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2.2.2 Integrals 101 to 200

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 101

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

19 19 100 91 90 90 97 90 92

N.S.

1 1.00 5.26 4.79 4.74 4.74 5.11 4.74 4.84

time (sec)

N/A 0.135 0.004 1.693 0.196 0.262 0.474 0.275 0.078

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 44 106 91 92 0 99 92 92

N.S.

1 1.10 2.65 2.28 2.30 0.00 2.48 2.30 2.30

time (sec)

N/A 0.151 0.004 1.687 0.219 0.000 0.492 0.284 0.083

Problem 103

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 72 104 91 92 92 99 92 91

N.S.

1 1.16 1.68 1.47 1.48 1.48 1.60 1.48 1.47

time (sec)

N/A 0.165 0.004 1.677 0.210 0.244 0.530 0.276 0.080

Problem 104

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

84 100 106 91 92 92 99 92 92

N.S.

1 1.19 1.26 1.08 1.10 1.10 1.18 1.10 1.10

time (sec)

N/A 0.184 0.005 1.684 0.191 0.286 0.554 0.271 4.661

Problem 105

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

106 128 106 91 92 92 99 92 92

N.S.

1 1.21 1.00 0.86 0.87 0.87 0.93 0.87 0.87

time (sec)

N/A 0.194 0.004 1.658 0.208 0.244 0.587 0.270 0.082

Problem 106

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

108 110 108 91 92 92 99 92 92

N.S.

1 1.02 1.00 0.84 0.85 0.85 0.92 0.85 0.85

time (sec)

N/A 0.221 0.004 1.700 0.196 0.259 0.606 0.269 4.602

Problem 107

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

108 110 108 91 92 92 99 92 92

N.S.

1 1.02 1.00 0.84 0.85 0.85 0.92 0.85 0.85

time (sec)

N/A 0.226 0.004 1.692 0.204 0.256 0.632 0.277 4.619

Problem 108

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

106 110 106 91 92 92 99 92 91

N.S.

1 1.04 1.00 0.86 0.87 0.87 0.93 0.87 0.86

time (sec)

N/A 0.228 0.004 1.717 0.202 0.239 0.673 0.280 0.088

Problem 109

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 91 90 90 107 90 90

N.S.

1 1.00 1.00 0.84 0.83 0.83 0.99 0.83 0.83

time (sec)

N/A 0.223 0.002 1.690 0.202 0.263 0.029 0.276 0.101

Problem 110

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 91 90 90 107 90 90

N.S.

1 1.00 1.00 0.84 0.83 0.83 0.99 0.83 0.83

time (sec)

N/A 0.211 0.003 1.726 0.195 0.245 0.028 0.293 4.613

Problem 111

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 91 90 90 107 90 90

N.S.

1 1.00 1.00 0.84 0.83 0.83 0.99 0.83 0.83

time (sec)

N/A 0.210 0.002 1.722 0.194 0.257 0.028 0.266 0.101

Problem 112

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

106 106 106 91 90 90 105 90 90

N.S.

1 1.00 1.00 0.86 0.85 0.85 0.99 0.85 0.85

time (sec)

N/A 0.214 0.004 1.717 0.192 0.248 0.030 0.305 4.558

Problem 113

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

101 101 101 88 87 87 102 87 87

N.S.

1 1.00 1.00 0.87 0.86 0.86 1.01 0.86 0.86

time (sec)

N/A 0.210 0.002 1.665 0.192 0.241 0.027 0.292 0.045

Problem 114

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

100 100 100 89 88 92 99 88 88

N.S.

1 1.00 1.00 0.89 0.88 0.92 0.99 0.88 0.88

time (sec)

N/A 0.217 0.009 1.768 0.195 0.264 0.067 0.267 0.057

Problem 115

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

98 98 98 89 89 92 100 89 91

N.S.

1 1.00 1.00 0.91 0.91 0.94 1.02 0.91 0.93

time (sec)

N/A 0.213 0.009 1.766 0.197 0.255 0.099 0.273 0.054

Problem 116

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

100 100 100 89 91 92 102 91 91

N.S.

1 1.00 1.00 0.89 0.91 0.92 1.02 0.91 0.91

time (sec)

N/A 0.217 0.009 1.702 0.198 0.256 0.123 0.267 4.591

Problem 117

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

102 102 102 89 91 92 102 91 91

N.S.

1 1.00 1.00 0.87 0.89 0.90 1.00 0.89 0.89

time (sec)

N/A 0.219 0.007 1.659 0.199 0.247 0.178 0.278 5.281

Problem 118

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

102 102 102 89 91 92 100 91 91

N.S.

1 1.00 1.00 0.87 0.89 0.90 0.98 0.89 0.89

time (sec)

N/A 0.218 0.014 1.680 0.202 0.254 0.207 0.312 0.056

Problem 119

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

100 100 100 89 91 92 99 91 91

N.S.

1 1.00 1.00 0.89 0.91 0.92 0.99 0.91 0.91

time (sec)

N/A 0.209 0.010 1.670 0.205 0.265 0.255 0.275 5.248

Problem 120

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

98 98 98 89 91 92 97 91 92

N.S.

1 1.00 1.00 0.91 0.93 0.94 0.99 0.93 0.94

time (sec)

N/A 0.212 0.012 1.699 0.202 0.244 0.295 0.288 0.076

Problem 121

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

99 99 99 88 90 92 95 90 90

N.S.

1 1.00 1.00 0.89 0.91 0.93 0.96 0.91 0.91

time (sec)

N/A 0.217 0.005 1.704 0.204 0.239 0.384 0.280 4.909

Problem 122

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

104 104 104 91 92 92 99 92 91

N.S.

1 1.00 1.00 0.88 0.88 0.88 0.95 0.88 0.88

time (sec)

N/A 0.216 0.012 1.707 0.199 0.252 0.410 0.285 0.083

Problem 123

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

106 106 106 91 92 92 99 92 92

N.S.

1 1.00 1.00 0.86 0.87 0.87 0.93 0.87 0.87

time (sec)

N/A 0.221 0.009 1.696 0.201 0.250 0.430 0.298 0.079

Problem 124

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

79 78 79 68 68 67 68 69 67

N.S.

1 0.99 1.00 0.86 0.86 0.85 0.86 0.87 0.85

time (sec)

N/A 0.205 0.008 1.712 0.207 0.248 0.086 0.279 0.067

Problem 125

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

81 81 81 71 72 170 119 77 65

N.S.

1 1.00 1.00 0.88 0.89 2.10 1.47 0.95 0.80

time (sec)

N/A 0.199 0.061 1.709 0.282 0.263 0.098 0.280 0.057

Problem 126

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 65 66 57 57 56 56 58 56

N.S.

1 0.98 1.00 0.86 0.86 0.85 0.85 0.88 0.85

time (sec)

N/A 0.186 0.017 1.728 0.185 0.250 0.077 0.272 0.083

Problem 127

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 60 60 148 107 65 54

N.S.

1 1.00 1.00 0.88 0.88 2.18 1.57 0.96 0.79

time (sec)

N/A 0.183 0.018 1.750 0.276 0.269 0.100 0.336 0.053

Problem 128

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 52 53 46 46 45 44 47 45

N.S.

1 0.98 1.00 0.87 0.87 0.85 0.83 0.89 0.85

time (sec)

N/A 0.178 0.004 1.715 0.191 0.260 0.075 0.380 5.281

Problem 129

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 49 50 126 95 55 43

N.S.

1 1.00 1.00 0.89 0.91 2.29 1.73 1.00 0.78

time (sec)

N/A 0.176 0.016 1.709 0.290 0.265 0.092 0.388 0.073

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 39 40 34 34 33 32 35 33

N.S.

1 0.98 1.00 0.85 0.85 0.82 0.80 0.88 0.82

time (sec)

N/A 0.167 0.004 1.715 0.203 0.246 0.068 0.342 5.348

Problem 131

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 38 37 99 80 40 32

N.S.

1 1.00 1.00 0.90 0.88 2.36 1.90 0.95 0.76

time (sec)

N/A 0.178 0.068 1.722 0.298 0.263 0.082 0.279 0.078

Problem 132

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 26 27 23 23 22 20 24 22

N.S.

1 0.96 1.00 0.85 0.85 0.81 0.74 0.89 0.81

time (sec)

N/A 0.163 0.007 1.691 0.195 0.248 0.070 0.308 0.038

Problem 133

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

31 31 31 27 26 82 56 26 23

N.S.

1 1.00 1.00 0.87 0.84 2.65 1.81 0.84 0.74

time (sec)

N/A 0.144 0.008 1.732 0.277 0.253 0.071 0.345 0.040

Problem 134

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

15 15 15 14 13 13 10 14 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.67 0.93 0.87

time (sec)

N/A 0.131 0.011 1.699 0.198 0.252 0.055 0.330 5.268

Problem 135

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

24 24 24 16 15 67 53 15 16

N.S.

1 1.00 1.00 0.67 0.62 2.79 2.21 0.62 0.67

time (sec)

N/A 0.132 0.003 1.701 0.289 0.269 0.070 0.319 5.260

Problem 136

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 26 22 21 23 18 15 24 18

N.S.

1 1.18 1.00 0.95 1.05 0.82 0.68 1.09 0.82

time (sec)

N/A 0.139 0.018 1.689 0.206 0.271 0.100 0.321 0.091

Problem 137

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

34 34 34 30 29 82 65 29 26

N.S.

1 1.00 1.00 0.88 0.85 2.41 1.91 0.85 0.76

time (sec)

N/A 0.137 0.018 1.739 0.289 0.256 0.082 0.388 0.051

Problem 138

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 36 35 32 33 33 31 43 31

N.S.

1 1.03 1.00 0.91 0.94 0.94 0.89 1.23 0.89

time (sec)

N/A 0.167 0.009 1.734 0.200 0.257 0.129 0.368 0.081

Problem 139

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 51 43 39 40 106 87 40 37

N.S.

1 1.19 1.00 0.91 0.93 2.47 2.02 0.93 0.86

time (sec)

N/A 0.153 0.023 1.734 0.284 0.278 0.110 0.317 5.298

Problem 140

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 50 49 44 47 45 42 57 46

N.S.

1 1.02 1.00 0.90 0.96 0.92 0.86 1.16 0.94

time (sec)

N/A 0.174 0.012 1.518 0.196 0.258 0.159 0.294 0.086

Problem 141

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

58 68 58 52 52 132 100 52 48

N.S.

1 1.17 1.00 0.90 0.90 2.28 1.72 0.90 0.83

time (sec)

N/A 0.171 0.025 1.736 0.280 0.258 0.127 0.280 0.067

Problem 142

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 64 63 56 58 58 56 70 58

N.S.

1 1.02 1.00 0.89 0.92 0.92 0.89 1.11 0.92

time (sec)

N/A 0.186 0.007 6.070 0.199 0.254 0.175 0.304 5.398

Problem 143

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 85 69 61 62 154 112 62 59

N.S.

1 1.23 1.00 0.88 0.90 2.23 1.62 0.90 0.86

time (sec)

N/A 0.184 0.020 1.742 0.280 0.271 0.152 0.308 0.071

Problem 144

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 76 75 66 69 69 68 81 68

N.S.

1 1.01 1.00 0.88 0.92 0.92 0.91 1.08 0.91

time (sec)

N/A 0.200 0.007 1.737 0.189 0.264 0.195 0.282 5.275

Problem 145

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 91 83 85 88 104 88 103 90

N.S.

1 0.97 0.88 0.90 0.94 1.11 0.94 1.10 0.96

time (sec)

N/A 0.225 0.035 1.724 0.195 0.260 0.153 0.279 0.089

Problem 146

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

105 108 93 87 93 234 151 95 88

N.S.

1 1.03 0.89 0.83 0.89 2.23 1.44 0.90 0.84

time (sec)

N/A 0.211 0.048 1.747 0.278 0.272 0.182 0.272 0.075

Problem 147

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 82 72 74 77 93 80 92 79

N.S.

1 0.99 0.87 0.89 0.93 1.12 0.96 1.11 0.95

time (sec)

N/A 0.208 0.016 1.725 0.208 0.270 0.146 0.292 5.221

Problem 148

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 95 82 76 82 212 134 84 77

N.S.

1 1.03 0.89 0.83 0.89 2.30 1.46 0.91 0.84

time (sec)

N/A 0.208 0.045 1.735 0.276 0.256 0.166 0.291 5.088

Problem 149

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 68 60 63 65 81 66 80 68

N.S.

1 0.97 0.86 0.90 0.93 1.16 0.94 1.14 0.97

time (sec)

N/A 0.202 0.015 4.947 0.194 0.252 0.142 0.291 0.076

Problem 150

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

79 82 71 65 71 190 124 73 66

N.S.

1 1.04 0.90 0.82 0.90 2.41 1.57 0.92 0.84

time (sec)

N/A 0.196 0.032 1.716 0.273 0.279 0.151 0.282 5.137

Problem 151

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 56 49 54 54 70 53 67 57

N.S.

1 0.98 0.86 0.95 0.95 1.23 0.93 1.18 1.00

time (sec)

N/A 0.187 0.012 6.056 0.200 0.316 0.124 0.282 0.087

Problem 152

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 69 60 54 59 164 107 61 56

N.S.

1 1.05 0.91 0.82 0.89 2.48 1.62 0.92 0.85

time (sec)

N/A 0.182 0.030 1.735 0.281 0.334 0.143 0.295 0.092

Problem 153

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 43 38 41 43 56 39 49 45

N.S.

1 0.98 0.86 0.93 0.98 1.27 0.89 1.11 1.02

time (sec)

N/A 0.178 0.012 6.080 0.196 0.290 0.112 0.296 0.050

Problem 154

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 58 51 42 45 136 83 42 43

N.S.

1 1.05 0.93 0.76 0.82 2.47 1.51 0.76 0.78

time (sec)

N/A 0.158 0.022 1.734 0.278 0.276 0.126 0.273 5.104

Problem 155

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 31 27 30 32 35 29 48 29

N.S.

1 0.94 0.82 0.91 0.97 1.06 0.88 1.45 0.88

time (sec)

N/A 0.165 0.006 6.040 0.187 0.249 0.090 0.284 0.046

Problem 156

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

45 45 45 36 36 120 78 35 33

N.S.

1 1.00 1.00 0.80 0.80 2.67 1.73 0.78 0.73

time (sec)

N/A 0.149 0.015 1.742 0.280 0.252 0.102 0.287 5.483

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 14 15 15 14 14

N.S.

1 1.00 1.00 0.94 0.88 0.94 0.94 0.88 0.88

time (sec)

N/A 0.128 0.002 6.049 0.185 0.248 0.080 0.289 0.036

Problem 158

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

45 45 45 36 35 120 78 35 33

N.S.

1 1.00 1.00 0.80 0.78 2.67 1.73 0.78 0.73

time (sec)

N/A 0.143 0.017 1.800 0.262 0.261 0.109 0.271 4.989

Problem 159

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 39 33 35 37 47 34 47 34

N.S.

1 1.03 0.87 0.92 0.97 1.24 0.89 1.24 0.89

time (sec)

N/A 0.169 0.010 1.735 0.182 0.256 0.187 0.275 0.062

Problem 160

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 61 54 45 49 136 92 47 44

N.S.

1 1.07 0.95 0.79 0.86 2.39 1.61 0.82 0.77

time (sec)

N/A 0.160 0.026 1.743 0.278 0.291 0.150 0.291 0.078

Problem 161

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 52 41 52 52 73 51 51 51

N.S.

1 1.06 0.84 1.06 1.06 1.49 1.04 1.04 1.04

time (sec)

N/A 0.186 0.024 6.079 0.202 0.269 0.184 0.280 4.587

Problem 162

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 78 67 55 64 172 114 59 58

N.S.

1 1.15 0.99 0.81 0.94 2.53 1.68 0.87 0.85

time (sec)

N/A 0.170 0.028 1.755 0.282 0.265 0.182 0.284 4.562

Problem 163

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 68 57 65 70 90 68 86 67

N.S.

1 1.03 0.86 0.98 1.06 1.36 1.03 1.30 1.02

time (sec)

N/A 0.197 0.035 1.745 0.187 0.253 0.233 0.300 4.520

Problem 164

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

81 95 80 67 75 198 126 70 70

N.S.

1 1.17 0.99 0.83 0.93 2.44 1.56 0.86 0.86

time (sec)

N/A 0.191 0.030 1.761 0.273 0.263 0.216 0.287 4.603

Problem 165

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

80 79 68 77 79 99 78 99 78

N.S.

1 0.99 0.85 0.96 0.99 1.24 0.98 1.24 0.98

time (sec)

N/A 0.211 0.035 1.744 0.197 0.258 0.251 0.289 0.119

Problem 166

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

94 112 91 77 86 220 138 81 80

N.S.

1 1.19 0.97 0.82 0.91 2.34 1.47 0.86 0.85

time (sec)

N/A 0.201 0.031 1.759 0.277 0.298 0.223 0.271 4.500

Problem 167

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 94 79 88 92 112 94 110 89

N.S.

1 1.01 0.85 0.95 0.99 1.20 1.01 1.18 0.96

time (sec)

N/A 0.224 0.046 1.743 0.188 0.255 0.277 0.278 4.504

Problem 168

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

114 111 97 97 111 137 119 114 111

N.S.

1 0.97 0.85 0.85 0.97 1.20 1.04 1.00 0.97

time (sec)

N/A 0.252 0.028 1.727 0.187 0.247 0.237 0.315 4.504

Problem 169

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

100 98 85 87 99 125 104 102 100

N.S.

1 0.98 0.85 0.87 0.99 1.25 1.04 1.02 1.00

time (sec)

N/A 0.238 0.023 1.735 0.199 0.271 0.235 0.272 0.080

Problem 170

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 89 75 76 89 115 92 92 90

N.S.

1 1.02 0.86 0.87 1.02 1.32 1.06 1.06 1.03

time (sec)

N/A 0.220 0.021 1.741 0.210 0.242 0.215 0.280 0.079

Problem 171

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

74 76 63 65 77 103 78 80 78

N.S.

1 1.03 0.85 0.88 1.04 1.39 1.05 1.08 1.05

time (sec)

N/A 0.210 0.017 1.736 0.200 0.246 0.207 0.275 4.467

Problem 172

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 62 48 54 66 91 68 62 68

N.S.

1 0.95 0.74 0.83 1.02 1.40 1.05 0.95 1.05

time (sec)

N/A 0.193 0.041 1.738 0.206 0.252 0.209 0.279 4.566

Problem 173

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 39 42 55 69 53 42 52

N.S.

1 1.04 0.80 0.86 1.12 1.41 1.08 0.86 1.06

time (sec)

N/A 0.189 0.013 1.736 0.192 0.258 0.159 0.301 0.064

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 24 23 36 36 36 22 37

N.S.

1 1.00 1.26 1.21 1.89 1.89 1.89 1.16 1.95

time (sec)

N/A 0.136 0.024 1.730 0.198 0.255 0.140 0.300 0.034

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 14 26 27 14 28

N.S.

1 1.00 1.00 0.94 0.88 1.62 1.69 0.88 1.75

time (sec)

N/A 0.132 0.002 1.733 0.207 0.259 0.109 0.290 4.474

Problem 176

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 55 43 46 60 90 56 59 56

N.S.

1 1.02 0.80 0.85 1.11 1.67 1.04 1.09 1.04

time (sec)

N/A 0.186 0.024 1.744 0.220 0.258 0.204 0.316 4.531

Problem 177

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 69 59 65 77 119 80 82 75

N.S.

1 1.03 0.88 0.97 1.15 1.78 1.19 1.22 1.12

time (sec)

N/A 0.203 0.044 1.750 0.200 0.256 0.263 0.292 0.080

Problem 178

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

86 88 74 77 92 134 90 80 88

N.S.

1 1.02 0.86 0.90 1.07 1.56 1.05 0.93 1.02

time (sec)

N/A 0.220 0.042 1.760 0.197 0.251 0.292 0.299 4.574

Problem 179

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

95 101 85 89 103 145 104 110 101

N.S.

1 1.06 0.89 0.94 1.08 1.53 1.09 1.16 1.06

time (sec)

N/A 0.229 0.053 1.755 0.192 0.259 0.302 0.302 4.561

Problem 180

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

112 109 96 100 114 156 116 119 111

N.S.

1 0.97 0.86 0.89 1.02 1.39 1.04 1.06 0.99

time (sec)

N/A 0.252 0.043 1.750 0.220 0.246 0.340 0.286 0.231

Problem 181

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

111 122 99 85 105 278 162 96 99

N.S.

1 1.10 0.89 0.77 0.95 2.50 1.46 0.86 0.89

time (sec)

N/A 0.228 0.043 1.758 0.285 0.265 0.249 0.273 0.081

Problem 182

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

98 109 88 74 93 256 144 84 87

N.S.

1 1.11 0.90 0.76 0.95 2.61 1.47 0.86 0.89

time (sec)

N/A 0.219 0.035 1.756 0.283 0.310 0.239 0.283 0.072

Problem 183

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

85 96 77 63 82 230 133 73 77

N.S.

1 1.13 0.91 0.74 0.96 2.71 1.56 0.86 0.91

time (sec)

N/A 0.211 0.036 1.711 0.301 0.331 0.229 0.297 0.094

Problem 184

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

74 85 66 51 68 202 107 54 64

N.S.

1 1.15 0.89 0.69 0.92 2.73 1.45 0.73 0.86

time (sec)

N/A 0.179 0.033 6.152 0.299 0.598 0.218 0.288 4.688

Problem 185

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 72 55 47 59 188 110 45 56

N.S.

1 1.12 0.86 0.73 0.92 2.94 1.72 0.70 0.88

time (sec)

N/A 0.168 0.030 1.760 0.289 0.258 0.175 0.313 0.108

Problem 186

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 70 58 49 62 190 110 50 55

N.S.

1 1.08 0.89 0.75 0.95 2.92 1.69 0.77 0.85

time (sec)

N/A 0.164 0.020 6.155 0.299 0.253 0.149 0.285 4.616

Problem 187

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 70 55 57 58 188 105 45 55

N.S.

1 1.13 0.89 0.92 0.94 3.03 1.69 0.73 0.89

time (sec)

N/A 0.161 0.024 1.756 0.274 0.263 0.158 0.302 4.498

Problem 188

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 88 68 54 71 202 116 57 66

N.S.

1 1.16 0.89 0.71 0.93 2.66 1.53 0.75 0.87

time (sec)

N/A 0.182 0.028 6.089 0.282 0.276 0.208 0.277 4.569

Problem 189

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

87 105 79 64 86 238 138 71 80

N.S.

1 1.21 0.91 0.74 0.99 2.74 1.59 0.82 0.92

time (sec)

N/A 0.191 0.028 1.780 0.283 0.264 0.255 0.315 4.496

Problem 190

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

100 122 90 75 97 264 150 80 92

N.S.

1 1.22 0.90 0.75 0.97 2.64 1.50 0.80 0.92

time (sec)

N/A 0.209 0.036 1.776 0.276 0.258 0.280 0.299 4.641

Problem 191

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

113 139 101 86 108 286 162 93 102

N.S.

1 1.23 0.89 0.76 0.96 2.53 1.43 0.82 0.90

time (sec)

N/A 0.220 0.034 1.771 0.274 0.266 0.294 0.302 4.710

Problem 192

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

216 212 169 151 242 346 260 168 242

N.S.

1 0.98 0.78 0.70 1.12 1.60 1.20 0.78 1.12

time (sec)

N/A 0.381 0.031 1.770 0.202 0.245 1.072 0.294 4.930

Problem 193

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

205 203 158 142 231 335 245 157 230

N.S.

1 0.99 0.77 0.69 1.13 1.63 1.20 0.77 1.12

time (sec)

N/A 0.369 0.019 1.771 0.218 0.274 1.019 0.280 4.833

Problem 194

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

188 185 145 129 220 322 233 139 220

N.S.

1 0.98 0.77 0.69 1.17 1.71 1.24 0.74 1.17

time (sec)

N/A 0.344 0.024 1.771 0.216 0.244 0.969 0.291 0.436

Problem 195

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

179 178 116 120 209 300 219 119 207

N.S.

1 0.99 0.65 0.67 1.17 1.68 1.22 0.66 1.16

time (sec)

N/A 0.328 0.022 1.766 0.203 0.254 0.835 0.282 4.785

Problem 196

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

19 19 101 100 190 190 202 99 192

N.S.

1 1.00 5.32 5.26 10.00 10.00 10.63 5.21 10.11

time (sec)

N/A 0.135 0.014 1.755 0.218 0.241 0.767 0.299 0.120

Problem 197

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

39 43 90 89 179 179 190 88 181

N.S.

1 1.10 2.31 2.28 4.59 4.59 4.87 2.26 4.64

time (sec)

N/A 0.156 0.012 1.756 0.204 0.251 0.693 0.298 4.481

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 70 79 78 168 168 178 77 170

N.S.

1 1.21 1.36 1.34 2.90 2.90 3.07 1.33 2.93

time (sec)

N/A 0.164 0.013 1.733 0.208 0.272 0.629 0.280 0.108

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 97 68 67 157 157 167 66 159

N.S.

1 1.26 0.88 0.87 2.04 2.04 2.17 0.86 2.06

time (sec)

N/A 0.181 0.013 1.763 0.203 0.249 0.578 0.281 0.106

Problem 200

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 95 57 56 146 146 155 55 148

N.S.

1 1.04 0.63 0.62 1.60 1.60 1.70 0.60 1.63

time (sec)

N/A 0.220 0.011 1.723 0.197 0.246 0.541 0.287 4.430

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