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Integrals 1 to 23

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 F(-2) A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 51 39 0 39 54 63 48

N.S.

1 1.00 0.65 0.50 0.00 0.50 0.69 0.81 0.62

time (sec)

N/A 0.087 0.192 0.108 0.000 0.261 0.112 0.254 12.564

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 46 32 0 32 48 69 49

N.S.

1 1.00 1.24 0.86 0.00 0.86 1.30 1.86 1.32

time (sec)

N/A 0.052 0.255 0.108 0.000 0.249 0.099 0.251 12.908

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 36 26 0 27 34 51 37

N.S.

1 1.00 0.72 0.52 0.00 0.54 0.68 1.02 0.74

time (sec)

N/A 0.065 0.112 0.123 0.000 0.260 0.080 0.256 12.320

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 27 19 0 20 26 37 31

N.S.

1 1.00 1.08 0.76 0.00 0.80 1.04 1.48 1.24

time (sec)

N/A 0.035 0.092 0.098 0.000 0.267 0.075 0.253 12.760

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 9 9 15 6 8 10 14

N.S.

1 1.00 0.64 0.64 1.07 0.43 0.57 0.71 1.00

time (sec)

N/A 0.022 0.026 0.104 0.234 0.268 0.198 0.256 12.484

Problem 6

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

9 9 12 9 7 11 7 15 11

N.S.

1 1.00 1.33 1.00 0.78 1.22 0.78 1.67 1.22

time (sec)

N/A 0.041 0.002 0.080 0.236 0.271 2.585 0.267 12.628

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 26 24 33 48 0 30 23

N.S.

1 1.00 2.17 2.00 2.75 4.00 0.00 2.50 1.92

time (sec)

N/A 0.044 0.183 0.081 0.215 0.262 0.000 0.252 12.732

Problem 8

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

15 15 15 12 12 16 0 12 9

N.S.

1 1.00 1.00 0.80 0.80 1.07 0.00 0.80 0.60

time (sec)

N/A 0.039 2.455 0.082 0.231 0.260 0.000 0.259 12.551

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 67 58 83 99 0 62 55

N.S.

1 1.00 2.39 2.07 2.96 3.54 0.00 2.21 1.96

time (sec)

N/A 0.052 0.263 0.105 0.240 0.276 0.000 0.261 12.746

Problem 10

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

33 33 23 21 24 36 0 24 25

N.S.

1 1.00 0.70 0.64 0.73 1.09 0.00 0.73 0.76

time (sec)

N/A 0.049 1.842 0.125 0.208 0.247 0.000 0.259 12.777

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 99 72 131 147 0 94 89

N.S.

1 1.00 2.48 1.80 3.28 3.68 0.00 2.35 2.22

time (sec)

N/A 0.062 0.325 0.156 0.217 0.294 0.000 0.264 12.471

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 85 106 106 248 0 151 110

N.S.

1 1.00 1.05 1.31 1.31 3.06 0.00 1.86 1.36

time (sec)

N/A 0.133 1.765 2.679 0.228 0.303 0.000 0.267 12.948

Problem 13

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

38 38 48 53 52 118 0 78 44

N.S.

1 1.00 1.26 1.39 1.37 3.11 0.00 2.05 1.16

time (sec)

N/A 0.084 1.228 0.629 0.224 0.281 0.000 0.253 12.121

Problem 14

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

12 12 20 13 12 45 0 22 16

N.S.

1 1.00 1.67 1.08 1.00 3.75 0.00 1.83 1.33

time (sec)

N/A 0.053 0.261 0.182 0.224 0.281 0.000 0.265 11.895

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 94 97 120 94 0 148 126

N.S.

1 1.00 1.31 1.35 1.67 1.31 0.00 2.06 1.75

time (sec)

N/A 0.159 0.334 0.644 0.315 0.294 0.000 0.264 12.050

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 151 170 244 184 0 273 263

N.S.

1 1.00 1.26 1.42 2.03 1.53 0.00 2.28 2.19

time (sec)

N/A 0.244 0.417 4.308 0.349 0.306 0.000 0.266 12.264

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 198 169 216 264 0 220 674

N.S.

1 1.00 1.96 1.67 2.14 2.61 0.00 2.18 6.67

time (sec)

N/A 0.213 1.649 1.461 0.315 0.384 0.000 0.280 12.384

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 67 81 107 135 0 108 170

N.S.

1 1.00 1.26 1.53 2.02 2.55 0.00 2.04 3.21

time (sec)

N/A 0.116 0.337 0.372 0.298 0.293 0.000 0.283 12.031

Problem 19

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

36 36 38 35 61 98 0 61 31

N.S.

1 1.00 1.06 0.97 1.69 2.72 0.00 1.69 0.86

time (sec)

N/A 0.036 0.041 0.163 0.317 0.275 0.000 0.281 11.911

Problem 20

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

66 66 62 84 106 146 0 94 94

N.S.

1 1.00 0.94 1.27 1.61 2.21 0.00 1.42 1.42

time (sec)

N/A 0.122 0.369 0.266 0.368 0.296 0.000 0.275 12.589

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 121 113 163 283 220 0 201 280

N.S.

1 1.00 0.93 1.35 2.34 1.82 0.00 1.66 2.31

time (sec)

N/A 0.216 0.808 1.795 0.353 0.287 0.000 0.274 12.845

Problem 22

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

12 12 17 13 12 39 0 13 14

N.S.

1 1.00 1.42 1.08 1.00 3.25 0.00 1.08 1.17

time (sec)

N/A 0.050 0.034 0.313 0.232 0.275 0.000 0.259 12.374

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 21 20 38 0 41 43

N.S.

1 1.00 1.00 1.05 1.00 1.90 0.00 2.05 2.15

time (sec)

N/A 0.049 0.227 3.423 0.225 0.290 0.000 0.275 12.695

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