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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 B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 74 99 205 86 88 92 119

N.S.

1 1.00 0.91 1.22 2.53 1.06 1.09 1.14 1.47

time (sec)

N/A 0.023 0.007 0.149 0.285 0.343 0.120 4.446 0.364

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 57 78 134 66 68 71 88

N.S.

1 1.00 0.93 1.28 2.20 1.08 1.11 1.16 1.44

time (sec)

N/A 0.018 0.005 0.155 0.280 0.342 0.099 3.680 0.245

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

41 41 40 57 75 46 46 50 57

N.S.

1 1.00 0.98 1.39 1.83 1.12 1.12 1.22 1.39

time (sec)

N/A 0.012 0.005 0.128 0.269 0.326 0.083 4.192 0.217

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

21 21 21 36 33 27 26 33 25

N.S.

1 1.00 1.00 1.71 1.57 1.29 1.24 1.57 1.19

time (sec)

N/A 0.007 0.004 0.094 0.273 0.343 0.058 3.364 0.062

Problem 5

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

15 15 17 22 17 16 12 16 15

N.S.

1 1.00 1.13 1.47 1.13 1.07 0.80 1.07 1.00

time (sec)

N/A 0.008 0.016 0.209 0.329 0.341 0.339 4.101 0.211

Problem 6

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

36 36 37 45 20 50 29 38 36

N.S.

1 1.00 1.03 1.25 0.56 1.39 0.81 1.06 1.00

time (sec)

N/A 0.011 0.027 0.245 0.328 0.335 0.355 3.920 0.227

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

63 63 48 66 21 72 48 60 64

N.S.

1 1.00 0.76 1.05 0.33 1.14 0.76 0.95 1.02

time (sec)

N/A 0.017 0.035 0.312 0.321 0.333 0.374 4.652 0.281

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

85 85 57 87 20 97 71 81 67

N.S.

1 1.00 0.67 1.02 0.24 1.14 0.84 0.95 0.79

time (sec)

N/A 0.022 0.015 0.237 0.330 0.340 0.441 6.281 0.192

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 75 0 84 0 0 0 96

N.S.

1 1.00 0.77 0.00 0.86 0.00 0.00 0.00 0.98

time (sec)

N/A 0.038 0.011 0.051 0.286 0.000 0.000 0.000 0.212

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 63 0 70 0 105 0 82

N.S.

1 1.00 0.85 0.00 0.95 0.00 1.42 0.00 1.11

time (sec)

N/A 0.030 0.008 0.032 0.271 0.000 74.034 0.000 0.169

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 50 0 53 0 90 53 46

N.S.

1 1.00 1.00 0.00 1.06 0.00 1.80 1.06 0.92

time (sec)

N/A 0.023 0.007 0.021 0.280 0.000 1.136 3.335 0.178

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 0 25 0 63 25 45

N.S.

1 1.00 1.00 0.00 1.00 0.00 2.52 1.00 1.80

time (sec)

N/A 0.016 0.003 0.029 0.263 0.000 1.123 2.894 0.153

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 58 0 47 0 92 0 67

N.S.

1 1.00 1.18 0.00 0.96 0.00 1.88 0.00 1.37

time (sec)

N/A 0.023 0.058 0.028 0.328 0.000 16.970 0.000 0.155

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 72 0 47 0 0 0 113

N.S.

1 1.00 0.94 0.00 0.61 0.00 0.00 0.00 1.47

time (sec)

N/A 0.028 0.059 0.028 0.323 0.000 0.000 0.000 0.180

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 85 0 47 0 0 0 140

N.S.

1 1.00 0.84 0.00 0.47 0.00 0.00 0.00 1.39

time (sec)

N/A 0.036 0.063 0.031 0.329 0.000 0.000 0.000 0.189

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 45 0 55 26 54 0 45

N.S.

1 1.00 1.00 0.00 1.22 0.58 1.20 0.00 1.00

time (sec)

N/A 0.021 0.021 0.025 0.082 0.106 3.949 0.000 0.179

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 112 15871 528 611 495 778 275

N.S.

1 1.00 0.85 121.15 4.03 4.66 3.78 5.94 2.10

time (sec)

N/A 0.055 0.041 1.449 0.308 0.393 1.014 1.971 0.362

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 85 4872 294 326 294 409 172

N.S.

1 1.00 0.86 49.21 2.97 3.29 2.97 4.13 1.74

time (sec)

N/A 0.040 0.010 0.549 0.296 0.345 0.550 3.898 0.256

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 59 130 136 142 146 178 94

N.S.

1 1.00 0.91 2.00 2.09 2.18 2.25 2.74 1.45

time (sec)

N/A 0.026 0.008 0.301 0.270 0.398 0.277 3.451 0.203

Problem 20

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

29 29 29 36 40 42 41 46 35

N.S.

1 1.00 1.00 1.24 1.38 1.45 1.41 1.59 1.21

time (sec)

N/A 0.011 0.007 0.197 0.295 0.372 0.138 3.575 0.154

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 63 311 0 46 0 49 -1

N.S.

1 1.00 1.00 4.94 0.00 0.73 0.00 0.78 -0.02

time (sec)

N/A 0.039 0.051 0.671 0.000 0.349 0.000 3.077 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 123 456 0 124 0 307 -1

N.S.

1 1.00 1.28 4.75 0.00 1.29 0.00 3.20 -0.01

time (sec)

N/A 0.045 0.049 0.683 0.000 0.372 0.000 2.717 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 144 734 0 277 0 1322 -1

N.S.

1 1.00 1.07 5.44 0.00 2.05 0.00 9.79 -0.01

time (sec)

N/A 0.058 0.071 0.702 0.000 0.377 0.000 3.327 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 152 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.115 0.149 0.048 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 127 0 0 0 0 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.088 0.049 0.036 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 106 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.068 0.034 0.028 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 80 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.058 0.012 0.023 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 139 0 0 0 0 0 -1

N.S.

1 1.00 1.20 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.078 0.086 0.033 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 163 0 0 0 0 0 -1

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.094 0.121 0.026 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 203 0 0 0 0 0 -1

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.110 0.152 0.024 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 103 0 0 59 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.57 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.080 0.034 0.000 0.086 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 88 0 60 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.68 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.049 0.041 0.039 0.052 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 21 26 0 23 42 23 20

N.S.

1 1.00 1.05 1.30 0.00 1.15 2.10 1.15 1.00

time (sec)

N/A 0.033 0.028 1.588 0.000 0.359 3.415 4.513 0.200

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 43 0 0 28 0 0 -1

N.S.

1 1.00 1.02 0.00 0.00 0.67 0.00 0.00 -0.02

time (sec)

N/A 0.054 0.026 0.179 0.000 0.372 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 315 1105 395 427 568 1224 526

N.S.

1 1.00 1.77 6.21 2.22 2.40 3.19 6.88 2.96

time (sec)

N/A 0.073 0.214 0.412 0.280 0.425 2.454 5.837 0.422

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 226 836 287 304 410 780 352

N.S.

1 1.00 1.52 5.61 1.93 2.04 2.75 5.23 2.36

time (sec)

N/A 0.051 0.155 0.380 0.284 0.399 1.279 4.247 0.345

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 150 585 190 195 252 430 212

N.S.

1 1.00 1.25 4.88 1.58 1.62 2.10 3.58 1.77

time (sec)

N/A 0.040 0.100 0.374 0.276 0.356 0.689 4.135 0.268

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 101 101 104 105 134 186 104

N.S.

1 1.00 1.11 1.11 1.14 1.15 1.47 2.04 1.14

time (sec)

N/A 0.027 0.039 0.239 0.280 0.385 0.396 3.751 0.248

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

29 29 29 36 40 42 41 46 35

N.S.

1 1.00 1.00 1.24 1.38 1.45 1.41 1.59 1.21

time (sec)

N/A 0.011 0.007 0.049 0.296 0.347 0.165 5.523 0.002

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 62 261 0 0 0 0 -1

N.S.

1 1.00 0.98 4.14 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.038 0.011 0.368 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 57 354 90 99 0 111 84

N.S.

1 1.00 0.77 4.78 1.22 1.34 0.00 1.50 1.14

time (sec)

N/A 0.025 0.046 0.379 0.306 0.366 0.000 5.806 1.139

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 83 633 174 258 0 302 173

N.S.

1 1.00 0.74 5.65 1.55 2.30 0.00 2.70 1.54

time (sec)

N/A 0.047 0.082 0.410 0.276 0.392 0.000 4.262 0.666

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 110 950 302 475 0 565 283

N.S.

1 1.00 0.78 6.74 2.14 3.37 0.00 4.01 2.01

time (sec)

N/A 0.061 0.110 0.495 0.302 0.382 0.000 3.834 0.937

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

365 365 612 6770 839 1127 1241 2385 1051

N.S.

1 1.00 1.68 18.55 2.30 3.09 3.40 6.53 2.88

time (sec)

N/A 0.358 0.380 1.019 0.300 0.393 2.549 3.381 0.741

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

287 287 400 4597 567 709 774 1339 591

N.S.

1 1.00 1.39 16.02 1.98 2.47 2.70 4.67 2.06

time (sec)

N/A 0.278 0.254 1.003 0.318 0.379 1.315 6.157 0.554

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 144 2616 324 369 394 595 268

N.S.

1 1.00 0.77 14.06 1.74 1.98 2.12 3.20 1.44

time (sec)

N/A 0.119 0.060 0.613 0.297 0.479 0.706 4.092 0.351

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 59 130 136 142 146 178 94

N.S.

1 1.00 0.91 2.00 2.09 2.18 2.25 2.74 1.45

time (sec)

N/A 0.026 0.012 0.078 0.280 0.346 0.368 5.249 0.002

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 194 2018 0 0 0 0 -1

N.S.

1 1.00 1.75 18.18 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.080 0.066 0.746 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 126 1092 0 0 0 0 -1

N.S.

1 1.00 0.95 8.27 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.064 0.062 0.398 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

202 202 204 1473 0 0 0 0 -1

N.S.

1 1.00 1.01 7.29 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.226 0.140 0.456 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 302 1815 0 0 0 0 -1

N.S.

1 1.00 0.95 5.73 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.375 0.240 0.468 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

598 598 1241 30495 1720 2694 2594 5282 2133

N.S.

1 1.00 2.08 50.99 2.88 4.51 4.34 8.83 3.57

time (sec)

N/A 0.388 0.826 3.487 0.353 0.411 5.208 3.983 1.212

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

432 432 809 20417 1172 1676 1578 2992 1157

N.S.

1 1.00 1.87 47.26 2.71 3.88 3.65 6.93 2.68

time (sec)

N/A 0.272 0.526 2.616 0.318 0.394 2.646 4.131 0.859

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

265 265 201 11547 687 859 836 1351 511

N.S.

1 1.00 0.76 43.57 2.59 3.24 3.15 5.10 1.93

time (sec)

N/A 0.156 0.100 1.624 0.301 0.382 1.359 6.180 0.567

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 85 4872 294 326 294 409 172

N.S.

1 1.00 0.86 49.21 2.97 3.29 2.97 4.13 1.74

time (sec)

N/A 0.039 0.017 0.116 0.299 0.368 0.584 4.081 0.002

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 335 9538 0 0 0 0 -1

N.S.

1 1.00 2.12 60.37 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.126 0.114 0.894 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 410 5626 0 0 0 0 -1

N.S.

1 1.00 2.16 29.61 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.112 0.226 1.406 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

342 342 620 0 0 0 0 0 -1

N.S.

1 1.00 1.81 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.385 0.477 0.167 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

564 564 843 0 0 0 0 0 -1

N.S.

1 1.00 1.49 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.706 0.723 0.191 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

340 340 258 37938 1217 1635 1372 2548 823

N.S.

1 1.00 0.76 111.58 3.58 4.81 4.04 7.49 2.42

time (sec)

N/A 0.199 0.152 3.079 0.338 0.401 2.647 6.445 0.801

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 112 15871 528 611 495 778 275

N.S.

1 1.00 0.85 121.15 4.03 4.66 3.78 5.94 2.10

time (sec)

N/A 0.053 0.023 0.275 0.299 0.357 1.088 4.123 0.002

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 503 33189 0 0 0 0 -1

N.S.

1 1.00 2.45 161.90 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.165 0.105 1.415 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

248 248 531 21740 0 0 0 0 -1

N.S.

1 1.00 2.14 87.66 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.159 0.469 1.701 0.000 0.000 0.000 0.000 0.000

Problem 64

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

19 19 19 25 23 22 24 23 23

N.S.

1 1.00 1.00 1.32 1.21 1.16 1.26 1.21 1.21

time (sec)

N/A 0.004 0.004 0.103 0.273 0.346 0.052 2.930 0.071

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

37 37 36 40 27 36 42 44 48

N.S.

1 1.00 0.97 1.08 0.73 0.97 1.14 1.19 1.30

time (sec)

N/A 0.010 0.004 0.104 0.276 0.347 0.075 2.818 0.288

Problem 66

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

55 55 51 55 37 51 63 62 73

N.S.

1 1.00 0.93 1.00 0.67 0.93 1.15 1.13 1.33

time (sec)

N/A 0.013 0.005 0.129 0.278 0.358 0.096 5.488 0.245

Problem 67

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 33 34 30 36 34 31

N.S.

1 1.00 1.00 1.32 1.36 1.20 1.44 1.36 1.24

time (sec)

N/A 0.012 0.006 0.109 0.275 0.318 0.086 5.777 0.078

Problem 68

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

49 49 48 52 38 48 63 65 94

N.S.

1 1.00 0.98 1.06 0.78 0.98 1.29 1.33 1.92

time (sec)

N/A 0.019 0.006 0.145 0.287 0.360 0.119 4.562 0.359

Problem 69

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

73 73 67 71 51 67 95 91 138

N.S.

1 1.00 0.92 0.97 0.70 0.92 1.30 1.25 1.89

time (sec)

N/A 0.024 0.007 0.137 0.277 0.382 0.149 4.799 0.367

Problem 70

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

24 24 24 36 35 35 36 40 29

N.S.

1 1.00 1.00 1.50 1.46 1.46 1.50 1.67 1.21

time (sec)

N/A 0.006 0.006 0.179 0.284 0.347 0.130 4.674 0.064

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 24 35 109 30 0 0 23

N.S.

1 1.00 1.00 1.46 4.54 1.25 0.00 0.00 0.96

time (sec)

N/A 0.020 0.006 0.367 0.292 0.352 0.000 0.000 0.394

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 19 0 15 17 0 15

N.S.

1 1.00 1.00 1.27 0.00 1.00 1.13 0.00 1.00

time (sec)

N/A 0.015 0.004 0.164 0.000 0.381 3.240 0.000 0.079

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A F C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 33 23 0 87 0 18

N.S.

1 1.00 1.00 2.06 1.44 0.00 5.44 0.00 1.12

time (sec)

N/A 0.012 0.003 0.101 0.281 0.000 1.452 0.000 0.034

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A F C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 33 23 0 87 0 18

N.S.

1 1.00 1.00 2.06 1.44 0.00 5.44 0.00 1.12

time (sec)

N/A 0.011 0.003 0.107 0.288 0.000 1.390 0.000 0.029

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

8 8 8 9 22 8 10 0 18

N.S.

1 1.00 1.00 1.12 2.75 1.00 1.25 0.00 2.25

time (sec)

N/A 0.005 0.002 0.086 0.306 0.357 1.318 0.000 0.029

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

10 10 10 9 9 9 7 9 8

N.S.

1 1.00 1.00 0.90 0.90 0.90 0.70 0.90 0.80

time (sec)

N/A 0.004 0.002 0.052 0.289 0.356 0.024 4.147 0.168

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 20 17 22 0 60 0 16

N.S.

1 1.00 1.00 0.85 1.10 0.00 3.00 0.00 0.80

time (sec)

N/A 0.014 0.003 0.106 0.299 0.000 1.833 0.000 0.030

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 27 19 23 0 102 0 18

N.S.

1 1.00 1.08 0.76 0.92 0.00 4.08 0.00 0.72

time (sec)

N/A 0.015 0.003 0.098 0.282 0.000 1.987 0.000 0.032

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A F A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 22 46 30 0 94 0 25

N.S.

1 1.00 1.05 2.19 1.43 0.00 4.48 0.00 1.19

time (sec)

N/A 0.016 0.004 0.175 0.316 0.000 2.003 0.000 0.084

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A F A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 22 46 30 0 94 0 25

N.S.

1 1.00 1.05 2.19 1.43 0.00 4.48 0.00 1.19

time (sec)

N/A 0.016 0.004 0.153 0.307 0.000 2.061 0.000 0.069

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 17 29 14 15 0 14

N.S.

1 1.00 1.00 1.21 2.07 1.00 1.07 0.00 1.00

time (sec)

N/A 0.014 0.003 0.181 0.304 0.357 1.946 0.000 0.056

Problem 82

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

17 17 16 17 16 18 14 14 14

N.S.

1 1.00 0.94 1.00 0.94 1.06 0.82 0.82 0.82

time (sec)

N/A 0.009 0.004 0.061 0.287 0.356 0.036 3.575 0.147

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 27 26 29 0 66 0 23

N.S.

1 1.00 1.04 1.00 1.12 0.00 2.54 0.00 0.88

time (sec)

N/A 0.016 0.003 0.162 0.327 0.000 2.346 0.000 0.161

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 34 28 30 0 109 0 25

N.S.

1 1.00 1.10 0.90 0.97 0.00 3.52 0.00 0.81

time (sec)

N/A 0.017 0.004 0.188 0.310 0.000 2.789 0.000 0.163

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 131 1300 131 179 173 342 116

N.S.

1 1.00 0.70 6.95 0.70 0.96 0.93 1.83 0.62

time (sec)

N/A 0.134 0.067 0.411 0.293 0.347 0.916 6.194 0.240

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 186 1102 150 0 0 0 -1

N.S.

1 1.00 1.05 6.23 0.85 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.203 0.045 0.282 0.275 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

285 285 216 5345 215 341 269 626 172

N.S.

1 1.00 0.76 18.75 0.75 1.20 0.94 2.20 0.60

time (sec)

N/A 0.155 0.096 0.907 0.284 0.357 1.573 3.050 0.264

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

299 299 266 3160 0 303 0 582 -1

N.S.

1 1.00 0.89 10.57 0.00 1.01 0.00 1.95 -0.00

time (sec)

N/A 0.327 0.560 1.123 0.000 0.356 0.000 5.133 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

219 219 197 1889 0 192 0 337 -1

N.S.

1 1.00 0.90 8.63 0.00 0.88 0.00 1.54 -0.00

time (sec)

N/A 0.209 0.249 0.933 0.000 0.349 0.000 3.660 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 126 937 0 108 0 159 -1

N.S.

1 1.00 0.91 6.74 0.00 0.78 0.00 1.14 -0.01

time (sec)

N/A 0.119 0.112 0.819 0.000 0.381 0.000 5.455 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 63 311 0 46 0 49 -1

N.S.

1 1.00 1.00 4.94 0.00 0.73 0.00 0.78 -0.02

time (sec)

N/A 0.032 0.014 0.055 0.000 0.399 0.000 2.702 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.025 0.129 0.198 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.023 0.361 0.158 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

339 339 1674 9517 0 676 0 3475 -1

N.S.

1 1.00 4.94 28.07 0.00 1.99 0.00 10.25 -0.00

time (sec)

N/A 0.568 0.621 1.230 0.000 0.409 0.000 5.700 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

259 259 1015 5123 0 433 0 2041 -1

N.S.

1 1.00 3.92 19.78 0.00 1.67 0.00 7.88 -0.00

time (sec)

N/A 0.370 0.348 1.007 0.000 0.394 0.000 6.245 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 208 2300 0 244 0 984 -1

N.S.

1 1.00 1.18 12.99 0.00 1.38 0.00 5.56 -0.01

time (sec)

N/A 0.182 0.189 0.701 0.000 0.376 0.000 3.296 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 123 456 0 124 0 307 -1

N.S.

1 1.00 1.28 4.75 0.00 1.29 0.00 3.20 -0.01

time (sec)

N/A 0.046 0.036 0.055 0.000 0.353 0.000 5.629 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.023 0.345 0.005 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.022 2.436 0.033 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

351 351 351 6545 0 1088 0 8396 -1

N.S.

1 1.00 1.00 18.65 0.00 3.10 0.00 23.92 -0.00

time (sec)

N/A 0.613 0.946 1.029 0.000 0.367 0.000 5.698 0.000

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