Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 81 | 160 | 50 | 134 | 0 | 46 | 403 |
N.S. | 1 | 1.00 | 0.98 | 1.93 | 0.60 | 1.61 | 0.00 | 0.55 | 4.86 |
time (sec) |
N/A | 0.037 | 0.055 | 0.423 | 0.478 | 0.398 | 0.000 | 0.396 | 1.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 70 | 61 | 37 | 115 | 0 | 36 | 344 |
N.S. | 1 | 1.00 | 0.96 | 0.84 | 0.51 | 1.58 | 0.00 | 0.49 | 4.71 |
time (sec) |
N/A | 0.025 | 0.041 | 0.388 | 0.471 | 0.385 | 0.000 | 0.379 | 1.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 80 | 82 | 35 | 116 | 0 | 35 | 516 |
N.S. | 1 | 1.00 | 0.82 | 0.85 | 0.36 | 1.20 | 0.00 | 0.36 | 5.32 |
time (sec) |
N/A | 0.038 | 0.043 | 0.420 | 0.467 | 0.365 | 0.000 | 0.395 | 2.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 104 | 105 | 51 | 147 | 0 | 49 | 705 |
N.S. | 1 | 1.00 | 0.87 | 0.88 | 0.42 | 1.22 | 0.00 | 0.41 | 5.88 |
time (sec) |
N/A | 0.054 | 0.080 | 0.459 | 0.480 | 0.356 | 0.000 | 0.391 | 1.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 120 | 128 | 64 | 184 | 0 | 58 | 871 |
N.S. | 1 | 1.00 | 0.83 | 0.88 | 0.44 | 1.27 | 0.00 | 0.40 | 6.01 |
time (sec) |
N/A | 0.076 | 0.152 | 0.589 | 0.475 | 0.391 | 0.000 | 0.398 | 2.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 139 | 151 | 75 | 210 | 0 | 70 | 1051 |
N.S. | 1 | 1.00 | 0.81 | 0.88 | 0.44 | 1.22 | 0.00 | 0.41 | 6.11 |
time (sec) |
N/A | 0.097 | 0.174 | 0.945 | 0.477 | 0.347 | 0.000 | 0.398 | 2.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 147 | 418 | 86 | 227 | 0 | 77 | 571 |
N.S. |
1 | 1.00 | 1.09 | 3.10 | 0.64 | 1.68 | 0.00 | 0.57 | 4.23 |
time (sec) |
N/A | 0.068 | 0.070 | 0.545 | 0.488 | 0.348 | 0.000 | 0.398 | 1.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 104 | 249 | 73 | 200 | 0 | 59 | 511 |
N.S. | 1 | 1.00 | 0.95 | 2.26 | 0.66 | 1.82 | 0.00 | 0.54 | 4.65 |
time (sec) |
N/A | 0.050 | 0.066 | 0.437 | 0.491 | 0.361 | 0.000 | 0.401 | 1.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 96 | 85 | 61 | 185 | 0 | 47 | 667 |
N.S. | 1 | 1.00 | 0.98 | 0.87 | 0.62 | 1.89 | 0.00 | 0.48 | 6.81 |
time (sec) |
N/A | 0.039 | 0.052 | 0.422 | 0.489 | 0.351 | 0.000 | 0.388 | 1.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 107 | 98 | 64 | 186 | 0 | 52 | 580 |
N.S. | 1 | 1.00 | 0.86 | 0.78 | 0.51 | 1.49 | 0.00 | 0.42 | 4.64 |
time (sec) |
N/A | 0.052 | 0.163 | 0.460 | 0.473 | 0.353 | 0.000 | 0.390 | 1.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 118 | 112 | 60 | 186 | 0 | 47 | 741 |
N.S. | 1 | 1.00 | 0.78 | 0.74 | 0.39 | 1.22 | 0.00 | 0.31 | 4.88 |
time (sec) |
N/A | 0.072 | 0.117 | 0.465 | 0.484 | 0.353 | 0.000 | 0.397 | 1.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 141 | 181 | 73 | 214 | 0 | 59 | 1077 |
N.S. | 1 | 1.00 | 0.80 | 1.03 | 0.41 | 1.22 | 0.00 | 0.34 | 6.12 |
time (sec) |
N/A | 0.093 | 0.206 | 0.617 | 0.481 | 0.350 | 0.000 | 0.395 | 2.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 156 | 207 | 86 | 250 | 0 | 71 | 1362 |
N.S. | 1 | 1.00 | 0.78 | 1.03 | 0.43 | 1.24 | 0.00 | 0.35 | 6.78 |
time (sec) |
N/A | 0.115 | 0.184 | 1.000 | 0.481 | 0.345 | 0.000 | 0.391 | 2.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 174 | 229 | 97 | 276 | 0 | 80 | 2151 |
N.S. |
1 | 1.00 | 0.76 | 1.00 | 0.43 | 1.21 | 0.00 | 0.35 | 9.43 |
time (sec) |
N/A | 0.138 | 0.236 | 1.819 | 0.485 | 0.345 | 0.000 | 0.395 | 1.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 104 | 304 | 0 | 141 | 0 | 60 | -1 |
N.S. | 1 | 1.00 | 0.73 | 2.14 | 0.00 | 0.99 | 0.00 | 0.42 | -0.01 |
time (sec) |
N/A | 0.054 | 0.059 | 0.127 | 0.000 | 0.360 | 0.000 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 84 | 174 | 0 | 114 | 0 | 48 | -1 |
N.S. | 1 | 1.00 | 0.81 | 1.67 | 0.00 | 1.10 | 0.00 | 0.46 | -0.01 |
time (sec) |
N/A | 0.035 | 0.045 | 0.121 | 0.000 | 0.369 | 0.000 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 62 | 75 | 0 | 93 | 0 | 36 | -1 |
N.S. | 1 | 1.00 | 1.02 | 1.23 | 0.00 | 1.52 | 0.00 | 0.59 | -0.02 |
time (sec) |
N/A | 0.020 | 0.026 | 0.122 | 0.000 | 0.351 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 52 | 149 | 40 | 89 | 0 | 57 | -1 |
N.S. | 1 | 1.00 | 1.06 | 3.04 | 0.82 | 1.82 | 0.00 | 1.16 | -0.02 |
time (sec) |
N/A | 0.020 | 0.029 | 0.126 | 0.506 | 0.354 | 0.000 | 0.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 34 | 29 | 15 | 15 | 0 | 59 | 210 |
N.S. | 1 | 1.00 | 0.97 | 0.83 | 0.43 | 0.43 | 0.00 | 1.69 | 6.00 |
time (sec) |
N/A | 0.010 | 0.024 | 0.121 | 0.488 | 0.359 | 0.000 | 0.412 | 1.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 48 | 59 | 34 | 34 | 0 | 112 | 174 |
N.S. |
1 | 1.00 | 0.67 | 0.82 | 0.47 | 0.47 | 0.00 | 1.56 | 2.42 |
time (sec) |
N/A | 0.023 | 0.029 | 0.120 | 0.473 | 0.350 | 0.000 | 0.387 | 1.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 66 | 105 | 45 | 45 | 0 | 138 | 234 |
N.S. |
1 | 1.00 | 0.60 | 0.95 | 0.41 | 0.41 | 0.00 | 1.25 | 2.13 |
time (sec) |
N/A | 0.037 | 0.043 | 0.127 | 0.473 | 0.342 | 0.000 | 0.403 | 1.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 82 | 151 | 56 | 56 | 0 | 166 | 294 |
N.S. |
1 | 1.00 | 0.55 | 1.02 | 0.38 | 0.38 | 0.00 | 1.12 | 1.99 |
time (sec) |
N/A | 0.055 | 0.047 | 0.134 | 0.478 | 0.346 | 0.000 | 0.400 | 1.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 122 | 471 | 0 | 163 | 0 | 147 | -1 |
N.S. | 1 | 1.00 | 0.69 | 2.66 | 0.00 | 0.92 | 0.00 | 0.83 | -0.01 |
time (sec) |
N/A | 0.072 | 0.067 | 0.122 | 0.000 | 0.360 | 0.000 | 0.405 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 105 | 304 | 0 | 140 | 0 | 122 | -1 |
N.S. | 1 | 1.00 | 0.76 | 2.19 | 0.00 | 1.01 | 0.00 | 0.88 | -0.01 |
time (sec) |
N/A | 0.052 | 0.047 | 0.121 | 0.000 | 0.356 | 0.000 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 83 | 165 | 0 | 119 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.82 | 1.63 | 0.00 | 1.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.035 | 0.049 | 0.121 | 0.000 | 0.356 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 77 | 280 | 0 | 109 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.95 | 3.46 | 0.00 | 1.35 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.037 | 0.036 | 0.121 | 0.000 | 0.352 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 74 | 315 | 0 | 109 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.06 | 4.50 | 0.00 | 1.56 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.030 | 0.052 | 0.120 | 0.000 | 0.337 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 34 | 29 | 15 | 31 | 0 | 33 | 332 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.43 | 0.89 | 0.00 | 0.94 | 9.49 |
time (sec) |
N/A | 0.010 | 0.066 | 0.128 | 0.478 | 0.352 | 0.000 | 0.392 | 1.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 48 | 59 | 34 | 45 | 0 | 59 | 228 |
N.S. |
1 | 1.00 | 0.67 | 0.82 | 0.47 | 0.62 | 0.00 | 0.82 | 3.17 |
time (sec) |
N/A | 0.022 | 0.032 | 0.130 | 0.485 | 0.363 | 0.000 | 0.413 | 1.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 66 | 105 | 45 | 56 | 0 | 78 | 288 |
N.S. |
1 | 1.00 | 0.60 | 0.95 | 0.41 | 0.51 | 0.00 | 0.71 | 2.62 |
time (sec) |
N/A | 0.039 | 0.040 | 0.141 | 0.475 | 0.338 | 0.000 | 0.408 | 1.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 82 | 151 | 56 | 67 | 0 | 97 | 348 |
N.S. |
1 | 1.00 | 0.55 | 1.02 | 0.38 | 0.45 | 0.00 | 0.66 | 2.35 |
time (sec) |
N/A | 0.054 | 0.051 | 0.168 | 0.470 | 0.344 | 0.000 | 0.397 | 1.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 121 | 471 | 0 | 162 | 0 | 204 | -1 |
N.S. |
1 | 1.00 | 0.70 | 2.71 | 0.00 | 0.93 | 0.00 | 1.17 | -0.01 |
time (sec) |
N/A | 0.068 | 0.056 | 0.122 | 0.000 | 0.346 | 0.000 | 0.404 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 101 | 286 | 0 | 141 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.74 | 2.10 | 0.00 | 1.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.049 | 0.038 | 0.122 | 0.000 | 0.366 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 101 | 460 | 0 | 137 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.83 | 3.80 | 0.00 | 1.13 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.053 | 0.050 | 0.124 | 0.000 | 0.359 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 97 | 501 | 0 | 138 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.92 | 4.73 | 0.00 | 1.30 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.046 | 0.048 | 0.122 | 0.000 | 0.330 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 95 | 532 | 0 | 137 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.02 | 5.72 | 0.00 | 1.47 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.041 | 0.038 | 0.122 | 0.000 | 0.354 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 34 | 29 | 15 | 42 | 0 | 33 | 396 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.43 | 1.20 | 0.00 | 0.94 | 11.31 |
time (sec) |
N/A | 0.010 | 0.034 | 0.126 | 0.478 | 0.331 | 0.000 | 0.407 | 1.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 48 | 59 | 34 | 56 | 0 | 59 | 293 |
N.S. |
1 | 1.00 | 0.67 | 0.82 | 0.47 | 0.78 | 0.00 | 0.82 | 4.07 |
time (sec) |
N/A | 0.024 | 0.035 | 0.140 | 0.471 | 0.348 | 0.000 | 0.437 | 1.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 66 | 105 | 45 | 67 | 0 | 78 | 353 |
N.S. |
1 | 1.00 | 0.60 | 0.95 | 0.41 | 0.61 | 0.00 | 0.71 | 3.21 |
time (sec) |
N/A | 0.038 | 0.037 | 0.176 | 0.476 | 0.335 | 0.000 | 0.419 | 1.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 82 | 151 | 56 | 78 | 0 | 97 | 413 |
N.S. |
1 | 1.00 | 0.55 | 1.02 | 0.38 | 0.53 | 0.00 | 0.66 | 2.79 |
time (sec) |
N/A | 0.053 | 0.054 | 0.269 | 0.467 | 0.335 | 0.000 | 0.412 | 1.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 105 | 304 | 0 | 140 | 0 | 64 | -1 |
N.S. |
1 | 1.00 | 0.72 | 2.10 | 0.00 | 0.97 | 0.00 | 0.44 | -0.01 |
time (sec) |
N/A | 0.056 | 0.064 | 0.127 | 0.000 | 0.366 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 88 | 174 | 0 | 119 | 0 | 52 | -1 |
N.S. | 1 | 1.00 | 0.82 | 1.63 | 0.00 | 1.11 | 0.00 | 0.49 | -0.01 |
time (sec) |
N/A | 0.037 | 0.050 | 0.125 | 0.000 | 0.372 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 66 | 80 | 0 | 91 | 0 | 38 | -1 |
N.S. | 1 | 1.00 | 1.05 | 1.27 | 0.00 | 1.44 | 0.00 | 0.60 | -0.02 |
time (sec) |
N/A | 0.020 | 0.040 | 0.125 | 0.000 | 0.340 | 0.000 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 33 | 24 | 0 | 57 | 0 | 23 | -1 |
N.S. | 1 | 1.00 | 1.10 | 0.80 | 0.00 | 1.90 | 0.00 | 0.77 | -0.03 |
time (sec) |
N/A | 0.009 | 0.024 | 0.125 | 0.000 | 0.363 | 0.000 | 0.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 32 | 29 | 15 | 15 | 0 | 30 | 101 |
N.S. | 1 | 1.00 | 0.97 | 0.88 | 0.45 | 0.45 | 0.00 | 0.91 | 3.06 |
time (sec) |
N/A | 0.010 | 0.030 | 0.127 | 0.474 | 0.341 | 0.000 | 0.391 | 1.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 46 | 59 | 33 | 23 | 0 | 55 | 218 |
N.S. | 1 | 1.00 | 0.64 | 0.82 | 0.46 | 0.32 | 0.00 | 0.76 | 3.03 |
time (sec) |
N/A | 0.022 | 0.042 | 0.126 | 0.464 | 0.339 | 0.000 | 0.387 | 1.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 66 | 105 | 45 | 34 | 0 | 77 | 227 |
N.S. |
1 | 1.00 | 0.60 | 0.95 | 0.41 | 0.31 | 0.00 | 0.70 | 2.06 |
time (sec) |
N/A | 0.038 | 0.067 | 0.133 | 0.475 | 0.328 | 0.000 | 0.383 | 1.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 82 | 151 | 55 | 45 | 0 | 103 | 287 |
N.S. |
1 | 1.00 | 0.55 | 1.02 | 0.37 | 0.30 | 0.00 | 0.70 | 1.94 |
time (sec) |
N/A | 0.053 | 0.072 | 0.129 | 0.472 | 0.344 | 0.000 | 0.378 | 1.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-1) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 122 | 428 | 0 | 196 | 0 | 75 | -1 |
N.S. |
1 | 1.00 | 0.73 | 2.58 | 0.00 | 1.18 | 0.00 | 0.45 | -0.01 |
time (sec) |
N/A | 0.077 | 0.161 | 0.128 | 0.000 | 0.331 | 0.000 | 0.399 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 104 | 261 | 0 | 175 | 0 | 63 | -1 |
N.S. |
1 | 1.00 | 0.81 | 2.04 | 0.00 | 1.37 | 0.00 | 0.49 | -0.01 |
time (sec) |
N/A | 0.051 | 0.066 | 0.126 | 0.000 | 0.360 | 0.000 | 0.395 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 81 | 130 | 0 | 145 | 0 | 48 | -1 |
N.S. | 1 | 1.00 | 0.94 | 1.51 | 0.00 | 1.69 | 0.00 | 0.56 | -0.01 |
time (sec) |
N/A | 0.037 | 0.098 | 0.120 | 0.000 | 0.344 | 0.000 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 55 | 42 | 0 | 119 | 0 | 39 | -1 |
N.S. | 1 | 1.00 | 1.06 | 0.81 | 0.00 | 2.29 | 0.00 | 0.75 | -0.02 |
time (sec) |
N/A | 0.018 | 0.091 | 0.120 | 0.000 | 0.355 | 0.000 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 32 | 29 | 0 | 22 | 0 | 15 | 163 |
N.S. | 1 | 1.00 | 0.97 | 0.88 | 0.00 | 0.67 | 0.00 | 0.45 | 4.94 |
time (sec) |
N/A | 0.009 | 0.027 | 0.122 | 0.000 | 0.339 | 0.000 | 0.389 | 1.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 43 | 59 | 32 | 34 | 0 | 50 | 281 |
N.S. | 1 | 1.00 | 0.63 | 0.87 | 0.47 | 0.50 | 0.00 | 0.74 | 4.13 |
time (sec) |
N/A | 0.023 | 0.034 | 0.122 | 0.474 | 0.319 | 0.000 | 0.389 | 1.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 64 | 105 | 45 | 49 | 0 | 107 | 286 |
N.S. |
1 | 1.00 | 0.58 | 0.95 | 0.41 | 0.45 | 0.00 | 0.97 | 2.60 |
time (sec) |
N/A | 0.039 | 0.043 | 0.123 | 0.493 | 0.326 | 0.000 | 0.398 | 1.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 80 | 151 | 54 | 58 | 0 | 161 | 346 |
N.S. |
1 | 1.00 | 0.54 | 1.02 | 0.36 | 0.39 | 0.00 | 1.09 | 2.34 |
time (sec) |
N/A | 0.055 | 0.047 | 0.121 | 0.473 | 0.338 | 0.000 | 0.410 | 1.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-1) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 121 | 348 | 0 | 241 | 0 | 75 | -1 |
N.S. |
1 | 1.00 | 0.79 | 2.27 | 0.00 | 1.58 | 0.00 | 0.49 | -0.01 |
time (sec) |
N/A | 0.067 | 0.081 | 0.132 | 0.000 | 0.376 | 0.000 | 0.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F(-2) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 101 | 180 | 0 | 214 | 0 | 61 | -1 |
N.S. |
1 | 1.00 | 0.91 | 1.62 | 0.00 | 1.93 | 0.00 | 0.55 | -0.01 |
time (sec) |
N/A | 0.048 | 0.060 | 0.127 | 0.000 | 0.361 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 78 | 59 | 0 | 186 | 0 | 49 | -1 |
N.S. | 1 | 1.00 | 1.04 | 0.79 | 0.00 | 2.48 | 0.00 | 0.65 | -0.01 |
time (sec) |
N/A | 0.031 | 0.044 | 0.128 | 0.000 | 0.392 | 0.000 | 0.402 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 34 | 92 | 0 | 33 | 0 | 15 | 229 |
N.S. | 1 | 1.00 | 0.97 | 2.63 | 0.00 | 0.94 | 0.00 | 0.43 | 6.54 |
time (sec) |
N/A | 0.011 | 0.036 | 0.121 | 0.000 | 0.336 | 0.000 | 0.398 | 1.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 47 | 58 | 0 | 43 | 0 | 25 | 346 |
N.S. | 1 | 1.00 | 0.66 | 0.82 | 0.00 | 0.61 | 0.00 | 0.35 | 4.87 |
time (sec) |
N/A | 0.022 | 0.029 | 0.122 | 0.000 | 0.340 | 0.000 | 0.386 | 1.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 66 | 104 | 45 | 58 | 0 | 62 | 348 |
N.S. |
1 | 1.00 | 0.62 | 0.98 | 0.42 | 0.55 | 0.00 | 0.58 | 3.28 |
time (sec) |
N/A | 0.039 | 0.041 | 0.125 | 0.470 | 0.326 | 0.000 | 0.394 | 1.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 79 | 150 | 56 | 71 | 0 | 119 | 406 |
N.S. |
1 | 1.00 | 0.54 | 1.03 | 0.38 | 0.49 | 0.00 | 0.82 | 2.78 |
time (sec) |
N/A | 0.059 | 0.049 | 0.131 | 0.476 | 0.335 | 0.000 | 0.411 | 1.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 100 | 196 | 67 | 82 | 0 | 173 | 466 |
N.S. |
1 | 1.00 | 0.54 | 1.05 | 0.36 | 0.44 | 0.00 | 0.93 | 2.51 |
time (sec) |
N/A | 0.075 | 0.049 | 0.127 | 0.466 | 0.448 | 0.000 | 0.426 | 1.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 71 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.032 | 0.111 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 146 | 654 | 139 | 374 | 0 | 332 | 546 |
N.S. | 1 | 1.00 | 0.88 | 3.96 | 0.84 | 2.27 | 0.00 | 2.01 | 3.31 |
time (sec) |
N/A | 0.098 | 0.076 | 7.020 | 0.538 | 0.358 | 0.000 | 0.394 | 1.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 106 | 492 | 101 | 255 | 0 | 226 | 418 |
N.S. | 1 | 1.00 | 0.88 | 4.07 | 0.83 | 2.11 | 0.00 | 1.87 | 3.45 |
time (sec) |
N/A | 0.053 | 0.057 | 2.541 | 0.528 | 0.365 | 0.000 | 0.390 | 1.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 71 | 315 | 68 | 168 | 0 | 140 | 304 |
N.S. | 1 | 1.00 | 0.87 | 3.84 | 0.83 | 2.05 | 0.00 | 1.71 | 3.71 |
time (sec) |
N/A | 0.031 | 0.048 | 0.970 | 0.528 | 0.354 | 0.000 | 0.392 | 1.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 41 | 175 | 42 | 91 | 0 | 76 | 205 |
N.S. | 1 | 1.00 | 0.85 | 3.65 | 0.88 | 1.90 | 0.00 | 1.58 | 4.27 |
time (sec) |
N/A | 0.014 | 0.040 | 0.399 | 0.535 | 0.363 | 0.000 | 0.395 | 1.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 21 | 39 | 51 | 28 | 121 |
N.S. | 1 | 1.00 | 1.00 | 1.05 | 1.05 | 1.95 | 2.55 | 1.40 | 6.05 |
time (sec) |
N/A | 0.005 | 0.013 | 0.374 | 0.508 | 0.387 | 0.203 | 0.400 | 1.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 60 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.014 | 0.063 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 67 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.030 | 0.057 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 67 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.047 | 0.037 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 34 | 676 | 38 | 33 | 0 | 90 | 96 |
N.S. | 1 | 1.00 | 0.92 | 18.27 | 1.03 | 0.89 | 0.00 | 2.43 | 2.59 |
time (sec) |
N/A | 0.015 | 0.038 | 0.124 | 0.264 | 0.352 | 0.000 | 0.387 | 1.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 20 | 19 | 13 | 76 | 71 | 19 |
N.S. | 1 | 1.00 | 0.87 | 0.87 | 0.83 | 0.57 | 3.30 | 3.09 | 0.83 |
time (sec) |
N/A | 0.015 | 0.017 | 0.122 | 0.291 | 0.405 | 7.947 | 0.391 | 1.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 20 | 19 | 13 | 160 | 71 | 19 |
N.S. | 1 | 1.00 | 0.87 | 0.87 | 0.83 | 0.57 | 6.96 | 3.09 | 0.83 |
time (sec) |
N/A | 0.006 | 0.012 | 0.075 | 0.301 | 0.601 | 4.155 | 0.378 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 15 | 16 | 10 | 80 | 69 | 16 |
N.S. | 1 | 1.00 | 1.12 | 0.94 | 1.00 | 0.62 | 5.00 | 4.31 | 1.00 |
time (sec) |
N/A | 0.002 | 0.005 | 0.100 | 0.305 | 0.512 | 2.225 | 0.398 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | C | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 23 | 34 | 8 | 0 | 15 | 59 |
N.S. | 1 | 1.00 | 0.90 | 1.10 | 1.62 | 0.38 | 0.00 | 0.71 | 2.81 |
time (sec) |
N/A | 0.022 | 0.013 | 0.079 | 0.256 | 0.351 | 0.000 | 0.410 | 1.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 18 | 18 | 17 | 13 | 68 | 70 | 17 |
N.S. | 1 | 1.00 | 1.06 | 1.06 | 1.00 | 0.76 | 4.00 | 4.12 | 1.00 |
time (sec) |
N/A | 0.006 | 0.013 | 0.091 | 0.297 | 0.406 | 3.958 | 0.405 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 18 | 20 | 19 | 11 | 80 | 71 | 16 |
N.S. | 1 | 1.00 | 0.78 | 0.87 | 0.83 | 0.48 | 3.48 | 3.09 | 0.70 |
time (sec) |
N/A | 0.006 | 0.011 | 0.089 | 0.300 | 0.354 | 7.727 | 0.397 | 1.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 47 | 21 | 33 | 58 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.74 | 0.78 | 1.22 | 2.15 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A | 0.025 | 0.014 | 0.224 | 0.291 | 0.446 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 81 | 479 | 56 | 88 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.59 | 9.39 | 1.10 | 1.73 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.045 | 0.012 | 0.170 | 0.302 | 0.416 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 109 | 501 | 78 | 118 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.42 | 6.51 | 1.01 | 1.53 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.063 | 0.024 | 0.171 | 0.305 | 0.425 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 307 | 271 | 5366 | 281 | 900 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.88 | 17.48 | 0.92 | 2.93 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.327 | 8.594 | 9.969 | 0.477 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 203 | 5062 | 215 | 746 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.88 | 21.91 | 0.93 | 3.23 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.264 | 6.879 | 1.330 | 0.483 | 0.454 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 366 | 361 | 142 | 552 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.44 | 2.41 | 0.95 | 3.68 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.160 | 4.844 | 0.914 | 0.478 | 0.400 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A | 0.111 | 12.321 | 0.090 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 144 | 1769 | 149 | 451 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.93 | 11.41 | 0.96 | 2.91 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.198 | 3.598 | 1.285 | 0.733 | 0.408 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 118 | 1710 | 125 | 382 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.92 | 13.36 | 0.98 | 2.98 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.179 | 4.037 | 1.041 | 0.718 | 0.387 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 91 | 1627 | 101 | 323 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 16.11 | 1.00 | 3.20 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.156 | 3.612 | 0.880 | 0.723 | 0.452 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 201 | 265 | 72 | 239 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.91 | 3.84 | 1.04 | 3.46 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.096 | 3.531 | 0.492 | 0.756 | 0.452 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.059 | 3.585 | 0.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 144 | 1773 | 146 | 424 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.86 | 10.55 | 0.87 | 2.52 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.212 | 3.169 | 1.282 | 0.718 | 0.372 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 119 | 1716 | 123 | 360 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.86 | 12.35 | 0.88 | 2.59 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.182 | 4.134 | 1.103 | 0.705 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 93 | 1635 | 100 | 306 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.85 | 14.86 | 0.91 | 2.78 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.156 | 4.081 | 0.941 | 0.700 | 0.352 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 200 | 299 | 73 | 228 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.63 | 3.93 | 0.96 | 3.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.098 | 3.490 | 0.510 | 0.706 | 0.385 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.049 | 3.759 | 0.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 303 | 265 | 5294 | 277 | 880 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.87 | 17.47 | 0.91 | 2.90 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.322 | 7.640 | 10.248 | 0.488 | 0.511 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 199 | 4990 | 213 | 730 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.87 | 21.79 | 0.93 | 3.19 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.267 | 6.169 | 1.447 | 0.483 | 0.440 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 369 | 361 | 142 | 540 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.46 | 2.41 | 0.95 | 3.60 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.162 | 3.332 | 1.018 | 0.487 | 0.479 | 0.000 | 0.000 | 0.000 |