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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 B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 104 81 81 192 197 252 73

N.S.

1 1.00 1.02 0.79 0.79 1.88 1.93 2.47 0.72

time (sec)

N/A 0.624 0.335 0.202 0.289 0.241 0.282 1.668 4.560

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 81 68 70 159 168 204 63

N.S.

1 1.00 0.98 0.82 0.84 1.92 2.02 2.46 0.76

time (sec)

N/A 0.506 0.218 0.211 0.285 0.235 0.216 0.969 4.816

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 74 60 59 120 121 156 51

N.S.

1 1.00 1.10 0.90 0.88 1.79 1.81 2.33 0.76

time (sec)

N/A 0.414 0.174 0.229 0.294 0.246 0.180 0.653 4.165

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 53 47 48 85 85 107 39

N.S.

1 1.00 1.08 0.96 0.98 1.73 1.73 2.18 0.80

time (sec)

N/A 0.324 0.116 0.198 0.302 0.226 0.168 0.484 4.706

Problem 5

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

34 34 43 37 37 47 44 58 25

N.S.

1 1.00 1.26 1.09 1.09 1.38 1.29 1.71 0.74

time (sec)

N/A 0.237 0.023 0.126 0.291 0.234 0.118 0.336 4.277

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

19 19 19 23 17 18 24 18 17

N.S.

1 1.00 1.00 1.21 0.89 0.95 1.26 0.95 0.89

time (sec)

N/A 0.147 0.001 0.090 0.214 0.230 0.095 0.305 5.095

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 21 31 27 37 17 20 34 19

N.S.

1 1.11 1.63 1.42 1.95 0.89 1.05 1.79 1.00

time (sec)

N/A 0.238 0.017 0.338 0.289 0.238 0.093 0.350 4.210

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 34 61 42 49 51 46 75 27

N.S.

1 1.06 1.91 1.31 1.53 1.59 1.44 2.34 0.84

time (sec)

N/A 0.323 0.035 0.366 0.292 0.243 0.151 0.411 4.624

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 68 50 58 83 80 102 47

N.S.

1 1.04 1.36 1.00 1.16 1.66 1.60 2.04 0.94

time (sec)

N/A 0.434 0.218 0.378 0.302 0.240 0.151 0.445 4.933

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 66 72 63 71 125 128 128 57

N.S.

1 1.03 1.12 0.98 1.11 1.95 2.00 2.00 0.89

time (sec)

N/A 0.536 0.209 0.380 0.308 0.230 0.179 0.544 4.435

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 85 93 73 83 156 158 158 70

N.S.

1 1.02 1.12 0.88 1.00 1.88 1.90 1.90 0.84

time (sec)

N/A 0.641 0.041 0.403 0.310 0.236 0.230 0.544 4.828

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 102 101 84 93 197 206 186 79

N.S.

1 1.02 1.01 0.84 0.93 1.97 2.06 1.86 0.79

time (sec)

N/A 0.771 0.041 0.414 0.284 0.232 0.285 0.588 4.761

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 112 108 82 95 217 219 274 86

N.S.

1 1.00 0.96 0.73 0.85 1.94 1.96 2.45 0.77

time (sec)

N/A 0.706 0.328 0.202 0.291 0.242 0.284 1.001 5.080

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 73 70 82 174 168 222 73

N.S.

1 1.00 0.78 0.75 0.88 1.87 1.81 2.39 0.78

time (sec)

N/A 0.564 0.225 0.174 0.295 0.245 0.334 0.731 4.155

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 76 61 68 137 136 170 60

N.S.

1 1.00 1.19 0.95 1.06 2.14 2.12 2.66 0.94

time (sec)

N/A 0.355 0.260 0.238 0.298 0.235 0.203 0.539 4.746

Problem 16

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

62 65 51 49 55 93 88 116 40

N.S.

1 1.05 0.82 0.79 0.89 1.50 1.42 1.87 0.65

time (sec)

N/A 0.342 0.175 0.217 0.635 0.238 0.170 0.418 4.393

Problem 17

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

38 38 34 40 41 56 53 66 29

N.S.

1 1.00 0.89 1.05 1.08 1.47 1.39 1.74 0.76

time (sec)

N/A 0.246 0.030 0.108 0.563 0.234 0.141 0.311 4.783

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

37 39 38 31 42 19 22 68 30

N.S.

1 1.05 1.03 0.84 1.14 0.51 0.59 1.84 0.81

time (sec)

N/A 0.272 0.036 0.648 0.298 0.243 0.118 0.490 4.482

Problem 19

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

38 43 48 43 56 58 51 85 29

N.S.

1 1.13 1.26 1.13 1.47 1.53 1.34 2.24 0.76

time (sec)

N/A 0.357 0.237 0.536 0.308 0.234 0.153 0.557 4.207

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 63 64 52 68 94 87 116 53

N.S.

1 1.09 1.10 0.90 1.17 1.62 1.50 2.00 0.91

time (sec)

N/A 0.463 0.217 0.647 0.299 0.234 0.234 0.675 4.918

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 79 105 63 83 139 136 146 68

N.S.

1 1.07 1.42 0.85 1.12 1.88 1.84 1.97 0.92

time (sec)

N/A 0.588 0.499 0.511 0.296 0.236 0.213 0.809 4.263

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 100 78 75 97 174 168 180 80

N.S.

1 1.08 0.84 0.81 1.04 1.87 1.81 1.94 0.86

time (sec)

N/A 0.712 0.699 0.615 0.446 0.245 0.704 0.892 5.337

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 119 145 86 109 219 218 212 92

N.S.

1 1.06 1.29 0.77 0.97 1.96 1.95 1.89 0.82

time (sec)

N/A 0.847 0.067 0.652 0.497 0.233 0.305 1.033 4.404

Problem 24

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

126 132 110 83 95 214 207 274 87

N.S.

1 1.05 0.87 0.66 0.75 1.70 1.64 2.17 0.69

time (sec)

N/A 0.793 0.554 0.244 0.704 0.241 0.313 0.765 4.499

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 94 67 72 82 177 173 222 73

N.S.

1 1.04 0.74 0.80 0.91 1.97 1.92 2.47 0.81

time (sec)

N/A 0.454 0.444 0.244 0.287 0.243 0.257 0.631 4.463

Problem 26

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

85 94 57 62 69 134 131 170 59

N.S.

1 1.11 0.67 0.73 0.81 1.58 1.54 2.00 0.69

time (sec)

N/A 0.441 0.363 0.200 0.290 0.246 0.203 0.461 4.121

Problem 27

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

63 67 46 51 76 97 94 118 41

N.S.

1 1.06 0.73 0.81 1.21 1.54 1.49 1.87 0.65

time (sec)

N/A 0.325 0.047 0.139 0.305 0.227 0.167 0.366 5.019

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

60 65 50 41 53 83 66 123 39

N.S.

1 1.08 0.83 0.68 0.88 1.38 1.10 2.05 0.65

time (sec)

N/A 0.533 0.283 0.430 0.293 0.240 0.219 0.601 4.455

Problem 29

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

69 71 48 43 56 91 71 119 38

N.S.

1 1.03 0.70 0.62 0.81 1.32 1.03 1.72 0.55

time (sec)

N/A 0.564 0.343 0.455 0.291 0.247 0.239 0.712 4.641

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

71 80 61 52 68 94 87 116 53

N.S.

1 1.13 0.86 0.73 0.96 1.32 1.23 1.63 0.75

time (sec)

N/A 0.507 0.200 0.418 0.440 0.229 0.205 0.865 4.605

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

101 115 80 64 83 139 136 146 68

N.S.

1 1.14 0.79 0.63 0.82 1.38 1.35 1.45 0.67

time (sec)

N/A 0.668 0.278 0.440 0.494 0.246 0.248 1.060 4.450

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

108 118 89 75 94 174 165 180 80

N.S.

1 1.09 0.82 0.69 0.87 1.61 1.53 1.67 0.74

time (sec)

N/A 0.809 0.384 0.469 0.303 0.227 0.336 1.317 5.136

Problem 33

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

126 136 110 85 109 219 218 212 92

N.S.

1 1.08 0.87 0.67 0.87 1.74 1.73 1.68 0.73

time (sec)

N/A 0.944 0.452 0.530 0.299 0.231 0.331 1.473 4.915

Problem 34

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

160 169 128 93 108 254 246 326 100

N.S.

1 1.06 0.80 0.58 0.68 1.59 1.54 2.04 0.62

time (sec)

N/A 1.041 0.462 0.288 0.298 0.235 0.817 0.893 4.884

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 123 82 82 95 217 218 274 87

N.S.

1 1.06 0.71 0.71 0.82 1.87 1.88 2.36 0.75

time (sec)

N/A 0.565 0.769 0.295 0.300 0.237 0.285 0.702 4.535

Problem 36

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

108 123 67 72 82 174 170 222 72

N.S.

1 1.14 0.62 0.67 0.76 1.61 1.57 2.06 0.67

time (sec)

N/A 0.540 0.272 0.276 0.302 0.228 0.281 0.546 4.806

Problem 37

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

89 96 58 61 108 137 138 170 59

N.S.

1 1.08 0.65 0.69 1.21 1.54 1.55 1.91 0.66

time (sec)

N/A 0.430 0.254 0.175 0.436 0.238 0.209 0.387 4.071

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

86 91 68 52 67 137 105 157 64

N.S.

1 1.06 0.79 0.60 0.78 1.59 1.22 1.83 0.74

time (sec)

N/A 0.708 0.361 0.452 0.438 0.237 0.258 0.855 4.729

Problem 39

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

71 74 58 49 67 58 51 163 63

N.S.

1 1.04 0.82 0.69 0.94 0.82 0.72 2.30 0.89

time (sec)

N/A 0.408 0.964 0.742 0.630 0.235 0.194 1.003 4.550

Problem 40

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

103 105 61 52 68 138 107 150 65

N.S.

1 1.02 0.59 0.50 0.66 1.34 1.04 1.46 0.63

time (sec)

N/A 0.814 0.829 0.487 0.292 0.234 0.491 1.264 4.136

Problem 41

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

103 117 78 63 83 139 136 146 68

N.S.

1 1.14 0.76 0.61 0.81 1.35 1.32 1.42 0.66

time (sec)

N/A 0.665 0.323 0.572 0.308 0.232 0.266 1.497 5.030

Problem 42

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

134 152 93 75 96 174 168 180 80

N.S.

1 1.13 0.69 0.56 0.72 1.30 1.25 1.34 0.60

time (sec)

N/A 0.839 0.403 0.435 0.306 0.237 1.272 1.342 4.571

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

142 157 108 85 109 219 218 212 92

N.S.

1 1.11 0.76 0.60 0.77 1.54 1.54 1.49 0.65

time (sec)

N/A 1.089 0.755 0.503 0.300 0.254 0.355 0.750 5.053

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

162 178 123 94 123 254 246 245 107

N.S.

1 1.10 0.76 0.58 0.76 1.57 1.52 1.51 0.66

time (sec)

N/A 1.247 0.337 0.411 0.587 0.253 4.275 0.858 5.329

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 120 114 102 0 221 219 114 125

N.S.

1 0.92 0.88 0.78 0.00 1.70 1.68 0.88 0.96

time (sec)

N/A 0.737 0.654 0.342 0.000 0.249 0.293 2.318 4.869

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 104 106 101 0 175 197 102 106

N.S.

1 0.95 0.97 0.93 0.00 1.61 1.81 0.94 0.97

time (sec)

N/A 0.604 0.543 0.299 0.000 0.250 0.279 1.614 4.270

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 86 92 78 0 138 134 85 91

N.S.

1 0.96 1.02 0.87 0.00 1.53 1.49 0.94 1.01

time (sec)

N/A 0.494 0.391 0.352 0.000 0.241 0.229 0.958 4.769

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 72 85 72 0 93 114 68 73

N.S.

1 0.97 1.15 0.97 0.00 1.26 1.54 0.92 0.99

time (sec)

N/A 0.380 0.327 0.271 0.000 0.235 0.194 0.683 4.619

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 51 71 56 0 55 88 58 61

N.S.

1 1.02 1.42 1.12 0.00 1.10 1.76 1.16 1.22

time (sec)

N/A 0.246 0.215 0.333 0.000 0.240 0.178 0.489 4.156

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 46 26 0 32 65 55 29

N.S.

1 1.00 1.39 0.79 0.00 0.97 1.97 1.67 0.88

time (sec)

N/A 0.202 0.098 0.229 0.000 0.239 0.116 0.413 4.919

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 35 26 0 32 60 58 29

N.S.

1 1.00 1.06 0.79 0.00 0.97 1.82 1.76 0.88

time (sec)

N/A 0.184 0.060 0.192 0.000 0.232 0.101 0.297 4.400

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 54 71 55 0 55 92 70 72

N.S.

1 1.15 1.51 1.17 0.00 1.17 1.96 1.49 1.53

time (sec)

N/A 0.320 0.315 0.371 0.000 0.241 0.169 0.411 4.754

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 80 78 0 99 116 89 96

N.S.

1 1.00 1.14 1.11 0.00 1.41 1.66 1.27 1.37

time (sec)

N/A 0.486 0.677 0.424 0.000 0.241 0.199 0.500 4.447

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 88 89 77 0 134 138 103 110

N.S.

1 0.98 0.99 0.86 0.00 1.49 1.53 1.14 1.22

time (sec)

N/A 0.618 1.054 0.394 0.000 0.240 0.214 0.566 5.015

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 104 96 102 0 181 196 114 126

N.S.

1 0.96 0.89 0.94 0.00 1.68 1.81 1.06 1.17

time (sec)

N/A 0.733 1.318 0.416 0.000 0.246 0.286 0.677 4.639

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 147 169 120 0 198 262 111 132

N.S.

1 1.04 1.19 0.85 0.00 1.39 1.85 0.78 0.93

time (sec)

N/A 0.860 0.705 0.437 0.000 0.241 0.312 2.341 4.376

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 133 148 104 0 151 214 98 114

N.S.

1 1.07 1.19 0.84 0.00 1.22 1.73 0.79 0.92

time (sec)

N/A 0.737 0.572 0.325 0.000 0.242 0.768 1.757 5.401

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 111 147 90 0 113 177 79 100

N.S.

1 1.07 1.41 0.87 0.00 1.09 1.70 0.76 0.96

time (sec)

N/A 0.610 0.539 0.328 0.000 0.238 0.257 1.046 4.288

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 87 95 72 0 66 148 69 84

N.S.

1 1.10 1.20 0.91 0.00 0.84 1.87 0.87 1.06

time (sec)

N/A 0.515 0.477 0.226 0.000 0.250 0.283 0.750 4.947

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 61 52 44 0 43 117 68 39

N.S.

1 1.03 0.88 0.75 0.00 0.73 1.98 1.15 0.66

time (sec)

N/A 0.335 0.298 0.240 0.000 0.235 0.164 0.534 4.571

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 65 66 26 0 32 73 67 46

N.S.

1 1.10 1.12 0.44 0.00 0.54 1.24 1.14 0.78

time (sec)

N/A 0.284 0.114 0.239 0.000 0.234 0.139 0.457 4.601

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 65 52 44 0 43 117 68 39

N.S.

1 1.07 0.85 0.72 0.00 0.70 1.92 1.11 0.64

time (sec)

N/A 0.263 0.082 0.206 0.000 0.232 0.141 0.341 4.385

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 85 82 72 0 66 150 81 97

N.S.

1 1.20 1.15 1.01 0.00 0.93 2.11 1.14 1.37

time (sec)

N/A 0.543 0.869 0.378 0.000 0.242 0.223 0.602 4.865

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 106 102 96 0 114 180 103 125

N.S.

1 1.09 1.05 0.99 0.00 1.18 1.86 1.06 1.29

time (sec)

N/A 0.739 1.380 0.494 0.000 0.248 0.279 0.755 4.677

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 133 114 105 0 151 216 109 135

N.S.

1 1.09 0.93 0.86 0.00 1.24 1.77 0.89 1.11

time (sec)

N/A 0.894 1.589 0.483 0.000 0.234 0.401 1.064 4.312

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 176 195 126 0 167 257 109 140

N.S.

1 1.09 1.21 0.78 0.00 1.04 1.60 0.68 0.87

time (sec)

N/A 1.010 0.796 0.414 0.000 0.236 0.386 2.430 5.319

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 155 187 111 0 120 214 89 122

N.S.

1 1.08 1.31 0.78 0.00 0.84 1.50 0.62 0.85

time (sec)

N/A 0.856 0.586 0.273 0.000 0.240 0.414 1.808 4.400

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 135 130 92 0 77 184 78 110

N.S.

1 1.13 1.09 0.77 0.00 0.65 1.55 0.66 0.92

time (sec)

N/A 0.750 0.501 0.358 0.000 0.242 0.290 1.191 4.865

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 103 75 60 0 54 156 78 49

N.S.

1 1.12 0.82 0.65 0.00 0.59 1.70 0.85 0.53

time (sec)

N/A 0.447 0.274 0.343 0.000 0.233 0.253 0.847 4.644

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 95 91 62 0 54 151 78 49

N.S.

1 1.08 1.03 0.70 0.00 0.61 1.72 0.89 0.56

time (sec)

N/A 0.419 0.549 0.331 0.000 0.228 0.207 0.720 4.482

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 97 91 60 0 54 153 78 49

N.S.

1 1.15 1.08 0.71 0.00 0.64 1.82 0.93 0.58

time (sec)

N/A 0.378 0.517 0.392 0.000 0.226 0.219 0.601 4.441

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 97 65 62 0 54 155 78 50

N.S.

1 1.10 0.74 0.70 0.00 0.61 1.76 0.89 0.57

time (sec)

N/A 0.358 0.140 0.293 0.000 0.230 0.184 0.367 4.696

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 120 108 89 0 77 187 91 120

N.S.

1 1.22 1.10 0.91 0.00 0.79 1.91 0.93 1.22

time (sec)

N/A 0.748 0.641 0.463 0.000 0.247 0.296 0.935 4.724

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 147 148 114 0 125 218 115 145

N.S.

1 1.11 1.11 0.86 0.00 0.94 1.64 0.86 1.09

time (sec)

N/A 0.983 1.898 0.474 0.000 0.247 0.324 0.848 4.341

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 193 265 128 0 135 248 100 132

N.S.

1 1.13 1.55 0.75 0.00 0.79 1.45 0.58 0.77

time (sec)

N/A 1.124 0.818 0.393 0.000 0.236 0.401 2.696 5.310

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 170 134 107 0 88 219 89 128

N.S.

1 1.16 0.91 0.73 0.00 0.60 1.49 0.61 0.87

time (sec)

N/A 0.990 0.590 0.427 0.000 0.232 1.350 2.089 4.578

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 145 108 80 0 65 189 88 59

N.S.

1 1.13 0.84 0.62 0.00 0.51 1.48 0.69 0.46

time (sec)

N/A 0.615 0.250 0.339 0.000 0.227 0.275 1.404 5.090

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 141 95 60 0 54 156 88 60

N.S.

1 1.12 0.75 0.48 0.00 0.43 1.24 0.70 0.48

time (sec)

N/A 0.621 0.621 0.336 0.000 0.236 0.482 1.081 4.775

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 127 69 44 0 43 117 83 92

N.S.

1 1.09 0.59 0.38 0.00 0.37 1.01 0.72 0.79

time (sec)

N/A 0.524 0.491 0.396 0.000 0.233 0.204 0.902 4.735

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 129 94 60 0 54 156 88 60

N.S.

1 1.17 0.85 0.55 0.00 0.49 1.42 0.80 0.55

time (sec)

N/A 0.477 0.167 0.315 0.000 0.227 0.286 0.677 4.460

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 129 113 80 0 65 189 88 60

N.S.

1 1.11 0.97 0.69 0.00 0.56 1.63 0.76 0.52

time (sec)

N/A 0.457 0.178 0.268 0.000 0.227 0.235 0.430 4.645

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 149 115 106 0 88 221 101 142

N.S.

1 1.24 0.96 0.88 0.00 0.73 1.84 0.84 1.18

time (sec)

N/A 0.966 1.199 0.406 0.000 0.245 0.382 1.202 5.014

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 182 150 132 0 136 252 123 165

N.S.

1 1.14 0.94 0.83 0.00 0.86 1.58 0.77 1.04

time (sec)

N/A 1.293 1.764 0.563 0.000 0.237 0.360 1.153 4.619

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 184 104 94 120 330 0 0 109

N.S.

1 1.10 0.62 0.56 0.71 1.96 0.00 0.00 0.65

time (sec)

N/A 0.901 0.780 1.161 0.301 0.243 0.000 0.000 0.371

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 132 90 93 120 285 0 0 100

N.S.

1 1.04 0.71 0.73 0.94 2.24 0.00 0.00 0.79

time (sec)

N/A 0.637 0.587 1.047 0.289 0.251 0.000 0.000 5.257

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 73 58 84 233 0 0 63

N.S.

1 1.00 0.96 0.76 1.11 3.07 0.00 0.00 0.83

time (sec)

N/A 0.315 0.367 1.004 0.295 0.254 0.000 0.000 0.322

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 67 53 83 187 0 0 54

N.S.

1 1.00 1.00 0.79 1.24 2.79 0.00 0.00 0.81

time (sec)

N/A 0.300 0.146 1.084 0.303 0.241 0.000 0.000 4.369

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 46 36 60 159 0 0 39

N.S.

1 1.00 1.00 0.78 1.30 3.46 0.00 0.00 0.85

time (sec)

N/A 0.204 0.064 0.950 0.295 0.233 0.000 0.000 4.866

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 71 211 107 336 0 0 61

N.S.

1 1.00 0.91 2.71 1.37 4.31 0.00 0.00 0.78

time (sec)

N/A 0.511 0.151 7.395 0.303 0.245 0.000 0.000 0.187

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

111 117 106 580 134 476 0 0 97

N.S.

1 1.05 0.95 5.23 1.21 4.29 0.00 0.00 0.87

time (sec)

N/A 0.709 0.405 7.933 0.313 0.253 0.000 0.000 4.603

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

145 158 116 669 179 519 0 0 124

N.S.

1 1.09 0.80 4.61 1.23 3.58 0.00 0.00 0.86

time (sec)

N/A 0.978 0.920 7.425 0.285 0.253 0.000 0.000 5.044

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

199 220 103 111 138 354 0 0 120

N.S.

1 1.11 0.52 0.56 0.69 1.78 0.00 0.00 0.60

time (sec)

N/A 1.169 0.978 1.097 0.279 0.250 0.000 0.000 4.485

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 95 76 102 315 0 0 84

N.S.

1 1.00 0.94 0.75 1.01 3.12 0.00 0.00 0.83

time (sec)

N/A 0.411 0.612 0.852 0.284 0.261 0.000 0.000 0.323

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 101 81 70 102 258 0 0 74

N.S.

1 1.10 0.88 0.76 1.11 2.80 0.00 0.00 0.80

time (sec)

N/A 0.392 0.331 0.870 0.287 0.237 0.000 0.000 5.101

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 69 54 83 215 0 0 61

N.S.

1 1.00 0.96 0.75 1.15 2.99 0.00 0.00 0.85

time (sec)

N/A 0.276 0.101 0.671 0.290 0.244 0.000 0.000 0.219

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 71 64 107 357 0 0 76

N.S.

1 1.00 0.90 0.81 1.35 4.52 0.00 0.00 0.96

time (sec)

N/A 0.506 0.168 1.257 0.286 0.241 0.000 0.000 4.397

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 151 107 99 132 501 0 0 112

N.S.

1 1.07 0.76 0.70 0.94 3.55 0.00 0.00 0.79

time (sec)

N/A 0.980 0.390 1.039 0.289 0.249 0.000 0.000 4.617

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 198 117 117 178 546 0 0 136

N.S.

1 1.08 0.64 0.64 0.97 2.97 0.00 0.00 0.74

time (sec)

N/A 1.278 1.028 1.085 0.284 0.249 0.000 0.000 5.070

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 224 116 131 156 412 0 0 142

N.S.

1 1.10 0.57 0.64 0.76 2.02 0.00 0.00 0.70

time (sec)

N/A 1.149 1.818 1.126 0.285 0.255 0.000 0.000 4.537

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 132 107 96 120 371 0 0 107

N.S.

1 1.02 0.82 0.74 0.92 2.85 0.00 0.00 0.82

time (sec)

N/A 0.510 1.107 0.901 0.274 0.251 0.000 0.000 5.092

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