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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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 52 51 44 47 41 48 59 55

N.S.

1 1.02 1.00 0.86 0.92 0.80 0.94 1.16 1.08

time (sec)

N/A 0.216 0.004 0.170 0.264 0.259 0.292 0.276 0.948

Problem 2

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

49 50 49 46 46 45 46 74 56

N.S.

1 1.02 1.00 0.94 0.94 0.92 0.94 1.51 1.14

time (sec)

N/A 0.224 0.011 0.124 0.179 0.260 0.257 0.269 0.873

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

41 42 41 36 38 32 39 51 46

N.S.

1 1.02 1.00 0.88 0.93 0.78 0.95 1.24 1.12

time (sec)

N/A 0.212 0.003 0.164 0.287 0.260 0.228 0.275 0.859

Problem 4

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

39 40 39 37 36 37 37 64 49

N.S.

1 1.03 1.00 0.95 0.92 0.95 0.95 1.64 1.26

time (sec)

N/A 0.216 0.008 0.108 0.180 0.294 0.193 0.266 0.806

Problem 5

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

31 32 31 25 28 23 31 36 39

N.S.

1 1.03 1.00 0.81 0.90 0.74 1.00 1.16 1.26

time (sec)

N/A 0.185 0.003 0.146 0.274 0.301 0.165 0.290 0.805

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 23 24 24 24 45 22

N.S.

1 1.00 1.00 0.96 1.00 1.00 1.00 1.88 0.92

time (sec)

N/A 0.177 0.002 0.103 0.195 0.254 0.087 0.273 0.151

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 37 33 56 0 0 38 0

N.S.

1 1.00 1.00 0.89 1.51 0.00 0.00 1.03 0.00

time (sec)

N/A 0.219 0.004 0.126 0.305 0.000 0.000 0.277 0.000

Problem 8

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 32 30 29 30 31 24 32 28

N.S.

1 1.07 1.00 0.97 1.00 1.03 0.80 1.07 0.93

time (sec)

N/A 0.203 0.003 0.099 0.185 0.256 0.102 0.270 0.238

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 30 36 26 23 24 24 40 44

N.S.

1 0.97 1.16 0.84 0.74 0.77 0.77 1.29 1.42

time (sec)

N/A 0.189 0.004 0.153 0.303 0.253 0.177 0.277 0.815

Problem 10

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

46 46 44 42 42 43 39 44 58

N.S.

1 1.00 0.96 0.91 0.91 0.93 0.85 0.96 1.26

time (sec)

N/A 0.223 0.010 0.122 0.186 0.254 0.201 0.271 0.927

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 43 36 35 37 33 32 51 47

N.S.

1 1.05 0.88 0.85 0.90 0.80 0.78 1.24 1.15

time (sec)

N/A 0.204 0.003 0.171 0.271 0.250 0.221 0.275 0.837

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 171 79 90 95 78 104 0 85

N.S.

1 1.64 0.76 0.87 0.91 0.75 1.00 0.00 0.82

time (sec)

N/A 1.103 0.019 0.279 0.308 0.277 0.357 0.000 0.952

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 181 95 205 0 0 0 0 0

N.S.

1 1.34 0.70 1.52 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.021 0.402 0.487 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 111 61 70 77 60 78 0 66

N.S.

1 1.39 0.76 0.88 0.96 0.75 0.98 0.00 0.82

time (sec)

N/A 0.731 0.016 0.291 0.280 0.260 0.266 0.000 0.219

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 129 76 185 0 0 0 0 0

N.S.

1 1.16 0.68 1.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.679 0.211 0.464 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 58 42 44 57 40 54 0 44

N.S.

1 1.09 0.79 0.83 1.08 0.75 1.02 0.00 0.83

time (sec)

N/A 0.420 0.012 0.260 0.282 0.258 0.196 0.000 0.157

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 80 56 130 0 0 0 0 55

N.S.

1 1.19 0.84 1.94 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.410 0.067 0.499 0.000 0.000 0.000 0.000 0.709

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

116 146 132 891 0 0 0 0 0

N.S.

1 1.26 1.14 7.68 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.651 0.047 5.668 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 76 64 222 0 0 0 0 0

N.S.

1 1.15 0.97 3.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.413 0.033 0.573 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 A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 60 56 64 56 57 53 60 50

N.S.

1 1.02 0.95 1.08 0.95 0.97 0.90 1.02 0.85

time (sec)

N/A 0.439 0.015 0.237 0.275 0.266 0.182 0.282 0.753

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 115 96 251 0 0 0 0 0

N.S.

1 1.02 0.85 2.22 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.642 0.187 0.718 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 A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 113 81 85 95 78 80 91 73

N.S.

1 1.27 0.91 0.96 1.07 0.88 0.90 1.02 0.82

time (sec)

N/A 0.759 0.015 0.287 0.306 0.283 0.232 0.274 0.810

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 447 125 1104 0 0 0 0 0

N.S.

1 2.30 0.64 5.69 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.662 0.519 29.340 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 F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

205 308 187 1108 0 0 0 0 0

N.S.

1 1.50 0.91 5.40 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.338 0.553 8.098 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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 256 96 857 0 0 0 0 0

N.S.

1 1.73 0.65 5.79 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.600 0.284 6.969 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

157 184 152 1036 0 0 0 0 0

N.S.

1 1.17 0.97 6.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.358 0.358 5.939 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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 117 76 592 0 0 0 0 0

N.S.

1 1.14 0.74 5.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.727 0.068 5.903 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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 112 90 187 0 0 0 0 0

N.S.

1 1.17 0.94 1.95 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.588 0.087 1.154 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

178 220 180 982 0 0 0 0 0

N.S.

1 1.24 1.01 5.52 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.896 0.064 6.607 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

93 116 83 1441 0 0 0 0 0

N.S.

1 1.25 0.89 15.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.620 0.053 8.941 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 C F F F A F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

105 106 90 2956 0 0 0 29 0

N.S.

1 1.01 0.86 28.15 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.723 0.123 6.764 0.000 0.000 0.000 0.284 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

167 183 151 1622 0 0 0 0 0

N.S.

1 1.10 0.90 9.71 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.380 0.194 25.043 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

152 226 126 852 0 0 0 0 0

N.S.

1 1.49 0.83 5.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.348 0.221 10.742 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

10 10 12 10 221 12 10 12 12

N.S.

1 1.00 1.20 1.00 22.10 1.20 1.00 1.20 1.20

time (sec)

N/A 0.170 0.642 0.771 2.291 0.267 1.954 0.291 0.691

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

10 10 12 10 183 12 10 12 12

N.S.

1 1.00 1.20 1.00 18.30 1.20 1.00 1.20 1.20

time (sec)

N/A 0.172 0.642 0.527 1.569 0.259 0.979 0.297 0.695

Problem 36

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

57 57 52 0 0 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.199 0.016 0.000 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 49 32 34 35 31 34 0 32

N.S.

1 1.22 0.80 0.85 0.88 0.78 0.85 0.00 0.80

time (sec)

N/A 0.508 0.021 0.480 0.278 0.271 0.138 0.000 0.740

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 66 51 126 0 0 0 0 0

N.S.

1 0.99 0.76 1.88 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.482 0.185 0.738 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 F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 20 24 19 19 0 19

N.S.

1 1.00 1.00 0.87 1.04 0.83 0.83 0.00 0.83

time (sec)

N/A 0.307 0.014 0.417 0.263 0.256 0.099 0.000 0.703

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 39 98 0 0 0 0 0

N.S.

1 1.00 0.81 2.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.319 0.068 0.353 0.000 0.000 0.000 0.000 0.000

Problem 41

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

8 8 8 7 6 6 7 8 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 1.00 0.75

time (sec)

N/A 0.168 0.004 0.517 0.179 0.250 0.319 0.265 0.681

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 55 43 117 0 0 0 0 0

N.S.

1 1.12 0.88 2.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.314 0.103 0.343 0.000 0.000 0.000 0.000 0.000

Problem 43

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 33 30 32 29 29 22 26 26

N.S.

1 1.10 1.00 1.07 0.97 0.97 0.73 0.87 0.87

time (sec)

N/A 0.315 0.012 0.354 0.265 0.255 0.140 0.272 0.098

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 74 55 178 0 0 0 0 0

N.S.

1 1.03 0.76 2.47 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.469 0.168 0.746 0.000 0.000 0.000 0.000 0.000

Problem 45

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

47 61 47 43 55 47 42 39 35

N.S.

1 1.30 1.00 0.91 1.17 1.00 0.89 0.83 0.74

time (sec)

N/A 0.542 0.017 0.415 0.280 0.258 0.251 0.268 0.103

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

206 334 626 261 189 0 0 0 0

N.S.

1 1.62 3.04 1.27 0.92 0.00 0.00 0.00 0.00

time (sec)

N/A 0.895 1.192 0.917 0.298 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 309 134 0 0 0 0 0

N.S.

1 1.00 1.64 0.71 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.416 1.421 0.764 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 B A A F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 311 592 183 187 0 0 0 0

N.S.

1 1.70 3.23 1.00 1.02 0.00 0.00 0.00 0.00

time (sec)

N/A 0.703 0.609 1.168 0.301 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 223 328 197 0 0 0 0 0

N.S.

1 1.00 1.47 0.88 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.480 2.045 0.816 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 342 619 257 183 0 0 0 0

N.S.

1 1.61 2.92 1.21 0.86 0.00 0.00 0.00 0.00

time (sec)

N/A 0.863 1.424 0.845 0.317 0.000 0.000 0.000 0.000

Problem 51

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

5 5 5 6 5 5 5 8 5

N.S.

1 1.00 1.00 1.20 1.00 1.00 1.00 1.60 1.00

time (sec)

N/A 0.173 0.060 0.286 0.177 0.247 0.092 0.268 0.709

Problem 52

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

13 13 13 14 13 13 17 15 13

N.S.

1 1.00 1.00 1.08 1.00 1.00 1.31 1.15 1.00

time (sec)

N/A 0.189 0.008 0.645 0.187 0.272 0.688 0.269 0.696

Problem 53

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

244 244 212 245 226 237 367 347 234

N.S.

1 1.00 0.87 1.00 0.93 0.97 1.50 1.42 0.96

time (sec)

N/A 0.663 0.057 0.515 0.189 0.268 0.567 0.275 0.250

Problem 54

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

168 168 149 167 159 167 243 252 190

N.S.

1 1.00 0.89 0.99 0.95 0.99 1.45 1.50 1.13

time (sec)

N/A 0.553 0.044 0.454 0.215 0.262 0.414 0.278 1.154

Problem 55

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

109 109 97 105 103 108 151 171 116

N.S.

1 1.00 0.89 0.96 0.94 0.99 1.39 1.57 1.06

time (sec)

N/A 0.370 0.030 0.432 0.214 0.263 0.310 0.279 1.014

Problem 56

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

58 58 67 57 53 57 73 99 62

N.S.

1 1.00 1.16 0.98 0.91 0.98 1.26 1.71 1.07

time (sec)

N/A 0.261 0.010 0.182 0.219 0.256 0.222 0.270 0.830

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

403 629 716 392 528 0 0 0 0

N.S.

1 1.56 1.78 0.97 1.31 0.00 0.00 0.00 0.00

time (sec)

N/A 1.052 1.217 1.316 0.352 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

801 797 806 2141 628 0 0 0 0

N.S.

1 1.00 1.01 2.67 0.78 0.00 0.00 0.00 0.00

time (sec)

N/A 1.517 5.297 1.592 0.382 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

16 16 18 14 0 16 15 16 16

N.S.

1 1.00 1.12 0.88 0.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.191 4.298 0.765 0.000 0.260 4.389 0.286 0.725

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 14 16 16 15 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.195 2.879 0.710 0.919 0.265 1.440 0.286 0.704

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 169 0 0 349 0 59 0

N.S.

1 1.00 2.56 0.00 0.00 5.29 0.00 0.89 0.00

time (sec)

N/A 0.281 0.183 0.000 0.000 0.300 0.000 0.302 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

134 136 262 0 0 712 0 126 0

N.S.

1 1.01 1.96 0.00 0.00 5.31 0.00 0.94 0.00

time (sec)

N/A 0.350 0.457 0.000 0.000 0.315 0.000 0.303 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

208 201 345 0 0 1278 0 208 0

N.S.

1 0.97 1.66 0.00 0.00 6.14 0.00 1.00 0.00

time (sec)

N/A 1.055 0.632 0.000 0.000 0.366 0.000 0.306 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

293 291 450 0 0 1986 0 340 0

N.S.

1 0.99 1.54 0.00 0.00 6.78 0.00 1.16 0.00

time (sec)

N/A 1.266 0.931 0.000 0.000 0.613 0.000 0.312 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 154 136 117 0 0 0 0 0

N.S.

1 0.79 0.70 0.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.379 0.997 0.870 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 116 89 99 0 0 0 0 0

N.S.

1 0.75 0.57 0.64 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.288 0.130 0.773 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 21 55 31 29 0 33 0

N.S.

1 1.00 0.60 1.57 0.89 0.83 0.00 0.94 0.00

time (sec)

N/A 0.197 0.032 0.568 0.270 0.298 0.000 0.281 0.000

Problem 68

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

79 82 37 101 63 52 0 55 0

N.S.

1 1.04 0.47 1.28 0.80 0.66 0.00 0.70 0.00

time (sec)

N/A 0.290 0.042 1.299 0.274 0.262 0.000 0.301 0.000

Problem 69

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

118 129 47 130 93 70 0 83 0

N.S.

1 1.09 0.40 1.10 0.79 0.59 0.00 0.70 0.00

time (sec)

N/A 0.394 0.046 1.407 0.271 0.270 0.000 0.300 0.000

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

32 37 25 24 26 21 31 32 22

N.S.

1 1.16 0.78 0.75 0.81 0.66 0.97 1.00 0.69

time (sec)

N/A 0.196 0.015 0.335 0.296 0.253 0.185 0.277 0.080

Problem 71

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

44 54 36 37 39 39 88 40 27

N.S.

1 1.23 0.82 0.84 0.89 0.89 2.00 0.91 0.61

time (sec)

N/A 0.213 0.019 0.359 0.264 0.255 0.257 0.277 0.734

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 28 35 38 26 0 0 22

N.S.

1 1.00 0.82 1.03 1.12 0.76 0.00 0.00 0.65

time (sec)

N/A 0.187 0.012 0.748 0.277 0.282 0.000 0.000 0.734

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 61 46 65 75 40 0 0 51

N.S.

1 1.09 0.82 1.16 1.34 0.71 0.00 0.00 0.91

time (sec)

N/A 0.268 0.020 0.964 0.283 0.257 0.000 0.000 0.072

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

41 42 41 39 38 39 39 40 35

N.S.

1 1.02 1.00 0.95 0.93 0.95 0.95 0.98 0.85

time (sec)

N/A 0.219 0.012 0.241 0.208 0.279 0.357 0.272 0.769

Problem 75

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

37 38 37 31 34 27 36 38 31

N.S.

1 1.03 1.00 0.84 0.92 0.73 0.97 1.03 0.84

time (sec)

N/A 0.206 0.006 0.286 0.291 0.263 0.274 0.269 0.709

Problem 76

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

31 31 31 28 28 28 31 47 27

N.S.

1 1.00 1.00 0.90 0.90 0.90 1.00 1.52 0.87

time (sec)

N/A 0.188 0.006 0.162 0.209 0.247 0.139 0.267 0.707

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 41 37 57 68 0 0 0 0

N.S.

1 1.11 1.00 1.54 1.84 0.00 0.00 0.00 0.00

time (sec)

N/A 0.255 0.008 0.276 0.331 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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 36 34 31 32 37 29 32 31

N.S.

1 1.06 1.00 0.91 0.94 1.09 0.85 0.94 0.91

time (sec)

N/A 0.193 0.006 0.129 0.214 0.279 0.213 0.276 0.769

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 34 38 31 27 28 29 29 32

N.S.

1 0.97 1.09 0.89 0.77 0.80 0.83 0.83 0.91

time (sec)

N/A 0.202 0.006 0.191 0.261 0.301 0.273 0.280 0.727

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 175 136 112 137 122 136 156 54

N.S.

1 1.15 0.89 0.74 0.90 0.80 0.89 1.03 0.36

time (sec)

N/A 0.421 0.033 0.395 0.290 0.272 9.749 0.286 0.484

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 164 133 109 135 111 126 153 52

N.S.

1 1.09 0.89 0.73 0.90 0.74 0.84 1.02 0.35

time (sec)

N/A 0.393 0.026 0.267 0.285 0.266 5.369 0.288 0.790

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 152 102 97 120 96 109 144 42

N.S.

1 1.15 0.77 0.73 0.91 0.73 0.83 1.09 0.32

time (sec)

N/A 0.367 0.034 0.261 0.282 0.274 2.978 0.278 0.139

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 149 105 98 123 107 114 135 44

N.S.

1 1.10 0.78 0.73 0.91 0.79 0.84 1.00 0.33

time (sec)

N/A 0.370 0.032 0.220 0.262 0.278 6.182 0.285 0.775

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 170 146 106 133 129 131 149 52

N.S.

1 1.13 0.97 0.71 0.89 0.86 0.87 0.99 0.35

time (sec)

N/A 0.400 0.038 0.300 0.270 0.263 12.597 0.282 0.845

Problem 85

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

51 52 40 32 31 27 39 33 31

N.S.

1 1.02 0.78 0.63 0.61 0.53 0.76 0.65 0.61

time (sec)

N/A 0.194 0.012 0.039 0.288 0.252 0.972 0.280 0.760

Problem 86

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

42 43 33 27 26 20 32 28 26

N.S.

1 1.02 0.79 0.64 0.62 0.48 0.76 0.67 0.62

time (sec)

N/A 0.193 0.010 0.039 0.264 0.270 0.525 0.285 0.763

Problem 87

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

22 29 22 17 16 12 19 14 16

N.S.

1 1.32 1.00 0.77 0.73 0.55 0.86 0.64 0.73

time (sec)

N/A 0.175 0.014 0.057 0.269 0.254 0.344 0.268 0.700

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 37 31 61 35 0 0 19 0

N.S.

1 1.19 1.00 1.97 1.13 0.00 0.00 0.61 0.00

time (sec)

N/A 0.254 0.006 0.224 0.299 0.000 0.000 0.284 0.000

Problem 89

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

23 32 29 18 17 19 92 19 17

N.S.

1 1.39 1.26 0.78 0.74 0.83 4.00 0.83 0.74

time (sec)

N/A 0.183 0.009 0.044 0.265 0.266 0.492 0.277 0.742

Problem 90

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

42 43 34 27 26 27 160 26 24

N.S.

1 1.02 0.81 0.64 0.62 0.64 3.81 0.62 0.57

time (sec)

N/A 0.187 0.009 0.047 0.268 0.252 1.139 0.275 0.760

Problem 91

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

36 35 29 25 24 24 85 39 24

N.S.

1 0.97 0.81 0.69 0.67 0.67 2.36 1.08 0.67

time (sec)

N/A 0.204 0.013 0.042 0.183 0.270 0.847 0.258 0.729

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 28 25 20 19 19 24 30 0

N.S.

1 0.97 0.86 0.69 0.66 0.66 0.83 1.03 0.00

time (sec)

N/A 0.187 0.010 0.038 0.190 0.265 0.486 0.291 0.000

Problem 93

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

18 18 18 15 14 14 17 18 14

N.S.

1 1.00 1.00 0.83 0.78 0.78 0.94 1.00 0.78

time (sec)

N/A 0.168 0.010 0.039 0.209 0.259 0.111 0.284 0.886

Problem 94

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

22 22 22 19 18 25 20 16 20

N.S.

1 1.00 1.00 0.86 0.82 1.14 0.91 0.73 0.91

time (sec)

N/A 0.173 0.010 0.040 0.201 0.264 0.331 0.265 0.752

Problem 95

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 29 26 25 33 143 23 27

N.S.

1 0.86 0.78 0.70 0.68 0.89 3.86 0.62 0.73

time (sec)

N/A 0.200 0.014 0.049 0.199 0.275 1.138 0.274 0.751

Problem 96

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

17 17 17 16 15 15 14 13 15

N.S.

1 1.00 1.00 0.94 0.88 0.88 0.82 0.76 0.88

time (sec)

N/A 0.173 0.001 0.192 0.203 0.251 0.066 0.264 0.060

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 45 40 83 0 63 0 0 0

N.S.

1 0.96 0.85 1.77 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.260 0.014 0.543 0.000 0.287 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 41 37 57 68 0 0 0 0

N.S.

1 1.11 1.00 1.54 1.84 0.00 0.00 0.00 0.00

time (sec)

N/A 0.256 0.007 0.418 0.334 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 99 95 131 104 92 155 617 133

N.S.

1 0.93 0.90 1.24 0.98 0.87 1.46 5.82 1.25

time (sec)

N/A 0.316 0.061 0.295 0.294 0.263 0.381 0.728 0.922

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 81 114 102 85 73 117 423 101

N.S.

1 1.01 1.42 1.28 1.06 0.91 1.46 5.29 1.26

time (sec)

N/A 0.300 0.032 0.243 0.306 0.272 0.309 0.633 1.525

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