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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 B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 111 84 194 58 0 80 83

N.S.

1 1.00 2.02 1.53 3.53 1.05 0.00 1.45 1.51

time (sec)

N/A 0.135 0.298 0.554 0.329 0.240 0.000 0.262 18.989

Problem 2

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

68 68 50 44 58 71 0 52 134

N.S.

1 1.00 0.74 0.65 0.85 1.04 0.00 0.76 1.97

time (sec)

N/A 0.085 0.163 0.439 0.236 0.250 0.000 0.265 19.047

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 62 50 94 38 0 49 51

N.S.

1 1.00 1.59 1.28 2.41 0.97 0.00 1.26 1.31

time (sec)

N/A 0.112 0.233 0.341 0.308 0.243 0.000 0.279 19.839

Problem 4

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

40 40 30 28 31 35 0 34 62

N.S.

1 1.00 0.75 0.70 0.78 0.88 0.00 0.85 1.55

time (sec)

N/A 0.063 0.067 0.351 0.207 0.248 0.000 0.264 18.909

Problem 5

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

9 9 9 17 9 9 0 9 25

N.S.

1 1.00 1.00 1.89 1.00 1.00 0.00 1.00 2.78

time (sec)

N/A 0.025 0.013 0.300 0.245 0.243 0.000 0.266 18.824

Problem 6

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 30 18 30 25 0 17 45

N.S.

1 1.00 2.00 1.20 2.00 1.67 0.00 1.13 3.00

time (sec)

N/A 0.049 0.170 0.410 0.341 0.264 0.000 0.285 18.869

Problem 7

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

16 16 11 13 18 19 0 14 36

N.S.

1 1.00 0.69 0.81 1.12 1.19 0.00 0.88 2.25

time (sec)

N/A 0.056 0.030 0.611 0.243 0.248 0.000 0.262 18.846

Problem 8

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

31 31 90 51 86 64 0 65 85

N.S.

1 1.00 2.90 1.65 2.77 2.06 0.00 2.10 2.74

time (sec)

N/A 0.084 0.161 0.843 0.347 0.263 0.000 0.271 18.975

Problem 9

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

36 36 26 25 29 45 0 29 80

N.S.

1 1.00 0.72 0.69 0.81 1.25 0.00 0.81 2.22

time (sec)

N/A 0.062 0.035 1.260 0.260 0.261 0.000 0.266 18.693

Problem 10

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

49 49 163 83 134 104 0 109 123

N.S.

1 1.00 3.33 1.69 2.73 2.12 0.00 2.22 2.51

time (sec)

N/A 0.102 0.166 1.701 0.334 0.263 0.000 0.274 19.086

Problem 11

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

58 58 39 41 42 70 0 41 113

N.S.

1 1.00 0.67 0.71 0.72 1.21 0.00 0.71 1.95

time (sec)

N/A 0.081 0.062 2.518 0.222 0.243 0.000 0.270 19.058

Problem 12

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

178 178 172 160 251 260 0 252 445

N.S.

1 1.00 0.97 0.90 1.41 1.46 0.00 1.42 2.50

time (sec)

N/A 0.356 0.872 1.192 0.232 0.373 0.000 0.278 22.462

Problem 13

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

113 113 115 101 120 144 0 139 172

N.S.

1 1.00 1.02 0.89 1.06 1.27 0.00 1.23 1.52

time (sec)

N/A 0.210 0.546 0.619 0.242 0.307 0.000 0.268 19.838

Problem 14

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

66 66 56 60 50 58 0 53 80

N.S.

1 1.00 0.85 0.91 0.76 0.88 0.00 0.80 1.21

time (sec)

N/A 0.109 0.072 0.430 0.251 0.270 0.000 0.273 19.249

Problem 15

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

19 19 11 21 11 11 0 12 55

N.S.

1 1.00 0.58 1.11 0.58 0.58 0.00 0.63 2.89

time (sec)

N/A 0.030 0.016 0.350 0.260 0.247 0.000 0.264 18.764

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 39 43 42 47 0 44 75

N.S.

1 1.00 1.03 1.13 1.11 1.24 0.00 1.16 1.97

time (sec)

N/A 0.080 0.058 0.921 0.252 0.275 0.000 0.268 19.080

Problem 17

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

72 72 85 86 84 151 0 90 157

N.S.

1 1.00 1.18 1.19 1.17 2.10 0.00 1.25 2.18

time (sec)

N/A 0.105 0.152 2.214 0.243 0.270 0.000 0.259 19.145

Problem 18

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

122 122 132 149 149 327 0 155 284

N.S.

1 1.00 1.08 1.22 1.22 2.68 0.00 1.27 2.33

time (sec)

N/A 0.147 0.315 4.687 0.226 0.303 0.000 0.275 19.374

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 205 194 190 0 483 0 216 4468

N.S.

1 1.29 1.22 1.19 0.00 3.04 0.00 1.36 28.10

time (sec)

N/A 0.390 1.305 0.826 0.000 0.297 0.000 0.283 27.542

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 112 87 106 0 296 0 103 2341

N.S.

1 1.33 1.04 1.26 0.00 3.52 0.00 1.23 27.87

time (sec)

N/A 0.206 0.384 0.470 0.000 0.290 0.000 0.281 20.923

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 71 75 0 206 0 80 697

N.S.

1 1.00 1.16 1.23 0.00 3.38 0.00 1.31 11.43

time (sec)

N/A 0.205 0.102 0.681 0.000 0.284 0.000 0.290 19.064

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 158 141 0 453 0 163 2163

N.S.

1 1.00 1.74 1.55 0.00 4.98 0.00 1.79 23.77

time (sec)

N/A 0.311 0.572 1.602 0.000 0.346 0.000 0.284 19.809

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 186 312 251 0 852 0 299 4075

N.S.

1 1.00 1.68 1.35 0.00 4.58 0.00 1.61 21.91

time (sec)

N/A 0.299 1.096 3.311 0.000 0.565 0.000 0.292 20.277

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