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 | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 24 | 24 | 23 | 23 | 26 | 23 | 125 | 23 |
N.S. |
1 | 0.00 | 1.20 | 1.20 | 1.15 | 1.15 | 1.30 | 1.15 | 6.25 | 1.15 |
time (sec) |
N/A | 0.000 | 0.185 | 0.458 | 0.062 | 0.082 | 0.106 | 0.115 | 0.222 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 23 | 28 | 15 | 14 | 23 | 14 | 15 | 29 | 14 |
N.S. |
1 | 1.53 | 1.87 | 1.00 | 0.93 | 1.53 | 0.93 | 1.00 | 1.93 | 0.93 |
time (sec) |
N/A | 0.410 | 0.044 | 0.139 | 0.030 | 0.081 | 0.049 | 0.122 | 0.207 | 2.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 28 | 30 | 25 | 29 | 29 | 31 | 827 | 29 |
N.S. |
1 | 1.00 | 0.90 | 0.97 | 0.81 | 0.94 | 0.94 | 1.00 | 26.68 | 0.94 |
time (sec) |
N/A | 0.326 | 0.033 | 8.029 | 0.151 | 0.077 | 0.347 | 0.462 | 2.430 | 3.135 |
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 | 26 | 17 | 16 | 18 | 18 | 29 | 18 | 24 | 16 |
N.S. |
1 | 1.44 | 0.94 | 0.89 | 1.00 | 1.00 | 1.61 | 1.00 | 1.33 | 0.89 |
time (sec) |
N/A | 0.153 | 0.002 | 0.102 | 0.037 | 0.093 | 0.066 | 0.112 | 0.201 | 2.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 70 | 44 | 17 | 50 | 23 | 12 | 16 | 43 | 16 |
N.S. |
1 | 2.59 | 1.63 | 0.63 | 1.85 | 0.85 | 0.44 | 0.59 | 1.59 | 0.59 |
time (sec) |
N/A | 0.597 | 0.051 | 0.355 | 0.073 | 0.081 | 0.083 | 0.109 | 0.199 | 2.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 28 | 25 | 24 | 24 | 22 | 0 | 28 | 0 |
N.S. |
1 | 0.00 | 1.04 | 0.93 | 0.89 | 0.89 | 0.81 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.044 | 0.591 | 0.153 | 0.085 | 0.151 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 23 | 26 | 39 | 20 | 36 | 60 | 22 |
N.S. |
1 | 0.00 | 1.04 | 0.92 | 1.04 | 1.56 | 0.80 | 1.44 | 2.40 | 0.88 |
time (sec) |
N/A | 0.000 | 0.318 | 0.211 | 0.176 | 0.082 | 0.139 | 0.120 | 0.201 | 2.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | B | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 36 | 67 | 42 | 60 | 56 | 52 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.44 | 2.68 | 1.68 | 2.40 | 2.24 | 2.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 3.132 | 0.163 | 0.080 | 1.906 | 0.196 | 0.210 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 23 | 12 | 12 | 22 | 11 | 7 | 11 | 14 | 11 |
N.S. |
1 | 1.64 | 0.86 | 0.86 | 1.57 | 0.79 | 0.50 | 0.79 | 1.00 | 0.79 |
time (sec) |
N/A | 0.175 | 0.041 | 0.121 | 0.026 | 0.089 | 0.037 | 0.106 | 0.209 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 33 | 33 | 21 | 27 | 47 | 29 | 47 | 40 | 22 |
N.S. |
1 | 1.38 | 1.38 | 0.88 | 1.12 | 1.96 | 1.21 | 1.96 | 1.67 | 0.92 |
time (sec) |
N/A | 0.965 | 0.143 | 2.915 | 0.139 | 0.093 | 0.056 | 0.114 | 0.200 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | A | F | F | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 0 | 19 | 22 | 19 | 17 | 0 | 218 | 18 |
N.S. |
1 | 0.88 | 0.00 | 0.76 | 0.88 | 0.76 | 0.68 | 0.00 | 8.72 | 0.72 |
time (sec) |
N/A | 0.414 | 0.000 | 1.173 | 0.166 | 0.078 | 0.489 | 0.000 | 0.214 | 3.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 54 | 49 | 38 | 62 | 39 | 36 | 73 | 62 | 47 |
N.S. |
1 | 1.69 | 1.53 | 1.19 | 1.94 | 1.22 | 1.12 | 2.28 | 1.94 | 1.47 |
time (sec) |
N/A | 0.257 | 0.092 | 0.450 | 0.027 | 0.075 | 0.071 | 0.112 | 0.216 | 0.053 |
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 | 26 | 70 | 44 | 40 | 64 | 51 | 66 | 64 | 63 | 45 |
N.S. |
1 | 2.69 | 1.69 | 1.54 | 2.46 | 1.96 | 2.54 | 2.46 | 2.42 | 1.73 |
time (sec) |
N/A | 0.256 | 0.005 | 0.145 | 0.025 | 0.075 | 0.126 | 0.114 | 0.209 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | C | A | A | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 22 | 76 | 21 | 17 | 41 | 19 | 21 |
N.S. |
1 | 0.00 | 0.00 | 1.10 | 3.80 | 1.05 | 0.85 | 2.05 | 0.95 | 1.05 |
time (sec) |
N/A | 0.000 | 0.000 | 0.790 | 0.086 | 0.087 | 0.134 | 0.136 | 0.202 | 2.916 |
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 | 14 | 14 | 17 | 19 | 20 | 15 | 52 | 16 | 20 |
N.S. |
1 | 0.70 | 0.70 | 0.85 | 0.95 | 1.00 | 0.75 | 2.60 | 0.80 | 1.00 |
time (sec) |
N/A | 0.197 | 0.012 | 0.194 | 0.031 | 0.068 | 0.230 | 0.111 | 0.202 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 79 | 76 | 104 | 98 | 73 | 123 | 83 | 0 |
N.S. |
1 | 0.00 | 2.55 | 2.45 | 3.35 | 3.16 | 2.35 | 3.97 | 2.68 | 0.00 |
time (sec) |
N/A | 0.000 | 10.061 | 0.437 | 0.079 | 0.085 | 3.719 | 0.138 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 57 | 57 | 62 | 50 | 50 | 56 | 50 | 61 | 57 |
N.S. |
1 | 2.04 | 2.04 | 2.21 | 1.79 | 1.79 | 2.00 | 1.79 | 2.18 | 2.04 |
time (sec) |
N/A | 0.190 | 0.005 | 0.187 | 0.026 | 0.079 | 0.027 | 0.112 | 0.208 | 2.540 |
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 | 22 | 51 | 27 | 28 | 27 | 31 | 27 | 32 | 26 | 27 |
N.S. |
1 | 2.32 | 1.23 | 1.27 | 1.23 | 1.41 | 1.23 | 1.45 | 1.18 | 1.23 |
time (sec) |
N/A | 0.598 | 0.063 | 0.329 | 0.150 | 0.084 | 0.120 | 0.126 | 0.206 | 2.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 44 | 52 | 234 | 76 | 87 | 108 | 120 | 55 |
N.S. |
1 | 0.00 | 1.69 | 2.00 | 9.00 | 2.92 | 3.35 | 4.15 | 4.62 | 2.12 |
time (sec) |
N/A | 0.000 | 0.234 | 0.524 | 0.164 | 0.107 | 0.192 | 0.127 | 0.208 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 61 | 24 | 19 | 72 | 18 | 17 | 31 | 33 | 18 |
N.S. |
1 | 3.39 | 1.33 | 1.06 | 4.00 | 1.00 | 0.94 | 1.72 | 1.83 | 1.00 |
time (sec) |
N/A | 0.205 | 0.033 | 0.190 | 0.108 | 0.083 | 0.069 | 0.117 | 0.210 | 2.607 |
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 | 33 | 27 | 24 | 26 | 29 | 34 | 26 | 30 | 51 | 28 |
N.S. |
1 | 0.82 | 0.73 | 0.79 | 0.88 | 1.03 | 0.79 | 0.91 | 1.55 | 0.85 |
time (sec) |
N/A | 0.319 | 0.016 | 0.178 | 0.027 | 0.081 | 0.233 | 0.108 | 0.198 | 0.072 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 13 | 12 | 14 | 11 | 10 | 20 | 13 | 11 |
N.S. |
1 | 0.00 | 0.87 | 0.80 | 0.93 | 0.73 | 0.67 | 1.33 | 0.87 | 0.73 |
time (sec) |
N/A | 0.000 | 0.015 | 0.066 | 0.065 | 0.082 | 0.058 | 0.113 | 0.188 | 2.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 56 | 80 | 159 | 79 | 83 | 0 | 157 | 317 |
N.S. |
1 | 0.00 | 1.60 | 2.29 | 4.54 | 2.26 | 2.37 | 0.00 | 4.49 | 9.06 |
time (sec) |
N/A | 0.000 | 0.399 | 1.599 | 0.182 | 0.100 | 0.464 | 0.000 | 0.744 | 2.914 |
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 | 29 | 0 | 32 | 27 | 33 | 24 | 22 | 53 | 20 | 36 |
N.S. |
1 | 0.00 | 1.10 | 0.93 | 1.14 | 0.83 | 0.76 | 1.83 | 0.69 | 1.24 |
time (sec) |
N/A | 0.000 | 0.144 | 0.538 | 0.112 | 0.078 | 0.127 | 0.112 | 0.206 | 3.338 |
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 | 26 | 21 | 21 | 20 | 27 | 27 | 14 | 21 | 26 | 19 |
N.S. |
1 | 0.81 | 0.81 | 0.77 | 1.04 | 1.04 | 0.54 | 0.81 | 1.00 | 0.73 |
time (sec) |
N/A | 0.525 | 0.045 | 0.284 | 0.054 | 0.085 | 0.064 | 0.118 | 0.211 | 3.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 25 | 23 | 80 | 0 | 0 | 92 | 27 |
N.S. |
1 | 0.00 | 0.97 | 0.83 | 0.77 | 2.67 | 0.00 | 0.00 | 3.07 | 0.90 |
time (sec) |
N/A | 0.000 | 0.116 | 6.762 | 0.175 | 0.108 | 0.000 | 0.000 | 81.506 | 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 | 13 | 7 | 7 | 6 | 5 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 0.54 | 0.54 | 0.46 | 0.38 | 0.38 | 0.38 | 0.38 | 0.38 | 0.38 |
time (sec) |
N/A | 0.121 | 0.000 | 0.027 | 0.023 | 0.070 | 0.020 | 0.112 | 0.179 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 32 | 40 | 0 | 38 | 31 | 41 | 96 | 26 |
N.S. |
1 | 0.96 | 1.19 | 1.48 | 0.00 | 1.41 | 1.15 | 1.52 | 3.56 | 0.96 |
time (sec) |
N/A | 3.383 | 0.087 | 1.524 | 0.000 | 0.093 | 0.515 | 0.658 | 0.186 | 2.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 24 | 24 | 50 | 0 | 49 | 42 | 0 | 44 | 39 |
N.S. |
1 | 0.92 | 0.92 | 1.92 | 0.00 | 1.88 | 1.62 | 0.00 | 1.69 | 1.50 |
time (sec) |
N/A | 0.908 | 0.668 | 0.314 | 0.000 | 0.084 | 1.965 | 0.000 | 0.195 | 2.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 4 | 4 | 6 | 5 | 5 | 5 | 5 | 4 | 5 |
N.S. |
1 | 0.44 | 0.44 | 0.67 | 0.56 | 0.56 | 0.56 | 0.56 | 0.44 | 0.56 |
time (sec) |
N/A | 0.122 | 0.000 | 0.030 | 0.025 | 0.059 | 0.014 | 0.107 | 0.178 | 0.001 |
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 | 21 | 24 | 29 | 24 | 29 | 29 | 29 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.14 | 1.38 | 1.14 | 1.38 | 1.38 | 1.38 | 0.95 |
time (sec) |
N/A | 0.000 | 0.943 | 0.230 | 0.140 | 0.083 | 0.056 | 0.119 | 0.177 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 24 | 117 | 136 | 0 | 147 | 1281 | 0 |
N.S. |
1 | 0.00 | 0.93 | 0.83 | 4.03 | 4.69 | 0.00 | 5.07 | 44.17 | 0.00 |
time (sec) |
N/A | 0.000 | 2.090 | 2.648 | 0.452 | 0.095 | 0.000 | 1.054 | 0.208 | 0.000 |
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 | 23 | 0 | 17 | 17 | 15 | 15 | 15 | 20 | 24 | 17 |
N.S. |
1 | 0.00 | 0.74 | 0.74 | 0.65 | 0.65 | 0.65 | 0.87 | 1.04 | 0.74 |
time (sec) |
N/A | 0.000 | 0.422 | 0.319 | 0.098 | 0.079 | 0.290 | 0.154 | 0.186 | 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 | 9 | 9 | 10 | 9 | 12 | 7 | 9 | 11 | 9 |
N.S. |
1 | 0.45 | 0.45 | 0.50 | 0.45 | 0.60 | 0.35 | 0.45 | 0.55 | 0.45 |
time (sec) |
N/A | 0.143 | 0.001 | 0.027 | 0.024 | 0.071 | 0.030 | 0.108 | 0.182 | 2.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 42 | 46 | 1730 | 109 | 0 | 191 | 112 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.64 | 61.79 | 3.89 | 0.00 | 6.82 | 4.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.190 | 0.103 | 8.733 | 0.116 | 0.000 | 0.932 | 0.199 | 0.000 |
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 | 28 | 0 | 157 | 471 | 274 | 285 | 456 | 375 | 431 | 271 |
N.S. |
1 | 0.00 | 5.61 | 16.82 | 9.79 | 10.18 | 16.29 | 13.39 | 15.39 | 9.68 |
time (sec) |
N/A | 0.000 | 0.440 | 15.275 | 0.616 | 0.131 | 1.709 | 1.752 | 0.242 | 3.652 |
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 | 15 | 13 | 9 | 8 | 8 | 10 | 8 | 12 | 8 |
N.S. |
1 | 1.15 | 1.00 | 0.69 | 0.62 | 0.62 | 0.77 | 0.62 | 0.92 | 0.62 |
time (sec) |
N/A | 0.151 | 0.013 | 0.062 | 0.030 | 0.074 | 0.037 | 0.111 | 0.184 | 0.024 |
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 | 21 | 19 | 45 | 21 | 21 | 21 | 20 | 21 | 22 | 18 |
N.S. |
1 | 0.90 | 2.14 | 1.00 | 1.00 | 1.00 | 0.95 | 1.00 | 1.05 | 0.86 |
time (sec) |
N/A | 0.609 | 0.555 | 0.561 | 0.159 | 0.076 | 0.127 | 0.149 | 0.181 | 2.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 0 | 14 | 20 | 17 | 27 | 19 | 23 | 18 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 1.25 | 1.06 | 1.69 | 1.19 | 1.44 | 1.12 |
time (sec) |
N/A | 0.000 | 0.000 | 10.954 | 0.231 | 0.084 | 2.629 | 0.151 | 0.185 | 2.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 42 | 37 | 46 | 40 | 36 | 0 | 179 | 44 |
N.S. |
1 | 0.00 | 1.50 | 1.32 | 1.64 | 1.43 | 1.29 | 0.00 | 6.39 | 1.57 |
time (sec) |
N/A | 0.000 | 0.369 | 6.085 | 0.163 | 0.090 | 0.815 | 0.000 | 200.012 | 2.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 27 | 72 | 47 | 29 | 28 | 33 | 21 |
N.S. |
1 | 0.00 | 1.17 | 1.12 | 3.00 | 1.96 | 1.21 | 1.17 | 1.38 | 0.88 |
time (sec) |
N/A | 0.000 | 1.374 | 0.206 | 0.105 | 0.086 | 11.522 | 0.117 | 0.177 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 51 | 55 | 75 | 56 | 0 | 93 | 180 | 72 |
N.S. |
1 | 0.00 | 1.65 | 1.77 | 2.42 | 1.81 | 0.00 | 3.00 | 5.81 | 2.32 |
time (sec) |
N/A | 0.000 | 0.158 | 0.683 | 0.146 | 0.095 | 0.000 | 0.295 | 200.020 | 2.811 |
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 | 25 | 42 | 25 | 20 | 39 | 26 | 24 | 22 | 22 | 19 |
N.S. |
1 | 1.68 | 1.00 | 0.80 | 1.56 | 1.04 | 0.96 | 0.88 | 0.88 | 0.76 |
time (sec) |
N/A | 0.364 | 0.033 | 0.196 | 0.030 | 0.081 | 0.100 | 0.119 | 0.151 | 2.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 80 | 25 | 60 | 72 | 48 | 76 | 67 | 71 | 35 |
N.S. |
1 | 2.96 | 0.93 | 2.22 | 2.67 | 1.78 | 2.81 | 2.48 | 2.63 | 1.30 |
time (sec) |
N/A | 0.282 | 0.075 | 0.297 | 0.029 | 0.084 | 0.123 | 0.112 | 0.154 | 2.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 11 | 10 | 10 | 10 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.91 | 0.91 | 1.18 | 0.91 |
time (sec) |
N/A | 0.164 | 0.005 | 0.158 | 0.034 | 0.079 | 0.060 | 0.107 | 0.164 | 2.578 |
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 | 27 | 25 | 21 | 22 | 22 | 22 | 38 | 90 |
N.S. |
1 | 0.00 | 1.08 | 1.00 | 0.84 | 0.88 | 0.88 | 0.88 | 1.52 | 3.60 |
time (sec) |
N/A | 0.000 | 0.193 | 0.446 | 0.071 | 0.084 | 0.117 | 0.157 | 0.164 | 2.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 44 | 28 | 34 | 34 | 0 | 386 | 36 | 0 |
N.S. |
1 | 0.00 | 1.33 | 0.85 | 1.03 | 1.03 | 0.00 | 11.70 | 1.09 | 0.00 |
time (sec) |
N/A | 0.000 | 10.085 | 0.365 | 0.133 | 0.079 | 0.000 | 0.229 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 18 | 184 | 17 | 22 | 33 | 29 | 17 |
N.S. |
1 | 0.00 | 0.89 | 0.95 | 9.68 | 0.89 | 1.16 | 1.74 | 1.53 | 0.89 |
time (sec) |
N/A | 0.000 | 0.021 | 0.454 | 0.048 | 0.083 | 0.092 | 0.119 | 0.161 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 111 | 141 | 145 | 124 | 168 | 0 | 493 | 163 |
N.S. |
1 | 0.00 | 3.96 | 5.04 | 5.18 | 4.43 | 6.00 | 0.00 | 17.61 | 5.82 |
time (sec) |
N/A | 0.000 | 1.092 | 0.099 | 0.759 | 0.098 | 1.104 | 0.000 | 1.479 | 3.240 |
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 | 32 | 0 | 30 | 25 | 21 | 25 | 19 | 29 | 24 | 24 |
N.S. |
1 | 0.00 | 0.94 | 0.78 | 0.66 | 0.78 | 0.59 | 0.91 | 0.75 | 0.75 |
time (sec) |
N/A | 0.000 | 0.057 | 1.463 | 0.057 | 0.076 | 0.058 | 0.116 | 0.167 | 2.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 162 | 29 | 33 | 34 | 36 | 31 | 0 | 43 | 36 |
N.S. |
1 | 5.40 | 0.97 | 1.10 | 1.13 | 1.20 | 1.03 | 0.00 | 1.43 | 1.20 |
time (sec) |
N/A | 1.381 | 0.148 | 0.058 | 0.143 | 0.101 | 1.075 | 0.000 | 2.475 | 3.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 30 | 28 | 27 | 27 | 26 | 27 | 663 | 71 |
N.S. |
1 | 1.07 | 1.07 | 1.00 | 0.96 | 0.96 | 0.93 | 0.96 | 23.68 | 2.54 |
time (sec) |
N/A | 0.578 | 0.063 | 0.634 | 0.125 | 0.078 | 0.121 | 0.263 | 0.186 | 3.325 |
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 | 36 | 32 | 32 | 30 | 32 | 27 | 33 | 51 | 140 |
N.S. |
1 | 1.33 | 1.19 | 1.19 | 1.11 | 1.19 | 1.00 | 1.22 | 1.89 | 5.19 |
time (sec) |
N/A | 0.678 | 0.662 | 1.284 | 0.071 | 0.096 | 0.129 | 0.188 | 2.643 | 2.840 |
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 | 27 | 0 | 25 | 24 | 23 | 23 | 22 | 23 | 159 | 23 |
N.S. |
1 | 0.00 | 0.93 | 0.89 | 0.85 | 0.85 | 0.81 | 0.85 | 5.89 | 0.85 |
time (sec) |
N/A | 0.000 | 0.229 | 0.182 | 0.065 | 0.083 | 0.075 | 0.121 | 0.188 | 2.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 36 | 52 | 40 | 75 | 51 | 0 | 56 | 32 |
N.S. |
1 | 0.00 | 1.57 | 2.26 | 1.74 | 3.26 | 2.22 | 0.00 | 2.43 | 1.39 |
time (sec) |
N/A | 0.000 | 0.044 | 0.413 | 0.115 | 0.081 | 0.130 | 0.000 | 0.186 | 2.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | B | A | A | A | B | B |
verified | N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 146774 | 45 | 113 | 41 | 37 | 43 | 48 | 43 |
N.S. |
1 | 0.00 | 5645.15 | 1.73 | 4.35 | 1.58 | 1.42 | 1.65 | 1.85 | 1.65 |
time (sec) |
N/A | 0.000 | 14.812 | 0.983 | 0.092 | 0.086 | 0.194 | 1.941 | 0.178 | 3.232 |
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 | 23 | 0 | 19 | 25 | 24 | 24 | 24 | 24 | 52 | 25 |
N.S. |
1 | 0.00 | 0.83 | 1.09 | 1.04 | 1.04 | 1.04 | 1.04 | 2.26 | 1.09 |
time (sec) |
N/A | 0.000 | 0.074 | 0.187 | 0.110 | 0.086 | 10.127 | 0.131 | 0.182 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 27 | 72 | 40 | 22 | 0 | 28 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 2.67 | 1.48 | 0.81 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 22.049 | 0.180 | 0.102 | 0.598 | 0.000 | 0.179 | 0.000 |
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 | 17 | 35 | 22 | 19 | 18 | 18 | 14 | 18 | 19 | 19 |
N.S. |
1 | 2.06 | 1.29 | 1.12 | 1.06 | 1.06 | 0.82 | 1.06 | 1.12 | 1.12 |
time (sec) |
N/A | 0.246 | 0.516 | 0.282 | 0.089 | 0.079 | 0.063 | 0.115 | 0.181 | 0.094 |
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 | 29 | 0 | 29 | 28 | 27 | 27 | 24 | 27 | 29 | 28 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 0.93 | 0.93 | 0.83 | 0.93 | 1.00 | 0.97 |
time (sec) |
N/A | 0.000 | 0.851 | 0.147 | 0.085 | 0.084 | 0.066 | 0.112 | 0.169 | 2.783 |
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 | 25 | 0 | 37 | 22 | 47 | 21 | 19 | 29 | 35 | 29 |
N.S. |
1 | 0.00 | 1.48 | 0.88 | 1.88 | 0.84 | 0.76 | 1.16 | 1.40 | 1.16 |
time (sec) |
N/A | 0.000 | 5.050 | 0.545 | 0.217 | 0.084 | 0.214 | 0.174 | 0.183 | 2.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 18 | 21 | 12 | 18 | 0 | 12 | 22 | 12 |
N.S. |
1 | 0.00 | 0.90 | 1.05 | 0.60 | 0.90 | 0.00 | 0.60 | 1.10 | 0.60 |
time (sec) |
N/A | 0.000 | 0.034 | 0.869 | 0.132 | 0.070 | 0.000 | 0.113 | 0.176 | 2.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F(-1) | B | B | B | B | F | B |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 25 | 0 | 79 | 60 | 70 | 79 | 136 | 92 |
N.S. |
1 | 1.09 | 1.09 | 0.00 | 3.43 | 2.61 | 3.04 | 3.43 | 5.91 | 4.00 |
time (sec) |
N/A | 1.879 | 1.166 | 0.000 | 0.530 | 0.086 | 0.219 | 0.390 | 200.029 | 2.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 33 | 40 | 67 | 67 | 0 | 71 | 56 | 29 |
N.S. |
1 | 0.00 | 1.18 | 1.43 | 2.39 | 2.39 | 0.00 | 2.54 | 2.00 | 1.04 |
time (sec) |
N/A | 0.000 | 0.074 | 4.406 | 0.166 | 0.082 | 0.000 | 0.162 | 0.206 | 3.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 15 | 19 | 13 | 56 | 0 | 0 | 16 | 12 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 0.87 | 3.73 | 0.00 | 0.00 | 1.07 | 0.80 |
time (sec) |
N/A | 0.000 | 0.234 | 0.618 | 0.244 | 0.089 | 0.000 | 0.000 | 0.183 | 3.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-1) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 45 | 23 | 42 | 36 | 25 | 32 | 0 | 25 | 0 |
N.S. |
1 | 1.80 | 0.92 | 1.68 | 1.44 | 1.00 | 1.28 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 13.764 | 1.610 | 15.715 | 0.077 | 0.083 | 3.586 | 0.000 | 0.184 | 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 | 21 | 32 | 26 | 25 | 23 | 23 | 27 | 23 | 18 | 26 |
N.S. |
1 | 1.52 | 1.24 | 1.19 | 1.10 | 1.10 | 1.29 | 1.10 | 0.86 | 1.24 |
time (sec) |
N/A | 0.165 | 0.008 | 0.155 | 0.028 | 0.067 | 0.049 | 0.112 | 0.178 | 0.043 |
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 | 26 | 0 | 26 | 22 | 41 | 43 | 34 | 0 | 46 | 46 |
N.S. |
1 | 0.00 | 1.00 | 0.85 | 1.58 | 1.65 | 1.31 | 0.00 | 1.77 | 1.77 |
time (sec) |
N/A | 0.000 | 0.850 | 0.317 | 0.257 | 0.092 | 0.142 | 0.000 | 5.026 | 2.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | B | F(-1) | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 48 | 92 | 83 | 65 | 63 | 0 | 103 | 0 |
N.S. |
1 | 0.00 | 1.50 | 2.88 | 2.59 | 2.03 | 1.97 | 0.00 | 3.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.206 | 0.223 | 0.745 | 0.083 | 0.373 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 42 | 42 | 34 | 52 | 44 | 73 | 1221 | 116 |
N.S. |
1 | 0.00 | 1.62 | 1.62 | 1.31 | 2.00 | 1.69 | 2.81 | 46.96 | 4.46 |
time (sec) |
N/A | 0.000 | 0.127 | 4.562 | 0.361 | 0.088 | 0.331 | 0.245 | 0.282 | 2.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 89 | 197 | 121 | 126 | 131 | 0 | 217 | 129 |
N.S. |
1 | 0.00 | 3.56 | 7.88 | 4.84 | 5.04 | 5.24 | 0.00 | 8.68 | 5.16 |
time (sec) |
N/A | 0.000 | 0.068 | 1.154 | 0.159 | 0.083 | 0.334 | 0.000 | 0.187 | 2.852 |
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 | 24 | 22 | 19 | 17 | 23 | 19 | 18 | 24 | 18 |
N.S. |
1 | 0.83 | 0.76 | 0.66 | 0.59 | 0.79 | 0.66 | 0.62 | 0.83 | 0.62 |
time (sec) |
N/A | 0.190 | 0.002 | 0.102 | 0.028 | 0.075 | 0.046 | 0.108 | 0.180 | 0.041 |
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 | 40 | 23 | 21 | 17 | 18 | 22 | 18 | 23 | 19 |
N.S. |
1 | 1.48 | 0.85 | 0.78 | 0.63 | 0.67 | 0.81 | 0.67 | 0.85 | 0.70 |
time (sec) |
N/A | 0.331 | 0.019 | 0.215 | 0.105 | 0.074 | 0.089 | 0.119 | 0.172 | 2.877 |
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 | 4 | 4 | 5 | 4 | 4 | 3 | 4 | 4 | 4 |
N.S. |
1 | 0.29 | 0.29 | 0.36 | 0.29 | 0.29 | 0.21 | 0.29 | 0.29 | 0.29 |
time (sec) |
N/A | 0.124 | 0.000 | 0.023 | 0.032 | 0.058 | 0.014 | 0.105 | 0.183 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 12 | 8 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 1.20 | 0.80 | 1.10 | 1.00 |
time (sec) |
N/A | 0.131 | 0.000 | 0.076 | 0.032 | 0.066 | 0.015 | 0.114 | 0.185 | 0.001 |
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 | 26 | 51 | 38 | 43 | 56 | 39 | 34 | 44 | 52 | 35 |
N.S. |
1 | 1.96 | 1.46 | 1.65 | 2.15 | 1.50 | 1.31 | 1.69 | 2.00 | 1.35 |
time (sec) |
N/A | 0.551 | 0.489 | 0.532 | 0.070 | 0.082 | 0.098 | 0.119 | 0.184 | 2.607 |
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 | 16 | 12 | 11 | 11 | 12 | 12 | 10 | 13 | 13 | 10 |
N.S. |
1 | 0.75 | 0.69 | 0.69 | 0.75 | 0.75 | 0.62 | 0.81 | 0.81 | 0.62 |
time (sec) |
N/A | 0.139 | 0.003 | 0.187 | 0.023 | 0.083 | 0.036 | 0.114 | 0.187 | 0.043 |
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 | 41 | 27 | 23 | 33 | 22 | 20 | 43 | 31 | 18 |
N.S. |
1 | 1.46 | 0.96 | 0.82 | 1.18 | 0.79 | 0.71 | 1.54 | 1.11 | 0.64 |
time (sec) |
N/A | 0.207 | 0.162 | 0.257 | 0.029 | 0.082 | 0.073 | 0.115 | 0.198 | 0.049 |
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 | 21 | 0 | 21 | 16 | 15 | 15 | 15 | 0 | 24 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.76 | 0.71 | 0.71 | 0.71 | 0.00 | 1.14 | 0.86 |
time (sec) |
N/A | 0.000 | 0.144 | 0.237 | 0.455 | 0.094 | 0.254 | 0.000 | 0.229 | 2.667 |
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 | 55 | 33 | 34 | 34 | 37 | 37 | 36 | 35 | 39 |
N.S. |
1 | 1.83 | 1.10 | 1.13 | 1.13 | 1.23 | 1.23 | 1.20 | 1.17 | 1.30 |
time (sec) |
N/A | 0.577 | 0.036 | 0.510 | 0.028 | 0.081 | 1.081 | 0.130 | 0.179 | 2.811 |
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 | 28 | 0 | 27 | 28 | 19 | 33 | 24 | 47 | 45 | 21 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.68 | 1.18 | 0.86 | 1.68 | 1.61 | 0.75 |
time (sec) |
N/A | 0.000 | 0.781 | 1.532 | 0.237 | 0.089 | 0.151 | 0.293 | 0.182 | 3.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 66 | 69 | 127 | 127 | 68 | 128 | 141 | 0 |
N.S. |
1 | 0.00 | 2.13 | 2.23 | 4.10 | 4.10 | 2.19 | 4.13 | 4.55 | 0.00 |
time (sec) |
N/A | 0.000 | 10.141 | 3.964 | 0.276 | 0.099 | 0.240 | 3.608 | 0.271 | 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 | 20 | 20 | 20 | 20 | 19 | 19 | 15 | 19 | 20 | 54 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.75 | 0.95 | 1.00 | 2.70 |
time (sec) |
N/A | 0.400 | 0.011 | 0.443 | 0.142 | 0.071 | 0.065 | 0.123 | 0.189 | 2.925 |
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 | 34 | 33 | 31 | 29 | 16 | 31 | 24 | 19 | 17 |
N.S. |
1 | 1.62 | 1.57 | 1.48 | 1.38 | 0.76 | 1.48 | 1.14 | 0.90 | 0.81 |
time (sec) |
N/A | 0.180 | 0.004 | 0.277 | 0.032 | 0.077 | 0.080 | 0.108 | 0.183 | 2.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 70 | 31 | 25 | 51 | 27 | 31 | 0 | 35 | 29 |
N.S. |
1 | 2.26 | 1.00 | 0.81 | 1.65 | 0.87 | 1.00 | 0.00 | 1.13 | 0.94 |
time (sec) |
N/A | 0.287 | 0.061 | 0.154 | 0.039 | 0.084 | 0.129 | 0.000 | 0.190 | 3.003 |
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 | 24 | 21 | 19 | 18 | 18 | 19 | 18 | 19 | 18 |
N.S. |
1 | 1.09 | 0.95 | 0.86 | 0.82 | 0.82 | 0.86 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 0.158 | 0.005 | 0.128 | 0.029 | 0.084 | 0.044 | 0.118 | 0.210 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 56 | 52 | 30 | 639 | 25 | 26 | 213 | 36 | 28 |
N.S. |
1 | 2.15 | 2.00 | 1.15 | 24.58 | 0.96 | 1.00 | 8.19 | 1.38 | 1.08 |
time (sec) |
N/A | 0.512 | 0.065 | 0.189 | 0.193 | 0.078 | 0.085 | 0.121 | 0.204 | 0.162 |
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 | 20 | 15 | 15 | 18 | 18 | 15 | 18 | 13 | 14 |
N.S. |
1 | 1.25 | 0.94 | 0.94 | 1.12 | 1.12 | 0.94 | 1.12 | 0.81 | 0.88 |
time (sec) |
N/A | 0.150 | 0.003 | 0.062 | 0.031 | 0.079 | 0.021 | 0.113 | 0.202 | 0.021 |
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 | 8 | 6 | 6 | 5 | 5 | 5 | 6 | 6 | 5 |
N.S. |
1 | 0.38 | 0.29 | 0.29 | 0.24 | 0.24 | 0.24 | 0.29 | 0.29 | 0.24 |
time (sec) |
N/A | 0.153 | 0.009 | 0.061 | 0.033 | 0.068 | 0.033 | 0.110 | 0.186 | 0.029 |
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 | 28 | 107 | 130 | 91 | 160 | 59 | 65 | 66 | 121 | 72 |
N.S. |
1 | 3.82 | 4.64 | 3.25 | 5.71 | 2.11 | 2.32 | 2.36 | 4.32 | 2.57 |
time (sec) |
N/A | 0.667 | 0.145 | 0.807 | 0.123 | 0.079 | 0.146 | 0.124 | 0.222 | 3.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 21 | 22 | 21 | 21 | 17 | 21 | 17 | 21 |
N.S. |
1 | 1.11 | 1.11 | 1.16 | 1.11 | 1.11 | 0.89 | 1.11 | 0.89 | 1.11 |
time (sec) |
N/A | 0.337 | 0.019 | 0.340 | 0.057 | 0.081 | 0.114 | 0.121 | 0.207 | 2.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 49 | 39 | 48 | 27 | 48 | 49 | 30 |
N.S. |
1 | 0.00 | 1.04 | 2.04 | 1.62 | 2.00 | 1.12 | 2.00 | 2.04 | 1.25 |
time (sec) |
N/A | 0.000 | 0.230 | 0.372 | 0.079 | 0.088 | 0.119 | 0.540 | 0.189 | 3.240 |
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 | 33 | 32 | 29 | 29 | 23 | 24 | 29 | 24 | 23 |
N.S. |
1 | 1.43 | 1.39 | 1.26 | 1.26 | 1.00 | 1.04 | 1.26 | 1.04 | 1.00 |
time (sec) |
N/A | 0.234 | 0.009 | 0.389 | 0.034 | 0.082 | 0.066 | 0.112 | 0.179 | 2.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 181 | 31 | 131 | 304 | 23 | 22 | 41 | 107 | 23 |
N.S. |
1 | 10.06 | 1.72 | 7.28 | 16.89 | 1.28 | 1.22 | 2.28 | 5.94 | 1.28 |
time (sec) |
N/A | 0.723 | 0.282 | 1.716 | 0.080 | 0.079 | 0.329 | 0.131 | 0.220 | 3.212 |
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 | 18 | 18 | 18 | 19 | 57 | 56 | 58 | 57 | 207 | 123 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 3.17 | 3.11 | 3.22 | 3.17 | 11.50 | 6.83 |
time (sec) |
N/A | 0.501 | 0.023 | 0.417 | 0.191 | 0.085 | 0.159 | 0.157 | 0.198 | 3.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | A | F | B |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 0 | 0 | 64 | 0 | 18 | 211 | 18 |
N.S. |
1 | 0.90 | 0.90 | 0.00 | 0.00 | 3.20 | 0.00 | 0.90 | 10.55 | 0.90 |
time (sec) |
N/A | 0.675 | 3.540 | 0.000 | 0.000 | 0.095 | 0.000 | 0.126 | 0.243 | 3.292 |
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 | 18 | 15 | 14 | 14 | 21 | 15 | 13 | 20 | 16 |
N.S. |
1 | 0.67 | 0.56 | 0.52 | 0.52 | 0.78 | 0.56 | 0.48 | 0.74 | 0.59 |
time (sec) |
N/A | 0.172 | 0.003 | 0.084 | 0.029 | 0.066 | 0.038 | 0.112 | 0.193 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | C | C | C | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 43 | 52 | 55 | 24 | 27 | 40 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.15 | 2.60 | 2.75 | 1.20 | 1.35 | 2.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.164 | 8.167 | 0.074 | 0.086 | 0.182 | 0.216 | 0.204 | 0.000 |
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 | 33 | 0 | 35 | 43 | 44 | 32 | 29 | 0 | 44 | 34 |
N.S. |
1 | 0.00 | 1.06 | 1.30 | 1.33 | 0.97 | 0.88 | 0.00 | 1.33 | 1.03 |
time (sec) |
N/A | 0.000 | 0.119 | 0.643 | 0.159 | 0.083 | 0.094 | 0.000 | 0.198 | 2.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 34 | 128 | 33 | 27 | 176 | 102 | 38 |
N.S. |
1 | 1.00 | 1.00 | 1.48 | 5.57 | 1.43 | 1.17 | 7.65 | 4.43 | 1.65 |
time (sec) |
N/A | 0.278 | 0.069 | 0.701 | 0.161 | 0.074 | 0.108 | 0.129 | 0.181 | 5.011 |