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2.2.2 Integrals 101 to 166

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 44 39 41 43 110 60 38

N.S.

1 1.00 1.13 1.00 1.05 1.10 2.82 1.54 0.97

time (sec)

N/A 0.017 0.006 0.041 0.267 1.072 38.418 0.404 0.377

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 48 39 35 30 42 72 41

N.S.

1 1.00 1.17 0.95 0.85 0.73 1.02 1.76 1.00

time (sec)

N/A 0.018 0.006 0.059 0.465 1.511 35.408 0.427 0.386

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 60 51 53 54 129 69 50

N.S.

1 1.00 1.09 0.93 0.96 0.98 2.35 1.25 0.91

time (sec)

N/A 0.023 0.010 0.052 0.260 1.463 131.390 0.434 0.401

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 179 165 148 399 255 167 114

N.S.

1 1.00 1.03 0.95 0.85 2.29 1.47 0.96 0.66

time (sec)

N/A 0.231 0.035 0.092 0.471 1.673 23.275 0.477 1.164

Problem 105

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

101 101 131 98 92 234 755 95 91

N.S.

1 1.00 1.30 0.97 0.91 2.32 7.48 0.94 0.90

time (sec)

N/A 0.069 0.030 0.028 0.466 1.330 12.936 0.432 2.295

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 170 148 137 505 245 137 107

N.S.

1 1.00 1.03 0.90 0.83 3.06 1.48 0.83 0.65

time (sec)

N/A 0.209 0.033 0.085 0.474 1.532 29.053 0.466 0.909

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 183 105 102 121 286 108 118

N.S.

1 1.00 1.59 0.91 0.89 1.05 2.49 0.94 1.03

time (sec)

N/A 0.064 0.031 0.066 0.466 1.157 58.144 0.495 2.567

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 181 167 152 439 264 171 122

N.S.

1 1.00 1.03 0.95 0.86 2.49 1.50 0.97 0.69

time (sec)

N/A 0.310 0.056 0.096 0.467 1.744 61.127 0.488 1.002

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 185 113 106 137 292 119 106

N.S.

1 1.00 1.58 0.97 0.91 1.17 2.50 1.02 0.91

time (sec)

N/A 0.069 0.020 0.047 0.484 1.604 29.536 0.432 1.936

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 170 154 137 408 246 157 113

N.S.

1 1.00 1.03 0.93 0.83 2.47 1.49 0.95 0.68

time (sec)

N/A 0.290 0.019 0.058 0.464 1.679 17.088 0.481 0.689

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 170 104 98 90 262 91 99

N.S.

1 1.00 1.63 1.00 0.94 0.87 2.52 0.88 0.95

time (sec)

N/A 0.057 0.026 0.046 0.479 1.293 24.348 0.430 1.828

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 179 159 147 595 264 161 120

N.S.

1 1.00 1.03 0.91 0.84 3.42 1.52 0.93 0.69

time (sec)

N/A 0.297 0.036 0.072 0.485 1.622 45.930 0.590 0.706

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 121 151 169 129 243 145 150

N.S.

1 1.00 0.98 1.22 1.36 1.04 1.96 1.17 1.21

time (sec)

N/A 0.177 0.055 0.101 0.552 1.348 151.091 0.468 1.140

Problem 114

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

154 154 141 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.173 0.195 0.018 0.000 0.000 0.000 0.000 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 85 113 126 91 194 100 112

N.S.

1 1.00 0.94 1.26 1.40 1.01 2.16 1.11 1.24

time (sec)

N/A 0.101 0.036 0.141 0.543 1.030 50.500 0.422 0.724

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 107 142 0 0 0 0 -1

N.S.

1 1.00 1.03 1.37 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.044 0.174 0.000 0.000 0.000 0.000 0.000

Problem 117

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

154 154 167 0 0 0 0 0 -1

N.S.

1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.212 0.076 0.015 0.000 0.000 0.000 0.000 0.000

Problem 118

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

100 100 125 0 0 0 0 0 -1

N.S.

1 1.00 1.25 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.128 0.102 0.014 0.000 0.000 0.000 0.000 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 98 118 110 102 207 0 152

N.S.

1 1.00 1.13 1.36 1.26 1.17 2.38 0.00 1.75

time (sec)

N/A 0.113 0.043 0.128 0.541 1.238 72.195 0.000 0.691

Problem 120

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

154 154 167 0 0 0 0 0 -1

N.S.

1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.189 0.261 0.016 0.000 0.000 0.000 0.000 0.000

Problem 121

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

240 240 346 0 0 0 0 0 -1

N.S.

1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.331 0.348 0.015 0.000 0.000 0.000 0.000 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 170 935 0 0 0 0 -1

N.S.

1 1.00 1.16 6.36 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.197 0.089 0.654 0.000 0.000 0.000 0.000 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 224 289 0 0 0 0 -1

N.S.

1 1.00 1.61 2.08 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.177 0.045 0.165 0.000 0.000 0.000 0.000 0.000

Problem 124

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

232 232 248 0 0 0 0 0 -1

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.334 0.125 0.016 0.000 0.000 0.000 0.000 0.000

Problem 125

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

133 133 240 0 0 0 0 0 -1

N.S.

1 1.00 1.80 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.216 0.268 0.016 0.000 0.000 0.000 0.000 0.000

Problem 126

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

146 146 196 0 0 0 0 0 -1

N.S.

1 1.00 1.34 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.226 0.221 0.015 0.000 0.000 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.016 1.343 0.015 0.000 0.000 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.015 0.867 0.015 0.000 0.000 0.000 0.000 0.000

Problem 129

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

75 75 65 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.044 0.016 0.000 0.000 0.000 0.000 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 0.227 0.015 0.000 0.000 0.000 0.000 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.016 0.234 0.014 0.000 0.000 0.000 0.000 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 55 56 45 41 46 81 45

N.S.

1 1.00 1.10 1.12 0.90 0.82 0.92 1.62 0.90

time (sec)

N/A 0.024 0.009 0.110 0.467 1.868 0.150 0.448 0.411

Problem 133

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 48 62 43 40 41 69 40

N.S.

1 1.00 1.12 1.44 1.00 0.93 0.95 1.60 0.93

time (sec)

N/A 0.021 0.007 0.051 0.263 0.800 0.131 0.405 0.352

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 44 47 36 31 36 72 36

N.S.

1 1.00 1.13 1.21 0.92 0.79 0.92 1.85 0.92

time (sec)

N/A 0.012 0.007 0.063 0.470 0.660 0.105 0.433 0.344

Problem 135

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

27 27 27 38 27 25 22 46 25

N.S.

1 1.00 1.00 1.41 1.00 0.93 0.81 1.70 0.93

time (sec)

N/A 0.009 0.003 0.066 0.266 0.758 0.084 0.453 0.303

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 94 0 0 0 72 32

N.S.

1 1.00 1.00 2.41 0.00 0.00 0.00 1.85 0.82

time (sec)

N/A 0.031 0.006 0.091 0.000 0.000 0.000 0.432 0.338

Problem 137

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

34 34 37 38 38 41 36 39 43

N.S.

1 1.00 1.09 1.12 1.12 1.21 1.06 1.15 1.26

time (sec)

N/A 0.014 0.008 0.053 0.274 0.657 0.302 0.448 0.344

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 48 47 42 37 44 60 50

N.S.

1 1.00 1.12 1.09 0.98 0.86 1.02 1.40 1.16

time (sec)

N/A 0.017 0.009 0.071 0.470 0.719 0.335 0.445 0.384

Problem 139

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

55 55 60 53 54 55 60 51 56

N.S.

1 1.00 1.09 0.96 0.98 1.00 1.09 0.93 1.02

time (sec)

N/A 0.026 0.008 0.076 0.266 0.696 0.409 0.443 0.369

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 111 163 134 125 144 0 140

N.S.

1 1.00 0.91 1.34 1.10 1.02 1.18 0.00 1.15

time (sec)

N/A 0.176 0.055 0.420 0.482 1.882 0.214 0.000 0.473

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 152 412 0 0 0 0 -1

N.S.

1 1.00 1.00 2.71 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.178 0.238 0.379 0.000 0.000 0.000 0.000 0.000

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 73 124 104 88 97 0 98

N.S.

1 1.00 0.89 1.51 1.27 1.07 1.18 0.00 1.20

time (sec)

N/A 0.099 0.032 0.359 0.474 0.938 0.143 0.000 0.404

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 105 357 0 0 0 0 -1

N.S.

1 1.00 1.27 4.30 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.077 0.072 0.213 0.000 0.000 0.000 0.000 0.000

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 148 1249 0 0 0 0 -1

N.S.

1 1.00 1.00 8.44 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.196 0.060 3.372 0.000 0.000 0.000 0.000 0.000

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 107 142 0 0 0 0 -1

N.S.

1 1.00 1.11 1.48 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.087 0.085 0.507 0.000 0.000 0.000 0.000 0.000

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 99 112 120 109 117 137 143

N.S.

1 1.00 1.18 1.33 1.43 1.30 1.39 1.63 1.70

time (sec)

N/A 0.090 0.043 0.944 0.498 0.757 0.370 0.432 2.749

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

214 214 253 569 0 0 0 0 -1

N.S.

1 1.00 1.18 2.66 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.420 0.443 6.785 0.000 0.000 0.000 0.000 0.000

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 330 6282 0 0 0 0 -1

N.S.

1 1.00 1.44 27.43 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.348 0.493 13.416 0.000 0.000 0.000 0.000 0.000

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 174 473 0 0 0 0 -1

N.S.

1 1.00 1.20 3.26 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.209 0.192 2.487 0.000 0.000 0.000 0.000 0.000

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 215 2333 0 0 0 0 -1

N.S.

1 1.00 1.81 19.61 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.156 0.175 3.202 0.000 0.000 0.000 0.000 0.000

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

230 230 219 2542 0 0 0 0 -1

N.S.

1 1.00 0.95 11.05 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.311 0.136 0.866 0.000 0.000 0.000 0.000 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 222 289 0 0 0 0 -1

N.S.

1 1.00 1.63 2.12 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.161 0.068 1.468 0.000 0.000 0.000 0.000 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 178 368 0 0 0 0 -1

N.S.

1 1.00 1.21 2.50 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.186 0.191 4.392 0.000 0.000 0.000 0.000 0.000

Problem 154

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

51 51 34 32 31 27 39 31 31

N.S.

1 1.00 0.67 0.63 0.61 0.53 0.76 0.61 0.61

time (sec)

N/A 0.010 0.010 0.024 0.471 1.090 1.320 0.415 0.349

Problem 155

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 28 27 26 20 32 26 26

N.S.

1 1.00 0.67 0.64 0.62 0.48 0.76 0.62 0.62

time (sec)

N/A 0.007 0.008 0.012 0.469 0.667 0.783 0.407 0.365

Problem 156

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

22 22 18 17 16 14 19 16 16

N.S.

1 1.00 0.82 0.77 0.73 0.64 0.86 0.73 0.73

time (sec)

N/A 0.004 0.013 0.011 0.471 1.214 0.693 0.429 0.074

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 31 61 35 0 0 0 24

N.S.

1 1.00 1.00 1.97 1.13 0.00 0.00 0.00 0.77

time (sec)

N/A 0.024 0.005 0.020 0.474 0.000 0.000 0.000 0.302

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 30 22 21 17 94 21 21

N.S.

1 1.00 1.11 0.81 0.78 0.63 3.48 0.78 0.78

time (sec)

N/A 0.008 0.008 0.010 0.477 2.374 0.566 0.440 0.348

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 34 27 26 26 160 26 24

N.S.

1 1.00 0.81 0.64 0.62 0.62 3.81 0.62 0.57

time (sec)

N/A 0.009 0.009 0.013 0.478 3.210 1.193 0.443 0.353

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 30 25 24 24 85 24 24

N.S.

1 1.00 0.83 0.69 0.67 0.67 2.36 0.67 0.67

time (sec)

N/A 0.010 0.011 0.012 0.267 2.531 0.978 0.449 0.351

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 25 20 19 19 24 19 -1

N.S.

1 1.00 0.86 0.69 0.66 0.66 0.83 0.66 -0.03

time (sec)

N/A 0.008 0.008 0.011 0.257 3.450 0.782 0.447 0.000

Problem 162

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

20 20 20 17 16 16 17 16 16

N.S.

1 1.00 1.00 0.85 0.80 0.80 0.85 0.80 0.80

time (sec)

N/A 0.005 0.007 0.020 0.263 3.861 0.118 0.412 0.346

Problem 163

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

22 22 22 19 18 26 20 18 22

N.S.

1 1.00 1.00 0.86 0.82 1.18 0.91 0.82 1.00

time (sec)

N/A 0.006 0.009 0.024 0.256 5.143 0.383 0.451 0.358

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 31 26 25 33 143 28 27

N.S.

1 1.00 0.84 0.70 0.68 0.89 3.86 0.76 0.73

time (sec)

N/A 0.010 0.014 0.027 0.261 3.127 1.180 0.415 0.354

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 33 57 50 0 0 0 25

N.S.

1 1.00 1.00 1.73 1.52 0.00 0.00 0.00 0.76

time (sec)

N/A 0.025 0.006 0.064 0.480 0.000 0.000 0.000 0.336

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 32 83 0 63 0 0 -1

N.S.

1 1.00 0.82 2.13 0.00 1.62 0.00 0.00 -0.03

time (sec)

N/A 0.027 0.010 0.080 0.000 2.295 0.000 0.000 0.000

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