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 | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 307 | 302 | 294 | 0 | 2912 | 0 | 3087 | 3104 | 7555 |
N.S. |
1 | 1.00 | 0.98 | 0.95 | 0.00 | 9.45 | 0.00 | 10.02 | 10.08 | 24.53 |
time (sec) |
N/A | 1.098 | 0.429 | 0.174 | 0.000 | 0.264 | 0.000 | 0.618 | 1.411 | 20.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 239 | 244 | 367 | 0 | 1631 | 0 | 306 | 3839 | 2588 |
N.S. |
1 | 1.14 | 1.17 | 1.76 | 0.00 | 7.80 | 0.00 | 1.46 | 18.37 | 12.38 |
time (sec) |
N/A | 0.824 | 0.212 | 0.316 | 0.000 | 0.112 | 0.000 | 1.070 | 0.265 | 20.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 133 | 194 | 267 | 0 | 973 | 554 | 212 | 1137 | 444 |
N.S. |
1 | 1.10 | 1.60 | 2.21 | 0.00 | 8.04 | 4.58 | 1.75 | 9.40 | 3.67 |
time (sec) |
N/A | 0.481 | 0.118 | 0.173 | 0.000 | 0.096 | 1.985 | 1.197 | 0.248 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 134 | 137 | 230 | 0 | 892 | 524 | 171 | 1091 | 423 |
N.S. |
1 | 1.13 | 1.15 | 1.93 | 0.00 | 7.50 | 4.40 | 1.44 | 9.17 | 3.55 |
time (sec) |
N/A | 0.461 | 0.135 | 0.164 | 0.000 | 0.095 | 1.489 | 1.109 | 0.259 | 18.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 145 | 145 | 216 | 0 | 907 | 580 | 161 | 1694 | 460 |
N.S. |
1 | 1.12 | 1.12 | 1.66 | 0.00 | 6.98 | 4.46 | 1.24 | 13.03 | 3.54 |
time (sec) |
N/A | 0.495 | 0.094 | 0.175 | 0.000 | 0.087 | 2.024 | 1.146 | 0.252 | 18.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 129 | 114 | 128 | 0 | 808 | 491 | 143 | 1055 | 400 |
N.S. |
1 | 1.14 | 1.01 | 1.13 | 0.00 | 7.15 | 4.35 | 1.27 | 9.34 | 3.54 |
time (sec) |
N/A | 0.451 | 0.071 | 0.165 | 0.000 | 0.091 | 1.207 | 1.125 | 0.213 | 18.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 126 | 106 | 126 | 0 | 809 | 481 | 144 | 1084 | 386 |
N.S. |
1 | 1.12 | 0.94 | 1.12 | 0.00 | 7.16 | 4.26 | 1.27 | 9.59 | 3.42 |
time (sec) |
N/A | 0.441 | 0.068 | 0.153 | 0.000 | 0.091 | 1.181 | 1.209 | 0.212 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 254 | 342 | 360 | 0 | 2017 | 0 | 323 | 4090 | 9339 |
N.S. |
1 | 1.27 | 1.71 | 1.80 | 0.00 | 10.08 | 0.00 | 1.62 | 20.45 | 46.70 |
time (sec) |
N/A | 0.893 | 0.312 | 0.211 | 0.000 | 0.372 | 0.000 | 1.099 | 0.186 | 25.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 298 | 402 | 412 | 0 | 2312 | 0 | 382 | 4941 | 10074 |
N.S. |
1 | 1.17 | 1.58 | 1.62 | 0.00 | 9.07 | 0.00 | 1.50 | 19.38 | 39.51 |
time (sec) |
N/A | 1.008 | 0.383 | 0.230 | 0.000 | 0.569 | 0.000 | 1.076 | 0.186 | 26.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 392 | 455 | 331 | 0 | 4279 | 0 | 2430 | 6796 | 10912 |
N.S. |
1 | 1.03 | 1.19 | 0.87 | 0.00 | 11.20 | 0.00 | 6.36 | 17.79 | 28.57 |
time (sec) |
N/A | 1.252 | 0.751 | 0.185 | 0.000 | 0.547 | 0.000 | 2.059 | 4.852 | 22.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 345 | 381 | 289 | 0 | 3725 | 0 | 4558 | 5719 | 9575 |
N.S. |
1 | 1.02 | 1.13 | 0.86 | 0.00 | 11.02 | 0.00 | 13.49 | 16.92 | 28.33 |
time (sec) |
N/A | 0.983 | 0.624 | 0.179 | 0.000 | 0.320 | 0.000 | 1.404 | 3.763 | 19.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 304 | 343 | 251 | 0 | 3128 | 627 | 1750 | 4644 | 8521 |
N.S. |
1 | 1.02 | 1.15 | 0.84 | 0.00 | 10.50 | 2.10 | 5.87 | 15.58 | 28.59 |
time (sec) |
N/A | 0.841 | 0.546 | 0.162 | 0.000 | 0.151 | 10.739 | 1.667 | 4.530 | 18.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 296 | 285 | 251 | 0 | 3128 | 648 | 1861 | 4644 | 8397 |
N.S. |
1 | 1.02 | 0.99 | 0.87 | 0.00 | 10.82 | 2.24 | 6.44 | 16.07 | 29.06 |
time (sec) |
N/A | 0.788 | 0.476 | 0.169 | 0.000 | 0.167 | 107.160 | 1.532 | 4.353 | 21.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 334 | 334 | 289 | 0 | 3777 | 0 | 4270 | 5719 | 9731 |
N.S. |
1 | 1.07 | 1.07 | 0.93 | 0.00 | 12.14 | 0.00 | 13.73 | 18.39 | 31.29 |
time (sec) |
N/A | 0.897 | 0.547 | 0.315 | 0.000 | 0.297 | 0.000 | 1.423 | 4.439 | 22.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 361 | 372 | 331 | 0 | 4323 | 0 | 2707 | 6794 | 10979 |
N.S. |
1 | 1.02 | 1.05 | 0.93 | 0.00 | 12.18 | 0.00 | 7.63 | 19.14 | 30.93 |
time (sec) |
N/A | 1.023 | 0.661 | 0.253 | 0.000 | 0.595 | 0.000 | 0.974 | 3.745 | 21.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 423 | 454 | 517 | 0 | 4924 | 0 | 5273 | 7940 | 12130 |
N.S. |
1 | 1.00 | 1.07 | 1.22 | 0.00 | 11.59 | 0.00 | 12.41 | 18.68 | 28.54 |
time (sec) |
N/A | 1.258 | 1.175 | 0.242 | 0.000 | 1.096 | 0.000 | 2.032 | 3.175 | 23.513 |
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 | 82 | 80 | 80 | 86 | 0 | 259 | 311 | 78 | 360 | 656 |
N.S. |
1 | 0.98 | 0.98 | 1.05 | 0.00 | 3.16 | 3.79 | 0.95 | 4.39 | 8.00 |
time (sec) |
N/A | 0.431 | 0.040 | 0.111 | 0.000 | 0.088 | 1.035 | 0.386 | 0.229 | 0.521 |
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 | 64 | 68 | 65 | 63 | 0 | 206 | 223 | 62 | 228 | 120 |
N.S. |
1 | 1.06 | 1.02 | 0.98 | 0.00 | 3.22 | 3.48 | 0.97 | 3.56 | 1.88 |
time (sec) |
N/A | 0.392 | 0.017 | 0.077 | 0.000 | 0.083 | 0.479 | 0.333 | 0.162 | 18.570 |
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 | 35 | 38 | 41 | 38 | 0 | 134 | 131 | 37 | 95 | 42 |
N.S. |
1 | 1.09 | 1.17 | 1.09 | 0.00 | 3.83 | 3.74 | 1.06 | 2.71 | 1.20 |
time (sec) |
N/A | 0.296 | 0.008 | 0.054 | 0.000 | 0.090 | 0.233 | 0.365 | 0.157 | 17.606 |
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 | 70 | 75 | 117 | 68 | 0 | 230 | 253 | 71 | 239 | 1015 |
N.S. |
1 | 1.07 | 1.67 | 0.97 | 0.00 | 3.29 | 3.61 | 1.01 | 3.41 | 14.50 |
time (sec) |
N/A | 0.419 | 0.052 | 0.081 | 0.000 | 0.105 | 2.298 | 0.344 | 0.164 | 0.683 |
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 | 89 | 95 | 139 | 87 | 0 | 298 | 350 | 95 | 399 | 2032 |
N.S. |
1 | 1.07 | 1.56 | 0.98 | 0.00 | 3.35 | 3.93 | 1.07 | 4.48 | 22.83 |
time (sec) |
N/A | 0.504 | 0.106 | 0.098 | 0.000 | 0.109 | 80.913 | 0.389 | 0.177 | 19.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 183 | 208 | 58 | 0 | 1051 | 129 | 2153 | 535 | 3000 |
N.S. |
1 | 1.02 | 1.16 | 0.32 | 0.00 | 5.87 | 0.72 | 12.03 | 2.99 | 16.76 |
time (sec) |
N/A | 0.630 | 0.087 | 0.104 | 0.000 | 0.100 | 1.118 | 0.569 | 0.182 | 18.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 160 | 137 | 43 | 0 | 551 | 75 | 513 | 343 | 416 |
N.S. |
1 | 1.07 | 0.91 | 0.29 | 0.00 | 3.67 | 0.50 | 3.42 | 2.29 | 2.77 |
time (sec) |
N/A | 0.465 | 0.072 | 0.086 | 0.000 | 0.089 | 0.380 | 0.548 | 0.184 | 17.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 137 | 40 | 0 | 605 | 87 | 1050 | 343 | 763 |
N.S. |
1 | 1.00 | 0.91 | 0.27 | 0.00 | 4.03 | 0.58 | 7.00 | 2.29 | 5.09 |
time (sec) |
N/A | 0.400 | 0.057 | 0.075 | 0.000 | 0.105 | 0.575 | 0.362 | 0.193 | 0.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 171 | 199 | 159 | 0 | 1108 | 148 | 1877 | 548 | 2979 |
N.S. |
1 | 0.99 | 1.16 | 0.92 | 0.00 | 6.44 | 0.86 | 10.91 | 3.19 | 17.32 |
time (sec) |
N/A | 0.510 | 0.273 | 0.116 | 0.000 | 0.123 | 1.318 | 0.694 | 0.179 | 18.537 |
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 | 69 | 66 | 62 | 63 | 74 | 156 | 138 | 60 | 207 | 166 |
N.S. |
1 | 0.96 | 0.90 | 0.91 | 1.07 | 2.26 | 2.00 | 0.87 | 3.00 | 2.41 |
time (sec) |
N/A | 0.413 | 0.027 | 0.105 | 0.107 | 0.100 | 0.633 | 0.140 | 0.152 | 0.420 |
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 | 56 | 65 | 51 | 49 | 60 | 134 | 110 | 46 | 126 | 153 |
N.S. |
1 | 1.16 | 0.91 | 0.88 | 1.07 | 2.39 | 1.96 | 0.82 | 2.25 | 2.73 |
time (sec) |
N/A | 0.384 | 0.015 | 0.069 | 0.106 | 0.075 | 0.320 | 0.162 | 0.162 | 0.180 |
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 | 31 | 39 | 31 | 26 | 37 | 91 | 53 | 23 | 62 | 31 |
N.S. |
1 | 1.26 | 1.00 | 0.84 | 1.19 | 2.94 | 1.71 | 0.74 | 2.00 | 1.00 |
time (sec) |
N/A | 0.287 | 0.007 | 0.063 | 0.107 | 0.073 | 0.158 | 0.138 | 0.165 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 89 | 90 | 64 | 85 | 146 | 184 | 71 | 138 | 183 |
N.S. |
1 | 1.16 | 1.17 | 0.83 | 1.10 | 1.90 | 2.39 | 0.92 | 1.79 | 2.38 |
time (sec) |
N/A | 0.471 | 0.038 | 0.081 | 0.105 | 0.081 | 2.294 | 0.139 | 0.161 | 19.699 |
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 | 97 | 105 | 146 | 82 | 123 | 204 | 372 | 126 | 258 | 389 |
N.S. |
1 | 1.08 | 1.51 | 0.85 | 1.27 | 2.10 | 3.84 | 1.30 | 2.66 | 4.01 |
time (sec) |
N/A | 0.530 | 0.068 | 0.098 | 0.108 | 0.083 | 13.097 | 0.149 | 0.168 | 19.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 145 | 144 | 57 | 0 | 603 | 105 | 511 | 202 | 1097 |
N.S. |
1 | 1.27 | 1.26 | 0.50 | 0.00 | 5.29 | 0.92 | 4.48 | 1.77 | 9.62 |
time (sec) |
N/A | 0.513 | 0.067 | 0.120 | 0.000 | 0.085 | 0.720 | 0.168 | 0.170 | 19.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 126 | 128 | 43 | 0 | 267 | 44 | 199 | 96 | 216 |
N.S. |
1 | 1.16 | 1.17 | 0.39 | 0.00 | 2.45 | 0.40 | 1.83 | 0.88 | 1.98 |
time (sec) |
N/A | 0.352 | 0.077 | 0.080 | 0.000 | 0.079 | 0.272 | 0.225 | 0.150 | 0.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 105 | 40 | 0 | 553 | 63 | 299 | 204 | 322 |
N.S. |
1 | 1.00 | 0.96 | 0.37 | 0.00 | 5.07 | 0.58 | 2.74 | 1.87 | 2.95 |
time (sec) |
N/A | 0.327 | 0.046 | 0.072 | 0.000 | 0.079 | 0.437 | 0.175 | 0.153 | 20.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 149 | 143 | 119 | 0 | 1612 | 134 | 698 | 323 | 2774 |
N.S. |
1 | 1.23 | 1.18 | 0.98 | 0.00 | 13.32 | 1.11 | 5.77 | 2.67 | 22.93 |
time (sec) |
N/A | 0.422 | 0.105 | 0.104 | 0.000 | 0.091 | 1.935 | 0.214 | 0.148 | 19.586 |
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 | 69 | 65 | 62 | 62 | 58 | 157 | 144 | 58 | 334 | 302 |
N.S. |
1 | 0.94 | 0.90 | 0.90 | 0.84 | 2.28 | 2.09 | 0.84 | 4.84 | 4.38 |
time (sec) |
N/A | 0.396 | 0.024 | 0.102 | 0.111 | 0.078 | 0.623 | 0.171 | 0.147 | 0.190 |
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 | 54 | 64 | 49 | 47 | 42 | 131 | 117 | 42 | 196 | 85 |
N.S. |
1 | 1.19 | 0.91 | 0.87 | 0.78 | 2.43 | 2.17 | 0.78 | 3.63 | 1.57 |
time (sec) |
N/A | 0.385 | 0.013 | 0.070 | 0.110 | 0.076 | 0.314 | 0.144 | 0.155 | 0.092 |
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 | 31 | 39 | 31 | 26 | 21 | 91 | 60 | 21 | 109 | 24 |
N.S. |
1 | 1.26 | 1.00 | 0.84 | 0.68 | 2.94 | 1.94 | 0.68 | 3.52 | 0.77 |
time (sec) |
N/A | 0.288 | 0.009 | 0.059 | 0.109 | 0.068 | 0.154 | 0.180 | 0.173 | 18.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 82 | 105 | 62 | 61 | 140 | 194 | 61 | 205 | 71 |
N.S. |
1 | 1.19 | 1.52 | 0.90 | 0.88 | 2.03 | 2.81 | 0.88 | 2.97 | 1.03 |
time (sec) |
N/A | 0.440 | 0.045 | 0.078 | 0.110 | 0.090 | 2.217 | 0.141 | 0.164 | 18.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 96 | 163 | 75 | 104 | 206 | 386 | 125 | 375 | 3313 |
N.S. |
1 | 1.08 | 1.83 | 0.84 | 1.17 | 2.31 | 4.34 | 1.40 | 4.21 | 37.22 |
time (sec) |
N/A | 0.500 | 0.072 | 0.100 | 0.109 | 0.086 | 12.797 | 0.153 | 0.167 | 21.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 490 | 164 | 57 | 0 | 615 | 105 | 533 | 640 | 1147 |
N.S. |
1 | 1.53 | 0.51 | 0.18 | 0.00 | 1.92 | 0.33 | 1.67 | 2.00 | 3.58 |
time (sec) |
N/A | 1.578 | 0.074 | 0.243 | 0.000 | 0.089 | 0.745 | 0.187 | 0.196 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 378 | 143 | 41 | 0 | 279 | 44 | 203 | 407 | 222 |
N.S. |
1 | 1.51 | 0.57 | 0.16 | 0.00 | 1.12 | 0.18 | 0.81 | 1.63 | 0.89 |
time (sec) |
N/A | 0.980 | 0.087 | 0.139 | 0.000 | 0.078 | 0.272 | 0.180 | 0.166 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 411 | 119 | 38 | 0 | 567 | 63 | 307 | 618 | 986 |
N.S. |
1 | 1.52 | 0.44 | 0.14 | 0.00 | 2.09 | 0.23 | 1.13 | 2.28 | 3.64 |
time (sec) |
N/A | 1.089 | 0.048 | 0.161 | 0.000 | 0.085 | 0.432 | 0.158 | 0.153 | 18.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 492 | 174 | 162 | 0 | 1582 | 134 | 742 | 887 | 2848 |
N.S. |
1 | 1.50 | 0.53 | 0.49 | 0.00 | 4.82 | 0.41 | 2.26 | 2.70 | 8.68 |
time (sec) |
N/A | 1.332 | 0.116 | 0.181 | 0.000 | 0.096 | 1.859 | 0.184 | 0.546 | 18.538 |
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 | 51 | 53 | 47 | 41 | 40 | 40 | 48 | 40 | 61 | 42 |
N.S. |
1 | 1.04 | 0.92 | 0.80 | 0.78 | 0.78 | 0.94 | 0.78 | 1.20 | 0.82 |
time (sec) |
N/A | 0.332 | 0.011 | 0.077 | 0.118 | 0.066 | 0.048 | 0.126 | 0.154 | 0.057 |
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 | 35 | 38 | 35 | 30 | 29 | 29 | 36 | 29 | 41 | 31 |
N.S. |
1 | 1.09 | 1.00 | 0.86 | 0.83 | 0.83 | 1.03 | 0.83 | 1.17 | 0.89 |
time (sec) |
N/A | 0.323 | 0.008 | 0.062 | 0.112 | 0.062 | 0.043 | 0.120 | 0.158 | 0.043 |
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 | 44 | 42 | 44 | 36 | 35 | 35 | 42 | 35 | 56 | 37 |
N.S. |
1 | 0.95 | 1.00 | 0.82 | 0.80 | 0.80 | 0.95 | 0.80 | 1.27 | 0.84 |
time (sec) |
N/A | 0.327 | 0.007 | 0.062 | 0.113 | 0.065 | 0.052 | 0.104 | 0.152 | 0.042 |
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 | 37 | 39 | 37 | 31 | 30 | 30 | 37 | 30 | 51 | 32 |
N.S. |
1 | 1.05 | 1.00 | 0.84 | 0.81 | 0.81 | 1.00 | 0.81 | 1.38 | 0.86 |
time (sec) |
N/A | 0.318 | 0.007 | 0.052 | 0.113 | 0.070 | 0.047 | 0.115 | 0.154 | 0.035 |
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 | 20 | 20 | 20 | 19 | 18 | 18 | 26 | 18 | 29 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 1.30 | 0.90 | 1.45 | 1.00 |
time (sec) |
N/A | 0.269 | 0.004 | 0.047 | 0.110 | 0.076 | 0.042 | 0.107 | 0.157 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 65 | 31 | 36 | 32 | 41 | 36 | 53 | 34 |
N.S. |
1 | 1.10 | 1.67 | 0.79 | 0.92 | 0.82 | 1.05 | 0.92 | 1.36 | 0.87 |
time (sec) |
N/A | 0.348 | 0.034 | 0.072 | 0.109 | 0.068 | 0.058 | 0.107 | 0.152 | 18.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 50 | 78 | 38 | 41 | 49 | 48 | 46 | 76 | 41 |
N.S. |
1 | 1.04 | 1.62 | 0.79 | 0.85 | 1.02 | 1.00 | 0.96 | 1.58 | 0.85 |
time (sec) |
N/A | 0.369 | 0.029 | 0.075 | 0.110 | 0.065 | 0.063 | 0.108 | 0.154 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 36 | 71 | 31 | 31 | 33 | 37 | 31 | 48 | 32 |
N.S. |
1 | 1.03 | 2.03 | 0.89 | 0.89 | 0.94 | 1.06 | 0.89 | 1.37 | 0.91 |
time (sec) |
N/A | 0.360 | 0.015 | 0.075 | 0.115 | 0.070 | 0.059 | 0.152 | 0.152 | 17.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 82 | 126 | 65 | 64 | 62 | 75 | 64 | 62 | 65 |
N.S. |
1 | 1.01 | 1.56 | 0.80 | 0.79 | 0.77 | 0.93 | 0.79 | 0.77 | 0.80 |
time (sec) |
N/A | 0.548 | 0.134 | 0.082 | 0.111 | 0.064 | 0.052 | 0.103 | 0.151 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 68 | 112 | 55 | 54 | 52 | 65 | 54 | 52 | 55 |
N.S. |
1 | 1.01 | 1.67 | 0.82 | 0.81 | 0.78 | 0.97 | 0.81 | 0.78 | 0.82 |
time (sec) |
N/A | 0.471 | 0.110 | 0.075 | 0.113 | 0.065 | 0.051 | 0.128 | 0.151 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 54 | 98 | 45 | 44 | 42 | 54 | 44 | 42 | 45 |
N.S. |
1 | 1.02 | 1.85 | 0.85 | 0.83 | 0.79 | 1.02 | 0.83 | 0.79 | 0.85 |
time (sec) |
N/A | 0.387 | 0.097 | 0.066 | 0.109 | 0.063 | 0.053 | 0.130 | 0.149 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 40 | 84 | 35 | 34 | 32 | 44 | 34 | 32 | 35 |
N.S. |
1 | 1.03 | 2.15 | 0.90 | 0.87 | 0.82 | 1.13 | 0.87 | 0.82 | 0.90 |
time (sec) |
N/A | 0.309 | 0.070 | 0.056 | 0.134 | 0.066 | 0.052 | 0.106 | 0.153 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 44 | 88 | 39 | 38 | 37 | 46 | 38 | 39 | 39 |
N.S. |
1 | 1.02 | 2.05 | 0.91 | 0.88 | 0.86 | 1.07 | 0.88 | 0.91 | 0.91 |
time (sec) |
N/A | 0.320 | 0.066 | 0.075 | 0.118 | 0.065 | 0.058 | 0.105 | 0.155 | 17.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 58 | 102 | 49 | 50 | 53 | 60 | 50 | 53 | 49 |
N.S. |
1 | 1.02 | 1.79 | 0.86 | 0.88 | 0.93 | 1.05 | 0.88 | 0.93 | 0.86 |
time (sec) |
N/A | 0.397 | 0.078 | 0.086 | 0.129 | 0.072 | 0.072 | 0.114 | 0.148 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 72 | 116 | 59 | 60 | 63 | 70 | 60 | 63 | 59 |
N.S. |
1 | 1.01 | 1.63 | 0.83 | 0.85 | 0.89 | 0.99 | 0.85 | 0.89 | 0.83 |
time (sec) |
N/A | 0.469 | 0.110 | 0.099 | 0.108 | 0.065 | 0.086 | 0.130 | 0.155 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 99 | 109 | 74 | 73 | 73 | 90 | 73 | 71 | 64 |
N.S. |
1 | 1.16 | 1.28 | 0.87 | 0.86 | 0.86 | 1.06 | 0.86 | 0.84 | 0.75 |
time (sec) |
N/A | 0.591 | 0.112 | 0.119 | 0.107 | 0.072 | 0.083 | 0.157 | 0.152 | 18.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 95 | 99 | 72 | 71 | 71 | 87 | 71 | 69 | 67 |
N.S. |
1 | 1.17 | 1.22 | 0.89 | 0.88 | 0.88 | 1.07 | 0.88 | 0.85 | 0.83 |
time (sec) |
N/A | 0.533 | 0.083 | 0.128 | 0.109 | 0.076 | 0.082 | 0.110 | 0.159 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 85 | 95 | 64 | 63 | 63 | 80 | 63 | 61 | 54 |
N.S. |
1 | 1.20 | 1.34 | 0.90 | 0.89 | 0.89 | 1.13 | 0.89 | 0.86 | 0.76 |
time (sec) |
N/A | 0.509 | 0.069 | 0.064 | 0.114 | 0.071 | 0.084 | 0.145 | 0.154 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 81 | 81 | 62 | 61 | 61 | 76 | 61 | 59 | 57 |
N.S. |
1 | 1.21 | 1.21 | 0.93 | 0.91 | 0.91 | 1.13 | 0.91 | 0.88 | 0.85 |
time (sec) |
N/A | 0.449 | 0.068 | 0.062 | 0.109 | 0.078 | 0.082 | 0.098 | 0.156 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 71 | 90 | 54 | 53 | 53 | 70 | 53 | 51 | 44 |
N.S. |
1 | 1.25 | 1.58 | 0.95 | 0.93 | 0.93 | 1.23 | 0.93 | 0.89 | 0.77 |
time (sec) |
N/A | 0.421 | 0.086 | 0.055 | 0.112 | 0.068 | 0.083 | 0.111 | 0.190 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 71 | 73 | 54 | 53 | 53 | 70 | 53 | 51 | 47 |
N.S. |
1 | 1.25 | 1.28 | 0.95 | 0.93 | 0.93 | 1.23 | 0.93 | 0.89 | 0.82 |
time (sec) |
N/A | 0.379 | 0.032 | 0.053 | 0.112 | 0.080 | 0.087 | 0.110 | 0.258 | 18.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 81 | 91 | 59 | 65 | 76 | 82 | 65 | 74 | 53 |
N.S. |
1 | 1.21 | 1.36 | 0.88 | 0.97 | 1.13 | 1.22 | 0.97 | 1.10 | 0.79 |
time (sec) |
N/A | 0.511 | 0.089 | 0.084 | 0.124 | 0.066 | 0.098 | 0.109 | 0.220 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 85 | 88 | 64 | 65 | 76 | 82 | 65 | 74 | 58 |
N.S. |
1 | 1.20 | 1.24 | 0.90 | 0.92 | 1.07 | 1.15 | 0.92 | 1.04 | 0.82 |
time (sec) |
N/A | 0.470 | 0.067 | 0.086 | 0.110 | 0.077 | 0.101 | 0.105 | 0.217 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 95 | 105 | 72 | 75 | 86 | 92 | 75 | 84 | 63 |
N.S. |
1 | 1.17 | 1.30 | 0.89 | 0.93 | 1.06 | 1.14 | 0.93 | 1.04 | 0.78 |
time (sec) |
N/A | 0.568 | 0.092 | 0.094 | 0.168 | 0.066 | 0.111 | 0.131 | 0.216 | 0.042 |
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 | 46 | 43 | 46 | 38 | 37 | 37 | 42 | 37 | 53 | 39 |
N.S. |
1 | 0.93 | 1.00 | 0.83 | 0.80 | 0.80 | 0.91 | 0.80 | 1.15 | 0.85 |
time (sec) |
N/A | 0.328 | 0.011 | 0.079 | 0.110 | 0.062 | 0.049 | 0.100 | 0.220 | 17.685 |
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 | 39 | 40 | 39 | 33 | 32 | 32 | 37 | 32 | 48 | 34 |
N.S. |
1 | 1.03 | 1.00 | 0.85 | 0.82 | 0.82 | 0.95 | 0.82 | 1.23 | 0.87 |
time (sec) |
N/A | 0.346 | 0.007 | 0.062 | 0.105 | 0.061 | 0.046 | 0.105 | 0.221 | 0.045 |
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 | 21 | 20 | 20 | 19 | 18 | 18 | 26 | 18 | 19 | 20 |
N.S. |
1 | 0.95 | 0.95 | 0.90 | 0.86 | 0.86 | 1.24 | 0.86 | 0.90 | 0.95 |
time (sec) |
N/A | 0.281 | 0.005 | 0.061 | 0.105 | 0.063 | 0.040 | 0.107 | 0.219 | 0.043 |
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 | 41 | 44 | 41 | 33 | 38 | 34 | 41 | 38 | 50 | 36 |
N.S. |
1 | 1.07 | 1.00 | 0.80 | 0.93 | 0.83 | 1.00 | 0.93 | 1.22 | 0.88 |
time (sec) |
N/A | 0.363 | 0.028 | 0.080 | 0.105 | 0.064 | 0.058 | 0.132 | 0.261 | 17.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 49 | 80 | 38 | 43 | 51 | 48 | 48 | 73 | 41 |
N.S. |
1 | 1.02 | 1.67 | 0.79 | 0.90 | 1.06 | 1.00 | 1.00 | 1.52 | 0.85 |
time (sec) |
N/A | 0.369 | 0.036 | 0.090 | 0.111 | 0.061 | 0.065 | 0.127 | 0.179 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 38 | 71 | 30 | 31 | 33 | 39 | 31 | 40 | 33 |
N.S. |
1 | 1.09 | 2.03 | 0.86 | 0.89 | 0.94 | 1.11 | 0.89 | 1.14 | 0.94 |
time (sec) |
N/A | 0.350 | 0.019 | 0.098 | 0.107 | 0.063 | 0.059 | 0.102 | 0.170 | 18.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 91 | 92 | 68 | 0 | 73 | 71 | 67 | 63 | 57 |
N.S. |
1 | 1.36 | 1.37 | 1.01 | 0.00 | 1.09 | 1.06 | 1.00 | 0.94 | 0.85 |
time (sec) |
N/A | 0.584 | 0.015 | 0.158 | 0.000 | 0.067 | 0.043 | 0.141 | 0.158 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 75 | 76 | 56 | 0 | 61 | 61 | 55 | 51 | 45 |
N.S. |
1 | 1.44 | 1.46 | 1.08 | 0.00 | 1.17 | 1.17 | 1.06 | 0.98 | 0.87 |
time (sec) |
N/A | 0.497 | 0.011 | 0.115 | 0.000 | 0.064 | 0.043 | 0.107 | 0.159 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 63 | 64 | 48 | 0 | 53 | 51 | 47 | 43 | 37 |
N.S. |
1 | 1.62 | 1.64 | 1.23 | 0.00 | 1.36 | 1.31 | 1.21 | 1.10 | 0.95 |
time (sec) |
N/A | 0.410 | 0.008 | 0.091 | 0.000 | 0.062 | 0.044 | 0.129 | 0.150 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 47 | 48 | 36 | 0 | 41 | 41 | 35 | 31 | 23 |
N.S. |
1 | 1.96 | 2.00 | 1.50 | 0.00 | 1.71 | 1.71 | 1.46 | 1.29 | 0.96 |
time (sec) |
N/A | 0.323 | 0.007 | 0.069 | 0.000 | 0.064 | 0.042 | 0.134 | 0.151 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 51 | 52 | 40 | 0 | 46 | 42 | 39 | 37 | 27 |
N.S. |
1 | 1.89 | 1.93 | 1.48 | 0.00 | 1.70 | 1.56 | 1.44 | 1.37 | 1.00 |
time (sec) |
N/A | 0.332 | 0.009 | 0.089 | 0.000 | 0.062 | 0.050 | 0.113 | 0.166 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 63 | 64 | 48 | 0 | 59 | 56 | 73 | 52 | 39 |
N.S. |
1 | 1.58 | 1.60 | 1.20 | 0.00 | 1.48 | 1.40 | 1.82 | 1.30 | 0.98 |
time (sec) |
N/A | 0.411 | 0.013 | 0.115 | 0.000 | 0.063 | 0.065 | 0.145 | 0.170 | 17.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 79 | 80 | 60 | 0 | 69 | 66 | 61 | 62 | 47 |
N.S. |
1 | 1.44 | 1.45 | 1.09 | 0.00 | 1.25 | 1.20 | 1.11 | 1.13 | 0.85 |
time (sec) |
N/A | 0.492 | 0.017 | 0.135 | 0.000 | 0.060 | 0.081 | 0.127 | 0.155 | 18.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 113 | 105 | 54 | 0 | 72 | 80 | 74 | 66 | 65 |
N.S. |
1 | 1.47 | 1.36 | 0.70 | 0.00 | 0.94 | 1.04 | 0.96 | 0.86 | 0.84 |
time (sec) |
N/A | 0.571 | 0.118 | 0.152 | 0.000 | 0.072 | 0.082 | 0.108 | 0.157 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 92 | 101 | 49 | 0 | 64 | 73 | 66 | 58 | 54 |
N.S. |
1 | 1.37 | 1.51 | 0.73 | 0.00 | 0.96 | 1.09 | 0.99 | 0.87 | 0.81 |
time (sec) |
N/A | 0.515 | 0.122 | 0.109 | 0.000 | 0.069 | 0.082 | 0.130 | 0.152 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 97 | 85 | 42 | 0 | 60 | 70 | 62 | 54 | 55 |
N.S. |
1 | 1.59 | 1.39 | 0.69 | 0.00 | 0.98 | 1.15 | 1.02 | 0.89 | 0.90 |
time (sec) |
N/A | 0.505 | 0.070 | 0.079 | 0.000 | 0.066 | 0.082 | 0.112 | 0.153 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 78 | 94 | 38 | 0 | 54 | 63 | 56 | 48 | 44 |
N.S. |
1 | 1.47 | 1.77 | 0.72 | 0.00 | 1.02 | 1.19 | 1.06 | 0.91 | 0.83 |
time (sec) |
N/A | 0.445 | 0.083 | 0.069 | 0.000 | 0.066 | 0.081 | 0.123 | 0.156 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 89 | 77 | 35 | 0 | 54 | 63 | 56 | 48 | 47 |
N.S. |
1 | 1.68 | 1.45 | 0.66 | 0.00 | 1.02 | 1.19 | 1.06 | 0.91 | 0.89 |
time (sec) |
N/A | 0.419 | 0.033 | 0.068 | 0.000 | 0.070 | 0.088 | 0.118 | 0.158 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 90 | 99 | 44 | 0 | 76 | 76 | 68 | 70 | 54 |
N.S. |
1 | 1.38 | 1.52 | 0.68 | 0.00 | 1.17 | 1.17 | 1.05 | 1.08 | 0.83 |
time (sec) |
N/A | 0.500 | 0.086 | 0.102 | 0.000 | 0.068 | 0.099 | 0.108 | 0.154 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 103 | 92 | 44 | 0 | 77 | 76 | 46 | 71 | 61 |
N.S. |
1 | 1.54 | 1.37 | 0.66 | 0.00 | 1.15 | 1.13 | 0.69 | 1.06 | 0.91 |
time (sec) |
N/A | 0.485 | 0.095 | 0.108 | 0.000 | 0.066 | 0.103 | 0.135 | 0.157 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 102 | 109 | 50 | 0 | 87 | 85 | 78 | 81 | 66 |
N.S. |
1 | 1.32 | 1.42 | 0.65 | 0.00 | 1.13 | 1.10 | 1.01 | 1.05 | 0.86 |
time (sec) |
N/A | 0.604 | 0.127 | 0.120 | 0.000 | 0.069 | 0.110 | 0.134 | 0.149 | 0.046 |
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 | 14 | 16 | 14 | 11 | 10 | 10 | 10 | 10 | 63 | 10 |
N.S. |
1 | 1.14 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 4.50 | 0.71 |
time (sec) |
N/A | 0.264 | 0.005 | 0.073 | 0.107 | 0.059 | 0.039 | 0.193 | 0.154 | 19.269 |
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 | 23 | 23 | 23 | 19 | 18 | 18 | 20 | 18 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 0.87 | 0.78 | 0.74 | 0.78 |
time (sec) |
N/A | 0.250 | 0.010 | 0.089 | 0.110 | 0.080 | 0.058 | 0.119 | 0.156 | 18.232 |
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 | 18 | 18 | 18 | 13 | 12 | 12 | 14 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.274 | 0.007 | 0.088 | 0.108 | 0.065 | 0.062 | 0.112 | 0.156 | 19.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 190 | 39 | 36 | 0 | 157 | 24 | 147 | 231 | 101 |
N.S. |
1 | 1.29 | 0.27 | 0.24 | 0.00 | 1.07 | 0.16 | 1.00 | 1.57 | 0.69 |
time (sec) |
N/A | 0.671 | 0.025 | 0.190 | 0.000 | 0.079 | 0.272 | 0.266 | 0.152 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 190 | 39 | 36 | 0 | 157 | 24 | 147 | 231 | 101 |
N.S. |
1 | 1.29 | 0.27 | 0.24 | 0.00 | 1.07 | 0.16 | 1.00 | 1.57 | 0.69 |
time (sec) |
N/A | 0.636 | 0.018 | 0.071 | 0.000 | 0.070 | 0.274 | 0.264 | 0.152 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 77 | 74 | 36 | 0 | 87 | 126 | 68 | 53 | 81 |
N.S. |
1 | 1.33 | 1.28 | 0.62 | 0.00 | 1.50 | 2.17 | 1.17 | 0.91 | 1.40 |
time (sec) |
N/A | 0.333 | 0.045 | 0.096 | 0.000 | 0.093 | 0.206 | 0.136 | 0.153 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 0 | 74 | 36 | 0 | 87 | 126 | 68 | 53 | 81 |
N.S. |
1 | 0.00 | 1.28 | 0.62 | 0.00 | 1.50 | 2.17 | 1.17 | 0.91 | 1.40 |
time (sec) |
N/A | 0.000 | 0.011 | 0.052 | 0.000 | 0.074 | 0.212 | 0.122 | 0.154 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 208 | 221 | 46 | 0 | 935 | 180 | 1160 | 592 | 921 |
N.S. |
1 | 1.06 | 1.13 | 0.23 | 0.00 | 4.77 | 0.92 | 5.92 | 3.02 | 4.70 |
time (sec) |
N/A | 0.734 | 0.119 | 0.160 | 0.000 | 0.080 | 1.532 | 2.415 | 0.206 | 18.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 0 | 221 | 46 | 0 | 935 | 180 | 1160 | 592 | 921 |
N.S. |
1 | 0.00 | 1.13 | 0.23 | 0.00 | 4.77 | 0.92 | 5.92 | 3.02 | 4.70 |
time (sec) |
N/A | 0.000 | 0.036 | 0.073 | 0.000 | 0.078 | 1.524 | 1.255 | 0.302 | 17.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 228 | 241 | 54 | 0 | 1995 | 376 | 3423 | 938 | 1956 |
N.S. |
1 | 1.06 | 1.12 | 0.25 | 0.00 | 9.24 | 1.74 | 15.85 | 4.34 | 9.06 |
time (sec) |
N/A | 0.938 | 0.252 | 0.206 | 0.000 | 0.092 | 7.447 | 38.882 | 0.689 | 19.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 0 | 241 | 54 | 0 | 1995 | 376 | 3423 | 938 | 1956 |
N.S. |
1 | 0.00 | 1.12 | 0.25 | 0.00 | 9.24 | 1.74 | 15.85 | 4.34 | 9.06 |
time (sec) |
N/A | 0.000 | 0.062 | 0.082 | 0.000 | 0.089 | 7.391 | 20.092 | 0.655 | 0.933 |
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 | 31 | 31 | 25 | 20 | 19 | 24 | 29 | 19 | 23 | 21 |
N.S. |
1 | 1.00 | 0.81 | 0.65 | 0.61 | 0.77 | 0.94 | 0.61 | 0.74 | 0.68 |
time (sec) |
N/A | 0.276 | 0.016 | 0.085 | 0.027 | 0.060 | 0.346 | 0.107 | 0.221 | 17.234 |