Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 37 | 26 | 0 | 39 | 32 | 27 | 23 | 39 |
N.S. |
1 | 1.00 | 1.09 | 0.76 | 0.00 | 1.15 | 0.94 | 0.79 | 0.68 | 1.15 |
time (sec) |
N/A | 0.307 | 0.103 | 0.051 | 0.000 | 0.272 | 0.245 | 0.144 | 0.180 | 22.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 78 | 50 | 41 | 0 | 49 | 48 | 43 | 43 | 27 |
N.S. |
1 | 1.26 | 0.81 | 0.66 | 0.00 | 0.79 | 0.77 | 0.69 | 0.69 | 0.44 |
time (sec) |
N/A | 0.363 | 0.138 | 0.024 | 0.000 | 0.307 | 0.264 | 0.147 | 0.174 | 23.640 |
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 | 19 | 18 | 14 | 13 | 16 | 17 | 16 | 12 | 13 |
N.S. |
1 | 1.00 | 0.95 | 0.74 | 0.68 | 0.84 | 0.89 | 0.84 | 0.63 | 0.68 |
time (sec) |
N/A | 0.263 | 0.018 | 0.042 | 0.030 | 0.080 | 0.084 | 0.152 | 0.177 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 66 | 52 | 50 | 67 | 61 | 100 | 55 | 53 | 162 |
N.S. |
1 | 1.22 | 0.96 | 0.93 | 1.24 | 1.13 | 1.85 | 1.02 | 0.98 | 3.00 |
time (sec) |
N/A | 0.501 | 0.137 | 3.673 | 0.106 | 0.095 | 0.582 | 0.178 | 0.180 | 0.109 |
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 | 14 | 14 | 14 | 13 | 12 | 12 | 32 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 2.29 | 0.86 | 0.79 | 0.86 |
time (sec) |
N/A | 0.308 | 0.018 | 0.049 | 0.030 | 0.085 | 0.703 | 0.125 | 0.164 | 22.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 63 | 56 | 33 | 46 | 63 | 54 | 50 | 57 | 71 |
N.S. |
1 | 1.03 | 0.92 | 0.54 | 0.75 | 1.03 | 0.89 | 0.82 | 0.93 | 1.16 |
time (sec) |
N/A | 0.453 | 0.447 | 0.122 | 0.102 | 0.089 | 0.742 | 0.141 | 0.182 | 0.190 |
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 | 43 | 37 | 31 | 30 | 32 | 39 | 30 | 27 | 32 |
N.S. |
1 | 1.16 | 1.00 | 0.84 | 0.81 | 0.86 | 1.05 | 0.81 | 0.73 | 0.86 |
time (sec) |
N/A | 0.389 | 0.067 | 0.129 | 0.112 | 0.099 | 0.629 | 0.109 | 0.168 | 23.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 63 | 56 | 32 | 45 | 64 | 53 | 49 | 57 | 71 |
N.S. |
1 | 1.03 | 0.92 | 0.52 | 0.74 | 1.05 | 0.87 | 0.80 | 0.93 | 1.16 |
time (sec) |
N/A | 0.396 | 0.081 | 0.112 | 0.106 | 0.098 | 0.695 | 0.153 | 0.166 | 23.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 33 | 29 | 22 | 21 | 21 | 36 | 22 | 19 | 25 |
N.S. |
1 | 1.06 | 0.94 | 0.71 | 0.68 | 0.68 | 1.16 | 0.71 | 0.61 | 0.81 |
time (sec) |
N/A | 0.354 | 0.025 | 0.067 | 0.030 | 0.083 | 0.814 | 0.136 | 0.197 | 0.050 |
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 | 65 | 67 | 60 | 36 | 51 | 65 | 53 | 54 | 65 | 79 |
N.S. |
1 | 1.03 | 0.92 | 0.55 | 0.78 | 1.00 | 0.82 | 0.83 | 1.00 | 1.22 |
time (sec) |
N/A | 0.425 | 0.087 | 0.117 | 0.108 | 0.084 | 0.764 | 0.131 | 0.163 | 23.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 69 | 57 | 42 | 0 | 51 | 48 | 45 | 50 | 0 |
N.S. |
1 | 1.11 | 0.92 | 0.68 | 0.00 | 0.82 | 0.77 | 0.73 | 0.81 | 0.00 |
time (sec) |
N/A | 0.328 | 0.129 | 0.015 | 0.000 | 0.288 | 0.287 | 0.106 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 82 | 59 | 55 | 0 | 61 | 58 | 55 | 60 | 0 |
N.S. |
1 | 1.09 | 0.79 | 0.73 | 0.00 | 0.81 | 0.77 | 0.73 | 0.80 | 0.00 |
time (sec) |
N/A | 0.414 | 0.144 | 0.016 | 0.000 | 0.284 | 0.359 | 0.140 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 75 | 65 | 48 | 0 | 59 | 51 | 53 | 58 | 0 |
N.S. |
1 | 1.10 | 0.96 | 0.71 | 0.00 | 0.87 | 0.75 | 0.78 | 0.85 | 0.00 |
time (sec) |
N/A | 0.397 | 0.191 | 0.017 | 0.000 | 0.444 | 0.328 | 0.137 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 75 | 60 | 0 | 73 | 58 | 67 | 78 | 0 |
N.S. |
1 | 1.06 | 0.94 | 0.75 | 0.00 | 0.91 | 0.72 | 0.84 | 0.98 | 0.00 |
time (sec) |
N/A | 0.407 | 0.138 | 0.019 | 0.000 | 0.296 | 0.420 | 0.140 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 116 | 83 | 67 | 0 | 101 | 66 | 88 | 82 | 0 |
N.S. |
1 | 1.06 | 0.76 | 0.61 | 0.00 | 0.93 | 0.61 | 0.81 | 0.75 | 0.00 |
time (sec) |
N/A | 0.448 | 0.362 | 0.022 | 0.000 | 0.853 | 0.435 | 0.140 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 43 | 32 | 0 | 47 | 37 | 33 | 35 | 0 |
N.S. |
1 | 1.04 | 0.91 | 0.68 | 0.00 | 1.00 | 0.79 | 0.70 | 0.74 | 0.00 |
time (sec) |
N/A | 0.363 | 0.106 | 0.016 | 0.000 | 0.233 | 0.343 | 0.143 | 0.190 | 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 | 67 | 72 | 63 | 52 | 49 | 48 | 58 | 60 | 51 | 102 |
N.S. |
1 | 1.07 | 0.94 | 0.78 | 0.73 | 0.72 | 0.87 | 0.90 | 0.76 | 1.52 |
time (sec) |
N/A | 0.527 | 0.160 | 0.152 | 0.112 | 0.072 | 2.607 | 0.129 | 0.169 | 0.047 |
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 | 71 | 74 | 67 | 54 | 51 | 50 | 60 | 62 | 53 | 118 |
N.S. |
1 | 1.04 | 0.94 | 0.76 | 0.72 | 0.70 | 0.85 | 0.87 | 0.75 | 1.66 |
time (sec) |
N/A | 0.511 | 0.122 | 0.152 | 0.107 | 0.074 | 2.524 | 0.132 | 0.166 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 54 | 32 | 60 | 46 | 23 | 44 | 46 | 42 | 43 |
N.S. |
1 | 1.04 | 0.62 | 1.15 | 0.88 | 0.44 | 0.85 | 0.88 | 0.81 | 0.83 |
time (sec) |
N/A | 0.381 | 0.079 | 0.116 | 0.109 | 0.071 | 0.200 | 0.134 | 0.183 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 31 | 14 | 0 | 37 | 19 | 25 | 25 | 0 |
N.S. |
1 | 0.90 | 1.55 | 0.70 | 0.00 | 1.85 | 0.95 | 1.25 | 1.25 | 0.00 |
time (sec) |
N/A | 0.455 | 0.112 | 0.033 | 0.000 | 0.234 | 0.514 | 0.132 | 0.162 | 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 | 43 | 45 | 39 | 30 | 29 | 29 | 36 | 30 | 41 | 53 |
N.S. |
1 | 1.05 | 0.91 | 0.70 | 0.67 | 0.67 | 0.84 | 0.70 | 0.95 | 1.23 |
time (sec) |
N/A | 0.450 | 0.049 | 0.187 | 0.104 | 0.079 | 0.359 | 0.131 | 0.198 | 0.039 |
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 | 116 | 124 | 130 | 90 | 89 | 76 | 105 | 89 | 90 | 88 |
N.S. |
1 | 1.07 | 1.12 | 0.78 | 0.77 | 0.66 | 0.91 | 0.77 | 0.78 | 0.76 |
time (sec) |
N/A | 0.571 | 0.098 | 0.017 | 0.028 | 0.069 | 1.204 | 0.152 | 0.177 | 23.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 31 | 16 | 0 | 35 | 20 | 25 | 27 | 0 |
N.S. |
1 | 1.00 | 1.55 | 0.80 | 0.00 | 1.75 | 1.00 | 1.25 | 1.35 | 0.00 |
time (sec) |
N/A | 0.415 | 0.004 | 0.025 | 0.000 | 0.252 | 0.384 | 0.130 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 52 | 59 | 38 | 0 | 85 | 39 | 49 | 44 | 0 |
N.S. |
1 | 1.18 | 1.34 | 0.86 | 0.00 | 1.93 | 0.89 | 1.11 | 1.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.139 | 0.016 | 0.000 | 0.582 | 0.409 | 0.135 | 0.190 | 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 | 54 | 57 | 51 | 50 | 58 | 45 | 73 | 61 | 63 | 50 |
N.S. |
1 | 1.06 | 0.94 | 0.93 | 1.07 | 0.83 | 1.35 | 1.13 | 1.17 | 0.93 |
time (sec) |
N/A | 0.832 | 0.081 | 0.043 | 0.033 | 0.078 | 1.501 | 0.124 | 0.161 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 77 | 64 | 50 | 0 | 69 | 48 | 44 | 58 | 0 |
N.S. |
1 | 1.10 | 0.91 | 0.71 | 0.00 | 0.99 | 0.69 | 0.63 | 0.83 | 0.00 |
time (sec) |
N/A | 0.352 | 0.156 | 0.015 | 0.000 | 0.596 | 0.333 | 0.121 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 19 | 16 | 15 | 15 | 17 | 15 | 13 | 15 |
N.S. |
1 | 1.21 | 1.00 | 0.84 | 0.79 | 0.79 | 0.89 | 0.79 | 0.68 | 0.79 |
time (sec) |
N/A | 0.291 | 0.024 | 0.056 | 0.030 | 0.077 | 0.064 | 0.126 | 0.177 | 23.066 |
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 | 77 | 77 | 67 | 50 | 49 | 49 | 71 | 50 | 51 | 47 |
N.S. |
1 | 1.00 | 0.87 | 0.65 | 0.64 | 0.64 | 0.92 | 0.65 | 0.66 | 0.61 |
time (sec) |
N/A | 0.378 | 0.061 | 0.074 | 0.030 | 0.079 | 0.284 | 0.137 | 0.155 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 224 | 76 | 289 | 0 | 167 | 0 | 171 | 271 | 255 |
N.S. |
1 | 2.80 | 0.95 | 3.61 | 0.00 | 2.09 | 0.00 | 2.14 | 3.39 | 3.19 |
time (sec) |
N/A | 0.897 | 0.209 | 0.616 | 0.000 | 0.090 | 0.000 | 0.315 | 0.183 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 97 | 81 | 130 | 0 | 87 | 0 | 81 | 85 | 0 |
N.S. |
1 | 1.09 | 0.91 | 1.46 | 0.00 | 0.98 | 0.00 | 0.91 | 0.96 | 0.00 |
time (sec) |
N/A | 0.506 | 0.175 | 0.042 | 0.000 | 2.266 | 0.000 | 0.286 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 67 | 55 | 68 | 0 | 62 | 0 | 65 | 66 | 0 |
N.S. |
1 | 1.10 | 0.90 | 1.11 | 0.00 | 1.02 | 0.00 | 1.07 | 1.08 | 0.00 |
time (sec) |
N/A | 1.087 | 0.216 | 0.060 | 0.000 | 1.572 | 0.000 | 0.382 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 361 | 76 | 57 | 81 | 0 | 151 | 113 | 158 |
N.S. |
1 | 1.00 | 6.45 | 1.36 | 1.02 | 1.45 | 0.00 | 2.70 | 2.02 | 2.82 |
time (sec) |
N/A | 0.611 | 0.491 | 0.180 | 0.106 | 0.090 | 0.000 | 0.165 | 0.174 | 26.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 101 | 66 | 58 | 0 | 78 | 0 | 80 | 63 | 52 |
N.S. |
1 | 1.40 | 0.92 | 0.81 | 0.00 | 1.08 | 0.00 | 1.11 | 0.88 | 0.72 |
time (sec) |
N/A | 0.677 | 0.206 | 0.100 | 0.000 | 0.081 | 0.000 | 0.144 | 0.167 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 12 | 12 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.86 | 0.86 | 0.79 | 0.86 |
time (sec) |
N/A | 0.456 | 0.006 | 0.091 | 0.102 | 0.075 | 0.063 | 0.121 | 0.183 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 56 | 44 | 45 | 43 | 60 | 43 | 43 | 43 |
N.S. |
1 | 1.08 | 0.92 | 0.72 | 0.74 | 0.70 | 0.98 | 0.70 | 0.70 | 0.70 |
time (sec) |
N/A | 0.477 | 0.068 | 0.358 | 0.025 | 0.070 | 0.707 | 0.137 | 0.177 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 121 | 103 | 85 | 85 | 91 | 116 | 84 | 84 | 84 |
N.S. |
1 | 1.06 | 0.90 | 0.75 | 0.75 | 0.80 | 1.02 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.543 | 0.096 | 4.197 | 0.025 | 0.070 | 0.918 | 0.117 | 0.165 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 60 | 111 | 102 | 0 | 180 | 73 | 92 | 105 | 46 |
N.S. |
1 | 1.11 | 2.06 | 1.89 | 0.00 | 3.33 | 1.35 | 1.70 | 1.94 | 0.85 |
time (sec) |
N/A | 0.350 | 0.283 | 0.076 | 0.000 | 0.092 | 1.015 | 0.186 | 0.194 | 22.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 60 | 111 | 102 | 0 | 180 | 73 | 92 | 105 | 62 |
N.S. |
1 | 1.11 | 2.06 | 1.89 | 0.00 | 3.33 | 1.35 | 1.70 | 1.94 | 1.15 |
time (sec) |
N/A | 0.460 | 0.008 | 0.028 | 0.000 | 0.083 | 2.376 | 0.185 | 0.168 | 22.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 55 | 39 | 0 | 112 | 0 | 123 | 107 | 67 |
N.S. |
1 | 1.00 | 1.04 | 0.74 | 0.00 | 2.11 | 0.00 | 2.32 | 2.02 | 1.26 |
time (sec) |
N/A | 0.319 | 0.713 | 0.695 | 0.000 | 0.085 | 0.000 | 0.137 | 0.180 | 22.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 26 | 17 | 25 | 0 | 54 | 33 | 35 |
N.S. |
1 | 1.00 | 1.09 | 1.13 | 0.74 | 1.09 | 0.00 | 2.35 | 1.43 | 1.52 |
time (sec) |
N/A | 0.262 | 0.024 | 0.072 | 0.103 | 0.074 | 0.000 | 0.142 | 0.184 | 22.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 54 | 58 | 36 | 37 | 0 | 39 | 27 | 180 |
N.S. |
1 | 1.00 | 1.64 | 1.76 | 1.09 | 1.12 | 0.00 | 1.18 | 0.82 | 5.45 |
time (sec) |
N/A | 0.284 | 0.093 | 0.076 | 0.031 | 0.072 | 0.000 | 0.115 | 0.155 | 27.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 57 | 35 | 2 | 2 | 0 | 31 | 2 | 0 |
N.S. |
1 | 1.00 | 1.27 | 0.78 | 0.04 | 0.04 | 0.00 | 0.69 | 0.04 | 0.00 |
time (sec) |
N/A | 0.525 | 1.348 | 0.071 | 0.115 | 0.072 | 0.000 | 0.134 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 57 | 35 | 2 | 2 | 0 | 31 | 2 | 0 |
N.S. |
1 | 1.00 | 1.27 | 0.78 | 0.04 | 0.04 | 0.00 | 0.69 | 0.04 | 0.00 |
time (sec) |
N/A | 0.402 | 0.003 | 0.049 | 0.105 | 0.069 | 0.000 | 0.147 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 57 | 35 | 2 | 2 | 0 | 31 | 2 | 0 |
N.S. |
1 | 1.00 | 1.27 | 0.78 | 0.04 | 0.04 | 0.00 | 0.69 | 0.04 | 0.00 |
time (sec) |
N/A | 0.472 | 0.002 | 0.048 | 0.105 | 0.074 | 0.000 | 0.126 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 57 | 20 | 2 | 2 | 0 | 12 | 2 | 0 |
N.S. |
1 | 1.00 | 1.27 | 0.44 | 0.04 | 0.04 | 0.00 | 0.27 | 0.04 | 0.00 |
time (sec) |
N/A | 0.562 | 5.380 | 0.027 | 0.104 | 0.073 | 0.000 | 0.142 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 39 | 41 | 0 | 6 | 0 | 6 | 5 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.79 | 0.00 | 0.12 | 0.00 | 0.12 | 0.10 | 0.00 |
time (sec) |
N/A | 0.587 | 3.296 | 0.084 | 0.000 | 0.070 | 0.000 | 0.127 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 39 | 21 | 6 | 6 | 0 | 6 | 5 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.40 | 0.12 | 0.12 | 0.00 | 0.12 | 0.10 | 0.00 |
time (sec) |
N/A | 0.591 | 2.943 | 0.028 | 0.105 | 0.072 | 0.000 | 0.138 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 67 | 40 | 0 | 8 | 0 | 8 | 7 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.59 | 0.00 | 0.12 | 0.00 | 0.12 | 0.10 | 0.00 |
time (sec) |
N/A | 0.699 | 3.103 | 0.026 | 0.000 | 0.077 | 0.000 | 0.135 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 39 | 29 | 27 | 25 | 0 | 54 | 22 | 19 |
N.S. |
1 | 1.00 | 1.26 | 0.94 | 0.87 | 0.81 | 0.00 | 1.74 | 0.71 | 0.61 |
time (sec) |
N/A | 0.261 | 0.313 | 0.099 | 0.102 | 0.078 | 0.000 | 0.130 | 0.167 | 22.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 23 | 29 | 25 | 25 | 0 | 54 | 22 | 19 |
N.S. |
1 | 1.00 | 0.74 | 0.94 | 0.81 | 0.81 | 0.00 | 1.74 | 0.71 | 0.61 |
time (sec) |
N/A | 0.680 | 0.291 | 0.133 | 0.073 | 0.083 | 0.000 | 0.166 | 0.179 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 23 | 29 | 0 | 25 | 0 | 68 | 18 | 19 |
N.S. |
1 | 1.00 | 0.74 | 0.94 | 0.00 | 0.81 | 0.00 | 2.19 | 0.58 | 0.61 |
time (sec) |
N/A | 0.484 | 0.293 | 0.046 | 0.000 | 0.073 | 0.000 | 0.126 | 0.174 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 23 | 29 | 0 | 25 | 0 | 68 | 18 | 19 |
N.S. |
1 | 1.00 | 0.74 | 0.94 | 0.00 | 0.81 | 0.00 | 2.19 | 0.58 | 0.61 |
time (sec) |
N/A | 0.476 | 0.285 | 0.016 | 0.000 | 0.075 | 0.000 | 0.143 | 0.184 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 23 | 29 | 0 | 25 | 0 | 68 | 18 | 19 |
N.S. |
1 | 1.00 | 0.74 | 0.94 | 0.00 | 0.81 | 0.00 | 2.19 | 0.58 | 0.61 |
time (sec) |
N/A | 1.128 | 0.302 | 0.059 | 0.000 | 0.074 | 0.000 | 0.169 | 0.184 | 23.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 50 | 38 | 58 | 85 | 44 | 172 | 0 | 52 | 0 |
N.S. |
1 | 1.16 | 0.88 | 1.35 | 1.98 | 1.02 | 4.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.398 | 0.212 | 0.090 | 0.037 | 0.082 | 1.238 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 50 | 59 | 0 | 80 | 0 | 133 | 58 | 60 |
N.S. |
1 | 1.00 | 0.77 | 0.91 | 0.00 | 1.23 | 0.00 | 2.05 | 0.89 | 0.92 |
time (sec) |
N/A | 0.522 | 0.226 | 0.168 | 0.000 | 0.075 | 0.000 | 0.172 | 0.183 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 206 | 179 | 729 | 0 | 1174 | 0 | 558 | 1279 | 0 |
N.S. |
1 | 1.06 | 0.92 | 3.74 | 0.00 | 6.02 | 0.00 | 2.86 | 6.56 | 0.00 |
time (sec) |
N/A | 0.701 | 1.488 | 0.240 | 0.000 | 0.119 | 0.000 | 0.153 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 119 | 128 | 102 | 84 | 73 | 0 | 97 | 103 | 1468 |
N.S. |
1 | 1.14 | 1.23 | 0.98 | 0.81 | 0.70 | 0.00 | 0.93 | 0.99 | 14.12 |
time (sec) |
N/A | 0.415 | 0.556 | 0.109 | 0.026 | 0.079 | 0.000 | 0.145 | 0.175 | 162.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 86 | 94 | 70 | 65 | 0 | 80 | 83 | 1056 |
N.S. |
1 | 1.12 | 1.06 | 1.16 | 0.86 | 0.80 | 0.00 | 0.99 | 1.02 | 13.04 |
time (sec) |
N/A | 0.370 | 0.345 | 0.063 | 0.030 | 0.080 | 0.000 | 0.133 | 0.187 | 100.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 59 | 50 | 78 | 55 | 48 | 0 | 62 | 46 | 868 |
N.S. |
1 | 1.16 | 0.98 | 1.53 | 1.08 | 0.94 | 0.00 | 1.22 | 0.90 | 17.02 |
time (sec) |
N/A | 0.318 | 0.175 | 0.056 | 0.032 | 0.121 | 0.000 | 0.125 | 0.167 | 68.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 45 | 74 | 42 | 46 | 0 | 43 | 42 | 277 |
N.S. |
1 | 1.00 | 1.45 | 2.39 | 1.35 | 1.48 | 0.00 | 1.39 | 1.35 | 8.94 |
time (sec) |
N/A | 0.237 | 0.166 | 0.048 | 0.028 | 0.070 | 0.000 | 0.139 | 0.181 | 35.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | B | F | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 73 | 105 | 42 | 74 | 0 | 73 | 104 | 150 |
N.S. |
1 | 1.00 | 2.35 | 3.39 | 1.35 | 2.39 | 0.00 | 2.35 | 3.35 | 4.84 |
time (sec) |
N/A | 0.328 | 0.605 | 0.066 | 0.026 | 0.084 | 0.000 | 0.127 | 0.185 | 25.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 33 | 39 | 29 | 67 | 0 | 105 | 106 | 50 |
N.S. |
1 | 1.00 | 0.70 | 0.83 | 0.62 | 1.43 | 0.00 | 2.23 | 2.26 | 1.06 |
time (sec) |
N/A | 0.339 | 0.166 | 0.066 | 0.026 | 0.076 | 0.000 | 0.160 | 0.241 | 22.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 28 | 13 | 43 | 0 | 143 | 53 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 0.65 | 2.15 | 0.00 | 7.15 | 2.65 | 0.80 |
time (sec) |
N/A | 0.324 | 0.166 | 0.067 | 0.033 | 0.081 | 0.000 | 0.176 | 0.213 | 22.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 103 | 49 | 55 | 57 | 115 | 0 | 213 | 222 | 96 |
N.S. |
1 | 1.11 | 0.53 | 0.59 | 0.61 | 1.24 | 0.00 | 2.29 | 2.39 | 1.03 |
time (sec) |
N/A | 0.386 | 0.227 | 0.067 | 0.032 | 0.086 | 0.000 | 0.209 | 0.199 | 22.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 131 | 57 | 63 | 71 | 141 | 0 | 267 | 279 | 118 |
N.S. |
1 | 1.13 | 0.49 | 0.54 | 0.61 | 1.22 | 0.00 | 2.30 | 2.41 | 1.02 |
time (sec) |
N/A | 0.404 | 0.303 | 0.073 | 0.039 | 0.094 | 0.000 | 0.229 | 0.196 | 22.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 159 | 65 | 71 | 85 | 163 | 0 | 321 | 338 | 142 |
N.S. |
1 | 1.14 | 0.47 | 0.51 | 0.61 | 1.17 | 0.00 | 2.31 | 2.43 | 1.02 |
time (sec) |
N/A | 0.424 | 0.282 | 0.073 | 0.032 | 0.113 | 0.000 | 0.274 | 0.196 | 22.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 52 | 69 | 56 | 47 | 67 | 0 | 35 | 36 | 53 |
N.S. |
1 | 0.48 | 0.63 | 0.51 | 0.43 | 0.61 | 0.00 | 0.32 | 0.33 | 0.49 |
time (sec) |
N/A | 0.405 | 0.345 | 0.113 | 0.043 | 0.077 | 0.000 | 0.170 | 0.194 | 22.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 40 | 61 | 48 | 31 | 59 | 0 | 27 | 28 | 44 |
N.S. |
1 | 0.52 | 0.79 | 0.62 | 0.40 | 0.77 | 0.00 | 0.35 | 0.36 | 0.57 |
time (sec) |
N/A | 0.403 | 0.374 | 0.107 | 0.044 | 0.077 | 0.000 | 0.134 | 0.168 | 22.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 32 | 53 | 40 | 12 | 51 | 0 | 19 | 20 | 37 |
N.S. |
1 | 0.63 | 1.04 | 0.78 | 0.24 | 1.00 | 0.00 | 0.37 | 0.39 | 0.73 |
time (sec) |
N/A | 0.345 | 0.262 | 0.054 | 0.046 | 0.083 | 0.000 | 0.192 | 0.198 | 22.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 34 | 61 | 53 | 0 | 99 | 0 | 28 | 50 | 0 |
N.S. |
1 | 0.67 | 1.20 | 1.04 | 0.00 | 1.94 | 0.00 | 0.55 | 0.98 | 0.00 |
time (sec) |
N/A | 0.370 | 0.289 | 0.066 | 0.000 | 0.091 | 0.000 | 0.125 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 49 | 78 | 81 | 0 | 113 | 0 | 44 | 125 | 0 |
N.S. |
1 | 0.73 | 1.16 | 1.21 | 0.00 | 1.69 | 0.00 | 0.66 | 1.87 | 0.00 |
time (sec) |
N/A | 0.378 | 0.403 | 0.072 | 0.000 | 0.101 | 0.000 | 0.140 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 72 | 90 | 114 | 0 | 141 | 0 | 70 | 204 | 0 |
N.S. |
1 | 0.70 | 0.87 | 1.11 | 0.00 | 1.37 | 0.00 | 0.68 | 1.98 | 0.00 |
time (sec) |
N/A | 0.407 | 0.378 | 0.077 | 0.000 | 0.093 | 0.000 | 0.129 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 93 | 100 | 129 | 0 | 164 | 0 | 88 | 285 | 0 |
N.S. |
1 | 0.67 | 0.72 | 0.93 | 0.00 | 1.18 | 0.00 | 0.63 | 2.05 | 0.00 |
time (sec) |
N/A | 0.423 | 0.427 | 0.078 | 0.000 | 0.108 | 0.000 | 0.126 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 21 | 34 | 52 | 37 | 34 | 66 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.21 | 1.86 | 1.32 | 1.21 | 2.36 | 0.71 |
time (sec) |
N/A | 0.248 | 0.055 | 0.258 | 0.106 | 0.073 | 7.078 | 0.141 | 0.196 | 22.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 21 | 0 | 52 | 0 | 34 | 66 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.00 | 1.86 | 0.00 | 1.21 | 2.36 | 0.00 |
time (sec) |
N/A | 0.374 | 0.003 | 0.179 | 0.000 | 0.069 | 0.000 | 0.123 | 0.187 | 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 | 22 | 22 | 22 | 19 | 18 | 18 | 17 | 18 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.82 | 0.77 | 0.82 | 0.77 | 0.82 |
time (sec) |
N/A | 0.242 | 0.009 | 0.137 | 0.024 | 0.070 | 0.063 | 0.115 | 0.188 | 22.122 |
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 | 22 | 22 | 22 | 19 | 18 | 18 | 17 | 18 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.82 | 0.77 | 0.82 | 0.77 | 0.82 |
time (sec) |
N/A | 0.412 | 0.002 | 0.095 | 0.031 | 0.102 | 0.212 | 0.151 | 0.187 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 12 | 0 | 11 | 36 | 11 | 17 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.00 | 0.65 | 2.12 | 0.65 | 1.00 | 0.65 |
time (sec) |
N/A | 0.267 | 0.055 | 0.063 | 0.000 | 0.097 | 0.193 | 0.132 | 0.179 | 22.581 |
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 | 17 | 17 | 17 | 125 | 0 | 11 | 0 | 11 | 486 | 0 |
N.S. |
1 | 1.00 | 1.00 | 7.35 | 0.00 | 0.65 | 0.00 | 0.65 | 28.59 | 0.00 |
time (sec) |
N/A | 0.357 | 0.057 | 0.059 | 0.000 | 0.108 | 0.000 | 0.917 | 0.903 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 23 | 7 | 6 | 19 | 7 | 19 | 6 | 6 |
N.S. |
1 | 1.00 | 2.30 | 0.70 | 0.60 | 1.90 | 0.70 | 1.90 | 0.60 | 0.60 |
time (sec) |
N/A | 0.204 | 0.045 | 0.240 | 0.108 | 0.072 | 0.063 | 0.138 | 0.174 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 23 | 34 | 6 | 25 | 49 | 12 | 11 | 32 |
N.S. |
1 | 1.00 | 2.30 | 3.40 | 0.60 | 2.50 | 4.90 | 1.20 | 1.10 | 3.20 |
time (sec) |
N/A | 0.204 | 0.002 | 0.050 | 0.104 | 0.069 | 0.531 | 0.138 | 0.172 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 23 | 7 | 6 | 19 | 7 | 19 | 6 | 6 |
N.S. |
1 | 1.00 | 2.30 | 0.70 | 0.60 | 1.90 | 0.70 | 1.90 | 0.60 | 0.60 |
time (sec) |
N/A | 0.225 | 0.001 | 0.042 | 0.105 | 0.069 | 0.573 | 0.126 | 0.160 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 23 | 7 | 8 | 29 | 7 | 26 | 6 | 6 |
N.S. |
1 | 1.00 | 1.92 | 0.58 | 0.67 | 2.42 | 0.58 | 2.17 | 0.50 | 0.50 |
time (sec) |
N/A | 0.228 | 0.093 | 0.109 | 0.110 | 0.076 | 0.267 | 0.139 | 0.181 | 22.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 44 | 31 | 8 | 29 | 39 | 13 | 15 | 30 |
N.S. |
1 | 1.00 | 3.67 | 2.58 | 0.67 | 2.42 | 3.25 | 1.08 | 1.25 | 2.50 |
time (sec) |
N/A | 0.228 | 0.046 | 0.046 | 0.105 | 0.082 | 0.537 | 0.130 | 0.219 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 44 | 7 | 8 | 29 | 7 | 26 | 6 | 6 |
N.S. |
1 | 1.00 | 3.67 | 0.58 | 0.67 | 2.42 | 0.58 | 2.17 | 0.50 | 0.50 |
time (sec) |
N/A | 0.253 | 0.001 | 0.055 | 0.110 | 0.078 | 0.598 | 0.312 | 0.213 | 22.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 12 | 23 | 5 | 8 | 29 | 3 | 24 | 4 | 4 |
N.S. |
1 | 3.00 | 5.75 | 1.25 | 2.00 | 7.25 | 0.75 | 6.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.225 | 0.091 | 0.101 | 0.106 | 0.081 | 0.328 | 0.171 | 0.246 | 22.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 12 | 44 | 29 | 8 | 29 | 39 | 13 | 14 | 33 |
N.S. |
1 | 3.00 | 11.00 | 7.25 | 2.00 | 7.25 | 9.75 | 3.25 | 3.50 | 8.25 |
time (sec) |
N/A | 0.226 | 0.047 | 0.040 | 0.109 | 0.073 | 0.543 | 0.142 | 0.210 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 12 | 44 | 5 | 8 | 29 | 3 | 24 | 4 | 4 |
N.S. |
1 | 3.00 | 11.00 | 1.25 | 2.00 | 7.25 | 0.75 | 6.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.246 | 0.002 | 0.047 | 0.102 | 0.071 | 0.565 | 0.145 | 0.206 | 0.059 |
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 | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 9 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.82 | 0.64 |
time (sec) |
N/A | 0.208 | 0.002 | 0.028 | 0.030 | 0.066 | 0.019 | 0.121 | 0.204 | 0.025 |
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 | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 9 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.82 | 0.64 |
time (sec) |
N/A | 0.230 | 0.001 | 0.024 | 0.030 | 0.069 | 0.058 | 0.120 | 0.207 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 44 | 24 | 0 | 26 | 7 | 10 | 11 | 0 |
N.S. |
1 | 1.00 | 1.63 | 0.89 | 0.00 | 0.96 | 0.26 | 0.37 | 0.41 | 0.00 |
time (sec) |
N/A | 0.246 | 0.047 | 0.113 | 0.000 | 0.076 | 0.750 | 0.137 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 44 | 30 | 0 | 26 | 0 | 10 | 11 | 0 |
N.S. |
1 | 1.00 | 1.63 | 1.11 | 0.00 | 0.96 | 0.00 | 0.37 | 0.41 | 0.00 |
time (sec) |
N/A | 0.237 | 0.003 | 0.014 | 0.000 | 0.076 | 0.000 | 0.140 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 56 | 28 | 14 | 14 | 15 | 26 | 9 | 0 |
N.S. |
1 | 1.00 | 2.24 | 1.12 | 0.56 | 0.56 | 0.60 | 1.04 | 0.36 | 0.00 |
time (sec) |
N/A | 0.240 | 0.027 | 0.082 | 0.029 | 0.068 | 0.665 | 0.127 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 56 | 28 | 0 | 14 | 0 | 21 | 9 | 0 |
N.S. |
1 | 1.00 | 1.93 | 0.97 | 0.00 | 0.48 | 0.00 | 0.72 | 0.31 | 0.00 |
time (sec) |
N/A | 0.245 | 0.002 | 0.016 | 0.000 | 0.099 | 0.000 | 0.127 | 0.195 | 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 | 11 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 8 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 0.73 | 0.82 |
time (sec) |
N/A | 0.202 | 0.002 | 0.037 | 0.024 | 0.066 | 0.020 | 0.102 | 0.197 | 22.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 20 | 17 | 12 | 16 | 0 | 9 | 8 | 16 |
N.S. |
1 | 1.00 | 1.82 | 1.55 | 1.09 | 1.45 | 0.00 | 0.82 | 0.73 | 1.45 |
time (sec) |
N/A | 0.209 | 0.074 | 0.044 | 0.029 | 0.073 | 0.000 | 0.126 | 0.197 | 22.741 |
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 | 9 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 6 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.78 | 0.78 | 0.67 | 0.78 |
time (sec) |
N/A | 0.199 | 0.001 | 0.028 | 0.028 | 0.067 | 0.022 | 0.109 | 0.197 | 22.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 22 | 19 | 7 | 23 | 0 | 7 | 6 | 18 |
N.S. |
1 | 1.00 | 2.44 | 2.11 | 0.78 | 2.56 | 0.00 | 0.78 | 0.67 | 2.00 |
time (sec) |
N/A | 0.207 | 0.074 | 0.047 | 0.028 | 0.069 | 0.000 | 0.132 | 0.185 | 22.858 |
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 | 13 | 13 | 13 | 10 | 9 | 12 | 10 | 9 | 11 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.92 | 0.77 | 0.69 | 0.85 | 0.69 |
time (sec) |
N/A | 0.195 | 0.002 | 0.036 | 0.024 | 0.064 | 0.024 | 0.115 | 0.228 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 22 | 20 | 12 | 19 | 0 | 9 | 11 | 20 |
N.S. |
1 | 1.00 | 1.69 | 1.54 | 0.92 | 1.46 | 0.00 | 0.69 | 0.85 | 1.54 |
time (sec) |
N/A | 0.207 | 0.070 | 0.043 | 0.031 | 0.071 | 0.000 | 0.122 | 0.178 | 22.526 |