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 | 140 | 140 | 142 | 123 | 127 | 131 | 124 | 128 | 135 | 121 |
N.S. |
1 | 1.00 | 1.01 | 0.88 | 0.91 | 0.94 | 0.89 | 0.91 | 0.96 | 0.86 |
time (sec) |
N/A | 0.522 | 0.041 | 0.795 | 0.035 | 0.065 | 0.856 | 0.212 | 0.274 | 10.841 |
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 | 140 | 140 | 142 | 123 | 127 | 131 | 128 | 128 | 135 | 121 |
N.S. |
1 | 1.00 | 1.01 | 0.88 | 0.91 | 0.94 | 0.91 | 0.91 | 0.96 | 0.86 |
time (sec) |
N/A | 0.514 | 0.041 | 0.784 | 0.035 | 0.064 | 1.234 | 0.180 | 0.271 | 10.853 |
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 | 138 | 138 | 139 | 122 | 127 | 131 | 128 | 128 | 135 | 121 |
N.S. |
1 | 1.00 | 1.01 | 0.88 | 0.92 | 0.95 | 0.93 | 0.93 | 0.98 | 0.88 |
time (sec) |
N/A | 0.529 | 0.043 | 0.807 | 0.026 | 0.066 | 1.760 | 0.184 | 0.278 | 0.062 |
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 | 138 | 138 | 140 | 121 | 127 | 131 | 126 | 128 | 135 | 121 |
N.S. |
1 | 1.00 | 1.01 | 0.88 | 0.92 | 0.95 | 0.91 | 0.93 | 0.98 | 0.88 |
time (sec) |
N/A | 0.515 | 0.044 | 0.896 | 0.026 | 0.064 | 2.525 | 0.375 | 0.285 | 10.827 |
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 | 137 | 137 | 139 | 119 | 126 | 131 | 126 | 127 | 135 | 119 |
N.S. |
1 | 1.00 | 1.01 | 0.87 | 0.92 | 0.96 | 0.92 | 0.93 | 0.99 | 0.87 |
time (sec) |
N/A | 0.519 | 0.049 | 0.790 | 0.026 | 0.069 | 3.331 | 0.180 | 0.279 | 0.072 |
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 | 138 | 138 | 140 | 119 | 125 | 131 | 124 | 126 | 135 | 118 |
N.S. |
1 | 1.00 | 1.01 | 0.86 | 0.91 | 0.95 | 0.90 | 0.91 | 0.98 | 0.86 |
time (sec) |
N/A | 0.496 | 0.051 | 0.799 | 0.032 | 0.068 | 4.483 | 0.190 | 0.280 | 10.873 |
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 | 92 | 83 | 143 | 122 | 128 | 131 | 129 | 129 | 133 | 118 |
N.S. |
1 | 0.90 | 1.55 | 1.33 | 1.39 | 1.42 | 1.40 | 1.40 | 1.45 | 1.28 |
time (sec) |
N/A | 0.378 | 0.055 | 0.839 | 0.032 | 0.067 | 5.566 | 0.144 | 0.275 | 10.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 114 | 123 | 129 | 129 | 131 | 131 | 131 | 120 |
N.S. |
1 | 1.00 | 3.68 | 3.97 | 4.16 | 4.16 | 4.23 | 4.23 | 4.23 | 3.87 |
time (sec) |
N/A | 0.268 | 0.031 | 0.773 | 0.027 | 0.063 | 6.909 | 0.173 | 0.289 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 115 | 123 | 129 | 129 | 131 | 131 | 131 | 123 |
N.S. |
1 | 0.96 | 2.21 | 2.37 | 2.48 | 2.48 | 2.52 | 2.52 | 2.52 | 2.37 |
time (sec) |
N/A | 0.292 | 0.029 | 0.862 | 0.033 | 0.064 | 7.934 | 0.159 | 0.284 | 10.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 67 | 149 | 123 | 129 | 129 | 131 | 131 | 131 | 123 |
N.S. |
1 | 0.94 | 2.10 | 1.73 | 1.82 | 1.82 | 1.85 | 1.85 | 1.85 | 1.73 |
time (sec) |
N/A | 0.300 | 0.043 | 0.770 | 0.033 | 0.073 | 9.486 | 0.190 | 0.277 | 10.632 |
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 | 90 | 84 | 153 | 123 | 129 | 129 | 131 | 131 | 131 | 123 |
N.S. |
1 | 0.93 | 1.70 | 1.37 | 1.43 | 1.43 | 1.46 | 1.46 | 1.46 | 1.37 |
time (sec) |
N/A | 0.319 | 0.042 | 0.825 | 0.027 | 0.069 | 10.519 | 0.231 | 0.281 | 0.130 |
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 | 109 | 101 | 153 | 123 | 129 | 129 | 131 | 131 | 131 | 123 |
N.S. |
1 | 0.93 | 1.40 | 1.13 | 1.18 | 1.18 | 1.20 | 1.20 | 1.20 | 1.13 |
time (sec) |
N/A | 0.338 | 0.042 | 0.764 | 0.028 | 0.067 | 12.493 | 0.166 | 0.287 | 10.607 |
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 | 128 | 118 | 151 | 123 | 129 | 129 | 131 | 131 | 131 | 123 |
N.S. |
1 | 0.92 | 1.18 | 0.96 | 1.01 | 1.01 | 1.02 | 1.02 | 1.02 | 0.96 |
time (sec) |
N/A | 0.363 | 0.049 | 0.761 | 0.026 | 0.062 | 14.073 | 0.160 | 0.264 | 0.124 |
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 | 151 | 151 | 151 | 123 | 129 | 129 | 131 | 131 | 131 | 123 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.85 | 0.85 | 0.87 | 0.87 | 0.87 | 0.81 |
time (sec) |
N/A | 0.522 | 0.054 | 0.774 | 0.028 | 0.062 | 15.620 | 0.171 | 0.278 | 0.128 |
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 | 149 | 149 | 149 | 123 | 129 | 129 | 131 | 131 | 131 | 121 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.87 | 0.87 | 0.88 | 0.88 | 0.88 | 0.81 |
time (sec) |
N/A | 0.511 | 0.047 | 0.813 | 0.036 | 0.061 | 17.479 | 0.192 | 0.273 | 0.124 |
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 | 151 | 151 | 151 | 123 | 129 | 129 | 131 | 131 | 131 | 121 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.85 | 0.85 | 0.87 | 0.87 | 0.87 | 0.80 |
time (sec) |
N/A | 0.515 | 0.050 | 0.751 | 0.026 | 0.064 | 19.227 | 0.182 | 0.283 | 0.132 |
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 | 83 | 83 | 83 | 61 | 61 | 61 | 73 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.73 | 0.73 | 0.88 | 0.73 | 0.72 | 0.73 |
time (sec) |
N/A | 0.378 | 0.003 | 0.931 | 0.026 | 0.062 | 0.020 | 0.162 | 0.299 | 0.077 |
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 | 83 | 83 | 83 | 61 | 61 | 61 | 75 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.73 | 0.73 | 0.90 | 0.73 | 0.72 | 0.73 |
time (sec) |
N/A | 0.378 | 0.003 | 0.823 | 0.032 | 0.070 | 0.024 | 0.195 | 0.283 | 0.076 |
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 | 91 | 91 | 81 | 60 | 59 | 59 | 73 | 59 | 60 | 59 |
N.S. |
1 | 1.00 | 0.89 | 0.66 | 0.65 | 0.65 | 0.80 | 0.65 | 0.66 | 0.65 |
time (sec) |
N/A | 0.401 | 0.003 | 0.924 | 0.027 | 0.060 | 0.026 | 0.182 | 0.275 | 0.075 |
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 | 80 | 80 | 81 | 61 | 61 | 61 | 73 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.01 | 0.76 | 0.76 | 0.76 | 0.91 | 0.76 | 0.75 | 0.76 |
time (sec) |
N/A | 0.383 | 0.003 | 0.816 | 0.024 | 0.059 | 0.021 | 0.178 | 0.275 | 0.075 |
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 | 73 | 79 | 61 | 61 | 61 | 71 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.08 | 0.84 | 0.84 | 0.84 | 0.97 | 0.84 | 0.82 | 0.84 |
time (sec) |
N/A | 0.369 | 0.003 | 0.938 | 0.035 | 0.062 | 0.021 | 0.156 | 0.269 | 0.076 |
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 | 64 | 64 | 81 | 61 | 61 | 61 | 73 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.27 | 0.95 | 0.95 | 0.95 | 1.14 | 0.95 | 0.94 | 0.95 |
time (sec) |
N/A | 0.352 | 0.003 | 0.817 | 0.029 | 0.064 | 0.028 | 0.184 | 0.282 | 0.075 |
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 | 55 | 81 | 61 | 61 | 61 | 73 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.47 | 1.11 | 1.11 | 1.11 | 1.33 | 1.11 | 1.09 | 1.11 |
time (sec) |
N/A | 0.352 | 0.003 | 0.883 | 0.030 | 0.059 | 0.024 | 0.148 | 0.270 | 0.076 |
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 | 46 | 46 | 83 | 61 | 61 | 61 | 75 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 1.80 | 1.33 | 1.33 | 1.33 | 1.63 | 1.33 | 1.30 | 1.33 |
time (sec) |
N/A | 0.325 | 0.003 | 0.817 | 0.031 | 0.069 | 0.021 | 0.174 | 0.270 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 83 | 61 | 61 | 61 | 75 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 2.24 | 1.65 | 1.65 | 1.65 | 2.03 | 1.65 | 1.62 | 1.65 |
time (sec) |
N/A | 0.319 | 0.003 | 0.876 | 0.025 | 0.061 | 0.022 | 0.180 | 0.282 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 79 | 61 | 61 | 61 | 71 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 2.82 | 2.18 | 2.18 | 2.18 | 2.54 | 2.18 | 2.14 | 2.18 |
time (sec) |
N/A | 0.312 | 0.003 | 0.802 | 0.034 | 0.058 | 0.025 | 0.179 | 0.284 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 77 | 61 | 61 | 61 | 70 | 61 | 60 | 61 |
N.S. |
1 | 1.00 | 4.05 | 3.21 | 3.21 | 3.21 | 3.68 | 3.21 | 3.16 | 3.21 |
time (sec) |
N/A | 0.279 | 0.003 | 0.786 | 0.030 | 0.062 | 0.022 | 0.161 | 0.269 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 13 | 12 | 55 | 65 | 62 | 56 | 55 |
N.S. |
1 | 1.00 | 1.00 | 1.44 | 1.33 | 6.11 | 7.22 | 6.89 | 6.22 | 6.11 |
time (sec) |
N/A | 0.227 | 0.002 | 0.832 | 0.036 | 0.060 | 0.027 | 0.183 | 0.281 | 0.072 |
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 | 72 | 72 | 96 | 57 | 56 | 56 | 68 | 57 | 56 | 56 |
N.S. |
1 | 1.00 | 1.33 | 0.79 | 0.78 | 0.78 | 0.94 | 0.79 | 0.78 | 0.78 |
time (sec) |
N/A | 0.323 | 0.013 | 0.755 | 0.031 | 0.061 | 0.041 | 0.191 | 0.268 | 0.075 |
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 | 72 | 72 | 72 | 59 | 58 | 62 | 66 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.81 | 0.86 | 0.92 | 0.82 | 0.86 | 0.81 |
time (sec) |
N/A | 0.348 | 0.005 | 0.815 | 0.025 | 0.060 | 0.043 | 0.145 | 0.289 | 0.075 |
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 | 70 | 70 | 70 | 58 | 58 | 62 | 66 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.89 | 0.94 | 0.84 | 0.89 | 0.83 |
time (sec) |
N/A | 0.345 | 0.004 | 0.780 | 0.030 | 0.063 | 0.058 | 0.196 | 0.295 | 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 | 70 | 70 | 70 | 58 | 58 | 62 | 65 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.89 | 0.93 | 0.84 | 0.89 | 0.83 |
time (sec) |
N/A | 0.344 | 0.005 | 0.835 | 0.035 | 0.067 | 0.053 | 0.125 | 0.276 | 0.056 |
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 | 70 | 70 | 70 | 58 | 58 | 62 | 63 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.89 | 0.90 | 0.84 | 0.89 | 0.83 |
time (sec) |
N/A | 0.347 | 0.004 | 0.764 | 0.031 | 0.067 | 0.054 | 0.127 | 0.272 | 0.038 |
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 | 72 | 72 | 72 | 58 | 58 | 62 | 63 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.86 | 0.88 | 0.82 | 0.86 | 0.81 |
time (sec) |
N/A | 0.346 | 0.005 | 0.787 | 0.031 | 0.071 | 0.057 | 0.145 | 0.271 | 0.033 |
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 | 72 | 72 | 72 | 58 | 58 | 62 | 65 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.86 | 0.90 | 0.82 | 0.86 | 0.81 |
time (sec) |
N/A | 0.352 | 0.004 | 0.812 | 0.033 | 0.060 | 0.061 | 0.157 | 0.283 | 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 | 70 | 70 | 70 | 58 | 58 | 62 | 63 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.89 | 0.90 | 0.84 | 0.89 | 0.83 |
time (sec) |
N/A | 0.367 | 0.004 | 0.760 | 0.024 | 0.063 | 0.058 | 0.142 | 0.268 | 0.027 |
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 | 70 | 70 | 70 | 58 | 58 | 62 | 61 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.89 | 0.87 | 0.84 | 0.89 | 0.83 |
time (sec) |
N/A | 0.358 | 0.004 | 0.772 | 0.032 | 0.062 | 0.076 | 0.178 | 0.291 | 0.026 |
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 | 70 | 70 | 70 | 58 | 58 | 62 | 60 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.89 | 0.86 | 0.84 | 0.89 | 0.83 |
time (sec) |
N/A | 0.354 | 0.004 | 0.803 | 0.032 | 0.062 | 0.072 | 0.144 | 0.275 | 0.033 |
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 | 70 | 70 | 70 | 56 | 56 | 62 | 58 | 57 | 62 | 62 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.89 | 0.83 | 0.81 | 0.89 | 0.89 |
time (sec) |
N/A | 0.353 | 0.005 | 0.851 | 0.031 | 0.063 | 0.070 | 0.232 | 0.271 | 10.556 |
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 | 74 | 74 | 74 | 58 | 58 | 62 | 60 | 59 | 62 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.78 | 0.84 | 0.81 | 0.80 | 0.84 | 0.78 |
time (sec) |
N/A | 0.355 | 0.004 | 0.799 | 0.026 | 0.064 | 0.074 | 0.191 | 0.266 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 75 | 60 | 60 | 60 | 61 | 60 | 60 | 56 |
N.S. |
1 | 1.00 | 6.25 | 5.00 | 5.00 | 5.00 | 5.08 | 5.00 | 5.00 | 4.67 |
time (sec) |
N/A | 0.245 | 0.004 | 0.745 | 0.026 | 0.060 | 0.073 | 0.180 | 0.271 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 77 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.00 | 3.08 | 2.40 | 2.40 | 2.40 | 2.44 | 2.40 | 2.40 | 2.40 |
time (sec) |
N/A | 0.265 | 0.004 | 0.746 | 0.029 | 0.061 | 0.104 | 0.200 | 0.320 | 10.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 42 | 79 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.14 | 2.14 | 1.62 | 1.62 | 1.62 | 1.65 | 1.62 | 1.62 | 1.62 |
time (sec) |
N/A | 0.264 | 0.004 | 0.815 | 0.039 | 0.061 | 0.115 | 0.212 | 0.280 | 0.033 |
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 | 59 | 83 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.20 | 1.69 | 1.22 | 1.22 | 1.22 | 1.24 | 1.22 | 1.22 | 1.22 |
time (sec) |
N/A | 0.283 | 0.004 | 0.749 | 0.026 | 0.061 | 0.089 | 0.178 | 0.289 | 10.523 |
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 | 76 | 83 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.25 | 1.36 | 0.98 | 0.98 | 0.98 | 1.00 | 0.98 | 0.98 | 0.98 |
time (sec) |
N/A | 0.296 | 0.004 | 0.808 | 0.025 | 0.065 | 0.084 | 0.220 | 0.271 | 0.033 |
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 | 93 | 81 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.27 | 1.11 | 0.82 | 0.82 | 0.82 | 0.84 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.312 | 0.004 | 0.829 | 0.036 | 0.062 | 0.089 | 0.169 | 0.283 | 10.665 |
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 | 85 | 110 | 81 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.29 | 0.95 | 0.71 | 0.71 | 0.71 | 0.72 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.321 | 0.004 | 0.762 | 0.029 | 0.060 | 0.085 | 0.189 | 0.289 | 10.637 |
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 | 97 | 127 | 79 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.31 | 0.81 | 0.62 | 0.62 | 0.62 | 0.63 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.343 | 0.004 | 0.739 | 0.031 | 0.065 | 0.096 | 0.186 | 0.278 | 0.034 |
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 | 81 | 81 | 81 | 60 | 60 | 60 | 61 | 60 | 60 | 60 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.74 | 0.74 | 0.75 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.345 | 0.004 | 0.856 | 0.031 | 0.066 | 0.101 | 0.198 | 0.265 | 10.695 |
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 | 83 | 83 | 83 | 60 | 60 | 60 | 61 | 60 | 60 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.72 | 0.72 | 0.73 | 0.72 | 0.72 | 0.70 |
time (sec) |
N/A | 0.349 | 0.007 | 0.762 | 0.025 | 0.066 | 0.097 | 0.189 | 0.290 | 0.037 |
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 | 134 | 134 | 127 | 136 | 149 | 188 | 143 | 152 | 63 | 279 |
N.S. |
1 | 1.00 | 0.95 | 1.01 | 1.11 | 1.40 | 1.07 | 1.13 | 0.47 | 2.08 |
time (sec) |
N/A | 0.615 | 0.071 | 1.096 | 0.031 | 0.072 | 0.288 | 0.210 | 0.279 | 0.075 |
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 | 113 | 113 | 107 | 116 | 123 | 164 | 119 | 126 | 52 | 173 |
N.S. |
1 | 1.00 | 0.95 | 1.03 | 1.09 | 1.45 | 1.05 | 1.12 | 0.46 | 1.53 |
time (sec) |
N/A | 0.542 | 0.065 | 1.025 | 0.026 | 0.072 | 0.250 | 0.208 | 0.285 | 10.843 |
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 | 90 | 90 | 87 | 90 | 101 | 140 | 92 | 104 | 41 | 115 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 1.12 | 1.56 | 1.02 | 1.16 | 0.46 | 1.28 |
time (sec) |
N/A | 0.472 | 0.057 | 1.129 | 0.027 | 0.079 | 0.236 | 0.197 | 0.297 | 0.055 |
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 | 69 | 69 | 66 | 67 | 74 | 113 | 68 | 75 | 29 | 77 |
N.S. |
1 | 1.00 | 0.96 | 0.97 | 1.07 | 1.64 | 0.99 | 1.09 | 0.42 | 1.12 |
time (sec) |
N/A | 0.418 | 0.065 | 1.025 | 0.026 | 0.071 | 0.197 | 0.168 | 0.282 | 0.063 |
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 | 45 | 41 | 46 | 53 | 72 | 44 | 51 | 17 | 54 |
N.S. |
1 | 1.00 | 0.91 | 1.02 | 1.18 | 1.60 | 0.98 | 1.13 | 0.38 | 1.20 |
time (sec) |
N/A | 0.355 | 0.027 | 1.111 | 0.034 | 0.067 | 0.147 | 0.240 | 0.280 | 11.142 |
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 | 32 | 32 | 31 | 33 | 34 | 37 | 27 | 32 | 10 | 32 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.06 | 1.16 | 0.84 | 1.00 | 0.31 | 1.00 |
time (sec) |
N/A | 0.322 | 0.013 | 1.004 | 0.037 | 0.071 | 0.085 | 0.204 | 0.280 | 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 | 42 | 42 | 38 | 42 | 44 | 62 | 32 | 48 | 15 | 39 |
N.S. |
1 | 1.00 | 0.90 | 1.00 | 1.05 | 1.48 | 0.76 | 1.14 | 0.36 | 0.93 |
time (sec) |
N/A | 0.354 | 0.029 | 1.089 | 0.033 | 0.074 | 0.140 | 0.230 | 0.301 | 10.972 |
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 | 65 | 65 | 56 | 64 | 67 | 107 | 128 | 71 | 26 | 58 |
N.S. |
1 | 1.00 | 0.86 | 0.98 | 1.03 | 1.65 | 1.97 | 1.09 | 0.40 | 0.89 |
time (sec) |
N/A | 0.414 | 0.042 | 1.095 | 0.033 | 0.079 | 0.253 | 0.200 | 0.268 | 11.018 |
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 | 85 | 85 | 85 | 84 | 99 | 150 | 184 | 106 | 43 | 104 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.16 | 1.76 | 2.16 | 1.25 | 0.51 | 1.22 |
time (sec) |
N/A | 0.468 | 0.080 | 1.064 | 0.031 | 0.074 | 0.299 | 0.189 | 0.264 | 10.975 |
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 | 113 | 113 | 106 | 109 | 128 | 179 | 219 | 133 | 54 | 131 |
N.S. |
1 | 1.00 | 0.94 | 0.96 | 1.13 | 1.58 | 1.94 | 1.18 | 0.48 | 1.16 |
time (sec) |
N/A | 0.519 | 0.104 | 1.237 | 0.038 | 0.074 | 0.381 | 0.193 | 0.272 | 0.114 |
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 | 133 | 133 | 129 | 127 | 152 | 203 | 243 | 157 | 65 | 150 |
N.S. |
1 | 1.00 | 0.97 | 0.95 | 1.14 | 1.53 | 1.83 | 1.18 | 0.49 | 1.13 |
time (sec) |
N/A | 0.566 | 0.097 | 1.066 | 0.032 | 0.073 | 0.369 | 0.205 | 0.270 | 10.972 |
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 | 143 | 143 | 147 | 140 | 168 | 257 | 168 | 149 | 109 | 180 |
N.S. |
1 | 1.00 | 1.03 | 0.98 | 1.17 | 1.80 | 1.17 | 1.04 | 0.76 | 1.26 |
time (sec) |
N/A | 0.636 | 0.057 | 1.093 | 0.037 | 0.075 | 0.766 | 0.216 | 0.287 | 11.011 |
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 | 121 | 121 | 129 | 115 | 143 | 231 | 144 | 124 | 97 | 141 |
N.S. |
1 | 1.00 | 1.07 | 0.95 | 1.18 | 1.91 | 1.19 | 1.02 | 0.80 | 1.17 |
time (sec) |
N/A | 0.564 | 0.048 | 1.096 | 0.040 | 0.078 | 0.732 | 0.194 | 0.275 | 0.087 |
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 | 97 | 97 | 97 | 89 | 120 | 193 | 119 | 96 | 85 | 118 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.24 | 1.99 | 1.23 | 0.99 | 0.88 | 1.22 |
time (sec) |
N/A | 0.488 | 0.039 | 1.052 | 0.037 | 0.070 | 0.613 | 0.231 | 0.273 | 10.663 |
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 | 72 | 75 | 73 | 71 | 100 | 128 | 100 | 76 | 71 | 96 |
N.S. |
1 | 1.04 | 1.01 | 0.99 | 1.39 | 1.78 | 1.39 | 1.06 | 0.99 | 1.33 |
time (sec) |
N/A | 0.396 | 0.028 | 1.026 | 0.037 | 0.075 | 0.342 | 0.203 | 0.274 | 0.082 |
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 | 59 | 59 | 42 | 47 | 71 | 71 | 75 | 45 | 26 | 68 |
N.S. |
1 | 1.00 | 0.71 | 0.80 | 1.20 | 1.20 | 1.27 | 0.76 | 0.44 | 1.15 |
time (sec) |
N/A | 0.380 | 0.018 | 1.060 | 0.029 | 0.065 | 0.263 | 0.230 | 0.304 | 10.393 |
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 | 38 | 38 | 27 | 33 | 50 | 50 | 53 | 25 | 23 | 52 |
N.S. |
1 | 1.00 | 0.71 | 0.87 | 1.32 | 1.32 | 1.39 | 0.66 | 0.61 | 1.37 |
time (sec) |
N/A | 0.332 | 0.013 | 1.103 | 0.037 | 0.066 | 0.195 | 0.212 | 0.294 | 0.031 |
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 | 72 | 72 | 65 | 69 | 91 | 156 | 90 | 71 | 97 | 84 |
N.S. |
1 | 1.00 | 0.90 | 0.96 | 1.26 | 2.17 | 1.25 | 0.99 | 1.35 | 1.17 |
time (sec) |
N/A | 0.405 | 0.050 | 1.027 | 0.029 | 0.072 | 0.276 | 0.235 | 0.297 | 10.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 102 | 106 | 134 | 267 | 204 | 122 | 119 | 118 |
N.S. |
1 | 1.00 | 0.92 | 0.95 | 1.21 | 2.41 | 1.84 | 1.10 | 1.07 | 1.06 |
time (sec) |
N/A | 0.516 | 0.069 | 1.052 | 0.039 | 0.077 | 0.391 | 0.200 | 0.274 | 10.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 123 | 130 | 172 | 318 | 264 | 157 | 138 | 168 |
N.S. |
1 | 1.00 | 0.91 | 0.96 | 1.27 | 2.36 | 1.96 | 1.16 | 1.02 | 1.24 |
time (sec) |
N/A | 0.574 | 0.138 | 1.064 | 0.038 | 0.077 | 0.515 | 0.211 | 0.264 | 0.137 |
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 | 166 | 166 | 148 | 158 | 193 | 333 | 291 | 175 | 149 | 195 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 1.16 | 2.01 | 1.75 | 1.05 | 0.90 | 1.17 |
time (sec) |
N/A | 0.686 | 0.150 | 1.132 | 0.033 | 0.076 | 0.501 | 0.190 | 0.305 | 10.563 |
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 | 171 | 171 | 151 | 163 | 213 | 349 | 216 | 172 | 172 | 210 |
N.S. |
1 | 1.00 | 0.88 | 0.95 | 1.25 | 2.04 | 1.26 | 1.01 | 1.01 | 1.23 |
time (sec) |
N/A | 0.732 | 0.106 | 1.055 | 0.038 | 0.081 | 1.659 | 0.234 | 0.285 | 10.586 |
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 | 146 | 146 | 130 | 129 | 190 | 311 | 190 | 144 | 159 | 187 |
N.S. |
1 | 1.00 | 0.89 | 0.88 | 1.30 | 2.13 | 1.30 | 0.99 | 1.09 | 1.28 |
time (sec) |
N/A | 0.651 | 0.091 | 1.102 | 0.036 | 0.078 | 1.415 | 0.203 | 0.295 | 0.128 |
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 | 106 | 107 | 113 | 111 | 170 | 222 | 172 | 124 | 147 | 161 |
N.S. |
1 | 1.01 | 1.07 | 1.05 | 1.60 | 2.09 | 1.62 | 1.17 | 1.39 | 1.52 |
time (sec) |
N/A | 0.475 | 0.049 | 1.033 | 0.037 | 0.076 | 1.055 | 0.202 | 0.267 | 10.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 76 | 85 | 139 | 139 | 150 | 93 | 48 | 128 |
N.S. |
1 | 1.00 | 1.33 | 1.49 | 2.44 | 2.44 | 2.63 | 1.63 | 0.84 | 2.25 |
time (sec) |
N/A | 0.313 | 0.038 | 1.062 | 0.039 | 0.068 | 0.775 | 0.190 | 0.265 | 0.052 |
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 | 87 | 87 | 63 | 78 | 119 | 119 | 126 | 70 | 64 | 113 |
N.S. |
1 | 1.00 | 0.72 | 0.90 | 1.37 | 1.37 | 1.45 | 0.80 | 0.74 | 1.30 |
time (sec) |
N/A | 0.447 | 0.028 | 1.033 | 0.033 | 0.068 | 0.527 | 0.200 | 0.287 | 0.046 |
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 | 61 | 46 | 56 | 95 | 95 | 100 | 46 | 53 | 93 |
N.S. |
1 | 1.00 | 0.75 | 0.92 | 1.56 | 1.56 | 1.64 | 0.75 | 0.87 | 1.52 |
time (sec) |
N/A | 0.384 | 0.021 | 1.085 | 0.033 | 0.066 | 0.360 | 0.179 | 0.267 | 10.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 35 | 72 | 72 | 76 | 25 | 45 | 74 |
N.S. |
1 | 1.00 | 0.71 | 0.92 | 1.89 | 1.89 | 2.00 | 0.66 | 1.18 | 1.95 |
time (sec) |
N/A | 0.330 | 0.013 | 1.118 | 0.033 | 0.080 | 0.279 | 0.218 | 0.276 | 10.613 |
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 | 102 | 102 | 89 | 95 | 137 | 250 | 141 | 95 | 197 | 130 |
N.S. |
1 | 1.00 | 0.87 | 0.93 | 1.34 | 2.45 | 1.38 | 0.93 | 1.93 | 1.27 |
time (sec) |
N/A | 0.497 | 0.073 | 1.049 | 0.039 | 0.076 | 0.410 | 0.181 | 0.288 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 142 | 148 | 202 | 427 | 275 | 168 | 223 | 180 |
N.S. |
1 | 1.00 | 0.90 | 0.94 | 1.29 | 2.72 | 1.75 | 1.07 | 1.42 | 1.15 |
time (sec) |
N/A | 0.660 | 0.103 | 1.144 | 0.041 | 0.079 | 0.623 | 0.202 | 0.287 | 10.543 |
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 | 177 | 177 | 162 | 172 | 242 | 484 | 335 | 205 | 242 | 230 |
N.S. |
1 | 1.00 | 0.92 | 0.97 | 1.37 | 2.73 | 1.89 | 1.16 | 1.37 | 1.30 |
time (sec) |
N/A | 0.744 | 0.193 | 1.214 | 0.046 | 0.084 | 0.607 | 0.175 | 0.284 | 10.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 61 | 49 | 44 | 361 | 27 | 418 | 78 | 24 | 431 |
N.S. |
1 | 0.54 | 0.43 | 0.39 | 3.17 | 0.24 | 3.67 | 0.68 | 0.21 | 3.78 |
time (sec) |
N/A | 0.394 | 1.026 | 0.592 | 0.039 | 0.063 | 2.569 | 0.199 | 0.278 | 11.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 61 | 49 | 44 | 301 | 27 | 357 | 78 | 24 | 340 |
N.S. |
1 | 0.54 | 0.43 | 0.39 | 2.64 | 0.24 | 3.13 | 0.68 | 0.21 | 2.98 |
time (sec) |
N/A | 0.366 | 1.023 | 0.588 | 0.035 | 0.066 | 1.902 | 0.233 | 0.283 | 10.730 |
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 | 114 | 61 | 49 | 44 | 241 | 27 | 292 | 78 | 24 | 271 |
N.S. |
1 | 0.54 | 0.43 | 0.39 | 2.11 | 0.24 | 2.56 | 0.68 | 0.21 | 2.38 |
time (sec) |
N/A | 0.365 | 1.025 | 0.569 | 0.034 | 0.069 | 1.721 | 0.264 | 0.278 | 10.649 |
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 | 114 | 61 | 95 | 44 | 183 | 27 | 228 | 77 | 24 | 176 |
N.S. |
1 | 0.54 | 0.83 | 0.39 | 1.61 | 0.24 | 2.00 | 0.68 | 0.21 | 1.54 |
time (sec) |
N/A | 0.350 | 0.851 | 0.545 | 0.034 | 0.063 | 1.420 | 0.253 | 0.280 | 10.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 91 | 33 | 125 | 24 | 156 | 74 | 21 | 77 |
N.S. |
1 | 1.00 | 1.32 | 0.48 | 1.81 | 0.35 | 2.26 | 1.07 | 0.30 | 1.12 |
time (sec) |
N/A | 0.323 | 0.902 | 0.484 | 0.034 | 0.067 | 0.935 | 0.237 | 0.283 | 10.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 52 | 44 | 54 | 133 | 22 | 0 | 46 | 20 | 122 |
N.S. |
1 | 0.50 | 0.42 | 0.51 | 1.27 | 0.21 | 0.00 | 0.44 | 0.19 | 1.16 |
time (sec) |
N/A | 0.341 | 1.024 | 0.512 | 0.037 | 0.068 | 0.000 | 0.242 | 0.291 | 10.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 50 | 44 | 44 | 175 | 26 | 0 | 47 | 24 | 207 |
N.S. |
1 | 0.49 | 0.43 | 0.43 | 1.70 | 0.25 | 0.00 | 0.46 | 0.23 | 2.01 |
time (sec) |
N/A | 0.348 | 1.024 | 0.513 | 0.029 | 0.065 | 0.000 | 0.246 | 0.284 | 11.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 55 | 225 | 38 | 172 | 29 | 0 | 50 | 26 | 134 |
N.S. |
1 | 0.51 | 2.08 | 0.35 | 1.59 | 0.27 | 0.00 | 0.46 | 0.24 | 1.24 |
time (sec) |
N/A | 0.342 | 0.547 | 0.506 | 0.036 | 0.066 | 0.000 | 0.239 | 0.293 | 11.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 46 | 34 | 195 | 27 | 0 | 77 | 24 | 43 |
N.S. |
1 | 1.00 | 0.61 | 0.45 | 2.60 | 0.36 | 0.00 | 1.03 | 0.32 | 0.57 |
time (sec) |
N/A | 0.357 | 0.478 | 0.594 | 0.038 | 0.069 | 0.000 | 0.259 | 0.295 | 10.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 61 | 47 | 34 | 255 | 27 | 0 | 77 | 24 | 43 |
N.S. |
1 | 0.54 | 0.41 | 0.30 | 2.24 | 0.24 | 0.00 | 0.68 | 0.21 | 0.38 |
time (sec) |
N/A | 0.352 | 0.402 | 0.631 | 0.037 | 0.067 | 0.000 | 0.188 | 0.273 | 10.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 61 | 49 | 34 | 315 | 27 | 0 | 77 | 24 | 43 |
N.S. |
1 | 0.54 | 0.43 | 0.30 | 2.76 | 0.24 | 0.00 | 0.68 | 0.21 | 0.38 |
time (sec) |
N/A | 0.355 | 0.503 | 0.698 | 0.035 | 0.069 | 0.000 | 0.284 | 0.259 | 10.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 61 | 49 | 34 | 375 | 27 | 0 | 77 | 24 | 43 |
N.S. |
1 | 0.54 | 0.43 | 0.30 | 3.29 | 0.24 | 0.00 | 0.68 | 0.21 | 0.38 |
time (sec) |
N/A | 0.355 | 0.529 | 0.787 | 0.037 | 0.072 | 0.000 | 0.223 | 0.271 | 10.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 92 | 421 | 73 | 8803 | 150 | 46 | 0 |
N.S. |
1 | 0.49 | 0.41 | 0.44 | 2.00 | 0.35 | 41.92 | 0.71 | 0.22 | 0.00 |
time (sec) |
N/A | 0.472 | 1.041 | 1.122 | 0.039 | 0.066 | 1.015 | 0.232 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 92 | 361 | 73 | 5448 | 150 | 46 | 0 |
N.S. |
1 | 0.49 | 0.41 | 0.44 | 1.72 | 0.35 | 25.94 | 0.71 | 0.22 | 0.00 |
time (sec) |
N/A | 0.452 | 1.043 | 1.076 | 0.039 | 0.065 | 0.937 | 0.221 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 92 | 301 | 73 | 3364 | 149 | 46 | 0 |
N.S. |
1 | 0.49 | 0.41 | 0.44 | 1.43 | 0.35 | 16.02 | 0.71 | 0.22 | 0.00 |
time (sec) |
N/A | 0.438 | 1.043 | 1.007 | 0.037 | 0.064 | 0.872 | 0.260 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 92 | 241 | 73 | 2071 | 150 | 46 | 0 |
N.S. |
1 | 0.49 | 0.41 | 0.44 | 1.15 | 0.35 | 9.86 | 0.71 | 0.22 | 0.00 |
time (sec) |
N/A | 0.447 | 1.038 | 1.096 | 0.035 | 0.067 | 0.831 | 0.265 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 89 | 87 | 92 | 183 | 73 | 1258 | 148 | 46 | 0 |
N.S. |
1 | 0.74 | 0.72 | 0.76 | 1.51 | 0.60 | 10.40 | 1.22 | 0.38 | 0.00 |
time (sec) |
N/A | 0.419 | 1.039 | 0.977 | 0.037 | 0.068 | 1.113 | 0.209 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 83 | 90 | 125 | 69 | 745 | 144 | 43 | 42 |
N.S. |
1 | 1.00 | 1.17 | 1.27 | 1.76 | 0.97 | 10.49 | 2.03 | 0.61 | 0.59 |
time (sec) |
N/A | 0.327 | 1.042 | 0.975 | 0.035 | 0.067 | 0.769 | 0.251 | 0.297 | 10.852 |
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 | 182 | 81 | 83 | 91 | 186 | 68 | 0 | 118 | 42 | 0 |
N.S. |
1 | 0.45 | 0.46 | 0.50 | 1.02 | 0.37 | 0.00 | 0.65 | 0.23 | 0.00 |
time (sec) |
N/A | 0.375 | 1.047 | 1.026 | 0.036 | 0.067 | 0.000 | 0.231 | 0.268 | 0.000 |