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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F(-2) A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 87 195 0 208 0 84 -1

N.S.

1 1.00 0.85 1.91 0.00 2.04 0.00 0.82 -0.01

time (sec)

N/A 0.063 0.457 0.141 0.000 1.288 0.000 4.737 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F(-2) B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 162 491 0 1062 0 847 -1

N.S.

1 1.00 1.98 5.99 0.00 12.95 0.00 10.33 -0.01

time (sec)

N/A 0.073 0.429 0.273 0.000 2.427 0.000 6.486 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F(-2) B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 146 307 0 813 0 703 -1

N.S.

1 1.00 2.21 4.65 0.00 12.32 0.00 10.65 -0.02

time (sec)

N/A 0.051 0.390 0.207 0.000 2.463 0.000 3.447 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 215 827 0 1544 0 1166 -1

N.S.

1 1.00 1.67 6.41 0.00 11.97 0.00 9.04 -0.01

time (sec)

N/A 0.112 0.688 0.168 0.000 3.594 0.000 5.006 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F(-1) B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 486 1868 0 3818 0 2986 -1

N.S.

1 1.00 2.17 8.34 0.00 17.04 0.00 13.33 -0.00

time (sec)

N/A 0.272 10.441 0.149 0.000 6.548 0.000 4.939 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F(-1) B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

328 328 604 3649 0 8134 0 30280 -1

N.S.

1 1.00 1.84 11.12 0.00 24.80 0.00 92.32 -0.00

time (sec)

N/A 0.596 11.824 0.172 0.000 28.658 0.000 10.031 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 241 1352 0 1919 0 0 -1

N.S.

1 1.00 1.49 8.35 0.00 11.85 0.00 0.00 -0.01

time (sec)

N/A 0.196 1.011 0.151 0.000 4.544 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 39 27 0 38 0 52 -1

N.S.

1 1.00 1.39 0.96 0.00 1.36 0.00 1.86 -0.04

time (sec)

N/A 0.012 0.152 0.276 0.000 1.558 0.000 6.764 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 142 0 0 0 0 0 -1

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.067 0.144 0.104 0.000 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

200 200 172 0 0 0 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.091 0.284 0.126 0.000 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 37 16 0 22 0 49 -1

N.S.

1 1.00 0.77 0.33 0.00 0.46 0.00 1.02 -0.02

time (sec)

N/A 0.010 0.070 0.089 0.000 1.190 0.000 2.257 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 62 84 0 82 0 143 -1

N.S.

1 1.00 0.89 1.20 0.00 1.17 0.00 2.04 -0.01

time (sec)

N/A 0.030 0.186 0.196 0.000 1.665 0.000 3.642 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F F F F F

verified

N/A NO Yes TBD TBD TBD TBD TBD TBD

size

1077 1077 600 714 0 0 0 0 -1

N.S.

1 1.00 0.56 0.66 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.042 3.132 0.268 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 75 341 0 161 0 171 -1

N.S.

1 1.00 0.77 3.48 0.00 1.64 0.00 1.74 -0.01

time (sec)

N/A 0.131 0.161 0.444 0.000 1.269 0.000 3.771 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 68 55 54 54 65 54 54

N.S.

1 1.00 1.00 0.81 0.79 0.79 0.96 0.79 0.79

time (sec)

N/A 0.028 0.003 0.099 0.286 5.340 0.015 3.547 0.062

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 56 45 44 44 53 44 44

N.S.

1 1.00 1.00 0.80 0.79 0.79 0.95 0.79 0.79

time (sec)

N/A 0.026 0.002 0.095 0.279 4.216 0.013 2.938 0.034

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 44 35 34 34 41 34 34

N.S.

1 1.00 1.00 0.80 0.77 0.77 0.93 0.77 0.77

time (sec)

N/A 0.017 0.001 0.085 0.301 5.536 0.011 2.197 0.025

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 25 24 24 26 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.87 0.80 0.80

time (sec)

N/A 0.010 0.001 0.033 0.288 3.266 0.006 3.452 0.023

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 42 34 33 33 49 33 35

N.S.

1 1.00 1.00 0.81 0.79 0.79 1.17 0.79 0.83

time (sec)

N/A 0.027 0.012 0.224 0.520 4.105 0.043 3.979 3.393

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 43 34 36 45 42 36 35

N.S.

1 1.00 1.00 0.79 0.84 1.05 0.98 0.84 0.81

time (sec)

N/A 0.017 0.012 0.115 0.498 3.033 0.051 5.821 0.038

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 53 47 56 75 63 46 55

N.S.

1 1.00 0.83 0.73 0.88 1.17 0.98 0.72 0.86

time (sec)

N/A 0.022 0.019 0.105 0.509 1.814 0.066 3.610 0.049

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 80 65 64 64 76 64 64

N.S.

1 1.00 1.00 0.81 0.80 0.80 0.95 0.80 0.80

time (sec)

N/A 0.036 0.003 0.124 0.281 1.702 0.019 5.545 0.085

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 66 55 54 54 63 54 54

N.S.

1 1.00 1.00 0.83 0.82 0.82 0.95 0.82 0.82

time (sec)

N/A 0.029 0.002 0.106 0.297 2.490 0.016 3.990 0.054

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 54 45 44 44 51 44 44

N.S.

1 1.00 1.00 0.83 0.81 0.81 0.94 0.81 0.81

time (sec)

N/A 0.027 0.002 0.133 0.284 1.757 0.012 4.340 0.034

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 46 35 34 34 41 34 34

N.S.

1 1.00 1.00 0.76 0.74 0.74 0.89 0.74 0.74

time (sec)

N/A 0.016 0.001 0.096 0.272 2.549 0.009 3.315 0.025

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 53 44 43 43 63 43 45

N.S.

1 1.00 0.95 0.79 0.77 0.77 1.12 0.77 0.80

time (sec)

N/A 0.031 0.014 0.117 0.488 2.379 0.049 2.868 3.449

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 59 51 52 78 65 52 51

N.S.

1 1.00 0.94 0.81 0.83 1.24 1.03 0.83 0.81

time (sec)

N/A 0.041 0.024 0.138 0.492 2.639 0.067 3.020 0.050

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 53 47 56 75 63 46 55

N.S.

1 1.00 0.83 0.73 0.88 1.17 0.98 0.72 0.86

time (sec)

N/A 0.036 0.018 0.112 0.497 2.324 0.071 3.326 3.442

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 63 57 76 105 83 56 75

N.S.

1 1.00 0.74 0.67 0.89 1.24 0.98 0.66 0.88

time (sec)

N/A 0.039 0.032 0.122 0.509 1.883 0.085 3.648 3.468

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 96 75 74 74 92 74 74

N.S.

1 1.00 1.00 0.78 0.77 0.77 0.96 0.77 0.77

time (sec)

N/A 0.043 0.004 0.099 0.271 2.051 0.021 3.759 0.121

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 82 65 64 64 78 64 64

N.S.

1 1.00 1.00 0.79 0.78 0.78 0.95 0.78 0.78

time (sec)

N/A 0.033 0.002 0.108 0.278 2.245 0.017 4.365 0.081

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 68 55 54 54 65 54 54

N.S.

1 1.00 1.00 0.81 0.79 0.79 0.96 0.79 0.79

time (sec)

N/A 0.029 0.002 0.114 0.278 3.040 0.014 3.632 0.054

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 56 45 44 44 53 44 44

N.S.

1 1.00 1.00 0.80 0.79 0.79 0.95 0.79 0.79

time (sec)

N/A 0.019 0.002 0.102 0.282 3.053 0.011 5.849 0.033

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 63 54 53 53 76 53 55

N.S.

1 1.00 0.90 0.77 0.76 0.76 1.09 0.76 0.79

time (sec)

N/A 0.032 0.017 0.121 0.496 2.362 0.052 5.398 0.043

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 77 61 62 88 78 62 61

N.S.

1 1.00 1.00 0.79 0.81 1.14 1.01 0.81 0.79

time (sec)

N/A 0.048 0.021 0.125 0.511 2.296 0.070 2.326 3.431

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 78 63 72 118 85 62 71

N.S.

1 1.00 0.93 0.75 0.86 1.40 1.01 0.74 0.85

time (sec)

N/A 0.058 0.027 0.128 0.502 3.408 0.089 5.611 3.426

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 72 64 63 63 87 63 65

N.S.

1 1.00 0.86 0.76 0.75 0.75 1.04 0.75 0.77

time (sec)

N/A 0.041 0.021 0.203 0.499 1.721 0.058 5.122 3.441

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 63 54 53 53 73 53 55

N.S.

1 1.00 0.90 0.77 0.76 0.76 1.04 0.76 0.79

time (sec)

N/A 0.032 0.016 0.129 0.503 2.616 0.051 4.698 0.042

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 52 44 43 43 60 43 45

N.S.

1 1.00 0.93 0.79 0.77 0.77 1.07 0.77 0.80

time (sec)

N/A 0.030 0.013 0.135 0.524 1.955 0.049 2.131 3.445

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 42 34 33 33 46 33 35

N.S.

1 1.00 1.00 0.81 0.79 0.79 1.10 0.79 0.83

time (sec)

N/A 0.024 0.008 0.113 0.523 2.171 0.044 3.806 0.039

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 73 60 59 59 83 59 79

N.S.

1 1.00 1.00 0.82 0.81 0.81 1.14 0.81 1.08

time (sec)

N/A 0.035 0.023 0.140 0.535 3.069 0.098 2.466 0.187

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 94 77 78 117 102 78 95

N.S.

1 1.00 1.00 0.82 0.83 1.24 1.09 0.83 1.01

time (sec)

N/A 0.055 0.060 0.144 0.586 2.015 0.130 3.376 3.567

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 104 89 98 177 119 88 115

N.S.

1 1.00 0.90 0.77 0.85 1.54 1.03 0.77 1.00

time (sec)

N/A 0.078 0.114 0.139 0.513 2.312 0.153 2.249 0.179

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 91 71 72 98 90 72 72

N.S.

1 1.00 1.00 0.78 0.79 1.08 0.99 0.79 0.79

time (sec)

N/A 0.056 0.036 0.109 0.500 1.482 0.073 3.438 3.462

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 77 61 62 88 75 62 61

N.S.

1 1.00 1.00 0.79 0.81 1.14 0.97 0.81 0.79

time (sec)

N/A 0.047 0.021 0.138 0.657 2.257 0.071 2.987 3.424

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 63 51 52 78 61 52 52

N.S.

1 1.00 1.00 0.81 0.83 1.24 0.97 0.83 0.83

time (sec)

N/A 0.040 0.022 0.150 0.512 0.938 0.069 1.550 3.404

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 43 34 36 45 42 36 36

N.S.

1 1.00 1.00 0.79 0.84 1.05 0.98 0.84 0.84

time (sec)

N/A 0.017 0.011 0.110 0.511 1.924 0.050 1.917 0.040

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 94 77 78 117 102 78 96

N.S.

1 1.00 1.00 0.82 0.83 1.24 1.09 0.83 1.02

time (sec)

N/A 0.055 0.045 0.142 0.510 1.648 0.127 1.413 3.578

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 106 94 96 167 122 96 115

N.S.

1 1.00 0.83 0.74 0.76 1.31 0.96 0.76 0.91

time (sec)

N/A 0.077 0.041 0.141 0.514 1.454 0.151 1.646 0.177

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 136 106 118 237 143 110 135

N.S.

1 1.00 0.92 0.72 0.80 1.60 0.97 0.74 0.91

time (sec)

N/A 0.104 0.055 0.158 0.500 2.305 0.174 1.052 3.586

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 98 73 82 128 95 72 81

N.S.

1 1.00 1.00 0.74 0.84 1.31 0.97 0.73 0.83

time (sec)

N/A 0.070 0.027 0.112 0.495 2.172 0.092 1.338 0.045

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 84 63 72 118 82 62 72

N.S.

1 1.00 1.00 0.75 0.86 1.40 0.98 0.74 0.86

time (sec)

N/A 0.060 0.026 0.123 0.509 1.909 0.087 2.002 0.049

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 51 47 56 75 63 46 56

N.S.

1 1.00 0.80 0.73 0.88 1.17 0.98 0.72 0.88

time (sec)

N/A 0.033 0.021 0.128 0.503 1.759 0.071 0.954 3.474

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 51 47 56 75 61 46 55

N.S.

1 1.00 0.80 0.73 0.88 1.17 0.95 0.72 0.86

time (sec)

N/A 0.021 0.021 0.109 0.507 1.565 0.065 1.427 0.044

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 99 89 98 177 122 88 116

N.S.

1 1.00 0.86 0.77 0.85 1.54 1.06 0.77 1.01

time (sec)

N/A 0.081 0.116 0.155 0.517 2.028 0.152 1.970 3.580

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 136 106 116 227 143 110 136

N.S.

1 1.00 0.85 0.66 0.72 1.42 0.89 0.69 0.85

time (sec)

N/A 0.102 0.088 0.163 0.518 2.388 0.174 1.027 3.597

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

181 181 151 118 138 297 163 116 155

N.S.

1 1.00 0.83 0.65 0.76 1.64 0.90 0.64 0.86

time (sec)

N/A 0.129 0.069 0.136 0.524 2.095 0.195 0.772 3.588

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

208 208 95 166 177 98 0 93 221

N.S.

1 1.00 0.46 0.80 0.85 0.47 0.00 0.45 1.06

time (sec)

N/A 0.192 0.808 0.145 0.519 1.797 0.000 1.444 5.028

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 85 132 143 88 0 83 187

N.S.

1 1.00 0.51 0.80 0.86 0.53 0.00 0.50 1.13

time (sec)

N/A 0.116 0.581 0.128 0.517 1.850 0.000 0.961 4.692

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 75 98 109 78 0 73 153

N.S.

1 1.00 0.60 0.79 0.88 0.63 0.00 0.59 1.23

time (sec)

N/A 0.060 0.363 0.123 0.505 2.191 0.000 1.673 4.185

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 65 64 75 68 0 63 119

N.S.

1 1.00 0.79 0.78 0.91 0.83 0.00 0.77 1.45

time (sec)

N/A 0.024 0.242 0.106 0.525 2.461 0.000 1.529 3.835

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 206 2065 0 2016 0 0 -1

N.S.

1 1.00 1.18 11.87 0.00 11.59 0.00 0.00 -0.01

time (sec)

N/A 0.285 0.203 0.688 0.000 3.967 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 419 16357 0 2102 0 0 -1

N.S.

1 1.00 2.23 87.01 0.00 11.18 0.00 0.00 -0.01

time (sec)

N/A 0.262 0.475 0.950 0.000 5.981 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 392 44343 0 2182 0 0 -1

N.S.

1 1.00 1.76 198.85 0.00 9.78 0.00 0.00 -0.00

time (sec)

N/A 0.301 0.588 1.003 0.000 5.790 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

231 231 105 185 206 108 0 103 -1

N.S.

1 1.00 0.45 0.80 0.89 0.47 0.00 0.45 -0.00

time (sec)

N/A 0.211 1.016 0.143 0.514 5.622 0.000 5.187 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 95 151 172 98 0 93 -1

N.S.

1 1.00 0.50 0.80 0.91 0.52 0.00 0.49 -0.01

time (sec)

N/A 0.121 0.782 0.144 0.512 4.443 0.000 4.644 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 85 117 138 88 0 83 -1

N.S.

1 1.00 0.58 0.80 0.94 0.60 0.00 0.56 -0.01

time (sec)

N/A 0.073 0.566 0.125 0.512 4.104 0.000 2.980 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 75 83 104 78 0 73 -1

N.S.

1 1.00 0.71 0.79 0.99 0.74 0.00 0.70 -0.01

time (sec)

N/A 0.031 0.374 0.104 0.542 2.177 0.000 3.893 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 228 3460 0 2027 0 0 -1

N.S.

1 1.00 1.16 17.56 0.00 10.29 0.00 0.00 -0.01

time (sec)

N/A 0.314 0.343 0.833 0.000 4.390 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

232 232 416 28185 0 2150 0 0 -1

N.S.

1 1.00 1.79 121.49 0.00 9.27 0.00 0.00 -0.00

time (sec)

N/A 0.369 0.520 0.982 0.000 2.793 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 572 81552 0 2183 0 0 -1

N.S.

1 1.00 2.57 365.70 0.00 9.79 0.00 0.00 -0.00

time (sec)

N/A 0.281 0.788 0.970 0.000 3.274 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

254 254 115 204 235 118 0 113 -1

N.S.

1 1.00 0.45 0.80 0.93 0.46 0.00 0.44 -0.00

time (sec)

N/A 0.237 1.282 0.142 0.514 2.907 0.000 4.177 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

212 212 105 170 201 108 0 103 -1

N.S.

1 1.00 0.50 0.80 0.95 0.51 0.00 0.49 -0.00

time (sec)

N/A 0.140 1.019 0.118 0.504 3.744 0.000 5.250 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 95 136 167 98 0 93 -1

N.S.

1 1.00 0.56 0.80 0.98 0.58 0.00 0.55 -0.01

time (sec)

N/A 0.080 0.775 0.121 0.545 2.637 0.000 4.179 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 85 102 133 88 0 83 -1

N.S.

1 1.00 0.66 0.80 1.04 0.69 0.00 0.65 -0.01

time (sec)

N/A 0.037 0.561 0.098 0.499 3.214 0.000 3.195 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

222 222 238 4860 0 2010 0 0 -1

N.S.

1 1.00 1.07 21.89 0.00 9.05 0.00 0.00 -0.00

time (sec)

N/A 0.353 0.550 0.814 0.000 1.837 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 433 40028 0 2161 0 0 -1

N.S.

1 1.00 1.70 156.97 0.00 8.47 0.00 0.00 -0.00

time (sec)

N/A 0.425 0.718 0.957 0.000 3.764 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

281 281 616 119458 0 2240 0 0 -1

N.S.

1 1.00 2.19 425.12 0.00 7.97 0.00 0.00 -0.00

time (sec)

N/A 0.422 0.859 1.090 0.000 3.508 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 85 147 148 88 0 83 -1

N.S.

1 1.00 0.46 0.79 0.80 0.48 0.00 0.45 -0.01

time (sec)

N/A 0.197 0.636 0.133 0.517 3.331 0.000 4.180 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 75 113 114 78 0 73 -1

N.S.

1 1.00 0.52 0.79 0.80 0.55 0.00 0.51 -0.01

time (sec)

N/A 0.114 0.455 0.141 0.510 1.503 0.000 2.610 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 65 79 80 68 0 63 -1

N.S.

1 1.00 0.64 0.78 0.79 0.67 0.00 0.62 -0.01

time (sec)

N/A 0.057 0.297 0.119 0.495 2.098 0.000 4.843 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 55 45 46 58 0 53 -1

N.S.

1 1.00 0.93 0.76 0.78 0.98 0.00 0.90 -0.02

time (sec)

N/A 0.021 0.156 0.096 0.505 1.775 0.000 4.927 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 135 684 0 2002 0 0 -1

N.S.

1 1.00 0.91 4.62 0.00 13.53 0.00 0.00 -0.01

time (sec)

N/A 0.200 0.188 0.569 0.000 2.374 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 230 5225 0 2102 0 0 -1

N.S.

1 1.00 1.22 27.79 0.00 11.18 0.00 0.00 -0.01

time (sec)

N/A 0.283 0.365 0.632 0.000 3.568 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 396 13040 0 2183 0 0 -1

N.S.

1 1.00 1.78 58.48 0.00 9.79 0.00 0.00 -0.00

time (sec)

N/A 0.306 0.634 0.646 0.000 2.860 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 85 166 148 112 0 82 -1

N.S.

1 1.00 0.51 1.00 0.89 0.67 0.00 0.49 -0.01

time (sec)

N/A 0.131 0.905 0.133 0.528 2.105 0.000 2.702 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 75 132 114 102 0 72 -1

N.S.

1 1.00 0.60 1.06 0.92 0.82 0.00 0.58 -0.01

time (sec)

N/A 0.079 0.638 0.132 0.514 1.782 0.000 4.178 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 65 98 80 92 0 62 -1

N.S.

1 1.00 0.79 1.20 0.98 1.12 0.00 0.76 -0.01

time (sec)

N/A 0.045 0.487 0.126 0.504 1.753 0.000 2.506 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 55 64 46 82 0 53 87

N.S.

1 1.00 1.22 1.42 1.02 1.82 0.00 1.18 1.93

time (sec)

N/A 0.019 0.263 0.102 0.501 1.681 0.000 3.506 0.227

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 199 718 0 2083 0 0 -1

N.S.

1 1.00 1.13 4.08 0.00 11.84 0.00 0.00 -0.01

time (sec)

N/A 0.267 0.346 0.642 0.000 2.800 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 414 5942 0 2173 0 0 -1

N.S.

1 1.00 1.96 28.16 0.00 10.30 0.00 0.00 -0.00

time (sec)

N/A 0.312 0.673 0.697 0.000 2.806 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

246 246 607 18981 0 2263 0 0 -1

N.S.

1 1.00 2.47 77.16 0.00 9.20 0.00 0.00 -0.00

time (sec)

N/A 0.337 1.118 0.862 0.000 2.739 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 85 214 253 132 0 81 -1

N.S.

1 1.00 0.58 1.46 1.72 0.90 0.00 0.55 -0.01

time (sec)

N/A 0.105 1.056 0.138 0.515 1.818 0.000 5.787 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 75 180 219 122 0 72 -1

N.S.

1 1.00 0.71 1.71 2.09 1.16 0.00 0.69 -0.01

time (sec)

N/A 0.066 0.790 0.133 0.519 1.757 0.000 4.290 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 65 146 185 112 0 61 -1

N.S.

1 1.00 0.96 2.15 2.72 1.65 0.00 0.90 -0.01

time (sec)

N/A 0.040 0.582 0.121 0.516 1.558 0.000 3.967 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 33 69 59 51 0 29 29

N.S.

1 1.00 0.70 1.47 1.26 1.09 0.00 0.62 0.62

time (sec)

N/A 0.014 0.346 0.117 0.285 2.075 0.000 4.185 0.090

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 209 751 0 2133 0 0 -1

N.S.

1 1.00 1.05 3.77 0.00 10.72 0.00 0.00 -0.01

time (sec)

N/A 0.303 0.635 0.632 0.000 2.390 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 416 5975 0 2253 0 0 -1

N.S.

1 1.00 1.78 25.53 0.00 9.63 0.00 0.00 -0.00

time (sec)

N/A 0.348 1.046 0.769 0.000 3.361 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F B F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 605 19014 0 2343 0 0 -1

N.S.

1 1.00 2.25 70.68 0.00 8.71 0.00 0.00 -0.00

time (sec)

N/A 0.382 1.201 0.819 0.000 6.358 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F(-2) A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

436 436 456 1186 0 1267 0 638 1299

N.S.

1 1.00 1.05 2.72 0.00 2.91 0.00 1.46 2.98

time (sec)

N/A 0.496 1.979 0.201 0.000 3.812 0.000 3.190 5.312

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