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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 F A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 56 36 32 0 43 0 45 0

N.S.

1 1.06 0.68 0.60 0.00 0.81 0.00 0.85 0.00

time (sec)

N/A 0.333 0.036 1.010 0.000 0.272 0.000 0.329 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 26 24 0 29 0 24 0

N.S.

1 1.00 0.76 0.71 0.00 0.85 0.00 0.71 0.00

time (sec)

N/A 0.267 0.039 0.476 0.000 0.269 0.000 0.336 0.000

Problem 3

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

14 14 14 16 13 19 17 17 40

N.S.

1 1.00 1.00 1.14 0.93 1.36 1.21 1.21 2.86

time (sec)

N/A 0.194 0.013 0.493 0.399 0.260 0.113 0.339 13.751

Problem 4

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

17 17 30 49 26 70 0 15 0

N.S.

1 1.00 1.76 2.88 1.53 4.12 0.00 0.88 0.00

time (sec)

N/A 0.199 0.023 0.722 0.456 0.272 0.000 0.362 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 55 70 314 58 0 81 0

N.S.

1 1.00 1.31 1.67 7.48 1.38 0.00 1.93 0.00

time (sec)

N/A 0.280 0.057 0.841 0.463 0.253 0.000 0.359 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 69 77 89 931 78 0 118 0

N.S.

1 1.13 1.26 1.46 15.26 1.28 0.00 1.93 0.00

time (sec)

N/A 0.368 0.147 0.832 0.630 0.277 0.000 0.371 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 101 65 192 0 110 0 0 0

N.S.

1 0.82 0.53 1.56 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.461 0.127 4.465 0.000 0.105 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 65 54 302 0 80 0 0 0

N.S.

1 0.89 0.74 4.14 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.330 0.078 1.448 0.000 0.095 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 47 41 163 0 69 0 0 0

N.S.

1 0.94 0.82 3.26 0.00 1.38 0.00 0.00 0.00

time (sec)

N/A 0.263 0.040 1.411 0.000 0.091 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 43 37 274 0 102 0 0 0

N.S.

1 0.90 0.77 5.71 0.00 2.12 0.00 0.00 0.00

time (sec)

N/A 0.266 0.036 1.169 0.000 0.100 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 67 48 239 0 139 0 0 0

N.S.

1 0.87 0.62 3.10 0.00 1.81 0.00 0.00 0.00

time (sec)

N/A 0.335 0.068 1.472 0.000 0.085 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 97 60 314 0 209 0 0 0

N.S.

1 0.79 0.49 2.55 0.00 1.70 0.00 0.00 0.00

time (sec)

N/A 0.460 0.162 1.368 0.000 0.099 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 92 53 61 85 82 0 57 0

N.S.

1 0.70 0.40 0.46 0.64 0.62 0.00 0.43 0.00

time (sec)

N/A 0.469 0.127 10.176 0.311 0.279 0.000 0.319 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 60 38 43 55 56 0 27 0

N.S.

1 0.77 0.49 0.55 0.71 0.72 0.00 0.35 0.00

time (sec)

N/A 0.327 0.080 0.577 0.320 0.269 0.000 0.308 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 29 25 24 22 36 0 15 0

N.S.

1 0.81 0.69 0.67 0.61 1.00 0.00 0.42 0.00

time (sec)

N/A 0.213 0.024 0.605 0.317 0.272 0.000 0.411 0.000

Problem 16

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

16 16 16 18 9 36 0 9 7

N.S.

1 1.00 1.00 1.12 0.56 2.25 0.00 0.56 0.44

time (sec)

N/A 0.217 0.018 0.559 0.296 0.272 0.000 0.413 13.215

Problem 17

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

68 38 34 37 23 74 0 23 44

N.S.

1 0.56 0.50 0.54 0.34 1.09 0.00 0.34 0.65

time (sec)

N/A 0.242 0.036 0.528 0.299 0.261 0.000 0.420 13.792

Problem 18

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

118 54 47 49 35 104 0 35 117

N.S.

1 0.46 0.40 0.42 0.30 0.88 0.00 0.30 0.99

time (sec)

N/A 0.254 0.054 0.641 0.324 0.279 0.000 0.405 15.910

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 89 74 0 0 0 0 0 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.279 0.122 0.000 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 83 72 0 0 0 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.270 0.082 0.000 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

74 88 68 0 0 0 0 0 0

N.S.

1 1.19 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.262 0.049 0.000 0.000 0.000 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

80 80 72 0 0 0 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.269 0.052 0.000 0.000 0.000 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(-2) F F F(-1)

verified

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

size

89 89 71 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 0.276 0.075 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 F F F(-2) F F F(-1)

verified

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

size

89 89 73 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.276 0.075 0.000 0.000 0.000 0.000 0.000 0.000

Problem 25

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

77 77 71 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.272 0.043 0.000 0.000 0.000 0.000 0.000 0.000

Problem 26

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

77 77 61 0 0 0 0 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.261 0.050 0.000 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 F F F F F F(-1)

verified

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

size

75 75 67 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.270 0.054 0.000 0.000 0.000 0.000 0.000 0.000

Problem 28

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

77 77 65 0 0 0 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.273 0.061 0.000 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 29 0 16 58 384 36

N.S.

1 1.00 1.00 1.16 0.00 0.64 2.32 15.36 1.44

time (sec)

N/A 0.232 0.035 1.102 0.000 0.264 0.356 0.738 14.438

Problem 30

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

79 79 73 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.280 0.036 0.000 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 B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 17 12 15 17 11

N.S.

1 1.00 1.00 0.81 1.06 0.75 0.94 1.06 0.69

time (sec)

N/A 0.144 0.007 0.194 0.287 0.274 0.020 0.326 13.574

Problem 32

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

33 33 26 20 40 28 110 25 33

N.S.

1 1.00 0.79 0.61 1.21 0.85 3.33 0.76 1.00

time (sec)

N/A 0.255 0.002 0.651 0.279 0.278 0.129 0.302 13.533

Problem 33

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

46 48 34 26 69 37 233 34 42

N.S.

1 1.04 0.74 0.57 1.50 0.80 5.07 0.74 0.91

time (sec)

N/A 0.309 0.002 1.046 0.298 0.272 0.259 0.307 14.012

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 63 42 34 104 46 376 43 51

N.S.

1 1.07 0.71 0.58 1.76 0.78 6.37 0.73 0.86

time (sec)

N/A 0.373 0.006 1.359 0.286 0.271 0.489 0.310 13.919

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 45 58 45 50 46 314 149 54

N.S.

1 0.73 0.94 0.73 0.81 0.74 5.06 2.40 0.87

time (sec)

N/A 0.307 0.139 0.719 0.264 0.269 10.455 0.309 0.094

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 37 43 35 40 36 143 105 38

N.S.

1 0.80 0.93 0.76 0.87 0.78 3.11 2.28 0.83

time (sec)

N/A 0.304 0.081 0.506 0.275 0.258 4.102 0.302 0.061

Problem 37

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

27 25 25 23 27 25 36 29 25

N.S.

1 0.93 0.93 0.85 1.00 0.93 1.33 1.07 0.93

time (sec)

N/A 0.287 0.055 0.400 0.283 0.264 1.515 0.308 13.946

Problem 38

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

13 13 13 16 15 15 34 15 15

N.S.

1 1.00 1.00 1.23 1.15 1.15 2.62 1.15 1.15

time (sec)

N/A 0.243 0.010 0.526 0.290 0.249 0.592 0.300 13.810

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 23 46 39 46 55 0 62 31

N.S.

1 0.79 1.59 1.34 1.59 1.90 0.00 2.14 1.07

time (sec)

N/A 0.267 0.090 0.550 0.291 0.252 0.000 0.305 0.085

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 54 146 63 70 98 0 149 55

N.S.

1 0.93 2.52 1.09 1.21 1.69 0.00 2.57 0.95

time (sec)

N/A 0.303 0.265 0.639 0.315 0.266 0.000 0.329 14.181

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 85 132 87 90 135 0 181 74

N.S.

1 1.04 1.61 1.06 1.10 1.65 0.00 2.21 0.90

time (sec)

N/A 0.310 2.744 0.815 0.303 0.274 0.000 0.333 0.106

Problem 42

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

73 81 44 57 72 56 1161 63 68

N.S.

1 1.11 0.60 0.78 0.99 0.77 15.90 0.86 0.93

time (sec)

N/A 0.309 0.207 0.627 0.392 0.276 6.573 0.301 14.065

Problem 43

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

49 52 34 44 49 45 502 50 45

N.S.

1 1.06 0.69 0.90 1.00 0.92 10.24 1.02 0.92

time (sec)

N/A 0.299 0.152 0.463 0.383 0.273 2.564 0.305 13.719

Problem 44

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

20 20 27 24 26 34 100 26 20

N.S.

1 1.00 1.35 1.20 1.30 1.70 5.00 1.30 1.00

time (sec)

N/A 0.322 0.010 0.398 0.363 0.256 0.924 0.304 13.749

Problem 45

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

13 13 13 14 13 21 41 13 13

N.S.

1 1.00 1.00 1.08 1.00 1.62 3.15 1.00 1.00

time (sec)

N/A 0.224 0.005 0.336 0.295 0.238 0.467 0.296 13.109

Problem 46

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

28 22 16 25 28 36 0 19 17

N.S.

1 0.79 0.57 0.89 1.00 1.29 0.00 0.68 0.61

time (sec)

N/A 0.288 0.044 0.515 0.266 0.262 0.000 0.318 14.112

Problem 47

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

46 34 49 35 42 56 0 42 38

N.S.

1 0.74 1.07 0.76 0.91 1.22 0.00 0.91 0.83

time (sec)

N/A 0.298 0.111 0.596 0.341 0.259 0.000 0.335 13.850

Problem 48

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

62 44 70 45 52 77 0 52 50

N.S.

1 0.71 1.13 0.73 0.84 1.24 0.00 0.84 0.81

time (sec)

N/A 0.310 0.096 0.879 0.282 0.245 0.000 0.312 13.875

Problem 49

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

65 49 59 47 52 46 156 57 48

N.S.

1 0.75 0.91 0.72 0.80 0.71 2.40 0.88 0.74

time (sec)

N/A 0.311 0.110 0.722 0.266 0.254 24.600 0.337 13.236

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 35 42 37 41 38 156 106 36

N.S.

1 0.74 0.89 0.79 0.87 0.81 3.32 2.26 0.77

time (sec)

N/A 0.286 0.067 0.634 0.283 0.256 10.897 0.339 0.056

Problem 51

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

33 28 31 29 28 28 156 28 26

N.S.

1 0.85 0.94 0.88 0.85 0.85 4.73 0.85 0.79

time (sec)

N/A 0.283 0.068 0.543 0.284 0.260 3.916 0.326 0.053

Problem 52

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

18 18 18 17 16 16 156 16 16

N.S.

1 1.00 1.00 0.94 0.89 0.89 8.67 0.89 0.89

time (sec)

N/A 0.258 0.009 0.549 0.277 0.263 1.920 0.314 12.979

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 35 61 49 59 70 0 107 41

N.S.

1 0.74 1.30 1.04 1.26 1.49 0.00 2.28 0.87

time (sec)

N/A 0.287 0.075 0.756 0.250 0.256 0.000 0.296 0.111

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 66 208 75 86 118 0 175 70

N.S.

1 0.85 2.67 0.96 1.10 1.51 0.00 2.24 0.90

time (sec)

N/A 0.313 0.380 0.889 0.230 0.253 0.000 0.330 12.938

Problem 55

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

69 64 46 56 64 59 1275 68 66

N.S.

1 0.93 0.67 0.81 0.93 0.86 18.48 0.99 0.96

time (sec)

N/A 0.314 0.206 0.743 0.357 0.275 16.725 0.293 13.086

Problem 56

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

38 32 42 34 37 49 551 44 31

N.S.

1 0.84 1.11 0.89 0.97 1.29 14.50 1.16 0.82

time (sec)

N/A 0.318 0.011 0.668 0.355 0.273 7.023 0.304 13.098

Problem 57

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

18 18 18 17 16 32 94 16 16

N.S.

1 1.00 1.00 0.94 0.89 1.78 5.22 0.89 0.89

time (sec)

N/A 0.272 0.012 0.516 0.258 0.267 2.790 0.306 12.596

Problem 58

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

32 29 26 25 25 34 238 25 24

N.S.

1 0.91 0.81 0.78 0.78 1.06 7.44 0.78 0.75

time (sec)

N/A 0.245 0.029 0.454 0.309 0.246 1.187 0.293 12.694

Problem 59

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

47 36 50 37 40 46 0 48 36

N.S.

1 0.77 1.06 0.79 0.85 0.98 0.00 1.02 0.77

time (sec)

N/A 0.294 0.101 0.698 0.306 0.244 0.000 0.309 12.699

Problem 60

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

65 48 46 47 52 72 0 34 48

N.S.

1 0.74 0.71 0.72 0.80 1.11 0.00 0.52 0.74

time (sec)

N/A 0.308 0.041 0.939 0.314 0.266 0.000 0.306 13.135

Problem 61

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

29 26 23 20 22 25 362 22 21

N.S.

1 0.90 0.79 0.69 0.76 0.86 12.48 0.76 0.72

time (sec)

N/A 0.239 0.005 0.579 0.311 0.264 1.810 0.285 12.891

Problem 62

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

37 32 27 24 28 31 675 28 33

N.S.

1 0.86 0.73 0.65 0.76 0.84 18.24 0.76 0.89

time (sec)

N/A 0.244 0.006 0.926 0.497 0.272 5.396 0.288 12.853

Problem 63

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

51 42 39 32 34 37 1083 34 43

N.S.

1 0.82 0.76 0.63 0.67 0.73 21.24 0.67 0.84

time (sec)

N/A 0.250 0.007 1.460 0.313 0.248 14.843 0.280 13.138

Problem 64

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

51 46 77 54 43 43 107 67 44

N.S.

1 0.90 1.51 1.06 0.84 0.84 2.10 1.31 0.86

time (sec)

N/A 0.233 0.075 1.370 0.383 0.247 0.221 0.308 13.143

Problem 65

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

31 29 54 34 34 27 58 40 27

N.S.

1 0.94 1.74 1.10 1.10 0.87 1.87 1.29 0.87

time (sec)

N/A 0.205 0.046 0.810 0.303 0.267 0.111 0.295 0.049

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 63 28 38 42 0 58 23

N.S.

1 1.00 2.42 1.08 1.46 1.62 0.00 2.23 0.88

time (sec)

N/A 0.241 0.049 0.524 0.293 0.267 0.000 0.294 12.974

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 118 52 58 95 0 121 42

N.S.

1 1.00 2.95 1.30 1.45 2.38 0.00 3.02 1.05

time (sec)

N/A 0.262 0.070 0.883 0.285 0.251 0.000 0.301 0.098

Problem 68

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

89 85 70 62 104 69 258 68 92

N.S.

1 0.96 0.79 0.70 1.17 0.78 2.90 0.76 1.03

time (sec)

N/A 0.344 0.124 1.265 0.362 0.256 0.329 0.298 14.219

Problem 69

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

61 59 45 44 74 50 158 43 68

N.S.

1 0.97 0.74 0.72 1.21 0.82 2.59 0.70 1.11

time (sec)

N/A 0.270 0.109 0.959 0.361 0.261 0.159 0.279 13.832

Problem 70

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

30 30 33 24 29 29 51 25 27

N.S.

1 1.00 1.10 0.80 0.97 0.97 1.70 0.83 0.90

time (sec)

N/A 0.155 0.042 0.387 0.297 0.267 0.081 0.279 13.514

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 22 23 32 0 39 16

N.S.

1 1.00 1.00 1.38 1.44 2.00 0.00 2.44 1.00

time (sec)

N/A 0.184 0.034 0.881 0.401 0.266 0.000 0.412 13.617

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

43 43 49 35 28 54 0 37 29

N.S.

1 1.00 1.14 0.81 0.65 1.26 0.00 0.86 0.67

time (sec)

N/A 0.272 0.065 1.090 0.280 0.250 0.000 0.405 13.875

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

65 56 95 56 45 81 0 61 49

N.S.

1 0.86 1.46 0.86 0.69 1.25 0.00 0.94 0.75

time (sec)

N/A 0.290 0.068 1.111 0.290 0.255 0.000 0.432 14.089

Problem 74

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

19 19 19 16 17 16 15 17 15

N.S.

1 1.00 1.00 0.84 0.89 0.84 0.79 0.89 0.79

time (sec)

N/A 0.146 0.021 0.219 0.248 0.257 0.021 0.376 13.518

Problem 75

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

50 50 43 41 39 47 110 42 44

N.S.

1 1.00 0.86 0.82 0.78 0.94 2.20 0.84 0.88

time (sec)

N/A 0.193 0.046 0.671 0.242 0.271 0.132 0.379 13.890

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 92 80 70 71 81 246 76 118

N.S.

1 1.06 0.92 0.80 0.82 0.93 2.83 0.87 1.36

time (sec)

N/A 0.319 0.070 1.008 0.236 0.269 0.274 0.384 13.981

Problem 77

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

140 150 113 110 108 123 410 118 147

N.S.

1 1.07 0.81 0.79 0.77 0.88 2.93 0.84 1.05

time (sec)

N/A 0.496 0.110 1.439 0.272 0.258 0.496 0.403 13.570

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 99 180 110 116 272 0 332 112

N.S.

1 0.93 1.70 1.04 1.09 2.57 0.00 3.13 1.06

time (sec)

N/A 0.296 1.273 1.322 0.373 0.297 0.000 0.429 0.172

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 73 150 70 88 218 0 173 72

N.S.

1 0.95 1.95 0.91 1.14 2.83 0.00 2.25 0.94

time (sec)

N/A 0.273 0.483 0.970 0.389 0.293 0.000 0.418 13.421

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 51 125 45 67 165 0 57 44

N.S.

1 0.98 2.40 0.87 1.29 3.17 0.00 1.10 0.85

time (sec)

N/A 0.238 0.265 0.556 0.319 0.284 0.000 0.390 0.099

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 97 29 50 117 367693 37 29

N.S.

1 1.00 2.62 0.78 1.35 3.16 9937.65 1.00 0.78

time (sec)

N/A 0.214 0.864 0.391 0.396 0.280 76.845 0.383 0.095

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 143 62 83 161 0 100 457

N.S.

1 0.98 2.60 1.13 1.51 2.93 0.00 1.82 8.31

time (sec)

N/A 0.241 0.535 0.628 0.406 0.281 0.000 0.398 14.661

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 94 224 107 120 327 0 196 592

N.S.

1 1.11 2.64 1.26 1.41 3.85 0.00 2.31 6.96

time (sec)

N/A 0.286 1.815 0.848 0.454 0.284 0.000 0.413 13.808

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 146 657 168 181 612 0 334 1105

N.S.

1 1.17 5.26 1.34 1.45 4.90 0.00 2.67 8.84

time (sec)

N/A 0.344 6.632 0.993 0.334 0.339 0.000 0.440 13.558

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 202 133 168 192 453 0 233 2244

N.S.

1 1.24 0.82 1.03 1.18 2.78 0.00 1.43 13.77

time (sec)

N/A 0.476 1.175 1.628 0.329 0.327 0.000 0.448 15.307

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 144 95 118 128 372 0 157 1892

N.S.

1 1.23 0.81 1.01 1.09 3.18 0.00 1.34 16.17

time (sec)

N/A 0.386 0.512 1.049 0.361 0.303 0.000 0.433 14.189

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 94 69 81 78 305 0 114 481

N.S.

1 1.22 0.90 1.05 1.01 3.96 0.00 1.48 6.25

time (sec)

N/A 0.288 0.349 0.709 0.345 0.284 0.000 0.431 14.138

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 46 48 46 260 0 81 104

N.S.

1 1.00 1.00 1.04 1.00 5.65 0.00 1.76 2.26

time (sec)

N/A 0.291 1.407 0.409 0.396 0.291 0.000 0.397 13.852

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 30 29 236 16298 64 33

N.S.

1 1.00 1.00 0.83 0.81 6.56 452.72 1.78 0.92

time (sec)

N/A 0.199 0.733 0.386 0.324 0.282 13.057 0.438 14.950

Problem 90

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

53 51 53 50 48 313 0 83 45

N.S.

1 0.96 1.00 0.94 0.91 5.91 0.00 1.57 0.85

time (sec)

N/A 0.241 0.551 0.630 0.301 0.293 0.000 0.494 14.008

Problem 91

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

77 72 119 69 69 451 0 111 68

N.S.

1 0.94 1.55 0.90 0.90 5.86 0.00 1.44 0.88

time (sec)

N/A 0.287 0.804 0.844 0.313 0.271 0.000 0.460 13.885

Problem 92

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

109 101 147 96 98 595 0 155 95

N.S.

1 0.93 1.35 0.88 0.90 5.46 0.00 1.42 0.87

time (sec)

N/A 0.310 2.311 1.129 0.356 0.289 0.000 0.472 13.775

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 129 137 130 137 789 0 215 130

N.S.

1 0.92 0.98 0.93 0.98 5.64 0.00 1.54 0.93

time (sec)

N/A 0.340 5.818 1.531 0.370 0.310 0.000 0.481 15.183

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 122 194 116 154 529 0 322 123

N.S.

1 0.95 1.52 0.91 1.20 4.13 0.00 2.52 0.96

time (sec)

N/A 0.341 1.307 1.603 0.363 0.313 0.000 0.476 0.222

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 97 172 90 131 427 0 342 95

N.S.

1 0.95 1.69 0.88 1.28 4.19 0.00 3.35 0.93

time (sec)

N/A 0.307 0.899 1.105 0.323 0.283 0.000 0.362 0.187

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 82 160 77 111 327 0 93 71

N.S.

1 0.99 1.93 0.93 1.34 3.94 0.00 1.12 0.86

time (sec)

N/A 0.258 0.527 0.716 0.328 0.282 0.000 0.429 13.527

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 73 149 65 98 282 0 79 62

N.S.

1 0.99 2.01 0.88 1.32 3.81 0.00 1.07 0.84

time (sec)

N/A 0.227 0.259 0.585 0.392 0.276 0.000 0.469 0.110

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 113 194 107 149 455 0 246 2039

N.S.

1 1.10 1.88 1.04 1.45 4.42 0.00 2.39 19.80

time (sec)

N/A 0.288 1.149 0.916 0.354 0.315 0.000 0.425 14.481

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 166 390 152 223 838 0 512 2338

N.S.

1 1.08 2.55 0.99 1.46 5.48 0.00 3.35 15.28

time (sec)

N/A 0.372 1.650 1.137 0.403 0.350 0.000 0.421 15.462

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 169 106 134 181 623 0 223 2295

N.S.

1 1.14 0.72 0.91 1.22 4.21 0.00 1.51 15.51

time (sec)

N/A 0.398 1.191 1.245 0.332 0.318 0.000 0.397 16.770

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