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2.2.2 Integrals 101 to 174

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 F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 112 127 117 441 0 126 158

N.S.

1 1.00 0.83 0.94 0.87 3.27 0.00 0.93 1.17

time (sec)

N/A 0.141 0.071 0.105 0.564 7.440 0.000 1.531 1.348

Problem 102

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

185 185 139 140 165 574 357 157 232

N.S.

1 1.00 0.75 0.76 0.89 3.10 1.93 0.85 1.25

time (sec)

N/A 0.240 0.079 0.098 0.591 16.492 97.099 1.258 1.556

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 126 115 136 480 282 122 -1

N.S.

1 1.00 0.81 0.74 0.88 3.10 1.82 0.79 -0.01

time (sec)

N/A 0.162 0.054 0.109 0.538 8.010 86.672 1.354 0.000

Problem 104

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

136 136 122 123 146 447 304 128 195

N.S.

1 1.00 0.90 0.90 1.07 3.29 2.24 0.94 1.43

time (sec)

N/A 0.114 0.066 0.108 0.527 4.874 74.147 1.126 1.391

Problem 105

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

119 119 99 97 111 357 178 97 -1

N.S.

1 1.00 0.83 0.82 0.93 3.00 1.50 0.82 -0.01

time (sec)

N/A 0.080 0.079 0.103 0.545 2.519 8.488 1.881 0.000

Problem 106

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

116 116 104 98 122 346 184 106 163

N.S.

1 1.00 0.90 0.84 1.05 2.98 1.59 0.91 1.41

time (sec)

N/A 0.050 0.079 0.135 0.519 5.312 3.771 1.596 1.327

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 117 130 133 488 0 128 -1

N.S.

1 1.00 0.90 1.00 1.02 3.75 0.00 0.98 -0.01

time (sec)

N/A 0.093 0.075 0.102 0.504 3.159 0.000 1.052 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 141 125 152 524 0 141 202

N.S.

1 1.00 0.98 0.87 1.06 3.64 0.00 0.98 1.40

time (sec)

N/A 0.154 0.068 0.108 0.512 5.993 0.000 1.691 1.400

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 147 169 172 696 0 162 229

N.S.

1 1.00 0.84 0.97 0.99 4.00 0.00 0.93 1.32

time (sec)

N/A 0.212 0.107 0.103 0.505 3.871 0.000 1.134 1.456

Problem 110

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 19 18 24 15 25 20

N.S.

1 1.00 1.00 0.95 0.90 1.20 0.75 1.25 1.00

time (sec)

N/A 0.015 0.007 0.122 0.290 2.038 0.027 1.612 0.912

Problem 111

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

23 23 18 23 22 14 22 17 14

N.S.

1 1.00 0.78 1.00 0.96 0.61 0.96 0.74 0.61

time (sec)

N/A 0.014 0.014 0.135 0.293 1.357 0.097 2.831 0.102

Problem 112

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

25 25 25 21 20 20 20 20 20

N.S.

1 1.00 1.00 0.84 0.80 0.80 0.80 0.80 0.80

time (sec)

N/A 0.015 0.010 0.123 0.484 1.780 0.026 2.238 0.038

Problem 113

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 22 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.73 0.80 0.80

time (sec)

N/A 0.017 0.005 0.125 0.496 1.254 0.029 1.959 0.035

Problem 114

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

210 210 210 233 219 482 384 250 289

N.S.

1 1.00 1.00 1.11 1.04 2.30 1.83 1.19 1.38

time (sec)

N/A 0.104 0.103 0.153 0.507 3.800 0.462 1.071 0.929

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

172 172 162 185 177 392 337 200 243

N.S.

1 1.00 0.94 1.08 1.03 2.28 1.96 1.16 1.41

time (sec)

N/A 0.082 0.080 0.147 0.510 2.869 0.428 0.958 0.944

Problem 116

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

136 136 128 137 137 304 185 152 193

N.S.

1 1.00 0.94 1.01 1.01 2.24 1.36 1.12 1.42

time (sec)

N/A 0.071 0.065 0.138 0.530 3.652 0.402 1.546 0.912

Problem 117

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

100 100 98 94 97 246 160 106 96

N.S.

1 1.00 0.98 0.94 0.97 2.46 1.60 1.06 0.96

time (sec)

N/A 0.041 0.057 0.142 0.520 4.571 0.362 1.187 0.936

Problem 118

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

84 84 83 79 82 223 150 86 76

N.S.

1 1.00 0.99 0.94 0.98 2.65 1.79 1.02 0.90

time (sec)

N/A 0.064 0.046 0.139 0.523 3.529 0.511 0.770 1.067

Problem 119

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

82 82 83 79 80 228 151 81 80

N.S.

1 1.00 1.01 0.96 0.98 2.78 1.84 0.99 0.98

time (sec)

N/A 0.061 0.059 0.128 0.497 6.338 1.052 1.064 0.111

Problem 120

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

104 104 103 94 99 268 167 105 94

N.S.

1 1.00 0.99 0.90 0.95 2.58 1.61 1.01 0.90

time (sec)

N/A 0.069 0.060 0.155 0.510 9.331 2.525 1.306 1.203

Problem 121

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

137 137 139 129 137 326 301 151 127

N.S.

1 1.00 1.01 0.94 1.00 2.38 2.20 1.10 0.93

time (sec)

N/A 0.086 0.083 0.130 0.505 5.801 6.658 1.746 0.981

Problem 122

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

175 175 174 163 179 414 354 201 161

N.S.

1 1.00 0.99 0.93 1.02 2.37 2.02 1.15 0.92

time (sec)

N/A 0.097 0.101 0.130 0.492 6.661 25.299 1.551 1.018

Problem 123

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

211 211 211 201 219 504 398 249 197

N.S.

1 1.00 1.00 0.95 1.04 2.39 1.89 1.18 0.93

time (sec)

N/A 0.117 0.118 0.127 0.499 4.181 40.337 3.081 0.988

Problem 124

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

240 240 227 229 234 600 444 252 413

N.S.

1 1.00 0.95 0.95 0.98 2.50 1.85 1.05 1.72

time (sec)

N/A 0.194 0.087 0.148 0.519 5.446 1.206 1.670 0.099

Problem 125

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

202 202 187 182 189 502 257 201 288

N.S.

1 1.00 0.93 0.90 0.94 2.49 1.27 1.00 1.43

time (sec)

N/A 0.162 0.071 0.151 0.520 4.249 1.138 3.475 0.966

Problem 126

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

163 163 148 139 145 438 221 152 153

N.S.

1 1.00 0.91 0.85 0.89 2.69 1.36 0.93 0.94

time (sec)

N/A 0.155 0.059 0.145 0.520 3.544 1.051 1.633 1.002

Problem 127

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

118 118 122 114 121 380 201 126 113

N.S.

1 1.00 1.03 0.97 1.03 3.22 1.70 1.07 0.96

time (sec)

N/A 0.084 0.061 0.164 0.521 1.769 0.853 2.605 0.100

Problem 128

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

112 112 115 107 119 373 197 122 112

N.S.

1 1.00 1.03 0.96 1.06 3.33 1.76 1.09 1.00

time (sec)

N/A 0.093 0.044 0.142 0.493 1.512 2.255 1.782 0.996

Problem 129

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

121 121 125 116 132 404 212 123 119

N.S.

1 1.00 1.03 0.96 1.09 3.34 1.75 1.02 0.98

time (sec)

N/A 0.106 0.052 0.132 0.512 1.452 5.869 3.140 0.131

Problem 130

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

152 152 151 137 154 470 226 151 145

N.S.

1 1.00 0.99 0.90 1.01 3.09 1.49 0.99 0.95

time (sec)

N/A 0.146 0.057 0.124 0.491 2.664 20.555 1.942 0.999

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 190 174 198 524 0 201 181

N.S.

1 1.00 1.01 0.92 1.05 2.77 0.00 1.06 0.96

time (sec)

N/A 0.203 0.071 0.132 0.527 2.617 0.000 1.414 0.987

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

230 230 230 210 243 622 0 252 219

N.S.

1 1.00 1.00 0.91 1.06 2.70 0.00 1.10 0.95

time (sec)

N/A 0.249 0.081 0.156 0.516 3.863 0.000 1.260 1.010

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

287 287 272 268 289 798 503 301 506

N.S.

1 1.00 0.95 0.93 1.01 2.78 1.75 1.05 1.76

time (sec)

N/A 0.332 0.108 0.155 0.532 4.228 19.714 2.178 0.999

Problem 134

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

247 247 232 219 244 700 316 250 348

N.S.

1 1.00 0.94 0.89 0.99 2.83 1.28 1.01 1.41

time (sec)

N/A 0.266 0.099 0.158 0.519 1.717 18.402 1.987 0.107

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

207 207 176 177 199 636 280 200 206

N.S.

1 1.00 0.85 0.86 0.96 3.07 1.35 0.97 1.00

time (sec)

N/A 0.222 0.115 0.142 0.496 2.850 16.436 1.531 0.954

Problem 136

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

167 167 156 151 174 579 260 173 163

N.S.

1 1.00 0.93 0.90 1.04 3.47 1.56 1.04 0.98

time (sec)

N/A 0.173 0.086 0.147 0.517 2.114 6.286 2.067 1.018

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

147 147 141 139 157 531 243 149 148

N.S.

1 1.00 0.96 0.95 1.07 3.61 1.65 1.01 1.01

time (sec)

N/A 0.103 0.081 0.144 0.523 0.806 3.827 1.485 1.047

Problem 138

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

153 153 155 140 164 553 250 153 149

N.S.

1 1.00 1.01 0.92 1.07 3.61 1.63 1.00 0.97

time (sec)

N/A 0.121 0.086 0.154 0.519 1.624 12.305 1.135 1.094

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 169 152 184 606 0 170 166

N.S.

1 1.00 1.01 0.90 1.10 3.61 0.00 1.01 0.99

time (sec)

N/A 0.161 0.098 0.157 0.498 3.828 0.000 1.679 1.027

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 196 176 206 668 0 198 192

N.S.

1 1.00 1.00 0.90 1.05 3.41 0.00 1.01 0.98

time (sec)

N/A 0.238 0.079 0.159 0.554 5.346 0.000 1.412 1.043

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 234 212 252 726 0 250 230

N.S.

1 1.00 1.00 0.91 1.08 3.10 0.00 1.07 0.98

time (sec)

N/A 0.326 0.095 0.145 0.532 4.153 0.000 1.800 1.046

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 276 248 297 820 0 301 268

N.S.

1 1.00 1.00 0.90 1.07 2.96 0.00 1.09 0.97

time (sec)

N/A 0.412 0.105 0.170 0.496 6.084 0.000 2.045 1.070

Problem 143

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

214 214 158 382 352 186 442 264 186

N.S.

1 1.00 0.74 1.79 1.64 0.87 2.07 1.23 0.87

time (sec)

N/A 0.175 0.135 0.118 0.288 2.983 0.564 1.605 1.191

Problem 144

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

167 167 122 286 267 141 340 197 146

N.S.

1 1.00 0.73 1.71 1.60 0.84 2.04 1.18 0.87

time (sec)

N/A 0.132 0.104 0.113 0.268 5.722 0.454 1.764 1.107

Problem 145

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

121 121 89 193 183 99 238 130 103

N.S.

1 1.00 0.74 1.60 1.51 0.82 1.97 1.07 0.85

time (sec)

N/A 0.094 0.067 0.114 0.298 4.030 0.356 1.519 1.064

Problem 146

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

103 103 86 139 124 211 102 127 99

N.S.

1 1.00 0.83 1.35 1.20 2.05 0.99 1.23 0.96

time (sec)

N/A 0.095 0.116 0.110 0.303 2.820 15.195 1.744 1.810

Problem 147

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

100 100 92 129 105 212 138 114 99

N.S.

1 1.00 0.92 1.29 1.05 2.12 1.38 1.14 0.99

time (sec)

N/A 0.137 0.195 0.129 0.314 2.482 29.206 1.794 1.947

Problem 148

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

114 114 102 167 129 233 194 141 133

N.S.

1 1.00 0.89 1.46 1.13 2.04 1.70 1.24 1.17

time (sec)

N/A 0.165 0.212 0.131 0.289 1.242 60.983 2.098 2.191

Problem 149

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

146 146 126 250 195 281 303 232 199

N.S.

1 1.00 0.86 1.71 1.34 1.92 2.08 1.59 1.36

time (sec)

N/A 0.199 0.239 0.129 0.290 1.153 85.984 1.081 2.543

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 159 342 278 371 444 361 277

N.S.

1 1.00 0.82 1.75 1.43 1.90 2.28 1.85 1.42

time (sec)

N/A 0.240 0.381 0.135 0.285 1.078 166.551 1.108 2.913

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

245 245 186 402 344 432 0 224 -1

N.S.

1 1.00 0.76 1.64 1.40 1.76 0.00 0.91 -0.00

time (sec)

N/A 0.178 0.341 0.120 0.300 1.201 0.000 0.867 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 151 306 259 343 444 175 -1

N.S.

1 1.00 0.78 1.58 1.34 1.77 2.29 0.90 -0.01

time (sec)

N/A 0.147 0.275 0.118 0.293 2.732 47.777 1.405 0.000

Problem 153

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

145 145 121 215 177 260 362 129 -1

N.S.

1 1.00 0.83 1.48 1.22 1.79 2.50 0.89 -0.01

time (sec)

N/A 0.084 0.158 0.120 0.270 2.436 11.338 1.254 0.000

Problem 154

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

117 117 105 145 120 229 250 121 -1

N.S.

1 1.00 0.90 1.24 1.03 1.96 2.14 1.03 -0.01

time (sec)

N/A 0.096 0.208 0.131 0.272 3.301 4.230 1.274 0.000

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

110 110 95 119 103 215 197 176 143

N.S.

1 1.00 0.86 1.08 0.94 1.95 1.79 1.60 1.30

time (sec)

N/A 0.088 0.205 0.125 0.280 4.367 2.228 1.210 2.199

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 98 141 129 231 456 324 105

N.S.

1 1.00 0.83 1.19 1.09 1.96 3.86 2.75 0.89

time (sec)

N/A 0.092 0.238 0.124 0.264 2.531 1.696 1.112 1.724

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 103 206 195 109 891 554 124

N.S.

1 1.00 0.74 1.47 1.39 0.78 6.36 3.96 0.89

time (sec)

N/A 0.126 0.221 0.131 0.280 3.303 2.306 1.004 1.280

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 134 298 278 152 1642 667 171

N.S.

1 1.00 0.71 1.58 1.47 0.80 8.69 3.53 0.90

time (sec)

N/A 0.175 0.304 0.125 0.274 7.509 3.067 1.217 1.282

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

381 381 251 562 1221 987 0 342 -1

N.S.

1 1.00 0.66 1.48 3.20 2.59 0.00 0.90 -0.00

time (sec)

N/A 0.460 1.084 0.390 0.317 6.517 0.000 1.172 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

279 279 207 531 986 816 9649 265 -1

N.S.

1 1.00 0.74 1.90 3.53 2.92 34.58 0.95 -0.00

time (sec)

N/A 0.311 0.889 0.115 0.312 5.323 211.751 1.200 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 173 500 753 653 6467 203 -1

N.S.

1 1.00 0.82 2.38 3.59 3.11 30.80 0.97 -0.00

time (sec)

N/A 0.271 0.660 0.106 0.319 5.553 98.692 2.449 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 192 147 469 533 491 3803 160 -1

N.S.

1 1.07 0.82 2.62 2.98 2.74 21.25 0.89 -0.01

time (sec)

N/A 0.219 0.614 0.106 0.305 4.313 69.638 1.459 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 98 440 335 141 2088 131 -1

N.S.

1 1.00 0.73 3.28 2.50 1.05 15.58 0.98 -0.01

time (sec)

N/A 0.146 0.425 0.109 0.309 4.098 51.257 0.895 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 179 133 394 313 182 2392 211 -1

N.S.

1 0.97 0.72 2.13 1.69 0.98 12.93 1.14 -0.01

time (sec)

N/A 0.174 0.487 0.107 0.314 4.234 82.954 1.070 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

242 242 165 396 337 225 2861 349 -1

N.S.

1 1.00 0.68 1.64 1.39 0.93 11.82 1.44 -0.00

time (sec)

N/A 0.220 0.528 0.191 0.289 4.312 128.926 1.407 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

281 275 202 446 398 270 3313 592 405

N.S.

1 0.98 0.72 1.59 1.42 0.96 11.79 2.11 1.44

time (sec)

N/A 0.282 0.587 0.268 0.293 5.528 202.100 2.563 2.397

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

334 334 234 542 489 311 0 938 421

N.S.

1 1.00 0.70 1.62 1.46 0.93 0.00 2.81 1.26

time (sec)

N/A 0.323 0.646 0.291 0.294 4.650 0.000 0.980 2.836

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

392 380 270 638 579 354 0 1162 -1

N.S.

1 0.97 0.69 1.63 1.48 0.90 0.00 2.96 -0.00

time (sec)

N/A 0.369 0.740 0.359 0.305 3.527 0.000 0.994 0.000

Problem 169

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

214 214 158 382 352 186 442 264 186

N.S.

1 1.00 0.74 1.79 1.64 0.87 2.07 1.23 0.87

time (sec)

N/A 0.152 0.034 0.145 0.380 1.302 0.563 0.936 1.203

Problem 170

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

167 167 122 286 267 141 340 197 146

N.S.

1 1.00 0.73 1.71 1.60 0.84 2.04 1.18 0.87

time (sec)

N/A 0.125 0.024 0.108 0.376 1.763 0.444 1.363 1.140

Problem 171

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

121 121 89 193 183 99 238 130 103

N.S.

1 1.00 0.74 1.60 1.51 0.82 1.97 1.07 0.85

time (sec)

N/A 0.097 0.019 0.116 0.386 0.804 0.361 1.335 1.084

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

261 257 200 597 826 705 6987 224 -1

N.S.

1 0.98 0.77 2.29 3.16 2.70 26.77 0.86 -0.00

time (sec)

N/A 0.501 0.713 0.105 0.472 2.814 113.642 1.395 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

214 250 176 544 597 567 5071 204 -1

N.S.

1 1.17 0.82 2.54 2.79 2.65 23.70 0.95 -0.00

time (sec)

N/A 0.290 0.674 0.113 0.448 3.576 78.314 1.743 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 138 539 421 187 2490 220 -1

N.S.

1 1.00 0.72 2.79 2.18 0.97 12.90 1.14 -0.01

time (sec)

N/A 0.240 0.524 0.101 0.430 3.319 106.661 1.901 0.000

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