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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 F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 165 268 361 191 0 191 228

N.S.

1 1.00 0.84 1.37 1.84 0.97 0.00 0.97 1.16

time (sec)

N/A 0.224 2.101 0.177 0.318 3.412 0.000 0.567 2.534

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 146 206 259 174 0 172 195

N.S.

1 1.00 1.04 1.47 1.85 1.24 0.00 1.23 1.39

time (sec)

N/A 0.151 1.187 0.100 0.298 2.654 0.000 0.519 2.300

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 122 171 219 157 0 153 163

N.S.

1 1.00 1.26 1.76 2.26 1.62 0.00 1.58 1.68

time (sec)

N/A 0.083 0.788 0.083 0.285 2.384 0.000 0.525 2.189

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 45 58 61 69 0 48 84

N.S.

1 1.00 0.96 1.23 1.30 1.47 0.00 1.02 1.79

time (sec)

N/A 0.052 0.036 0.052 0.297 2.504 0.000 0.479 3.709

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 72 84 103 111 0 103 91

N.S.

1 1.00 1.31 1.53 1.87 2.02 0.00 1.87 1.65

time (sec)

N/A 0.046 0.321 0.045 0.279 2.733 0.000 0.482 1.513

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 169 64 165 94 0 77 46

N.S.

1 1.00 3.02 1.14 2.95 1.68 0.00 1.38 0.82

time (sec)

N/A 0.122 0.312 0.123 0.511 3.148 0.000 0.503 1.484

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 53 47 188 94 0 57 40

N.S.

1 1.00 0.75 0.66 2.65 1.32 0.00 0.80 0.56

time (sec)

N/A 0.187 0.065 0.128 0.521 1.816 0.000 0.483 1.389

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 171 63 233 137 0 72 96

N.S.

1 1.00 1.68 0.62 2.28 1.34 0.00 0.71 0.94

time (sec)

N/A 0.273 0.653 0.142 0.500 2.681 0.000 0.516 1.450

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 227 77 320 184 0 88 124

N.S.

1 1.00 1.71 0.58 2.41 1.38 0.00 0.66 0.93

time (sec)

N/A 0.334 0.676 0.165 0.503 3.958 0.000 0.519 1.496

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 283 90 365 227 0 104 146

N.S.

1 1.00 1.73 0.55 2.23 1.38 0.00 0.63 0.89

time (sec)

N/A 0.417 0.930 0.174 0.518 3.218 0.000 0.549 1.536

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 189 288 385 208 0 210 259

N.S.

1 1.00 1.01 1.53 2.05 1.11 0.00 1.12 1.38

time (sec)

N/A 0.185 2.327 0.138 0.287 2.933 0.000 0.584 2.619

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 165 267 361 191 0 191 227

N.S.

1 1.00 1.25 2.02 2.73 1.45 0.00 1.45 1.72

time (sec)

N/A 0.111 1.968 0.111 0.283 2.353 0.000 0.578 2.593

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 61 93 101 86 0 65 122

N.S.

1 1.00 0.90 1.37 1.49 1.26 0.00 0.96 1.79

time (sec)

N/A 0.057 0.040 0.075 0.271 2.929 0.000 0.538 4.959

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 122 169 219 157 0 153 163

N.S.

1 1.00 1.26 1.74 2.26 1.62 0.00 1.58 1.68

time (sec)

N/A 0.088 0.857 0.077 0.305 3.365 0.000 0.551 2.133

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 101 96 116 127 0 104 104

N.S.

1 1.00 1.31 1.25 1.51 1.65 0.00 1.35 1.35

time (sec)

N/A 0.107 0.486 0.056 0.283 2.709 0.000 0.545 1.552

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 240 94 296 137 0 111 85

N.S.

1 1.00 3.08 1.21 3.79 1.76 0.00 1.42 1.09

time (sec)

N/A 0.152 2.798 0.122 0.505 3.542 0.000 0.507 1.479

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 177 66 296 168 0 80 45

N.S.

1 1.00 2.01 0.75 3.36 1.91 0.00 0.91 0.51

time (sec)

N/A 0.266 1.282 0.144 0.513 2.878 0.000 0.510 1.437

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 53 60 306 137 0 73 96

N.S.

1 1.00 0.52 0.59 3.00 1.34 0.00 0.72 0.94

time (sec)

N/A 0.338 0.093 0.154 0.503 2.114 0.000 0.528 1.378

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 227 76 417 184 0 88 122

N.S.

1 1.00 1.71 0.57 3.14 1.38 0.00 0.66 0.92

time (sec)

N/A 0.435 0.644 0.165 0.511 4.925 0.000 0.547 1.438

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 283 90 439 227 0 104 146

N.S.

1 1.00 1.73 0.55 2.68 1.38 0.00 0.63 0.89

time (sec)

N/A 0.517 0.957 0.189 0.521 3.104 0.000 0.583 1.461

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 153 384 137 653 260 0 153 145

N.S.

1 1.12 2.82 1.01 4.80 1.91 0.00 1.12 1.07

time (sec)

N/A 0.284 3.437 0.169 0.493 2.311 0.000 0.569 1.495

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 753 105 447 237 0 134 112

N.S.

1 1.00 7.38 1.03 4.38 2.32 0.00 1.31 1.10

time (sec)

N/A 0.220 6.281 0.138 0.498 2.283 0.000 0.512 1.471

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 216 66 290 185 0 80 46

N.S.

1 1.00 2.54 0.78 3.41 2.18 0.00 0.94 0.54

time (sec)

N/A 0.247 1.174 0.135 0.512 2.166 0.000 0.510 1.410

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 67 47 184 100 0 60 38

N.S.

1 1.00 1.00 0.70 2.75 1.49 0.00 0.90 0.57

time (sec)

N/A 0.167 0.054 0.131 0.534 2.864 0.000 0.468 1.375

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 113 46 129 92 0 53 41

N.S.

1 1.00 1.85 0.75 2.11 1.51 0.00 0.87 0.67

time (sec)

N/A 0.108 0.342 0.113 0.497 3.316 0.000 0.487 1.336

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 135 60 110 76 0 81 69

N.S.

1 1.00 1.96 0.87 1.59 1.10 0.00 1.17 1.00

time (sec)

N/A 0.085 0.585 0.105 0.498 2.397 0.000 0.494 1.422

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 39 32 49 87 0 95 58

N.S.

1 1.00 0.85 0.70 1.07 1.89 0.00 2.07 1.26

time (sec)

N/A 0.051 0.054 0.118 0.510 2.140 0.000 0.504 1.468

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 257 88 159 166 0 110 161

N.S.

1 1.00 2.62 0.90 1.62 1.69 0.00 1.12 1.64

time (sec)

N/A 0.107 1.349 0.126 0.521 3.027 0.000 0.498 1.544

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 315 101 181 179 0 122 185

N.S.

1 1.00 1.90 0.61 1.09 1.08 0.00 0.73 1.11

time (sec)

N/A 0.162 1.360 0.134 0.494 2.029 0.000 0.506 1.635

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 383 114 202 250 0 135 209

N.S.

1 1.00 1.82 0.54 0.96 1.19 0.00 0.64 1.00

time (sec)

N/A 0.215 1.313 0.141 0.528 2.778 0.000 0.551 1.779

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 557 118 610 311 0 154 134

N.S.

1 1.00 3.44 0.73 3.77 1.92 0.00 0.95 0.83

time (sec)

N/A 0.325 6.169 0.166 0.502 2.620 0.000 0.557 1.490

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 231 77 430 259 0 102 50

N.S.

1 1.00 1.56 0.52 2.91 1.75 0.00 0.69 0.34

time (sec)

N/A 0.441 1.325 0.161 0.504 3.190 0.000 0.559 1.421

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 90 60 301 147 0 80 93

N.S.

1 1.00 0.94 0.62 3.14 1.53 0.00 0.83 0.97

time (sec)

N/A 0.288 0.083 0.145 0.527 3.117 0.000 0.545 1.404

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 171 61 229 147 0 80 93

N.S.

1 1.00 1.78 0.64 2.39 1.53 0.00 0.83 0.97

time (sec)

N/A 0.221 0.519 0.139 0.504 2.569 0.000 0.519 1.396

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 169 58 173 133 0 71 85

N.S.

1 1.00 1.92 0.66 1.97 1.51 0.00 0.81 0.97

time (sec)

N/A 0.155 0.500 0.132 0.502 3.646 0.000 0.493 1.377

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 197 73 132 118 0 102 82

N.S.

1 1.00 1.56 0.58 1.05 0.94 0.00 0.81 0.65

time (sec)

N/A 0.144 1.029 0.124 0.480 3.565 0.000 0.557 1.425

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 257 88 158 166 0 116 161

N.S.

1 1.00 2.57 0.88 1.58 1.66 0.00 1.16 1.61

time (sec)

N/A 0.106 1.115 0.125 0.487 4.164 0.000 0.557 1.504

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 39 48 60 127 0 129 94

N.S.

1 1.00 0.58 0.72 0.90 1.90 0.00 1.93 1.40

time (sec)

N/A 0.064 0.077 0.133 0.494 4.073 0.000 0.551 1.569

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 362 114 203 250 0 142 209

N.S.

1 1.00 2.81 0.88 1.57 1.94 0.00 1.10 1.62

time (sec)

N/A 0.129 1.482 0.141 0.504 4.052 0.000 0.574 1.852

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 441 127 223 292 0 154 233

N.S.

1 1.00 2.10 0.60 1.06 1.39 0.00 0.73 1.11

time (sec)

N/A 0.180 1.799 0.161 0.498 3.021 0.000 0.591 2.041

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

252 252 499 140 247 334 0 169 257

N.S.

1 1.00 1.98 0.56 0.98 1.33 0.00 0.67 1.02

time (sec)

N/A 0.229 2.308 0.161 0.509 3.295 0.000 0.608 2.328

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 121 391 0 404 0 295 -1

N.S.

1 1.00 0.69 2.23 0.00 2.31 0.00 1.69 -0.01

time (sec)

N/A 0.134 1.131 1.240 0.000 3.915 0.000 1.546 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 111 302 0 376 0 263 -1

N.S.

1 1.00 0.79 2.16 0.00 2.69 0.00 1.88 -0.01

time (sec)

N/A 0.115 1.242 0.237 0.000 2.925 0.000 1.347 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 97 142 0 340 0 232 -1

N.S.

1 1.00 0.92 1.35 0.00 3.24 0.00 2.21 -0.01

time (sec)

N/A 0.109 0.876 0.220 0.000 2.684 0.000 1.271 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 70 115 159 255 0 193 -1

N.S.

1 1.00 1.06 1.74 2.41 3.86 0.00 2.92 -0.02

time (sec)

N/A 0.072 0.353 0.171 0.543 2.311 0.000 1.187 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 90 116 0 290 0 196 -1

N.S.

1 1.00 1.30 1.68 0.00 4.20 0.00 2.84 -0.01

time (sec)

N/A 0.100 0.661 0.204 0.000 2.849 0.000 1.105 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 78 214 0 369 0 296 -1

N.S.

1 1.00 0.75 2.06 0.00 3.55 0.00 2.85 -0.01

time (sec)

N/A 0.108 0.254 0.222 0.000 3.781 0.000 1.118 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 78 311 0 441 0 391 -1

N.S.

1 1.00 0.56 2.24 0.00 3.17 0.00 2.81 -0.01

time (sec)

N/A 0.116 0.276 0.273 0.000 3.814 0.000 1.178 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 78 402 0 517 0 487 -1

N.S.

1 1.00 0.45 2.31 0.00 2.97 0.00 2.80 -0.01

time (sec)

N/A 0.121 0.256 0.304 0.000 4.245 0.000 1.235 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 122 392 0 416 0 297 -1

N.S.

1 1.00 0.69 2.21 0.00 2.35 0.00 1.68 -0.01

time (sec)

N/A 0.128 1.021 0.228 0.000 3.880 0.000 1.608 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 112 232 0 384 0 265 -1

N.S.

1 1.00 0.79 1.63 0.00 2.70 0.00 1.87 -0.01

time (sec)

N/A 0.116 0.873 0.209 0.000 2.645 0.000 1.465 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 96 212 1076 330 0 227 -1

N.S.

1 1.00 0.95 2.10 10.65 3.27 0.00 2.25 -0.01

time (sec)

N/A 0.083 0.704 0.175 0.593 3.453 0.000 1.205 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 93 194 0 293 0 198 -1

N.S.

1 1.00 1.33 2.77 0.00 4.19 0.00 2.83 -0.01

time (sec)

N/A 0.110 0.602 0.175 0.000 4.121 0.000 1.161 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 113 215 0 381 0 318 -1

N.S.

1 1.00 1.11 2.11 0.00 3.74 0.00 3.12 -0.01

time (sec)

N/A 0.112 0.684 0.214 0.000 2.972 0.000 1.283 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 102 304 0 453 0 428 -1

N.S.

1 1.00 0.74 2.22 0.00 3.31 0.00 3.12 -0.01

time (sec)

N/A 0.119 0.762 0.244 0.000 2.773 0.000 1.455 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 102 401 0 537 0 555 -1

N.S.

1 1.00 0.59 2.33 0.00 3.12 0.00 3.23 -0.01

time (sec)

N/A 0.132 1.318 0.264 0.000 3.087 0.000 1.602 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

212 212 134 483 0 474 0 329 -1

N.S.

1 1.00 0.63 2.28 0.00 2.24 0.00 1.55 -0.00

time (sec)

N/A 0.133 1.279 0.303 0.000 2.752 0.000 1.766 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 124 323 0 440 0 297 -1

N.S.

1 1.00 0.70 1.82 0.00 2.49 0.00 1.68 -0.01

time (sec)

N/A 0.121 0.966 0.213 0.000 2.864 0.000 1.516 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 110 303 1501 382 0 227 -1

N.S.

1 1.00 0.83 2.30 11.37 2.89 0.00 1.72 -0.01

time (sec)

N/A 0.102 0.840 0.183 0.613 3.348 0.000 1.429 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 96 120 0 315 0 268 -1

N.S.

1 1.00 0.93 1.17 0.00 3.06 0.00 2.60 -0.01

time (sec)

N/A 0.120 0.740 0.182 0.000 3.147 0.000 1.249 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 102 351 0 367 0 243 -1

N.S.

1 1.00 1.38 4.74 0.00 4.96 0.00 3.28 -0.01

time (sec)

N/A 0.109 4.359 0.203 0.000 3.541 0.000 1.447 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

104 104 196 306 0 477 0 428 -1

N.S.

1 1.00 1.88 2.94 0.00 4.59 0.00 4.12 -0.01

time (sec)

N/A 0.122 5.470 0.237 0.000 3.512 0.000 1.413 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

140 140 361 395 0 569 0 556 -1

N.S.

1 1.00 2.58 2.82 0.00 4.06 0.00 3.97 -0.01

time (sec)

N/A 0.124 8.039 0.250 0.000 3.187 0.000 1.603 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

172 172 205 492 0 649 0 672 -1

N.S.

1 1.00 1.19 2.86 0.00 3.77 0.00 3.91 -0.01

time (sec)

N/A 0.135 3.595 0.299 0.000 4.352 0.000 1.835 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 153 544 0 597 0 0 -1

N.S.

1 1.00 0.83 2.94 0.00 3.23 0.00 0.00 -0.01

time (sec)

N/A 0.183 1.592 0.260 0.000 4.980 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 166 372 0 561 0 0 -1

N.S.

1 1.00 1.09 2.45 0.00 3.69 0.00 0.00 -0.01

time (sec)

N/A 0.160 1.365 0.230 0.000 3.661 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 124 329 0 473 0 0 -1

N.S.

1 1.00 1.04 2.76 0.00 3.97 0.00 0.00 -0.01

time (sec)

N/A 0.125 0.480 0.226 0.000 3.780 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 82 144 0 321 0 0 -1

N.S.

1 1.00 0.94 1.66 0.00 3.69 0.00 0.00 -0.01

time (sec)

N/A 0.094 0.284 0.180 0.000 4.267 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 101 195 0 474 0 0 -1

N.S.

1 1.00 0.83 1.61 0.00 3.92 0.00 0.00 -0.01

time (sec)

N/A 0.128 0.578 0.218 0.000 3.771 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

161 161 5576 377 0 566 0 0 -1

N.S.

1 1.00 34.63 2.34 0.00 3.52 0.00 0.00 -0.01

time (sec)

N/A 0.158 24.248 0.247 0.000 4.864 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

196 196 5592 545 0 662 0 0 -1

N.S.

1 1.00 28.53 2.78 0.00 3.38 0.00 0.00 -0.01

time (sec)

N/A 0.186 24.130 0.341 0.000 2.297 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 196 552 0 685 0 0 -1

N.S.

1 1.00 0.97 2.72 0.00 3.37 0.00 0.00 -0.00

time (sec)

N/A 0.194 1.557 0.245 0.000 3.662 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 132 377 0 593 0 0 -1

N.S.

1 1.00 0.78 2.23 0.00 3.51 0.00 0.00 -0.01

time (sec)

N/A 0.163 1.884 0.226 0.000 4.448 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 134 128 369 0 585 0 0 -1

N.S.

1 1.13 1.08 3.10 0.00 4.92 0.00 0.00 -0.01

time (sec)

N/A 0.129 1.119 0.183 0.000 2.813 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 130 130 371 0 548 0 0 -1

N.S.

1 1.15 1.15 3.28 0.00 4.85 0.00 0.00 -0.01

time (sec)

N/A 0.112 1.057 0.155 0.000 4.323 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 154 377 0 560 0 0 -1

N.S.

1 1.00 0.87 2.13 0.00 3.16 0.00 0.00 -0.01

time (sec)

N/A 0.162 1.249 0.208 0.000 3.476 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

214 214 5612 387 0 608 0 0 -1

N.S.

1 1.00 26.22 1.81 0.00 2.84 0.00 0.00 -0.00

time (sec)

N/A 0.183 24.317 0.264 0.000 2.991 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

249 249 5629 725 0 776 0 0 -1

N.S.

1 1.00 22.61 2.91 0.00 3.12 0.00 0.00 -0.00

time (sec)

N/A 0.230 24.234 0.446 0.000 3.135 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 180 726 0 801 0 0 -1

N.S.

1 1.00 0.69 2.79 0.00 3.08 0.00 0.00 -0.00

time (sec)

N/A 0.232 3.700 0.272 0.000 7.112 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 164 550 0 706 0 0 -1

N.S.

1 1.00 0.72 2.40 0.00 3.08 0.00 0.00 -0.00

time (sec)

N/A 0.201 2.722 0.236 0.000 4.729 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 136 553 0 696 0 0 -1

N.S.

1 1.00 0.71 2.90 0.00 3.64 0.00 0.00 -0.01

time (sec)

N/A 0.163 1.614 0.230 0.000 7.149 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 136 545 0 696 0 0 -1

N.S.

1 1.00 0.72 2.88 0.00 3.68 0.00 0.00 -0.01

time (sec)

N/A 0.153 1.526 0.195 0.000 5.080 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 181 134 543 0 656 0 0 -1

N.S.

1 1.22 0.91 3.67 0.00 4.43 0.00 0.00 -0.01

time (sec)

N/A 0.132 1.485 0.169 0.000 4.862 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

230 230 158 545 0 662 0 0 -1

N.S.

1 1.00 0.69 2.37 0.00 2.88 0.00 0.00 -0.00

time (sec)

N/A 0.206 1.511 0.237 0.000 3.689 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

269 269 5650 725 0 768 0 0 -1

N.S.

1 1.00 21.00 2.70 0.00 2.86 0.00 0.00 -0.00

time (sec)

N/A 0.227 24.263 0.295 0.000 4.659 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 149 194 1393 497 0 0 -1

N.S.

1 1.00 0.81 1.05 7.53 2.69 0.00 0.00 -0.01

time (sec)

N/A 0.242 6.433 0.730 0.630 3.994 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 162 184 767 461 0 0 -1

N.S.

1 1.00 1.17 1.32 5.52 3.32 0.00 0.00 -0.01

time (sec)

N/A 0.177 2.237 0.270 0.590 3.407 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 99 164 264 380 0 0 -1

N.S.

1 1.00 1.06 1.76 2.84 4.09 0.00 0.00 -0.01

time (sec)

N/A 0.117 1.333 0.250 0.569 2.711 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 102 127 42 216 0 0 -1

N.S.

1 1.00 2.12 2.65 0.88 4.50 0.00 0.00 -0.02

time (sec)

N/A 0.058 0.600 0.253 0.541 2.750 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 86 100 69 0 0 72 -1

N.S.

1 1.00 1.69 1.96 1.35 0.00 0.00 1.41 -0.02

time (sec)

N/A 0.061 0.926 0.268 0.494 0.000 0.000 1.446 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 107 162 440 0 0 147 -1

N.S.

1 1.00 1.11 1.69 4.58 0.00 0.00 1.53 -0.01

time (sec)

N/A 0.131 1.124 0.250 0.570 0.000 0.000 1.573 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 152 226 1288 0 0 178 -1

N.S.

1 1.00 1.07 1.59 9.07 0.00 0.00 1.25 -0.01

time (sec)

N/A 0.183 1.362 0.270 0.749 0.000 0.000 1.854 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 198 288 2681 0 0 208 -1

N.S.

1 1.00 1.05 1.53 14.26 0.00 0.00 1.11 -0.01

time (sec)

N/A 0.243 1.951 0.274 3.315 0.000 0.000 1.927 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 157 189 1460 505 0 0 -1

N.S.

1 1.00 0.83 0.99 7.68 2.66 0.00 0.00 -0.01

time (sec)

N/A 0.245 1.356 0.266 0.642 3.440 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 159 171 518 376 0 0 -1

N.S.

1 1.00 1.54 1.66 5.03 3.65 0.00 0.00 -0.01

time (sec)

N/A 0.077 1.455 0.257 0.571 2.720 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 128 149 264 377 0 0 -1

N.S.

1 1.00 1.38 1.60 2.84 4.05 0.00 0.00 -0.01

time (sec)

N/A 0.121 0.813 0.246 0.576 2.958 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 105 149 65 0 0 0 -1

N.S.

1 1.00 1.01 1.43 0.62 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.074 1.254 0.233 0.563 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 115 161 101 0 0 120 -1

N.S.

1 1.00 1.15 1.61 1.01 0.00 0.00 1.20 -0.01

time (sec)

N/A 0.127 0.726 0.233 0.526 0.000 0.000 1.677 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 153 227 1937 0 0 170 -1

N.S.

1 1.00 1.05 1.55 13.27 0.00 0.00 1.16 -0.01

time (sec)

N/A 0.197 1.239 0.248 0.809 0.000 0.000 2.040 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 199 289 3777 0 0 200 -1

N.S.

1 1.00 1.02 1.47 19.27 0.00 0.00 1.02 -0.01

time (sec)

N/A 0.255 2.212 0.290 3.335 0.000 0.000 1.717 0.000

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