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 | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 51 | 43 | 49 | 64 | 41 | 42 | 73 | 48 |
N.S. |
1 | 0.96 | 0.96 | 0.81 | 0.92 | 1.21 | 0.77 | 0.79 | 1.38 | 0.91 |
time (sec) |
N/A | 0.360 | 0.012 | 0.168 | 0.026 | 0.073 | 0.133 | 0.114 | 0.147 | 14.751 |
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 | 66 | 63 | 56 | 75 | 100 | 73 | 50 | 99 | 71 |
N.S. |
1 | 0.93 | 0.89 | 0.79 | 1.06 | 1.41 | 1.03 | 0.70 | 1.39 | 1.00 |
time (sec) |
N/A | 0.398 | 0.013 | 0.170 | 0.028 | 0.075 | 0.188 | 0.129 | 0.149 | 14.896 |
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 | 89 | 82 | 71 | 67 | 93 | 126 | 94 | 58 | 129 | 90 |
N.S. |
1 | 0.92 | 0.80 | 0.75 | 1.04 | 1.42 | 1.06 | 0.65 | 1.45 | 1.01 |
time (sec) |
N/A | 0.423 | 0.016 | 0.171 | 0.035 | 0.073 | 0.242 | 0.116 | 0.144 | 14.883 |
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 | 111 | 102 | 158 | 119 | 0 | 119 | 0 | 206 | 95 | 113 |
N.S. |
1 | 0.92 | 1.42 | 1.07 | 0.00 | 1.07 | 0.00 | 1.86 | 0.86 | 1.02 |
time (sec) |
N/A | 0.627 | 0.075 | 0.288 | 0.000 | 0.095 | 0.000 | 0.134 | 0.151 | 15.041 |
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 | 82 | 70 | 64 | 101 | 0 | 97 | 0 | 139 | 62 | 90 |
N.S. |
1 | 0.85 | 0.78 | 1.23 | 0.00 | 1.18 | 0.00 | 1.70 | 0.76 | 1.10 |
time (sec) |
N/A | 0.479 | 0.113 | 0.247 | 0.000 | 0.082 | 0.000 | 0.136 | 0.156 | 14.813 |
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 | 50 | 46 | 80 | 98 | 70 | 67 | 0 | 68 | 34 | 56 |
N.S. |
1 | 0.92 | 1.60 | 1.96 | 1.40 | 1.34 | 0.00 | 1.36 | 0.68 | 1.12 |
time (sec) |
N/A | 0.374 | 0.079 | 0.221 | 0.117 | 0.079 | 0.000 | 0.121 | 0.148 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 22 | 19 | 0 | 19 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.05 | 0.90 | 0.00 | 0.90 | 0.86 | 0.90 |
time (sec) |
N/A | 0.295 | 0.011 | 0.220 | 0.034 | 0.070 | 0.000 | 0.117 | 0.146 | 0.024 |
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 | 63 | 67 | 40 | 110 | 0 | 71 | 0 | 72 | 94 | 89 |
N.S. |
1 | 1.06 | 0.63 | 1.75 | 0.00 | 1.13 | 0.00 | 1.14 | 1.49 | 1.41 |
time (sec) |
N/A | 0.373 | 0.040 | 0.259 | 0.000 | 0.083 | 0.000 | 0.124 | 0.150 | 14.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 100 | 51 | 151 | 0 | 107 | 0 | 0 | 181 | 139 |
N.S. |
1 | 1.02 | 0.52 | 1.54 | 0.00 | 1.09 | 0.00 | 0.00 | 1.85 | 1.42 |
time (sec) |
N/A | 0.537 | 0.075 | 0.289 | 0.000 | 0.109 | 0.000 | 0.000 | 0.161 | 0.036 |
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 | 130 | 125 | 72 | 192 | 0 | 143 | 0 | 180 | 268 | 272 |
N.S. |
1 | 0.96 | 0.55 | 1.48 | 0.00 | 1.10 | 0.00 | 1.38 | 2.06 | 2.09 |
time (sec) |
N/A | 0.688 | 0.079 | 0.315 | 0.000 | 0.082 | 0.000 | 0.124 | 0.152 | 14.691 |
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 | 66 | 53 | 53 | 52 | 61 | 71 | 58 | 112 | 57 | 63 |
N.S. |
1 | 0.80 | 0.80 | 0.79 | 0.92 | 1.08 | 0.88 | 1.70 | 0.86 | 0.95 |
time (sec) |
N/A | 0.404 | 0.025 | 0.206 | 0.032 | 0.073 | 0.249 | 0.111 | 0.150 | 0.054 |
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 | 45 | 45 | 44 | 52 | 62 | 44 | 100 | 49 | 51 |
N.S. |
1 | 0.82 | 0.82 | 0.80 | 0.95 | 1.13 | 0.80 | 1.82 | 0.89 | 0.93 |
time (sec) |
N/A | 0.392 | 0.017 | 0.191 | 0.027 | 0.073 | 0.211 | 0.134 | 0.146 | 0.048 |
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 | 42 | 33 | 33 | 34 | 42 | 44 | 32 | 72 | 36 | 42 |
N.S. |
1 | 0.79 | 0.79 | 0.81 | 1.00 | 1.05 | 0.76 | 1.71 | 0.86 | 1.00 |
time (sec) |
N/A | 0.366 | 0.014 | 0.176 | 0.032 | 0.076 | 0.153 | 0.114 | 0.147 | 14.950 |
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 | 25 | 20 | 22 | 23 | 25 | 23 | 19 | 56 | 22 | 25 |
N.S. |
1 | 0.80 | 0.88 | 0.92 | 1.00 | 0.92 | 0.76 | 2.24 | 0.88 | 1.00 |
time (sec) |
N/A | 0.320 | 0.005 | 0.162 | 0.030 | 0.078 | 0.111 | 0.114 | 0.150 | 14.811 |
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 | 20 | 23 | 18 | 19 | 20 | 20 | 19 | 41 | 18 | 18 |
N.S. |
1 | 1.15 | 0.90 | 0.95 | 1.00 | 1.00 | 0.95 | 2.05 | 0.90 | 0.90 |
time (sec) |
N/A | 0.335 | 0.009 | 0.145 | 0.025 | 0.084 | 0.050 | 0.112 | 0.145 | 0.023 |
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 | 18 | 22 | 18 | 28 | 35 | 27 | 36 | 35 | 33 | 16 |
N.S. |
1 | 1.22 | 1.00 | 1.56 | 1.94 | 1.50 | 2.00 | 1.94 | 1.83 | 0.89 |
time (sec) |
N/A | 0.352 | 0.007 | 0.150 | 0.025 | 0.068 | 0.075 | 0.124 | 0.147 | 14.693 |
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 | 58 | 56 | 56 | 49 | 54 | 59 | 58 | 85 | 63 | 53 |
N.S. |
1 | 0.97 | 0.97 | 0.84 | 0.93 | 1.02 | 1.00 | 1.47 | 1.09 | 0.91 |
time (sec) |
N/A | 0.394 | 0.016 | 0.152 | 0.026 | 0.081 | 0.175 | 0.117 | 0.147 | 0.053 |
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 | 76 | 71 | 71 | 61 | 70 | 93 | 75 | 95 | 102 | 68 |
N.S. |
1 | 0.93 | 0.93 | 0.80 | 0.92 | 1.22 | 0.99 | 1.25 | 1.34 | 0.89 |
time (sec) |
N/A | 0.403 | 0.018 | 0.158 | 0.027 | 0.082 | 0.203 | 0.115 | 0.148 | 14.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 128 | 438 | 153 | 0 | 177 | 0 | 265 | 232 | 161 |
N.S. |
1 | 0.91 | 3.13 | 1.09 | 0.00 | 1.26 | 0.00 | 1.89 | 1.66 | 1.15 |
time (sec) |
N/A | 0.782 | 0.597 | 0.365 | 0.000 | 0.122 | 0.000 | 0.142 | 0.154 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 92 | 321 | 134 | 0 | 149 | 0 | 197 | 184 | 138 |
N.S. |
1 | 0.83 | 2.89 | 1.21 | 0.00 | 1.34 | 0.00 | 1.77 | 1.66 | 1.24 |
time (sec) |
N/A | 0.625 | 0.428 | 0.325 | 0.000 | 0.090 | 0.000 | 0.153 | 0.152 | 14.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 66 | 156 | 498 | 0 | 97 | 0 | 104 | 134 | 102 |
N.S. |
1 | 0.86 | 2.03 | 6.47 | 0.00 | 1.26 | 0.00 | 1.35 | 1.74 | 1.32 |
time (sec) |
N/A | 0.466 | 0.171 | 0.257 | 0.000 | 0.091 | 0.000 | 0.128 | 0.148 | 14.827 |
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 | 63 | 64 | 67 | 102 | 0 | 67 | 0 | 73 | 96 | 90 |
N.S. |
1 | 1.02 | 1.06 | 1.62 | 0.00 | 1.06 | 0.00 | 1.16 | 1.52 | 1.43 |
time (sec) |
N/A | 0.365 | 0.024 | 0.277 | 0.000 | 0.079 | 0.000 | 0.126 | 0.147 | 14.980 |
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 | 63 | 65 | 38 | 102 | 0 | 71 | 0 | 73 | 93 | 89 |
N.S. |
1 | 1.03 | 0.60 | 1.62 | 0.00 | 1.13 | 0.00 | 1.16 | 1.48 | 1.41 |
time (sec) |
N/A | 0.381 | 0.059 | 0.299 | 0.000 | 0.084 | 0.000 | 0.127 | 0.150 | 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 | 45 | 49 | 30 | 29 | 45 | 53 | 68 | 38 | 29 | 116 |
N.S. |
1 | 1.09 | 0.67 | 0.64 | 1.00 | 1.18 | 1.51 | 0.84 | 0.64 | 2.58 |
time (sec) |
N/A | 0.377 | 0.019 | 0.246 | 0.040 | 0.079 | 14.465 | 0.113 | 0.146 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 106 | 78 | 186 | 0 | 142 | 0 | 0 | 114 | 188 |
N.S. |
1 | 0.96 | 0.71 | 1.69 | 0.00 | 1.29 | 0.00 | 0.00 | 1.04 | 1.71 |
time (sec) |
N/A | 0.426 | 0.051 | 0.368 | 0.000 | 0.086 | 0.000 | 0.000 | 0.150 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 132 | 76 | 227 | 0 | 151 | 0 | 0 | 172 | 275 |
N.S. |
1 | 0.92 | 0.53 | 1.59 | 0.00 | 1.06 | 0.00 | 0.00 | 1.20 | 1.92 |
time (sec) |
N/A | 0.651 | 0.092 | 0.401 | 0.000 | 0.090 | 0.000 | 0.000 | 0.153 | 15.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 169 | 101 | 172 | 0 | 386 | 0 | 0 | 127 | 0 |
N.S. |
1 | 0.64 | 0.38 | 0.65 | 0.00 | 1.47 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.514 | 0.060 | 0.187 | 0.000 | 0.156 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 137 | 95 | 154 | 0 | 364 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.63 | 0.43 | 0.70 | 0.00 | 1.66 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.479 | 0.064 | 0.184 | 0.000 | 0.133 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 107 | 87 | 136 | 0 | 330 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.63 | 0.51 | 0.80 | 0.00 | 1.93 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.451 | 0.054 | 0.182 | 0.000 | 0.132 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 84 | 70 | 108 | 0 | 266 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.67 | 0.56 | 0.86 | 0.00 | 2.13 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.434 | 0.046 | 0.180 | 0.000 | 0.102 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 65 | 65 | 91 | 0 | 249 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.77 | 0.77 | 1.08 | 0.00 | 2.96 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.403 | 0.035 | 0.176 | 0.000 | 0.116 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 116 | 105 | 168 | 0 | 447 | 0 | 0 | 71 | 0 |
N.S. |
1 | 0.74 | 0.67 | 1.07 | 0.00 | 2.85 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.453 | 0.050 | 0.186 | 0.000 | 0.134 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 147 | 126 | 276 | 0 | 526 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.74 | 0.64 | 1.39 | 0.00 | 2.66 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.500 | 0.121 | 0.203 | 0.000 | 0.142 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 187 | 139 | 365 | 0 | 600 | 0 | 0 | 233 | 0 |
N.S. |
1 | 0.75 | 0.56 | 1.47 | 0.00 | 2.41 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.535 | 0.147 | 0.213 | 0.000 | 0.144 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 91 | 155 | 0 | 243 | 2222 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.07 | 0.00 | 1.68 | 15.32 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.391 | 0.147 | 0.211 | 0.000 | 0.084 | 13.121 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 123 | 83 | 144 | 0 | 221 | 740 | 0 | 105 | 0 |
N.S. |
1 | 1.02 | 0.69 | 1.20 | 0.00 | 1.84 | 6.17 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.370 | 0.083 | 0.220 | 0.000 | 0.082 | 11.108 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 102 | 75 | 108 | 0 | 191 | 144 | 0 | 87 | 0 |
N.S. |
1 | 1.06 | 0.78 | 1.12 | 0.00 | 1.99 | 1.50 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.365 | 0.069 | 0.215 | 0.000 | 0.093 | 3.485 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 79 | 57 | 103 | 0 | 145 | 173 | 0 | 59 | 0 |
N.S. |
1 | 1.11 | 0.80 | 1.45 | 0.00 | 2.04 | 2.44 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.350 | 0.054 | 0.193 | 0.000 | 0.080 | 12.370 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 51 | 99 | 0 | 134 | 0 | 97 | 34 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.94 | 0.00 | 2.63 | 0.00 | 1.90 | 0.67 | 0.00 |
time (sec) |
N/A | 0.328 | 0.021 | 0.194 | 0.000 | 0.073 | 0.000 | 0.147 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 82 | 44 | 152 | 0 | 184 | 0 | 171 | 62 | 0 |
N.S. |
1 | 1.15 | 0.62 | 2.14 | 0.00 | 2.59 | 0.00 | 2.41 | 0.87 | 0.00 |
time (sec) |
N/A | 0.343 | 0.020 | 0.197 | 0.000 | 0.093 | 0.000 | 0.161 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 109 | 55 | 203 | 0 | 247 | 0 | 246 | 114 | 0 |
N.S. |
1 | 1.14 | 0.57 | 2.11 | 0.00 | 2.57 | 0.00 | 2.56 | 1.19 | 0.00 |
time (sec) |
N/A | 0.360 | 0.023 | 0.210 | 0.000 | 0.100 | 0.000 | 0.175 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 136 | 59 | 249 | 0 | 303 | 0 | 317 | 175 | 0 |
N.S. |
1 | 1.14 | 0.50 | 2.09 | 0.00 | 2.55 | 0.00 | 2.66 | 1.47 | 0.00 |
time (sec) |
N/A | 0.386 | 0.021 | 0.217 | 0.000 | 0.093 | 0.000 | 0.235 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 163 | 46 | 293 | 0 | 355 | 0 | 392 | 236 | 0 |
N.S. |
1 | 1.12 | 0.32 | 2.01 | 0.00 | 2.43 | 0.00 | 2.68 | 1.62 | 0.00 |
time (sec) |
N/A | 0.409 | 0.032 | 0.214 | 0.000 | 0.096 | 0.000 | 0.338 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 159 | 85 | 172 | 0 | 386 | 0 | 0 | 127 | 0 |
N.S. |
1 | 0.61 | 0.33 | 0.66 | 0.00 | 1.48 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.480 | 0.056 | 0.203 | 0.000 | 0.127 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 131 | 77 | 154 | 0 | 364 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.60 | 0.35 | 0.71 | 0.00 | 1.68 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.456 | 0.046 | 0.205 | 0.000 | 0.142 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 109 | 66 | 136 | 0 | 330 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.63 | 0.38 | 0.79 | 0.00 | 1.91 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.447 | 0.035 | 0.200 | 0.000 | 0.109 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 85 | 42 | 109 | 0 | 268 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.67 | 0.33 | 0.86 | 0.00 | 2.11 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.431 | 0.020 | 0.194 | 0.000 | 0.118 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 110 | 105 | 165 | 0 | 442 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.71 | 0.68 | 1.06 | 0.00 | 2.85 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.439 | 0.039 | 0.211 | 0.000 | 0.196 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 139 | 120 | 276 | 0 | 513 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.71 | 0.62 | 1.42 | 0.00 | 2.63 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.472 | 0.121 | 0.230 | 0.000 | 0.138 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 182 | 139 | 364 | 0 | 600 | 0 | 0 | 233 | 0 |
N.S. |
1 | 0.73 | 0.56 | 1.46 | 0.00 | 2.41 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.529 | 0.167 | 0.249 | 0.000 | 0.155 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 219 | 147 | 416 | 0 | 668 | 0 | 0 | 320 | 0 |
N.S. |
1 | 0.75 | 0.50 | 1.42 | 0.00 | 2.28 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.567 | 0.142 | 0.247 | 0.000 | 0.142 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 169 | 108 | 172 | 0 | 386 | 0 | 0 | 127 | 0 |
N.S. |
1 | 0.64 | 0.41 | 0.65 | 0.00 | 1.47 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.494 | 0.136 | 0.204 | 0.000 | 0.111 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 137 | 95 | 154 | 0 | 364 | 0 | 0 | 109 | 0 |
N.S. |
1 | 0.63 | 0.44 | 0.71 | 0.00 | 1.68 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.463 | 0.077 | 0.208 | 0.000 | 0.153 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 105 | 87 | 136 | 0 | 330 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.61 | 0.50 | 0.79 | 0.00 | 1.91 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.434 | 0.055 | 0.207 | 0.000 | 0.133 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 87 | 71 | 109 | 0 | 268 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.69 | 0.56 | 0.87 | 0.00 | 2.13 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.421 | 0.045 | 0.201 | 0.000 | 0.111 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 67 | 67 | 91 | 0 | 250 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.77 | 0.77 | 1.05 | 0.00 | 2.87 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.409 | 0.044 | 0.198 | 0.000 | 0.112 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 69 | 69 | 92 | 0 | 254 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.78 | 0.78 | 1.05 | 0.00 | 2.89 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.438 | 0.042 | 0.206 | 0.000 | 0.110 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 116 | 107 | 168 | 0 | 453 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.73 | 0.67 | 1.06 | 0.00 | 2.85 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.485 | 0.052 | 0.226 | 0.000 | 0.148 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 150 | 127 | 276 | 0 | 528 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.72 | 0.61 | 1.33 | 0.00 | 2.54 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.506 | 0.146 | 0.238 | 0.000 | 0.192 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 187 | 139 | 367 | 0 | 600 | 0 | 0 | 233 | 0 |
N.S. |
1 | 0.74 | 0.55 | 1.46 | 0.00 | 2.38 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.563 | 0.201 | 0.260 | 0.000 | 0.167 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 193 | 133 | 232 | 0 | 359 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.02 | 0.70 | 1.23 | 0.00 | 1.90 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.509 | 0.339 | 0.214 | 0.000 | 0.105 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 171 | 125 | 224 | 0 | 337 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.04 | 0.76 | 1.37 | 0.00 | 2.05 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.447 | 0.170 | 0.211 | 0.000 | 0.089 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 149 | 116 | 214 | 0 | 299 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.07 | 0.83 | 1.54 | 0.00 | 2.15 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.451 | 0.081 | 0.208 | 0.000 | 0.093 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 127 | 96 | 195 | 0 | 248 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.12 | 0.85 | 1.73 | 0.00 | 2.19 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.413 | 0.066 | 0.245 | 0.000 | 0.102 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 107 | 93 | 170 | 0 | 234 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.15 | 1.00 | 1.83 | 0.00 | 2.52 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.401 | 0.030 | 0.185 | 0.000 | 0.100 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 104 | 96 | 136 | 0 | 233 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.08 | 1.00 | 1.42 | 0.00 | 2.43 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.387 | 0.033 | 0.178 | 0.000 | 0.094 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 115 | 95 | 134 | 0 | 232 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.21 | 1.00 | 1.41 | 0.00 | 2.44 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.382 | 0.040 | 0.205 | 0.000 | 0.098 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 67 | 229 | 0 | 301 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.10 | 0.56 | 1.92 | 0.00 | 2.53 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.420 | 0.038 | 0.216 | 0.000 | 0.102 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 161 | 77 | 273 | 0 | 373 | 0 | 0 | 304 | 0 |
N.S. |
1 | 1.09 | 0.52 | 1.84 | 0.00 | 2.52 | 0.00 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.449 | 0.044 | 0.220 | 0.000 | 0.094 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 191 | 82 | 317 | 0 | 445 | 0 | 0 | 475 | 0 |
N.S. |
1 | 1.10 | 0.47 | 1.83 | 0.00 | 2.57 | 0.00 | 0.00 | 2.75 | 0.00 |
time (sec) |
N/A | 0.489 | 0.045 | 0.229 | 0.000 | 0.095 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 188 | 152 | 227 | 0 | 408 | 0 | 0 | 129 | 0 |
N.S. |
1 | 0.62 | 0.50 | 0.74 | 0.00 | 1.34 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.524 | 0.330 | 0.217 | 0.000 | 0.126 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 164 | 200 | 209 | 0 | 386 | 0 | 0 | 117 | 0 |
N.S. |
1 | 0.62 | 0.76 | 0.79 | 0.00 | 1.47 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.491 | 0.382 | 0.217 | 0.000 | 0.121 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 132 | 97 | 191 | 0 | 352 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.61 | 0.45 | 0.88 | 0.00 | 1.62 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.463 | 0.056 | 0.214 | 0.000 | 0.115 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 100 | 80 | 164 | 0 | 298 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.60 | 0.48 | 0.99 | 0.00 | 1.80 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.444 | 0.054 | 0.215 | 0.000 | 0.121 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 82 | 82 | 140 | 0 | 282 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.67 | 0.67 | 1.14 | 0.00 | 2.29 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.411 | 0.055 | 0.210 | 0.000 | 0.106 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 88 | 86 | 143 | 0 | 286 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.70 | 0.68 | 1.13 | 0.00 | 2.27 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.449 | 0.061 | 0.209 | 0.000 | 0.128 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 94 | 44 | 143 | 0 | 294 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.72 | 0.34 | 1.09 | 0.00 | 2.24 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.450 | 0.036 | 0.208 | 0.000 | 0.123 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 139 | 162 | 279 | 0 | 492 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.70 | 0.81 | 1.40 | 0.00 | 2.47 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.509 | 0.135 | 0.246 | 0.000 | 0.180 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 177 | 234 | 315 | 0 | 596 | 0 | 0 | 177 | 0 |
N.S. |
1 | 0.71 | 0.93 | 1.25 | 0.00 | 2.37 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.527 | 0.626 | 0.257 | 0.000 | 0.152 | 0.000 | 0.000 | 0.183 | 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 | 163 | 154 | 102 | 0 | 0 | 0 | 0 | 0 | 938 | 0 |
N.S. |
1 | 0.94 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.75 | 0.00 |
time (sec) |
N/A | 0.420 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 93 | 108 | 81 | 0 | 0 | 0 | 0 | 0 | 345 | 0 |
N.S. |
1 | 1.16 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.71 | 0.00 |
time (sec) |
N/A | 0.356 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 68 | 46 | 0 | 0 | 0 | 270 | 0 | 89 | 0 |
N.S. |
1 | 1.15 | 0.78 | 0.00 | 0.00 | 0.00 | 4.58 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.297 | 0.013 | 0.000 | 0.000 | 0.000 | 4.750 | 0.000 | 0.150 | 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 | 114 | 123 | 87 | 0 | 0 | 0 | 0 | 0 | 218 | 0 |
N.S. |
1 | 1.08 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.361 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 164 | 183 | 116 | 0 | 0 | 0 | 0 | 0 | 1759 | 0 |
N.S. |
1 | 1.12 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.73 | 0.00 |
time (sec) |
N/A | 0.443 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 0 | 0 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.80 | 0.00 |
time (sec) |
N/A | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 0 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 0 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 0 | 0 | 0 | 0 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.360 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.381 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.379 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 50 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.364 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 129 | 262 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 0.99 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.415 | 0.464 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 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 | 187 | 194 | 149 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.469 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 109 | 95 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.98 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.385 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 145 | 97 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.04 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.454 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.420 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.410 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.410 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
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 | 118 | 99 | 92 | 165 | 0 | 120 | 0 | 217 | 168 | 138 |
N.S. |
1 | 0.84 | 0.78 | 1.40 | 0.00 | 1.02 | 0.00 | 1.84 | 1.42 | 1.17 |
time (sec) |
N/A | 0.514 | 0.040 | 0.303 | 0.000 | 0.089 | 0.000 | 0.152 | 0.153 | 0.044 |