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2.2.1 Integrals 1 to 100

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

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 11 19 19 12 23

N.S.

1 1.00 1.00 1.09 1.00 1.73 1.73 1.09 2.09

time (sec)

N/A 0.159 0.005 0.248 0.191 0.253 0.333 0.300 0.075

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 18 41 0 18 18

N.S.

1 1.00 1.00 1.10 1.80 4.10 0.00 1.80 1.80

time (sec)

N/A 0.170 0.007 0.579 0.186 0.251 0.000 0.280 0.075

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 34 27 65 267 0 76 81

N.S.

1 1.00 1.00 0.79 1.91 7.85 0.00 2.24 2.38

time (sec)

N/A 0.233 0.015 0.670 0.284 0.258 0.000 0.289 0.078

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 32 26 23 90 164 0 31 31

N.S.

1 1.23 1.00 0.88 3.46 6.31 0.00 1.19 1.19

time (sec)

N/A 0.187 0.009 0.627 0.196 0.245 0.000 0.281 2.031

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 55 41 112 812 0 102 189

N.S.

1 1.09 1.00 0.75 2.04 14.76 0.00 1.85 3.44

time (sec)

N/A 0.333 0.017 0.839 0.291 0.243 0.000 0.267 2.016

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 46 41 33 205 344 0 42 42

N.S.

1 1.12 1.00 0.80 5.00 8.39 0.00 1.02 1.02

time (sec)

N/A 0.203 0.015 0.700 0.193 0.256 0.000 0.279 2.024

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 27 19 17 49 116 0 18 30

N.S.

1 1.42 1.00 0.89 2.58 6.11 0.00 0.95 1.58

time (sec)

N/A 0.190 0.007 0.637 0.192 0.255 0.000 0.283 1.999

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 40 35 27 137 280 0 30 30

N.S.

1 1.14 1.00 0.77 3.91 8.00 0.00 0.86 0.86

time (sec)

N/A 0.199 0.008 0.766 0.194 0.270 0.000 0.273 2.072

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 51 217 0 190 0 0 0

N.S.

1 1.00 0.77 3.29 0.00 2.88 0.00 0.00 0.00

time (sec)

N/A 0.326 0.103 1.743 0.000 0.081 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 49 103 0 96 0 0 0

N.S.

1 1.00 0.79 1.66 0.00 1.55 0.00 0.00 0.00

time (sec)

N/A 0.323 0.058 0.642 0.000 0.077 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 40 135 0 24 0 0 0

N.S.

1 1.00 1.00 3.38 0.00 0.60 0.00 0.00 0.00

time (sec)

N/A 0.241 0.042 0.469 0.000 0.080 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 40 135 0 150 0 0 0

N.S.

1 1.00 1.00 3.38 0.00 3.75 0.00 0.00 0.00

time (sec)

N/A 0.240 0.050 0.794 0.000 0.083 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 53 174 0 223 0 0 0

N.S.

1 1.00 0.80 2.64 0.00 3.38 0.00 0.00 0.00

time (sec)

N/A 0.322 0.060 1.229 0.000 0.083 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 59 188 0 370 0 0 0

N.S.

1 1.00 0.89 2.85 0.00 5.61 0.00 0.00 0.00

time (sec)

N/A 0.315 0.085 1.915 0.000 0.081 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

102 104 68 0 0 478 0 0 0

N.S.

1 1.02 0.67 0.00 0.00 4.69 0.00 0.00 0.00

time (sec)

N/A 0.464 0.252 0.000 0.000 0.087 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

74 74 56 0 0 215 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 2.91 0.00 0.00 0.00

time (sec)

N/A 0.345 0.097 0.000 0.000 0.080 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

70 70 52 0 0 107 0 0 0

N.S.

1 1.00 0.74 0.00 0.00 1.53 0.00 0.00 0.00

time (sec)

N/A 0.338 0.063 0.000 0.000 0.083 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

42 42 42 0 0 27 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.64 0.00 0.00 0.00

time (sec)

N/A 0.239 0.041 0.000 0.000 0.072 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 42 244 0 154 0 0 0

N.S.

1 1.00 1.00 5.81 0.00 3.67 0.00 0.00 0.00

time (sec)

N/A 0.240 0.050 0.514 0.000 0.086 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

76 76 63 0 0 231 0 0 0

N.S.

1 1.00 0.83 0.00 0.00 3.04 0.00 0.00 0.00

time (sec)

N/A 0.340 0.092 0.000 0.000 0.087 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

76 76 64 0 0 379 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 4.99 0.00 0.00 0.00

time (sec)

N/A 0.341 0.112 0.000 0.000 0.089 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

104 112 70 0 0 483 0 0 0

N.S.

1 1.08 0.67 0.00 0.00 4.64 0.00 0.00 0.00

time (sec)

N/A 0.454 0.165 0.000 0.000 0.103 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

75 75 60 0 0 0 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 0.076 0.000 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 104 81 230 156 1604 0 124 0

N.S.

1 1.16 0.90 2.56 1.73 17.82 0.00 1.38 0.00

time (sec)

N/A 0.227 0.100 6.479 0.282 0.267 0.000 0.273 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 73 65 208 112 812 0 102 0

N.S.

1 1.12 1.00 3.20 1.72 12.49 0.00 1.57 0.00

time (sec)

N/A 0.205 0.070 6.337 0.280 0.261 0.000 0.296 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 42 46 183 65 267 0 76 0

N.S.

1 1.05 1.15 4.58 1.62 6.68 0.00 1.90 0.00

time (sec)

N/A 0.199 0.046 0.515 0.277 0.274 0.000 0.273 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 29 130 11 19 0 12 0

N.S.

1 1.00 2.64 11.82 1.00 1.73 0.00 1.09 0.00

time (sec)

N/A 0.185 0.022 0.492 0.193 0.247 0.000 0.296 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 26 22 97 26 10 29 23 53

N.S.

1 1.18 1.00 4.41 1.18 0.45 1.32 1.05 2.41

time (sec)

N/A 0.192 0.066 0.464 0.195 0.255 0.255 0.267 0.146

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 57 44 201 54 32 54 48 0

N.S.

1 1.12 0.86 3.94 1.06 0.63 1.06 0.94 0.00

time (sec)

N/A 0.206 0.082 0.456 0.187 0.254 0.407 0.262 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 88 47 305 82 66 80 70 0

N.S.

1 1.16 0.62 4.01 1.08 0.87 1.05 0.92 0.00

time (sec)

N/A 0.213 0.093 0.470 0.187 0.268 1.795 0.280 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 119 57 409 100 108 104 92 0

N.S.

1 1.18 0.56 4.05 0.99 1.07 1.03 0.91 0.00

time (sec)

N/A 0.218 0.148 0.484 0.190 0.259 17.860 0.299 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 78 38 127 72 1082 0 65 0

N.S.

1 1.20 0.58 1.95 1.11 16.65 0.00 1.00 0.00

time (sec)

N/A 0.216 0.042 5.907 0.322 0.280 0.000 0.275 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 53 24 106 39 310 0 48 0

N.S.

1 1.15 0.52 2.30 0.85 6.74 0.00 1.04 0.00

time (sec)

N/A 0.205 0.037 0.137 0.327 0.270 0.000 0.271 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 28 16 72 8 145 0 8 0

N.S.

1 1.12 0.64 2.88 0.32 5.80 0.00 0.32 0.00

time (sec)

N/A 0.188 0.008 0.178 0.318 0.273 0.000 0.268 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 16 13 58 17 79 12 14 33

N.S.

1 1.23 1.00 4.46 1.31 6.08 0.92 1.08 2.54

time (sec)

N/A 0.187 0.032 0.160 0.286 0.251 0.300 0.273 1.959

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 47 25 130 35 277 31 29 0

N.S.

1 1.31 0.69 3.61 0.97 7.69 0.86 0.81 0.00

time (sec)

N/A 0.200 0.021 0.134 0.286 0.256 0.455 0.297 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 77 33 196 53 580 49 41 0

N.S.

1 1.40 0.60 3.56 0.96 10.55 0.89 0.75 0.00

time (sec)

N/A 0.219 0.034 0.127 0.290 0.260 1.533 0.284 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 107 39 262 71 970 66 53 0

N.S.

1 1.45 0.53 3.54 0.96 13.11 0.89 0.72 0.00

time (sec)

N/A 0.237 0.046 0.136 0.290 0.284 13.430 0.268 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

121 107 63 0 0 1382 0 0 0

N.S.

1 0.88 0.52 0.00 0.00 11.42 0.00 0.00 0.00

time (sec)

N/A 0.624 0.135 0.000 0.000 0.113 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 75 47 0 0 391 0 0 0

N.S.

1 1.09 0.68 0.00 0.00 5.67 0.00 0.00 0.00

time (sec)

N/A 0.433 0.060 0.000 0.000 0.090 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

46 53 36 0 0 60 0 0 0

N.S.

1 1.15 0.78 0.00 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.354 0.042 0.000 0.000 0.076 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 57 38 0 0 126 0 0 0

N.S.

1 1.19 0.79 0.00 0.00 2.62 0.00 0.00 0.00

time (sec)

N/A 0.356 0.066 0.000 0.000 0.081 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 77 47 0 0 407 0 0 0

N.S.

1 1.00 0.61 0.00 0.00 5.29 0.00 0.00 0.00

time (sec)

N/A 0.442 0.123 0.000 0.000 0.085 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

121 111 63 0 0 718 0 0 0

N.S.

1 0.92 0.52 0.00 0.00 5.93 0.00 0.00 0.00

time (sec)

N/A 0.613 0.122 0.000 0.000 0.105 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 84 54 72 620 2804 0 51 498

N.S.

1 0.52 0.33 0.44 3.80 17.20 0.00 0.31 3.06

time (sec)

N/A 0.281 0.231 137.222 0.294 0.373 0.000 0.276 2.035

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 68 42 60 322 1475 0 39 356

N.S.

1 0.58 0.36 0.51 2.75 12.61 0.00 0.33 3.04

time (sec)

N/A 0.275 0.126 144.832 0.279 0.280 0.000 0.292 0.101

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 46 30 46 120 516 0 27 46

N.S.

1 0.75 0.49 0.75 1.97 8.46 0.00 0.44 0.75

time (sec)

N/A 0.262 0.069 0.169 0.290 0.258 0.000 0.278 1.961

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 29 13 81 0 13 71

N.S.

1 1.00 1.00 1.93 0.87 5.40 0.00 0.87 4.73

time (sec)

N/A 0.240 0.009 0.188 0.281 0.240 0.000 0.266 0.052

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 29 23 89 30 253 0 28 0

N.S.

1 0.81 0.64 2.47 0.83 7.03 0.00 0.78 0.00

time (sec)

N/A 0.231 0.049 0.165 0.285 0.259 0.000 0.289 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 62 38 230 65 1141 0 52 0

N.S.

1 0.72 0.44 2.67 0.76 13.27 0.00 0.60 0.00

time (sec)

N/A 0.352 0.067 0.175 0.292 0.261 0.000 0.263 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 92 55 362 103 2600 0 76 0

N.S.

1 0.70 0.42 2.74 0.78 19.70 0.00 0.58 0.00

time (sec)

N/A 0.494 0.107 0.155 0.284 0.321 0.000 0.275 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 46 28 60 54 36 0 42 59

N.S.

1 1.05 0.64 1.36 1.23 0.82 0.00 0.95 1.34

time (sec)

N/A 0.480 0.265 8.395 0.200 0.244 0.000 0.298 2.007

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 31 23 54 46 30 0 37 53

N.S.

1 1.35 1.00 2.35 2.00 1.30 0.00 1.61 2.30

time (sec)

N/A 0.414 0.055 2.526 0.197 0.245 0.000 0.280 1.985

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 26 16 42 42 14 0 28 41

N.S.

1 0.96 0.59 1.56 1.56 0.52 0.00 1.04 1.52

time (sec)

N/A 0.393 0.046 0.825 0.200 0.253 0.000 0.281 1.971

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 19 16 23 35 50 0 32 15

N.S.

1 1.12 0.94 1.35 2.06 2.94 0.00 1.88 0.88

time (sec)

N/A 0.319 0.022 0.249 0.198 0.246 0.000 0.285 0.065

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 42 44 20 48 103 0 52 51

N.S.

1 1.27 1.33 0.61 1.45 3.12 0.00 1.58 1.55

time (sec)

N/A 0.467 0.056 0.362 0.199 0.240 0.000 0.281 2.121

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 25 23 90 71 0 31 91

N.S.

1 1.00 1.09 1.00 3.91 3.09 0.00 1.35 3.96

time (sec)

N/A 0.438 0.293 0.330 0.201 0.255 0.000 0.292 2.076

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 59 59 38 99 630 0 90 121

N.S.

1 1.28 1.28 0.83 2.15 13.70 0.00 1.96 2.63

time (sec)

N/A 0.603 0.185 0.477 0.205 0.249 0.000 0.290 1.993

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 40 39 39 292 219 0 59 236

N.S.

1 1.18 1.15 1.15 8.59 6.44 0.00 1.74 6.94

time (sec)

N/A 0.467 0.230 0.892 0.194 0.233 0.000 0.284 1.994

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 157 219 305 0 1812 0 197 275

N.S.

1 1.19 1.66 2.31 0.00 13.73 0.00 1.49 2.08

time (sec)

N/A 0.837 0.788 48.288 0.000 0.274 0.000 0.274 2.604

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 66 136 128 490 0 87 123

N.S.

1 1.00 1.08 2.23 2.10 8.03 0.00 1.43 2.02

time (sec)

N/A 0.394 0.215 10.408 0.198 0.259 0.000 0.279 2.222

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 97 76 130 0 536 0 100 173

N.S.

1 1.18 0.93 1.59 0.00 6.54 0.00 1.22 2.11

time (sec)

N/A 0.557 0.179 2.280 0.000 0.281 0.000 0.269 2.221

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 19 19 31 46 78 0 34 20

N.S.

1 0.95 0.95 1.55 2.30 3.90 0.00 1.70 1.00

time (sec)

N/A 0.310 0.012 0.495 0.192 0.250 0.000 0.275 1.970

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 59 50 48 59 58 0 65 148

N.S.

1 1.11 0.94 0.91 1.11 1.09 0.00 1.23 2.79

time (sec)

N/A 0.349 0.124 0.305 0.191 0.260 0.000 0.265 2.328

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 77 75 77 0 452 0 64 151

N.S.

1 1.17 1.14 1.17 0.00 6.85 0.00 0.97 2.29

time (sec)

N/A 0.425 0.340 0.393 0.000 0.259 0.000 0.261 2.192

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 128 93 82 148 828 0 174 255

N.S.

1 1.51 1.09 0.96 1.74 9.74 0.00 2.05 3.00

time (sec)

N/A 0.480 0.491 0.598 0.212 0.282 0.000 0.290 2.464

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 135 156 127 0 2340 0 149 295

N.S.

1 1.22 1.41 1.14 0.00 21.08 0.00 1.34 2.66

time (sec)

N/A 0.659 0.748 1.099 0.000 0.269 0.000 0.299 2.335

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 76 63 43 80 139 0 86 88

N.S.

1 1.13 0.94 0.64 1.19 2.07 0.00 1.28 1.31

time (sec)

N/A 0.497 0.426 0.328 0.193 0.244 0.000 0.265 2.097

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 61 53 35 66 100 0 70 70

N.S.

1 1.13 0.98 0.65 1.22 1.85 0.00 1.30 1.30

time (sec)

N/A 0.426 0.069 0.262 0.186 0.249 0.000 0.276 2.015

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 42 45 30 56 70 0 51 52

N.S.

1 1.02 1.10 0.73 1.37 1.71 0.00 1.24 1.27

time (sec)

N/A 0.382 0.045 0.230 0.184 0.240 0.000 0.265 1.991

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 27 32 20 41 47 0 35 34

N.S.

1 1.04 1.23 0.77 1.58 1.81 0.00 1.35 1.31

time (sec)

N/A 0.326 0.262 0.185 0.191 0.241 0.000 0.268 1.997

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 10 9 12 14 0 11 11

N.S.

1 1.00 0.91 0.82 1.09 1.27 0.00 1.00 1.00

time (sec)

N/A 0.196 0.012 0.073 0.188 0.284 0.000 0.271 1.926

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 23 19 23 29 0 20 31

N.S.

1 1.00 1.15 0.95 1.15 1.45 0.00 1.00 1.55

time (sec)

N/A 0.330 0.042 0.125 0.275 0.271 0.000 0.280 2.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 30 33 45 127 0 36 58

N.S.

1 1.00 1.15 1.27 1.73 4.88 0.00 1.38 2.23

time (sec)

N/A 0.423 0.095 0.267 0.273 0.255 0.000 0.279 2.042

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 47 41 46 73 325 0 48 73

N.S.

1 1.04 0.91 1.02 1.62 7.22 0.00 1.07 1.62

time (sec)

N/A 0.478 0.122 0.311 0.303 0.264 0.000 0.271 2.036

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 58 23 33 48 0 29 24

N.S.

1 1.00 2.00 0.79 1.14 1.66 0.00 1.00 0.83

time (sec)

N/A 0.194 0.374 0.184 0.183 0.270 0.000 0.272 1.949

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 59 25 35 50 0 29 24

N.S.

1 1.00 1.97 0.83 1.17 1.67 0.00 0.97 0.80

time (sec)

N/A 0.195 0.365 0.177 0.194 0.276 0.000 0.274 1.964

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

98 102 99 0 0 924 0 151 0

N.S.

1 1.04 1.01 0.00 0.00 9.43 0.00 1.54 0.00

time (sec)

N/A 0.556 0.459 0.000 0.000 0.293 0.000 0.404 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 75 0 0 697 0 118 0

N.S.

1 1.00 1.14 0.00 0.00 10.56 0.00 1.79 0.00

time (sec)

N/A 0.303 0.192 0.000 0.000 0.268 0.000 0.384 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

37 37 60 0 0 637 0 83 0

N.S.

1 1.00 1.62 0.00 0.00 17.22 0.00 2.24 0.00

time (sec)

N/A 0.197 0.125 0.000 0.000 0.270 0.000 0.334 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 118 0 0 868 0 177 0

N.S.

1 1.00 1.39 0.00 0.00 10.21 0.00 2.08 0.00

time (sec)

N/A 0.405 1.399 0.000 0.000 0.282 0.000 0.648 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

114 120 177 0 0 1190 0 236 0

N.S.

1 1.05 1.55 0.00 0.00 10.44 0.00 2.07 0.00

time (sec)

N/A 0.577 4.942 0.000 0.000 0.296 0.000 0.345 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

38 38 70 0 0 642 0 101 0

N.S.

1 1.00 1.84 0.00 0.00 16.89 0.00 2.66 0.00

time (sec)

N/A 0.201 1.411 0.000 0.000 0.284 0.000 0.338 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

87 87 118 0 0 871 0 0 0

N.S.

1 1.00 1.36 0.00 0.00 10.01 0.00 0.00 0.00

time (sec)

N/A 0.433 2.627 0.000 0.000 0.286 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

19 19 39 0 0 233 0 52 0

N.S.

1 1.00 2.05 0.00 0.00 12.26 0.00 2.74 0.00

time (sec)

N/A 0.194 0.045 0.000 0.000 0.247 0.000 0.297 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 51 0 0 235 0 69 0

N.S.

1 1.00 2.43 0.00 0.00 11.19 0.00 3.29 0.00

time (sec)

N/A 0.199 0.785 0.000 0.000 0.279 0.000 0.281 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 114 78 92 211 1028 0 141 233

N.S.

1 1.07 0.73 0.86 1.97 9.61 0.00 1.32 2.18

time (sec)

N/A 0.440 0.269 1.414 0.281 0.267 0.000 0.272 2.105

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 74 55 66 114 521 0 92 165

N.S.

1 1.01 0.75 0.90 1.56 7.14 0.00 1.26 2.26

time (sec)

N/A 0.259 0.142 0.906 0.280 0.275 0.000 0.275 2.063

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 32 34 41 157 0 43 70

N.S.

1 1.00 0.97 1.03 1.24 4.76 0.00 1.30 2.12

time (sec)

N/A 0.299 0.073 0.665 0.197 0.276 0.000 0.284 0.098

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 17 16 26 24 17 38

N.S.

1 1.00 1.00 1.06 1.00 1.62 1.50 1.06 2.38

time (sec)

N/A 0.144 0.005 0.124 0.197 0.253 0.362 0.267 0.059

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 60 83 0 270 0 56 131

N.S.

1 1.00 1.02 1.41 0.00 4.58 0.00 0.95 2.22

time (sec)

N/A 0.279 0.200 0.208 0.000 0.290 0.000 0.277 0.373

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 134 203 164 0 1207 0 134 296

N.S.

1 1.23 1.86 1.50 0.00 11.07 0.00 1.23 2.72

time (sec)

N/A 0.640 0.519 0.279 0.000 0.289 0.000 0.303 2.546

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 217 205 251 0 4125 0 261 0

N.S.

1 1.25 1.18 1.45 0.00 23.84 0.00 1.51 0.00

time (sec)

N/A 1.050 1.141 0.400 0.000 0.323 0.000 0.297 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 106 168 0 0 0 0 0 0

N.S.

1 1.00 1.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.245 5.392 0.000 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 171 126 264 0 2402 0 182 251

N.S.

1 1.17 0.86 1.81 0.00 16.45 0.00 1.25 1.72

time (sec)

N/A 1.472 0.353 0.567 0.000 0.288 0.000 0.280 2.446

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 129 99 203 0 1562 0 133 209

N.S.

1 1.15 0.88 1.81 0.00 13.95 0.00 1.19 1.87

time (sec)

N/A 1.031 0.215 0.375 0.000 0.281 0.000 0.272 2.329

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 96 78 153 0 860 0 92 167

N.S.

1 1.13 0.92 1.80 0.00 10.12 0.00 1.08 1.96

time (sec)

N/A 0.731 0.161 0.269 0.000 0.277 0.000 0.278 2.189

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 65 57 94 0 430 0 62 139

N.S.

1 1.05 0.92 1.52 0.00 6.94 0.00 1.00 2.24

time (sec)

N/A 0.373 0.216 0.225 0.000 0.262 0.000 0.297 2.160

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 41 36 0 165 0 32 43

N.S.

1 1.00 0.98 0.86 0.00 3.93 0.00 0.76 1.02

time (sec)

N/A 0.273 0.036 0.087 0.000 0.251 0.000 0.264 1.983

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 51 0 219 0 45 286

N.S.

1 1.00 1.00 0.94 0.00 4.06 0.00 0.83 5.30

time (sec)

N/A 0.418 0.105 0.228 0.000 0.297 0.000 0.274 4.437

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