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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

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 0.159 0.009 0.166 0.211 0.398 0.015 0.276 0.045

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 37 33 28 27 27 29 29 28

N.S.

1 1.12 1.00 0.85 0.82 0.82 0.88 0.88 0.85

time (sec)

N/A 0.178 0.009 0.145 0.199 0.362 0.016 0.276 0.040

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 0.185 0.006 0.133 0.214 0.348 0.017 0.269 9.028

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 34 33 28 27 27 29 29 28

N.S.

1 1.03 1.00 0.85 0.82 0.82 0.88 0.88 0.85

time (sec)

N/A 0.178 0.009 0.129 0.210 0.244 0.017 0.276 0.039

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

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 0.168 0.006 0.203 0.209 0.246 0.017 0.272 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

29 32 29 28 28 25 27 30 26

N.S.

1 1.10 1.00 0.97 0.97 0.86 0.93 1.03 0.90

time (sec)

N/A 0.171 0.011 0.111 0.193 0.246 0.046 0.283 9.003

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

26 26 26 24 24 28 20 23 24

N.S.

1 1.00 1.00 0.92 0.92 1.08 0.77 0.88 0.92

time (sec)

N/A 0.164 0.010 0.034 0.209 0.245 0.044 0.279 9.031

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

29 30 29 26 28 30 26 42 25

N.S.

1 1.03 1.00 0.90 0.97 1.03 0.90 1.45 0.86

time (sec)

N/A 0.168 0.014 0.036 0.226 0.252 0.093 0.295 0.044

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

26 26 27 25 26 29 27 28 26

N.S.

1 1.00 1.04 0.96 1.00 1.12 1.04 1.08 1.00

time (sec)

N/A 0.162 0.013 0.033 0.216 0.246 0.099 0.274 0.036

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

29 33 31 26 30 31 29 39 29

N.S.

1 1.14 1.07 0.90 1.03 1.07 1.00 1.34 1.00

time (sec)

N/A 0.174 0.019 0.027 0.213 0.380 0.196 0.286 0.053

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

31 31 33 28 29 29 32 31 29

N.S.

1 1.00 1.06 0.90 0.94 0.94 1.03 1.00 0.94

time (sec)

N/A 0.166 0.013 0.028 0.206 0.414 0.188 0.286 0.039

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

55 55 55 52 51 51 56 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 1.02 0.96 0.93

time (sec)

N/A 0.216 0.012 1.787 0.207 0.405 0.024 0.278 0.061

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

55 59 55 52 51 51 53 53 51

N.S.

1 1.07 1.00 0.95 0.93 0.93 0.96 0.96 0.93

time (sec)

N/A 0.213 0.009 1.772 0.216 0.361 0.022 0.279 0.049

Problem 14

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 56 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 1.02 0.96 0.93

time (sec)

N/A 0.198 0.012 1.797 0.204 0.258 0.025 0.272 0.051

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

42 46 51 52 51 51 53 53 51

N.S.

1 1.10 1.21 1.24 1.21 1.21 1.26 1.26 1.21

time (sec)

N/A 0.202 0.014 1.764 0.233 0.245 0.022 0.265 0.048

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

50 50 50 49 48 48 53 50 48

N.S.

1 1.00 1.00 0.98 0.96 0.96 1.06 1.00 0.96

time (sec)

N/A 0.194 0.010 1.793 0.260 0.251 0.022 0.457 0.047

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

43 50 51 51 52 49 49 53 48

N.S.

1 1.16 1.19 1.19 1.21 1.14 1.14 1.23 1.12

time (sec)

N/A 0.187 0.019 1.714 0.212 0.237 0.061 0.370 0.042

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

48 48 48 49 48 53 48 48 48

N.S.

1 1.00 1.00 1.02 1.00 1.10 1.00 1.00 1.00

time (sec)

N/A 0.191 0.021 1.724 0.207 0.242 0.059 0.366 0.051

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

51 52 49 48 52 54 48 70 48

N.S.

1 1.02 0.96 0.94 1.02 1.06 0.94 1.37 0.94

time (sec)

N/A 0.199 0.028 1.807 0.217 0.245 0.114 0.541 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

48 48 50 46 50 52 51 50 50

N.S.

1 1.00 1.04 0.96 1.04 1.08 1.06 1.04 1.04

time (sec)

N/A 0.191 0.022 1.726 0.231 0.254 0.123 0.277 0.050

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

51 52 50 46 54 55 51 72 51

N.S.

1 1.02 0.98 0.90 1.06 1.08 1.00 1.41 1.00

time (sec)

N/A 0.199 0.032 1.743 0.255 0.391 0.281 0.284 9.035

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

48 48 48 45 51 53 54 53 50

N.S.

1 1.00 1.00 0.94 1.06 1.10 1.12 1.10 1.04

time (sec)

N/A 0.189 0.023 1.713 0.202 0.478 0.313 0.289 9.035

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

51 55 53 46 55 55 56 66 51

N.S.

1 1.08 1.04 0.90 1.08 1.08 1.10 1.29 1.00

time (sec)

N/A 0.201 0.030 1.705 0.209 0.365 0.529 0.289 9.174

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

53 53 59 48 53 53 58 55 52

N.S.

1 1.00 1.11 0.91 1.00 1.00 1.09 1.04 0.98

time (sec)

N/A 0.197 0.020 1.729 0.207 0.311 0.570 0.291 9.001

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

75 75 75 76 73 73 80 77 69

N.S.

1 1.00 1.00 1.01 0.97 0.97 1.07 1.03 0.92

time (sec)

N/A 0.221 0.016 1.781 0.219 0.262 0.026 0.291 0.039

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

68 72 69 76 73 73 82 77 69

N.S.

1 1.06 1.01 1.12 1.07 1.07 1.21 1.13 1.01

time (sec)

N/A 0.231 0.021 1.767 0.224 0.251 0.028 0.286 0.032

Problem 27

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 76 73 73 82 77 69

N.S.

1 1.00 1.00 1.01 0.97 0.97 1.09 1.03 0.92

time (sec)

N/A 0.211 0.013 1.792 0.215 0.260 0.028 0.282 0.032

Problem 28

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

42 46 69 76 73 73 80 77 69

N.S.

1 1.10 1.64 1.81 1.74 1.74 1.90 1.83 1.64

time (sec)

N/A 0.193 0.021 1.773 0.219 0.270 0.028 0.288 0.032

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

70 70 70 73 70 70 76 73 65

N.S.

1 1.00 1.00 1.04 1.00 1.00 1.09 1.04 0.93

time (sec)

N/A 0.210 0.013 1.794 0.217 0.233 0.024 0.281 0.031

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

60 63 71 76 74 71 80 78 67

N.S.

1 1.05 1.18 1.27 1.23 1.18 1.33 1.30 1.12

time (sec)

N/A 0.195 0.023 1.722 0.206 0.248 0.079 0.292 0.037

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

65 65 65 71 69 75 68 70 65

N.S.

1 1.00 1.00 1.09 1.06 1.15 1.05 1.08 1.00

time (sec)

N/A 0.205 0.026 1.730 0.209 0.245 0.077 0.286 0.034

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

71 73 73 73 74 77 78 97 67

N.S.

1 1.03 1.03 1.03 1.04 1.08 1.10 1.37 0.94

time (sec)

N/A 0.223 0.033 1.764 0.212 0.238 0.128 0.269 0.041

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

69 69 71 70 73 75 75 74 68

N.S.

1 1.00 1.03 1.01 1.06 1.09 1.09 1.07 0.99

time (sec)

N/A 0.219 0.026 1.909 0.206 0.256 0.138 0.267 0.058

Problem 34

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

72 73 73 68 76 76 75 98 76

N.S.

1 1.01 1.01 0.94 1.06 1.06 1.04 1.36 1.06

time (sec)

N/A 0.221 0.034 1.879 0.238 0.243 0.306 0.276 8.875

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

68 68 68 64 73 75 78 75 73

N.S.

1 1.00 1.00 0.94 1.07 1.10 1.15 1.10 1.07

time (sec)

N/A 0.208 0.028 1.916 0.206 0.238 0.339 0.279 0.057

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

71 72 71 64 77 77 78 99 75

N.S.

1 1.01 1.00 0.90 1.08 1.08 1.10 1.39 1.06

time (sec)

N/A 0.221 0.040 2.157 0.233 0.236 0.667 0.284 0.067

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

66 66 66 63 73 75 80 77 71

N.S.

1 1.00 1.00 0.95 1.11 1.14 1.21 1.17 1.08

time (sec)

N/A 0.213 0.031 2.116 0.237 0.234 0.769 0.283 8.912

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

63 66 77 64 77 77 82 90 75

N.S.

1 1.05 1.22 1.02 1.22 1.22 1.30 1.43 1.19

time (sec)

N/A 0.201 0.036 1.873 0.222 0.236 1.272 0.276 0.082

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

73 73 73 66 75 75 83 79 74

N.S.

1 1.00 1.00 0.90 1.03 1.03 1.14 1.08 1.01

time (sec)

N/A 0.211 0.031 1.862 0.214 0.243 2.469 0.276 8.867

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

49 53 78 66 75 75 83 79 76

N.S.

1 1.08 1.59 1.35 1.53 1.53 1.69 1.61 1.55

time (sec)

N/A 0.173 0.021 1.856 0.198 0.235 3.521 0.291 8.907

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

119 93 119 123 124 274 204 133 144

N.S.

1 0.78 1.00 1.03 1.04 2.30 1.71 1.12 1.21

time (sec)

N/A 0.228 0.081 1.781 0.297 0.251 0.237 0.297 0.055

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

96 95 92 92 97 98 94 101 100

N.S.

1 0.99 0.96 0.96 1.01 1.02 0.98 1.05 1.04

time (sec)

N/A 0.266 0.045 1.772 0.231 0.250 0.190 0.292 8.933

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

98 80 98 99 100 228 180 108 118

N.S.

1 0.82 1.00 1.01 1.02 2.33 1.84 1.10 1.20

time (sec)

N/A 0.216 0.068 1.767 0.301 0.251 0.218 0.301 0.042

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

75 74 71 73 74 75 70 77 76

N.S.

1 0.99 0.95 0.97 0.99 1.00 0.93 1.03 1.01

time (sec)

N/A 0.233 0.032 1.754 0.238 0.244 0.179 0.276 0.060

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

77 67 77 75 78 178 153 85 96

N.S.

1 0.87 1.00 0.97 1.01 2.31 1.99 1.10 1.25

time (sec)

N/A 0.207 0.055 1.821 0.309 0.246 0.196 0.271 0.067

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

54 53 47 50 50 51 46 52 52

N.S.

1 0.98 0.87 0.93 0.93 0.94 0.85 0.96 0.96

time (sec)

N/A 0.206 0.023 1.821 0.216 0.240 0.154 0.271 0.071

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

58 56 57 51 53 129 90 57 70

N.S.

1 0.97 0.98 0.88 0.91 2.22 1.55 0.98 1.21

time (sec)

N/A 0.181 0.041 1.781 0.319 0.261 0.178 0.289 8.986

Problem 48

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 34 31 32 31 30 27 32 31

N.S.

1 0.97 0.89 0.91 0.89 0.86 0.77 0.91 0.89

time (sec)

N/A 0.181 0.014 1.745 0.217 0.234 0.130 0.273 0.057

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

40 40 40 34 34 99 82 34 31

N.S.

1 1.00 1.00 0.85 0.85 2.48 2.05 0.85 0.78

time (sec)

N/A 0.158 0.023 1.849 0.325 0.255 0.144 0.274 0.054

Problem 50

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 37 34 33 35 32 26 34 32

N.S.

1 1.09 1.00 0.97 1.03 0.94 0.76 1.00 0.94

time (sec)

N/A 0.186 0.016 2.074 0.208 0.230 0.392 0.288 8.984

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

42 42 42 37 36 105 82 36 35

N.S.

1 1.00 1.00 0.88 0.86 2.50 1.95 0.86 0.83

time (sec)

N/A 0.186 0.029 1.800 0.304 0.238 0.169 0.280 8.966

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

41 41 41 39 51 103 75 38 33

N.S.

1 1.00 1.00 0.95 1.24 2.51 1.83 0.93 0.80

time (sec)

N/A 0.188 0.028 1.789 0.298 0.240 0.183 0.286 0.112

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

49 51 49 46 48 47 41 71 46

N.S.

1 1.04 1.00 0.94 0.98 0.96 0.84 1.45 0.94

time (sec)

N/A 0.203 0.025 1.729 0.226 0.268 0.401 0.272 0.108

Problem 54

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 58 60 54 56 135 129 57 53

N.S.

1 0.95 0.98 0.89 0.92 2.21 2.11 0.93 0.87

time (sec)

N/A 0.175 0.058 1.946 0.298 0.254 0.212 0.273 8.991

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

70 71 70 64 70 73 61 100 70

N.S.

1 1.01 1.00 0.91 1.00 1.04 0.87 1.43 1.00

time (sec)

N/A 0.221 0.033 1.962 0.217 0.237 0.454 0.293 8.940

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

78 75 78 74 79 184 163 81 70

N.S.

1 0.96 1.00 0.95 1.01 2.36 2.09 1.04 0.90

time (sec)

N/A 0.191 0.055 1.991 0.287 0.446 0.250 0.279 8.942

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

92 93 96 86 96 98 88 126 92

N.S.

1 1.01 1.04 0.93 1.04 1.07 0.96 1.37 1.00

time (sec)

N/A 0.240 0.042 1.840 0.216 0.384 0.496 0.275 8.944

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

133 133 134 123 136 350 238 139 203

N.S.

1 1.00 1.01 0.92 1.02 2.63 1.79 1.05 1.53

time (sec)

N/A 0.416 0.113 1.802 0.342 0.548 0.419 0.280 8.881

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

105 102 93 103 107 148 104 135 121

N.S.

1 0.97 0.89 0.98 1.02 1.41 0.99 1.29 1.15

time (sec)

N/A 0.270 0.074 1.804 0.215 0.526 0.392 0.278 0.066

Problem 60

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

110 111 111 100 112 298 211 115 141

N.S.

1 1.01 1.01 0.91 1.02 2.71 1.92 1.05 1.28

time (sec)

N/A 0.357 0.092 1.827 0.288 0.252 0.387 0.273 8.857

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

83 79 72 76 82 121 78 106 86

N.S.

1 0.95 0.87 0.92 0.99 1.46 0.94 1.28 1.04

time (sec)

N/A 0.238 0.061 1.881 0.201 0.245 0.366 0.282 0.074

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

89 89 89 75 85 240 129 88 104

N.S.

1 1.00 1.00 0.84 0.96 2.70 1.45 0.99 1.17

time (sec)

N/A 0.259 0.078 1.779 0.289 0.264 0.350 0.286 8.888

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

61 58 50 59 60 81 56 70 62

N.S.

1 0.95 0.82 0.97 0.98 1.33 0.92 1.15 1.02

time (sec)

N/A 0.212 0.043 1.763 0.201 0.279 0.311 0.288 0.075

Problem 64

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

68 71 68 57 61 208 114 59 59

N.S.

1 1.04 1.00 0.84 0.90 3.06 1.68 0.87 0.87

time (sec)

N/A 0.195 0.056 1.843 0.294 0.247 0.274 0.277 8.893

Problem 65

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 39 41 38 40 44 36 37 37

N.S.

1 0.95 1.00 0.93 0.98 1.07 0.88 0.90 0.90

time (sec)

N/A 0.188 0.015 1.789 0.205 0.237 0.189 0.276 8.872

Problem 66

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

63 63 63 57 57 182 112 57 51

N.S.

1 1.00 1.00 0.90 0.90 2.89 1.78 0.90 0.81

time (sec)

N/A 0.177 0.049 1.956 0.302 0.374 0.214 0.295 8.921

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

51 53 46 48 51 70 46 52 47

N.S.

1 1.04 0.90 0.94 1.00 1.37 0.90 1.02 0.92

time (sec)

N/A 0.202 0.035 2.024 0.200 0.371 0.227 0.271 0.126

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

70 72 70 62 63 210 114 62 63

N.S.

1 1.03 1.00 0.89 0.90 3.00 1.63 0.89 0.90

time (sec)

N/A 0.209 0.036 1.822 0.295 0.396 0.262 0.287 9.029

Problem 69

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

73 72 64 76 76 117 70 80 78

N.S.

1 0.99 0.88 1.04 1.04 1.60 0.96 1.10 1.07

time (sec)

N/A 0.233 0.058 1.754 0.215 0.504 0.532 0.303 8.937

Problem 70

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

90 100 90 78 93 250 184 85 83

N.S.

1 1.11 1.00 0.87 1.03 2.78 2.04 0.94 0.92

time (sec)

N/A 0.314 0.080 1.802 0.285 0.284 0.311 0.271 8.946

Problem 71

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 96 85 96 106 154 100 150 100

N.S.

1 0.99 0.88 0.99 1.09 1.59 1.03 1.55 1.03

time (sec)

N/A 0.260 0.107 1.737 0.213 0.256 0.587 0.293 8.952

Problem 72

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

111 125 112 99 119 308 218 112 104

N.S.

1 1.13 1.01 0.89 1.07 2.77 1.96 1.01 0.94

time (sec)

N/A 0.462 0.090 1.833 0.289 0.270 0.357 0.280 8.992

Problem 73

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

140 150 133 119 147 416 252 138 177

N.S.

1 1.07 0.95 0.85 1.05 2.97 1.80 0.99 1.26

time (sec)

N/A 0.562 0.119 1.788 0.304 0.266 0.758 0.273 0.087

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

111 108 94 102 116 179 119 132 118

N.S.

1 0.97 0.85 0.92 1.05 1.61 1.07 1.19 1.06

time (sec)

N/A 0.279 0.070 1.756 0.216 0.251 0.807 0.285 8.946

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

118 126 113 95 120 358 214 111 138

N.S.

1 1.07 0.96 0.81 1.02 3.03 1.81 0.94 1.17

time (sec)

N/A 0.404 0.096 1.817 0.290 0.263 0.683 0.281 8.973

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

89 86 92 82 94 142 94 93 95

N.S.

1 0.97 1.03 0.92 1.06 1.60 1.06 1.04 1.07

time (sec)

N/A 0.242 0.039 1.765 0.229 0.252 0.694 0.288 0.092

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

95 101 92 77 94 328 194 80 92

N.S.

1 1.06 0.97 0.81 0.99 3.45 2.04 0.84 0.97

time (sec)

N/A 0.263 0.076 1.767 0.282 0.257 0.584 0.304 9.016

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

67 65 64 57 72 89 70 55 70

N.S.

1 0.97 0.96 0.85 1.07 1.33 1.04 0.82 1.04

time (sec)

N/A 0.225 0.031 1.752 0.212 0.393 0.494 0.292 8.921

Problem 79

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 95 83 76 92 301 155 78 82

N.S.

1 1.06 0.92 0.84 1.02 3.34 1.72 0.87 0.91

time (sec)

N/A 0.216 0.088 1.773 0.289 0.465 0.408 0.290 0.112

Problem 80

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 30 29 42 42 42 28 44

N.S.

1 1.00 0.94 0.91 1.31 1.31 1.31 0.88 1.38

time (sec)

N/A 0.158 0.017 1.780 0.211 0.427 0.278 0.279 8.866

Problem 81

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

92 92 84 77 92 300 150 78 82

N.S.

1 1.00 0.91 0.84 1.00 3.26 1.63 0.85 0.89

time (sec)

N/A 0.196 0.064 1.836 0.286 0.401 0.302 0.286 8.967

Problem 82

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

68 69 59 61 77 119 75 76 71

N.S.

1 1.01 0.87 0.90 1.13 1.75 1.10 1.12 1.04

time (sec)

N/A 0.222 0.053 1.822 0.201 0.239 0.294 0.288 0.145

Problem 83

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

96 107 96 82 96 324 194 82 113

N.S.

1 1.11 1.00 0.85 1.00 3.38 2.02 0.85 1.18

time (sec)

N/A 0.268 0.066 1.836 0.294 0.267 0.358 0.282 8.984

Problem 84

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

97 96 86 100 109 197 107 105 107

N.S.

1 0.99 0.89 1.03 1.12 2.03 1.10 1.08 1.10

time (sec)

N/A 0.265 0.064 1.777 0.204 0.243 0.594 0.274 8.976

Problem 85

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

117 130 119 98 128 368 226 108 114

N.S.

1 1.11 1.02 0.84 1.09 3.15 1.93 0.92 0.97

time (sec)

N/A 0.384 0.075 1.789 0.293 0.266 0.401 0.281 9.045

Problem 86

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

121 121 108 123 137 229 136 132 131

N.S.

1 1.00 0.89 1.02 1.13 1.89 1.12 1.09 1.08

time (sec)

N/A 0.292 0.084 1.789 0.207 0.249 0.668 0.280 0.132

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

140 159 140 119 154 426 260 135 135

N.S.

1 1.14 1.00 0.85 1.10 3.04 1.86 0.96 0.96

time (sec)

N/A 0.719 0.082 1.839 0.288 0.281 0.447 0.299 9.128

Problem 88

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

148 149 135 143 170 267 165 201 155

N.S.

1 1.01 0.91 0.97 1.15 1.80 1.11 1.36 1.05

time (sec)

N/A 0.339 0.129 1.809 0.214 0.427 0.697 0.290 9.113

Problem 89

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

218 214 189 178 321 368 345 245 289

N.S.

1 0.98 0.87 0.82 1.47 1.69 1.58 1.12 1.33

time (sec)

N/A 0.391 1.399 1.873 0.223 0.533 0.768 0.297 10.298

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 180 170 159 273 321 318 211 233

N.S.

1 0.99 0.94 0.88 1.51 1.77 1.76 1.17 1.29

time (sec)

N/A 0.359 1.052 1.804 0.221 0.574 0.714 0.294 9.819

Problem 91

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

125 128 147 140 225 272 287 177 177

N.S.

1 1.02 1.18 1.12 1.80 2.18 2.30 1.42 1.42

time (sec)

N/A 0.271 0.886 1.809 0.209 0.539 0.680 0.296 9.624

Problem 92

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

107 111 126 116 177 223 255 140 140

N.S.

1 1.04 1.18 1.08 1.65 2.08 2.38 1.31 1.31

time (sec)

N/A 0.247 0.615 2.114 0.211 0.269 0.626 0.297 9.673

Problem 93

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

100 94 97 91 128 172 0 103 117

N.S.

1 0.94 0.97 0.91 1.28 1.72 0.00 1.03 1.17

time (sec)

N/A 0.261 0.189 2.046 0.215 0.264 0.000 0.284 9.428

Problem 94

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

97 89 87 83 105 161 0 87 0

N.S.

1 0.92 0.90 0.86 1.08 1.66 0.00 0.90 0.00

time (sec)

N/A 0.265 0.263 1.845 0.211 0.282 0.000 0.327 0.000

Problem 95

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

80 86 99 86 96 160 0 163 0

N.S.

1 1.08 1.24 1.08 1.20 2.00 0.00 2.04 0.00

time (sec)

N/A 0.260 0.164 2.038 0.215 0.277 0.000 0.442 0.000

Problem 96

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

61 65 44 47 111 59 0 250 113

N.S.

1 1.07 0.72 0.77 1.82 0.97 0.00 4.10 1.85

time (sec)

N/A 0.228 0.164 2.007 0.216 0.268 0.000 0.696 9.256

Problem 97

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

96 99 66 66 161 85 0 310 160

N.S.

1 1.03 0.69 0.69 1.68 0.89 0.00 3.23 1.67

time (sec)

N/A 0.262 0.191 1.807 0.215 0.294 0.000 0.891 9.428

Problem 98

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

133 133 88 84 209 109 0 370 210

N.S.

1 1.00 0.66 0.63 1.57 0.82 0.00 2.78 1.58

time (sec)

N/A 0.293 0.245 1.795 0.213 0.289 0.000 1.404 9.760

Problem 99

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

170 167 110 104 257 133 0 430 260

N.S.

1 0.98 0.65 0.61 1.51 0.78 0.00 2.53 1.53

time (sec)

N/A 0.339 0.260 1.944 0.218 0.488 0.000 1.854 10.218

Problem 100

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

131 127 82 91 106 106 0 140 103

N.S.

1 0.97 0.63 0.69 0.81 0.81 0.00 1.07 0.79

time (sec)

N/A 0.278 0.088 2.415 0.226 0.426 0.000 0.294 9.127

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