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2.2.1 Integrals 1 to 100

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

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

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 156 64 84 100 67 114 0 98

N.S.

1 1.38 0.57 0.74 0.88 0.59 1.01 0.00 0.87

time (sec)

N/A 0.291 0.039 0.270 0.190 0.250 0.561 0.000 0.107

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 125 56 77 81 59 104 70 85

N.S.

1 1.39 0.62 0.86 0.90 0.66 1.16 0.78 0.94

time (sec)

N/A 0.263 0.031 0.249 0.204 0.263 0.557 0.280 0.503

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 92 46 67 62 51 90 0 71

N.S.

1 1.23 0.61 0.89 0.83 0.68 1.20 0.00 0.95

time (sec)

N/A 0.235 0.025 0.217 0.207 0.264 0.522 0.000 0.462

Problem 4

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

42 61 38 59 42 43 78 53 51

N.S.

1 1.45 0.90 1.40 1.00 1.02 1.86 1.26 1.21

time (sec)

N/A 0.192 0.023 0.204 0.206 0.278 0.541 0.276 0.045

Problem 5

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

29 29 26 41 25 37 61 41 32

N.S.

1 1.00 0.90 1.41 0.86 1.28 2.10 1.41 1.10

time (sec)

N/A 0.167 0.012 0.190 0.183 0.259 0.452 0.295 0.039

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 29 48 18 58 48 68 32

N.S.

1 1.00 1.16 1.92 0.72 2.32 1.92 2.72 1.28

time (sec)

N/A 0.197 0.012 0.209 0.177 0.268 1.629 0.288 0.040

Problem 7

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

38 38 47 34 29 66 26 75 33

N.S.

1 1.00 1.24 0.89 0.76 1.74 0.68 1.97 0.87

time (sec)

N/A 0.197 0.022 0.225 0.190 0.254 1.149 0.283 0.039

Problem 8

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 63 57 53 48 83 48 153 52

N.S.

1 1.00 0.90 0.84 0.76 1.32 0.76 2.43 0.83

time (sec)

N/A 0.229 0.031 0.255 0.191 0.261 1.628 0.294 0.043

Problem 9

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

90 92 70 68 67 92 75 161 74

N.S.

1 1.02 0.78 0.76 0.74 1.02 0.83 1.79 0.82

time (sec)

N/A 0.257 0.036 0.247 0.209 0.261 1.758 0.287 0.039

Problem 10

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

113 118 76 77 86 101 122 237 95

N.S.

1 1.04 0.67 0.68 0.76 0.89 1.08 2.10 0.84

time (sec)

N/A 0.290 0.040 0.274 0.203 0.259 2.957 0.299 0.033

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 48 46 56 46 41 46 43

N.S.

1 1.00 1.00 0.96 1.17 0.96 0.85 0.96 0.90

time (sec)

N/A 0.208 0.017 0.245 0.284 0.249 0.081 0.280 0.475

Problem 12

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

39 39 39 37 47 37 31 37 36

N.S.

1 1.00 1.00 0.95 1.21 0.95 0.79 0.95 0.92

time (sec)

N/A 0.202 0.011 0.235 0.286 0.248 0.071 0.268 0.461

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 29 38 29 22 29 27

N.S.

1 1.00 1.00 1.00 1.31 1.00 0.76 1.00 0.93

time (sec)

N/A 0.187 0.009 0.238 0.293 0.261 0.055 0.293 0.065

Problem 14

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 30 20 28 21 12 15 19

N.S.

1 1.00 1.58 1.05 1.47 1.11 0.63 0.79 1.00

time (sec)

N/A 0.173 0.010 0.236 0.284 0.258 0.071 0.279 0.047

Problem 15

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

13 13 13 13 21 15 17 12 14

N.S.

1 1.00 1.00 1.00 1.62 1.15 1.31 0.92 1.08

time (sec)

N/A 0.177 0.006 0.223 0.282 0.254 0.071 0.271 0.500

Problem 16

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

26 26 26 26 31 26 32 21 17

N.S.

1 1.00 1.00 1.00 1.19 1.00 1.23 0.81 0.65

time (sec)

N/A 0.187 0.009 0.273 0.260 0.255 0.082 0.276 0.066

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

36 36 36 38 42 39 42 31 27

N.S.

1 1.00 1.00 1.06 1.17 1.08 1.17 0.86 0.75

time (sec)

N/A 0.196 0.009 0.246 0.278 0.262 0.106 0.275 0.083

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

48 48 48 48 51 47 54 39 34

N.S.

1 1.00 1.00 1.00 1.06 0.98 1.12 0.81 0.71

time (sec)

N/A 0.205 0.011 0.260 0.290 0.249 0.127 0.279 0.078

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 154 80 124 114 88 0 0 137

N.S.

1 1.12 0.58 0.91 0.83 0.64 0.00 0.00 1.00

time (sec)

N/A 0.810 0.042 0.420 0.186 0.260 0.000 0.000 0.502

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 125 63 111 95 80 0 0 114

N.S.

1 1.23 0.62 1.09 0.93 0.78 0.00 0.00 1.12

time (sec)

N/A 0.711 0.039 0.395 0.205 0.275 0.000 0.000 0.069

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 89 54 106 76 72 0 0 104

N.S.

1 0.97 0.59 1.15 0.83 0.78 0.00 0.00 1.13

time (sec)

N/A 0.562 0.043 0.342 0.209 0.263 0.000 0.000 0.495

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 42 93 57 60 0 0 72

N.S.

1 1.00 0.70 1.55 0.95 1.00 0.00 0.00 1.20

time (sec)

N/A 0.226 0.030 0.349 0.211 0.278 0.000 0.000 0.466

Problem 23

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

51 50 55 101 46 100 0 0 73

N.S.

1 0.98 1.08 1.98 0.90 1.96 0.00 0.00 1.43

time (sec)

N/A 0.444 0.032 0.274 0.204 0.270 0.000 0.000 0.511

Problem 24

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

63 63 61 80 60 109 0 0 75

N.S.

1 1.00 0.97 1.27 0.95 1.73 0.00 0.00 1.19

time (sec)

N/A 0.413 0.037 0.336 0.211 0.265 0.000 0.000 0.063

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 79 105 81 130 0 0 99

N.S.

1 1.00 0.86 1.14 0.88 1.41 0.00 0.00 1.08

time (sec)

N/A 0.462 0.058 0.313 0.180 0.265 0.000 0.000 0.480

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 89 116 100 139 0 0 116

N.S.

1 1.00 0.76 0.99 0.85 1.19 0.00 0.00 0.99

time (sec)

N/A 0.483 0.057 0.372 0.187 0.279 0.000 0.000 0.468

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 65 67 77 70 56 60 60

N.S.

1 1.00 1.00 1.03 1.18 1.08 0.86 0.92 0.92

time (sec)

N/A 0.230 0.033 0.260 0.266 0.274 0.122 0.271 0.505

Problem 28

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

53 53 53 58 67 62 44 51 51

N.S.

1 1.00 1.00 1.09 1.26 1.17 0.83 0.96 0.96

time (sec)

N/A 0.222 0.028 0.266 0.293 0.267 0.106 0.279 0.066

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

45 45 45 50 60 53 36 43 43

N.S.

1 1.00 1.00 1.11 1.33 1.18 0.80 0.96 0.96

time (sec)

N/A 0.203 0.021 0.237 0.294 0.253 0.085 0.288 0.068

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

31 31 42 33 44 43 22 25 32

N.S.

1 1.00 1.35 1.06 1.42 1.39 0.71 0.81 1.03

time (sec)

N/A 0.182 0.018 0.234 0.286 0.253 0.089 0.283 0.490

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

16 16 16 15 22 18 10 13 14

N.S.

1 1.00 1.00 0.94 1.38 1.12 0.62 0.81 0.88

time (sec)

N/A 0.178 0.009 0.242 0.272 0.257 0.101 0.290 0.084

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

38 38 38 44 53 60 44 35 37

N.S.

1 1.00 1.00 1.16 1.39 1.58 1.16 0.92 0.97

time (sec)

N/A 0.201 0.020 0.272 0.289 0.273 0.151 0.287 0.501

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

52 52 52 53 69 77 58 46 43

N.S.

1 1.00 1.00 1.02 1.33 1.48 1.12 0.88 0.83

time (sec)

N/A 0.208 0.034 0.277 0.285 0.267 0.165 0.284 0.567

Problem 34

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

62 62 62 61 77 86 70 54 55

N.S.

1 1.00 1.00 0.98 1.24 1.39 1.13 0.87 0.89

time (sec)

N/A 0.219 0.028 0.275 0.284 0.256 0.179 0.282 0.141

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 125 56 77 76 59 0 0 85

N.S.

1 1.39 0.62 0.86 0.84 0.66 0.00 0.00 0.94

time (sec)

N/A 0.273 0.031 0.270 0.293 0.303 0.000 0.000 0.069

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 92 46 67 59 51 0 0 71

N.S.

1 1.23 0.61 0.89 0.79 0.68 0.00 0.00 0.95

time (sec)

N/A 0.237 0.023 0.254 0.277 0.267 0.000 0.000 0.463

Problem 37

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

42 61 38 59 42 43 0 53 51

N.S.

1 1.45 0.90 1.40 1.00 1.02 0.00 1.26 1.21

time (sec)

N/A 0.204 0.022 0.237 0.297 0.263 0.000 0.284 0.464

Problem 38

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

29 29 26 48 25 37 0 41 32

N.S.

1 1.00 0.90 1.66 0.86 1.28 0.00 1.41 1.10

time (sec)

N/A 0.170 0.015 0.252 0.265 0.287 0.000 0.302 0.451

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 29 121 26 58 0 68 32

N.S.

1 1.00 1.16 4.84 1.04 2.32 0.00 2.72 1.28

time (sec)

N/A 0.204 0.014 0.234 0.284 0.264 0.000 0.291 0.039

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 47 34 0 66 0 0 33

N.S.

1 1.00 1.24 0.89 0.00 1.74 0.00 0.00 0.87

time (sec)

N/A 0.200 0.022 0.243 0.000 0.265 0.000 0.000 0.039

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 64 57 60 0 83 0 0 52

N.S.

1 1.02 0.90 0.95 0.00 1.32 0.00 0.00 0.83

time (sec)

N/A 0.229 0.033 0.246 0.000 0.274 0.000 0.000 0.042

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 92 70 68 0 92 0 0 74

N.S.

1 1.02 0.78 0.76 0.00 1.02 0.00 0.00 0.82

time (sec)

N/A 0.254 0.039 0.253 0.000 0.257 0.000 0.000 0.039

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 118 76 77 0 101 0 0 95

N.S.

1 1.04 0.67 0.68 0.00 0.89 0.00 0.00 0.84

time (sec)

N/A 0.286 0.042 0.277 0.000 0.270 0.000 0.000 0.034

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

49 49 49 48 44 46 41 68 43

N.S.

1 1.00 1.00 0.98 0.90 0.94 0.84 1.39 0.88

time (sec)

N/A 0.208 0.019 0.194 0.176 0.266 0.068 0.292 0.060

Problem 45

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

40 40 40 40 35 37 31 58 36

N.S.

1 1.00 1.00 1.00 0.88 0.92 0.78 1.45 0.90

time (sec)

N/A 0.203 0.011 0.205 0.189 0.248 0.067 0.290 0.459

Problem 46

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

30 30 30 31 28 29 22 52 27

N.S.

1 1.00 1.00 1.03 0.93 0.97 0.73 1.73 0.90

time (sec)

N/A 0.189 0.011 0.198 0.187 0.260 0.051 0.290 0.486

Problem 47

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

20 20 30 19 16 21 14 65 19

N.S.

1 1.00 1.50 0.95 0.80 1.05 0.70 3.25 0.95

time (sec)

N/A 0.177 0.011 0.216 0.218 0.247 0.059 0.287 0.454

Problem 48

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

14 14 14 14 12 15 17 44 14

N.S.

1 1.00 1.00 1.00 0.86 1.07 1.21 3.14 1.00

time (sec)

N/A 0.183 0.007 0.189 0.216 0.279 0.072 0.282 0.497

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 25 34 26 32 34 17

N.S.

1 1.00 1.00 0.93 1.26 0.96 1.19 1.26 0.63

time (sec)

N/A 0.193 0.010 0.217 0.207 0.249 0.084 0.281 0.486

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 37 34 50 39 42 54 26

N.S.

1 1.00 1.00 0.92 1.35 1.05 1.14 1.46 0.70

time (sec)

N/A 0.199 0.010 0.238 0.213 0.260 0.100 0.280 0.077

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 49 44 57 47 54 67 33

N.S.

1 1.00 1.00 0.90 1.16 0.96 1.10 1.37 0.67

time (sec)

N/A 0.206 0.012 0.263 0.203 0.267 0.122 0.295 0.481

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 154 80 124 216 88 0 0 138

N.S.

1 1.12 0.58 0.91 1.58 0.64 0.00 0.00 1.01

time (sec)

N/A 0.798 0.043 0.371 0.285 0.253 0.000 0.000 0.514

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 125 63 111 181 80 0 0 115

N.S.

1 1.23 0.62 1.09 1.77 0.78 0.00 0.00 1.13

time (sec)

N/A 0.702 0.040 0.363 0.298 0.259 0.000 0.000 0.075

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 89 60 106 112 72 0 0 105

N.S.

1 0.97 0.65 1.15 1.22 0.78 0.00 0.00 1.14

time (sec)

N/A 0.547 0.040 0.327 0.260 0.280 0.000 0.000 0.481

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 42 93 65 60 0 0 73

N.S.

1 1.00 0.70 1.55 1.08 1.00 0.00 0.00 1.22

time (sec)

N/A 0.227 0.027 0.328 0.266 0.289 0.000 0.000 0.473

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 50 55 649 0 100 0 0 74

N.S.

1 0.96 1.06 12.48 0.00 1.92 0.00 0.00 1.42

time (sec)

N/A 0.442 0.034 0.293 0.000 0.298 0.000 0.000 0.494

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 61 82 0 109 0 0 76

N.S.

1 1.00 0.95 1.28 0.00 1.70 0.00 0.00 1.19

time (sec)

N/A 0.417 0.040 0.355 0.000 0.275 0.000 0.000 0.476

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 79 108 0 130 0 0 100

N.S.

1 1.00 0.85 1.16 0.00 1.40 0.00 0.00 1.08

time (sec)

N/A 0.456 0.057 0.395 0.000 0.270 0.000 0.000 0.472

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 89 116 0 139 0 0 117

N.S.

1 1.00 0.75 0.98 0.00 1.18 0.00 0.00 0.99

time (sec)

N/A 0.475 0.053 0.460 0.000 0.276 0.000 0.000 0.071

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 139 95 125 0 146 0 0 139

N.S.

1 1.00 0.68 0.90 0.00 1.05 0.00 0.00 1.00

time (sec)

N/A 0.514 0.060 0.425 0.000 0.268 0.000 0.000 0.504

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

339 317 82 0 0 244 0 0 0

N.S.

1 0.94 0.24 0.00 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.424 0.030 0.000 0.000 0.269 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

295 280 63 0 0 236 0 0 0

N.S.

1 0.95 0.21 0.00 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 0.405 0.016 0.000 0.000 0.266 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

268 239 41 0 0 209 0 0 0

N.S.

1 0.89 0.15 0.00 0.00 0.78 0.00 0.00 0.00

time (sec)

N/A 0.365 0.022 0.000 0.000 0.264 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

267 266 97 0 0 243 0 0 0

N.S.

1 1.00 0.36 0.00 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.413 0.027 0.000 0.000 0.275 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F B F F(-2) F(-1)

verified

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

size

92 96 71 0 0 151 0 0 0

N.S.

1 1.04 0.77 0.00 0.00 1.64 0.00 0.00 0.00

time (sec)

N/A 0.212 0.013 0.000 0.000 0.279 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

132 135 81 0 0 175 0 0 0

N.S.

1 1.02 0.61 0.00 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.240 0.015 0.000 0.000 0.263 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

170 172 93 0 0 184 0 0 0

N.S.

1 1.01 0.55 0.00 0.00 1.08 0.00 0.00 0.00

time (sec)

N/A 0.282 0.020 0.000 0.000 0.258 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

202 209 99 0 0 192 0 0 0

N.S.

1 1.03 0.49 0.00 0.00 0.95 0.00 0.00 0.00

time (sec)

N/A 0.306 0.023 0.000 0.000 0.276 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

240 248 111 0 0 200 0 0 0

N.S.

1 1.03 0.46 0.00 0.00 0.83 0.00 0.00 0.00

time (sec)

N/A 0.336 0.028 0.000 0.000 0.269 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

337 330 148 0 0 254 0 0 0

N.S.

1 0.98 0.44 0.00 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.455 0.083 0.000 0.000 0.278 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

339 317 82 0 0 247 0 0 0

N.S.

1 0.94 0.24 0.00 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.442 0.025 0.000 0.000 0.273 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

295 280 61 0 0 239 0 0 0

N.S.

1 0.95 0.21 0.00 0.00 0.81 0.00 0.00 0.00

time (sec)

N/A 0.405 0.018 0.000 0.000 0.272 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

268 239 41 0 0 215 0 0 0

N.S.

1 0.89 0.15 0.00 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 0.365 0.025 0.000 0.000 0.266 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

267 266 96 0 0 243 0 0 0

N.S.

1 1.00 0.36 0.00 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.417 0.024 0.000 0.000 0.278 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F B F F(-2) F(-1)

verified

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

size

92 96 68 0 0 157 0 0 0

N.S.

1 1.04 0.74 0.00 0.00 1.71 0.00 0.00 0.00

time (sec)

N/A 0.224 0.011 0.000 0.000 0.276 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

132 135 81 0 0 179 0 0 0

N.S.

1 1.02 0.61 0.00 0.00 1.36 0.00 0.00 0.00

time (sec)

N/A 0.238 0.014 0.000 0.000 0.260 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

170 172 93 0 0 187 0 0 0

N.S.

1 1.01 0.55 0.00 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.287 0.019 0.000 0.000 0.277 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

202 207 99 0 0 195 0 0 0

N.S.

1 1.02 0.49 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.312 0.024 0.000 0.000 0.272 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

373 372 96 0 0 251 0 0 0

N.S.

1 1.00 0.26 0.00 0.00 0.67 0.00 0.00 0.00

time (sec)

N/A 0.500 0.034 0.000 0.000 0.269 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

371 354 86 0 0 244 0 0 0

N.S.

1 0.95 0.23 0.00 0.00 0.66 0.00 0.00 0.00

time (sec)

N/A 0.476 0.028 0.000 0.000 0.266 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

324 314 72 0 0 236 0 0 0

N.S.

1 0.97 0.22 0.00 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.437 0.026 0.000 0.000 0.280 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

299 273 41 0 0 209 0 0 0

N.S.

1 0.91 0.14 0.00 0.00 0.70 0.00 0.00 0.00

time (sec)

N/A 0.392 0.032 0.000 0.000 0.274 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

293 292 112 0 0 267 0 0 0

N.S.

1 1.00 0.38 0.00 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.446 0.031 0.000 0.000 0.279 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

121 127 87 0 0 152 0 0 0

N.S.

1 1.05 0.72 0.00 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.231 0.016 0.000 0.000 0.281 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

163 166 99 0 0 176 0 0 0

N.S.

1 1.02 0.61 0.00 0.00 1.08 0.00 0.00 0.00

time (sec)

N/A 0.259 0.020 0.000 0.000 0.263 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

203 205 106 0 0 184 0 0 0

N.S.

1 1.01 0.52 0.00 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.304 0.024 0.000 0.000 0.275 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F(-1) F(-2) F(-1)

verified

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

size

233 240 118 0 0 192 0 0 0

N.S.

1 1.03 0.51 0.00 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 0.336 0.030 0.000 0.000 0.271 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

337 330 127 0 0 255 0 0 0

N.S.

1 0.98 0.38 0.00 0.00 0.76 0.00 0.00 0.00

time (sec)

N/A 0.457 0.079 0.000 0.000 0.300 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

339 317 73 0 0 247 0 0 0

N.S.

1 0.94 0.22 0.00 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.435 0.029 0.000 0.000 0.284 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

295 280 63 0 0 238 0 0 0

N.S.

1 0.95 0.21 0.00 0.00 0.81 0.00 0.00 0.00

time (sec)

N/A 0.399 0.012 0.000 0.000 0.268 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

268 239 41 0 0 213 0 0 0

N.S.

1 0.89 0.15 0.00 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.349 0.024 0.000 0.000 0.265 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

267 266 96 0 0 243 0 0 0

N.S.

1 1.00 0.36 0.00 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.422 0.018 0.000 0.000 0.264 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F B F F(-2) F(-1)

verified

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

size

92 96 69 0 0 156 0 0 0

N.S.

1 1.04 0.75 0.00 0.00 1.70 0.00 0.00 0.00

time (sec)

N/A 0.228 0.011 0.000 0.000 0.261 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

132 135 81 0 0 178 0 0 0

N.S.

1 1.02 0.61 0.00 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.243 0.015 0.000 0.000 0.266 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

170 172 92 0 0 187 0 0 0

N.S.

1 1.01 0.54 0.00 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.282 0.022 0.000 0.000 0.263 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

202 209 99 0 0 195 0 0 0

N.S.

1 1.03 0.49 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.313 0.026 0.000 0.000 0.270 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

337 330 127 0 0 251 0 0 0

N.S.

1 0.98 0.38 0.00 0.00 0.74 0.00 0.00 0.00

time (sec)

N/A 0.460 0.095 0.000 0.000 0.274 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

339 317 73 0 0 243 0 0 0

N.S.

1 0.94 0.22 0.00 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.443 0.025 0.000 0.000 0.273 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

295 280 63 0 0 236 0 0 0

N.S.

1 0.95 0.21 0.00 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 0.408 0.013 0.000 0.000 0.279 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F A F F(-2) F(-1)

verified

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

size

268 239 39 0 0 209 0 0 0

N.S.

1 0.89 0.15 0.00 0.00 0.78 0.00 0.00 0.00

time (sec)

N/A 0.372 0.033 0.000 0.000 0.280 0.000 0.000 0.000

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