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
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 176 | 112 | 194 | 170 | 293 | 230 | 127 | 288 | 0 |
N.S. |
1 | 1.28 | 0.81 | 1.41 | 1.23 | 2.12 | 1.67 | 0.92 | 2.09 | 0.00 |
time (sec) |
N/A | 0.538 | 0.792 | 0.740 | 0.034 | 0.092 | 7.390 | 0.129 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 137 | 90 | 151 | 130 | 253 | 185 | 100 | 251 | 0 |
N.S. |
1 | 1.27 | 0.83 | 1.40 | 1.20 | 2.34 | 1.71 | 0.93 | 2.32 | 0.00 |
time (sec) |
N/A | 0.407 | 0.550 | 0.553 | 0.028 | 0.093 | 6.999 | 0.129 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 90 | 75 | 104 | 94 | 210 | 131 | 88 | 159 | 91 |
N.S. |
1 | 1.06 | 0.88 | 1.22 | 1.11 | 2.47 | 1.54 | 1.04 | 1.87 | 1.07 |
time (sec) |
N/A | 0.263 | 0.475 | 0.539 | 0.033 | 0.090 | 4.942 | 0.127 | 0.157 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 99 | 100 | 114 | 93 | 602 | 274 | 0 | 280 | 102 |
N.S. |
1 | 1.11 | 1.12 | 1.28 | 1.04 | 6.76 | 3.08 | 0.00 | 3.15 | 1.15 |
time (sec) |
N/A | 0.350 | 0.644 | 0.526 | 0.032 | 0.110 | 8.458 | 0.000 | 0.159 | 2.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 93 | 112 | 98 | 220 | 282 | 125 | 256 | 103 |
N.S. |
1 | 1.05 | 1.06 | 1.27 | 1.11 | 2.50 | 3.20 | 1.42 | 2.91 | 1.17 |
time (sec) |
N/A | 0.303 | 0.511 | 0.526 | 0.033 | 0.090 | 8.497 | 0.136 | 0.160 | 2.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 124 | 99 | 165 | 136 | 281 | 332 | 198 | 417 | 143 |
N.S. |
1 | 1.10 | 0.88 | 1.46 | 1.20 | 2.49 | 2.94 | 1.75 | 3.69 | 1.27 |
time (sec) |
N/A | 0.447 | 0.734 | 0.539 | 0.034 | 0.093 | 7.867 | 0.132 | 0.163 | 2.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 165 | 130 | 210 | 177 | 321 | 547 | 296 | 450 | 167 |
N.S. |
1 | 1.10 | 0.87 | 1.40 | 1.18 | 2.14 | 3.65 | 1.97 | 3.00 | 1.11 |
time (sec) |
N/A | 0.654 | 0.789 | 0.628 | 0.032 | 0.094 | 16.003 | 0.152 | 0.162 | 3.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 189 | 137 | 258 | 221 | 384 | 466 | 521 | 481 | 213 |
N.S. |
1 | 1.07 | 0.78 | 1.47 | 1.26 | 2.18 | 2.65 | 2.96 | 2.73 | 1.21 |
time (sec) |
N/A | 0.849 | 1.088 | 0.585 | 0.034 | 0.105 | 13.381 | 0.147 | 0.175 | 3.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 230 | 145 | 286 | 290 | 455 | 1003 | 204 | 437 | 0 |
N.S. |
1 | 1.24 | 0.78 | 1.54 | 1.56 | 2.45 | 5.39 | 1.10 | 2.35 | 0.00 |
time (sec) |
N/A | 0.681 | 1.096 | 0.624 | 0.036 | 0.111 | 14.922 | 0.136 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 195 | 123 | 239 | 248 | 417 | 911 | 174 | 400 | 0 |
N.S. |
1 | 1.29 | 0.81 | 1.58 | 1.64 | 2.76 | 6.03 | 1.15 | 2.65 | 0.00 |
time (sec) |
N/A | 0.593 | 0.891 | 0.599 | 0.036 | 0.099 | 14.291 | 0.136 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 150 | 118 | 210 | 191 | 334 | 588 | 134 | 262 | 0 |
N.S. |
1 | 1.16 | 0.91 | 1.63 | 1.48 | 2.59 | 4.56 | 1.04 | 2.03 | 0.00 |
time (sec) |
N/A | 0.503 | 0.805 | 0.681 | 0.044 | 0.095 | 11.110 | 0.135 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 120 | 91 | 167 | 152 | 291 | 496 | 101 | 245 | 0 |
N.S. |
1 | 1.20 | 0.91 | 1.67 | 1.52 | 2.91 | 4.96 | 1.01 | 2.45 | 0.00 |
time (sec) |
N/A | 0.383 | 0.848 | 0.599 | 0.038 | 0.095 | 10.414 | 0.133 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 66 | 68 | 117 | 91 | 289 | 72 | 176 | 89 |
N.S. |
1 | 1.00 | 0.78 | 0.80 | 1.38 | 1.07 | 3.40 | 0.85 | 2.07 | 1.05 |
time (sec) |
N/A | 0.246 | 0.635 | 0.532 | 0.031 | 0.081 | 8.956 | 0.131 | 0.149 | 2.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 108 | 96 | 168 | 130 | 296 | 937 | 113 | 380 | 0 |
N.S. |
1 | 1.06 | 0.94 | 1.65 | 1.27 | 2.90 | 9.19 | 1.11 | 3.73 | 0.00 |
time (sec) |
N/A | 0.333 | 0.854 | 0.526 | 0.034 | 0.098 | 18.481 | 0.134 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 137 | 131 | 170 | 147 | 342 | 1057 | 168 | 429 | 166 |
N.S. |
1 | 0.96 | 0.92 | 1.20 | 1.04 | 2.41 | 7.44 | 1.18 | 3.02 | 1.17 |
time (sec) |
N/A | 0.458 | 0.924 | 0.548 | 0.036 | 0.100 | 16.107 | 0.138 | 0.160 | 2.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 178 | 133 | 242 | 201 | 440 | 1875 | 271 | 675 | 224 |
N.S. |
1 | 1.14 | 0.85 | 1.55 | 1.29 | 2.82 | 12.02 | 1.74 | 4.33 | 1.44 |
time (sec) |
N/A | 0.634 | 1.030 | 0.541 | 0.037 | 0.109 | 28.330 | 0.137 | 0.191 | 3.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 62 | 59 | 83 | 66 | 133 | 100 | 64 | 0 |
N.S. |
1 | 1.00 | 0.58 | 0.55 | 0.78 | 0.62 | 1.24 | 0.93 | 0.60 | 0.00 |
time (sec) |
N/A | 0.306 | 0.102 | 0.389 | 0.040 | 0.067 | 0.299 | 0.123 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 65 | 56 | 83 | 58 | 133 | 95 | 61 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.52 | 0.78 | 0.54 | 1.24 | 0.89 | 0.57 | 0.00 |
time (sec) |
N/A | 0.291 | 0.090 | 0.510 | 0.027 | 0.066 | 0.268 | 0.121 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 65 | 61 | 83 | 58 | 131 | 97 | 63 | 0 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 0.79 | 0.55 | 1.25 | 0.92 | 0.60 | 0.00 |
time (sec) |
N/A | 0.278 | 0.102 | 0.283 | 0.038 | 0.069 | 0.320 | 0.122 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 64 | 61 | 86 | 61 | 129 | 119 | 65 | 0 |
N.S. |
1 | 1.00 | 0.62 | 0.59 | 0.83 | 0.59 | 1.25 | 1.16 | 0.63 | 0.00 |
time (sec) |
N/A | 0.285 | 0.110 | 0.128 | 0.035 | 0.071 | 0.408 | 0.128 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 61 | 61 | 86 | 61 | 128 | 116 | 68 | 0 |
N.S. |
1 | 1.00 | 0.59 | 0.59 | 0.83 | 0.59 | 1.24 | 1.13 | 0.66 | 0.00 |
time (sec) |
N/A | 0.286 | 0.105 | 0.127 | 0.031 | 0.070 | 0.331 | 0.123 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 475 | 248 | 405 | 477 | 3486 | 1285 | 595 | 639 | 0 |
N.S. |
1 | 1.30 | 0.68 | 1.11 | 1.30 | 9.52 | 3.51 | 1.63 | 1.75 | 0.00 |
time (sec) |
N/A | 1.179 | 0.591 | 3.432 | 0.132 | 0.232 | 28.345 | 0.134 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 449 | 230 | 384 | 422 | 3365 | 1222 | 544 | 610 | 0 |
N.S. |
1 | 1.32 | 0.68 | 1.13 | 1.24 | 9.90 | 3.59 | 1.60 | 1.79 | 0.00 |
time (sec) |
N/A | 1.035 | 0.492 | 0.770 | 0.124 | 0.229 | 22.327 | 0.138 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 426 | 217 | 365 | 427 | 3318 | 1164 | 524 | 590 | 0 |
N.S. |
1 | 1.34 | 0.68 | 1.15 | 1.34 | 10.43 | 3.66 | 1.65 | 1.86 | 0.00 |
time (sec) |
N/A | 0.914 | 0.401 | 0.764 | 0.133 | 0.218 | 24.677 | 0.141 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 404 | 204 | 323 | 380 | 3363 | 0 | 487 | 577 | 0 |
N.S. |
1 | 1.37 | 0.69 | 1.10 | 1.29 | 11.44 | 0.00 | 1.66 | 1.96 | 0.00 |
time (sec) |
N/A | 0.797 | 0.415 | 0.748 | 0.123 | 0.338 | 0.000 | 0.135 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 428 | 205 | 335 | 405 | 3429 | 0 | 483 | 606 | 0 |
N.S. |
1 | 1.46 | 0.70 | 1.14 | 1.38 | 11.70 | 0.00 | 1.65 | 2.07 | 0.00 |
time (sec) |
N/A | 0.913 | 0.396 | 0.637 | 0.119 | 0.480 | 0.000 | 0.144 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 458 | 204 | 332 | 379 | 3409 | 0 | 475 | 630 | 0 |
N.S. |
1 | 1.55 | 0.69 | 1.13 | 1.28 | 11.56 | 0.00 | 1.61 | 2.14 | 0.00 |
time (sec) |
N/A | 1.020 | 0.386 | 0.658 | 0.116 | 0.361 | 0.000 | 0.135 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 485 | 220 | 362 | 426 | 3386 | 0 | 506 | 679 | 0 |
N.S. |
1 | 1.51 | 0.69 | 1.13 | 1.33 | 10.55 | 0.00 | 1.58 | 2.12 | 0.00 |
time (sec) |
N/A | 1.111 | 0.444 | 0.718 | 0.125 | 0.502 | 0.000 | 0.141 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 504 | 260 | 402 | 501 | 3697 | 4189 | 617 | 1244 | 0 |
N.S. |
1 | 1.24 | 0.64 | 0.99 | 1.24 | 9.13 | 10.34 | 1.52 | 3.07 | 0.00 |
time (sec) |
N/A | 1.237 | 1.281 | 0.812 | 0.116 | 0.276 | 107.111 | 0.141 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 474 | 241 | 381 | 448 | 3694 | 4012 | 568 | 1227 | 0 |
N.S. |
1 | 1.27 | 0.64 | 1.02 | 1.20 | 9.88 | 10.73 | 1.52 | 3.28 | 0.00 |
time (sec) |
N/A | 1.127 | 1.263 | 0.763 | 0.138 | 0.271 | 83.209 | 0.145 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 448 | 234 | 380 | 468 | 3584 | 3900 | 550 | 1208 | 0 |
N.S. |
1 | 1.31 | 0.68 | 1.11 | 1.37 | 10.48 | 11.40 | 1.61 | 3.53 | 0.00 |
time (sec) |
N/A | 0.985 | 1.250 | 0.733 | 0.130 | 0.259 | 70.348 | 0.141 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 378 | 223 | 362 | 414 | 3500 | 4184 | 517 | 1201 | 0 |
N.S. |
1 | 1.11 | 0.66 | 1.06 | 1.22 | 10.29 | 12.31 | 1.52 | 3.53 | 0.00 |
time (sec) |
N/A | 0.759 | 1.128 | 0.695 | 0.122 | 0.397 | 75.227 | 0.147 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 413 | 238 | 389 | 454 | 3700 | 4014 | 543 | 1273 | 0 |
N.S. |
1 | 1.18 | 0.68 | 1.11 | 1.30 | 10.57 | 11.47 | 1.55 | 3.64 | 0.00 |
time (sec) |
N/A | 0.831 | 1.423 | 0.736 | 0.134 | 0.514 | 82.537 | 0.137 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 446 | 243 | 388 | 437 | 3722 | 4048 | 546 | 1309 | 0 |
N.S. |
1 | 1.16 | 0.63 | 1.01 | 1.14 | 9.69 | 10.54 | 1.42 | 3.41 | 0.00 |
time (sec) |
N/A | 0.903 | 1.357 | 0.862 | 0.117 | 0.425 | 106.932 | 0.144 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 481 | 267 | 421 | 499 | 3715 | 4245 | 585 | 1360 | 0 |
N.S. |
1 | 1.17 | 0.65 | 1.02 | 1.21 | 9.04 | 10.33 | 1.42 | 3.31 | 0.00 |
time (sec) |
N/A | 0.966 | 1.356 | 0.773 | 0.133 | 0.606 | 135.629 | 0.142 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 127 | 180 | 230 | 829 | 6390 | 1558 | 1061 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.99 | 1.27 | 4.58 | 35.30 | 8.61 | 5.86 | 0.00 |
time (sec) |
N/A | 0.427 | 1.663 | 0.538 | 0.057 | 0.088 | 1.035 | 0.146 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 79 | 118 | 138 | 339 | 2504 | 692 | 453 | 0 |
N.S. |
1 | 1.00 | 0.66 | 0.99 | 1.16 | 2.85 | 21.04 | 5.82 | 3.81 | 0.00 |
time (sec) |
N/A | 0.350 | 0.457 | 0.079 | 0.050 | 0.086 | 0.607 | 0.130 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 43 | 68 | 66 | 117 | 604 | 214 | 129 | 0 |
N.S. |
1 | 1.00 | 0.62 | 0.99 | 0.96 | 1.70 | 8.75 | 3.10 | 1.87 | 0.00 |
time (sec) |
N/A | 0.243 | 0.124 | 0.071 | 0.037 | 0.077 | 0.481 | 0.122 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 112 | 0 | 0 | 0 | 379 | 0 | 401 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 2.51 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.385 | 0.963 | 0.000 | 0.000 | 0.000 | 3.968 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 174 | 160 | 0 | 0 | 0 | 1828 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.85 | 0.00 | 0.00 | 0.00 | 9.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.391 | 1.474 | 0.000 | 0.000 | 0.000 | 45.927 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 176 | 160 | 0 | 0 | 0 | 5258 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.82 | 0.00 | 0.00 | 0.00 | 27.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 1.705 | 0.000 | 0.000 | 0.000 | 127.581 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 253 | 177 | 0 | 0 | 0 | 468 | 0 | 162 | 0 |
N.S. |
1 | 1.06 | 0.74 | 0.00 | 0.00 | 0.00 | 1.96 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.642 | 2.118 | 0.000 | 0.000 | 0.000 | 10.288 | 0.000 | 1.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 251 | 176 | 0 | 0 | 0 | 230 | 0 | 76 | 0 |
N.S. |
1 | 1.10 | 0.77 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.609 | 0.934 | 0.000 | 0.000 | 0.000 | 3.765 | 0.000 | 0.419 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 243 | 176 | 0 | 0 | 0 | 223 | 0 | 84 | 0 |
N.S. |
1 | 1.06 | 0.77 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.614 | 0.913 | 0.000 | 0.000 | 0.000 | 3.162 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 217 | 179 | 0 | 0 | 0 | 223 | 0 | 148 | 0 |
N.S. |
1 | 0.95 | 0.79 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.429 | 2.326 | 0.000 | 0.000 | 0.000 | 11.762 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 232 | 179 | 0 | 0 | 0 | 223 | 0 | 224 | 0 |
N.S. |
1 | 0.92 | 0.71 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.469 | 4.064 | 0.000 | 0.000 | 0.000 | 156.205 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 232 | 179 | 0 | 0 | 0 | 0 | 0 | 300 | 0 |
N.S. |
1 | 0.92 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.454 | 5.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.728 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 52 | 51 | 51 | 56 | 57 | 54 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.84 | 0.84 | 0.92 | 0.93 | 0.89 | 0.93 |
time (sec) |
N/A | 0.280 | 0.019 | 0.143 | 0.026 | 0.062 | 0.026 | 0.122 | 0.156 | 2.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 52 | 51 | 51 | 56 | 57 | 54 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.84 | 0.84 | 0.92 | 0.93 | 0.89 | 0.93 |
time (sec) |
N/A | 0.280 | 0.014 | 0.095 | 0.026 | 0.067 | 0.022 | 0.130 | 0.154 | 2.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 56 | 49 | 48 | 48 | 53 | 54 | 52 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.86 | 0.86 | 0.95 | 0.96 | 0.93 | 0.96 |
time (sec) |
N/A | 0.241 | 0.012 | 0.094 | 0.045 | 0.062 | 0.022 | 0.125 | 0.178 | 2.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 52 | 48 | 53 | 48 | 51 | 54 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.89 | 0.98 | 0.89 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.256 | 0.024 | 0.053 | 0.033 | 0.067 | 0.069 | 0.122 | 0.163 | 2.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 55 | 50 | 50 | 53 | 53 | 53 | 54 | 51 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 0.93 | 0.98 | 0.98 | 0.98 | 1.00 | 0.94 |
time (sec) |
N/A | 0.263 | 0.025 | 0.067 | 0.025 | 0.062 | 0.125 | 0.124 | 0.156 | 2.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 53 | 48 | 51 | 53 | 56 | 54 | 54 | 51 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.94 | 0.98 | 1.04 | 1.00 | 1.00 | 0.94 |
time (sec) |
N/A | 0.251 | 0.030 | 0.069 | 0.026 | 0.062 | 0.421 | 0.122 | 0.184 | 2.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 101 | 94 | 93 | 93 | 107 | 105 | 89 | 108 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.92 | 0.92 | 1.06 | 1.04 | 0.88 | 1.07 |
time (sec) |
N/A | 0.340 | 0.025 | 0.413 | 0.026 | 0.063 | 0.034 | 0.116 | 0.156 | 2.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 101 | 94 | 93 | 93 | 107 | 105 | 89 | 108 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.92 | 0.92 | 1.06 | 1.04 | 0.88 | 1.07 |
time (sec) |
N/A | 0.337 | 0.022 | 0.388 | 0.025 | 0.067 | 0.029 | 0.120 | 0.157 | 2.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 96 | 91 | 90 | 90 | 104 | 102 | 87 | 106 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.94 | 0.94 | 1.08 | 1.06 | 0.91 | 1.10 |
time (sec) |
N/A | 0.286 | 0.019 | 0.398 | 0.031 | 0.064 | 0.032 | 0.122 | 0.160 | 1.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 94 | 96 | 90 | 95 | 99 | 100 | 89 | 105 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.96 | 1.01 | 1.05 | 1.06 | 0.95 | 1.12 |
time (sec) |
N/A | 0.302 | 0.031 | 0.401 | 0.035 | 0.064 | 0.103 | 0.115 | 0.155 | 1.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 93 | 95 | 92 | 95 | 100 | 99 | 89 | 103 |
N.S. |
1 | 1.00 | 0.99 | 1.01 | 0.98 | 1.01 | 1.06 | 1.05 | 0.95 | 1.10 |
time (sec) |
N/A | 0.318 | 0.032 | 0.394 | 0.028 | 0.068 | 0.186 | 0.123 | 0.157 | 1.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 93 | 90 | 93 | 95 | 102 | 100 | 89 | 103 |
N.S. |
1 | 1.00 | 0.99 | 0.96 | 0.99 | 1.01 | 1.09 | 1.06 | 0.95 | 1.10 |
time (sec) |
N/A | 0.328 | 0.021 | 0.384 | 0.026 | 0.066 | 0.652 | 0.123 | 0.158 | 1.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 210 | 233 | 212 | 452 | 384 | 243 | 175 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.01 | 2.15 | 1.83 | 1.16 | 0.83 | 0.00 |
time (sec) |
N/A | 0.454 | 0.159 | 0.569 | 0.107 | 0.080 | 0.540 | 0.129 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 162 | 185 | 173 | 368 | 337 | 196 | 151 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.08 | 1.01 | 2.14 | 1.96 | 1.14 | 0.88 | 0.00 |
time (sec) |
N/A | 0.390 | 0.122 | 0.465 | 0.106 | 0.080 | 0.489 | 0.121 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 135 | 137 | 132 | 286 | 185 | 147 | 127 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.01 | 0.97 | 2.10 | 1.36 | 1.08 | 0.93 | 0.00 |
time (sec) |
N/A | 0.346 | 0.105 | 0.463 | 0.111 | 0.080 | 0.457 | 0.123 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 98 | 94 | 95 | 236 | 160 | 104 | 99 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.94 | 0.95 | 2.36 | 1.60 | 1.04 | 0.99 | 0.00 |
time (sec) |
N/A | 0.283 | 0.081 | 0.468 | 0.124 | 0.080 | 0.414 | 0.116 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 83 | 78 | 79 | 211 | 150 | 83 | 81 | 97 |
N.S. |
1 | 1.00 | 0.99 | 0.93 | 0.94 | 2.51 | 1.79 | 0.99 | 0.96 | 1.15 |
time (sec) |
N/A | 0.310 | 0.084 | 0.480 | 0.121 | 0.083 | 0.547 | 0.125 | 0.151 | 1.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 83 | 79 | 79 | 216 | 151 | 80 | 72 | 107 |
N.S. |
1 | 1.00 | 1.01 | 0.96 | 0.96 | 2.63 | 1.84 | 0.98 | 0.88 | 1.30 |
time (sec) |
N/A | 0.316 | 0.082 | 0.480 | 0.114 | 0.078 | 1.036 | 0.124 | 0.151 | 1.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 103 | 94 | 96 | 246 | 167 | 102 | 72 | 135 |
N.S. |
1 | 1.00 | 0.98 | 0.90 | 0.91 | 2.34 | 1.59 | 0.97 | 0.69 | 1.29 |
time (sec) |
N/A | 0.352 | 0.093 | 1.888 | 0.111 | 0.079 | 2.520 | 0.127 | 0.152 | 1.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 139 | 128 | 135 | 292 | 301 | 149 | 86 | 177 |
N.S. |
1 | 1.00 | 1.01 | 0.93 | 0.98 | 2.12 | 2.18 | 1.08 | 0.62 | 1.28 |
time (sec) |
N/A | 0.376 | 0.129 | 0.576 | 0.108 | 0.078 | 7.714 | 0.129 | 0.154 | 1.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 174 | 165 | 174 | 374 | 354 | 196 | 111 | 213 |
N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.99 | 2.12 | 2.01 | 1.11 | 0.63 | 1.21 |
time (sec) |
N/A | 0.419 | 0.181 | 0.468 | 0.110 | 0.081 | 12.171 | 0.130 | 0.155 | 1.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 211 | 199 | 215 | 458 | 398 | 245 | 137 | 249 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.01 | 2.16 | 1.88 | 1.16 | 0.65 | 1.17 |
time (sec) |
N/A | 0.495 | 0.191 | 0.477 | 0.112 | 0.084 | 26.169 | 0.124 | 0.155 | 1.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 249 | 227 | 230 | 229 | 572 | 444 | 246 | 318 | 0 |
N.S. |
1 | 1.09 | 0.99 | 1.00 | 1.00 | 2.50 | 1.94 | 1.07 | 1.39 | 0.00 |
time (sec) |
N/A | 0.623 | 0.136 | 0.789 | 0.113 | 0.081 | 1.075 | 0.117 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 209 | 187 | 180 | 0 | 478 | 257 | 196 | 347 | 0 |
N.S. |
1 | 1.11 | 0.99 | 0.96 | 0.00 | 2.54 | 1.37 | 1.04 | 1.85 | 0.00 |
time (sec) |
N/A | 0.534 | 0.107 | 0.586 | 0.000 | 0.081 | 1.141 | 0.129 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 171 | 148 | 137 | 0 | 424 | 221 | 149 | 314 | 0 |
N.S. |
1 | 1.15 | 0.99 | 0.92 | 0.00 | 2.85 | 1.48 | 1.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.506 | 0.082 | 0.574 | 0.000 | 0.085 | 1.014 | 0.124 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 127 | 122 | 112 | 0 | 364 | 201 | 123 | 283 | 0 |
N.S. |
1 | 1.02 | 0.98 | 0.90 | 0.00 | 2.94 | 1.62 | 0.99 | 2.28 | 0.00 |
time (sec) |
N/A | 0.390 | 0.078 | 0.469 | 0.000 | 0.080 | 0.777 | 0.121 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 119 | 115 | 107 | 0 | 353 | 197 | 119 | 279 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.93 | 0.00 | 3.07 | 1.71 | 1.03 | 2.43 | 0.00 |
time (sec) |
N/A | 0.417 | 0.062 | 0.474 | 0.000 | 0.082 | 2.225 | 0.121 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 126 | 125 | 116 | 0 | 378 | 212 | 120 | 305 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.93 | 0.00 | 3.02 | 1.70 | 0.96 | 2.44 | 0.00 |
time (sec) |
N/A | 0.412 | 0.067 | 0.481 | 0.000 | 0.084 | 4.808 | 0.124 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 156 | 151 | 139 | 0 | 432 | 226 | 147 | 335 | 203 |
N.S. |
1 | 1.03 | 1.00 | 0.92 | 0.00 | 2.86 | 1.50 | 0.97 | 2.22 | 1.34 |
time (sec) |
N/A | 0.620 | 0.091 | 0.583 | 0.000 | 0.083 | 11.951 | 0.126 | 0.147 | 1.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 195 | 190 | 173 | 0 | 488 | 394 | 197 | 367 | 241 |
N.S. |
1 | 1.03 | 1.01 | 0.92 | 0.00 | 2.58 | 2.08 | 1.04 | 1.94 | 1.28 |
time (sec) |
N/A | 0.719 | 0.117 | 0.488 | 0.000 | 0.085 | 31.079 | 0.124 | 0.152 | 1.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 240 | 230 | 212 | 238 | 582 | 449 | 247 | 305 | 0 |
N.S. |
1 | 1.03 | 0.98 | 0.91 | 1.02 | 2.49 | 1.92 | 1.06 | 1.30 | 0.00 |
time (sec) |
N/A | 0.921 | 0.143 | 0.483 | 0.117 | 0.083 | 57.082 | 0.122 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 303 | 272 | 267 | 283 | 762 | 503 | 294 | 447 | 0 |
N.S. |
1 | 1.09 | 0.98 | 0.96 | 1.02 | 2.75 | 1.82 | 1.06 | 1.61 | 0.00 |
time (sec) |
N/A | 0.953 | 0.188 | 0.566 | 0.119 | 0.085 | 6.716 | 0.125 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 262 | 232 | 219 | 239 | 668 | 316 | 244 | 410 | 0 |
N.S. |
1 | 1.11 | 0.99 | 0.93 | 1.02 | 2.84 | 1.34 | 1.04 | 1.74 | 0.00 |
time (sec) |
N/A | 0.914 | 0.149 | 0.487 | 0.114 | 0.086 | 6.967 | 0.121 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 219 | 176 | 176 | 194 | 614 | 280 | 195 | 370 | 0 |
N.S. |
1 | 1.12 | 0.90 | 0.90 | 0.99 | 3.15 | 1.44 | 1.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.736 | 0.171 | 0.460 | 0.110 | 0.081 | 6.458 | 0.119 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 174 | 156 | 148 | 170 | 556 | 260 | 169 | 347 | 0 |
N.S. |
1 | 1.04 | 0.93 | 0.89 | 1.02 | 3.33 | 1.56 | 1.01 | 2.08 | 0.00 |
time (sec) |
N/A | 0.569 | 0.141 | 0.452 | 0.113 | 0.081 | 5.332 | 0.121 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 160 | 141 | 137 | 155 | 511 | 243 | 147 | 327 | 0 |
N.S. |
1 | 1.09 | 0.96 | 0.93 | 1.05 | 3.48 | 1.65 | 1.00 | 2.22 | 0.00 |
time (sec) |
N/A | 0.419 | 0.121 | 0.463 | 0.107 | 0.086 | 3.401 | 0.122 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 170 | 152 | 142 | 160 | 512 | 250 | 149 | 332 | 0 |
N.S. |
1 | 1.09 | 0.97 | 0.91 | 1.03 | 3.28 | 1.60 | 0.96 | 2.13 | 0.00 |
time (sec) |
N/A | 0.465 | 0.238 | 0.460 | 0.114 | 0.084 | 8.702 | 0.123 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 190 | 169 | 153 | 182 | 569 | 270 | 166 | 352 | 0 |
N.S. |
1 | 1.08 | 0.96 | 0.87 | 1.03 | 3.23 | 1.53 | 0.94 | 2.00 | 0.00 |
time (sec) |
N/A | 0.568 | 0.155 | 0.483 | 0.113 | 0.088 | 22.480 | 0.126 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 214 | 196 | 177 | 202 | 628 | 284 | 194 | 371 | 272 |
N.S. |
1 | 1.07 | 0.98 | 0.88 | 1.01 | 3.14 | 1.42 | 0.97 | 1.86 | 1.36 |
time (sec) |
N/A | 0.985 | 0.127 | 0.454 | 0.117 | 0.084 | 52.947 | 0.124 | 0.155 | 1.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 252 | 234 | 211 | 247 | 678 | 450 | 245 | 394 | 313 |
N.S. |
1 | 1.06 | 0.98 | 0.89 | 1.04 | 2.85 | 1.89 | 1.03 | 1.66 | 1.32 |
time (sec) |
N/A | 1.161 | 0.157 | 0.467 | 0.116 | 0.089 | 119.809 | 0.131 | 0.152 | 1.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 296 | 276 | 250 | 291 | 772 | 0 | 295 | 434 | 0 |
N.S. |
1 | 1.05 | 0.98 | 0.89 | 1.03 | 2.74 | 0.00 | 1.05 | 1.54 | 0.00 |
time (sec) |
N/A | 1.408 | 0.183 | 0.470 | 0.111 | 0.084 | 0.000 | 0.122 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 216 | 194 | 169 | 331 | 412 | 279 | 215 | 304 | 0 |
N.S. |
1 | 0.88 | 0.79 | 0.69 | 1.35 | 1.68 | 1.14 | 0.88 | 1.24 | 0.00 |
time (sec) |
N/A | 0.471 | 1.436 | 0.592 | 0.038 | 0.151 | 0.602 | 0.137 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 187 | 153 | 135 | 246 | 327 | 216 | 167 | 245 | 0 |
N.S. |
1 | 0.98 | 0.80 | 0.71 | 1.29 | 1.71 | 1.13 | 0.87 | 1.28 | 0.00 |
time (sec) |
N/A | 0.371 | 0.368 | 0.632 | 0.035 | 0.108 | 0.453 | 0.143 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 167 | 138 | 118 | 182 | 268 | 340 | 153 | 230 | 0 |
N.S. |
1 | 0.98 | 0.81 | 0.69 | 1.07 | 1.58 | 2.00 | 0.90 | 1.35 | 0.00 |
time (sec) |
N/A | 0.404 | 0.702 | 0.587 | 0.035 | 0.096 | 1.553 | 0.139 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 137 | 117 | 110 | 128 | 257 | 269 | 201 | 198 | 0 |
N.S. |
1 | 0.96 | 0.82 | 0.77 | 0.90 | 1.80 | 1.88 | 1.41 | 1.38 | 0.00 |
time (sec) |
N/A | 0.369 | 0.482 | 0.558 | 0.039 | 0.093 | 1.728 | 0.146 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 143 | 112 | 110 | 114 | 260 | 250 | 398 | 181 | 150 |
N.S. |
1 | 1.05 | 0.82 | 0.81 | 0.84 | 1.91 | 1.84 | 2.93 | 1.33 | 1.10 |
time (sec) |
N/A | 0.377 | 0.596 | 0.536 | 0.033 | 0.094 | 1.919 | 0.144 | 0.164 | 1.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 156 | 132 | 124 | 143 | 271 | 551 | 662 | 183 | 190 |
N.S. |
1 | 1.16 | 0.98 | 0.92 | 1.06 | 2.01 | 4.08 | 4.90 | 1.36 | 1.41 |
time (sec) |
N/A | 0.403 | 0.486 | 0.549 | 0.035 | 0.109 | 2.338 | 0.151 | 0.168 | 2.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 157 | 99 | 91 | 193 | 138 | 1078 | 772 | 213 | 0 |
N.S. |
1 | 1.11 | 0.70 | 0.65 | 1.37 | 0.98 | 7.65 | 5.48 | 1.51 | 0.00 |
time (sec) |
N/A | 0.471 | 0.490 | 0.543 | 0.032 | 0.131 | 2.482 | 0.144 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 187 | 137 | 123 | 275 | 182 | 1890 | 884 | 274 | 0 |
N.S. |
1 | 0.98 | 0.72 | 0.64 | 1.44 | 0.95 | 9.90 | 4.63 | 1.43 | 0.00 |
time (sec) |
N/A | 0.491 | 0.686 | 0.559 | 0.035 | 0.195 | 3.248 | 0.148 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 217 | 171 | 154 | 359 | 224 | 2990 | 996 | 333 | 0 |
N.S. |
1 | 0.89 | 0.70 | 0.63 | 1.48 | 0.92 | 12.30 | 4.10 | 1.37 | 0.00 |
time (sec) |
N/A | 0.516 | 0.862 | 0.571 | 0.036 | 0.301 | 4.320 | 0.150 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 240 | 260 | 201 | 407 | 496 | 505 | 264 | 363 | 0 |
N.S. |
1 | 0.81 | 0.88 | 0.68 | 1.37 | 1.67 | 1.70 | 0.89 | 1.22 | 0.00 |
time (sec) |
N/A | 0.503 | 2.136 | 0.611 | 0.039 | 0.206 | 0.703 | 0.135 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 209 | 185 | 170 | 319 | 413 | 396 | 216 | 304 | 0 |
N.S. |
1 | 0.87 | 0.77 | 0.71 | 1.32 | 1.71 | 1.64 | 0.90 | 1.26 | 0.00 |
time (sec) |
N/A | 0.386 | 0.546 | 0.567 | 0.038 | 0.141 | 0.540 | 0.137 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 189 | 175 | 150 | 252 | 356 | 777 | 204 | 294 | 0 |
N.S. |
1 | 0.86 | 0.80 | 0.68 | 1.15 | 1.63 | 3.55 | 0.93 | 1.34 | 0.00 |
time (sec) |
N/A | 0.433 | 1.287 | 0.562 | 0.039 | 0.109 | 2.261 | 0.149 | 0.176 | 0.000 |