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2.2.2 Integrals 101 to 200

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 46 39 0 147 0 35 35

N.S.

1 1.00 1.21 1.03 0.00 3.87 0.00 0.92 0.92

time (sec)

N/A 0.220 0.046 0.142 0.000 0.252 0.000 0.287 0.177

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 20 13 12 43 0 46 51

N.S.

1 1.00 1.67 1.08 1.00 3.58 0.00 3.83 4.25

time (sec)

N/A 0.215 0.332 0.316 0.191 0.260 0.000 0.278 1.998

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 68 75 85 0 384 0 85 230

N.S.

1 1.19 1.32 1.49 0.00 6.74 0.00 1.49 4.04

time (sec)

N/A 0.488 0.410 0.797 0.000 0.273 0.000 0.263 2.216

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 39 50 102 110 434 0 106 88

N.S.

1 0.98 1.25 2.55 2.75 10.85 0.00 2.65 2.20

time (sec)

N/A 0.259 3.290 1.824 0.191 0.272 0.000 0.272 2.139

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 62 42 35 36 92 0 42 34

N.S.

1 1.03 0.70 0.58 0.60 1.53 0.00 0.70 0.57

time (sec)

N/A 0.271 0.231 1.599 0.202 0.257 0.000 0.262 2.107

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 35 34 24 27 56 0 25 23

N.S.

1 1.40 1.36 0.96 1.08 2.24 0.00 1.00 0.92

time (sec)

N/A 0.434 0.036 0.555 0.192 0.245 0.000 0.265 1.989

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 40 24 23 22 51 0 30 22

N.S.

1 1.05 0.63 0.61 0.58 1.34 0.00 0.79 0.58

time (sec)

N/A 0.248 0.022 0.255 0.192 0.249 0.000 0.273 0.117

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 25 19 12 11 23 0 11 11

N.S.

1 1.47 1.12 0.71 0.65 1.35 0.00 0.65 0.65

time (sec)

N/A 0.367 0.019 0.146 0.202 0.252 0.000 0.266 1.894

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 24 16 19 12 23 0 10 10

N.S.

1 2.40 1.60 1.90 1.20 2.30 0.00 1.00 1.00

time (sec)

N/A 0.367 0.116 0.330 0.277 0.262 0.000 0.280 1.858

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 13 10 22 18 78 0 27 21

N.S.

1 0.87 0.67 1.47 1.20 5.20 0.00 1.80 1.40

time (sec)

N/A 0.222 0.085 0.878 0.268 0.257 0.000 0.280 1.853

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A C B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 30 17 38 33 140 0 25 22

N.S.

1 1.50 0.85 1.90 1.65 7.00 0.00 1.25 1.10

time (sec)

N/A 0.409 0.316 2.130 0.286 0.251 0.000 0.272 1.877

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 14 14 75 84 0 18 18

N.S.

1 1.00 0.82 0.82 4.41 4.94 0.00 1.06 1.06

time (sec)

N/A 0.227 0.092 0.929 0.194 0.242 0.000 0.282 0.073

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 135 48 0 231 0 122 0

N.S.

1 1.00 6.43 2.29 0.00 11.00 0.00 5.81 0.00

time (sec)

N/A 0.228 21.225 0.179 0.000 0.268 0.000 0.269 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 242 144 184 154 1229 0 216 135

N.S.

1 1.65 0.98 1.25 1.05 8.36 0.00 1.47 0.92

time (sec)

N/A 0.626 0.937 5.811 0.202 0.271 0.000 0.275 2.305

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 157 167 174 0 1873 0 164 262

N.S.

1 1.16 1.24 1.29 0.00 13.87 0.00 1.21 1.94

time (sec)

N/A 0.853 1.712 2.002 0.000 0.286 0.000 0.295 2.697

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 143 73 100 80 334 0 104 82

N.S.

1 1.68 0.86 1.18 0.94 3.93 0.00 1.22 0.96

time (sec)

N/A 0.375 0.463 0.586 0.203 0.262 0.000 0.268 2.056

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 88 79 92 0 431 0 71 158

N.S.

1 1.22 1.10 1.28 0.00 5.99 0.00 0.99 2.19

time (sec)

N/A 0.489 0.333 0.241 0.000 0.302 0.000 0.278 2.214

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 60 60 54 0 200 0 48 164

N.S.

1 1.20 1.20 1.08 0.00 4.00 0.00 0.96 3.28

time (sec)

N/A 0.377 0.240 0.441 0.000 0.280 0.000 0.280 4.155

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 35 19 51 46 117 0 76 323

N.S.

1 1.21 0.66 1.76 1.59 4.03 0.00 2.62 11.14

time (sec)

N/A 0.247 0.152 1.598 0.269 0.277 0.000 0.281 2.328

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 98 85 121 0 856 0 102 166

N.S.

1 1.18 1.02 1.46 0.00 10.31 0.00 1.23 2.00

time (sec)

N/A 0.470 0.699 4.428 0.000 0.337 0.000 0.280 4.769

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 87 60 145 133 909 0 201 123

N.S.

1 1.10 0.76 1.84 1.68 11.51 0.00 2.54 1.56

time (sec)

N/A 0.310 0.308 11.103 0.285 0.292 0.000 0.275 2.118

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 33 38 41 38 41 0 26 65

N.S.

1 1.06 1.23 1.32 1.23 1.32 0.00 0.84 2.10

time (sec)

N/A 0.332 0.173 0.606 0.283 0.265 0.000 0.254 0.536

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 67 40 44 55 571 0 47 69

N.S.

1 1.56 0.93 1.02 1.28 13.28 0.00 1.09 1.60

time (sec)

N/A 0.607 0.250 0.159 0.285 0.260 0.000 0.298 1.958

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 60 32 30 43 354 0 39 35

N.S.

1 1.62 0.86 0.81 1.16 9.57 0.00 1.05 0.95

time (sec)

N/A 0.513 0.191 0.155 0.276 0.276 0.000 0.261 1.925

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 39 34 30 29 186 0 35 29

N.S.

1 1.34 1.17 1.03 1.00 6.41 0.00 1.21 1.00

time (sec)

N/A 0.404 0.179 0.134 0.262 0.329 0.000 0.272 1.905

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 32 31 18 17 73 0 17 17

N.S.

1 1.68 1.63 0.95 0.89 3.84 0.00 0.89 0.89

time (sec)

N/A 0.294 0.097 0.103 0.270 0.281 0.000 0.262 1.906

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 14 11 10 26 27 10 14

N.S.

1 1.00 0.88 0.69 0.62 1.62 1.69 0.62 0.88

time (sec)

N/A 0.174 0.010 0.035 0.179 0.274 0.252 0.268 0.002

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 24 18 11 10 26 27 10 12

N.S.

1 1.50 1.12 0.69 0.62 1.62 1.69 0.62 0.75

time (sec)

N/A 0.192 0.049 0.049 0.177 0.264 0.253 0.279 0.053

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 24 47 18 24 73 92 18 21

N.S.

1 1.26 2.47 0.95 1.26 3.84 4.84 0.95 1.11

time (sec)

N/A 0.220 0.185 0.065 0.180 0.268 0.315 0.270 1.858

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 44 47 28 38 196 160 36 21

N.S.

1 1.42 1.52 0.90 1.23 6.32 5.16 1.16 0.68

time (sec)

N/A 0.334 0.195 0.134 0.189 0.264 0.472 0.265 1.877

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 49 54 30 54 357 197 40 29

N.S.

1 1.32 1.46 0.81 1.46 9.65 5.32 1.08 0.78

time (sec)

N/A 0.414 0.210 0.152 0.185 0.255 0.595 0.272 0.070

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 56 39 35 0 259 0 135 34

N.S.

1 1.24 0.87 0.78 0.00 5.76 0.00 3.00 0.76

time (sec)

N/A 0.332 0.794 0.064 0.000 0.263 0.000 0.285 1.956

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 41 32 26 0 131 0 71 25

N.S.

1 1.28 1.00 0.81 0.00 4.09 0.00 2.22 0.78

time (sec)

N/A 0.258 0.579 0.074 0.000 0.268 0.000 0.306 1.926

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 41 30 25 0 85 0 64 24

N.S.

1 1.37 1.00 0.83 0.00 2.83 0.00 2.13 0.80

time (sec)

N/A 0.260 0.537 0.082 0.000 0.255 0.000 0.289 1.991

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 57 36 35 0 166 0 89 32

N.S.

1 1.16 0.73 0.71 0.00 3.39 0.00 1.82 0.65

time (sec)

N/A 0.328 0.653 0.073 0.000 0.282 0.000 0.281 1.967

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 45 35 0 436 0 197 34

N.S.

1 1.00 1.00 0.78 0.00 9.69 0.00 4.38 0.76

time (sec)

N/A 0.338 1.013 0.081 0.000 0.277 0.000 0.311 1.976

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 37 26 0 242 0 133 25

N.S.

1 1.00 1.09 0.76 0.00 7.12 0.00 3.91 0.74

time (sec)

N/A 0.262 0.808 0.084 0.000 0.257 0.000 0.297 1.961

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 37 35 0 189 0 88 36

N.S.

1 1.00 0.88 0.83 0.00 4.50 0.00 2.10 0.86

time (sec)

N/A 0.326 0.892 0.087 0.000 0.264 0.000 0.312 1.951

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 48 35 0 166 0 113 31

N.S.

1 1.00 0.98 0.71 0.00 3.39 0.00 2.31 0.63

time (sec)

N/A 0.359 0.912 0.086 0.000 0.269 0.000 0.283 1.943

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 131 112 107 146 1294 0 141 163

N.S.

1 1.35 1.15 1.10 1.51 13.34 0.00 1.45 1.68

time (sec)

N/A 1.076 0.931 0.222 0.287 0.293 0.000 0.274 2.372

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 109 91 78 94 637 0 97 111

N.S.

1 1.43 1.20 1.03 1.24 8.38 0.00 1.28 1.46

time (sec)

N/A 0.794 0.443 0.178 0.274 0.285 0.000 0.273 2.270

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 77 74 66 67 264 0 74 73

N.S.

1 1.28 1.23 1.10 1.12 4.40 0.00 1.23 1.22

time (sec)

N/A 0.570 0.406 0.140 0.275 0.275 0.000 0.278 2.167

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 63 66 44 50 73 0 57 58

N.S.

1 1.24 1.29 0.86 0.98 1.43 0.00 1.12 1.14

time (sec)

N/A 0.402 0.270 0.122 0.261 0.262 0.000 0.267 0.345

Problem 144

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

39 39 49 38 37 42 148 43 42

N.S.

1 1.00 1.26 0.97 0.95 1.08 3.79 1.10 1.08

time (sec)

N/A 0.285 0.213 0.101 0.184 0.250 0.444 0.287 0.097

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 48 50 39 36 43 134 43 42

N.S.

1 1.23 1.28 1.00 0.92 1.10 3.44 1.10 1.08

time (sec)

N/A 0.309 0.088 0.072 0.186 0.257 0.442 0.279 0.069

Problem 146

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

63 61 59 56 63 76 372 59 57

N.S.

1 0.97 0.94 0.89 1.00 1.21 5.90 0.94 0.90

time (sec)

N/A 0.453 0.142 0.109 0.186 0.271 0.712 0.273 2.202

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 81 65 67 82 271 636 76 74

N.S.

1 1.27 1.02 1.05 1.28 4.23 9.94 1.19 1.16

time (sec)

N/A 0.535 0.266 0.113 0.191 0.271 1.054 0.261 2.178

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 99 77 76 119 648 882 100 110

N.S.

1 1.30 1.01 1.00 1.57 8.53 11.61 1.32 1.45

time (sec)

N/A 0.709 0.437 0.171 0.188 0.286 1.418 0.281 2.240

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 131 92 96 169 1299 1013 143 164

N.S.

1 1.39 0.98 1.02 1.80 13.82 10.78 1.52 1.74

time (sec)

N/A 0.971 0.491 0.204 0.191 0.302 2.245 0.285 2.329

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 58 49 73 68 184 0 169 68

N.S.

1 1.07 0.91 1.35 1.26 3.41 0.00 3.13 1.26

time (sec)

N/A 0.391 0.183 0.873 0.338 0.264 0.000 0.296 2.024

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 28 64 24 36 28 0 24 23

N.S.

1 0.93 2.13 0.80 1.20 0.93 0.00 0.80 0.77

time (sec)

N/A 0.228 0.032 0.120 0.212 0.249 0.000 0.269 1.941

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 53 64 83 48 62 0 54 39

N.S.

1 1.18 1.42 1.84 1.07 1.38 0.00 1.20 0.87

time (sec)

N/A 0.234 0.274 0.113 0.265 0.260 0.000 0.271 1.959

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 26 37 36 33 0 37 25

N.S.

1 1.00 1.13 1.61 1.57 1.43 0.00 1.61 1.09

time (sec)

N/A 0.207 0.213 0.102 0.188 0.252 0.000 0.294 1.922

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 47 58 71 45 58 0 51 36

N.S.

1 1.18 1.45 1.78 1.12 1.45 0.00 1.28 0.90

time (sec)

N/A 0.202 0.212 0.085 0.285 0.244 0.000 0.276 1.933

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 16 21 11 10 18 27 21 18

N.S.

1 1.33 1.75 0.92 0.83 1.50 2.25 1.75 1.50

time (sec)

N/A 0.203 0.038 0.122 0.176 0.252 0.464 0.263 1.965

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 54 62 88 47 54 0 52 37

N.S.

1 1.32 1.51 2.15 1.15 1.32 0.00 1.27 0.90

time (sec)

N/A 0.231 0.203 0.093 0.270 0.261 0.000 0.282 1.889

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 27 35 30 38 0 33 25

N.S.

1 1.00 1.29 1.67 1.43 1.81 0.00 1.57 1.19

time (sec)

N/A 0.214 0.187 0.092 0.180 0.265 0.000 0.276 1.876

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 49 86 41 53 61 0 40 40

N.S.

1 1.04 1.83 0.87 1.13 1.30 0.00 0.85 0.85

time (sec)

N/A 0.252 0.121 0.074 0.182 0.271 0.000 0.293 1.942

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 89 154 100 66 104 0 72 60

N.S.

1 1.31 2.26 1.47 0.97 1.53 0.00 1.06 0.88

time (sec)

N/A 0.300 3.167 0.097 0.263 0.289 0.000 0.277 1.983

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 53 163 54 53 74 0 54 42

N.S.

1 1.29 3.98 1.32 1.29 1.80 0.00 1.32 1.02

time (sec)

N/A 0.265 3.669 0.081 0.186 0.279 0.000 0.262 1.854

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 153 86 60 97 0 66 54

N.S.

1 1.00 2.55 1.43 1.00 1.62 0.00 1.10 0.90

time (sec)

N/A 0.231 2.601 0.097 0.267 0.266 0.000 0.280 1.893

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 28 18 19 28 63 21 28

N.S.

1 1.00 2.00 1.29 1.36 2.00 4.50 1.50 2.00

time (sec)

N/A 0.213 0.067 0.087 0.195 0.271 1.921 0.287 1.911

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 93 153 104 69 97 0 77 60

N.S.

1 1.08 1.78 1.21 0.80 1.13 0.00 0.90 0.70

time (sec)

N/A 0.296 3.350 0.127 0.267 0.269 0.000 0.279 1.912

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 155 55 50 82 0 57 48

N.S.

1 1.00 2.58 0.92 0.83 1.37 0.00 0.95 0.80

time (sec)

N/A 0.275 3.329 0.123 0.192 0.259 0.000 0.275 1.920

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 46 0 0 0 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.239 0.131 0.000 0.000 0.000 0.000 0.000 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

79 97 77 0 0 0 0 0 0

N.S.

1 1.23 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.312 0.241 0.000 0.000 0.000 0.000 0.000 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

177 198 108 0 0 0 0 0 0

N.S.

1 1.12 0.61 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.459 0.284 0.000 0.000 0.000 0.000 0.000 0.000

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

79 79 259 0 0 0 0 0 0

N.S.

1 1.00 3.28 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.247 0.610 0.000 0.000 0.000 0.000 0.000 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

99 99 126 0 0 0 0 0 0

N.S.

1 1.00 1.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 0.785 0.000 0.000 0.000 0.000 0.000 0.000

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

52 52 83 0 0 0 0 0 0

N.S.

1 1.00 1.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.207 0.661 0.000 0.000 0.000 0.000 0.000 0.000

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 111 125 0 0 0 0 0 0

N.S.

1 1.03 1.16 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.255 0.841 0.000 0.000 0.000 0.000 0.000 0.000

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

162 177 142 0 0 0 0 0 0

N.S.

1 1.09 0.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.305 0.879 0.000 0.000 0.000 0.000 0.000 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

194 209 223 0 0 0 0 0 0

N.S.

1 1.08 1.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.338 1.261 0.000 0.000 0.000 0.000 0.000 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

61 61 171 0 0 0 0 0 0

N.S.

1 1.00 2.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.220 0.629 0.000 0.000 0.000 0.000 0.000 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

61 61 171 0 0 0 0 0 0

N.S.

1 1.00 2.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.236 0.682 0.000 0.000 0.000 0.000 0.000 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

61 61 171 0 0 0 0 0 0

N.S.

1 1.00 2.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.232 0.692 0.000 0.000 0.000 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

58 94 198 0 0 0 0 0 0

N.S.

1 1.62 3.41 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.328 7.481 0.000 0.000 0.000 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

62 98 207 0 0 0 0 0 0

N.S.

1 1.58 3.34 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.337 5.200 0.000 0.000 0.000 0.000 0.000 0.000

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

54 90 193 0 0 0 0 0 0

N.S.

1 1.67 3.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.314 7.248 0.000 0.000 0.000 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

52 87 198 0 0 0 0 0 0

N.S.

1 1.67 3.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.308 8.422 0.000 0.000 0.000 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 29 40 25 24 76 46 74 34

N.S.

1 1.16 1.60 1.00 0.96 3.04 1.84 2.96 1.36

time (sec)

N/A 0.221 0.076 0.217 0.175 0.261 4.792 0.364 1.856

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

58 92 197 0 0 0 0 0 0

N.S.

1 1.59 3.40 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.326 3.876 0.000 0.000 0.000 0.000 0.000 0.000

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 91 191 0 0 0 0 0 0

N.S.

1 1.65 3.47 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 4.051 0.000 0.000 0.000 0.000 0.000 0.000

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 182 155 0 0 0 0 0 0

N.S.

1 1.38 1.17 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.511 7.191 0.000 0.000 0.000 0.000 0.000 0.000

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

136 186 165 0 0 0 0 0 0

N.S.

1 1.37 1.21 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.476 4.621 0.000 0.000 0.000 0.000 0.000 0.000

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

130 180 151 0 0 0 0 0 0

N.S.

1 1.38 1.16 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.470 6.751 0.000 0.000 0.000 0.000 0.000 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

126 176 160 0 0 0 0 0 0

N.S.

1 1.40 1.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.460 8.395 0.000 0.000 0.000 0.000 0.000 0.000

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 33 49 47 37 72 0 37 34

N.S.

1 1.18 1.75 1.68 1.32 2.57 0.00 1.32 1.21

time (sec)

N/A 0.232 0.169 0.223 0.253 0.274 0.000 0.372 1.840

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

134 181 158 0 0 0 0 0 0

N.S.

1 1.35 1.18 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.476 3.917 0.000 0.000 0.000 0.000 0.000 0.000

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 182 156 0 0 0 0 0 0

N.S.

1 1.35 1.16 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.478 3.645 0.000 0.000 0.000 0.000 0.000 0.000

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 53 52 56 330 572 0 127 95

N.S.

1 1.23 1.21 1.30 7.67 13.30 0.00 2.95 2.21

time (sec)

N/A 0.295 0.239 0.468 0.265 0.301 0.000 0.383 1.889

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 47 44 44 499 171 0 67 163

N.S.

1 1.04 0.98 0.98 11.09 3.80 0.00 1.49 3.62

time (sec)

N/A 0.303 0.124 0.815 0.272 0.275 0.000 0.395 1.888

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 75 67 71 855 1576 0 161 229

N.S.

1 1.14 1.02 1.08 12.95 23.88 0.00 2.44 3.47

time (sec)

N/A 0.381 0.304 1.680 0.323 0.277 0.000 0.400 1.876

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

87 123 158 0 0 0 0 0 0

N.S.

1 1.41 1.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.369 13.623 0.000 0.000 0.000 0.000 0.000 0.000

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

168 212 312 0 0 0 0 0 0

N.S.

1 1.26 1.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.526 14.696 0.000 0.000 0.000 0.000 0.000 0.000

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

306 361 600 0 0 0 0 0 0

N.S.

1 1.18 1.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.773 16.670 0.000 0.000 0.000 0.000 0.000 0.000

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

115 115 387 0 0 0 0 0 0

N.S.

1 1.00 3.37 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.393 1.207 0.000 0.000 0.000 0.000 0.000 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

135 135 174 0 0 0 0 0 0

N.S.

1 1.00 1.29 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.441 1.250 0.000 0.000 0.000 0.000 0.000 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 62 76 0 626 0 0 65

N.S.

1 1.00 0.85 1.04 0.00 8.58 0.00 0.00 0.89

time (sec)

N/A 0.336 0.333 1.283 0.000 0.268 0.000 0.000 2.977

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 71 57 74 0 334 0 0 51

N.S.

1 1.01 0.81 1.06 0.00 4.77 0.00 0.00 0.73

time (sec)

N/A 0.332 0.166 0.487 0.000 0.262 0.000 0.000 2.613

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