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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 A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 98 117 109 124 184 0 109

N.S.

1 1.00 0.84 1.00 0.93 1.06 1.57 0.00 0.93

time (sec)

N/A 0.074 0.050 0.122 0.482 4.120 1.716 0.000 0.739

Problem 2

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

105 105 88 107 99 113 167 0 99

N.S.

1 1.00 0.84 1.02 0.94 1.08 1.59 0.00 0.94

time (sec)

N/A 0.066 0.038 0.084 0.462 2.014 1.521 0.000 0.711

Problem 3

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

91 91 76 96 88 104 158 0 87

N.S.

1 1.00 0.84 1.05 0.97 1.14 1.74 0.00 0.96

time (sec)

N/A 0.055 0.035 0.103 0.470 1.588 1.415 0.000 0.382

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 84 79 73 89 128 0 73

N.S.

1 1.00 1.58 1.49 1.38 1.68 2.42 0.00 1.38

time (sec)

N/A 0.022 0.007 0.076 0.473 3.320 1.249 0.000 0.324

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 76 113 0 0 0 0 63

N.S.

1 1.00 1.00 1.49 0.00 0.00 0.00 0.00 0.83

time (sec)

N/A 0.059 0.006 0.059 0.000 0.000 0.000 0.000 0.618

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 78 127 0 0 0 0 93

N.S.

1 1.00 1.01 1.65 0.00 0.00 0.00 0.00 1.21

time (sec)

N/A 0.072 0.033 0.060 0.000 0.000 0.000 0.000 0.859

Problem 7

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

65 65 76 98 75 99 182 0 79

N.S.

1 1.00 1.17 1.51 1.15 1.52 2.80 0.00 1.22

time (sec)

N/A 0.040 0.037 0.128 0.469 2.483 1.827 0.000 0.541

Problem 8

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

106 106 89 108 87 109 197 0 176

N.S.

1 1.00 0.84 1.02 0.82 1.03 1.86 0.00 1.66

time (sec)

N/A 0.068 0.033 0.107 0.475 3.204 2.544 0.000 0.883

Problem 9

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

124 124 100 119 102 119 214 0 116

N.S.

1 1.00 0.81 0.96 0.82 0.96 1.73 0.00 0.94

time (sec)

N/A 0.068 0.049 0.138 0.484 2.191 4.019 0.000 0.580

Problem 10

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

166 166 124 171 185 172 270 0 152

N.S.

1 1.00 0.75 1.03 1.11 1.04 1.63 0.00 0.92

time (sec)

N/A 0.118 0.075 0.151 0.469 2.539 2.230 0.000 0.756

Problem 11

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

152 152 116 159 174 160 250 0 140

N.S.

1 1.00 0.76 1.05 1.14 1.05 1.64 0.00 0.92

time (sec)

N/A 0.104 0.065 0.129 0.472 1.836 1.988 0.000 0.740

Problem 12

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

136 136 101 146 155 148 240 0 125

N.S.

1 1.00 0.74 1.07 1.14 1.09 1.76 0.00 0.92

time (sec)

N/A 0.092 0.054 0.143 0.473 2.674 1.861 0.000 0.683

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 57 114 138 127 206 0 109

N.S.

1 1.00 0.69 1.37 1.66 1.53 2.48 0.00 1.31

time (sec)

N/A 0.033 0.027 0.077 0.488 2.401 1.540 0.000 0.399

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 103 177 142 0 0 0 131

N.S.

1 1.00 0.80 1.37 1.10 0.00 0.00 0.00 1.02

time (sec)

N/A 0.089 0.047 0.070 0.595 0.000 0.000 0.000 0.725

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 79 149 0 0 0 0 141

N.S.

1 1.00 0.89 1.67 0.00 0.00 0.00 0.00 1.58

time (sec)

N/A 0.101 0.048 0.069 0.000 0.000 0.000 0.000 0.603

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 137 206 0 0 0 0 161

N.S.

1 1.00 0.90 1.36 0.00 0.00 0.00 0.00 1.06

time (sec)

N/A 0.117 0.046 0.091 0.000 0.000 0.000 0.000 0.745

Problem 17

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 87 109 146 144 144 253 0 120

N.S.

1 1.00 1.25 1.68 1.66 1.66 2.91 0.00 1.38

time (sec)

N/A 0.057 0.040 0.122 0.463 3.278 5.182 0.000 0.641

Problem 18

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

161 161 119 161 152 155 275 0 142

N.S.

1 1.00 0.74 1.00 0.94 0.96 1.71 0.00 0.88

time (sec)

N/A 0.109 0.110 0.164 0.473 2.916 9.205 0.000 0.696

Problem 19

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

171 171 129 173 183 167 287 0 244

N.S.

1 1.00 0.75 1.01 1.07 0.98 1.68 0.00 1.43

time (sec)

N/A 0.115 0.048 0.131 0.466 1.440 15.021 0.000 0.919

Problem 20

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

205 205 154 210 261 202 328 0 186

N.S.

1 1.00 0.75 1.02 1.27 0.99 1.60 0.00 0.91

time (sec)

N/A 0.133 0.071 0.167 0.479 1.594 2.796 0.000 0.886

Problem 21

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

191 191 146 198 242 190 316 0 174

N.S.

1 1.00 0.76 1.04 1.27 0.99 1.65 0.00 0.91

time (sec)

N/A 0.121 0.061 0.133 0.476 2.087 2.464 0.000 0.828

Problem 22

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

157 157 132 185 222 177 296 0 160

N.S.

1 1.00 0.84 1.18 1.41 1.13 1.89 0.00 1.02

time (sec)

N/A 0.070 0.058 0.128 0.469 1.270 2.401 0.000 0.728

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 77 144 197 161 267 0 147

N.S.

1 1.00 0.77 1.44 1.97 1.61 2.67 0.00 1.47

time (sec)

N/A 0.037 0.028 0.084 0.472 1.458 2.118 0.000 0.693

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 139 220 184 0 0 0 196

N.S.

1 1.00 0.82 1.29 1.08 0.00 0.00 0.00 1.15

time (sec)

N/A 0.126 0.066 0.091 0.605 0.000 0.000 0.000 0.833

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 150 216 201 0 0 0 195

N.S.

1 1.00 0.93 1.33 1.24 0.00 0.00 0.00 1.20

time (sec)

N/A 0.120 0.065 0.084 0.602 0.000 0.000 0.000 0.721

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 164 228 0 0 0 0 205

N.S.

1 1.00 0.91 1.27 0.00 0.00 0.00 0.00 1.14

time (sec)

N/A 0.127 0.064 0.092 0.000 0.000 0.000 0.000 0.726

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 171 244 0 0 0 0 221

N.S.

1 1.00 0.90 1.29 0.00 0.00 0.00 0.00 1.17

time (sec)

N/A 0.147 0.057 0.090 0.000 0.000 0.000 0.000 0.973

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 141 187 202 174 311 0 154

N.S.

1 1.00 1.37 1.82 1.96 1.69 3.02 0.00 1.50

time (sec)

N/A 0.066 0.142 0.163 0.474 1.447 15.910 0.000 0.665

Problem 29

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

150 150 149 197 224 185 326 0 174

N.S.

1 1.00 0.99 1.31 1.49 1.23 2.17 0.00 1.16

time (sec)

N/A 0.077 0.054 0.138 0.467 2.332 28.597 0.000 0.951

Problem 30

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

214 214 161 212 248 198 347 0 192

N.S.

1 1.00 0.75 0.99 1.16 0.93 1.62 0.00 0.90

time (sec)

N/A 0.130 0.608 0.175 0.480 1.580 49.481 0.000 1.059

Problem 31

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

238 238 178 246 337 230 389 0 217

N.S.

1 1.00 0.75 1.03 1.42 0.97 1.63 0.00 0.91

time (sec)

N/A 0.155 0.076 0.172 0.470 1.701 3.476 0.000 2.589

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 170 234 318 218 367 0 205

N.S.

1 1.00 0.88 1.21 1.65 1.13 1.90 0.00 1.06

time (sec)

N/A 0.126 0.074 0.111 0.470 1.623 3.111 0.000 0.642

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 158 221 290 206 360 0 191

N.S.

1 1.00 0.89 1.24 1.63 1.16 2.02 0.00 1.07

time (sec)

N/A 0.083 0.071 0.134 0.475 1.841 2.812 0.000 0.793

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 77 172 264 188 316 0 175

N.S.

1 1.00 0.62 1.38 2.11 1.50 2.53 0.00 1.40

time (sec)

N/A 0.043 0.022 0.091 0.476 1.638 2.300 0.000 0.743

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 174 260 220 0 0 0 248

N.S.

1 1.00 0.86 1.28 1.08 0.00 0.00 0.00 1.22

time (sec)

N/A 0.149 0.072 0.092 0.600 0.000 0.000 0.000 0.986

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 181 257 240 0 0 0 253

N.S.

1 1.00 0.95 1.35 1.26 0.00 0.00 0.00 1.33

time (sec)

N/A 0.160 0.079 0.105 0.620 0.000 0.000 0.000 0.816

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

173 173 163 237 251 0 0 0 258

N.S.

1 1.00 0.94 1.37 1.45 0.00 0.00 0.00 1.49

time (sec)

N/A 0.148 0.073 0.097 0.630 0.000 0.000 0.000 0.892

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 193 262 0 0 0 0 261

N.S.

1 1.00 0.96 1.30 0.00 0.00 0.00 0.00 1.30

time (sec)

N/A 0.159 0.070 0.090 0.000 0.000 0.000 0.000 0.833

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 210 287 0 0 0 0 298

N.S.

1 1.00 0.93 1.26 0.00 0.00 0.00 0.00 1.31

time (sec)

N/A 0.171 0.064 0.106 0.000 0.000 0.000 0.000 0.943

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 167 223 275 202 366 0 186

N.S.

1 1.00 1.43 1.91 2.35 1.73 3.13 0.00 1.59

time (sec)

N/A 0.071 0.061 0.145 0.474 0.948 49.269 0.000 0.734

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 178 236 290 216 388 0 208

N.S.

1 1.00 1.06 1.40 1.73 1.29 2.31 0.00 1.24

time (sec)

N/A 0.081 0.985 0.197 0.489 1.385 91.683 0.000 0.897

Problem 42

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

243 243 187 248 329 228 398 0 317

N.S.

1 1.00 0.77 1.02 1.35 0.94 1.64 0.00 1.30

time (sec)

N/A 0.140 0.081 0.158 0.467 1.487 154.497 0.000 1.174

Problem 43

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

196 196 166 312 0 0 0 0 -1

N.S.

1 1.00 0.85 1.59 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.215 0.302 0.164 0.000 0.000 0.000 0.000 0.000

Problem 44

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

156 156 132 267 0 0 0 0 -1

N.S.

1 1.00 0.85 1.71 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.134 0.121 0.095 0.000 0.000 0.000 0.000 0.000

Problem 45

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

110 110 108 214 0 0 0 0 -1

N.S.

1 1.00 0.98 1.95 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.076 0.115 0.089 0.000 0.000 0.000 0.000 0.000

Problem 46

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

59 59 60 125 0 0 0 0 -1

N.S.

1 1.00 1.02 2.12 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.038 0.012 0.065 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 83 193 0 43 0 0 -1

N.S.

1 1.00 1.54 3.57 0.00 0.80 0.00 0.00 -0.02

time (sec)

N/A 0.051 0.093 0.093 0.000 1.109 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 126 246 0 98 0 0 -1

N.S.

1 1.00 1.26 2.46 0.00 0.98 0.00 0.00 -0.01

time (sec)

N/A 0.117 0.156 0.089 0.000 1.212 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 178 306 0 130 0 0 -1

N.S.

1 1.00 1.11 1.90 0.00 0.81 0.00 0.00 -0.01

time (sec)

N/A 0.175 0.277 0.115 0.000 1.391 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 220 340 0 155 0 0 -1

N.S.

1 1.00 1.12 1.73 0.00 0.79 0.00 0.00 -0.01

time (sec)

N/A 0.250 0.329 0.117 0.000 1.113 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 186 317 0 0 0 0 -1

N.S.

1 1.00 0.92 1.56 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.167 0.700 0.150 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 153 271 0 0 0 0 -1

N.S.

1 1.00 0.92 1.62 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.139 0.529 0.115 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 138 252 0 0 0 0 -1

N.S.

1 1.00 1.13 2.07 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.364 0.109 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 42 68 0 50 116 0 -1

N.S.

1 1.00 0.61 0.99 0.00 0.72 1.68 0.00 -0.01

time (sec)

N/A 0.035 0.027 0.091 0.000 1.700 0.965 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

150 150 138 251 0 127 0 0 -1

N.S.

1 1.00 0.92 1.67 0.00 0.85 0.00 0.00 -0.01

time (sec)

N/A 0.143 0.477 0.110 0.000 1.413 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 175 329 0 182 0 0 -1

N.S.

1 1.00 0.90 1.70 0.00 0.94 0.00 0.00 -0.01

time (sec)

N/A 0.171 0.791 0.124 0.000 1.243 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

244 244 219 345 0 221 0 0 -1

N.S.

1 1.00 0.90 1.41 0.00 0.91 0.00 0.00 -0.00

time (sec)

N/A 0.198 1.062 0.135 0.000 1.664 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

256 256 235 364 358 0 0 0 -1

N.S.

1 1.00 0.92 1.42 1.40 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.215 0.654 0.160 0.357 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 216 321 334 0 0 0 -1

N.S.

1 1.00 0.96 1.43 1.48 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.183 0.519 0.142 0.341 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 187 299 291 0 0 0 -1

N.S.

1 1.00 1.06 1.70 1.65 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.161 0.400 0.125 0.324 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 63 109 70 85 189 0 -1

N.S.

1 1.00 0.72 1.24 0.80 0.97 2.15 0.00 -0.01

time (sec)

N/A 0.058 0.045 0.153 0.271 2.104 5.630 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 55 82 65 75 158 0 -1

N.S.

1 1.00 0.60 0.89 0.71 0.82 1.72 0.00 -0.01

time (sec)

N/A 0.040 0.036 0.096 0.283 1.254 1.822 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 198 327 406 201 0 0 -1

N.S.

1 1.00 1.02 1.68 2.08 1.03 0.00 0.00 -0.01

time (sec)

N/A 0.186 0.611 0.132 0.333 1.963 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

250 250 241 380 0 263 0 0 -1

N.S.

1 1.00 0.96 1.52 0.00 1.05 0.00 0.00 -0.00

time (sec)

N/A 0.212 1.027 0.142 0.000 1.794 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

306 306 274 431 590 311 0 0 -1

N.S.

1 1.00 0.90 1.41 1.93 1.02 0.00 0.00 -0.00

time (sec)

N/A 0.238 1.319 0.152 0.360 2.066 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 73 79 83 93 168 0 -1

N.S.

1 1.00 0.73 0.79 0.83 0.93 1.68 0.00 -0.01

time (sec)

N/A 0.038 0.036 0.129 0.273 3.383 1.576 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 53 140 126 21 0 0 -1

N.S.

1 1.00 1.08 2.86 2.57 0.43 0.00 0.00 -0.02

time (sec)

N/A 0.045 0.063 0.078 0.470 5.315 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

287 287 285 474 0 0 0 0 -1

N.S.

1 1.00 0.99 1.65 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.435 0.528 0.211 0.000 0.000 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 241 442 0 0 0 0 -1

N.S.

1 1.00 0.95 1.73 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.362 0.383 0.229 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 208 391 0 0 0 0 -1

N.S.

1 1.00 0.99 1.85 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.272 0.284 0.170 0.000 0.000 0.000 0.000 0.000

Problem 71

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

130 130 151 344 0 0 0 0 -1

N.S.

1 1.00 1.16 2.65 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.093 0.132 0.194 0.000 0.000 0.000 0.000 0.000

Problem 72

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

216 216 272 7034 0 0 0 0 -1

N.S.

1 1.00 1.26 32.56 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.299 0.263 2.566 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

228 228 289 5899 0 0 0 0 -1

N.S.

1 1.00 1.27 25.87 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.342 0.239 2.644 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 190 448 0 0 0 0 -1

N.S.

1 1.00 1.19 2.82 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.251 0.155 0.548 0.000 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 240 514 0 0 0 0 -1

N.S.

1 1.00 1.07 2.29 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.320 0.325 0.649 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

373 373 342 624 0 0 0 0 -1

N.S.

1 1.00 0.92 1.67 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.699 0.744 0.288 0.000 0.000 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

333 333 306 586 0 0 0 0 -1

N.S.

1 1.00 0.92 1.76 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.620 0.748 0.321 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

293 293 257 530 0 0 0 0 -1

N.S.

1 1.00 0.88 1.81 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.449 0.429 0.253 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 205 469 0 0 0 0 -1

N.S.

1 1.00 1.07 2.44 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.121 0.347 0.168 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

300 300 360 1542 0 0 0 0 -1

N.S.

1 1.00 1.20 5.14 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.414 0.380 4.228 0.000 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 378 11833 0 0 0 0 -1

N.S.

1 1.00 1.19 37.33 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.463 0.329 2.901 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

337 337 388 1565 0 0 0 0 -1

N.S.

1 1.00 1.15 4.64 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.472 0.507 6.798 0.000 0.000 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

267 267 253 619 0 0 0 0 -1

N.S.

1 1.00 0.95 2.32 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.202 0.413 0.588 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

438 438 408 720 0 0 0 0 -1

N.S.

1 1.00 0.93 1.64 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.004 1.163 0.312 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

402 402 369 682 0 0 0 0 -1

N.S.

1 1.00 0.92 1.70 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.847 0.885 0.342 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

307 307 325 626 0 0 0 0 -1

N.S.

1 1.00 1.06 2.04 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.446 0.746 0.229 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

226 226 267 553 0 0 0 0 -1

N.S.

1 1.00 1.18 2.45 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.159 0.479 0.202 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

385 385 465 1651 0 0 0 0 -1

N.S.

1 1.00 1.21 4.29 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.552 0.464 6.457 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

402 402 512 1702 0 0 0 0 -1

N.S.

1 1.00 1.27 4.23 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.542 0.323 8.267 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

416 416 500 1746 0 0 0 0 -1

N.S.

1 1.00 1.20 4.20 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.539 0.691 7.015 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

429 429 595 1726 0 0 0 0 -1

N.S.

1 1.00 1.39 4.02 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.640 0.431 10.272 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

293 293 322 701 0 0 0 0 -1

N.S.

1 1.00 1.10 2.39 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.252 0.510 0.707 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

384 384 363 760 0 0 0 0 -1

N.S.

1 1.00 0.95 1.98 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.277 0.827 1.041 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

513 513 401 797 0 0 0 0 -1

N.S.

1 1.00 0.78 1.55 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.371 1.006 0.872 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 421 1227 0 0 0 0 -1

N.S.

1 1.00 1.18 3.45 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.606 0.615 7.988 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 330 1113 0 0 0 0 -1

N.S.

1 1.00 1.19 4.02 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.373 0.346 4.636 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 239 4395 0 0 0 0 -1

N.S.

1 1.00 1.24 22.89 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.235 0.291 1.310 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 95 1003 0 0 0 0 -1

N.S.

1 1.00 0.97 10.23 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.113 0.024 2.501 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 173 1741 0 136 0 0 -1

N.S.

1 1.00 1.97 19.78 0.00 1.55 0.00 0.00 -0.01

time (sec)

N/A 0.124 0.173 1.111 0.000 0.638 0.000 0.000 0.000

Problem 100

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

186 186 265 9130 0 0 0 0 -1

N.S.

1 1.00 1.42 49.09 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.294 0.536 1.588 0.000 0.000 0.000 0.000 0.000

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