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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 150 101 89 107 206 138 93 0

N.S.

1 1.18 0.80 0.70 0.84 1.62 1.09 0.73 0.00

time (sec)

N/A 0.259 0.169 4.330 0.200 0.314 0.444 0.305 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 122 87 80 86 175 122 81 0

N.S.

1 1.17 0.84 0.77 0.83 1.68 1.17 0.78 0.00

time (sec)

N/A 0.222 0.139 3.394 0.201 0.271 0.421 0.292 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 94 77 65 67 157 107 68 0

N.S.

1 1.18 0.96 0.81 0.84 1.96 1.34 0.85 0.00

time (sec)

N/A 0.196 0.123 3.376 0.197 0.286 0.428 0.284 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 68 68 54 45 128 90 55 52

N.S.

1 1.01 1.01 0.81 0.67 1.91 1.34 0.82 0.78

time (sec)

N/A 0.173 0.139 3.375 0.188 0.285 0.346 0.296 5.720

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F(-2) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 81 90 79 59 341 129 0 68

N.S.

1 1.03 1.14 1.00 0.75 4.32 1.63 0.00 0.86

time (sec)

N/A 0.223 0.170 3.349 0.193 0.293 1.966 0.000 5.976

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 88 78 59 333 124 102 89

N.S.

1 1.00 1.17 1.04 0.79 4.44 1.65 1.36 1.19

time (sec)

N/A 0.226 0.154 3.405 0.211 0.318 1.947 0.285 6.487

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 84 90 73 83 377 107 163 94

N.S.

1 1.05 1.12 0.91 1.04 4.71 1.34 2.04 1.18

time (sec)

N/A 0.225 0.242 3.427 0.198 0.284 1.992 0.306 6.447

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 172 118 113 126 254 168 115 0

N.S.

1 1.15 0.79 0.75 0.84 1.69 1.12 0.77 0.00

time (sec)

N/A 0.278 0.222 3.450 0.188 0.294 0.518 0.312 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 144 107 104 105 223 150 103 0

N.S.

1 1.13 0.84 0.82 0.83 1.76 1.18 0.81 0.00

time (sec)

N/A 0.250 0.253 3.510 0.207 0.305 0.473 0.303 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 116 101 89 86 205 134 89 0

N.S.

1 1.13 0.98 0.86 0.83 1.99 1.30 0.86 0.00

time (sec)

N/A 0.212 0.215 3.409 0.220 0.344 0.449 0.303 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 90 87 70 61 176 119 76 54

N.S.

1 1.03 1.00 0.80 0.70 2.02 1.37 0.87 0.62

time (sec)

N/A 0.182 0.229 3.384 0.201 0.323 0.400 0.289 6.202

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F(-2) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 112 110 109 88 439 274 0 83

N.S.

1 1.06 1.04 1.03 0.83 4.14 2.58 0.00 0.78

time (sec)

N/A 0.249 0.298 3.391 0.203 0.311 4.260 0.000 6.140

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 111 111 113 88 411 243 124 86

N.S.

1 1.03 1.03 1.05 0.81 3.81 2.25 1.15 0.80

time (sec)

N/A 0.254 0.265 3.408 0.199 0.300 2.276 0.296 6.732

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 103 109 102 112 425 224 191 91

N.S.

1 0.93 0.98 0.92 1.01 3.83 2.02 1.72 0.82

time (sec)

N/A 0.251 0.319 3.424 0.205 0.313 2.910 0.306 7.272

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 194 137 137 145 302 199 140 0

N.S.

1 1.12 0.79 0.79 0.84 1.75 1.15 0.81 0.00

time (sec)

N/A 0.291 0.294 3.430 0.186 0.287 0.626 0.295 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 166 125 128 124 271 184 128 0

N.S.

1 1.11 0.83 0.85 0.83 1.81 1.23 0.85 0.00

time (sec)

N/A 0.262 0.290 3.422 0.202 0.290 0.593 0.303 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 138 118 108 105 253 168 114 0

N.S.

1 1.10 0.94 0.86 0.83 2.01 1.33 0.90 0.00

time (sec)

N/A 0.228 0.292 3.527 0.196 0.293 0.552 0.334 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 112 107 86 77 224 150 101 54

N.S.

1 1.05 1.00 0.80 0.72 2.09 1.40 0.94 0.50

time (sec)

N/A 0.197 0.306 3.382 0.196 0.268 0.460 0.313 5.873

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F(-2) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 141 130 139 119 539 474 0 101

N.S.

1 1.07 0.98 1.05 0.90 4.08 3.59 0.00 0.77

time (sec)

N/A 0.287 0.406 3.391 0.190 0.273 5.944 0.000 6.073

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 142 133 157 120 519 420 150 104

N.S.

1 1.04 0.98 1.15 0.88 3.82 3.09 1.10 0.76

time (sec)

N/A 0.289 0.371 3.413 0.203 0.278 2.623 0.311 6.724

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 142 132 145 143 535 381 219 111

N.S.

1 1.01 0.94 1.03 1.01 3.79 2.70 1.55 0.79

time (sec)

N/A 0.298 0.453 3.394 0.200 0.320 3.210 0.320 7.041

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 126 77 65 88 158 121 74 0

N.S.

1 1.21 0.74 0.62 0.85 1.52 1.16 0.71 0.00

time (sec)

N/A 0.252 0.147 3.391 0.215 0.276 0.399 0.300 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 98 74 56 67 127 102 61 93

N.S.

1 1.21 0.91 0.69 0.83 1.57 1.26 0.75 1.15

time (sec)

N/A 0.220 0.311 3.384 0.199 0.268 0.393 0.306 6.343

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 70 58 46 47 109 87 50 82

N.S.

1 1.25 1.04 0.82 0.84 1.95 1.55 0.89 1.46

time (sec)

N/A 0.193 0.131 3.502 0.209 0.262 0.411 0.294 6.400

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 46 37 29 92 71 39 36

N.S.

1 1.00 1.07 0.86 0.67 2.14 1.65 0.91 0.84

time (sec)

N/A 0.164 0.121 3.381 0.194 0.279 0.317 0.301 5.915

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F(-2) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 66 52 33 273 70 0 42

N.S.

1 1.00 1.25 0.98 0.62 5.15 1.32 0.00 0.79

time (sec)

N/A 0.193 0.107 3.383 0.187 0.283 1.204 0.000 6.148

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 57 49 37 101 41 65 39

N.S.

1 1.00 1.21 1.04 0.79 2.15 0.87 1.38 0.83

time (sec)

N/A 0.178 0.128 3.409 0.189 0.466 1.079 0.287 5.730

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 74 65 55 56 123 66 146 58

N.S.

1 1.03 0.90 0.76 0.78 1.71 0.92 2.03 0.81

time (sec)

N/A 0.215 0.217 3.415 0.194 0.286 1.652 0.302 5.810

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 100 74 77 85 197 117 70 0

N.S.

1 1.23 0.91 0.95 1.05 2.43 1.44 0.86 0.00

time (sec)

N/A 0.294 0.244 3.428 0.193 0.285 3.633 0.294 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 72 69 68 64 164 83 58 61

N.S.

1 1.09 1.05 1.03 0.97 2.48 1.26 0.88 0.92

time (sec)

N/A 0.207 0.272 3.530 0.196 0.278 2.714 0.300 6.065

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 53 55 46 147 66 48 53

N.S.

1 1.00 1.10 1.15 0.96 3.06 1.38 1.00 1.10

time (sec)

N/A 0.179 0.215 3.378 0.191 0.304 2.345 0.313 5.638

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 26 31 35 46 23 24

N.S.

1 1.00 0.96 0.93 1.11 1.25 1.64 0.82 0.86

time (sec)

N/A 0.147 0.194 3.381 0.209 0.258 1.874 0.307 6.046

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 57 61 48 146 206 59 50

N.S.

1 1.00 1.21 1.30 1.02 3.11 4.38 1.26 1.06

time (sec)

N/A 0.192 0.201 3.390 0.203 0.289 3.302 0.311 6.489

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 76 71 80 68 169 235 96 70

N.S.

1 1.09 1.01 1.14 0.97 2.41 3.36 1.37 1.00

time (sec)

N/A 0.226 0.206 3.421 0.202 0.294 4.145 0.328 6.077

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 102 83 88 89 211 124 171 94

N.S.

1 1.07 0.87 0.93 0.94 2.22 1.31 1.80 0.99

time (sec)

N/A 0.330 0.297 3.523 0.193 0.275 3.961 0.305 5.942

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 85 72 97 102 239 400 70 0

N.S.

1 1.08 0.91 1.23 1.29 3.03 5.06 0.89 0.00

time (sec)

N/A 0.279 0.337 3.412 0.194 0.280 5.333 0.315 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 59 44 41 70 63 141 36 51

N.S.

1 1.11 0.83 0.77 1.32 1.19 2.66 0.68 0.96

time (sec)

N/A 0.189 0.323 3.404 0.184 0.265 4.252 0.305 5.459

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 47 32 29 51 49 95 26 34

N.S.

1 0.94 0.64 0.58 1.02 0.98 1.90 0.52 0.68

time (sec)

N/A 0.166 0.309 3.380 0.192 0.287 3.876 0.290 5.412

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 43 40 48 62 146 37 41

N.S.

1 1.00 0.84 0.78 0.94 1.22 2.86 0.73 0.80

time (sec)

N/A 0.154 0.329 3.381 0.198 0.275 3.593 0.325 5.580

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 81 79 98 80 239 840 82 80

N.S.

1 1.07 1.04 1.29 1.05 3.14 11.05 1.08 1.05

time (sec)

N/A 0.223 0.320 3.460 0.186 0.298 8.428 0.315 6.374

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 113 94 122 100 264 910 119 96

N.S.

1 1.09 0.90 1.17 0.96 2.54 8.75 1.14 0.92

time (sec)

N/A 0.341 0.362 3.442 0.182 0.275 6.905 0.302 6.645

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 138 102 146 122 307 1034 197 123

N.S.

1 1.07 0.79 1.13 0.95 2.38 8.02 1.53 0.95

time (sec)

N/A 0.467 0.443 3.492 0.191 0.314 7.939 0.302 6.740

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 39 39 25 28 31 24 19 20

N.S.

1 1.44 1.44 0.93 1.04 1.15 0.89 0.70 0.74

time (sec)

N/A 0.161 0.091 3.481 0.271 0.286 0.083 0.314 0.043

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 39 39 25 28 31 24 19 20

N.S.

1 1.44 1.44 0.93 1.04 1.15 0.89 0.70 0.74

time (sec)

N/A 0.187 0.001 3.392 0.262 0.280 0.082 0.312 0.033

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 33 15 22 26 27 30 14

N.S.

1 1.00 1.94 0.88 1.29 1.53 1.59 1.76 0.82

time (sec)

N/A 0.139 0.008 3.416 0.282 0.262 0.036 0.290 5.407

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

6 6 6 7 6 6 5 6 6

N.S.

1 1.00 1.00 1.17 1.00 1.00 0.83 1.00 1.00

time (sec)

N/A 0.134 0.004 3.411 0.280 0.278 0.036 0.301 0.041

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 233 156 295 435 522 3806 204 0

N.S.

1 1.09 0.73 1.38 2.04 2.45 17.87 0.96 0.00

time (sec)

N/A 0.816 1.053 3.706 0.215 0.311 34.303 0.348 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 178 127 334 447 467 3448 138 0

N.S.

1 1.19 0.85 2.23 2.98 3.11 22.99 0.92 0.00

time (sec)

N/A 0.578 0.859 3.496 0.218 0.312 44.840 0.358 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 154 89 95 240 137 740 112 196

N.S.

1 1.17 0.67 0.72 1.82 1.04 5.61 0.85 1.48

time (sec)

N/A 0.501 0.691 3.557 0.208 0.293 20.663 0.314 5.672

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 162 79 76 253 122 575 81 186

N.S.

1 1.09 0.53 0.51 1.70 0.82 3.86 0.54 1.25

time (sec)

N/A 0.448 0.712 3.488 0.206 0.297 31.270 0.325 5.567

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 145 84 85 179 131 660 95 133

N.S.

1 1.04 0.60 0.61 1.29 0.94 4.75 0.68 0.96

time (sec)

N/A 0.363 0.839 3.485 0.187 0.317 20.049 0.311 5.499

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 139 87 88 197 134 904 94 133

N.S.

1 1.00 0.63 0.63 1.42 0.96 6.50 0.68 0.96

time (sec)

N/A 0.334 0.671 3.426 0.195 0.355 30.654 0.307 5.475

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 125 76 73 123 119 796 82 99

N.S.

1 1.05 0.64 0.61 1.03 1.00 6.69 0.69 0.83

time (sec)

N/A 0.281 0.793 3.590 0.187 0.397 19.626 0.321 5.763

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 121 92 96 153 137 1880 112 115

N.S.

1 0.95 0.72 0.76 1.20 1.08 14.80 0.88 0.91

time (sec)

N/A 0.245 0.607 3.494 0.196 0.285 24.192 0.317 5.759

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 156 130 193 157 465 6613 152 159

N.S.

1 1.13 0.94 1.40 1.14 3.37 47.92 1.10 1.15

time (sec)

N/A 0.362 0.914 3.428 0.198 0.326 32.006 0.300 6.299

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 212 168 277 228 525 6922 239 225

N.S.

1 1.13 0.89 1.47 1.21 2.79 36.82 1.27 1.20

time (sec)

N/A 0.756 0.937 3.481 0.215 0.345 42.510 0.314 6.747

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 246 173 327 265 688 11198 325 279

N.S.

1 1.12 0.79 1.49 1.21 3.14 51.13 1.48 1.27

time (sec)

N/A 0.986 1.141 3.482 0.215 0.337 62.494 0.305 7.465

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

45 45 43 0 0 0 97 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 2.16 0.00 0.00

time (sec)

N/A 0.170 0.007 0.000 0.000 0.000 0.614 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 82 0 0 0 189 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 2.08 0.00 0.00

time (sec)

N/A 0.205 0.055 0.000 0.000 0.000 1.674 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

76 76 56 0 0 0 201 0 0

N.S.

1 1.00 0.74 0.00 0.00 0.00 2.64 0.00 0.00

time (sec)

N/A 0.192 0.070 0.000 0.000 0.000 1.817 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

121 121 99 0 0 0 291 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 2.40 0.00 0.00

time (sec)

N/A 0.315 0.137 0.000 0.000 0.000 2.309 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 65 54 53 53 60 57 57

N.S.

1 1.00 1.00 0.83 0.82 0.82 0.92 0.88 0.88

time (sec)

N/A 0.260 0.015 0.081 0.188 0.250 0.017 0.304 5.760

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 65 54 53 53 60 57 57

N.S.

1 1.00 1.00 0.83 0.82 0.82 0.92 0.88 0.88

time (sec)

N/A 0.251 0.012 0.078 0.185 0.253 0.017 0.318 6.280

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 65 54 53 53 60 57 57

N.S.

1 1.00 1.00 0.83 0.82 0.82 0.92 0.88 0.88

time (sec)

N/A 0.246 0.007 0.074 0.184 0.267 0.019 0.299 6.182

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 60 51 50 50 56 54 54

N.S.

1 1.00 1.00 0.85 0.83 0.83 0.93 0.90 0.90

time (sec)

N/A 0.225 0.006 0.073 0.191 0.253 0.017 0.282 5.885

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 56 51 48 48 54 53 52

N.S.

1 1.00 1.00 0.91 0.86 0.86 0.96 0.95 0.93

time (sec)

N/A 0.227 0.011 0.027 0.198 0.274 0.061 0.278 5.950

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 50 48 55 49 50 49

N.S.

1 1.00 1.00 0.93 0.89 1.02 0.91 0.93 0.91

time (sec)

N/A 0.233 0.021 0.031 0.195 0.258 0.069 0.290 5.964

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 51 48 48 55 51 48 47

N.S.

1 1.00 0.94 0.89 0.89 1.02 0.94 0.89 0.87

time (sec)

N/A 0.230 0.017 0.030 0.205 0.267 0.146 0.304 6.118

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 55 49 49 55 54 50 50

N.S.

1 1.00 1.02 0.91 0.91 1.02 1.00 0.93 0.93

time (sec)

N/A 0.225 0.013 0.030 0.202 0.268 0.370 0.316 6.052

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 109 98 102 101 101 110 105 108

N.S.

1 1.00 0.90 0.94 0.93 0.93 1.01 0.96 0.99

time (sec)

N/A 0.326 0.026 3.360 0.189 0.253 0.023 0.332 5.804

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 109 92 102 101 101 110 105 108

N.S.

1 1.00 0.84 0.94 0.93 0.93 1.01 0.96 0.99

time (sec)

N/A 0.323 0.032 3.382 0.181 0.247 0.023 0.314 5.729

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 104 92 102 101 101 110 105 107

N.S.

1 1.00 0.88 0.98 0.97 0.97 1.06 1.01 1.03

time (sec)

N/A 0.299 0.025 3.351 0.186 0.250 0.025 0.298 5.729

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 88 99 98 98 107 102 105

N.S.

1 1.00 0.89 1.00 0.99 0.99 1.08 1.03 1.06

time (sec)

N/A 0.301 0.021 3.381 0.190 0.258 0.026 0.292 5.658

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 88 96 96 96 104 100 103

N.S.

1 1.00 0.96 1.04 1.04 1.04 1.13 1.09 1.12

time (sec)

N/A 0.294 0.028 3.383 0.186 0.263 0.089 0.307 5.728

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 90 88 98 96 103 99 98 92

N.S.

1 1.00 0.98 1.09 1.07 1.14 1.10 1.09 1.02

time (sec)

N/A 0.312 0.038 3.360 0.196 0.267 0.101 0.311 5.565

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 98 87 95 96 103 100 97 103

N.S.

1 1.00 0.89 0.97 0.98 1.05 1.02 0.99 1.05

time (sec)

N/A 0.289 0.024 3.448 0.207 0.256 0.182 0.304 5.671

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 98 83 92 97 103 100 97 106

N.S.

1 1.00 0.85 0.94 0.99 1.05 1.02 0.99 1.08

time (sec)

N/A 0.293 0.032 3.384 0.186 0.256 0.447 0.298 5.830

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 149 148 145 145 163 153 153

N.S.

1 1.00 1.00 0.99 0.97 0.97 1.09 1.03 1.03

time (sec)

N/A 0.396 0.018 3.576 0.191 0.269 0.027 0.293 5.871

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 125 148 145 145 165 153 153

N.S.

1 1.00 0.84 0.99 0.97 0.97 1.11 1.03 1.03

time (sec)

N/A 0.359 0.041 3.431 0.201 0.268 0.027 0.303 5.845

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 138 124 148 145 145 163 153 153

N.S.

1 1.00 0.90 1.07 1.05 1.05 1.18 1.11 1.11

time (sec)

N/A 0.342 0.036 3.424 0.193 0.268 0.027 0.369 5.785

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 133 121 144 142 142 158 149 149

N.S.

1 1.00 0.91 1.08 1.07 1.07 1.19 1.12 1.12

time (sec)

N/A 0.344 0.029 3.446 0.197 0.278 0.028 0.282 5.770

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 129 121 142 140 140 158 148 147

N.S.

1 1.00 0.94 1.10 1.09 1.09 1.22 1.15 1.14

time (sec)

N/A 0.325 0.042 3.421 0.193 0.269 0.122 0.301 5.853

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 124 123 145 139 147 150 145 121

N.S.

1 1.00 0.99 1.17 1.12 1.19 1.21 1.17 0.98

time (sec)

N/A 0.348 0.054 3.428 0.187 0.268 0.135 0.305 6.016

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 135 124 142 139 147 151 144 143

N.S.

1 1.00 0.92 1.05 1.03 1.09 1.12 1.07 1.06

time (sec)

N/A 0.341 0.040 3.430 0.188 0.280 0.221 0.288 6.006

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 139 124 141 142 147 155 146 148

N.S.

1 1.00 0.89 1.01 1.02 1.06 1.12 1.05 1.06

time (sec)

N/A 0.349 0.029 3.430 0.191 0.269 0.481 0.291 6.221

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 151 130 141 145 332 316 161 0

N.S.

1 1.00 0.86 0.93 0.96 2.20 2.09 1.07 0.00

time (sec)

N/A 0.368 0.047 3.441 0.278 0.298 0.545 0.301 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 114 128 127 270 274 137 0

N.S.

1 1.00 0.88 0.98 0.98 2.08 2.11 1.05 0.00

time (sec)

N/A 0.328 0.060 3.438 0.280 0.290 0.526 0.300 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 95 95 98 238 245 112 0

N.S.

1 1.00 0.86 0.86 0.88 2.14 2.21 1.01 0.00

time (sec)

N/A 0.300 0.033 3.412 0.276 0.287 0.484 0.295 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 81 85 82 180 211 88 0

N.S.

1 1.00 0.88 0.92 0.89 1.96 2.29 0.96 0.00

time (sec)

N/A 0.272 0.040 3.459 0.295 0.275 0.453 0.319 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 68 65 64 157 219 66 79

N.S.

1 1.00 0.93 0.89 0.88 2.15 3.00 0.90 1.08

time (sec)

N/A 0.241 0.028 3.369 0.278 0.298 0.420 0.289 5.572

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 73 73 65 158 0 66 0

N.S.

1 1.00 1.01 1.01 0.90 2.19 0.00 0.92 0.00

time (sec)

N/A 0.280 0.041 3.423 0.284 0.313 0.000 0.275 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 75 67 67 165 0 68 78

N.S.

1 1.00 0.99 0.88 0.88 2.17 0.00 0.89 1.03

time (sec)

N/A 0.281 0.031 3.425 0.280 0.300 0.000 0.282 5.618

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 84 89 76 205 0 80 97

N.S.

1 1.00 0.91 0.97 0.83 2.23 0.00 0.87 1.05

time (sec)

N/A 0.299 0.050 3.417 0.279 0.320 0.000 0.301 5.715

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 179 139 134 150 468 335 159 0

N.S.

1 1.02 0.79 0.76 0.85 2.66 1.90 0.90 0.00

time (sec)

N/A 0.533 0.082 3.549 0.276 0.288 1.866 0.289 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 155 128 124 127 372 289 131 0

N.S.

1 1.01 0.83 0.81 0.82 2.42 1.88 0.85 0.00

time (sec)

N/A 0.507 0.052 3.449 0.286 0.273 1.712 0.286 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 131 100 103 108 357 284 111 152

N.S.

1 0.98 0.75 0.77 0.81 2.66 2.12 0.83 1.13

time (sec)

N/A 0.468 0.050 3.406 0.300 0.274 1.602 0.298 5.735

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 109 92 78 84 287 212 81 0

N.S.

1 1.08 0.91 0.77 0.83 2.84 2.10 0.80 0.00

time (sec)

N/A 0.360 0.032 3.435 0.279 0.282 1.250 0.276 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 99 83 88 89 257 233 88 110

N.S.

1 1.06 0.89 0.95 0.96 2.76 2.51 0.95 1.18

time (sec)

N/A 0.252 0.053 3.466 0.288 0.273 0.988 0.285 5.600

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 104 85 99 87 296 0 93 0

N.S.

1 1.09 0.89 1.04 0.92 3.12 0.00 0.98 0.00

time (sec)

N/A 0.316 0.051 3.479 0.284 0.303 0.000 0.297 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 115 110 96 105 336 0 103 133

N.S.

1 1.05 1.00 0.87 0.95 3.05 0.00 0.94 1.21

time (sec)

N/A 0.399 0.045 3.552 0.291 0.296 0.000 0.279 6.186

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