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 | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 74 | 87 | 188 | 78 | 88 | 88 | 119 | 119 |
N.S. |
1 | 1.02 | 0.91 | 1.07 | 2.32 | 0.96 | 1.09 | 1.09 | 1.47 | 1.47 |
time (sec) |
N/A | 0.463 | 0.013 | 0.575 | 0.043 | 0.084 | 0.119 | 0.118 | 0.170 | 25.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 64 | 57 | 67 | 125 | 60 | 68 | 68 | 90 | 88 |
N.S. |
1 | 1.05 | 0.93 | 1.10 | 2.05 | 0.98 | 1.11 | 1.11 | 1.48 | 1.44 |
time (sec) |
N/A | 0.381 | 0.008 | 0.501 | 0.036 | 0.074 | 0.105 | 0.119 | 0.182 | 25.635 |
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 | 45 | 40 | 47 | 71 | 42 | 46 | 48 | 61 | 57 |
N.S. |
1 | 1.10 | 0.98 | 1.15 | 1.73 | 1.02 | 1.12 | 1.17 | 1.49 | 1.39 |
time (sec) |
N/A | 0.328 | 0.007 | 0.356 | 0.032 | 0.088 | 0.088 | 0.119 | 0.167 | 25.575 |
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 | 26 | 21 | 22 | 31 | 25 | 26 | 31 | 32 | 25 |
N.S. |
1 | 1.24 | 1.00 | 1.05 | 1.48 | 1.19 | 1.24 | 1.48 | 1.52 | 1.19 |
time (sec) |
N/A | 0.277 | 0.008 | 0.229 | 0.029 | 0.070 | 0.066 | 0.117 | 0.175 | 0.064 |
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 | 15 | 15 | 15 | 22 | 17 | 16 | 12 | 16 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 1.13 | 1.07 | 0.80 | 1.07 | 1.13 | 1.00 |
time (sec) |
N/A | 0.278 | 0.012 | 0.681 | 0.088 | 0.067 | 0.255 | 0.126 | 0.179 | 25.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 34 | 36 | 43 | 20 | 47 | 29 | 37 | 66 | 36 |
N.S. |
1 | 0.94 | 1.00 | 1.19 | 0.56 | 1.31 | 0.81 | 1.03 | 1.83 | 1.00 |
time (sec) |
N/A | 0.321 | 0.017 | 0.700 | 0.102 | 0.076 | 0.262 | 0.119 | 0.179 | 25.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 58 | 47 | 64 | 21 | 67 | 48 | 58 | 13 | 64 |
N.S. |
1 | 0.92 | 0.75 | 1.02 | 0.33 | 1.06 | 0.76 | 0.92 | 0.21 | 1.02 |
time (sec) |
N/A | 0.377 | 0.021 | 0.711 | 0.101 | 0.068 | 0.271 | 0.120 | 0.176 | 25.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 82 | 57 | 87 | 20 | 90 | 71 | 78 | 13 | 67 |
N.S. |
1 | 0.96 | 0.67 | 1.02 | 0.24 | 1.06 | 0.84 | 0.92 | 0.15 | 0.79 |
time (sec) |
N/A | 0.442 | 0.026 | 0.720 | 0.086 | 0.076 | 0.288 | 0.122 | 0.182 | 25.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 94 | 75 | 0 | 78 | 0 | 0 | 0 | 159 | 96 |
N.S. |
1 | 0.96 | 0.77 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 | 1.62 | 0.98 |
time (sec) |
N/A | 0.566 | 0.018 | 0.000 | 0.029 | 0.000 | 0.000 | 0.000 | 0.182 | 25.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 71 | 63 | 0 | 65 | 0 | 105 | 0 | 110 | 82 |
N.S. |
1 | 0.96 | 0.85 | 0.00 | 0.88 | 0.00 | 1.42 | 0.00 | 1.49 | 1.11 |
time (sec) |
N/A | 0.505 | 0.014 | 0.000 | 0.030 | 0.000 | 53.455 | 0.000 | 0.192 | 25.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | F(-2) | B | C | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 48 | 50 | 0 | 49 | 0 | 90 | 52 | 56 | 46 |
N.S. |
1 | 0.96 | 1.00 | 0.00 | 0.98 | 0.00 | 1.80 | 1.04 | 1.12 | 0.92 |
time (sec) |
N/A | 0.431 | 0.012 | 0.000 | 0.031 | 0.000 | 0.866 | 0.126 | 0.208 | 25.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | F(-2) | B | C | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 0 | 25 | 0 | 63 | 25 | 24 | 45 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.00 | 0.00 | 2.52 | 1.00 | 0.96 | 1.80 |
time (sec) |
N/A | 0.381 | 0.005 | 0.000 | 0.037 | 0.000 | 0.903 | 0.130 | 0.274 | 25.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 47 | 58 | 0 | 45 | 0 | 92 | 0 | 24 | 67 |
N.S. |
1 | 0.96 | 1.18 | 0.00 | 0.92 | 0.00 | 1.88 | 0.00 | 0.49 | 1.37 |
time (sec) |
N/A | 0.442 | 0.115 | 0.000 | 0.116 | 0.000 | 12.117 | 0.000 | 0.178 | 25.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 73 | 72 | 0 | 45 | 0 | 0 | 0 | 24 | 113 |
N.S. |
1 | 0.95 | 0.94 | 0.00 | 0.58 | 0.00 | 0.00 | 0.00 | 0.31 | 1.47 |
time (sec) |
N/A | 0.502 | 0.094 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 | 0.202 | 25.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 99 | 85 | 0 | 45 | 0 | 0 | 0 | 24 | 140 |
N.S. |
1 | 0.98 | 0.84 | 0.00 | 0.45 | 0.00 | 0.00 | 0.00 | 0.24 | 1.39 |
time (sec) |
N/A | 0.568 | 0.104 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 | 0.180 | 25.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | C | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 41 | 45 | 0 | 53 | 27 | 54 | 0 | 59 | 45 |
N.S. |
1 | 0.91 | 1.00 | 0.00 | 1.18 | 0.60 | 1.20 | 0.00 | 1.31 | 1.00 |
time (sec) |
N/A | 0.355 | 0.040 | 0.000 | 0.092 | 0.087 | 2.931 | 0.000 | 0.182 | 25.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 119 | 112 | 525 | 500 | 614 | 495 | 758 | 450 | 275 |
N.S. |
1 | 0.91 | 0.85 | 4.01 | 3.82 | 4.69 | 3.78 | 5.79 | 3.44 | 2.10 |
time (sec) |
N/A | 0.530 | 0.063 | 3.054 | 0.052 | 0.082 | 0.943 | 0.133 | 0.173 | 25.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 92 | 85 | 322 | 282 | 324 | 294 | 399 | 265 | 172 |
N.S. |
1 | 0.93 | 0.86 | 3.25 | 2.85 | 3.27 | 2.97 | 4.03 | 2.68 | 1.74 |
time (sec) |
N/A | 0.437 | 0.016 | 1.387 | 0.061 | 0.095 | 0.516 | 0.121 | 0.179 | 25.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 59 | 111 | 131 | 140 | 146 | 174 | 129 | 94 |
N.S. |
1 | 1.00 | 0.91 | 1.71 | 2.02 | 2.15 | 2.25 | 2.68 | 1.98 | 1.45 |
time (sec) |
N/A | 0.350 | 0.012 | 0.746 | 0.041 | 0.082 | 0.264 | 0.122 | 0.237 | 25.886 |
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 | 29 | 29 | 29 | 36 | 40 | 40 | 41 | 45 | 42 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.38 | 1.38 | 1.41 | 1.55 | 1.45 | 1.21 |
time (sec) |
N/A | 0.271 | 0.009 | 0.484 | 0.030 | 0.087 | 0.150 | 0.124 | 0.209 | 25.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 311 | 0 | 46 | 0 | 49 | 75 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.94 | 0.00 | 0.73 | 0.00 | 0.78 | 1.19 | 0.00 |
time (sec) |
N/A | 0.431 | 0.123 | 1.719 | 0.000 | 0.101 | 0.000 | 0.121 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 94 | 123 | 456 | 0 | 117 | 0 | 286 | 232 | 0 |
N.S. |
1 | 0.98 | 1.28 | 4.75 | 0.00 | 1.22 | 0.00 | 2.98 | 2.42 | 0.00 |
time (sec) |
N/A | 0.500 | 0.067 | 1.907 | 0.000 | 0.079 | 0.000 | 0.132 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 136 | 144 | 734 | 0 | 263 | 0 | 1218 | 483 | 0 |
N.S. |
1 | 1.01 | 1.07 | 5.44 | 0.00 | 1.95 | 0.00 | 9.02 | 3.58 | 0.00 |
time (sec) |
N/A | 0.604 | 0.099 | 2.386 | 0.000 | 0.088 | 0.000 | 0.142 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 171 | 152 | 0 | 0 | 0 | 0 | 0 | 699 | 0 |
N.S. |
1 | 0.96 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.91 | 0.00 |
time (sec) |
N/A | 0.773 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 140 | 127 | 0 | 0 | 0 | 0 | 0 | 437 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.06 | 0.00 |
time (sec) |
N/A | 0.686 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 109 | 106 | 0 | 0 | 0 | 0 | 0 | 344 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.10 | 0.00 |
time (sec) |
N/A | 0.568 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.501 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 139 | 0 | 0 | 0 | 0 | 0 | 268 | 0 |
N.S. |
1 | 0.98 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
time (sec) |
N/A | 0.597 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 158 | 163 | 0 | 0 | 0 | 0 | 0 | 543 | 0 |
N.S. |
1 | 1.01 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.48 | 0.00 |
time (sec) |
N/A | 0.721 | 0.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 202 | 203 | 0 | 0 | 0 | 0 | 0 | 901 | 0 |
N.S. |
1 | 1.05 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.69 | 0.00 |
time (sec) |
N/A | 0.843 | 0.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 103 | 0 | 0 | 59 | 0 | 0 | 645 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.57 | 0.00 | 0.00 | 6.26 | 0.00 |
time (sec) |
N/A | 0.448 | 0.123 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 0 | 59 | 0 | 0 | 0 | 615 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.00 | 6.99 | 0.00 |
time (sec) |
N/A | 0.431 | 0.090 | 0.000 | 0.058 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 26 | 0 | 22 | 0 | 22 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 0.00 | 1.10 | 0.00 | 1.10 | 1.90 | 1.00 |
time (sec) |
N/A | 0.399 | 0.036 | 4.572 | 0.000 | 0.076 | 0.000 | 0.145 | 0.180 | 26.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 0 | 0 | 27 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.64 | 0.00 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.483 | 0.157 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 160 | 315 | 589 | 393 | 471 | 568 | 1209 | 510 | 526 |
N.S. |
1 | 0.90 | 1.77 | 3.31 | 2.21 | 2.65 | 3.19 | 6.79 | 2.87 | 2.96 |
time (sec) |
N/A | 0.531 | 0.337 | 2.693 | 0.040 | 0.080 | 2.320 | 0.134 | 0.219 | 25.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 136 | 226 | 428 | 284 | 340 | 410 | 770 | 362 | 352 |
N.S. |
1 | 0.91 | 1.52 | 2.87 | 1.91 | 2.28 | 2.75 | 5.17 | 2.43 | 2.36 |
time (sec) |
N/A | 0.498 | 0.221 | 1.705 | 0.041 | 0.097 | 1.246 | 0.146 | 0.215 | 25.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 112 | 150 | 265 | 187 | 221 | 252 | 424 | 233 | 212 |
N.S. |
1 | 0.93 | 1.25 | 2.21 | 1.56 | 1.84 | 2.10 | 3.53 | 1.94 | 1.77 |
time (sec) |
N/A | 0.443 | 0.154 | 1.224 | 0.037 | 0.089 | 0.661 | 0.123 | 0.211 | 25.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 88 | 95 | 98 | 102 | 119 | 134 | 183 | 123 | 104 |
N.S. |
1 | 0.97 | 1.04 | 1.08 | 1.12 | 1.31 | 1.47 | 2.01 | 1.35 | 1.14 |
time (sec) |
N/A | 0.422 | 0.054 | 0.835 | 0.034 | 0.094 | 0.391 | 0.123 | 0.234 | 25.854 |
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 | 29 | 29 | 29 | 36 | 40 | 40 | 41 | 45 | 42 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.38 | 1.38 | 1.41 | 1.55 | 1.45 | 1.21 |
time (sec) |
N/A | 0.290 | 0.009 | 0.131 | 0.034 | 0.093 | 0.137 | 0.125 | 0.229 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 62 | 217 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 0.98 | 3.44 | 0.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.471 | 0.019 | 1.396 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 70 | 57 | 127 | 85 | 95 | 333 | 88 | 135 | 84 |
N.S. |
1 | 0.95 | 0.77 | 1.72 | 1.15 | 1.28 | 4.50 | 1.19 | 1.82 | 1.14 |
time (sec) |
N/A | 0.340 | 0.075 | 1.526 | 0.035 | 0.091 | 2.942 | 0.119 | 0.209 | 26.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 95 | 83 | 283 | 167 | 274 | 1945 | 201 | 478 | 173 |
N.S. |
1 | 0.85 | 0.74 | 2.53 | 1.49 | 2.45 | 17.37 | 1.79 | 4.27 | 1.54 |
time (sec) |
N/A | 0.447 | 0.106 | 2.037 | 0.038 | 0.107 | 13.015 | 0.120 | 0.221 | 26.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 121 | 110 | 455 | 301 | 507 | 0 | 401 | 979 | 283 |
N.S. |
1 | 0.86 | 0.78 | 3.23 | 2.13 | 3.60 | 0.00 | 2.84 | 6.94 | 2.01 |
time (sec) |
N/A | 0.482 | 0.140 | 3.089 | 0.044 | 0.093 | 0.000 | 0.123 | 0.241 | 26.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 312 | 360 | 1343 | 827 | 1190 | 1241 | 2345 | 1120 | 1051 |
N.S. |
1 | 0.85 | 0.99 | 3.68 | 2.27 | 3.26 | 3.40 | 6.42 | 3.07 | 2.88 |
time (sec) |
N/A | 1.007 | 0.278 | 3.805 | 0.071 | 0.141 | 2.413 | 0.157 | 0.221 | 25.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 252 | 247 | 850 | 554 | 760 | 774 | 1315 | 705 | 591 |
N.S. |
1 | 0.88 | 0.86 | 2.96 | 1.93 | 2.65 | 2.70 | 4.58 | 2.46 | 2.06 |
time (sec) |
N/A | 0.909 | 0.158 | 2.776 | 0.049 | 0.116 | 1.294 | 0.137 | 0.214 | 25.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 144 | 459 | 314 | 401 | 394 | 583 | 363 | 268 |
N.S. |
1 | 1.00 | 0.77 | 2.47 | 1.69 | 2.16 | 2.12 | 3.13 | 1.95 | 1.44 |
time (sec) |
N/A | 0.679 | 0.084 | 1.512 | 0.044 | 0.081 | 0.685 | 0.133 | 0.195 | 25.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 59 | 111 | 131 | 140 | 146 | 174 | 129 | 94 |
N.S. |
1 | 1.00 | 0.91 | 1.71 | 2.02 | 2.15 | 2.25 | 2.68 | 1.98 | 1.45 |
time (sec) |
N/A | 0.366 | 0.010 | 0.283 | 0.046 | 0.078 | 0.274 | 0.125 | 0.199 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 106 | 194 | 737 | 0 | 0 | 0 | 0 | 219 | 0 |
N.S. |
1 | 0.95 | 1.75 | 6.64 | 0.00 | 0.00 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.775 | 0.178 | 2.813 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 118 | 126 | 537 | 0 | 0 | 0 | 0 | 789 | 0 |
N.S. |
1 | 0.89 | 0.95 | 4.07 | 0.00 | 0.00 | 0.00 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 0.660 | 0.092 | 1.850 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 230 | 204 | 661 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 1.01 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.261 | 0.194 | 2.579 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 380 | 302 | 755 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.95 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.095 | 0.374 | 4.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 598 | 598 | 475 | 2719 | 1687 | 2802 | 2594 | 5182 | 2328 | 2133 |
N.S. |
1 | 1.00 | 0.79 | 4.55 | 2.82 | 4.69 | 4.34 | 8.67 | 3.89 | 3.57 |
time (sec) |
N/A | 1.679 | 0.454 | 8.865 | 0.098 | 0.139 | 4.517 | 0.198 | 0.265 | 26.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 432 | 432 | 333 | 1733 | 1140 | 1771 | 1578 | 2932 | 1452 | 1157 |
N.S. |
1 | 1.00 | 0.77 | 4.01 | 2.64 | 4.10 | 3.65 | 6.79 | 3.36 | 2.68 |
time (sec) |
N/A | 1.287 | 0.242 | 5.799 | 0.079 | 0.120 | 2.488 | 0.174 | 0.196 | 26.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 265 | 201 | 906 | 662 | 923 | 836 | 1321 | 743 | 511 |
N.S. |
1 | 1.00 | 0.76 | 3.42 | 2.50 | 3.48 | 3.15 | 4.98 | 2.80 | 1.93 |
time (sec) |
N/A | 0.855 | 0.131 | 3.388 | 0.060 | 0.097 | 1.285 | 0.140 | 0.192 | 25.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 92 | 85 | 322 | 282 | 324 | 294 | 399 | 265 | 172 |
N.S. |
1 | 0.93 | 0.86 | 3.25 | 2.85 | 3.27 | 2.97 | 4.03 | 2.68 | 1.74 |
time (sec) |
N/A | 0.440 | 0.017 | 0.522 | 0.041 | 0.110 | 0.501 | 0.131 | 0.188 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 149 | 335 | 1396 | 0 | 0 | 0 | 0 | 331 | 0 |
N.S. |
1 | 0.94 | 2.12 | 8.84 | 0.00 | 0.00 | 0.00 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.973 | 0.309 | 4.466 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 161 | 410 | 1268 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 2.16 | 6.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.007 | 0.425 | 4.696 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 325 | 620 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.367 | 0.815 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 564 | 584 | 843 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.369 | 1.183 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 340 | 258 | 1493 | 1163 | 1756 | 1372 | 2488 | 1260 | 823 |
N.S. |
1 | 1.00 | 0.76 | 4.39 | 3.42 | 5.16 | 4.04 | 7.32 | 3.71 | 2.42 |
time (sec) |
N/A | 1.007 | 0.238 | 6.745 | 0.095 | 0.099 | 2.365 | 0.156 | 0.191 | 25.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 119 | 112 | 525 | 500 | 614 | 495 | 758 | 450 | 275 |
N.S. |
1 | 0.91 | 0.85 | 4.01 | 3.82 | 4.69 | 3.78 | 5.79 | 3.44 | 2.10 |
time (sec) |
N/A | 0.523 | 0.026 | 1.189 | 0.054 | 0.092 | 0.937 | 0.132 | 0.179 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 191 | 503 | 2172 | 0 | 0 | 0 | 0 | 443 | 0 |
N.S. |
1 | 0.93 | 2.45 | 10.60 | 0.00 | 0.00 | 0.00 | 0.00 | 2.16 | 0.00 |
time (sec) |
N/A | 1.163 | 0.302 | 7.090 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 204 | 531 | 2156 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 2.14 | 8.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.233 | 0.816 | 7.704 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 24 | 19 | 20 | 23 | 22 | 24 | 23 | 26 | 23 |
N.S. |
1 | 1.26 | 1.00 | 1.05 | 1.21 | 1.16 | 1.26 | 1.21 | 1.37 | 1.21 |
time (sec) |
N/A | 0.277 | 0.006 | 0.219 | 0.027 | 0.069 | 0.063 | 0.114 | 0.247 | 0.066 |
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 | 41 | 36 | 40 | 27 | 36 | 42 | 44 | 49 | 48 |
N.S. |
1 | 1.11 | 0.97 | 1.08 | 0.73 | 0.97 | 1.14 | 1.19 | 1.32 | 1.30 |
time (sec) |
N/A | 0.333 | 0.004 | 0.365 | 0.027 | 0.070 | 0.082 | 0.119 | 0.253 | 25.535 |
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 | 55 | 58 | 51 | 55 | 37 | 51 | 63 | 62 | 72 | 73 |
N.S. |
1 | 1.05 | 0.93 | 1.00 | 0.67 | 0.93 | 1.15 | 1.13 | 1.31 | 1.33 |
time (sec) |
N/A | 0.376 | 0.009 | 0.430 | 0.032 | 0.106 | 0.098 | 0.120 | 0.204 | 25.394 |
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 | 25 | 32 | 25 | 28 | 34 | 30 | 36 | 34 | 50 | 31 |
N.S. |
1 | 1.28 | 1.00 | 1.12 | 1.36 | 1.20 | 1.44 | 1.36 | 2.00 | 1.24 |
time (sec) |
N/A | 0.325 | 0.010 | 0.239 | 0.032 | 0.066 | 0.098 | 0.121 | 0.186 | 0.078 |
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 | 49 | 53 | 48 | 52 | 38 | 48 | 63 | 65 | 94 | 94 |
N.S. |
1 | 1.08 | 0.98 | 1.06 | 0.78 | 0.98 | 1.29 | 1.33 | 1.92 | 1.92 |
time (sec) |
N/A | 0.379 | 0.010 | 0.404 | 0.037 | 0.083 | 0.131 | 0.123 | 0.229 | 26.287 |
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 | 73 | 74 | 67 | 71 | 51 | 67 | 95 | 91 | 138 | 138 |
N.S. |
1 | 1.01 | 0.92 | 0.97 | 0.70 | 0.92 | 1.30 | 1.25 | 1.89 | 1.89 |
time (sec) |
N/A | 0.425 | 0.012 | 0.491 | 0.031 | 0.093 | 0.154 | 0.118 | 0.174 | 26.124 |
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 | 24 | 29 | 24 | 32 | 35 | 32 | 36 | 39 | 35 | 29 |
N.S. |
1 | 1.21 | 1.00 | 1.33 | 1.46 | 1.33 | 1.50 | 1.62 | 1.46 | 1.21 |
time (sec) |
N/A | 0.293 | 0.010 | 0.477 | 0.029 | 0.081 | 0.135 | 0.120 | 0.192 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 54 | 102 | 27 | 0 | 0 | 122 | 23 |
N.S. |
1 | 1.00 | 1.00 | 2.25 | 4.25 | 1.12 | 0.00 | 0.00 | 5.08 | 0.96 |
time (sec) |
N/A | 0.340 | 0.012 | 2.957 | 0.042 | 0.089 | 0.000 | 0.000 | 0.197 | 25.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 0 | 14 | 17 | 0 | 39 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.00 | 0.93 | 1.13 | 0.00 | 2.60 | 1.00 |
time (sec) |
N/A | 0.314 | 0.006 | 0.503 | 0.000 | 0.079 | 2.920 | 0.000 | 0.178 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 33 | 20 | 0 | 87 | 0 | 33 | 18 |
N.S. |
1 | 1.00 | 1.00 | 2.06 | 1.25 | 0.00 | 5.44 | 0.00 | 2.06 | 1.12 |
time (sec) |
N/A | 0.310 | 0.004 | 0.302 | 0.032 | 0.000 | 1.439 | 0.000 | 0.188 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 33 | 20 | 0 | 87 | 0 | 33 | 18 |
N.S. |
1 | 1.00 | 1.00 | 2.06 | 1.25 | 0.00 | 5.44 | 0.00 | 2.06 | 1.12 |
time (sec) |
N/A | 0.304 | 0.004 | 0.294 | 0.028 | 0.000 | 1.441 | 0.000 | 0.190 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 9 | 19 | 7 | 10 | 0 | 29 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 2.38 | 0.88 | 1.25 | 0.00 | 3.62 | 2.25 |
time (sec) |
N/A | 0.247 | 0.004 | 0.299 | 0.027 | 0.073 | 1.294 | 0.000 | 0.190 | 0.029 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.245 | 0.004 | 0.379 | 0.034 | 0.072 | 0.034 | 0.124 | 0.182 | 25.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 19 | 0 | 60 | 0 | 33 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.95 | 0.00 | 3.00 | 0.00 | 1.65 | 0.80 |
time (sec) |
N/A | 0.317 | 0.005 | 0.298 | 0.029 | 0.000 | 1.564 | 0.000 | 0.195 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 19 | 20 | 0 | 102 | 0 | 33 | 18 |
N.S. |
1 | 1.00 | 1.08 | 0.76 | 0.80 | 0.00 | 4.08 | 0.00 | 1.32 | 0.72 |
time (sec) |
N/A | 0.326 | 0.005 | 0.298 | 0.034 | 0.000 | 1.733 | 0.000 | 0.178 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 22 | 40 | 27 | 0 | 94 | 0 | 39 | 25 |
N.S. |
1 | 1.00 | 1.05 | 1.90 | 1.29 | 0.00 | 4.48 | 0.00 | 1.86 | 1.19 |
time (sec) |
N/A | 0.316 | 0.005 | 0.457 | 0.059 | 0.000 | 1.898 | 0.000 | 0.180 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 22 | 40 | 27 | 0 | 94 | 0 | 39 | 25 |
N.S. |
1 | 1.00 | 1.05 | 1.90 | 1.29 | 0.00 | 4.48 | 0.00 | 1.86 | 1.19 |
time (sec) |
N/A | 0.313 | 0.005 | 0.467 | 0.059 | 0.000 | 1.930 | 0.000 | 0.186 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 26 | 13 | 15 | 0 | 36 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.86 | 0.93 | 1.07 | 0.00 | 2.57 | 1.00 |
time (sec) |
N/A | 0.311 | 0.004 | 0.451 | 0.078 | 0.074 | 1.797 | 0.000 | 0.184 | 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 | 17 | 17 | 16 | 15 | 15 | 16 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.88 | 0.88 | 0.94 | 0.82 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.258 | 0.004 | 0.309 | 0.027 | 0.079 | 0.045 | 0.118 | 0.202 | 25.603 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 27 | 24 | 26 | 0 | 66 | 0 | 39 | 23 |
N.S. |
1 | 1.00 | 1.04 | 0.92 | 1.00 | 0.00 | 2.54 | 0.00 | 1.50 | 0.88 |
time (sec) |
N/A | 0.332 | 0.005 | 0.456 | 0.060 | 0.000 | 2.510 | 0.000 | 0.234 | 25.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 34 | 26 | 27 | 0 | 109 | 0 | 39 | 25 |
N.S. |
1 | 1.00 | 1.10 | 0.84 | 0.87 | 0.00 | 3.52 | 0.00 | 1.26 | 0.81 |
time (sec) |
N/A | 0.324 | 0.005 | 0.460 | 0.069 | 0.000 | 2.536 | 0.000 | 0.226 | 25.525 |
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 | 187 | 164 | 163 | 172 | 131 | 179 | 173 | 342 | 149 | 116 |
N.S. |
1 | 0.88 | 0.87 | 0.92 | 0.70 | 0.96 | 0.93 | 1.83 | 0.80 | 0.62 |
time (sec) |
N/A | 0.648 | 0.060 | 1.082 | 0.038 | 0.075 | 0.787 | 0.127 | 0.192 | 26.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 186 | 172 | 483 | 150 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.05 | 0.97 | 2.73 | 0.85 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 1.322 | 0.097 | 0.937 | 0.036 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 260 | 261 | 215 | 341 | 269 | 626 | 238 | 172 |
N.S. |
1 | 1.00 | 0.91 | 0.92 | 0.75 | 1.20 | 0.94 | 2.20 | 0.84 | 0.60 |
time (sec) |
N/A | 0.878 | 0.084 | 1.974 | 0.046 | 0.075 | 1.391 | 0.128 | 0.194 | 26.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 266 | 9346 | 0 | 305 | 0 | 582 | 396 | 0 |
N.S. |
1 | 1.00 | 0.89 | 31.26 | 0.00 | 1.02 | 0.00 | 1.95 | 1.32 | 0.00 |
time (sec) |
N/A | 1.351 | 1.010 | 3.338 | 0.000 | 0.075 | 0.000 | 0.153 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 219 | 197 | 4963 | 0 | 192 | 0 | 337 | 285 | 0 |
N.S. |
1 | 1.00 | 0.90 | 22.66 | 0.00 | 0.88 | 0.00 | 1.54 | 1.30 | 0.00 |
time (sec) |
N/A | 0.964 | 0.272 | 2.579 | 0.000 | 0.093 | 0.000 | 0.135 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 126 | 937 | 0 | 105 | 0 | 159 | 174 | 0 |
N.S. |
1 | 1.00 | 0.91 | 6.74 | 0.00 | 0.76 | 0.00 | 1.14 | 1.25 | 0.00 |
time (sec) |
N/A | 0.686 | 0.109 | 1.973 | 0.000 | 0.088 | 0.000 | 0.129 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 311 | 0 | 46 | 0 | 49 | 75 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.94 | 0.00 | 0.73 | 0.00 | 0.78 | 1.19 | 0.00 |
time (sec) |
N/A | 0.415 | 0.017 | 0.208 | 0.000 | 0.065 | 0.000 | 0.126 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 31 | 20 | 26 | 211 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.29 | 0.83 | 1.08 | 8.79 | 1.08 |
time (sec) |
N/A | 0.319 | 0.267 | 0.086 | 0.112 | 0.101 | 1.184 | 0.114 | 0.193 | 25.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 55 | 22 | 26 | 73 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 2.29 | 0.92 | 1.08 | 3.04 | 1.08 |
time (sec) |
N/A | 0.328 | 0.571 | 0.030 | 0.111 | 0.080 | 2.490 | 0.113 | 0.182 | 25.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 585 | 1674 | 9517 | 0 | 681 | 0 | 3473 | 1465 | 0 |
N.S. |
1 | 1.73 | 4.94 | 28.07 | 0.00 | 2.01 | 0.00 | 10.24 | 4.32 | 0.00 |
time (sec) |
N/A | 2.133 | 0.801 | 3.336 | 0.000 | 0.109 | 0.000 | 0.206 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 425 | 1015 | 5123 | 0 | 433 | 0 | 2031 | 1045 | 0 |
N.S. |
1 | 1.64 | 3.92 | 19.78 | 0.00 | 1.67 | 0.00 | 7.84 | 4.03 | 0.00 |
time (sec) |
N/A | 1.532 | 0.407 | 2.771 | 0.000 | 0.082 | 0.000 | 0.170 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 257 | 208 | 2300 | 0 | 239 | 0 | 973 | 627 | 0 |
N.S. |
1 | 1.45 | 1.18 | 12.99 | 0.00 | 1.35 | 0.00 | 5.50 | 3.54 | 0.00 |
time (sec) |
N/A | 1.240 | 0.227 | 2.142 | 0.000 | 0.076 | 0.000 | 0.149 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 94 | 123 | 456 | 0 | 117 | 0 | 286 | 232 | 0 |
N.S. |
1 | 0.98 | 1.28 | 4.75 | 0.00 | 1.22 | 0.00 | 2.98 | 2.42 | 0.00 |
time (sec) |
N/A | 0.490 | 0.049 | 0.422 | 0.000 | 0.080 | 0.000 | 0.125 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 188 | 63 | 22 | 26 | 805 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 7.83 | 2.62 | 0.92 | 1.08 | 33.54 | 1.08 |
time (sec) |
N/A | 0.313 | 0.374 | 0.031 | 0.123 | 0.076 | 2.904 | 0.119 | 0.229 | 25.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 289 | 104 | 24 | 26 | 145 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 12.04 | 4.33 | 1.00 | 1.08 | 6.04 | 1.08 |
time (sec) |
N/A | 0.318 | 3.460 | 0.063 | 0.131 | 0.071 | 11.902 | 0.128 | 0.259 | 25.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 753 | 351 | 6505 | 0 | 1090 | 0 | 8422 | 0 | 0 |
N.S. |
1 | 2.15 | 1.00 | 18.53 | 0.00 | 3.11 | 0.00 | 23.99 | 0.00 | 0.00 |
time (sec) |
N/A | 3.083 | 1.309 | 3.029 | 0.000 | 0.121 | 0.000 | 0.244 | 0.252 | 0.000 |