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2.2 Detailed conclusion table per each integral for all CAS systems

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 and IntegrateAlgebraic to I.A.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

172 172 172 176 175 218 236 210 182 0

N.S.

1 1.00 1.00 1.02 1.02 1.27 1.37 1.22 1.06 0.00

time (sec)

N/A 0.192 0.087 0.000 0.668 1.101 0.101 0.308 0.102 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

130 130 130 135 134 165 173 161 143 0

N.S.

1 1.00 1.00 1.04 1.03 1.27 1.33 1.24 1.10 0.00

time (sec)

N/A 0.135 0.070 0.001 0.754 1.073 0.092 0.294 0.838 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

94 94 96 94 93 114 121 114 99 0

N.S.

1 1.00 1.02 1.00 0.99 1.21 1.29 1.21 1.05 0.00

time (sec)

N/A 0.083 0.037 0.001 0.566 1.172 0.082 0.281 0.047 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

56 56 56 53 52 62 63 66 54 0

N.S.

1 1.00 1.00 0.95 0.93 1.11 1.12 1.18 0.96 0.00

time (sec)

N/A 0.037 0.013 0.002 0.554 0.630 0.070 0.335 0.048 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A B A B F

verified

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

size

81 81 72 119 74 191 206 80 108 0

N.S.

1 1.00 0.89 1.47 0.91 2.36 2.54 0.99 1.33 0.00

time (sec)

N/A 0.080 0.054 0.006 1.237 1.423 0.618 0.310 0.115 0.001

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

108 108 95 163 101 318 190 95 95 0

N.S.

1 1.00 0.88 1.51 0.94 2.94 1.76 0.88 0.88 0.00

time (sec)

N/A 0.085 0.065 0.012 1.205 1.443 1.366 0.363 0.167 0.001

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A B A B F

verified

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

size

130 130 130 175 145 471 246 135 136 0

N.S.

1 1.00 1.00 1.35 1.12 3.62 1.89 1.04 1.05 0.00

time (sec)

N/A 0.108 0.083 0.010 1.431 1.341 3.133 0.458 0.968 0.001

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A B A A B F

verified

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

size

171 171 171 210 194 642 313 184 176 0

N.S.

1 1.00 1.00 1.23 1.13 3.75 1.83 1.08 1.03 0.00

time (sec)

N/A 0.163 0.104 0.010 1.570 1.467 6.658 0.343 0.177 0.001

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

226 226 226 237 236 289 304 283 233 0

N.S.

1 1.00 1.00 1.05 1.04 1.28 1.35 1.25 1.03 0.00

time (sec)

N/A 0.214 0.085 0.001 0.634 1.164 0.112 0.241 0.857 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

158 158 158 169 168 202 216 202 158 0

N.S.

1 1.00 1.00 1.07 1.06 1.28 1.37 1.28 1.00 0.00

time (sec)

N/A 0.167 0.064 0.001 0.614 0.871 0.099 0.357 0.069 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

94 94 96 101 100 114 121 120 99 0

N.S.

1 1.00 1.02 1.07 1.06 1.21 1.29 1.28 1.05 0.00

time (sec)

N/A 0.081 0.031 0.000 0.765 1.048 0.082 0.288 0.047 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A B A B F

verified

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

size

142 142 115 243 160 366 347 178 203 0

N.S.

1 1.00 0.81 1.71 1.13 2.58 2.44 1.25 1.43 0.00

time (sec)

N/A 0.208 0.071 0.006 1.351 1.195 1.038 0.294 0.857 0.001

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A B A B F

verified

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

size

164 164 134 299 186 552 483 195 257 0

N.S.

1 1.00 0.82 1.82 1.13 3.37 2.95 1.19 1.57 0.00

time (sec)

N/A 0.232 0.099 0.013 1.939 1.382 2.827 0.327 0.167 0.001

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A B A B F

verified

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

size

207 207 183 397 236 777 400 238 243 0

N.S.

1 1.00 0.88 1.92 1.14 3.75 1.93 1.15 1.17 0.00

time (sec)

N/A 0.239 0.130 0.013 2.012 1.426 11.984 0.449 0.976 0.001

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A B B A B F

verified

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

size

240 240 242 360 304 1024 486 311 303 0

N.S.

1 1.00 1.01 1.50 1.27 4.27 2.02 1.30 1.26 0.00

time (sec)

N/A 0.280 0.177 0.013 2.007 1.118 42.072 0.304 0.976 0.001

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

310 310 310 339 326 409 423 401 335 0

N.S.

1 1.00 1.00 1.09 1.05 1.32 1.36 1.29 1.08 0.00

time (sec)

N/A 0.387 0.130 0.003 0.859 1.209 0.126 0.376 0.116 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

226 226 226 244 239 289 304 289 233 0

N.S.

1 1.00 1.00 1.08 1.06 1.28 1.35 1.28 1.03 0.00

time (sec)

N/A 0.216 0.088 0.001 0.836 1.223 0.111 0.347 0.846 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B F

verified

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

size

130 130 130 149 146 165 173 173 143 0

N.S.

1 1.00 1.00 1.15 1.12 1.27 1.33 1.33 1.10 0.00

time (sec)

N/A 0.135 0.055 0.001 0.841 0.848 0.093 0.353 0.815 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A B A B F

verified

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

size

227 227 179 401 266 586 508 307 312 0

N.S.

1 1.00 0.79 1.77 1.17 2.58 2.24 1.35 1.37 0.00

time (sec)

N/A 0.371 0.108 0.007 2.029 1.004 1.492 0.494 0.849 0.001

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A B A B F

verified

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

size

242 242 176 475 296 834 661 321 389 0

N.S.

1 1.00 0.73 1.96 1.22 3.45 2.73 1.33 1.61 0.00

time (sec)

N/A 0.399 0.128 0.015 1.978 1.239 4.749 0.370 0.977 0.001

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A B A B F

verified

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

size

291 291 219 589 343 1102 865 371 495 0

N.S.

1 1.00 0.75 2.02 1.18 3.79 2.97 1.27 1.70 0.00

time (sec)

N/A 0.416 0.168 0.015 1.944 1.556 26.162 0.387 0.223 0.001

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

348 348 295 735 416 1422 0 447 444 0

N.S.

1 1.00 0.85 2.11 1.20 4.09 0.00 1.28 1.28 0.00

time (sec)

N/A 0.450 0.219 0.014 2.389 1.381 0.000 0.368 1.187 0.001

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

128 128 124 1942 0 777 0 0 -1 151

N.S.

1 1.00 0.97 15.17 0.00 6.07 0.00 0.00 -0.01 1.18

time (sec)

N/A 0.142 0.265 0.033 0.000 4.882 0.000 0.000 0.000 0.385

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

304 304 265 1541 0 1718 0 0 -1 266

N.S.

1 1.00 0.87 5.07 0.00 5.65 0.00 0.00 -0.00 0.88

time (sec)

N/A 0.299 0.366 0.038 0.000 20.972 0.000 0.000 0.000 0.669

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

166 166 150 1052 0 1111 0 0 -1 175

N.S.

1 1.00 0.90 6.34 0.00 6.69 0.00 0.00 -0.01 1.05

time (sec)

N/A 0.105 0.339 0.016 0.000 6.224 0.000 0.000 0.000 0.355

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

91 91 88 646 0 737 0 0 -1 114

N.S.

1 1.00 0.97 7.10 0.00 8.10 0.00 0.00 -0.01 1.25

time (sec)

N/A 0.048 0.116 0.011 0.000 4.140 0.000 0.000 0.000 0.245

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F B F A F B

verified

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

size

49 49 49 306 0 241 0 74 -1 103

N.S.

1 1.00 1.00 6.24 0.00 4.92 0.00 1.51 -0.02 2.10

time (sec)

N/A 0.020 0.011 0.011 0.000 1.559 0.000 0.363 0.000 0.110

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

122 122 113 782 0 0 0 173 -1 239

N.S.

1 1.00 0.93 6.41 0.00 0.00 0.00 1.42 -0.01 1.96

time (sec)

N/A 0.111 0.210 0.031 0.000 0.000 0.000 0.524 0.000 0.427

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

203 203 531 1865 0 0 0 479 -1 2522

N.S.

1 1.00 2.62 9.19 0.00 0.00 0.00 2.36 -0.00 12.42

time (sec)

N/A 0.265 2.639 0.036 0.000 0.000 0.000 26.049 0.000 6.798

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F B F B F A

verified

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

size

113 113 191 1622 0 513 0 336 -1 146

N.S.

1 1.00 1.69 14.35 0.00 4.54 0.00 2.97 -0.01 1.29

time (sec)

N/A 0.119 0.808 0.029 0.000 5.765 0.000 3.395 0.000 0.623

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