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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 C A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 230 183 34 221 767 109 241 599

N.S.

1 0.93 0.74 0.14 0.89 3.11 0.44 0.98 2.43

time (sec)

N/A 0.419 0.057 0.200 0.282 0.260 0.322 0.266 0.376

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 230 184 35 221 767 110 241 603

N.S.

1 0.93 0.74 0.14 0.89 3.11 0.45 0.98 2.44

time (sec)

N/A 0.394 0.033 0.193 0.286 0.256 0.323 0.284 13.696

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 85 95 36 109 755 110 230 579

N.S.

1 0.99 1.10 0.42 1.27 8.78 1.28 2.67 6.73

time (sec)

N/A 0.195 0.021 0.198 0.278 0.265 0.361 0.269 0.333

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 85 95 37 109 755 110 228 579

N.S.

1 0.99 1.10 0.43 1.27 8.78 1.28 2.65 6.73

time (sec)

N/A 0.195 0.020 0.191 0.284 0.281 0.334 0.267 13.680

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

40 40 33 35 39 33 41 52 29

N.S.

1 1.00 0.82 0.88 0.98 0.82 1.02 1.30 0.72

time (sec)

N/A 0.172 0.016 0.236 0.273 0.238 0.053 0.276 0.091

Problem 6

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 51 44 40 39 42 49 40 21

N.S.

1 1.00 0.86 0.78 0.76 0.82 0.96 0.78 0.41

time (sec)

N/A 0.193 0.011 0.200 0.270 0.258 0.046 0.260 13.563

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 32 13 25 29 32 29 12

N.S.

1 1.00 2.00 0.81 1.56 1.81 2.00 1.81 0.75

time (sec)

N/A 0.143 0.013 0.214 0.269 0.248 0.041 0.272 0.104

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

16 16 16 13 12 12 15 12 12

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.94 0.75 0.75

time (sec)

N/A 0.144 0.005 0.199 0.271 0.256 0.052 0.291 0.028

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 60 204 100 148 138 0 57

N.S.

1 1.00 0.80 2.72 1.33 1.97 1.84 0.00 0.76

time (sec)

N/A 0.202 0.017 0.247 0.299 0.283 0.172 0.000 13.896

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 106 91 204 70 151 131 0 43

N.S.

1 1.00 0.86 1.92 0.66 1.42 1.24 0.00 0.41

time (sec)

N/A 0.238 0.015 0.245 0.276 0.264 0.203 0.000 13.854

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 60 83 302 137 87 92 57

N.S.

1 1.00 0.80 1.11 4.03 1.83 1.16 1.23 0.76

time (sec)

N/A 0.202 0.025 0.272 0.282 0.263 0.096 0.287 0.070

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 90 75 75 302 140 80 100 41

N.S.

1 1.00 0.83 0.83 3.36 1.56 0.89 1.11 0.46

time (sec)

N/A 0.238 0.016 0.222 0.288 0.253 0.094 0.267 13.571

Problem 13

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

13 13 25 18 17 17 22 19 9

N.S.

1 1.00 1.92 1.38 1.31 1.31 1.69 1.46 0.69

time (sec)

N/A 0.145 0.006 0.224 0.293 0.262 0.070 0.263 13.492

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 45 36 0 71 70 0 0

N.S.

1 1.00 2.81 2.25 0.00 4.44 4.38 0.00 0.00

time (sec)

N/A 0.152 10.020 1.888 0.000 0.085 0.848 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 45 36 0 69 70 0 0

N.S.

1 1.00 1.29 1.03 0.00 1.97 2.00 0.00 0.00

time (sec)

N/A 0.184 10.020 1.130 0.000 0.074 0.881 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

43 43 74 88 0 56 61 0 0

N.S.

1 1.00 1.72 2.05 0.00 1.30 1.42 0.00 0.00

time (sec)

N/A 0.180 10.031 1.927 0.000 0.076 0.799 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

89 63 74 88 0 53 60 0 0

N.S.

1 0.71 0.83 0.99 0.00 0.60 0.67 0.00 0.00

time (sec)

N/A 0.213 10.026 1.139 0.000 0.074 0.822 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 47 38 0 73 66 0 0

N.S.

1 1.00 0.53 0.43 0.00 0.82 0.74 0.00 0.00

time (sec)

N/A 0.180 10.018 1.514 0.000 0.080 0.786 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 152 47 38 0 73 66 0 0

N.S.

1 1.00 0.31 0.25 0.00 0.48 0.43 0.00 0.00

time (sec)

N/A 0.241 10.015 0.471 0.000 0.078 0.780 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

90 90 76 90 0 87 70 0 0

N.S.

1 1.00 0.84 1.00 0.00 0.97 0.78 0.00 0.00

time (sec)

N/A 0.186 10.026 2.491 0.000 0.076 0.837 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

156 156 76 90 0 84 71 0 0

N.S.

1 1.00 0.49 0.58 0.00 0.54 0.46 0.00 0.00

time (sec)

N/A 0.253 10.019 0.795 0.000 0.080 0.854 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 15 0 76 0 0 0

N.S.

1 1.00 1.00 1.50 0.00 7.60 0.00 0.00 0.00

time (sec)

N/A 0.131 0.410 1.981 0.000 0.081 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 47 38 0 65 71 0 0

N.S.

1 1.00 4.70 3.80 0.00 6.50 7.10 0.00 0.00

time (sec)

N/A 0.144 10.021 1.200 0.000 0.076 0.900 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 24 28 0 73 0 0 0

N.S.

1 1.00 1.04 1.22 0.00 3.17 0.00 0.00 0.00

time (sec)

N/A 0.165 0.006 0.477 0.000 0.086 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 47 38 0 62 71 0 0

N.S.

1 1.00 2.04 1.65 0.00 2.70 3.09 0.00 0.00

time (sec)

N/A 0.179 10.020 1.146 0.000 0.080 0.862 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 90 181 71 0 162 122 189 94

N.S.

1 1.10 2.21 0.87 0.00 1.98 1.49 2.30 1.15

time (sec)

N/A 0.242 0.076 0.090 0.000 0.254 0.286 0.700 14.338

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 90 181 71 0 162 122 191 98

N.S.

1 1.10 2.21 0.87 0.00 1.98 1.49 2.33 1.20

time (sec)

N/A 0.248 0.075 0.088 0.000 0.259 0.286 0.688 0.100

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 88 189 75 0 176 110 195 30

N.S.

1 1.13 2.42 0.96 0.00 2.26 1.41 2.50 0.38

time (sec)

N/A 0.241 0.071 0.080 0.000 0.263 0.302 0.714 14.382

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 94 189 75 0 179 121 197 88

N.S.

1 1.09 2.20 0.87 0.00 2.08 1.41 2.29 1.02

time (sec)

N/A 0.244 0.067 0.079 0.000 0.254 0.293 0.711 0.105

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 182 88 0 172 121 189 99

N.S.

1 1.00 2.33 1.13 0.00 2.21 1.55 2.42 1.27

time (sec)

N/A 0.252 0.083 0.068 0.000 0.261 0.300 0.679 13.987

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 182 69 0 173 110 190 57

N.S.

1 1.00 2.33 0.88 0.00 2.22 1.41 2.44 0.73

time (sec)

N/A 0.245 0.079 0.066 0.000 0.270 0.303 0.699 13.569

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 190 61 0 168 112 199 29

N.S.

1 1.00 2.71 0.87 0.00 2.40 1.60 2.84 0.41

time (sec)

N/A 0.235 0.082 0.063 0.000 0.261 0.312 0.772 0.124

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 190 61 0 168 112 200 29

N.S.

1 1.00 2.71 0.87 0.00 2.40 1.60 2.86 0.41

time (sec)

N/A 0.236 0.084 0.062 0.000 0.258 0.324 0.687 13.198

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 134 250 121 0 244 158 6331 129

N.S.

1 1.00 1.87 0.90 0.00 1.82 1.18 47.25 0.96

time (sec)

N/A 0.330 0.123 0.224 0.000 0.255 0.362 1.009 0.192

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 152 248 119 0 232 160 6341 232

N.S.

1 1.17 1.91 0.92 0.00 1.78 1.23 48.78 1.78

time (sec)

N/A 0.295 0.077 0.093 0.000 0.263 0.393 1.041 13.935

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 152 248 119 0 232 160 6341 232

N.S.

1 1.17 1.91 0.92 0.00 1.78 1.23 48.78 1.78

time (sec)

N/A 0.309 0.030 0.052 0.000 0.262 0.382 1.097 13.832

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

29 29 29 26 25 25 26 25 12

N.S.

1 1.00 1.00 0.90 0.86 0.86 0.90 0.86 0.41

time (sec)

N/A 0.187 0.016 0.073 0.200 0.287 0.237 0.261 0.113

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 67 138 52 0 164 117 51 55

N.S.

1 1.12 2.30 0.87 0.00 2.73 1.95 0.85 0.92

time (sec)

N/A 0.224 0.133 0.071 0.000 0.259 0.254 0.269 13.774

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 71 126 74 0 110 95 0 66

N.S.

1 1.15 2.03 1.19 0.00 1.77 1.53 0.00 1.06

time (sec)

N/A 0.207 0.053 0.122 0.000 0.273 0.208 0.000 13.575

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 75 134 66 0 120 83 0 24

N.S.

1 1.14 2.03 1.00 0.00 1.82 1.26 0.00 0.36

time (sec)

N/A 0.206 0.047 0.086 0.000 0.253 0.217 0.000 13.198

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 81 83 35 0 31 42 39 29

N.S.

1 1.80 1.84 0.78 0.00 0.69 0.93 0.87 0.64

time (sec)

N/A 0.204 0.060 0.110 0.000 0.249 0.058 0.265 0.095

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

15 15 17 12 11 19 22 11 19

N.S.

1 1.00 1.13 0.80 0.73 1.27 1.47 0.73 1.27

time (sec)

N/A 0.152 0.008 0.064 0.279 0.257 0.062 0.272 13.611

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

14 14 14 12 11 11 14 11 11

N.S.

1 1.00 1.00 0.86 0.79 0.79 1.00 0.79 0.79

time (sec)

N/A 0.146 0.004 0.036 0.275 0.237 0.044 0.283 0.027

Problem 44

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

38 43 97 34 33 33 44 33 29

N.S.

1 1.13 2.55 0.89 0.87 0.87 1.16 0.87 0.76

time (sec)

N/A 0.181 0.153 0.067 0.292 0.237 0.059 0.271 13.745

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 51 99 35 0 29 42 45 29

N.S.

1 1.06 2.06 0.73 0.00 0.60 0.88 0.94 0.60

time (sec)

N/A 0.190 0.074 0.080 0.000 0.246 0.055 0.278 0.091

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 55 97 35 0 33 44 52 29

N.S.

1 1.20 2.11 0.76 0.00 0.72 0.96 1.13 0.63

time (sec)

N/A 0.195 0.181 0.101 0.000 0.249 0.061 0.294 13.719

Problem 47

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

21 21 17 16 17 15 14 46 15

N.S.

1 1.00 0.81 0.76 0.81 0.71 0.67 2.19 0.71

time (sec)

N/A 0.166 0.006 0.240 0.283 0.247 0.045 0.262 0.058

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 55 101 35 0 31 42 52 29

N.S.

1 1.20 2.20 0.76 0.00 0.67 0.91 1.13 0.63

time (sec)

N/A 0.186 0.210 0.079 0.000 0.255 0.062 0.306 13.650

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 51 99 27 0 26 29 46 21

N.S.

1 1.16 2.25 0.61 0.00 0.59 0.66 1.05 0.48

time (sec)

N/A 0.188 0.073 0.086 0.000 0.246 0.054 0.290 0.061

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 33 14 16 0 15 12 42 15

N.S.

1 1.43 0.61 0.70 0.00 0.65 0.52 1.83 0.65

time (sec)

N/A 0.184 0.010 0.090 0.000 0.251 0.054 0.300 0.081

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

11 11 12 11 12 12 8 12 12

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.73 1.09 1.09

time (sec)

N/A 0.144 0.005 0.027 0.197 0.262 0.040 0.266 0.044

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

39 41 29 26 29 25 26 33 14

N.S.

1 1.05 0.74 0.67 0.74 0.64 0.67 0.85 0.36

time (sec)

N/A 0.201 0.008 0.043 0.203 0.263 0.051 0.271 0.306

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 109 42 39 0 47 46 77 20

N.S.

1 2.48 0.95 0.89 0.00 1.07 1.05 1.75 0.45

time (sec)

N/A 0.274 0.010 0.087 0.000 0.247 0.049 0.310 13.329

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 127 78 0 109 94 0 63

N.S.

1 1.00 1.92 1.18 0.00 1.65 1.42 0.00 0.95

time (sec)

N/A 0.212 0.055 0.060 0.000 0.249 0.218 0.000 0.070

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 81 84 34 0 28 39 39 30

N.S.

1 1.76 1.83 0.74 0.00 0.61 0.85 0.85 0.65

time (sec)

N/A 0.189 0.045 0.047 0.000 0.241 0.061 0.276 13.492

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

9 9 12 10 9 17 14 9 17

N.S.

1 1.00 1.33 1.11 1.00 1.89 1.56 1.00 1.89

time (sec)

N/A 0.146 0.006 0.048 0.281 0.260 0.066 0.277 0.061

Problem 57

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

11 11 11 11 11 11 7 11 11

N.S.

1 1.00 1.00 1.00 1.00 1.00 0.64 1.00 1.00

time (sec)

N/A 0.147 0.006 0.025 0.191 0.254 0.041 0.264 0.027

Problem 58

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

29 29 29 24 25 25 26 25 12

N.S.

1 1.00 1.00 0.83 0.86 0.86 0.90 0.86 0.41

time (sec)

N/A 0.167 0.005 0.031 0.193 0.254 0.052 0.257 0.066

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 42 39 0 45 46 34 20

N.S.

1 1.00 0.84 0.78 0.00 0.90 0.92 0.68 0.40

time (sec)

N/A 0.193 0.010 0.037 0.000 0.252 0.048 0.271 0.063

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 42 39 0 43 46 41 20

N.S.

1 1.00 0.84 0.78 0.00 0.86 0.92 0.82 0.40

time (sec)

N/A 0.187 0.010 0.043 0.000 0.251 0.051 0.298 13.207

Problem 61

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 22 27 27 22 34 15

N.S.

1 1.00 1.00 0.71 0.87 0.87 0.71 1.10 0.48

time (sec)

N/A 0.170 0.004 0.191 0.190 0.245 0.046 0.264 0.071

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 42 39 0 45 46 41 20

N.S.

1 1.00 0.84 0.78 0.00 0.90 0.92 0.82 0.40

time (sec)

N/A 0.192 0.010 0.046 0.000 0.259 0.055 0.297 13.357

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 42 39 0 45 46 40 20

N.S.

1 1.00 0.84 0.78 0.00 0.90 0.92 0.80 0.40

time (sec)

N/A 0.190 0.015 0.044 0.000 0.273 0.048 0.271 0.072

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 42 39 0 45 46 41 20

N.S.

1 1.00 0.84 0.78 0.00 0.90 0.92 0.82 0.40

time (sec)

N/A 0.189 0.013 0.052 0.000 0.261 0.048 0.287 0.089

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 32 12 25 29 32 29 11

N.S.

1 1.00 2.29 0.86 1.79 2.07 2.29 2.07 0.79

time (sec)

N/A 0.147 0.012 0.030 0.275 0.239 0.046 0.276 13.368

Problem 66

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 49 31 26 29 27 29 33 15

N.S.

1 1.26 0.79 0.67 0.74 0.69 0.74 0.85 0.38

time (sec)

N/A 0.200 0.006 0.044 0.196 0.276 0.048 0.269 13.242

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 117 42 39 0 45 46 77 20

N.S.

1 2.44 0.88 0.81 0.00 0.94 0.96 1.60 0.42

time (sec)

N/A 0.260 0.014 0.050 0.000 0.245 0.050 0.327 0.132

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 63 124 74 0 101 88 0 73

N.S.

1 1.02 2.00 1.19 0.00 1.63 1.42 0.00 1.18

time (sec)

N/A 0.206 0.043 0.113 0.000 0.252 0.193 0.000 0.070

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 89 83 35 0 31 41 26 29

N.S.

1 1.82 1.69 0.71 0.00 0.63 0.84 0.53 0.59

time (sec)

N/A 0.229 0.102 0.103 0.000 0.248 0.053 0.271 13.277

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 79 81 35 0 31 41 26 29

N.S.

1 1.84 1.88 0.81 0.00 0.72 0.95 0.60 0.67

time (sec)

N/A 0.188 0.054 0.096 0.000 0.243 0.051 0.283 0.089

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 89 83 35 0 31 41 26 29

N.S.

1 1.82 1.69 0.71 0.00 0.63 0.84 0.53 0.59

time (sec)

N/A 0.206 0.065 0.092 0.000 0.278 0.057 0.265 0.086

Problem 72

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

2 2 2 3 2 2 2 2 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.135 0.003 0.032 0.269 0.240 0.059 0.290 13.386

Problem 73

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

38 37 99 34 33 31 41 26 29

N.S.

1 0.97 2.61 0.89 0.87 0.82 1.08 0.68 0.76

time (sec)

N/A 0.173 0.131 0.049 0.277 0.243 0.054 0.267 0.085

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

35 35 30 35 39 29 39 39 29

N.S.

1 1.00 0.86 1.00 1.11 0.83 1.11 1.11 0.83

time (sec)

N/A 0.172 0.011 0.217 0.281 0.248 0.049 0.274 13.347

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 12 8 0 7 7 30 7

N.S.

1 1.00 0.52 0.35 0.00 0.30 0.30 1.30 0.30

time (sec)

N/A 0.178 0.007 0.067 0.000 0.239 0.050 0.277 13.276

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

11 11 10 11 10 10 7 11 10

N.S.

1 1.00 0.91 1.00 0.91 0.91 0.64 1.00 0.91

time (sec)

N/A 0.141 0.004 0.027 0.196 0.235 0.036 0.298 13.361

Problem 77

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

65 63 29 22 21 21 19 43 12

N.S.

1 0.97 0.45 0.34 0.32 0.32 0.29 0.66 0.18

time (sec)

N/A 0.231 0.005 0.037 0.198 0.257 0.048 0.280 0.269

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 102 40 35 0 36 39 39 18

N.S.

1 2.37 0.93 0.81 0.00 0.84 0.91 0.91 0.42

time (sec)

N/A 0.263 0.010 0.076 0.000 0.240 0.048 0.288 13.528

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 105 40 35 0 39 39 39 18

N.S.

1 2.28 0.87 0.76 0.00 0.85 0.85 0.85 0.39

time (sec)

N/A 0.261 0.016 0.077 0.000 0.234 0.050 0.302 0.232

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 125 78 0 100 87 0 76

N.S.

1 1.00 2.02 1.26 0.00 1.61 1.40 0.00 1.23

time (sec)

N/A 0.205 0.060 0.063 0.000 0.236 0.204 0.000 0.062

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 89 87 35 0 31 42 26 31

N.S.

1 1.78 1.74 0.70 0.00 0.62 0.84 0.52 0.62

time (sec)

N/A 0.187 0.066 0.049 0.000 0.255 0.055 0.284 13.145

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 79 82 35 0 31 42 26 31

N.S.

1 1.80 1.86 0.80 0.00 0.70 0.95 0.59 0.70

time (sec)

N/A 0.182 0.041 0.050 0.000 0.251 0.067 0.271 0.085

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 87 10 14 0 13 10 26 13

N.S.

1 2.23 0.26 0.36 0.00 0.33 0.26 0.67 0.33

time (sec)

N/A 0.190 0.006 0.059 0.000 0.247 0.050 0.274 13.513

Problem 84

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

9 9 9 10 9 9 5 7 9

N.S.

1 1.00 1.00 1.11 1.00 1.00 0.56 0.78 1.00

time (sec)

N/A 0.143 0.004 0.027 0.197 0.258 0.032 0.265 0.032

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

25 25 25 22 21 21 19 35 10

N.S.

1 1.00 1.00 0.88 0.84 0.84 0.76 1.40 0.40

time (sec)

N/A 0.165 0.005 0.032 0.198 0.249 0.051 0.268 0.063

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

46 46 40 35 34 34 39 34 18

N.S.

1 1.00 0.87 0.76 0.74 0.74 0.85 0.74 0.39

time (sec)

N/A 0.183 0.008 0.218 0.281 0.265 0.042 0.268 13.246

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 40 35 0 39 39 39 18

N.S.

1 1.00 0.87 0.76 0.00 0.85 0.85 0.85 0.39

time (sec)

N/A 0.178 0.010 0.047 0.000 0.258 0.047 0.262 0.062

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 19 3 13 13 12 15 2

N.S.

1 1.00 9.50 1.50 6.50 6.50 6.00 7.50 1.00

time (sec)

N/A 0.134 0.002 0.023 0.199 0.258 0.045 0.266 0.065

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 85 40 34 55 39 39 39 18

N.S.

1 2.24 1.05 0.89 1.45 1.03 1.03 1.03 0.47

time (sec)

N/A 0.242 0.009 0.044 0.280 0.254 0.055 0.282 0.119

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 102 40 35 0 39 39 39 18

N.S.

1 2.17 0.85 0.74 0.00 0.83 0.83 0.83 0.38

time (sec)

N/A 0.259 0.012 0.042 0.000 0.265 0.050 0.296 0.074

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 105 40 35 0 39 39 39 18

N.S.

1 2.28 0.87 0.76 0.00 0.85 0.85 0.85 0.39

time (sec)

N/A 0.257 0.010 0.046 0.000 0.273 0.048 0.285 0.118

Problem 92

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

43 53 99 34 33 33 46 33 29

N.S.

1 1.23 2.30 0.79 0.77 0.77 1.07 0.77 0.67

time (sec)

N/A 0.181 0.076 0.061 0.281 0.275 0.062 0.289 13.395

Problem 93

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

43 53 99 34 33 33 46 33 29

N.S.

1 1.23 2.30 0.79 0.77 0.77 1.07 0.77 0.67

time (sec)

N/A 0.185 0.017 0.036 0.339 0.258 0.066 0.278 0.002

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 27 24 23 34 22 25 17

N.S.

1 1.00 1.29 1.14 1.10 1.62 1.05 1.19 0.81

time (sec)

N/A 0.149 0.010 0.036 0.189 0.251 0.044 0.271 13.453

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 53 26 38 49 53 44 17

N.S.

1 1.00 1.89 0.93 1.36 1.75 1.89 1.57 0.61

time (sec)

N/A 0.154 0.015 0.051 0.282 0.254 0.299 0.271 13.524

Problem 96

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 72 45 51 55 474 57 290

N.S.

1 1.00 2.00 1.25 1.42 1.53 13.17 1.58 8.06

time (sec)

N/A 0.175 0.034 0.067 0.292 0.266 0.793 0.287 13.410

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 91 73 40 0 147 46 41 117

N.S.

1 1.23 0.99 0.54 0.00 1.99 0.62 0.55 1.58

time (sec)

N/A 0.187 0.061 0.070 0.000 0.268 0.091 0.295 0.122

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 87 97 78 69 69 740 69 827

N.S.

1 1.05 1.17 0.94 0.83 0.83 8.92 0.83 9.96

time (sec)

N/A 0.258 0.089 0.122 0.284 0.263 0.630 0.281 13.439

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 128 147 136 105 185 874 109 897

N.S.

1 1.08 1.24 1.14 0.88 1.55 7.34 0.92 7.54

time (sec)

N/A 0.317 0.163 0.162 0.277 0.286 0.935 0.286 13.587

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 256 111 38 0 625 122 604 771

N.S.

1 1.09 0.47 0.16 0.00 2.67 0.52 2.58 3.29

time (sec)

N/A 0.455 0.081 0.159 0.000 0.283 0.640 0.540 13.521

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