17 2.11 1.64

time (sec)

N/A 0.389 0.131 0.197 0.035 0.122 0.000 0.117 0.211 2.444

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 106 46 20 20 187 22

N.S.

1 1.00 1.09 0.82 4.82 2.09 0.91 0.91 8.50 1.00

time (sec)

N/A 0.201 22.342 0.232 0.442 0.090 2.139 0.194 0.239 2.736

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 18 0 46 20 20 211 22

N.S.

1 1.00 1.09 0.82 0.00 2.09 0.91 0.91 9.59 1.00

time (sec)

N/A 0.204 21.123 0.224 0.000 0.092 5.696 0.279 0.252 2.704

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

601 602 460 0 0 0 0 0 82 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 1.322 0.714 0.000 0.000 0.000 0.000 0.000 0.237 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

361 362 286 0 0 0 0 0 80 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 0.22 0.00

time (sec)

N/A 1.087 0.468 0.000 0.000 0.000 0.000 0.000 0.272 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 69 69 90 0 254 0 61 74 155

N.S.

1 1.01 1.01 1.32 0.00 3.74 0.00 0.90 1.09 2.28

time (sec)

N/A 0.373 0.120 0.184 0.000 0.105 0.000 0.109 0.222 2.881

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 66 27 20 20 95 22

N.S.

1 1.00 1.09 0.82 3.00 1.23 0.91 0.91 4.32 1.00

time (sec)

N/A 0.283 5.848 0.136 0.375 0.103 2.263 0.172 0.224 2.422

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 66 27 20 20 104 22

N.S.

1 1.00 1.09 0.82 3.00 1.23 0.91 0.91 4.73 1.00

time (sec)

N/A 0.337 5.990 0.131 0.439 0.080 5.834 0.273 0.234 2.503

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1755 1754 1769 0 0 0 0 0 0 0

N.S.

1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.990 5.087 0.000 0.000 0.000 0.000 0.000 0.414 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1027 1026 986 0 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.180 3.214 0.000 0.000 0.000 0.000 0.000 0.283 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

127 152 232 177 0 1387 0 148 597 344

N.S.

1 1.20 1.83 1.39 0.00 10.92 0.00 1.17 4.70 2.71

time (sec)

N/A 1.036 0.348 0.204 0.000 0.128 0.000 0.124 0.226 2.814

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 317 48 22 20 1870 22

N.S.

1 1.00 1.09 0.82 14.41 2.18 1.00 0.91 85.00 1.00

time (sec)

N/A 0.322 51.936 0.164 0.992 0.109 5.204 1.145 0.331 2.853

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 324 48 22 3 9455 22

N.S.

1 1.00 1.09 0.82 14.73 2.18 1.00 0.14 429.77 1.00

time (sec)

N/A 0.331 51.441 0.157 1.545 0.107 25.126 1.384 0.593 2.748

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 22 19 22 24 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.20 1.20

time (sec)

N/A 0.465 14.240 0.088 0.204 0.095 48.062 0.541 0.220 2.372

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F B F F B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD TBD

size

44 44 42 155 0 122 0 0 33 110

N.S.

1 1.00 0.95 3.52 0.00 2.77 0.00 0.00 0.75 2.50

time (sec)

N/A 0.388 0.223 1.563 0.000 0.107 0.000 0.000 0.193 2.248

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD TBD

size

135 135 260 368 0 664 0 0 44 0

N.S.

1 1.00 1.93 2.73 0.00 4.92 0.00 0.00 0.33 0.00

time (sec)

N/A 0.446 0.398 1.511 0.000 0.128 0.000 0.000 0.221 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

217 217 0 0 0 1082 0 0 44 0

N.S.

1 1.00 0.00 0.00 0.00 4.99 0.00 0.00 0.20 0.00

time (sec)

N/A 0.463 0.000 0.000 0.000 0.131 0.000 0.000 0.232 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F B F F B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD TBD

size

79 56 57 271 0 646 0 0 115 158

N.S.

1 0.71 0.72 3.43 0.00 8.18 0.00 0.00 1.46 2.00

time (sec)

N/A 0.496 0.654 18.230 0.000 0.096 0.000 0.000 0.208 2.294

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

208 135 501 0 0 2972 0 0 326 0

N.S.

1 0.65 2.41 0.00 0.00 14.29 0.00 0.00 1.57 0.00

time (sec)

N/A 0.523 3.499 0.000 0.000 0.181 0.000 0.000 0.244 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

363 236 0 0 0 5453 0 0 599 0

N.S.

1 0.65 0.00 0.00 0.00 15.02 0.00 0.00 1.65 0.00

time (sec)

N/A 0.711 0.000 0.000 0.000 0.199 0.000 0.000 0.211 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F B F F B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD TBD

size

87 80 80 317 0 511 0 0 85 409

N.S.

1 0.92 0.92 3.64 0.00 5.87 0.00 0.00 0.98 4.70

time (sec)

N/A 0.482 0.429 0.697 0.000 0.118 0.000 0.000 0.209 2.931

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD TBD

size

307 252 859 585 0 1286 0 0 108 0

N.S.

1 0.82 2.80 1.91 0.00 4.19 0.00 0.00 0.35 0.00

time (sec)

N/A 0.910 2.429 0.684 0.000 0.116 0.000 0.000 0.229 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

452 371 0 0 0 2005 0 0 108 0

N.S.

1 0.82 0.00 0.00 0.00 4.44 0.00 0.00 0.24 0.00

time (sec)

N/A 1.776 0.000 0.000 0.000 0.134 0.000 0.000 0.278 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD TBD

size

157 159 233 491 0 3547 0 0 638 0

N.S.

1 1.01 1.48 3.13 0.00 22.59 0.00 0.00 4.06 0.00

time (sec)

N/A 1.409 0.803 8.799 0.000 0.157 0.000 0.000 0.217 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

717 563 469 0 0 9020 0 0 0 0

N.S.

1 0.79 0.65 0.00 0.00 12.58 0.00 0.00 0.00 0.00

time (sec)

N/A 1.538 4.164 0.000 0.000 0.260 0.000 0.000 0.246 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1284 1019 0 0 0 16192 0 0 0 0

N.S.

1 0.79 0.00 0.00 0.00 12.61 0.00 0.00 0.00 0.00

time (sec)

N/A 2.587 0.000 0.000 0.000 0.422 0.000 0.000 0.296 0.000

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