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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 0.013 0.005 0.123 0.197 0.258 0.016 0.286 4.809

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 0.021 0.006 0.080 0.179 0.250 0.017 0.283 0.038

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

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 0.009 0.005 0.113 0.190 0.263 0.020 0.279 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

29 29 29 27 28 25 27 30 26

N.S.

1 1.00 1.00 0.93 0.97 0.86 0.93 1.03 0.90

time (sec)

N/A 0.014 0.007 0.066 0.194 0.259 0.045 0.267 0.035

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

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 0.013 0.007 0.027 0.198 0.260 0.040 0.290 0.041

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 29 29 26 28 30 26 42 25

N.S.

1 1.00 1.00 0.90 0.97 1.03 0.90 1.45 0.86

time (sec)

N/A 0.021 0.008 0.031 0.195 0.250 0.099 0.286 0.044

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 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 0.011 0.010 0.027 0.179 0.268 0.100 0.275 4.878

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 29 31 26 30 31 29 39 29

N.S.

1 1.00 1.07 0.90 1.03 1.07 1.00 1.34 1.00

time (sec)

N/A 0.018 0.012 0.028 0.183 0.251 0.180 0.271 0.052

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

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 0.014 0.008 0.026 0.186 0.249 0.191 0.291 0.038

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

33 33 35 28 29 29 32 31 30

N.S.

1 1.00 1.06 0.85 0.88 0.88 0.97 0.94 0.91

time (sec)

N/A 0.016 0.007 0.026 0.190 0.245 0.260 0.291 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

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 0.026 0.007 2.480 0.199 0.256 0.021 0.277 0.055

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

42 42 51 52 51 51 53 53 51

N.S.

1 1.00 1.21 1.24 1.21 1.21 1.26 1.26 1.21

time (sec)

N/A 0.051 0.009 2.583 0.197 0.269 0.021 0.284 0.058

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

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 0.021 0.005 2.521 0.186 0.266 0.022 0.296 0.046

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

43 43 51 49 52 49 49 53 48

N.S.

1 1.00 1.19 1.14 1.21 1.14 1.14 1.23 1.12

time (sec)

N/A 0.023 0.011 2.554 0.180 0.279 0.059 0.277 0.041

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

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 0.020 0.011 2.472 0.199 0.267 0.060 0.304 0.051

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

51 51 49 48 52 54 48 70 48

N.S.

1 1.00 0.96 0.94 1.02 1.06 0.94 1.37 0.94

time (sec)

N/A 0.036 0.016 2.509 0.186 0.271 0.123 0.290 0.046

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

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 0.020 0.014 2.483 0.188 0.261 0.118 0.285 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

51 51 50 46 54 55 51 72 51

N.S.

1 1.00 0.98 0.90 1.06 1.08 1.00 1.41 1.00

time (sec)

N/A 0.027 0.018 2.510 0.185 0.290 0.268 0.277 4.915

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

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 0.021 0.015 2.505 0.187 0.255 0.303 0.277 4.854

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

51 51 54 46 55 55 56 66 51

N.S.

1 1.00 1.06 0.90 1.08 1.08 1.10 1.29 1.00

time (sec)

N/A 0.026 0.019 2.503 0.181 0.297 0.516 0.283 4.893

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

53 53 56 48 53 53 58 55 52

N.S.

1 1.00 1.06 0.91 1.00 1.00 1.09 1.04 0.98

time (sec)

N/A 0.019 0.012 2.490 0.207 0.297 0.560 0.269 0.039

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 55 48 53 53 58 55 53

N.S.

1 1.00 1.15 1.00 1.10 1.10 1.21 1.15 1.10

time (sec)

N/A 0.022 0.019 2.491 0.188 0.276 0.832 0.408 0.037

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

117 117 117 121 119 119 136 125 107

N.S.

1 1.00 1.00 1.03 1.02 1.02 1.16 1.07 0.91

time (sec)

N/A 0.119 0.013 2.540 0.192 0.309 0.027 0.384 4.962

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

117 117 117 121 119 119 138 125 107

N.S.

1 1.00 1.00 1.03 1.02 1.02 1.18 1.07 0.91

time (sec)

N/A 0.063 0.012 2.543 0.184 0.306 0.028 0.286 0.043

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

122 122 117 121 119 119 136 125 107

N.S.

1 1.00 0.96 0.99 0.98 0.98 1.11 1.02 0.88

time (sec)

N/A 0.230 0.011 2.521 0.182 0.268 0.038 0.302 0.043

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

117 117 117 121 119 119 136 125 107

N.S.

1 1.00 1.00 1.03 1.02 1.02 1.16 1.07 0.91

time (sec)

N/A 0.053 0.010 2.534 0.184 0.282 0.026 0.289 0.042

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

95 95 107 120 119 119 133 124 107

N.S.

1 1.00 1.13 1.26 1.25 1.25 1.40 1.31 1.13

time (sec)

N/A 0.154 0.016 2.502 0.181 0.313 0.036 0.283 0.042

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

117 117 117 121 119 119 136 125 107

N.S.

1 1.00 1.00 1.03 1.02 1.02 1.16 1.07 0.91

time (sec)

N/A 0.049 0.011 2.500 0.179 0.259 0.034 0.279 0.042

Problem 29

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

67 67 114 119 118 118 131 123 106

N.S.

1 1.00 1.70 1.78 1.76 1.76 1.96 1.84 1.58

time (sec)

N/A 0.109 0.010 2.493 0.184 0.277 0.030 0.289 0.042

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

117 117 117 120 119 119 134 124 106

N.S.

1 1.00 1.00 1.03 1.02 1.02 1.15 1.06 0.91

time (sec)

N/A 0.062 0.011 2.487 0.184 0.269 0.028 0.286 0.043

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 107 120 119 119 133 124 107

N.S.

1 1.00 2.55 2.86 2.83 2.83 3.17 2.95 2.55

time (sec)

N/A 0.047 0.017 2.490 0.184 0.277 0.030 0.300 0.044

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

109 109 109 117 115 115 129 121 103

N.S.

1 1.00 1.00 1.07 1.06 1.06 1.18 1.11 0.94

time (sec)

N/A 0.037 0.016 2.599 0.196 0.265 0.030 0.274 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

88 88 113 119 120 117 134 126 105

N.S.

1 1.00 1.28 1.35 1.36 1.33 1.52 1.43 1.19

time (sec)

N/A 0.064 0.021 2.475 0.203 0.251 0.109 0.278 0.047

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

108 108 108 121 116 121 126 120 104

N.S.

1 1.00 1.00 1.12 1.07 1.12 1.17 1.11 0.96

time (sec)

N/A 0.040 0.020 2.472 0.195 0.272 0.103 0.286 0.043

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

113 113 115 121 120 123 131 145 105

N.S.

1 1.00 1.02 1.07 1.06 1.09 1.16 1.28 0.93

time (sec)

N/A 0.085 0.027 2.570 0.192 0.294 0.155 0.280 0.052

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

108 108 110 118 118 121 128 122 106

N.S.

1 1.00 1.02 1.09 1.09 1.12 1.19 1.13 0.98

time (sec)

N/A 0.043 0.022 2.553 0.179 0.271 0.171 0.271 0.047

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

112 112 112 117 122 123 128 149 113

N.S.

1 1.00 1.00 1.04 1.09 1.10 1.14 1.33 1.01

time (sec)

N/A 0.076 0.026 2.562 0.182 0.248 0.331 0.284 4.936

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

111 111 111 113 120 121 129 123 111

N.S.

1 1.00 1.00 1.02 1.08 1.09 1.16 1.11 1.00

time (sec)

N/A 0.053 0.022 2.563 0.180 0.303 0.377 0.299 0.048

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

114 114 116 111 123 123 128 151 118

N.S.

1 1.00 1.02 0.97 1.08 1.08 1.12 1.32 1.04

time (sec)

N/A 0.075 0.025 2.569 0.198 0.292 0.728 0.287 0.052

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

111 111 111 108 120 121 131 124 116

N.S.

1 1.00 1.00 0.97 1.08 1.09 1.18 1.12 1.05

time (sec)

N/A 0.048 0.025 2.565 0.196 0.292 0.830 0.290 0.069

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

112 112 116 106 123 123 129 150 122

N.S.

1 1.00 1.04 0.95 1.10 1.10 1.15 1.34 1.09

time (sec)

N/A 0.073 0.036 2.604 0.187 0.274 1.522 0.292 4.926

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

108 108 115 102 119 121 129 123 119

N.S.

1 1.00 1.06 0.94 1.10 1.12 1.19 1.14 1.10

time (sec)

N/A 0.045 0.022 2.447 0.194 0.256 3.124 0.297 4.923

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

113 113 116 102 123 123 129 147 121

N.S.

1 1.00 1.03 0.90 1.09 1.09 1.14 1.30 1.07

time (sec)

N/A 0.072 0.037 2.575 0.204 0.302 5.022 0.299 4.945

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

108 108 122 101 119 121 131 125 119

N.S.

1 1.00 1.13 0.94 1.10 1.12 1.21 1.16 1.10

time (sec)

N/A 0.048 0.028 2.566 0.195 0.268 35.602 0.279 0.080

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

91 91 118 102 123 123 133 138 121

N.S.

1 1.00 1.30 1.12 1.35 1.35 1.46 1.52 1.33

time (sec)

N/A 0.043 0.036 2.574 0.199 0.284 27.098 0.298 0.095

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 113 119 104 121 121 0 127 120

N.S.

1 1.00 1.05 0.92 1.07 1.07 0.00 1.12 1.06

time (sec)

N/A 0.046 0.020 2.553 0.185 0.288 0.000 0.287 4.978

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 118 104 121 121 134 127 121

N.S.

1 1.00 2.46 2.17 2.52 2.52 2.79 2.65 2.52

time (sec)

N/A 0.022 0.020 2.526 0.182 0.288 135.983 0.295 0.066

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 121 104 121 121 0 127 121

N.S.

1 1.00 1.03 0.89 1.03 1.03 0.00 1.09 1.03

time (sec)

N/A 0.043 0.020 2.552 0.183 0.244 0.000 0.299 0.066

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 121 104 121 121 0 127 120

N.S.

1 1.00 1.59 1.37 1.59 1.59 0.00 1.67 1.58

time (sec)

N/A 0.039 0.019 2.545 0.190 0.252 0.000 0.297 4.914

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 117 104 121 121 0 127 122

N.S.

1 1.00 1.00 0.89 1.03 1.03 0.00 1.09 1.04

time (sec)

N/A 0.043 0.030 2.568 0.198 0.247 0.000 0.301 0.066

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 121 104 121 121 0 127 121

N.S.

1 1.00 1.03 0.89 1.03 1.03 0.00 1.09 1.03

time (sec)

N/A 0.060 0.020 2.569 0.187 0.256 0.000 0.292 0.066

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 117 104 121 121 0 127 122

N.S.

1 1.00 1.00 0.89 1.03 1.03 0.00 1.09 1.04

time (sec)

N/A 0.043 0.027 2.577 0.188 0.255 0.000 0.299 0.070

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 121 104 121 121 0 127 122

N.S.

1 1.00 1.03 0.89 1.03 1.03 0.00 1.09 1.04

time (sec)

N/A 0.060 0.020 2.576 0.183 0.254 0.000 0.308 0.068

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 117 104 121 121 0 127 122

N.S.

1 1.00 1.00 0.89 1.03 1.03 0.00 1.09 1.04

time (sec)

N/A 0.043 0.027 2.572 0.191 0.255 0.000 0.289 5.028

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 121 104 121 121 0 127 122

N.S.

1 1.00 1.03 0.89 1.03 1.03 0.00 1.09 1.04

time (sec)

N/A 0.060 0.021 2.572 0.202 0.307 0.000 0.294 0.069

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

98 98 98 99 100 228 180 108 118

N.S.

1 1.00 1.00 1.01 1.02 2.33 1.84 1.10 1.20

time (sec)

N/A 0.046 0.049 2.609 0.271 0.262 0.229 0.285 5.057

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

75 75 71 68 74 75 70 77 76

N.S.

1 1.00 0.95 0.91 0.99 1.00 0.93 1.03 1.01

time (sec)

N/A 0.062 0.022 2.488 0.191 0.260 0.180 0.285 4.887

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

77 77 77 75 78 178 153 85 96

N.S.

1 1.00 1.00 0.97 1.01 2.31 1.99 1.10 1.25

time (sec)

N/A 0.050 0.033 2.501 0.283 0.303 0.208 0.295 0.064

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

54 54 47 49 50 51 46 52 52

N.S.

1 1.00 0.87 0.91 0.93 0.94 0.85 0.96 0.96

time (sec)

N/A 0.047 0.014 2.522 0.188 0.249 0.155 0.293 4.911

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

58 58 57 51 53 129 90 57 70

N.S.

1 1.00 0.98 0.88 0.91 2.22 1.55 0.98 1.21

time (sec)

N/A 0.023 0.027 2.595 0.265 0.274 0.194 0.282 4.995

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

35 35 31 32 31 30 27 32 31

N.S.

1 1.00 0.89 0.91 0.89 0.86 0.77 0.91 0.89

time (sec)

N/A 0.023 0.009 2.465 0.188 0.254 0.137 0.297 0.056

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 40 34 34 99 82 34 31

N.S.

1 1.00 1.03 0.87 0.87 2.54 2.10 0.87 0.79

time (sec)

N/A 0.011 0.018 2.472 0.292 0.276 0.144 0.280 4.922

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

34 34 34 33 35 32 26 36 32

N.S.

1 1.00 1.00 0.97 1.03 0.94 0.76 1.06 0.94

time (sec)

N/A 0.023 0.010 2.490 0.189 0.259 0.425 0.275 0.094

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 42 37 36 105 82 36 35

N.S.

1 1.00 0.98 0.86 0.84 2.44 1.91 0.84 0.81

time (sec)

N/A 0.015 0.018 2.493 0.268 0.281 0.177 0.290 0.061

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

50 50 49 46 48 47 41 71 46

N.S.

1 1.00 0.98 0.92 0.96 0.94 0.82 1.42 0.92

time (sec)

N/A 0.037 0.015 2.501 0.198 0.258 0.428 0.275 5.028

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

59 59 60 54 56 135 129 57 53

N.S.

1 1.00 1.02 0.92 0.95 2.29 2.19 0.97 0.90

time (sec)

N/A 0.028 0.036 2.520 0.273 0.259 0.222 0.301 0.071

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

69 69 70 64 70 73 61 100 70

N.S.

1 1.00 1.01 0.93 1.01 1.06 0.88 1.45 1.01

time (sec)

N/A 0.048 0.020 2.504 0.184 0.280 0.457 0.281 4.987

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 78 74 79 184 163 81 70

N.S.

1 1.00 0.98 0.92 0.99 2.30 2.04 1.01 0.88

time (sec)

N/A 0.038 0.036 2.510 0.275 0.273 0.269 0.286 4.927

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

93 93 96 86 96 98 88 126 92

N.S.

1 1.00 1.03 0.92 1.03 1.05 0.95 1.35 0.99

time (sec)

N/A 0.058 0.026 2.515 0.203 0.284 0.514 0.283 5.016

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

99 99 101 91 103 234 187 106 89

N.S.

1 1.00 1.02 0.92 1.04 2.36 1.89 1.07 0.90

time (sec)

N/A 0.044 0.047 2.516 0.279 0.276 0.299 0.281 0.096

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

126 126 113 122 131 172 131 159 181

N.S.

1 1.00 0.90 0.97 1.04 1.37 1.04 1.26 1.44

time (sec)

N/A 0.123 0.051 2.490 0.188 0.254 0.442 0.293 5.018

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

131 131 134 123 136 350 238 139 203

N.S.

1 1.00 1.02 0.94 1.04 2.67 1.82 1.06 1.55

time (sec)

N/A 0.101 0.069 2.624 0.269 0.285 0.417 0.274 5.008

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

104 104 93 102 107 148 104 135 121

N.S.

1 1.00 0.89 0.98 1.03 1.42 1.00 1.30 1.16

time (sec)

N/A 0.084 0.044 2.598 0.196 0.277 0.422 0.282 4.974

Problem 74

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

110 110 111 100 112 298 211 115 141

N.S.

1 1.00 1.01 0.91 1.02 2.71 1.92 1.05 1.28

time (sec)

N/A 0.080 0.059 2.658 0.303 0.283 0.394 0.287 0.057

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

82 82 72 76 82 121 78 106 86

N.S.

1 1.00 0.88 0.93 1.00 1.48 0.95 1.29 1.05

time (sec)

N/A 0.059 0.047 2.503 0.191 0.323 0.391 0.282 0.075

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

87 87 89 75 85 240 129 88 104

N.S.

1 1.00 1.02 0.86 0.98 2.76 1.48 1.01 1.20

time (sec)

N/A 0.053 0.053 2.655 0.278 0.290 0.348 0.277 0.074

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

60 60 50 57 60 81 56 91 62

N.S.

1 1.00 0.83 0.95 1.00 1.35 0.93 1.52 1.03

time (sec)

N/A 0.048 0.025 2.538 0.199 0.266 0.323 0.273 5.053

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 67 68 57 61 208 114 59 59

N.S.

1 1.00 1.01 0.85 0.91 3.10 1.70 0.88 0.88

time (sec)

N/A 0.037 0.047 2.521 0.283 0.292 0.296 0.288 5.190

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

41 41 41 38 40 44 36 65 37

N.S.

1 1.00 1.00 0.93 0.98 1.07 0.88 1.59 0.90

time (sec)

N/A 0.026 0.009 2.534 0.188 0.290 0.196 0.282 0.056

Problem 80

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 0.014 0.030 2.516 0.279 0.283 0.222 0.280 5.151

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

51 51 46 48 51 70 46 63 47

N.S.

1 1.00 0.90 0.94 1.00 1.37 0.90 1.24 0.92

time (sec)

N/A 0.033 0.020 2.502 0.195 0.279 0.227 0.283 0.128

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

71 71 70 62 63 210 114 62 63

N.S.

1 1.00 0.99 0.87 0.89 2.96 1.61 0.87 0.89

time (sec)

N/A 0.044 0.023 2.516 0.269 0.292 0.262 0.308 4.922

Problem 83

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

76 76 64 76 76 117 70 82 78

N.S.

1 1.00 0.84 1.00 1.00 1.54 0.92 1.08 1.03

time (sec)

N/A 0.056 0.031 2.519 0.186 0.283 0.525 0.297 4.905

Problem 84

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 90 90 78 93 250 184 85 83

N.S.

1 1.00 1.00 0.87 1.03 2.78 2.04 0.94 0.92

time (sec)

N/A 0.074 0.047 2.477 0.280 0.269 0.313 0.276 4.896

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

97 97 85 96 106 154 100 150 100

N.S.

1 1.00 0.88 0.99 1.09 1.59 1.03 1.55 1.03

time (sec)

N/A 0.073 0.064 2.508 0.216 0.301 0.580 0.279 4.836

Problem 86

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

113 113 112 99 119 308 218 112 104

N.S.

1 1.00 0.99 0.88 1.05 2.73 1.93 0.99 0.92

time (sec)

N/A 0.130 0.050 2.557 0.279 0.308 0.365 0.294 5.097

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

124 124 110 117 136 184 129 178 126

N.S.

1 1.00 0.89 0.94 1.10 1.48 1.04 1.44 1.02

time (sec)

N/A 0.101 0.061 2.485 0.194 0.299 0.675 0.277 5.348

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

150 150 136 147 165 231 170 183 225

N.S.

1 1.00 0.91 0.98 1.10 1.54 1.13 1.22 1.50

time (sec)

N/A 0.165 0.057 2.606 0.195 0.284 0.923 0.278 0.094

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

128 128 116 126 141 205 143 159 155

N.S.

1 1.00 0.91 0.98 1.10 1.60 1.12 1.24 1.21

time (sec)

N/A 0.117 0.047 2.515 0.206 0.276 0.859 0.285 5.154

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

109 109 94 101 116 179 119 132 118

N.S.

1 1.00 0.86 0.93 1.06 1.64 1.09 1.21 1.08

time (sec)

N/A 0.104 0.041 2.618 0.193 0.300 0.830 0.282 0.079

Problem 91

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

88 88 92 76 94 142 94 93 95

N.S.

1 1.00 1.05 0.86 1.07 1.61 1.07 1.06 1.08

time (sec)

N/A 0.063 0.026 2.508 0.191 0.278 0.717 0.277 5.010

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

66 66 64 57 72 89 70 61 70

N.S.

1 1.00 0.97 0.86 1.09 1.35 1.06 0.92 1.06

time (sec)

N/A 0.047 0.017 2.511 0.197 0.256 0.511 0.295 0.071

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

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 0.014 0.011 2.503 0.187 0.260 0.267 0.284 0.033

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

68 68 59 61 77 119 75 76 71

N.S.

1 1.00 0.87 0.90 1.13 1.75 1.10 1.12 1.04

time (sec)

N/A 0.046 0.031 2.525 0.192 0.293 0.302 0.299 0.144

Problem 95

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

101 101 87 97 109 197 107 138 107

N.S.

1 1.00 0.86 0.96 1.08 1.95 1.06 1.37 1.06

time (sec)

N/A 0.076 0.038 2.529 0.195 0.289 0.646 0.285 0.114

Problem 96

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

124 124 108 123 137 229 136 133 131

N.S.

1 1.00 0.87 0.99 1.10 1.85 1.10 1.07 1.06

time (sec)

N/A 0.097 0.054 2.548 0.192 0.313 0.682 0.293 4.938

Problem 97

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

149 149 135 143 170 267 165 201 155

N.S.

1 1.00 0.91 0.96 1.14 1.79 1.11 1.35 1.04

time (sec)

N/A 0.115 0.081 2.495 0.202 0.284 0.750 0.304 4.987

Problem 98

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

158 158 158 144 171 468 280 162 246

N.S.

1 1.00 1.00 0.91 1.08 2.96 1.77 1.03 1.56

time (sec)

N/A 0.196 0.060 2.520 0.272 0.316 0.803 0.271 4.949

Problem 99

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

138 138 133 119 147 416 252 138 177

N.S.

1 1.00 0.96 0.86 1.07 3.01 1.83 1.00 1.28

time (sec)

N/A 0.150 0.071 2.629 0.275 0.307 0.811 0.272 0.070

Problem 100

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

116 116 113 95 120 358 214 111 138

N.S.

1 1.00 0.97 0.82 1.03 3.09 1.84 0.96 1.19

time (sec)

N/A 0.110 0.057 2.638 0.295 0.303 0.715 0.276 4.971

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