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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 B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 57 55 53 94 394 149 97

N.S.

1 1.00 1.27 1.22 1.18 2.09 8.76 3.31 2.16

time (sec)

N/A 0.168 0.051 0.072 0.177 0.279 0.280 0.294 10.241

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

33 33 33 28 27 27 29 29 28

N.S.

1 1.00 1.00 0.85 0.82 0.82 0.88 0.88 0.85

time (sec)

N/A 0.177 0.005 0.034 0.182 0.257 0.017 0.281 0.045

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

33 33 33 28 27 27 29 29 28

N.S.

1 1.00 1.00 0.85 0.82 0.82 0.88 0.88 0.85

time (sec)

N/A 0.178 0.004 0.020 0.173 0.248 0.018 0.284 0.038

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

33 33 33 28 27 27 29 29 28

N.S.

1 1.00 1.00 0.85 0.82 0.82 0.88 0.88 0.85

time (sec)

N/A 0.172 0.004 0.017 0.180 0.354 0.018 0.263 0.038

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

33 33 29 28 27 27 29 29 28

N.S.

1 1.00 0.88 0.85 0.82 0.82 0.88 0.88 0.85

time (sec)

N/A 0.175 0.004 0.026 0.182 0.348 0.020 0.261 0.038

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

28 28 28 25 24 24 26 26 25

N.S.

1 1.00 1.00 0.89 0.86 0.86 0.93 0.93 0.89

time (sec)

N/A 0.164 0.004 0.011 0.175 0.352 0.020 0.264 0.038

Problem 7

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

24 24 24 22 22 22 22 22 22

N.S.

1 1.00 1.00 0.92 0.92 0.92 0.92 0.92 0.92

time (sec)

N/A 0.162 0.005 0.024 0.179 0.354 0.047 0.253 0.035

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

22 22 22 23 22 26 19 23 22

N.S.

1 1.00 1.00 1.05 1.00 1.18 0.86 1.05 1.00

time (sec)

N/A 0.161 0.007 0.016 0.174 0.578 0.069 0.256 0.042

Problem 9

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 27 28 26 25 29 27 26 25

N.S.

1 1.00 1.04 0.96 0.93 1.07 1.00 0.96 0.93

time (sec)

N/A 0.167 0.008 0.019 0.177 0.287 0.112 0.250 9.881

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

31 31 28 28 27 27 31 27 27

N.S.

1 1.00 0.90 0.90 0.87 0.87 1.00 0.87 0.87

time (sec)

N/A 0.166 0.007 0.016 0.178 0.262 0.142 0.260 0.039

Problem 11

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

33 33 29 28 27 27 31 27 28

N.S.

1 1.00 0.88 0.85 0.82 0.82 0.94 0.82 0.85

time (sec)

N/A 0.167 0.006 0.016 0.216 0.275 0.178 0.250 0.040

Problem 12

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

33 33 31 28 27 27 31 27 28

N.S.

1 1.00 0.94 0.85 0.82 0.82 0.94 0.82 0.85

time (sec)

N/A 0.166 0.008 0.016 0.201 0.246 0.214 0.250 0.040

Problem 13

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

33 33 31 28 27 27 31 27 28

N.S.

1 1.00 0.94 0.85 0.82 0.82 0.94 0.82 0.85

time (sec)

N/A 0.163 0.007 0.016 0.174 0.264 0.244 0.254 0.039

Problem 14

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

71 71 71 84 91 217 1027 340 179

N.S.

1 1.00 1.00 1.18 1.28 3.06 14.46 4.79 2.52

time (sec)

N/A 0.219 0.104 0.195 0.185 0.298 0.390 0.256 10.115

Problem 15

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

55 55 55 52 51 51 54 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 0.98 0.96 0.93

time (sec)

N/A 0.206 0.008 0.161 0.183 0.273 0.022 0.264 9.956

Problem 16

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

55 55 55 52 51 51 54 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 0.98 0.96 0.93

time (sec)

N/A 0.200 0.006 0.173 0.179 0.241 0.022 0.257 0.049

Problem 17

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

55 55 55 52 51 51 54 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 0.98 0.96 0.93

time (sec)

N/A 0.196 0.006 0.170 0.179 0.248 0.022 0.259 0.049

Problem 18

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

55 55 49 52 51 51 54 53 51

N.S.

1 1.00 0.89 0.95 0.93 0.93 0.98 0.96 0.93

time (sec)

N/A 0.204 0.008 0.161 0.182 0.248 0.024 0.262 0.050

Problem 19

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

55 55 49 52 51 51 54 53 51

N.S.

1 1.00 0.89 0.95 0.93 0.93 0.98 0.96 0.93

time (sec)

N/A 0.188 0.009 0.165 0.173 0.276 0.023 0.261 0.048

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

38 38 47 49 48 48 49 49 47

N.S.

1 1.00 1.24 1.29 1.26 1.26 1.29 1.29 1.24

time (sec)

N/A 0.182 0.008 0.155 0.180 0.337 0.023 0.276 0.046

Problem 21

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 40 43 46 46 46 46 46 45

N.S.

1 0.87 0.93 1.00 1.00 1.00 1.00 1.00 0.98

time (sec)

N/A 0.173 0.012 0.170 0.180 0.347 0.061 0.274 0.041

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

44 44 43 44 46 52 42 46 46

N.S.

1 1.00 0.98 1.00 1.05 1.18 0.95 1.05 1.05

time (sec)

N/A 0.181 0.021 0.135 0.179 0.328 0.086 0.259 0.047

Problem 23

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

44 44 44 43 46 53 46 47 46

N.S.

1 1.00 1.00 0.98 1.05 1.20 1.05 1.07 1.05

time (sec)

N/A 0.179 0.017 0.152 0.177 0.328 0.180 0.269 9.993

Problem 24

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 49 47 46 50 53 54 51 48

N.S.

1 1.00 0.96 0.94 1.02 1.08 1.10 1.04 0.98

time (sec)

N/A 0.188 0.017 0.161 0.178 0.564 0.271 0.267 9.947

Problem 25

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

53 45 50 48 51 51 56 51 49

N.S.

1 0.85 0.94 0.91 0.96 0.96 1.06 0.96 0.92

time (sec)

N/A 0.157 0.010 0.163 0.181 0.242 0.346 0.265 0.038

Problem 26

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

55 55 53 48 51 51 56 51 51

N.S.

1 1.00 0.96 0.87 0.93 0.93 1.02 0.93 0.93

time (sec)

N/A 0.182 0.011 0.157 0.179 0.255 0.441 0.262 0.037

Problem 27

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

96 96 87 112 129 381 2026 603 291

N.S.

1 1.00 0.91 1.17 1.34 3.97 21.10 6.28 3.03

time (sec)

N/A 0.242 0.114 0.182 0.184 0.270 0.534 0.293 10.167

Problem 28

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

75 75 75 75 73 73 80 77 69

N.S.

1 1.00 1.00 1.00 0.97 0.97 1.07 1.03 0.92

time (sec)

N/A 0.230 0.013 0.134 0.179 0.266 0.025 0.249 0.040

Problem 29

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

75 75 75 75 73 73 82 77 69

N.S.

1 1.00 1.00 1.00 0.97 0.97 1.09 1.03 0.92

time (sec)

N/A 0.222 0.009 0.118 0.182 0.277 0.024 0.258 0.032

Problem 30

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

75 75 75 75 73 73 82 77 69

N.S.

1 1.00 1.00 1.00 0.97 0.97 1.09 1.03 0.92

time (sec)

N/A 0.217 0.008 0.026 0.172 0.285 0.025 0.253 0.032

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

75 75 75 75 73 73 80 77 69

N.S.

1 1.00 1.00 1.00 0.97 0.97 1.07 1.03 0.92

time (sec)

N/A 0.227 0.008 0.023 0.184 0.291 0.026 0.256 0.031

Problem 32

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

75 75 75 75 73 73 82 77 69

N.S.

1 1.00 1.00 1.00 0.97 0.97 1.09 1.03 0.92

time (sec)

N/A 0.216 0.007 0.015 0.178 0.272 0.025 0.267 0.032

Problem 33

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

62 62 67 76 73 73 80 76 68

N.S.

1 1.00 1.08 1.23 1.18 1.18 1.29 1.23 1.10

time (sec)

N/A 0.210 0.010 0.016 0.189 0.252 0.026 0.246 0.031

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 67 73 69 69 73 72 65

N.S.

1 1.00 1.76 1.92 1.82 1.82 1.92 1.89 1.71

time (sec)

N/A 0.180 0.007 0.014 0.176 0.259 0.026 0.254 0.031

Problem 35

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

66 53 63 70 68 68 73 70 63

N.S.

1 0.80 0.95 1.06 1.03 1.03 1.11 1.06 0.95

time (sec)

N/A 0.188 0.016 0.019 0.179 0.362 0.075 0.255 0.037

Problem 36

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 65 67 69 69 75 70 71 65

N.S.

1 1.00 1.03 1.06 1.06 1.15 1.08 1.09 1.00

time (sec)

N/A 0.222 0.024 0.023 0.178 0.318 0.108 0.249 0.040

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

65 65 71 63 69 74 68 69 70

N.S.

1 1.00 1.09 0.97 1.06 1.14 1.05 1.06 1.08

time (sec)

N/A 0.215 0.013 0.021 0.183 0.319 0.187 0.258 9.897

Problem 38

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

64 64 73 61 69 75 73 70 70

N.S.

1 1.00 1.14 0.95 1.08 1.17 1.14 1.09 1.09

time (sec)

N/A 0.211 0.022 0.022 0.177 0.334 0.371 0.257 0.066

Problem 39

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

69 58 71 64 72 75 80 73 71

N.S.

1 0.84 1.03 0.93 1.04 1.09 1.16 1.06 1.03

time (sec)

N/A 0.191 0.022 0.028 0.184 0.515 0.560 0.255 0.077

Problem 40

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

71 45 72 66 73 73 82 75 71

N.S.

1 0.63 1.01 0.93 1.03 1.03 1.15 1.06 1.00

time (sec)

N/A 0.161 0.013 0.021 0.178 0.281 0.704 0.260 9.902

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

75 75 74 66 73 73 82 75 73

N.S.

1 1.00 0.99 0.88 0.97 0.97 1.09 1.00 0.97

time (sec)

N/A 0.210 0.013 0.020 0.178 0.268 0.866 0.256 0.046

Problem 42

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

75 75 75 66 73 73 82 75 74

N.S.

1 1.00 1.00 0.88 0.97 0.97 1.09 1.00 0.99

time (sec)

N/A 0.204 0.013 0.020 0.174 0.253 1.093 0.254 0.045

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

87 87 80 82 93 94 85 95 94

N.S.

1 1.00 0.92 0.94 1.07 1.08 0.98 1.09 1.08

time (sec)

N/A 0.249 0.020 0.048 0.187 0.258 0.128 0.247 0.051

Problem 44

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

66 66 61 63 69 71 61 70 72

N.S.

1 1.00 0.92 0.95 1.05 1.08 0.92 1.06 1.09

time (sec)

N/A 0.222 0.015 0.029 0.178 0.262 0.116 0.249 9.992

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

45 45 41 43 46 47 37 46 46

N.S.

1 1.00 0.91 0.96 1.02 1.04 0.82 1.02 1.02

time (sec)

N/A 0.193 0.010 0.026 0.182 0.268 0.097 0.261 10.035

Problem 46

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 26 25 24 20 26 26

N.S.

1 1.00 1.00 1.04 1.00 0.96 0.80 1.04 1.04

time (sec)

N/A 0.167 0.006 0.023 0.179 0.263 0.079 0.251 0.047

Problem 47

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 35 29 30 30 29 41 32 28

N.S.

1 1.17 0.97 1.00 1.00 0.97 1.37 1.07 0.93

time (sec)

N/A 0.185 0.007 0.028 0.180 0.303 0.218 0.249 0.100

Problem 48

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

43 43 42 44 43 41 95 51 33

N.S.

1 1.00 0.98 1.02 1.00 0.95 2.21 1.19 0.77

time (sec)

N/A 0.187 0.014 0.049 0.175 0.262 0.185 0.251 0.091

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

62 62 58 62 63 68 131 75 73

N.S.

1 1.00 0.94 1.00 1.02 1.10 2.11 1.21 1.18

time (sec)

N/A 0.208 0.021 0.045 0.179 0.264 0.228 0.261 0.090

Problem 50

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

86 86 81 82 89 94 165 99 97

N.S.

1 1.00 0.94 0.95 1.03 1.09 1.92 1.15 1.13

time (sec)

N/A 0.232 0.034 0.043 0.181 0.279 0.252 0.264 0.098

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

90 90 87 92 98 139 92 102 115

N.S.

1 1.00 0.97 1.02 1.09 1.54 1.02 1.13 1.28

time (sec)

N/A 0.260 0.035 0.033 0.189 0.266 0.222 0.258 9.753

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

69 69 66 67 75 111 68 77 77

N.S.

1 1.00 0.96 0.97 1.09 1.61 0.99 1.12 1.12

time (sec)

N/A 0.226 0.032 0.030 0.174 0.250 0.190 0.253 0.061

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

45 45 41 47 50 69 44 48 56

N.S.

1 1.00 0.91 1.04 1.11 1.53 0.98 1.07 1.24

time (sec)

N/A 0.194 0.019 0.027 0.182 0.254 0.144 0.253 9.683

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

32 32 31 32 35 39 27 33 31

N.S.

1 1.00 0.97 1.00 1.09 1.22 0.84 1.03 0.97

time (sec)

N/A 0.178 0.009 0.027 0.178 0.255 0.097 0.252 0.046

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

42 42 38 41 43 61 32 47 40

N.S.

1 1.00 0.90 0.98 1.02 1.45 0.76 1.12 0.95

time (sec)

N/A 0.191 0.018 0.033 0.179 0.267 0.139 0.253 9.894

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

65 81 56 63 69 111 128 74 57

N.S.

1 1.25 0.86 0.97 1.06 1.71 1.97 1.14 0.88

time (sec)

N/A 0.250 0.025 0.039 0.180 0.275 0.256 0.251 0.091

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

85 85 85 85 100 151 184 107 105

N.S.

1 1.00 1.00 1.00 1.18 1.78 2.16 1.26 1.24

time (sec)

N/A 0.246 0.047 0.044 0.182 0.275 0.290 0.247 9.895

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

113 113 106 107 129 180 219 134 132

N.S.

1 1.00 0.94 0.95 1.14 1.59 1.94 1.19 1.17

time (sec)

N/A 0.276 0.059 0.046 0.180 0.296 0.322 0.252 10.054

Problem 59

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

94 94 86 92 106 167 107 99 108

N.S.

1 1.00 0.91 0.98 1.13 1.78 1.14 1.05 1.15

time (sec)

N/A 0.262 0.036 0.032 0.183 0.282 0.374 0.251 9.995

Problem 60

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

71 71 75 71 83 131 83 70 87

N.S.

1 1.00 1.06 1.00 1.17 1.85 1.17 0.99 1.23

time (sec)

N/A 0.225 0.018 0.034 0.184 0.260 0.282 0.251 9.964

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

55 55 54 51 63 79 63 52 63

N.S.

1 1.00 0.98 0.93 1.15 1.44 1.15 0.95 1.15

time (sec)

N/A 0.202 0.018 0.029 0.200 0.263 0.172 0.246 9.834

Problem 62

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

36 28 26 25 38 38 39 24 39

N.S.

1 0.78 0.72 0.69 1.06 1.06 1.08 0.67 1.08

time (sec)

N/A 0.148 0.006 0.026 0.176 0.264 0.134 0.250 9.816

Problem 63

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

57 57 53 55 68 109 63 59 62

N.S.

1 1.00 0.93 0.96 1.19 1.91 1.11 1.04 1.09

time (sec)

N/A 0.201 0.028 0.036 0.184 0.256 0.204 0.254 0.067

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 81 83 104 195 168 103 84

N.S.

1 1.00 0.92 0.94 1.18 2.22 1.91 1.17 0.95

time (sec)

N/A 0.248 0.032 0.045 0.183 0.280 0.318 0.252 9.748

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 128 102 106 136 234 219 127 132

N.S.

1 1.16 0.93 0.96 1.24 2.13 1.99 1.15 1.20

time (sec)

N/A 0.311 0.054 0.047 0.179 0.264 0.364 0.251 9.780

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

140 140 129 132 165 263 262 159 163

N.S.

1 1.00 0.92 0.94 1.18 1.88 1.87 1.14 1.16

time (sec)

N/A 0.327 0.082 0.056 0.179 0.284 0.417 0.257 9.798

Problem 67

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

200 192 175 133 288 349 270 186 267

N.S.

1 0.96 0.88 0.66 1.44 1.74 1.35 0.93 1.34

time (sec)

N/A 0.356 0.840 0.188 0.184 0.269 0.457 0.269 10.744

Problem 68

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

165 160 201 116 242 302 238 158 215

N.S.

1 0.97 1.22 0.70 1.47 1.83 1.44 0.96 1.30

time (sec)

N/A 0.307 0.679 0.181 0.179 0.261 0.474 0.273 10.488

Problem 69

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

113 112 137 102 198 253 206 130 165

N.S.

1 0.99 1.21 0.90 1.75 2.24 1.82 1.15 1.46

time (sec)

N/A 0.237 0.554 0.148 0.179 0.277 0.544 0.267 10.339

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

97 97 122 82 154 204 167 100 127

N.S.

1 1.00 1.26 0.85 1.59 2.10 1.72 1.03 1.31

time (sec)

N/A 0.214 0.394 0.133 0.192 0.276 0.420 0.269 10.415

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

92 82 87 61 109 153 0 75 101

N.S.

1 0.89 0.95 0.66 1.18 1.66 0.00 0.82 1.10

time (sec)

N/A 0.223 0.123 0.118 0.188 0.265 0.000 0.278 10.248

Problem 72

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

83 77 82 57 89 138 0 80 0

N.S.

1 0.93 0.99 0.69 1.07 1.66 0.00 0.96 0.00

time (sec)

N/A 0.224 0.179 0.142 0.179 0.270 0.000 0.268 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 74 91 61 85 141 0 140 0

N.S.

1 1.01 1.25 0.84 1.16 1.93 0.00 1.92 0.00

time (sec)

N/A 0.224 0.119 0.119 0.184 0.284 0.000 0.281 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 36 37 100 55 0 191 100

N.S.

1 1.00 0.63 0.65 1.75 0.96 0.00 3.35 1.75

time (sec)

N/A 0.196 0.119 0.128 0.190 0.263 0.000 0.275 10.446

Problem 75

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

90 89 56 54 146 80 0 251 146

N.S.

1 0.99 0.62 0.60 1.62 0.89 0.00 2.79 1.62

time (sec)

N/A 0.235 0.137 0.165 0.178 0.268 0.000 0.267 10.611

Problem 76

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

125 121 78 70 192 105 0 311 192

N.S.

1 0.97 0.62 0.56 1.54 0.84 0.00 2.49 1.54

time (sec)

N/A 0.262 0.168 0.195 0.179 0.267 0.000 0.267 10.976

Problem 77

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

160 153 100 88 238 129 0 371 238

N.S.

1 0.96 0.62 0.55 1.49 0.81 0.00 2.32 1.49

time (sec)

N/A 0.301 0.189 0.205 0.176 0.253 0.000 0.268 11.111

Problem 78

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

195 185 123 105 284 153 0 431 284

N.S.

1 0.95 0.63 0.54 1.46 0.78 0.00 2.21 1.46

time (sec)

N/A 0.344 0.219 0.284 0.187 0.246 0.000 0.270 11.561

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 229 258 167 370 446 502 247 0

N.S.

1 0.96 1.08 0.70 1.55 1.87 2.11 1.04 0.00

time (sec)

N/A 0.389 1.324 0.234 0.185 0.266 0.533 0.276 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

203 197 236 148 324 399 444 220 0

N.S.

1 0.97 1.16 0.73 1.60 1.97 2.19 1.08 0.00

time (sec)

N/A 0.347 1.076 0.217 0.187 0.283 0.533 0.275 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 149 219 133 280 350 386 192 0

N.S.

1 0.99 1.45 0.88 1.85 2.32 2.56 1.27 0.00

time (sec)

N/A 0.268 0.882 0.178 0.179 0.274 0.598 0.273 0.000

Problem 82

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

134 134 167 116 236 297 326 160 208

N.S.

1 1.00 1.25 0.87 1.76 2.22 2.43 1.19 1.55

time (sec)

N/A 0.247 0.722 0.167 0.183 0.267 0.470 0.269 10.384

Problem 83

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

132 124 181 99 189 256 490 136 0

N.S.

1 0.94 1.37 0.75 1.43 1.94 3.71 1.03 0.00

time (sec)

N/A 0.257 0.570 0.148 0.186 0.276 2.120 0.273 0.000

Problem 84

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

126 118 110 82 147 205 0 107 0

N.S.

1 0.94 0.87 0.65 1.17 1.63 0.00 0.85 0.00

time (sec)

N/A 0.266 0.184 0.143 0.178 0.259 0.000 0.273 0.000

Problem 85

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

118 103 101 73 129 186 0 107 0

N.S.

1 0.87 0.86 0.62 1.09 1.58 0.00 0.91 0.00

time (sec)

N/A 0.252 0.319 0.141 0.177 0.259 0.000 0.281 0.000

Problem 86

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

120 106 111 78 146 170 0 170 0

N.S.

1 0.88 0.92 0.65 1.22 1.42 0.00 1.42 0.00

time (sec)

N/A 0.265 0.234 0.167 0.188 0.250 0.000 0.282 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 97 100 78 158 188 0 259 0

N.S.

1 1.02 1.05 0.82 1.66 1.98 0.00 2.73 0.00

time (sec)

N/A 0.258 0.193 0.162 0.177 0.258 0.000 0.281 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 36 39 176 78 0 311 142

N.S.

1 1.00 0.63 0.68 3.09 1.37 0.00 5.46 2.49

time (sec)

N/A 0.194 0.178 0.169 0.190 0.249 0.000 0.271 11.009

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 89 56 56 222 104 0 371 188

N.S.

1 0.99 0.62 0.62 2.47 1.16 0.00 4.12 2.09

time (sec)

N/A 0.228 0.213 0.190 0.183 0.254 0.000 0.266 11.583

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 121 79 73 268 130 0 431 234

N.S.

1 0.97 0.63 0.58 2.14 1.04 0.00 3.45 1.87

time (sec)

N/A 0.266 0.257 0.248 0.190 0.259 0.000 0.266 11.861

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 153 100 90 314 153 0 491 280

N.S.

1 0.96 0.62 0.56 1.96 0.96 0.00 3.07 1.75

time (sec)

N/A 0.303 0.290 0.296 0.192 0.258 0.000 0.279 12.400

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 185 122 106 360 177 0 551 326

N.S.

1 0.95 0.63 0.54 1.85 0.91 0.00 2.83 1.67

time (sec)

N/A 0.333 0.124 0.362 0.197 0.281 0.000 0.299 13.116

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

276 266 296 265 452 541 826 307 0

N.S.

1 0.96 1.07 0.96 1.64 1.96 2.99 1.11 0.00

time (sec)

N/A 0.428 1.892 0.172 0.183 0.278 0.649 0.291 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

241 234 277 241 406 496 741 280 0

N.S.

1 0.97 1.15 1.00 1.68 2.06 3.07 1.16 0.00

time (sec)

N/A 0.391 1.585 0.152 0.184 0.270 0.589 0.285 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 186 257 217 362 447 656 251 0

N.S.

1 0.98 1.36 1.15 1.92 2.37 3.47 1.33 0.00

time (sec)

N/A 0.303 1.382 0.125 0.193 0.278 0.679 0.282 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 171 238 193 318 392 570 219 0

N.S.

1 1.00 1.39 1.13 1.86 2.29 3.33 1.28 0.00

time (sec)

N/A 0.287 1.074 0.106 0.187 0.268 0.548 0.293 0.000

Problem 97

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

170 161 212 169 271 351 886 196 0

N.S.

1 0.95 1.25 0.99 1.59 2.06 5.21 1.15 0.00

time (sec)

N/A 0.294 0.935 0.109 0.193 0.274 3.129 0.297 0.000

Problem 98

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

169 161 200 116 226 304 796 168 0

N.S.

1 0.95 1.18 0.69 1.34 1.80 4.71 0.99 0.00

time (sec)

N/A 0.312 0.743 0.177 0.187 0.282 0.805 0.276 0.000

Problem 99

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

155 144 129 97 187 253 0 139 0

N.S.

1 0.93 0.83 0.63 1.21 1.63 0.00 0.90 0.00

time (sec)

N/A 0.298 0.233 0.177 0.194 0.268 0.000 0.283 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 140 126 92 0 240 0 139 0

N.S.

1 0.92 0.82 0.60 0.00 1.57 0.00 0.91 0.00

time (sec)

N/A 0.301 0.449 0.204 0.000 0.267 0.000 0.284 0.000

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