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 | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 29 | 46 | 46 | 27 | 49 | 0 |
N.S. |
1 | 0.00 | 0.97 | 0.94 | 1.48 | 1.48 | 0.87 | 1.58 | 0.00 |
time (sec) |
N/A | 0.000 | 8.325 | 0.109 | 0.257 | 0.262 | 0.102 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 16 | 16 | 0 | 24 | 12 | 28 | 15 |
N.S. |
1 | 0.84 | 0.84 | 0.84 | 0.00 | 1.26 | 0.63 | 1.47 | 0.79 |
time (sec) |
N/A | 0.287 | 0.021 | 0.654 | 0.000 | 0.256 | 0.065 | 0.264 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 861 | 37 | 36 | 37 | 24 | 46 | 51 | 34 |
N.S. |
1 | 39.14 | 1.68 | 1.64 | 1.68 | 1.09 | 2.09 | 2.32 | 1.55 |
time (sec) |
N/A | 2.335 | 0.892 | 2.470 | 0.316 | 0.280 | 0.210 | 0.281 | 14.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 56 | 24 | 20 | 19 | 25 | 20 | 19 | 21 |
N.S. |
1 | 2.33 | 1.00 | 0.83 | 0.79 | 1.04 | 0.83 | 0.79 | 0.88 |
time (sec) |
N/A | 0.266 | 0.047 | 0.188 | 0.349 | 0.268 | 0.117 | 0.270 | 13.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 11 | 11 | 9 | 9 | 9 | 8 | 9 | 8 |
N.S. |
1 | 0.50 | 0.50 | 0.41 | 0.41 | 0.41 | 0.36 | 0.41 | 0.36 |
time (sec) |
N/A | 0.127 | 0.001 | 0.016 | 0.197 | 0.255 | 0.020 | 0.255 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 7 | 7 | 6 | 5 | 5 | 3 | 5 | 5 |
N.S. |
1 | 0.44 | 0.44 | 0.38 | 0.31 | 0.31 | 0.19 | 0.31 | 0.31 |
time (sec) |
N/A | 0.119 | 0.000 | 0.026 | 0.178 | 0.254 | 0.018 | 0.252 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 76 | 89 | 74 | 75 | 89 | 100 |
N.S. |
1 | 0.00 | 0.00 | 2.81 | 3.30 | 2.74 | 2.78 | 3.30 | 3.70 |
time (sec) |
N/A | 0.000 | 0.000 | 7.508 | 0.480 | 0.264 | 0.151 | 0.564 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 38 | 21 | 20 | 29 | 19 | 19 | 44 | 19 |
N.S. |
1 | 1.81 | 1.00 | 0.95 | 1.38 | 0.90 | 0.90 | 2.10 | 0.90 |
time (sec) |
N/A | 0.336 | 0.087 | 0.191 | 0.286 | 0.273 | 0.085 | 0.254 | 14.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 55 | 49 | 35 | 105 | 31 | 34 | 33 | 32 |
N.S. |
1 | 2.62 | 2.33 | 1.67 | 5.00 | 1.48 | 1.62 | 1.57 | 1.52 |
time (sec) |
N/A | 0.318 | 0.021 | 0.086 | 0.185 | 0.266 | 0.099 | 0.259 | 14.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 28 | 42 | 42 | 29 | 42 | 42 |
N.S. |
1 | 0.00 | 1.11 | 1.04 | 1.56 | 1.56 | 1.07 | 1.56 | 1.56 |
time (sec) |
N/A | 0.000 | 0.043 | 0.816 | 0.223 | 0.284 | 0.071 | 0.279 | 15.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 23 | 22 | 54 | 44 | 65 | 57 | 60 |
N.S. |
1 | 1.12 | 0.88 | 0.85 | 2.08 | 1.69 | 2.50 | 2.19 | 2.31 |
time (sec) |
N/A | 0.342 | 2.462 | 0.548 | 0.273 | 0.278 | 0.155 | 0.281 | 15.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 58 | 22 | 19 | 23 | 41 | 24 | 23 | 23 |
N.S. |
1 | 2.32 | 0.88 | 0.76 | 0.92 | 1.64 | 0.96 | 0.92 | 0.92 |
time (sec) |
N/A | 0.386 | 0.031 | 0.175 | 0.192 | 0.286 | 0.273 | 0.267 | 14.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 49 | 27 | 30 | 55 | 43 | 36 | 59 | 33 |
N.S. |
1 | 1.75 | 0.96 | 1.07 | 1.96 | 1.54 | 1.29 | 2.11 | 1.18 |
time (sec) |
N/A | 0.266 | 0.294 | 0.076 | 0.199 | 0.260 | 0.092 | 0.257 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 23 | 24 | 29 | 26 | 22 | 31 | 31 |
N.S. |
1 | 0.93 | 0.85 | 0.89 | 1.07 | 0.96 | 0.81 | 1.15 | 1.15 |
time (sec) |
N/A | 0.505 | 0.037 | 0.727 | 0.331 | 0.270 | 0.115 | 0.645 | 15.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 129 | 131 | 89 | 94 | 95 | 112 | 123 | 0 |
N.S. |
1 | 4.30 | 4.37 | 2.97 | 3.13 | 3.17 | 3.73 | 4.10 | 0.00 |
time (sec) |
N/A | 8.588 | 0.281 | 1.865 | 0.346 | 0.298 | 0.408 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 52 | 86 | 52 | 44 | 73 | 50 |
N.S. |
1 | 0.00 | 0.00 | 1.86 | 3.07 | 1.86 | 1.57 | 2.61 | 1.79 |
time (sec) |
N/A | 0.000 | 0.000 | 179.063 | 0.975 | 0.272 | 0.298 | 1.043 | 14.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 0 | 0 | 28 | 52 | 27 | 26 | 27 | 51 |
N.S. |
1 | 0.00 | 0.00 | 0.62 | 1.16 | 0.60 | 0.58 | 0.60 | 1.13 |
time (sec) |
N/A | 0.000 | 0.000 | 161.965 | 0.420 | 0.273 | 0.466 | 3.317 | 13.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 31 | 33 | 30 | 29 | 29 | 26 | 29 | 29 |
N.S. |
1 | 0.89 | 0.94 | 0.86 | 0.83 | 0.83 | 0.74 | 0.83 | 0.83 |
time (sec) |
N/A | 0.719 | 0.469 | 9.919 | 0.218 | 0.274 | 0.119 | 0.298 | 13.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 51 | 23 | 30 | 26 | 27 | 26 | 25 |
N.S. |
1 | 0.00 | 1.89 | 0.85 | 1.11 | 0.96 | 1.00 | 0.96 | 0.93 |
time (sec) |
N/A | 0.000 | 1.800 | 0.111 | 0.235 | 0.263 | 0.089 | 0.277 | 14.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 22 | 25 | 21 | 24 | 24 | 21 | 25 |
N.S. |
1 | 0.96 | 0.85 | 0.96 | 0.81 | 0.92 | 0.92 | 0.81 | 0.96 |
time (sec) |
N/A | 0.377 | 0.078 | 0.579 | 0.283 | 0.269 | 0.074 | 0.253 | 13.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 23 | 21 | 22 | 24 | 0 | 23 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 0.84 | 0.88 | 0.96 | 0.00 | 0.92 |
time (sec) |
N/A | 0.000 | 0.458 | 6.967 | 0.297 | 0.273 | 3.164 | 0.000 | 13.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 8 | 8 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 0.80 | 0.80 | 0.80 | 0.70 | 0.70 | 0.50 | 0.70 | 0.70 |
time (sec) |
N/A | 0.125 | 0.000 | 0.052 | 0.179 | 0.254 | 0.022 | 0.252 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 32 | 32 | 33 | 32 | 31 | 37 | 34 | 32 |
N.S. |
1 | 1.14 | 1.14 | 1.18 | 1.14 | 1.11 | 1.32 | 1.21 | 1.14 |
time (sec) |
N/A | 0.719 | 0.022 | 0.125 | 0.181 | 0.271 | 0.757 | 0.275 | 13.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 21 | 19 | 14 | 17 | 13 | 12 | 16 | 13 |
N.S. |
1 | 1.31 | 1.19 | 0.88 | 1.06 | 0.81 | 0.75 | 1.00 | 0.81 |
time (sec) |
N/A | 0.177 | 0.006 | 0.501 | 0.177 | 0.246 | 0.044 | 0.272 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 72 | 140 | 76 | 71 | 100 | 75 | 74 | 109 |
N.S. |
1 | 2.77 | 5.38 | 2.92 | 2.73 | 3.85 | 2.88 | 2.85 | 4.19 |
time (sec) |
N/A | 0.371 | 0.084 | 0.110 | 0.179 | 0.244 | 0.212 | 0.259 | 13.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 98 | 78 | 57 | 146 | 50 | 70 | 73 | 66 |
N.S. |
1 | 3.27 | 2.60 | 1.90 | 4.87 | 1.67 | 2.33 | 2.43 | 2.20 |
time (sec) |
N/A | 0.425 | 0.101 | 0.517 | 0.193 | 0.257 | 0.094 | 0.259 | 13.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 29 | 35 | 233 | 37 | 34 | 61 | 69 |
N.S. |
1 | 0.00 | 0.94 | 1.13 | 7.52 | 1.19 | 1.10 | 1.97 | 2.23 |
time (sec) |
N/A | 0.000 | 0.377 | 51.603 | 0.907 | 0.275 | 0.400 | 0.882 | 15.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 20 | 19 | 18 | 22 | 27 | 14 | 44 | 17 |
N.S. |
1 | 0.71 | 0.68 | 0.64 | 0.79 | 0.96 | 0.50 | 1.57 | 0.61 |
time (sec) |
N/A | 0.612 | 0.095 | 0.291 | 0.307 | 0.250 | 0.134 | 0.274 | 14.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 17 | 16 | 15 | 15 | 14 | 16 | 16 |
N.S. |
1 | 0.89 | 0.89 | 0.84 | 0.79 | 0.79 | 0.74 | 0.84 | 0.84 |
time (sec) |
N/A | 0.188 | 0.009 | 0.025 | 0.181 | 0.285 | 0.050 | 0.261 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 30 | 0 | 89 | 26 | 0 | 52 |
N.S. |
1 | 0.00 | 0.93 | 1.03 | 0.00 | 3.07 | 0.90 | 0.00 | 1.79 |
time (sec) |
N/A | 0.000 | 0.143 | 1.846 | 0.000 | 0.275 | 0.280 | 0.000 | 14.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 17 | 26 | 23 | 22 | 16 | 16 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 1.44 | 1.28 | 1.22 | 0.89 | 0.89 |
time (sec) |
N/A | 0.219 | 0.064 | 0.217 | 0.209 | 0.272 | 0.120 | 0.264 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 35 | 37 | 40 | 40 | 32 | 40 | 0 |
N.S. |
1 | 0.00 | 1.25 | 1.32 | 1.43 | 1.43 | 1.14 | 1.43 | 0.00 |
time (sec) |
N/A | 0.000 | 0.439 | 0.776 | 0.214 | 0.272 | 0.070 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 127 | 49 | 34 | 102 | 31 | 41 | 36 | 36 |
N.S. |
1 | 6.35 | 2.45 | 1.70 | 5.10 | 1.55 | 2.05 | 1.80 | 1.80 |
time (sec) |
N/A | 0.733 | 0.105 | 0.260 | 0.303 | 0.258 | 0.184 | 0.258 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 45 | 45 | 43 | 44 | 44 | 36 | 48 | 50 |
N.S. |
1 | 1.29 | 1.29 | 1.23 | 1.26 | 1.26 | 1.03 | 1.37 | 1.43 |
time (sec) |
N/A | 0.800 | 1.051 | 0.697 | 0.318 | 0.253 | 0.135 | 0.337 | 15.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 294 | 129 | 133 | 306 | 119 | 143 | 123 | 126 |
N.S. |
1 | 14.00 | 6.14 | 6.33 | 14.57 | 5.67 | 6.81 | 5.86 | 6.00 |
time (sec) |
N/A | 0.695 | 0.348 | 0.196 | 0.187 | 0.274 | 0.208 | 0.265 | 14.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 211 | 46 | 51 | 141 | 63 | 68 | 94 | 63 |
N.S. |
1 | 10.05 | 2.19 | 2.43 | 6.71 | 3.00 | 3.24 | 4.48 | 3.00 |
time (sec) |
N/A | 1.150 | 0.585 | 0.119 | 0.253 | 0.265 | 0.060 | 0.262 | 14.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 38 | 24 | 39 | 31 | 27 | 31 | 31 |
N.S. |
1 | 0.00 | 1.15 | 0.73 | 1.18 | 0.94 | 0.82 | 0.94 | 0.94 |
time (sec) |
N/A | 0.000 | 10.137 | 0.176 | 0.228 | 0.265 | 0.085 | 0.305 | 14.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 28 | 30 | 24 | 28 | 28 | 20 | 28 | 26 |
N.S. |
1 | 1.33 | 1.43 | 1.14 | 1.33 | 1.33 | 0.95 | 1.33 | 1.24 |
time (sec) |
N/A | 0.163 | 0.000 | 0.128 | 0.196 | 0.270 | 0.023 | 0.256 | 14.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 27 | 30 | 28 | 28 | 24 | 31 | 21 |
N.S. |
1 | 0.00 | 1.59 | 1.76 | 1.65 | 1.65 | 1.41 | 1.82 | 1.24 |
time (sec) |
N/A | 0.000 | 0.178 | 0.520 | 0.219 | 0.291 | 0.076 | 0.265 | 13.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 35 | 33 | 32 | 34 | 0 | 33 |
N.S. |
1 | 0.00 | 0.90 | 1.17 | 1.10 | 1.07 | 1.13 | 0.00 | 1.10 |
time (sec) |
N/A | 0.000 | 0.350 | 1.852 | 0.303 | 0.291 | 0.075 | 0.000 | 14.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 25 | 15 | 15 | 28 | 14 | 15 | 20 | 14 |
N.S. |
1 | 1.14 | 0.68 | 0.68 | 1.27 | 0.64 | 0.68 | 0.91 | 0.64 |
time (sec) |
N/A | 0.329 | 0.168 | 0.314 | 0.224 | 0.280 | 0.045 | 0.262 | 13.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 39 | 28 | 32 | 42 | 31 | 29 | 0 | 29 |
N.S. |
1 | 1.34 | 0.97 | 1.10 | 1.45 | 1.07 | 1.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.568 | 0.041 | 1.115 | 0.282 | 0.284 | 0.156 | 0.000 | 14.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 26 | 18 | 17 | 18 | 15 | 14 | 18 | 17 |
N.S. |
1 | 1.37 | 0.95 | 0.89 | 0.95 | 0.79 | 0.74 | 0.95 | 0.89 |
time (sec) |
N/A | 0.314 | 0.170 | 0.173 | 0.237 | 0.293 | 0.057 | 0.262 | 12.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 7 | 7 | 8 | 7 | 7 | 7 | 7 | 8 |
N.S. |
1 | 0.54 | 0.54 | 0.62 | 0.54 | 0.54 | 0.54 | 0.54 | 0.62 |
time (sec) |
N/A | 0.129 | 0.001 | 0.039 | 0.179 | 0.271 | 0.039 | 0.264 | 13.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 32 | 32 | 31 | 32 | 32 | 29 | 32 | 31 |
N.S. |
1 | 1.10 | 1.10 | 1.07 | 1.10 | 1.10 | 1.00 | 1.10 | 1.07 |
time (sec) |
N/A | 0.196 | 0.004 | 0.065 | 0.181 | 0.278 | 0.031 | 0.259 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 17 | 21 | 14 | 16 | 15 | 17 | 16 | 15 |
N.S. |
1 | 0.65 | 0.81 | 0.54 | 0.62 | 0.58 | 0.65 | 0.62 | 0.58 |
time (sec) |
N/A | 0.132 | 0.002 | 0.085 | 0.188 | 0.271 | 0.032 | 0.261 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 45 | 56 | 98 | 49 | 56 | 70 | 127 |
N.S. |
1 | 0.00 | 2.14 | 2.67 | 4.67 | 2.33 | 2.67 | 3.33 | 6.05 |
time (sec) |
N/A | 0.000 | 0.183 | 1.730 | 0.307 | 0.277 | 4.662 | 0.322 | 14.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 21 | 19 | 19 | 36 | 33 | 15 | 39 | 19 |
N.S. |
1 | 0.72 | 0.66 | 0.66 | 1.24 | 1.14 | 0.52 | 1.34 | 0.66 |
time (sec) |
N/A | 0.887 | 0.486 | 3.296 | 0.213 | 0.295 | 0.118 | 0.312 | 13.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 41 | 38 | 57 | 54 | 56 | 44 | 56 | 109 |
N.S. |
1 | 1.41 | 1.31 | 1.97 | 1.86 | 1.93 | 1.52 | 1.93 | 3.76 |
time (sec) |
N/A | 0.289 | 0.044 | 0.597 | 0.185 | 0.337 | 0.237 | 0.263 | 13.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 38 | 36 | 32 | 32 | 32 | 32 | 32 | 32 |
N.S. |
1 | 1.81 | 1.71 | 1.52 | 1.52 | 1.52 | 1.52 | 1.52 | 1.52 |
time (sec) |
N/A | 0.198 | 0.089 | 0.052 | 0.188 | 0.286 | 0.052 | 0.262 | 13.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 50 | 56 | 0 | 56 | 58 | 0 | 89 |
N.S. |
1 | 0.00 | 1.39 | 1.56 | 0.00 | 1.56 | 1.61 | 0.00 | 2.47 |
time (sec) |
N/A | 0.000 | 0.645 | 31.417 | 0.000 | 0.273 | 54.666 | 0.000 | 13.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 35 | 26 | 19 | 25 | 18 | 20 | 25 | 14 |
N.S. |
1 | 1.94 | 1.44 | 1.06 | 1.39 | 1.00 | 1.11 | 1.39 | 0.78 |
time (sec) |
N/A | 0.157 | 0.007 | 0.037 | 0.188 | 0.255 | 0.068 | 0.264 | 13.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 14 | 12 | 11 | 12 | 12 | 12 | 8 |
N.S. |
1 | 0.87 | 0.61 | 0.52 | 0.48 | 0.52 | 0.52 | 0.52 | 0.35 |
time (sec) |
N/A | 0.150 | 0.006 | 0.220 | 0.176 | 0.261 | 0.032 | 0.257 | 13.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 43 | 43 | 34 | 33 | 33 | 39 | 33 | 25 |
N.S. |
1 | 1.59 | 1.59 | 1.26 | 1.22 | 1.22 | 1.44 | 1.22 | 0.93 |
time (sec) |
N/A | 0.388 | 0.927 | 0.277 | 0.200 | 0.291 | 0.062 | 0.257 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 18 | 0 | 9 | 8 | 9 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.50 | 0.44 | 0.50 | 0.94 |
time (sec) |
N/A | 0.480 | 0.087 | 0.551 | 0.000 | 0.267 | 0.075 | 0.267 | 14.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 22 | 37 | 37 | 17 | 54 | 78 |
N.S. |
1 | 0.00 | 1.12 | 0.88 | 1.48 | 1.48 | 0.68 | 2.16 | 3.12 |
time (sec) |
N/A | 0.000 | 0.786 | 11.385 | 0.237 | 0.278 | 0.176 | 0.284 | 14.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 34 | 25 | 29 | 24 | 19 | 24 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.74 | 0.85 | 0.71 | 0.56 | 0.71 | 0.79 |
time (sec) |
N/A | 0.000 | 1.219 | 0.226 | 0.240 | 0.278 | 0.081 | 0.298 | 13.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.67 |
time (sec) |
N/A | 0.139 | 0.003 | 0.779 | 0.182 | 0.256 | 0.084 | 0.266 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 10 | 19 | 10 | 8 | 9 | 9 |
N.S. |
1 | 0.86 | 0.86 | 0.71 | 1.36 | 0.71 | 0.57 | 0.64 | 0.64 |
time (sec) |
N/A | 0.170 | 0.043 | 0.084 | 0.238 | 0.314 | 0.043 | 0.256 | 13.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 49 | 31 | 44 | 57 | 38 | 76 | 61 | 38 |
N.S. |
1 | 1.69 | 1.07 | 1.52 | 1.97 | 1.31 | 2.62 | 2.10 | 1.31 |
time (sec) |
N/A | 0.183 | 0.004 | 0.102 | 0.178 | 0.262 | 0.111 | 0.263 | 13.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 37 | 21 | 35 | 15 | 21 | 52 |
N.S. |
1 | 0.00 | 0.95 | 1.68 | 0.95 | 1.59 | 0.68 | 0.95 | 2.36 |
time (sec) |
N/A | 0.000 | 0.270 | 0.735 | 0.215 | 0.266 | 0.085 | 0.336 | 13.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | B | A | A | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 0 | 105 | 87 | 58 | 48 | 86 | 32 |
N.S. |
1 | 0.97 | 0.00 | 3.00 | 2.49 | 1.66 | 1.37 | 2.46 | 0.91 |
time (sec) |
N/A | 2.036 | 0.000 | 85.065 | 0.526 | 0.270 | 0.418 | 10.276 | 15.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 93 | 34 | 31 | 58 | 22 | 32 | 46 | 19 |
N.S. |
1 | 4.65 | 1.70 | 1.55 | 2.90 | 1.10 | 1.60 | 2.30 | 0.95 |
time (sec) |
N/A | 0.225 | 0.015 | 0.124 | 0.187 | 0.270 | 0.078 | 0.264 | 13.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 19 | 25 | 21 | 19 | 20 | 20 | 20 | 20 |
N.S. |
1 | 0.95 | 1.25 | 1.05 | 0.95 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.504 | 0.023 | 0.192 | 0.241 | 0.275 | 0.462 | 0.273 | 15.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 61 | 38 | 35 | 59 | 59 | 66 | 61 | 40 |
N.S. |
1 | 2.44 | 1.52 | 1.40 | 2.36 | 2.36 | 2.64 | 2.44 | 1.60 |
time (sec) |
N/A | 1.784 | 0.108 | 0.252 | 0.235 | 0.272 | 0.105 | 0.272 | 13.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 22 | 29 | 21 | 18 | 35 | 14 | 19 | 18 |
N.S. |
1 | 1.38 | 1.81 | 1.31 | 1.12 | 2.19 | 0.88 | 1.19 | 1.12 |
time (sec) |
N/A | 0.239 | 0.028 | 0.734 | 0.182 | 0.274 | 0.057 | 0.270 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 25 | 105 | 73 | 31 | 92 | 73 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 4.57 | 3.17 | 1.35 | 4.00 | 3.17 |
time (sec) |
N/A | 0.000 | 0.042 | 0.888 | 0.314 | 0.271 | 0.083 | 0.280 | 14.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 30 | 9 | 8 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 3.33 | 1.00 | 0.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 0.008 | 0.035 | 0.195 | 0.276 | 0.041 | 0.252 | 14.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 15 | 17 | 17 | 12 | 17 | 17 |
N.S. |
1 | 0.94 | 0.94 | 0.83 | 0.94 | 0.94 | 0.67 | 0.94 | 0.94 |
time (sec) |
N/A | 0.151 | 0.000 | 0.049 | 0.184 | 0.253 | 0.022 | 0.277 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 32 | 30 | 30 | 36 | 45 | 104 |
N.S. |
1 | 0.00 | 1.00 | 1.14 | 1.07 | 1.07 | 1.29 | 1.61 | 3.71 |
time (sec) |
N/A | 0.000 | 0.079 | 6.383 | 0.222 | 0.268 | 0.151 | 0.285 | 14.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 36 | 38 | 62 | 49 | 29 | 35 | 36 |
N.S. |
1 | 0.00 | 1.24 | 1.31 | 2.14 | 1.69 | 1.00 | 1.21 | 1.24 |
time (sec) |
N/A | 0.000 | 0.082 | 1.036 | 0.332 | 0.294 | 0.138 | 0.732 | 15.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 25 | 21 | 20 | 59 | 22 | 0 | 21 |
N.S. |
1 | 0.00 | 0.83 | 0.70 | 0.67 | 1.97 | 0.73 | 0.00 | 0.70 |
time (sec) |
N/A | 0.000 | 0.946 | 0.225 | 0.488 | 0.260 | 0.219 | 0.000 | 15.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 28 | 19 | 19 | 18 | 19 | 17 | 19 | 17 |
N.S. |
1 | 1.33 | 0.90 | 0.90 | 0.86 | 0.90 | 0.81 | 0.90 | 0.81 |
time (sec) |
N/A | 0.236 | 0.012 | 2.094 | 0.189 | 0.263 | 0.108 | 0.264 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 22 | 27 | 27 | 22 | 21 | 27 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.23 | 1.23 | 1.00 | 0.95 | 1.23 |
time (sec) |
N/A | 0.000 | 0.353 | 0.793 | 0.237 | 0.272 | 0.052 | 0.278 | 15.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 42 | 35 | 37 | 35 | 35 | 36 | 35 | 40 |
N.S. |
1 | 1.75 | 1.46 | 1.54 | 1.46 | 1.46 | 1.50 | 1.46 | 1.67 |
time (sec) |
N/A | 0.461 | 0.032 | 0.315 | 0.220 | 0.256 | 0.086 | 0.260 | 13.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 58 | 30 | 53 | 0 | 65 | 76 | 78 | 63 |
N.S. |
1 | 2.42 | 1.25 | 2.21 | 0.00 | 2.71 | 3.17 | 3.25 | 2.62 |
time (sec) |
N/A | 1.105 | 0.693 | 0.438 | 0.000 | 0.254 | 0.152 | 0.269 | 13.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 35 | 32 | 28 | 30 | 26 | 26 | 26 | 30 |
N.S. |
1 | 1.59 | 1.45 | 1.27 | 1.36 | 1.18 | 1.18 | 1.18 | 1.36 |
time (sec) |
N/A | 0.163 | 0.094 | 0.205 | 0.180 | 0.268 | 0.053 | 0.263 | 14.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 22 | 22 | 23 | 22 | 23 | 25 |
N.S. |
1 | 0.00 | 0.93 | 0.81 | 0.81 | 0.85 | 0.81 | 0.85 | 0.93 |
time (sec) |
N/A | 0.000 | 0.443 | 24.602 | 0.394 | 0.254 | 0.504 | 1.935 | 15.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 24 | 24 | 16 | 15 | 15 | 20 | 96 | 17 |
N.S. |
1 | 1.26 | 1.26 | 0.84 | 0.79 | 0.79 | 1.05 | 5.05 | 0.89 |
time (sec) |
N/A | 0.221 | 0.032 | 0.209 | 0.192 | 0.257 | 0.070 | 0.264 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 19 | 20 | 21 | 29 | 20 | 19 | 102 | 21 |
N.S. |
1 | 0.83 | 0.87 | 0.91 | 1.26 | 0.87 | 0.83 | 4.43 | 0.91 |
time (sec) |
N/A | 0.476 | 0.176 | 0.932 | 0.319 | 0.261 | 0.105 | 0.273 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 18 | 15 | 14 | 24 | 17 | 14 | 18 |
N.S. |
1 | 1.21 | 0.95 | 0.79 | 0.74 | 1.26 | 0.89 | 0.74 | 0.95 |
time (sec) |
N/A | 0.276 | 0.044 | 0.173 | 0.184 | 0.268 | 0.099 | 0.268 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 75 | 27 | 23 | 37 | 26 | 22 | 32 | 29 |
N.S. |
1 | 3.26 | 1.17 | 1.00 | 1.61 | 1.13 | 0.96 | 1.39 | 1.26 |
time (sec) |
N/A | 0.968 | 0.287 | 0.361 | 0.269 | 0.283 | 0.101 | 0.281 | 15.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 35 | 21 | 24 | 129 | 23 | 20 | 31 | 33 |
N.S. |
1 | 1.59 | 0.95 | 1.09 | 5.86 | 1.05 | 0.91 | 1.41 | 1.50 |
time (sec) |
N/A | 0.217 | 0.143 | 0.130 | 0.331 | 0.266 | 0.073 | 0.263 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 31 | 20 | 20 | 151 | 23 | 19 | 25 | 20 |
N.S. |
1 | 1.63 | 1.05 | 1.05 | 7.95 | 1.21 | 1.00 | 1.32 | 1.05 |
time (sec) |
N/A | 0.197 | 0.335 | 0.070 | 0.324 | 0.273 | 0.056 | 0.262 | 15.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 65 | 64 | 53 | 51 | 58 | 53 | 53 | 49 |
N.S. |
1 | 2.41 | 2.37 | 1.96 | 1.89 | 2.15 | 1.96 | 1.96 | 1.81 |
time (sec) |
N/A | 0.262 | 0.019 | 0.092 | 0.188 | 0.276 | 0.314 | 0.257 | 14.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 60 | 53 | 77 | 62 | 0 | 64 | 62 |
N.S. |
1 | 0.00 | 2.31 | 2.04 | 2.96 | 2.38 | 0.00 | 2.46 | 2.38 |
time (sec) |
N/A | 0.000 | 0.507 | 92.541 | 0.403 | 0.272 | 0.000 | 2.623 | 17.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 244 | 80 | 66 | 64 | 71 | 67 | 0 |
N.S. |
1 | 0.00 | 10.17 | 3.33 | 2.75 | 2.67 | 2.96 | 2.79 | 0.00 |
time (sec) |
N/A | 0.000 | 32.225 | 40.021 | 0.227 | 0.332 | 0.746 | 1.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 24 | 25 | 22 | 22 | 26 | 24 | 24 |
N.S. |
1 | 0.96 | 0.92 | 0.96 | 0.85 | 0.85 | 1.00 | 0.92 | 0.92 |
time (sec) |
N/A | 0.163 | 0.010 | 1.909 | 0.192 | 0.262 | 0.103 | 0.259 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 33 | 33 | 28 | 34 | 27 | 31 | 34 | 32 |
N.S. |
1 | 1.38 | 1.38 | 1.17 | 1.42 | 1.12 | 1.29 | 1.42 | 1.33 |
time (sec) |
N/A | 1.059 | 0.241 | 0.196 | 0.336 | 0.311 | 0.118 | 0.298 | 14.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 13 | 14 | 20 | 13 | 14 | 13 | 13 |
N.S. |
1 | 0.00 | 1.08 | 1.17 | 1.67 | 1.08 | 1.17 | 1.08 | 1.08 |
time (sec) |
N/A | 0.000 | 0.165 | 0.815 | 0.216 | 0.266 | 0.116 | 0.265 | 15.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 24 | 22 | 26 | 28 | 24 | 37 | 21 |
N.S. |
1 | 0.91 | 1.04 | 0.96 | 1.13 | 1.22 | 1.04 | 1.61 | 0.91 |
time (sec) |
N/A | 0.705 | 0.436 | 0.280 | 0.240 | 0.264 | 0.217 | 0.274 | 14.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 15 | 14 | 13 | 13 | 12 | 27 | 13 |
N.S. |
1 | 0.00 | 0.60 | 0.56 | 0.52 | 0.52 | 0.48 | 1.08 | 0.52 |
time (sec) |
N/A | 0.000 | 0.196 | 0.197 | 0.276 | 0.249 | 0.089 | 0.273 | 13.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 43 | 37 | 42 | 0 | 46 | 0 |
N.S. |
1 | 0.00 | 1.03 | 1.48 | 1.28 | 1.45 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.000 | 0.106 | 10.796 | 0.316 | 0.255 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 64 | 45 | 50 | 63 | 39 | 70 | 50 | 43 |
N.S. |
1 | 2.00 | 1.41 | 1.56 | 1.97 | 1.22 | 2.19 | 1.56 | 1.34 |
time (sec) |
N/A | 0.332 | 0.080 | 0.395 | 0.222 | 0.319 | 0.106 | 0.258 | 14.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 154 | 93 | 49 | 114 | 199 | 765 | 56 | 47 |
N.S. |
1 | 5.50 | 3.32 | 1.75 | 4.07 | 7.11 | 27.32 | 2.00 | 1.68 |
time (sec) |
N/A | 0.839 | 0.075 | 2.837 | 0.199 | 0.282 | 4.149 | 0.265 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 93 | 63 | 57 | 0 | 51 | 58 | 83 | 73 |
N.S. |
1 | 3.32 | 2.25 | 2.04 | 0.00 | 1.82 | 2.07 | 2.96 | 2.61 |
time (sec) |
N/A | 0.538 | 7.499 | 0.431 | 0.000 | 0.299 | 0.088 | 0.281 | 14.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 89 | 86 | 52 | 109 | 41 | 49 | 68 | 58 |
N.S. |
1 | 3.07 | 2.97 | 1.79 | 3.76 | 1.41 | 1.69 | 2.34 | 2.00 |
time (sec) |
N/A | 0.366 | 0.086 | 0.650 | 0.289 | 0.302 | 0.128 | 0.264 | 14.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 27 | 25 | 32 | 27 | 0 | 49 |
N.S. |
1 | 0.00 | 0.89 | 0.96 | 0.89 | 1.14 | 0.96 | 0.00 | 1.75 |
time (sec) |
N/A | 0.000 | 5.105 | 4.500 | 0.372 | 0.285 | 62.538 | 0.000 | 14.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 27 | 35 | 27 | 26 | 35 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.17 | 1.52 | 1.17 | 1.13 | 1.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.328 | 2.879 | 0.299 | 0.268 | 0.178 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 86 | 28 | 28 | 0 | 25 | 0 | 36 | 36 |
N.S. |
1 | 3.19 | 1.04 | 1.04 | 0.00 | 0.93 | 0.00 | 1.33 | 1.33 |
time (sec) |
N/A | 0.818 | 0.185 | 0.750 | 0.000 | 0.282 | 0.000 | 0.406 | 14.245 |