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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 B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 105 65 95 83 221 89 225

N.S.

1 1.00 1.03 0.64 0.93 0.81 2.17 0.87 2.21

time (sec)

N/A 0.286 0.297 1.735 0.269 0.302 0.257 0.307 9.632

Problem 2

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

129 129 115 76 143 96 379 106 294

N.S.

1 1.00 0.89 0.59 1.11 0.74 2.94 0.82 2.28

time (sec)

N/A 0.319 0.371 2.075 0.245 0.288 0.376 0.307 9.557

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 101 33 180 70 1221 67 78

N.S.

1 1.00 1.91 0.62 3.40 1.32 23.04 1.26 1.47

time (sec)

N/A 0.371 0.118 0.383 0.295 0.272 1.767 0.315 6.035

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 87 29 128 53 665 56 59

N.S.

1 1.00 2.07 0.69 3.05 1.26 15.83 1.33 1.40

time (sec)

N/A 0.259 0.080 0.365 0.281 0.323 0.884 0.315 5.951

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 24 48 20 78 35 221 44 46

N.S.

1 0.89 1.78 0.74 2.89 1.30 8.19 1.63 1.70

time (sec)

N/A 0.286 0.065 0.301 0.277 0.286 0.427 0.297 6.248

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 42 22 32 28 34 19 19

N.S.

1 1.00 2.47 1.29 1.88 1.65 2.00 1.12 1.12

time (sec)

N/A 0.217 0.017 0.254 0.279 0.288 0.209 0.314 5.934

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 29 14 16 22 10 13 13

N.S.

1 1.00 2.42 1.17 1.33 1.83 0.83 1.08 1.08

time (sec)

N/A 0.161 0.010 0.218 0.211 0.270 0.121 0.285 0.024

Problem 8

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

20 20 40 21 31 53 0 24 23

N.S.

1 1.00 2.00 1.05 1.55 2.65 0.00 1.20 1.15

time (sec)

N/A 0.251 0.047 0.326 0.197 0.281 0.000 0.304 6.155

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 27 63 36 68 91 0 53 49

N.S.

1 1.04 2.42 1.38 2.62 3.50 0.00 2.04 1.88

time (sec)

N/A 0.351 0.190 0.440 0.214 0.308 0.000 0.341 6.612

Problem 10

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

42 43 83 54 97 134 0 73 69

N.S.

1 1.02 1.98 1.29 2.31 3.19 0.00 1.74 1.64

time (sec)

N/A 0.425 0.286 0.476 0.210 0.267 0.000 0.329 5.894

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 113 68 120 168 0 96 89

N.S.

1 0.98 2.05 1.24 2.18 3.05 0.00 1.75 1.62

time (sec)

N/A 0.457 0.623 0.466 0.211 0.307 0.000 0.299 5.989

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 72 100 43 198 105 1423 72 77

N.S.

1 1.09 1.52 0.65 3.00 1.59 21.56 1.09 1.17

time (sec)

N/A 0.393 0.241 0.536 0.306 0.270 3.603 0.301 6.465

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 51 84 37 144 95 779 51 62

N.S.

1 1.09 1.79 0.79 3.06 2.02 16.57 1.09 1.32

time (sec)

N/A 0.499 0.188 0.391 0.319 0.288 1.943 0.298 5.887

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 69 33 90 82 321 35 34

N.S.

1 1.11 1.97 0.94 2.57 2.34 9.17 1.00 0.97

time (sec)

N/A 0.325 0.133 0.336 0.300 0.301 1.016 0.296 5.643

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 32 21 22 62 60 87 21 21

N.S.

1 0.97 0.64 0.67 1.88 1.82 2.64 0.64 0.64

time (sec)

N/A 0.231 0.033 0.322 0.211 0.274 0.578 0.319 5.713

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 32 31 24 74 58 134 29 29

N.S.

1 0.97 0.94 0.73 2.24 1.76 4.06 0.88 0.88

time (sec)

N/A 0.222 0.100 0.327 0.204 0.258 0.312 0.292 5.637

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 129 40 89 117 0 40 38

N.S.

1 1.00 3.39 1.05 2.34 3.08 0.00 1.05 1.00

time (sec)

N/A 0.350 0.440 0.599 0.203 0.298 0.000 0.305 6.059

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 53 166 56 126 168 0 69 91

N.S.

1 1.18 3.69 1.24 2.80 3.73 0.00 1.53 2.02

time (sec)

N/A 0.504 0.922 0.535 0.202 0.287 0.000 0.314 5.925

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 70 203 70 155 220 0 93 111

N.S.

1 1.09 3.17 1.09 2.42 3.44 0.00 1.45 1.73

time (sec)

N/A 0.590 0.828 0.543 0.222 0.275 0.000 0.303 6.372

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 84 238 90 178 266 0 114 101

N.S.

1 1.29 3.66 1.38 2.74 4.09 0.00 1.75 1.55

time (sec)

N/A 0.645 3.178 0.570 0.229 0.299 0.000 0.313 5.888

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 114 191 63 306 158 3288 99 110

N.S.

1 1.13 1.89 0.62 3.03 1.56 32.55 0.98 1.09

time (sec)

N/A 0.715 0.128 0.671 0.307 0.287 17.818 0.319 6.619

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 104 170 57 252 145 2259 88 93

N.S.

1 1.16 1.89 0.63 2.80 1.61 25.10 0.98 1.03

time (sec)

N/A 0.566 0.115 0.609 0.306 0.274 11.374 0.310 6.352

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 76 140 51 198 132 1425 67 78

N.S.

1 1.07 1.97 0.72 2.79 1.86 20.07 0.94 1.10

time (sec)

N/A 0.710 0.099 0.509 0.301 0.279 6.697 0.300 5.963

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 69 112 47 144 119 777 51 50

N.S.

1 1.17 1.90 0.80 2.44 2.02 13.17 0.86 0.85

time (sec)

N/A 0.537 0.177 0.451 0.295 0.263 3.853 0.297 5.965

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 27 30 104 90 206 29 29

N.S.

1 1.04 0.54 0.60 2.08 1.80 4.12 0.58 0.58

time (sec)

N/A 0.341 0.046 0.347 0.194 0.257 2.203 0.302 5.883

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 54 25 38 116 88 277 37 37

N.S.

1 1.08 0.50 0.76 2.32 1.76 5.54 0.74 0.74

time (sec)

N/A 0.304 0.034 0.344 0.196 0.289 1.209 0.306 6.231

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 54 45 33 128 92 348 45 45

N.S.

1 1.08 0.90 0.66 2.56 1.84 6.96 0.90 0.90

time (sec)

N/A 0.291 0.107 0.334 0.201 0.257 0.603 0.294 5.955

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 67 160 54 143 168 0 56 54

N.S.

1 1.16 2.76 0.93 2.47 2.90 0.00 0.97 0.93

time (sec)

N/A 0.502 0.716 0.510 0.213 0.292 0.000 0.291 6.207

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 75 206 76 180 225 0 85 129

N.S.

1 1.15 3.17 1.17 2.77 3.46 0.00 1.31 1.98

time (sec)

N/A 0.667 1.130 0.536 0.204 0.270 0.000 0.282 6.168

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 100 247 84 209 276 0 109 97

N.S.

1 1.16 2.87 0.98 2.43 3.21 0.00 1.27 1.13

time (sec)

N/A 0.794 1.265 0.648 0.206 0.298 0.000 0.305 6.083

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 116 299 110 232 333 0 128 117

N.S.

1 1.13 2.90 1.07 2.25 3.23 0.00 1.24 1.14

time (sec)

N/A 0.830 1.665 0.658 0.203 0.289 0.000 0.297 6.142

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 179 165 83 0 132 0 147 0

N.S.

1 1.13 1.04 0.53 0.00 0.84 0.00 0.93 0.00

time (sec)

N/A 0.757 0.584 0.585 0.000 0.275 0.000 0.317 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 138 141 73 0 111 0 120 0

N.S.

1 1.13 1.16 0.60 0.00 0.91 0.00 0.98 0.00

time (sec)

N/A 0.562 0.383 0.495 0.000 0.277 0.000 0.301 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 97 117 63 0 92 0 93 0

N.S.

1 1.13 1.36 0.73 0.00 1.07 0.00 1.08 0.00

time (sec)

N/A 0.409 0.429 0.483 0.000 0.268 0.000 0.321 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 81 51 0 67 0 65 0

N.S.

1 1.00 1.45 0.91 0.00 1.20 0.00 1.16 0.00

time (sec)

N/A 0.266 0.148 0.526 0.000 0.262 0.000 0.308 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 65 43 0 50 0 36 33

N.S.

1 1.00 2.50 1.65 0.00 1.92 0.00 1.38 1.27

time (sec)

N/A 0.173 0.026 0.365 0.000 0.274 0.000 0.311 0.225

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 94 68 0 219 0 67 0

N.S.

1 1.00 2.54 1.84 0.00 5.92 0.00 1.81 0.00

time (sec)

N/A 0.219 0.291 0.509 0.000 0.275 0.000 0.455 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 178 104 0 258 0 122 0

N.S.

1 1.00 2.78 1.62 0.00 4.03 0.00 1.91 0.00

time (sec)

N/A 0.321 0.662 0.676 0.000 0.298 0.000 0.611 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 103 249 132 0 319 0 155 0

N.S.

1 1.01 2.44 1.29 0.00 3.13 0.00 1.52 0.00

time (sec)

N/A 0.457 0.755 0.668 0.000 0.287 0.000 0.505 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 144 285 158 0 361 0 184 0

N.S.

1 1.04 2.07 1.14 0.00 2.62 0.00 1.33 0.00

time (sec)

N/A 0.612 1.137 0.884 0.000 0.279 0.000 0.620 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 97 67 0 223 0 104 0

N.S.

1 1.00 2.55 1.76 0.00 5.87 0.00 2.74 0.00

time (sec)

N/A 0.218 0.302 1.014 0.000 0.283 0.000 0.383 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 96 70 0 223 0 106 0

N.S.

1 1.00 2.46 1.79 0.00 5.72 0.00 2.72 0.00

time (sec)

N/A 0.224 0.428 0.753 0.000 0.293 0.000 0.373 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 95 69 0 221 0 69 0

N.S.

1 1.00 2.38 1.72 0.00 5.52 0.00 1.72 0.00

time (sec)

N/A 0.221 0.225 0.549 0.000 0.286 0.000 0.326 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 182 165 85 0 145 0 152 0

N.S.

1 1.12 1.02 0.52 0.00 0.90 0.00 0.94 0.00

time (sec)

N/A 0.771 1.210 0.517 0.000 0.288 0.000 0.347 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 131 145 75 0 122 0 124 0

N.S.

1 1.13 1.25 0.65 0.00 1.05 0.00 1.07 0.00

time (sec)

N/A 0.525 1.565 0.485 0.000 0.271 0.000 0.547 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 91 157 63 0 99 0 95 0

N.S.

1 1.06 1.83 0.73 0.00 1.15 0.00 1.10 0.00

time (sec)

N/A 0.367 1.019 0.538 0.000 0.273 0.000 0.409 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 89 53 0 76 0 67 0

N.S.

1 1.00 1.51 0.90 0.00 1.29 0.00 1.14 0.00

time (sec)

N/A 0.254 0.058 0.420 0.000 0.300 0.000 0.525 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 118 84 0 239 0 104 0

N.S.

1 1.00 1.79 1.27 0.00 3.62 0.00 1.58 0.00

time (sec)

N/A 0.370 1.010 0.636 0.000 0.283 0.000 0.802 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 180 103 0 268 0 125 0

N.S.

1 1.00 2.73 1.56 0.00 4.06 0.00 1.89 0.00

time (sec)

N/A 0.349 1.975 0.669 0.000 0.271 0.000 0.346 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 106 250 126 0 337 0 158 0

N.S.

1 1.00 2.36 1.19 0.00 3.18 0.00 1.49 0.00

time (sec)

N/A 0.479 1.301 0.707 0.000 0.300 0.000 0.328 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 147 286 144 0 380 0 188 0

N.S.

1 1.02 1.99 1.00 0.00 2.64 0.00 1.31 0.00

time (sec)

N/A 0.632 2.702 0.731 0.000 0.276 0.000 0.362 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

203 227 187 95 0 192 0 192 0

N.S.

1 1.12 0.92 0.47 0.00 0.95 0.00 0.95 0.00

time (sec)

N/A 1.001 1.363 3.572 0.000 0.282 0.000 0.338 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 165 167 85 0 167 0 162 0

N.S.

1 1.13 1.14 0.58 0.00 1.14 0.00 1.11 0.00

time (sec)

N/A 0.648 1.322 1.274 0.000 0.277 0.000 0.345 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 125 271 75 0 140 0 132 0

N.S.

1 1.08 2.34 0.65 0.00 1.21 0.00 1.14 0.00

time (sec)

N/A 0.465 3.053 0.713 0.000 0.268 0.000 0.329 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 93 117 65 0 115 0 102 0

N.S.

1 1.04 1.31 0.73 0.00 1.29 0.00 1.15 0.00

time (sec)

N/A 0.335 0.149 0.497 0.000 0.270 0.000 0.311 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 101 143 103 0 279 0 141 0

N.S.

1 1.03 1.46 1.05 0.00 2.85 0.00 1.44 0.00

time (sec)

N/A 0.519 5.707 1.087 0.000 0.307 0.000 0.336 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 100 182 127 0 308 0 159 0

N.S.

1 1.06 1.94 1.35 0.00 3.28 0.00 1.69 0.00

time (sec)

N/A 0.510 6.102 2.566 0.000 0.313 0.000 0.615 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 108 252 126 0 359 0 164 0

N.S.

1 1.02 2.38 1.19 0.00 3.39 0.00 1.55 0.00

time (sec)

N/A 0.550 6.032 8.270 0.000 0.293 0.000 0.512 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 150 288 144 0 408 0 196 0

N.S.

1 1.04 2.00 1.00 0.00 2.83 0.00 1.36 0.00

time (sec)

N/A 0.690 6.447 26.534 0.000 0.275 0.000 0.442 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 191 370 162 0 473 0 228 0

N.S.

1 1.05 2.03 0.89 0.00 2.60 0.00 1.25 0.00

time (sec)

N/A 0.880 6.088 75.632 0.000 0.314 0.000 0.616 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 154 150 130 0 234 0 163 0

N.S.

1 1.11 1.08 0.94 0.00 1.68 0.00 1.17 0.00

time (sec)

N/A 0.731 0.507 0.688 0.000 0.286 0.000 0.360 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 112 105 96 0 209 0 121 0

N.S.

1 1.07 1.00 0.91 0.00 1.99 0.00 1.15 0.00

time (sec)

N/A 0.443 0.482 0.670 0.000 0.275 0.000 0.317 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 98 96 0 191 0 118 99

N.S.

1 1.00 1.36 1.33 0.00 2.65 0.00 1.64 1.38

time (sec)

N/A 0.286 0.201 0.827 0.000 0.301 0.000 0.342 0.802

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 73 75 0 167 0 111 49

N.S.

1 1.00 1.55 1.60 0.00 3.55 0.00 2.36 1.04

time (sec)

N/A 0.193 0.021 0.704 0.000 0.284 0.000 0.319 0.230

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 128 96 0 290 0 142 0

N.S.

1 1.00 1.52 1.14 0.00 3.45 0.00 1.69 0.00

time (sec)

N/A 0.404 0.420 0.670 0.000 0.285 0.000 0.376 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 118 168 133 0 412 0 217 0

N.S.

1 1.08 1.54 1.22 0.00 3.78 0.00 1.99 0.00

time (sec)

N/A 0.581 1.368 0.708 0.000 0.304 0.000 0.618 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 160 307 162 0 492 0 222 0

N.S.

1 1.10 2.10 1.11 0.00 3.37 0.00 1.52 0.00

time (sec)

N/A 0.841 2.737 0.793 0.000 0.319 0.000 0.579 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 199 178 193 0 314 0 197 0

N.S.

1 1.09 0.97 1.05 0.00 1.72 0.00 1.08 0.00

time (sec)

N/A 1.018 0.663 0.664 0.000 0.292 0.000 0.672 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 154 156 193 0 295 0 197 0

N.S.

1 1.06 1.08 1.33 0.00 2.03 0.00 1.36 0.00

time (sec)

N/A 0.741 0.474 0.663 0.000 0.281 0.000 0.788 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 109 134 147 0 274 0 172 0

N.S.

1 1.04 1.28 1.40 0.00 2.61 0.00 1.64 0.00

time (sec)

N/A 0.446 0.447 0.706 0.000 0.302 0.000 0.321 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 108 123 0 253 0 137 0

N.S.

1 1.00 1.40 1.60 0.00 3.29 0.00 1.78 0.00

time (sec)

N/A 0.297 0.269 0.606 0.000 0.310 0.000 0.329 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 108 125 0 252 0 133 0

N.S.

1 1.00 1.40 1.62 0.00 3.27 0.00 1.73 0.00

time (sec)

N/A 0.279 0.091 0.645 0.000 0.286 0.000 0.342 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 120 223 172 0 453 0 138 0

N.S.

1 1.05 1.96 1.51 0.00 3.97 0.00 1.21 0.00

time (sec)

N/A 0.588 0.943 0.741 0.000 0.293 0.000 0.376 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 152 449 219 0 539 0 260 0

N.S.

1 1.06 3.12 1.52 0.00 3.74 0.00 1.81 0.00

time (sec)

N/A 0.827 1.725 0.799 0.000 0.296 0.000 0.386 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 200 620 299 0 626 0 205 0

N.S.

1 1.08 3.33 1.61 0.00 3.37 0.00 1.10 0.00

time (sec)

N/A 1.109 4.628 0.878 0.000 0.345 0.000 0.588 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 247 221 323 0 381 0 241 0

N.S.

1 1.12 1.00 1.46 0.00 1.72 0.00 1.09 0.00

time (sec)

N/A 1.341 0.794 0.890 0.000 0.323 0.000 0.636 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 199 197 293 0 360 0 143 0

N.S.

1 1.09 1.08 1.60 0.00 1.97 0.00 0.78 0.00

time (sec)

N/A 1.006 0.679 0.763 0.000 0.290 0.000 0.590 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 155 173 243 0 341 0 191 0

N.S.

1 1.07 1.19 1.68 0.00 2.35 0.00 1.32 0.00

time (sec)

N/A 0.743 0.544 0.815 0.000 0.282 0.000 0.355 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 113 196 193 0 320 0 162 0

N.S.

1 1.06 1.83 1.80 0.00 2.99 0.00 1.51 0.00

time (sec)

N/A 0.451 0.433 0.769 0.000 0.291 0.000 0.363 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 112 196 193 0 318 0 81 0

N.S.

1 1.05 1.83 1.80 0.00 2.97 0.00 0.76 0.00

time (sec)

N/A 0.378 0.284 0.688 0.000 0.301 0.000 0.332 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 112 196 199 0 320 0 153 0

N.S.

1 1.05 1.83 1.86 0.00 2.99 0.00 1.43 0.00

time (sec)

N/A 0.358 0.095 0.692 0.000 0.303 0.000 0.318 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 156 296 262 0 539 0 163 0

N.S.

1 1.08 2.06 1.82 0.00 3.74 0.00 1.13 0.00

time (sec)

N/A 0.828 1.624 0.890 0.000 0.296 0.000 0.396 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 190 509 356 0 631 0 205 0

N.S.

1 1.09 2.93 2.05 0.00 3.63 0.00 1.18 0.00

time (sec)

N/A 1.091 3.371 1.023 0.000 0.284 0.000 0.611 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 242 680 404 0 715 0 298 0

N.S.

1 1.08 3.04 1.80 0.00 3.19 0.00 1.33 0.00

time (sec)

N/A 1.392 3.964 0.988 0.000 0.305 0.000 0.596 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 164 275 210 330 0 0 0

N.S.

1 1.00 4.43 7.43 5.68 8.92 0.00 0.00 0.00

time (sec)

N/A 0.226 0.729 5.816 0.309 0.386 0.000 0.000 0.000

Problem 86

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

38 38 119 236 0 341 0 95 0

N.S.

1 1.00 3.13 6.21 0.00 8.97 0.00 2.50 0.00

time (sec)

N/A 0.239 0.809 6.312 0.000 0.372 0.000 0.427 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 44 38 0 28 0 0 0

N.S.

1 1.00 2.59 2.24 0.00 1.65 0.00 0.00 0.00

time (sec)

N/A 0.189 0.394 2.248 0.000 0.258 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 47 40 0 163 0 0 0

N.S.

1 1.00 1.12 0.95 0.00 3.88 0.00 0.00 0.00

time (sec)

N/A 0.235 0.114 2.082 0.000 0.297 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 45 42 0 31 0 146 0

N.S.

1 1.00 1.45 1.35 0.00 1.00 0.00 4.71 0.00

time (sec)

N/A 0.205 0.287 1.994 0.000 0.256 0.000 0.751 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 48 43 0 168 0 149 0

N.S.

1 1.00 1.14 1.02 0.00 4.00 0.00 3.55 0.00

time (sec)

N/A 0.227 0.190 1.983 0.000 0.302 0.000 1.257 0.000

Problem 91

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

184 193 121 0 0 0 0 0 0

N.S.

1 1.05 0.66 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.636 0.297 0.000 0.000 0.000 0.000 0.000 0.000

Problem 92

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

161 180 160 0 0 0 0 0 0

N.S.

1 1.12 0.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.856 0.806 0.000 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 F F F F F F(-1)

verified

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

size

126 136 151 0 0 0 0 0 0

N.S.

1 1.08 1.20 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.556 0.858 0.000 0.000 0.000 0.000 0.000 0.000

Problem 94

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

96 96 138 0 0 0 0 0 0

N.S.

1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.361 0.311 0.000 0.000 0.000 0.000 0.000 0.000

Problem 95

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

66 66 124 0 0 0 0 0 0

N.S.

1 1.00 1.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.246 0.129 0.000 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 77 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.356 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 77 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.374 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 98

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

162 180 258 0 0 0 0 0 0

N.S.

1 1.11 1.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.903 1.622 0.000 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 F F F F F F(-1)

verified

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

size

127 138 250 0 0 0 0 0 0

N.S.

1 1.09 1.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.532 3.641 0.000 0.000 0.000 0.000 0.000 0.000

Problem 100

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

97 97 234 0 0 0 0 0 0

N.S.

1 1.00 2.41 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.371 2.098 0.000 0.000 0.000 0.000 0.000 0.000

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