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 | 23 | 19 | 19 | 20 | 19 | 17 | 19 | 19 | 19 | 24 |
N.S. |
1 | 0.83 | 0.83 | 0.87 | 0.83 | 0.74 | 0.83 | 0.83 | 0.83 | 1.04 |
time (sec) |
N/A | 0.181 | 0.004 | 0.161 | 0.029 | 0.083 | 0.059 | 0.124 | 0.176 | 2.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 31 | 22 | 21 | 20 | 20 | 20 | 23 | 22 | 20 |
N.S. |
1 | 1.24 | 0.88 | 0.84 | 0.80 | 0.80 | 0.80 | 0.92 | 0.88 | 0.80 |
time (sec) |
N/A | 0.230 | 0.012 | 0.386 | 0.035 | 0.100 | 0.179 | 0.120 | 0.174 | 0.147 |
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 | 11 | 11 | 9 | 10 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 0.85 | 0.85 | 0.69 | 0.77 | 0.77 | 0.77 | 0.77 | 0.85 | 0.77 |
time (sec) |
N/A | 0.201 | 0.014 | 0.076 | 0.026 | 0.078 | 0.074 | 0.112 | 0.177 | 2.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 30 | 25 | 25 | 25 | 19 | 30 | 26 | 22 |
N.S. |
1 | 0.00 | 1.20 | 1.00 | 1.00 | 1.00 | 0.76 | 1.20 | 1.04 | 0.88 |
time (sec) |
N/A | 0.000 | 2.263 | 0.285 | 0.080 | 0.075 | 0.069 | 0.120 | 0.188 | 3.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 30 | 36 | 36 | 22 | 60 | 36 | 28 |
N.S. |
1 | 0.00 | 1.04 | 1.25 | 1.50 | 1.50 | 0.92 | 2.50 | 1.50 | 1.17 |
time (sec) |
N/A | 0.000 | 0.112 | 5.167 | 0.094 | 0.076 | 0.063 | 0.121 | 0.185 | 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 | 11 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 10 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.73 | 0.73 | 0.64 | 0.73 | 0.91 | 0.73 |
time (sec) |
N/A | 0.149 | 0.004 | 0.059 | 0.023 | 0.073 | 0.034 | 0.109 | 0.181 | 0.021 |
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 | 32 | 21 | 19 | 18 | 30 | 22 | 35 | 33 | 18 |
N.S. |
1 | 1.60 | 1.05 | 0.95 | 0.90 | 1.50 | 1.10 | 1.75 | 1.65 | 0.90 |
time (sec) |
N/A | 0.175 | 0.008 | 0.201 | 0.028 | 0.079 | 0.041 | 0.108 | 0.180 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 16 | 16 | 17 | 28 | 18 | 15 | 87 | 31 | 16 |
N.S. |
1 | 0.73 | 0.73 | 0.77 | 1.27 | 0.82 | 0.68 | 3.95 | 1.41 | 0.73 |
time (sec) |
N/A | 0.210 | 0.016 | 0.426 | 0.060 | 0.075 | 0.060 | 0.116 | 0.181 | 2.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 31 | 43 | 31 | 31 | 31 | 42 | 44 | 0 |
N.S. |
1 | 0.00 | 1.15 | 1.59 | 1.15 | 1.15 | 1.15 | 1.56 | 1.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.059 | 15.099 | 0.114 | 0.079 | 0.247 | 0.254 | 0.191 | 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 | 13 | 16 | 15 | 13 | 14 | 14 | 12 | 14 | 13 | 12 |
N.S. |
1 | 1.23 | 1.15 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 1.00 | 0.92 |
time (sec) |
N/A | 0.145 | 0.000 | 0.061 | 0.028 | 0.064 | 0.021 | 0.107 | 0.173 | 3.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 36 | 41 | 38 | 46 | 48 | 0 | 541 | 0 |
N.S. |
1 | 0.00 | 1.16 | 1.32 | 1.23 | 1.48 | 1.55 | 0.00 | 17.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.406 | 3.891 | 0.163 | 0.085 | 0.183 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 24 | 124 | 90 | 32 | 0 | 32 | 139 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 4.59 | 3.33 | 1.19 | 0.00 | 1.19 | 5.15 |
time (sec) |
N/A | 0.000 | 2.935 | 39.599 | 0.373 | 0.091 | 0.959 | 0.000 | 0.230 | 3.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 40 | 33 | 57 | 36 | 32 | 56 | 60 | 59 |
N.S. |
1 | 0.00 | 1.18 | 0.97 | 1.68 | 1.06 | 0.94 | 1.65 | 1.76 | 1.74 |
time (sec) |
N/A | 0.000 | 0.392 | 45.691 | 0.272 | 0.095 | 0.518 | 0.261 | 0.516 | 3.293 |
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 | 22 | 24 | 22 | 21 | 31 | 28 | 15 | 48 | 37 | 23 |
N.S. |
1 | 1.09 | 1.00 | 0.95 | 1.41 | 1.27 | 0.68 | 2.18 | 1.68 | 1.05 |
time (sec) |
N/A | 0.972 | 0.071 | 0.337 | 0.087 | 0.084 | 0.109 | 0.130 | 0.170 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 23 | 16 | 16 | 26 | 22 | 12 | 22 | 20 | 15 |
N.S. |
1 | 1.35 | 0.94 | 0.94 | 1.53 | 1.29 | 0.71 | 1.29 | 1.18 | 0.88 |
time (sec) |
N/A | 0.218 | 0.041 | 0.237 | 0.058 | 0.077 | 0.060 | 0.116 | 0.165 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 22 | 18 | 16 | 15 | 15 | 12 | 15 | 16 | 19 |
N.S. |
1 | 1.16 | 0.95 | 0.84 | 0.79 | 0.79 | 0.63 | 0.79 | 0.84 | 1.00 |
time (sec) |
N/A | 0.184 | 0.005 | 0.181 | 0.034 | 0.084 | 0.073 | 0.130 | 0.170 | 2.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 20 | 20 | 18 | 16 | 17 | 15 | 16 | 27 | 17 |
N.S. |
1 | 0.95 | 0.95 | 0.86 | 0.76 | 0.81 | 0.71 | 0.76 | 1.29 | 0.81 |
time (sec) |
N/A | 0.219 | 0.022 | 0.265 | 0.027 | 0.080 | 0.096 | 0.141 | 0.165 | 2.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 52 | 56 | 53 | 42 | 39 | 55 | 197 | 383 |
N.S. |
1 | 0.00 | 1.68 | 1.81 | 1.71 | 1.35 | 1.26 | 1.77 | 6.35 | 12.35 |
time (sec) |
N/A | 0.000 | 0.109 | 2.043 | 0.190 | 0.077 | 0.237 | 0.649 | 200.023 | 3.423 |
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 | 28 | 49 | 30 | 30 | 27 | 27 | 26 | 29 | 30 | 29 |
N.S. |
1 | 1.75 | 1.07 | 1.07 | 0.96 | 0.96 | 0.93 | 1.04 | 1.07 | 1.04 |
time (sec) |
N/A | 3.745 | 0.249 | 3.626 | 0.076 | 0.105 | 0.185 | 0.127 | 0.167 | 3.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 60 | 74 | 59 | 31 | 393 | 58 | 30 |
N.S. |
1 | 0.00 | 0.96 | 2.61 | 3.22 | 2.57 | 1.35 | 17.09 | 2.52 | 1.30 |
time (sec) |
N/A | 0.000 | 0.091 | 62.107 | 0.128 | 0.086 | 0.474 | 40.273 | 0.187 | 3.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 143 | 22 | 22 | 31 | 34 | 29 | 34 | 28 | 33 |
N.S. |
1 | 5.72 | 0.88 | 0.88 | 1.24 | 1.36 | 1.16 | 1.36 | 1.12 | 1.32 |
time (sec) |
N/A | 0.629 | 0.041 | 0.713 | 0.043 | 0.079 | 1.264 | 0.115 | 0.170 | 2.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 136 | 25 | 54 | 117 | 56 | 56 | 76 | 62 | 22 |
N.S. |
1 | 5.91 | 1.09 | 2.35 | 5.09 | 2.43 | 2.43 | 3.30 | 2.70 | 0.96 |
time (sec) |
N/A | 0.705 | 5.735 | 1.221 | 0.044 | 0.088 | 0.118 | 0.112 | 0.172 | 0.143 |
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 | 4 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 |
time (sec) |
N/A | 0.126 | 0.000 | 0.029 | 0.029 | 0.073 | 0.044 | 0.110 | 0.180 | 0.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 149 | 13 | 27 | 48 | 26 | 26 | 26 | 26 | 13 |
N.S. |
1 | 9.93 | 0.87 | 1.80 | 3.20 | 1.73 | 1.73 | 1.73 | 1.73 | 0.87 |
time (sec) |
N/A | 1.065 | 0.128 | 0.477 | 0.068 | 0.079 | 0.056 | 0.112 | 0.173 | 2.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 27 | 21 | 20 | 41 | 20 | 0 | 25 | 23 |
N.S. |
1 | 1.00 | 0.93 | 0.72 | 0.69 | 1.41 | 0.69 | 0.00 | 0.86 | 0.79 |
time (sec) |
N/A | 0.483 | 0.926 | 0.315 | 0.140 | 0.096 | 0.277 | 0.000 | 0.174 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 19 | 19 | 18 | 18 | 17 | 22 | 19 | 18 |
N.S. |
1 | 0.00 | 0.79 | 0.79 | 0.75 | 0.75 | 0.71 | 0.92 | 0.79 | 0.75 |
time (sec) |
N/A | 0.000 | 0.506 | 0.146 | 0.087 | 0.091 | 0.101 | 0.114 | 0.165 | 0.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 35 | 22 | 29 | 0 | 33 | 19 | 60 | 24 | 0 |
N.S. |
1 | 1.52 | 0.96 | 1.26 | 0.00 | 1.43 | 0.83 | 2.61 | 1.04 | 0.00 |
time (sec) |
N/A | 1.402 | 0.166 | 0.686 | 0.000 | 0.084 | 5.505 | 0.133 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 27 | 21 | 22 | 22 | 71 | 42 | 29 | 53 |
N.S. |
1 | 0.00 | 0.79 | 0.62 | 0.65 | 0.65 | 2.09 | 1.24 | 0.85 | 1.56 |
time (sec) |
N/A | 0.000 | 2.885 | 0.460 | 0.083 | 0.087 | 0.220 | 0.125 | 0.169 | 3.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 18 | 16 | 17 | 23 | 22 | 14 | 16 | 19 | 17 |
N.S. |
1 | 1.12 | 1.00 | 1.06 | 1.44 | 1.38 | 0.88 | 1.00 | 1.19 | 1.06 |
time (sec) |
N/A | 0.257 | 0.021 | 0.138 | 0.058 | 0.081 | 0.041 | 0.114 | 0.179 | 3.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 88 | 22 | 22 | 0 | 22 | 19 | 34 | 23 | 21 |
N.S. |
1 | 3.38 | 0.85 | 0.85 | 0.00 | 0.85 | 0.73 | 1.31 | 0.88 | 0.81 |
time (sec) |
N/A | 0.746 | 0.069 | 16.325 | 0.000 | 0.081 | 0.307 | 0.137 | 0.172 | 3.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 113 | 124 | 548 | 86 | 112 | 126 | 179 | 113 |
N.S. |
1 | 0.00 | 4.71 | 5.17 | 22.83 | 3.58 | 4.67 | 5.25 | 7.46 | 4.71 |
time (sec) |
N/A | 0.000 | 0.054 | 1.386 | 0.194 | 0.099 | 0.778 | 0.127 | 0.173 | 3.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 26 | 29 | 61 | 25 | 31 | 28 | 30 | 24 |
N.S. |
1 | 0.00 | 1.24 | 1.38 | 2.90 | 1.19 | 1.48 | 1.33 | 1.43 | 1.14 |
time (sec) |
N/A | 0.000 | 1.553 | 0.446 | 0.154 | 0.087 | 0.086 | 0.115 | 0.168 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 59 | 31 | 0 | 32 | 31 | 0 | 58 | 295 |
N.S. |
1 | 0.00 | 1.74 | 0.91 | 0.00 | 0.94 | 0.91 | 0.00 | 1.71 | 8.68 |
time (sec) |
N/A | 0.000 | 0.264 | 15.493 | 0.000 | 0.085 | 0.292 | 0.000 | 0.183 | 3.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 22 | 22 | 19 | 18 | 24 | 15 | 18 | 27 | 20 |
N.S. |
1 | 0.76 | 0.76 | 0.66 | 0.62 | 0.83 | 0.52 | 0.62 | 0.93 | 0.69 |
time (sec) |
N/A | 0.214 | 0.010 | 0.239 | 0.040 | 0.079 | 0.078 | 0.115 | 0.174 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 38 | 40 | 53 | 53 | 36 | 60 | 63 | 0 |
N.S. |
1 | 0.00 | 1.23 | 1.29 | 1.71 | 1.71 | 1.16 | 1.94 | 2.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.054 | 2.592 | 0.188 | 0.089 | 0.201 | 0.176 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 19 | 16 | 56 | 19 | 0 | 21 | 18 |
N.S. |
1 | 0.00 | 0.90 | 0.90 | 0.76 | 2.67 | 0.90 | 0.00 | 1.00 | 0.86 |
time (sec) |
N/A | 0.000 | 0.515 | 1.992 | 0.210 | 0.099 | 0.433 | 0.000 | 13.220 | 3.311 |
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 | 23 | 39 | 32 | 31 | 34 | 25 | 29 | 25 | 29 | 26 |
N.S. |
1 | 1.70 | 1.39 | 1.35 | 1.48 | 1.09 | 1.26 | 1.09 | 1.26 | 1.13 |
time (sec) |
N/A | 0.218 | 0.005 | 0.213 | 0.042 | 0.082 | 0.099 | 0.108 | 0.165 | 3.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 75 | 31 | 35 | 38 | 37 | 35 | 32 | 35 |
N.S. |
1 | 1.12 | 2.88 | 1.19 | 1.35 | 1.46 | 1.42 | 1.35 | 1.23 | 1.35 |
time (sec) |
N/A | 0.156 | 0.000 | 0.149 | 0.042 | 0.076 | 0.020 | 0.115 | 0.156 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 38 | 63 | 56 | 57 | 60 | 86 | 97 | 0 |
N.S. |
1 | 0.00 | 1.58 | 2.62 | 2.33 | 2.38 | 2.50 | 3.58 | 4.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.127 | 14.551 | 4.394 | 0.107 | 0.694 | 70.114 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 39 | 29 | 27 | 53 | 34 | 27 | 35 | 42 | 23 |
N.S. |
1 | 1.95 | 1.45 | 1.35 | 2.65 | 1.70 | 1.35 | 1.75 | 2.10 | 1.15 |
time (sec) |
N/A | 0.813 | 0.060 | 1.855 | 0.073 | 0.073 | 0.144 | 0.143 | 0.171 | 3.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 41 | 48 | 62 | 62 | 39 | 74 | 77 | 0 |
N.S. |
1 | 0.00 | 1.24 | 1.45 | 1.88 | 1.88 | 1.18 | 2.24 | 2.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.169 | 0.036 | 0.213 | 0.113 | 0.458 | 0.283 | 0.203 | 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 | 27 | 21 | 13 | 14 | 16 | 17 | 15 | 18 | 21 | 12 |
N.S. |
1 | 0.78 | 0.48 | 0.52 | 0.59 | 0.63 | 0.56 | 0.67 | 0.78 | 0.44 |
time (sec) |
N/A | 0.165 | 0.002 | 0.045 | 0.028 | 0.072 | 0.058 | 0.108 | 0.163 | 0.031 |
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 | 18 | 31 | 17 | 17 | 16 | 17 | 15 | 17 | 19 | 17 |
N.S. |
1 | 1.72 | 0.94 | 0.94 | 0.89 | 0.94 | 0.83 | 0.94 | 1.06 | 0.94 |
time (sec) |
N/A | 0.219 | 0.336 | 0.096 | 0.101 | 0.101 | 0.050 | 0.110 | 0.171 | 3.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 57 | 57 | 53 | 65 | 49 | 51 | 52 | 57 | 57 |
N.S. |
1 | 2.71 | 2.71 | 2.52 | 3.10 | 2.33 | 2.43 | 2.48 | 2.71 | 2.71 |
time (sec) |
N/A | 0.293 | 0.012 | 0.903 | 0.036 | 0.083 | 0.089 | 0.124 | 0.163 | 2.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 30 | 68 | 33 | 66 | 65 | 69 | 0 | 69 |
N.S. |
1 | 0.00 | 0.88 | 2.00 | 0.97 | 1.94 | 1.91 | 2.03 | 0.00 | 2.03 |
time (sec) |
N/A | 0.000 | 0.056 | 1.955 | 0.440 | 0.078 | 0.292 | 1.323 | 0.273 | 3.820 |
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 | 16 | 13 | 16 | 10 | 11 | 11 | 14 | 11 | 12 | 9 |
N.S. |
1 | 0.81 | 1.00 | 0.62 | 0.69 | 0.69 | 0.88 | 0.69 | 0.75 | 0.56 |
time (sec) |
N/A | 0.134 | 0.001 | 0.036 | 0.037 | 0.066 | 0.018 | 0.119 | 0.165 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 14 | 17 | 16 | 20 | 14 | 24 | 23 | 12 |
N.S. |
1 | 0.00 | 0.47 | 0.57 | 0.53 | 0.67 | 0.47 | 0.80 | 0.77 | 0.40 |
time (sec) |
N/A | 0.000 | 0.046 | 0.083 | 0.099 | 0.084 | 0.074 | 0.112 | 0.172 | 3.060 |
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 | 8 | 10 | 9 | 7 | 8 | 8 | 7 | 9 | 7 | 6 |
N.S. |
1 | 1.25 | 1.12 | 0.88 | 1.00 | 1.00 | 0.88 | 1.12 | 0.88 | 0.75 |
time (sec) |
N/A | 0.142 | 0.002 | 0.066 | 0.034 | 0.078 | 0.035 | 0.119 | 0.177 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 41 | 37 | 37 | 42 | 46 | 38 | 49 |
N.S. |
1 | 0.00 | 1.03 | 1.37 | 1.23 | 1.23 | 1.40 | 1.53 | 1.27 | 1.63 |
time (sec) |
N/A | 0.000 | 3.738 | 0.181 | 0.097 | 0.097 | 0.120 | 0.151 | 0.419 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 76 | 19 | 20 | 19 | 19 | 15 | 75 | 16 | 15 |
N.S. |
1 | 4.75 | 1.19 | 1.25 | 1.19 | 1.19 | 0.94 | 4.69 | 1.00 | 0.94 |
time (sec) |
N/A | 0.911 | 0.098 | 0.385 | 0.080 | 0.081 | 0.071 | 0.121 | 0.194 | 3.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 27 | 31 | 30 | 30 | 26 | 30 | 21 | 23 |
N.S. |
1 | 0.00 | 1.29 | 1.48 | 1.43 | 1.43 | 1.24 | 1.43 | 1.00 | 1.10 |
time (sec) |
N/A | 0.000 | 0.390 | 1.269 | 0.070 | 0.085 | 0.326 | 0.137 | 0.221 | 3.228 |
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 | 18 | 17 | 17 | 14 | 13 | 13 | 19 | 13 | 15 | 14 |
N.S. |
1 | 0.94 | 0.94 | 0.78 | 0.72 | 0.72 | 1.06 | 0.72 | 0.83 | 0.78 |
time (sec) |
N/A | 0.146 | 0.001 | 0.056 | 0.032 | 0.072 | 0.028 | 0.108 | 0.214 | 2.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 42 | 39 | 44 | 39 | 39 | 602 | 43 | 34 |
N.S. |
1 | 0.00 | 1.17 | 1.08 | 1.22 | 1.08 | 1.08 | 16.72 | 1.19 | 0.94 |
time (sec) |
N/A | 0.000 | 0.192 | 0.084 | 0.086 | 0.084 | 0.205 | 0.172 | 0.221 | 3.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 77 | 51 | 49 | 44 | 41 | 49 | 50 | 69 | 55 |
N.S. |
1 | 3.35 | 2.22 | 2.13 | 1.91 | 1.78 | 2.13 | 2.17 | 3.00 | 2.39 |
time (sec) |
N/A | 0.308 | 0.210 | 0.717 | 0.034 | 0.085 | 0.088 | 0.114 | 0.198 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | C | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 127 | 34 | 1184 | 150 | 150 | 87 | 25 | 113 |
N.S. |
1 | 0.00 | 4.38 | 1.17 | 40.83 | 5.17 | 5.17 | 3.00 | 0.86 | 3.90 |
time (sec) |
N/A | 0.000 | 0.180 | 0.692 | 0.196 | 0.095 | 0.612 | 0.130 | 0.215 | 3.241 |
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 | 20 | 20 | 20 | 20 | 22 | 19 | 17 | 19 | 22 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.10 | 0.95 | 0.85 | 0.95 | 1.10 | 0.95 |
time (sec) |
N/A | 0.711 | 0.344 | 0.653 | 0.160 | 0.079 | 0.225 | 0.148 | 0.213 | 3.048 |
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 | 18 | 22 | 20 | 14 | 16 | 17 | 15 | 16 | 19 | 13 |
N.S. |
1 | 1.22 | 1.11 | 0.78 | 0.89 | 0.94 | 0.83 | 0.89 | 1.06 | 0.72 |
time (sec) |
N/A | 0.188 | 0.002 | 0.086 | 0.027 | 0.073 | 0.040 | 0.107 | 0.201 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | F | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 38 | 1829 | 189 | 55 | 48 | 0 | 187 | 50 |
N.S. |
1 | 0.00 | 1.19 | 57.16 | 5.91 | 1.72 | 1.50 | 0.00 | 5.84 | 1.56 |
time (sec) |
N/A | 0.000 | 0.074 | 6.455 | 0.124 | 0.096 | 0.528 | 0.000 | 200.027 | 3.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 64 | 43 | 49 | 78 | 81 | 61 | 118 | 99 | 41 |
N.S. |
1 | 2.00 | 1.34 | 1.53 | 2.44 | 2.53 | 1.91 | 3.69 | 3.09 | 1.28 |
time (sec) |
N/A | 11.664 | 2.932 | 20.948 | 0.103 | 0.100 | 0.193 | 0.182 | 0.393 | 3.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 196 | 26 | 25 | 19 | 25 | 28 | 25 |
N.S. |
1 | 0.00 | 0.96 | 7.00 | 0.93 | 0.89 | 0.68 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.000 | 0.423 | 0.056 | 0.114 | 0.084 | 0.171 | 0.165 | 0.196 | 0.185 |
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 | 20 | 6 | 6 | 7 | 6 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 0.30 | 0.30 | 0.35 | 0.30 | 0.30 | 0.25 | 0.30 | 0.30 | 0.30 |
time (sec) |
N/A | 0.134 | 0.002 | 0.060 | 0.036 | 0.078 | 0.037 | 0.112 | 0.197 | 2.890 |
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 | 21 | 33 | 19 | 30 | 28 | 28 | 36 | 28 | 27 | 30 |
N.S. |
1 | 1.57 | 0.90 | 1.43 | 1.33 | 1.33 | 1.71 | 1.33 | 1.29 | 1.43 |
time (sec) |
N/A | 0.241 | 0.074 | 0.194 | 0.031 | 0.079 | 0.073 | 0.113 | 0.200 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 23 | 63 | 22 | 22 | 22 | 23 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.79 | 2.17 | 0.76 | 0.76 | 0.76 | 0.79 | 0.76 |
time (sec) |
N/A | 0.000 | 0.071 | 0.867 | 0.163 | 0.085 | 24.859 | 0.152 | 0.191 | 2.796 |
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 | 27 | 37 | 35 | 34 | 53 | 29 | 34 | 32 | 27 | 31 |
N.S. |
1 | 1.37 | 1.30 | 1.26 | 1.96 | 1.07 | 1.26 | 1.19 | 1.00 | 1.15 |
time (sec) |
N/A | 0.266 | 0.010 | 0.251 | 0.031 | 0.093 | 0.118 | 0.113 | 0.200 | 2.994 |
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 | 34 | 20 | 23 | 17 | 24 | 20 | 15 | 16 | 21 | 12 |
N.S. |
1 | 0.59 | 0.68 | 0.50 | 0.71 | 0.59 | 0.44 | 0.47 | 0.62 | 0.35 |
time (sec) |
N/A | 0.254 | 0.011 | 0.133 | 0.026 | 0.075 | 0.054 | 0.117 | 0.193 | 2.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 11 | 10 | 22 | 12 | 22 | 14 | 10 |
N.S. |
1 | 0.00 | 1.00 | 0.69 | 0.62 | 1.38 | 0.75 | 1.38 | 0.88 | 0.62 |
time (sec) |
N/A | 0.000 | 0.056 | 0.245 | 0.133 | 0.102 | 0.120 | 0.146 | 0.191 | 2.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 28 | 28 | 54 | 55 | 54 | 61 | 0 | 66 | 60 |
N.S. |
1 | 1.04 | 1.04 | 2.00 | 2.04 | 2.00 | 2.26 | 0.00 | 2.44 | 2.22 |
time (sec) |
N/A | 3.068 | 0.054 | 78.815 | 0.371 | 0.088 | 5.005 | 0.000 | 0.295 | 3.009 |
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 | 30 | 39 | 25 | 22 | 25 | 25 | 20 | 31 | 23 | 24 |
N.S. |
1 | 1.30 | 0.83 | 0.73 | 0.83 | 0.83 | 0.67 | 1.03 | 0.77 | 0.80 |
time (sec) |
N/A | 0.252 | 0.009 | 0.131 | 0.027 | 0.070 | 0.212 | 0.106 | 0.187 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | F | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 40 | 62 | 177 | 51 | 0 | 0 | 159 |
N.S. |
1 | 0.00 | 0.00 | 1.33 | 2.07 | 5.90 | 1.70 | 0.00 | 0.00 | 5.30 |
time (sec) |
N/A | 0.000 | 0.000 | 123.529 | 2.282 | 0.104 | 2.590 | 0.000 | 2.306 | 3.615 |
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 | 22 | 13 | 20 | 20 | 8 | 20 | 21 | 12 |
N.S. |
1 | 1.00 | 1.69 | 1.00 | 1.54 | 1.54 | 0.62 | 1.54 | 1.62 | 0.92 |
time (sec) |
N/A | 0.925 | 0.599 | 0.114 | 0.060 | 0.088 | 0.042 | 0.114 | 0.186 | 2.965 |
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 | 5 | 5 | 5 | 5 | 4 | 11 | 3 | 11 | 5 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 2.20 | 0.60 | 2.20 | 1.00 | 0.80 |
time (sec) |
N/A | 0.148 | 0.001 | 0.030 | 0.029 | 0.080 | 0.029 | 0.112 | 0.191 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 16 | 32 | 32 | 37 | 35 | 41 | 35 |
N.S. |
1 | 0.00 | 0.86 | 0.73 | 1.45 | 1.45 | 1.68 | 1.59 | 1.86 | 1.59 |
time (sec) |
N/A | 0.000 | 0.539 | 0.694 | 0.090 | 0.078 | 0.077 | 0.133 | 0.211 | 3.289 |
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 | 13 | 13 | 12 | 22 | 21 | 17 | 12 | 41 | 12 |
N.S. |
1 | 0.93 | 0.93 | 0.86 | 1.57 | 1.50 | 1.21 | 0.86 | 2.93 | 0.86 |
time (sec) |
N/A | 0.320 | 0.019 | 0.130 | 0.066 | 0.104 | 0.090 | 0.109 | 0.195 | 2.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 128 | 36 | 80 | 69 | 32 | 35 | 100 | 35 |
N.S. |
1 | 1.35 | 4.92 | 1.38 | 3.08 | 2.65 | 1.23 | 1.35 | 3.85 | 1.35 |
time (sec) |
N/A | 2.745 | 0.055 | 1.966 | 0.155 | 0.092 | 0.135 | 0.128 | 0.200 | 3.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 20 | 22 | 25 | 24 | 19 | 20 | 29 | 21 |
N.S. |
1 | 1.08 | 0.80 | 0.88 | 1.00 | 0.96 | 0.76 | 0.80 | 1.16 | 0.84 |
time (sec) |
N/A | 0.405 | 0.394 | 0.134 | 0.061 | 0.078 | 0.077 | 0.122 | 0.202 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 9 | 11 | 13 | 12 | 12 | 14 | 0 | 19 | 14 |
N.S. |
1 | 0.69 | 0.85 | 1.00 | 0.92 | 0.92 | 1.08 | 0.00 | 1.46 | 1.08 |
time (sec) |
N/A | 0.543 | 0.072 | 0.208 | 0.218 | 0.087 | 0.199 | 0.000 | 0.201 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 22 | 21 | 21 | 22 | 35 | 23 | 21 |
N.S. |
1 | 0.00 | 1.04 | 0.92 | 0.88 | 0.88 | 0.92 | 1.46 | 0.96 | 0.88 |
time (sec) |
N/A | 0.000 | 5.037 | 24.849 | 0.080 | 0.091 | 0.161 | 0.135 | 0.194 | 3.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 82 | 20 | 21 | 22 | 22 | 19 | 22 | 20 | 20 |
N.S. |
1 | 4.10 | 1.00 | 1.05 | 1.10 | 1.10 | 0.95 | 1.10 | 1.00 | 1.00 |
time (sec) |
N/A | 1.068 | 0.076 | 0.428 | 0.141 | 0.083 | 0.074 | 0.128 | 0.185 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 16 | 12 | 15 | 11 | 16 | 12 | 11 | 18 | 13 |
N.S. |
1 | 0.94 | 0.71 | 0.88 | 0.65 | 0.94 | 0.71 | 0.65 | 1.06 | 0.76 |
time (sec) |
N/A | 0.312 | 0.024 | 0.137 | 0.089 | 0.092 | 0.071 | 0.117 | 0.807 | 2.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 29 | 31 | 32 | 29 | 29 | 0 | 34 | 36 |
N.S. |
1 | 0.00 | 1.07 | 1.15 | 1.19 | 1.07 | 1.07 | 0.00 | 1.26 | 1.33 |
time (sec) |
N/A | 0.000 | 0.213 | 1.254 | 0.146 | 0.090 | 0.164 | 0.000 | 0.465 | 3.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 37 | 0 | 97 | 41 | 37 | 99 | 37 | 0 |
N.S. |
1 | 0.00 | 1.32 | 0.00 | 3.46 | 1.46 | 1.32 | 3.54 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.070 | 0.000 | 0.169 | 0.085 | 0.228 | 75.936 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 145 | 19 | 72 | 66 | 66 | 71 | 66 | 74 | 15 |
N.S. |
1 | 7.63 | 1.00 | 3.79 | 3.47 | 3.47 | 3.74 | 3.47 | 3.89 | 0.79 |
time (sec) |
N/A | 0.465 | 1.030 | 0.215 | 0.108 | 0.094 | 0.129 | 0.128 | 0.193 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 41 | 38 | 71 | 71 | 36 | 1712 | 0 | 0 |
N.S. |
1 | 0.00 | 1.46 | 1.36 | 2.54 | 2.54 | 1.29 | 61.14 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.112 | 0.051 | 0.202 | 0.098 | 0.211 | 24.425 | 0.708 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 17 | 64 | 100 | 48 | 20 | 58 | 69 | 18 |
N.S. |
1 | 0.00 | 0.85 | 3.20 | 5.00 | 2.40 | 1.00 | 2.90 | 3.45 | 0.90 |
time (sec) |
N/A | 0.000 | 0.443 | 0.711 | 0.172 | 0.097 | 0.127 | 0.129 | 0.200 | 2.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 28 | 25 | 55 | 29 | 100 | 31 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 0.96 | 2.12 | 1.12 | 3.85 | 1.19 | 1.08 |
time (sec) |
N/A | 0.000 | 1.968 | 2.328 | 0.130 | 0.081 | 0.188 | 0.136 | 6.247 | 3.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 132 | 58 | 92 | 125 | 72 | 70 | 131 | 79 | 72 |
N.S. |
1 | 4.40 | 1.93 | 3.07 | 4.17 | 2.40 | 2.33 | 4.37 | 2.63 | 2.40 |
time (sec) |
N/A | 0.403 | 0.032 | 0.626 | 0.108 | 0.093 | 0.116 | 0.114 | 0.192 | 3.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 50 | 41 | 39 | 39 | 37 | 47 | 845 | 47 |
N.S. |
1 | 0.00 | 1.39 | 1.14 | 1.08 | 1.08 | 1.03 | 1.31 | 23.47 | 1.31 |
time (sec) |
N/A | 0.000 | 0.114 | 1.019 | 0.085 | 0.088 | 0.275 | 0.155 | 0.255 | 3.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 50 | 40 | 30 | 26 | 53 | 30 | 31 |
N.S. |
1 | 0.00 | 0.96 | 2.08 | 1.67 | 1.25 | 1.08 | 2.21 | 1.25 | 1.29 |
time (sec) |
N/A | 0.000 | 0.039 | 3.648 | 0.060 | 0.088 | 0.197 | 0.151 | 0.198 | 3.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | F(-1) | A | A | A | F | F | B |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 135 | 0 | 0 | 49 | 40 | 34 | 0 | 0 | 52 |
N.S. |
1 | 4.22 | 0.00 | 0.00 | 1.53 | 1.25 | 1.06 | 0.00 | 0.00 | 1.62 |
time (sec) |
N/A | 6.666 | 0.000 | 0.000 | 0.415 | 0.089 | 102.581 | 0.000 | 2.072 | 3.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 121 | 34 | 30 | 29 | 47 | 32 | 53 | 48 | 29 |
N.S. |
1 | 3.90 | 1.10 | 0.97 | 0.94 | 1.52 | 1.03 | 1.71 | 1.55 | 0.94 |
time (sec) |
N/A | 1.999 | 0.055 | 1.996 | 0.153 | 0.094 | 0.202 | 0.134 | 0.206 | 2.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | F(-2) | F(-1) | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 30 | 668 | 27 | 0 | 0 | 33 | 27 |
N.S. |
1 | 0.00 | 0.00 | 0.97 | 21.55 | 0.87 | 0.00 | 0.00 | 1.06 | 0.87 |
time (sec) |
N/A | 0.000 | 0.000 | 54.921 | 0.195 | 0.087 | 0.000 | 0.000 | 0.208 | 3.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 25 | 25 | 30 | 22 | 27 | 73 | 27 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 1.00 | 1.20 | 0.88 | 1.08 | 2.92 | 1.08 |
time (sec) |
N/A | 0.000 | 0.100 | 30.986 | 0.172 | 0.106 | 0.291 | 0.458 | 0.222 | 3.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 25 | 21 | 14 | 23 | 18 | 12 | 13 | 18 | 14 |
N.S. |
1 | 1.56 | 1.31 | 0.88 | 1.44 | 1.12 | 0.75 | 0.81 | 1.12 | 0.88 |
time (sec) |
N/A | 0.337 | 0.019 | 0.095 | 0.051 | 0.090 | 0.044 | 0.113 | 0.203 | 2.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 17 | 17 | 16 | 15 | 15 | 20 | 15 | 13 | 15 |
N.S. |
1 | 1.31 | 1.31 | 1.23 | 1.15 | 1.15 | 1.54 | 1.15 | 1.00 | 1.15 |
time (sec) |
N/A | 0.173 | 0.003 | 0.140 | 0.030 | 0.081 | 0.092 | 0.107 | 0.203 | 2.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 60 | 92 | 158 | 188 | 112 | 255 | 269 | 146 |
N.S. |
1 | 0.00 | 2.31 | 3.54 | 6.08 | 7.23 | 4.31 | 9.81 | 10.35 | 5.62 |
time (sec) |
N/A | 0.000 | 10.113 | 18.614 | 0.130 | 0.096 | 0.192 | 0.175 | 0.206 | 3.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 21 | 27 | 25 | 26 | 21 | 140 | 27 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 1.29 | 1.19 | 1.24 | 1.00 | 6.67 | 1.29 |
time (sec) |
N/A | 0.000 | 0.000 | 1.113 | 0.206 | 0.083 | 0.144 | 0.175 | 0.215 | 2.950 |
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 | 23 | 23 | 20 | 20 | 22 | 24 | 20 | 24 | 27 | 24 |
N.S. |
1 | 1.00 | 0.87 | 0.87 | 0.96 | 1.04 | 0.87 | 1.04 | 1.17 | 1.04 |
time (sec) |
N/A | 0.285 | 0.160 | 0.085 | 0.026 | 0.107 | 0.064 | 0.112 | 0.259 | 2.766 |
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 | 14 | 14 | 15 | 14 | 15 | 8 | 14 | 16 | 16 |
N.S. |
1 | 0.64 | 0.64 | 0.68 | 0.64 | 0.68 | 0.36 | 0.64 | 0.73 | 0.73 |
time (sec) |
N/A | 0.171 | 0.001 | 0.032 | 0.031 | 0.073 | 0.027 | 0.111 | 0.195 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 30 | 28 | 32 | 41 | 116 | 50 | 35 |
N.S. |
1 | 0.00 | 1.00 | 1.30 | 1.22 | 1.39 | 1.78 | 5.04 | 2.17 | 1.52 |
time (sec) |
N/A | 0.000 | 0.089 | 101.756 | 0.298 | 0.095 | 14.994 | 0.970 | 0.227 | 3.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 63 | 58 | 85 | 57 | 51 | 57 | 57 | 113 |
N.S. |
1 | 0.00 | 2.62 | 2.42 | 3.54 | 2.38 | 2.12 | 2.38 | 2.38 | 4.71 |
time (sec) |
N/A | 0.000 | 0.049 | 2.874 | 0.094 | 0.079 | 0.103 | 0.430 | 0.196 | 4.952 |