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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 A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 94 97 96 96 107 98 88

N.S.

1 1.00 1.00 1.03 1.02 1.02 1.14 1.04 0.94

time (sec)

N/A 0.048 0.017 0.105 0.276 1.103 0.016 1.693 4.775

Problem 2

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

70 70 70 73 70 70 76 73 65

N.S.

1 1.00 1.00 1.04 1.00 1.00 1.09 1.04 0.93

time (sec)

N/A 0.032 0.012 0.104 0.278 0.809 0.014 0.727 4.753

Problem 3

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

50 50 50 49 48 48 53 50 48

N.S.

1 1.00 1.00 0.98 0.96 0.96 1.06 1.00 0.96

time (sec)

N/A 0.020 0.010 0.089 0.280 1.394 0.011 1.045 0.047

Problem 4

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

28 28 28 25 24 24 26 26 25

N.S.

1 1.00 1.00 0.89 0.86 0.86 0.93 0.93 0.89

time (sec)

N/A 0.010 0.005 0.084 0.295 0.850 0.006 0.919 0.036

Problem 5

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

40 40 40 34 34 99 82 34 31

N.S.

1 1.00 1.00 0.85 0.85 2.48 2.05 0.85 0.78

time (sec)

N/A 0.014 0.020 0.075 0.515 0.788 0.136 1.176 0.060

Problem 6

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

63 63 63 57 57 182 112 57 51

N.S.

1 1.00 1.00 0.90 0.90 2.89 1.78 0.90 0.81

time (sec)

N/A 0.015 0.036 0.069 0.512 0.679 0.199 0.882 5.006

Problem 7

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

92 92 82 77 92 300 150 78 82

N.S.

1 1.00 0.89 0.84 1.00 3.26 1.63 0.85 0.89

time (sec)

N/A 0.023 0.047 0.083 0.516 0.538 0.283 0.970 5.061

Problem 8

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

122 122 122 125 124 124 136 131 116

N.S.

1 1.00 1.00 1.02 1.02 1.02 1.11 1.07 0.95

time (sec)

N/A 0.054 0.017 0.103 0.274 0.731 0.017 1.965 4.945

Problem 9

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

82 82 82 87 82 82 97 91 75

N.S.

1 1.00 1.00 1.06 1.00 1.00 1.18 1.11 0.91

time (sec)

N/A 0.034 0.015 0.118 0.298 1.351 0.013 1.776 0.047

Problem 10

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

50 50 50 49 48 48 53 50 48

N.S.

1 1.00 1.00 0.98 0.96 0.96 1.06 1.00 0.96

time (sec)

N/A 0.020 0.005 0.095 0.270 1.171 0.011 2.600 0.046

Problem 11

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

63 63 59 64 68 179 172 72 90

N.S.

1 1.00 0.94 1.02 1.08 2.84 2.73 1.14 1.43

time (sec)

N/A 0.031 0.036 0.076 0.516 0.952 0.220 1.767 0.088

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 89 92 96 302 236 95 124

N.S.

1 1.00 1.09 1.12 1.17 3.68 2.88 1.16 1.51

time (sec)

N/A 0.067 0.048 0.084 0.504 0.716 0.382 2.064 5.021

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 121 124 138 449 223 126 130

N.S.

1 1.00 1.04 1.07 1.19 3.87 1.92 1.09 1.12

time (sec)

N/A 0.050 0.070 0.094 0.508 0.776 0.541 2.418 5.030

Problem 14

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

154 154 161 177 167 167 189 187 152

N.S.

1 1.00 1.05 1.15 1.08 1.08 1.23 1.21 0.99

time (sec)

N/A 0.073 0.019 0.100 0.354 0.730 0.021 1.631 4.905

Problem 15

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

122 122 122 125 124 124 136 131 116

N.S.

1 1.00 1.00 1.02 1.02 1.02 1.11 1.07 0.95

time (sec)

N/A 0.051 0.015 0.107 0.349 0.787 0.019 2.976 4.875

Problem 16

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

70 70 70 73 70 70 76 73 65

N.S.

1 1.00 1.00 1.04 1.00 1.00 1.09 1.04 0.93

time (sec)

N/A 0.031 0.009 0.105 0.304 0.510 0.014 2.222 0.034

Problem 17

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

98 98 93 116 122 290 238 130 145

N.S.

1 1.00 0.95 1.18 1.24 2.96 2.43 1.33 1.48

time (sec)

N/A 0.045 0.044 0.089 0.519 0.532 0.314 1.678 4.870

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 107 138 147 444 314 152 181

N.S.

1 1.00 1.00 1.29 1.37 4.15 2.93 1.42 1.69

time (sec)

N/A 0.067 0.042 0.087 0.499 0.593 0.573 1.951 0.100

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 141 167 187 618 422 180 240

N.S.

1 1.00 1.08 1.28 1.44 4.75 3.25 1.38 1.85

time (sec)

N/A 0.117 0.057 0.094 0.520 0.470 1.001 1.228 4.956

Problem 20

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

142 142 136 196 187 428 326 198 216

N.S.

1 1.00 0.96 1.38 1.32 3.01 2.30 1.39 1.52

time (sec)

N/A 0.067 0.063 0.130 0.508 0.439 0.432 1.067 4.861

Problem 21

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

98 98 92 116 122 292 238 129 146

N.S.

1 1.00 0.94 1.18 1.24 2.98 2.43 1.32 1.49

time (sec)

N/A 0.041 0.048 0.085 0.515 1.484 0.315 2.306 0.076

Problem 22

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

63 63 59 64 69 181 172 72 90

N.S.

1 1.00 0.94 1.02 1.10 2.87 2.73 1.14 1.43

time (sec)

N/A 0.028 0.036 0.073 0.516 1.519 0.224 2.257 4.902

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 40 34 33 98 82 33 32

N.S.

1 1.00 1.03 0.87 0.85 2.51 2.10 0.85 0.82

time (sec)

N/A 0.011 0.019 0.070 0.506 1.617 0.135 1.420 0.055

Problem 24

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

70 70 61 55 54 292 712 54 135

N.S.

1 1.00 0.87 0.79 0.77 4.17 10.17 0.77 1.93

time (sec)

N/A 0.019 0.032 0.108 0.508 1.696 2.729 1.836 0.320

Problem 25

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

109 109 95 93 133 711 0 122 2500

N.S.

1 1.00 0.87 0.85 1.22 6.52 0.00 1.12 22.94

time (sec)

N/A 0.060 0.129 0.150 0.504 1.064 0.000 1.430 5.688

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 158 158 277 1585 0 217 2500

N.S.

1 1.00 0.99 0.99 1.73 9.91 0.00 1.36 15.62

time (sec)

N/A 0.130 0.163 0.193 0.538 1.626 0.000 1.256 6.869

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 192 290 294 810 502 306 386

N.S.

1 1.00 1.00 1.51 1.53 4.22 2.61 1.59 2.01

time (sec)

N/A 0.108 0.067 0.094 0.502 0.787 1.113 0.845 5.024

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 142 206 213 612 403 220 261

N.S.

1 1.00 1.00 1.45 1.50 4.31 2.84 1.55 1.84

time (sec)

N/A 0.082 0.062 0.106 0.498 0.653 0.817 2.216 5.054

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 106 139 147 442 314 152 182

N.S.

1 1.00 1.00 1.31 1.39 4.17 2.96 1.43 1.72

time (sec)

N/A 0.065 0.044 0.088 0.498 0.813 0.594 1.125 0.102

Problem 30

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 88 94 95 297 236 94 124

N.S.

1 1.00 1.07 1.15 1.16 3.62 2.88 1.15 1.51

time (sec)

N/A 0.069 0.045 0.090 0.491 0.799 0.394 1.349 5.062

Problem 31

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

63 63 63 57 57 181 112 57 51

N.S.

1 1.00 1.00 0.90 0.90 2.87 1.78 0.90 0.81

time (sec)

N/A 0.016 0.033 0.071 0.500 0.596 0.208 1.295 5.042

Problem 32

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

108 108 109 95 132 699 0 121 2500

N.S.

1 1.00 1.01 0.88 1.22 6.47 0.00 1.12 23.15

time (sec)

N/A 0.056 0.098 0.151 0.507 0.628 0.000 1.983 5.766

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 136 133 294 1681 0 232 2500

N.S.

1 1.00 0.81 0.80 1.76 10.07 0.00 1.39 14.97

time (sec)

N/A 0.134 0.226 0.198 0.503 1.192 0.000 1.674 6.875

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

230 230 197 198 529 3239 0 332 2500

N.S.

1 1.00 0.86 0.86 2.30 14.08 0.00 1.44 10.87

time (sec)

N/A 0.217 0.277 0.254 0.519 2.863 0.000 1.564 7.793

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 196 311 334 1044 615 340 409

N.S.

1 1.00 1.00 1.59 1.70 5.33 3.14 1.73 2.09

time (sec)

N/A 0.154 0.085 0.102 0.524 0.525 7.268 1.487 5.023

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 160 231 253 817 515 254 318

N.S.

1 1.00 1.00 1.44 1.58 5.11 3.22 1.59 1.99

time (sec)

N/A 0.132 0.066 0.109 0.492 0.490 1.826 1.430 0.135

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 139 170 185 606 422 178 240

N.S.

1 1.00 1.07 1.31 1.42 4.66 3.25 1.37 1.85

time (sec)

N/A 0.112 0.055 0.102 0.524 0.455 1.021 1.382 5.052

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 124 124 138 449 223 126 130

N.S.

1 1.00 1.07 1.07 1.19 3.87 1.92 1.09 1.12

time (sec)

N/A 0.053 0.065 0.087 0.502 0.477 0.536 3.320 5.023

Problem 39

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

92 92 84 76 92 301 150 78 81

N.S.

1 1.00 0.91 0.83 1.00 3.27 1.63 0.85 0.88

time (sec)

N/A 0.022 0.045 0.076 0.492 1.082 0.287 2.847 5.016

Problem 40

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

161 161 158 158 278 1587 0 218 2500

N.S.

1 1.00 0.98 0.98 1.73 9.86 0.00 1.35 15.53

time (sec)

N/A 0.128 0.190 0.205 0.496 1.044 0.000 1.450 6.892

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

236 236 197 196 530 3251 0 333 2500

N.S.

1 1.00 0.83 0.83 2.25 13.78 0.00 1.41 10.59

time (sec)

N/A 0.212 0.280 0.225 0.522 2.876 0.000 1.167 7.855

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

315 315 233 257 820 5070 0 574 2500

N.S.

1 1.00 0.74 0.82 2.60 16.10 0.00 1.82 7.94

time (sec)

N/A 0.311 0.612 0.315 0.584 9.251 0.000 1.743 8.555

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 24 23 33 33 31 20 31

N.S.

1 1.00 0.71 0.68 0.97 0.97 0.91 0.59 0.91

time (sec)

N/A 0.006 0.006 0.162 0.275 1.721 0.042 2.426 4.995

Problem 44

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

47 47 41 33 48 67 46 54 47

N.S.

1 1.00 0.87 0.70 1.02 1.43 0.98 1.15 1.00

time (sec)

N/A 0.010 0.010 0.096 0.529 0.915 0.061 0.914 0.042

Problem 45

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

231 231 180 300 281 398 484 201 -1

N.S.

1 1.00 0.78 1.30 1.22 1.72 2.10 0.87 -0.00

time (sec)

N/A 0.120 0.247 0.066 0.297 2.274 28.780 0.963 0.000

Problem 46

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

149 149 122 187 168 264 291 129 -1

N.S.

1 1.00 0.82 1.26 1.13 1.77 1.95 0.87 -0.01

time (sec)

N/A 0.060 0.158 0.063 0.279 3.457 8.462 0.729 0.000

Problem 47

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

87 87 74 98 81 158 144 70 -1

N.S.

1 1.00 0.85 1.13 0.93 1.82 1.66 0.80 -0.01

time (sec)

N/A 0.019 0.085 0.056 0.298 2.676 3.297 0.677 0.000

Problem 48

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

46 46 48 36 28 94 41 37 35

N.S.

1 1.00 1.04 0.78 0.61 2.04 0.89 0.80 0.76

time (sec)

N/A 0.007 0.007 0.047 0.282 1.277 0.894 0.657 4.712

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

82 82 99 645 0 596 0 0 -1

N.S.

1 1.00 1.21 7.87 0.00 7.27 0.00 0.00 -0.01

time (sec)

N/A 0.042 0.198 0.128 0.000 1.152 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 99 1945 0 369 0 217 -1

N.S.

1 1.00 1.21 23.72 0.00 4.50 0.00 2.65 -0.01

time (sec)

N/A 0.025 0.312 0.060 0.000 1.026 0.000 1.659 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 146 4113 0 698 0 487 -1

N.S.

1 1.00 0.98 27.60 0.00 4.68 0.00 3.27 -0.01

time (sec)

N/A 0.062 0.883 0.066 0.000 1.485 0.000 1.991 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

208 208 227 6475 0 1220 0 958 -1

N.S.

1 1.00 1.09 31.13 0.00 5.87 0.00 4.61 -0.00

time (sec)

N/A 0.148 10.774 0.078 0.000 1.334 0.000 2.210 0.000

Problem 53

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

272 272 225 364 364 502 665 260 -1

N.S.

1 1.00 0.83 1.34 1.34 1.85 2.44 0.96 -0.00

time (sec)

N/A 0.146 0.359 0.063 0.315 0.729 172.356 0.968 0.000

Problem 54

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

196 196 158 235 227 344 440 175 -1

N.S.

1 1.00 0.81 1.20 1.16 1.76 2.24 0.89 -0.01

time (sec)

N/A 0.077 0.256 0.059 0.283 0.581 35.721 0.622 0.000

Problem 55

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

118 118 99 130 116 210 253 103 -1

N.S.

1 1.00 0.84 1.10 0.98 1.78 2.14 0.87 -0.01

time (sec)

N/A 0.026 0.154 0.054 0.274 0.549 10.121 0.597 0.000

Problem 56

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

65 65 60 52 43 124 70 49 37

N.S.

1 1.00 0.92 0.80 0.66 1.91 1.08 0.75 0.57

time (sec)

N/A 0.010 0.014 0.000 0.280 0.512 1.533 0.506 4.709

Problem 57

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

113 113 126 1227 0 721 0 0 -1

N.S.

1 1.00 1.12 10.86 0.00 6.38 0.00 0.00 -0.01

time (sec)

N/A 0.072 0.315 0.095 0.000 0.789 0.000 0.000 0.000

Problem 58

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

131 131 145 3349 0 907 0 317 -1

N.S.

1 1.00 1.11 25.56 0.00 6.92 0.00 2.42 -0.01

time (sec)

N/A 0.062 0.547 0.062 0.000 0.608 0.000 0.569 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 1002 6921 0 526 0 451 -1

N.S.

1 1.00 8.87 61.25 0.00 4.65 0.00 3.99 -0.01

time (sec)

N/A 0.040 3.601 0.066 0.000 0.624 0.000 1.828 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 247 12816 0 972 0 919 -1

N.S.

1 1.00 1.24 64.40 0.00 4.88 0.00 4.62 -0.01

time (sec)

N/A 0.080 10.613 0.072 0.000 0.801 0.000 1.653 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

300 300 362 22502 0 1604 0 1557 -1

N.S.

1 1.00 1.21 75.01 0.00 5.35 0.00 5.19 -0.00

time (sec)

N/A 0.253 11.025 0.086 0.000 1.763 0.000 5.114 0.000

Problem 62

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

349 349 269 428 447 608 0 321 -1

N.S.

1 1.00 0.77 1.23 1.28 1.74 0.00 0.92 -0.00

time (sec)

N/A 0.169 0.474 0.069 0.327 0.827 0.000 0.725 0.000

Problem 63

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

241 241 190 283 286 420 0 221 -1

N.S.

1 1.00 0.79 1.17 1.19 1.74 0.00 0.92 -0.00

time (sec)

N/A 0.100 0.332 0.059 0.307 0.562 0.000 0.598 0.000

Problem 64

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

149 149 123 162 151 260 316 135 -1

N.S.

1 1.00 0.83 1.09 1.01 1.74 2.12 0.91 -0.01

time (sec)

N/A 0.035 0.206 0.053 0.305 0.512 37.844 0.565 0.000

Problem 65

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

84 84 71 68 58 146 97 63 37

N.S.

1 1.00 0.85 0.81 0.69 1.74 1.15 0.75 0.44

time (sec)

N/A 0.016 0.016 0.046 0.308 0.505 2.783 0.583 4.693

Problem 66

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

157 157 157 2048 0 935 0 0 -1

N.S.

1 1.00 1.00 13.04 0.00 5.96 0.00 0.00 -0.01

time (sec)

N/A 0.136 0.394 0.090 0.000 1.167 0.000 0.000 0.000

Problem 67

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

175 175 187 5230 0 1236 0 405 -1

N.S.

1 1.00 1.07 29.89 0.00 7.06 0.00 2.31 -0.01

time (sec)

N/A 0.147 0.665 0.130 0.000 0.969 0.000 0.570 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 266 10683 0 1517 0 659 -1

N.S.

1 1.00 1.37 55.07 0.00 7.82 0.00 3.40 -0.01

time (sec)

N/A 0.131 1.485 0.072 0.000 0.813 0.000 0.524 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

144 144 201 19519 0 706 0 846 -1

N.S.

1 1.00 1.40 135.55 0.00 4.90 0.00 5.88 -0.01

time (sec)

N/A 0.048 10.569 0.075 0.000 0.629 0.000 1.520 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

249 249 306 34027 0 1258 0 1448 -1

N.S.

1 1.00 1.23 136.65 0.00 5.05 0.00 5.82 -0.00

time (sec)

N/A 0.094 10.750 0.083 0.000 1.031 0.000 5.209 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 46 33 0 42 0 95 83

N.S.

1 1.00 1.53 1.10 0.00 1.40 0.00 3.17 2.77

time (sec)

N/A 0.010 0.077 0.225 0.000 0.467 0.000 0.895 0.394

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 45 84 59 67 0 70 59

N.S.

1 1.00 1.67 3.11 2.19 2.48 0.00 2.59 2.19

time (sec)

N/A 0.009 0.089 0.194 0.504 0.428 0.000 0.865 0.167

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 49 187 110 74 0 118 85

N.S.

1 1.00 1.96 7.48 4.40 2.96 0.00 4.72 3.40

time (sec)

N/A 0.009 0.049 0.225 0.496 0.472 0.000 0.828 5.347

Problem 74

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

169 169 138 227 199 300 400 150 -1

N.S.

1 1.00 0.82 1.34 1.18 1.78 2.37 0.89 -0.01

time (sec)

N/A 0.098 0.165 0.062 0.277 0.573 13.174 0.864 0.000

Problem 75

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

108 108 90 133 109 192 238 90 -1

N.S.

1 1.00 0.83 1.23 1.01 1.78 2.20 0.83 -0.01

time (sec)

N/A 0.040 0.096 0.060 0.299 0.510 4.422 1.081 0.000

Problem 76

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

58 58 59 63 47 113 126 49 86

N.S.

1 1.00 1.02 1.09 0.81 1.95 2.17 0.84 1.48

time (sec)

N/A 0.012 0.050 0.064 0.290 0.553 1.597 0.817 5.515

Problem 77

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 13 59 17 37 20

N.S.

1 1.00 1.00 0.84 0.52 2.36 0.68 1.48 0.80

time (sec)

N/A 0.004 0.004 0.050 0.306 0.532 0.467 0.669 0.121

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 67 300 0 241 0 70 -1

N.S.

1 1.00 1.37 6.12 0.00 4.92 0.00 1.43 -0.02

time (sec)

N/A 0.014 0.100 0.061 0.000 0.548 0.000 0.706 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 118 810 0 463 0 242 -1

N.S.

1 1.00 1.17 8.02 0.00 4.58 0.00 2.40 -0.01

time (sec)

N/A 0.036 0.300 0.061 0.000 0.584 0.000 0.695 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 160 1843 0 864 0 538 -1

N.S.

1 1.00 0.98 11.31 0.00 5.30 0.00 3.30 -0.01

time (sec)

N/A 0.083 0.753 0.073 0.000 0.759 0.000 2.314 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 198 331 311 584 0 235 -1

N.S.

1 1.00 0.77 1.29 1.21 2.27 0.00 0.91 -0.00

time (sec)

N/A 0.178 0.414 0.099 0.271 0.584 0.000 0.652 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 139 215 197 416 0 157 -1

N.S.

1 1.00 0.82 1.27 1.17 2.46 0.00 0.93 -0.01

time (sec)

N/A 0.126 0.270 0.083 0.279 0.537 0.000 0.572 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 105 95 123 108 276 0 92 -1

N.S.

1 1.17 1.06 1.37 1.20 3.07 0.00 1.02 -0.01

time (sec)

N/A 0.040 0.178 0.079 0.282 0.526 0.000 0.630 0.000

Problem 84

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

54 54 58 55 46 167 60 50 53

N.S.

1 1.00 1.07 1.02 0.85 3.09 1.11 0.93 0.98

time (sec)

N/A 0.012 0.084 0.061 0.325 0.506 2.362 0.830 5.117

Problem 85

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

16 16 16 15 14 23 17 14 14

N.S.

1 1.00 1.00 0.94 0.88 1.44 1.06 0.88 0.88

time (sec)

N/A 0.001 0.002 0.047 0.291 0.553 0.312 0.684 0.040

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 96 723 0 441 0 107 -1

N.S.

1 1.00 1.22 9.15 0.00 5.58 0.00 1.35 -0.01

time (sec)

N/A 0.028 0.234 0.063 0.000 0.656 0.000 0.654 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 151 1906 0 864 0 318 -1

N.S.

1 1.00 1.06 13.33 0.00 6.04 0.00 2.22 -0.01

time (sec)

N/A 0.076 0.664 0.067 0.000 0.769 0.000 1.165 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 1392 4035 0 1482 0 643 -1

N.S.

1 1.00 6.19 17.93 0.00 6.59 0.00 2.86 -0.00

time (sec)

N/A 0.173 13.591 0.088 0.000 1.169 0.000 1.658 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 202 360 392 684 0 237 -1

N.S.

1 1.00 0.79 1.41 1.54 2.68 0.00 0.93 -0.00

time (sec)

N/A 0.167 0.404 0.141 0.286 0.655 0.000 0.717 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 143 246 254 486 0 158 -1

N.S.

1 1.00 0.83 1.43 1.48 2.83 0.00 0.92 -0.01

time (sec)

N/A 0.104 0.275 0.099 0.303 0.577 0.000 0.647 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 103 156 147 318 0 103 -1

N.S.

1 1.00 0.98 1.49 1.40 3.03 0.00 0.98 -0.01

time (sec)

N/A 0.035 0.205 0.061 0.296 0.495 0.000 0.576 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 37 90 68 54 144 40 33

N.S.

1 1.00 0.79 1.91 1.45 1.15 3.06 0.85 0.70

time (sec)

N/A 0.007 0.081 0.055 0.287 0.525 4.499 0.579 4.785

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 29 32 31 47 95 27 28

N.S.

1 1.00 0.74 0.82 0.79 1.21 2.44 0.69 0.72

time (sec)

N/A 0.004 0.004 0.048 0.290 0.623 0.443 0.631 4.754

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 130 1378 0 764 0 320 -1

N.S.

1 1.00 1.07 11.30 0.00 6.26 0.00 2.62 -0.01

time (sec)

N/A 0.074 0.393 0.064 0.000 0.836 0.000 0.683 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

202 202 219 3449 0 1440 0 620 -1

N.S.

1 1.00 1.08 17.07 0.00 7.13 0.00 3.07 -0.00

time (sec)

N/A 0.155 1.305 0.084 0.000 1.431 0.000 1.147 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

313 313 367 7121 0 2250 0 1010 -1

N.S.

1 1.00 1.17 22.75 0.00 7.19 0.00 3.23 -0.00

time (sec)

N/A 0.288 3.781 0.088 0.000 12.309 0.000 2.132 0.000

Problem 97

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

224 224 163 536 465 229 0 218 326

N.S.

1 1.00 0.73 2.39 2.08 1.02 0.00 0.97 1.46

time (sec)

N/A 0.071 0.350 0.091 0.355 4.670 0.000 0.904 5.152

Problem 98

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

174 174 107 301 249 151 0 138 176

N.S.

1 1.00 0.61 1.73 1.43 0.87 0.00 0.79 1.01

time (sec)

N/A 0.049 0.198 0.073 0.295 2.373 0.000 0.883 4.987

Problem 99

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

91 91 60 132 103 87 566 72 87

N.S.

1 1.00 0.66 1.45 1.13 0.96 6.22 0.79 0.96

time (sec)

N/A 0.018 0.118 0.056 0.295 1.182 11.433 0.996 4.849

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 29 32 31 47 95 27 28

N.S.

1 1.00 0.74 0.82 0.79 1.21 2.44 0.69 0.72

time (sec)

N/A 0.004 0.051 0.056 0.284 1.105 0.416 0.698 4.787

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