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 | C | C | C | C | F | C | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 34 | 35 | 57 | 50 | 0 | 53 | 16 | 34 |
N.S. |
1 | 0.00 | 34.00 | 35.00 | 57.00 | 50.00 | 0.00 | 53.00 | 16.00 | 34.00 |
time (sec) |
N/A | 0.000 | 0.039 | 0.178 | 0.041 | 0.079 | 0.000 | 0.116 | 0.155 | 0.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | C | C | F | C | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 24 | 20 | 19 | 21 | 0 | 20 | 16 | 19 |
N.S. |
1 | 0.00 | 24.00 | 20.00 | 19.00 | 21.00 | 0.00 | 20.00 | 16.00 | 19.00 |
time (sec) |
N/A | 0.000 | 0.027 | 0.171 | 0.043 | 0.074 | 0.000 | 0.133 | 0.151 | 23.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | C | C | F | C | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 21 | 20 | 19 | 21 | 0 | 20 | 18 | 21 |
N.S. |
1 | 0.00 | 21.00 | 20.00 | 19.00 | 21.00 | 0.00 | 20.00 | 18.00 | 21.00 |
time (sec) |
N/A | 0.000 | 0.028 | 0.174 | 0.034 | 0.071 | 0.000 | 0.129 | 0.157 | 0.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | C | C | F | C | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 31 | 35 | 54 | 52 | 0 | 53 | 18 | 34 |
N.S. |
1 | 0.00 | 31.00 | 35.00 | 54.00 | 52.00 | 0.00 | 53.00 | 18.00 | 34.00 |
time (sec) |
N/A | 0.000 | 0.040 | 0.172 | 0.040 | 0.066 | 0.000 | 0.110 | 0.152 | 23.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 78 | 168 | 0 | 79 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.00 | 78.00 | 168.00 | 0.00 | 79.00 | 0.00 | 0.00 | 16.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.135 | 0.191 | 0.000 | 0.080 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 67 | 119 | 0 | 78 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.00 | 67.00 | 119.00 | 0.00 | 78.00 | 0.00 | 0.00 | 14.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.118 | 0.174 | 0.000 | 0.085 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 69 | 120 | 0 | 78 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.00 | 69.00 | 120.00 | 0.00 | 78.00 | 0.00 | 0.00 | 16.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.120 | 0.182 | 0.000 | 0.095 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 0 | 78 | 168 | 0 | 119 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.00 | 78.00 | 168.00 | 0.00 | 119.00 | 0.00 | 0.00 | 18.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.129 | 0.197 | 0.000 | 0.108 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 125 | 68 | 117 | 203 | 92 | 0 | 111 | 97 | 171 |
N.S. |
1 | 1.10 | 0.60 | 1.03 | 1.78 | 0.81 | 0.00 | 0.97 | 0.85 | 1.50 |
time (sec) |
N/A | 0.587 | 0.090 | 0.121 | 0.037 | 0.076 | 0.000 | 0.146 | 0.162 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 60 | 109 | 166 | 84 | 0 | 0 | 77 | 133 |
N.S. |
1 | 1.06 | 0.67 | 1.21 | 1.84 | 0.93 | 0.00 | 0.00 | 0.86 | 1.48 |
time (sec) |
N/A | 0.509 | 0.058 | 0.094 | 0.030 | 0.077 | 0.000 | 0.000 | 0.158 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 49 | 100 | 128 | 73 | 0 | 77 | 56 | 98 |
N.S. |
1 | 1.03 | 0.78 | 1.59 | 2.03 | 1.16 | 0.00 | 1.22 | 0.89 | 1.56 |
time (sec) |
N/A | 0.443 | 0.043 | 0.078 | 0.027 | 0.091 | 0.000 | 0.131 | 0.155 | 23.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 41 | 90 | 90 | 64 | 0 | 57 | 39 | 58 |
N.S. |
1 | 1.00 | 1.14 | 2.50 | 2.50 | 1.78 | 0.00 | 1.58 | 1.08 | 1.61 |
time (sec) |
N/A | 0.367 | 0.036 | 0.070 | 0.033 | 0.107 | 0.000 | 0.150 | 0.167 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 36 | 131 | 69 | 57 | 0 | 63 | 56 | 37 |
N.S. |
1 | 1.18 | 1.64 | 5.95 | 3.14 | 2.59 | 0.00 | 2.86 | 2.55 | 1.68 |
time (sec) |
N/A | 0.392 | 0.019 | 0.078 | 0.106 | 0.074 | 0.000 | 0.139 | 0.170 | 23.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 27 | 76 | 53 | 46 | 0 | 66 | 59 | 55 |
N.S. |
1 | 1.17 | 1.12 | 3.17 | 2.21 | 1.92 | 0.00 | 2.75 | 2.46 | 2.29 |
time (sec) |
N/A | 0.348 | 0.024 | 0.085 | 0.107 | 0.077 | 0.000 | 0.138 | 0.163 | 23.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 60 | 42 | 85 | 91 | 60 | 0 | 143 | 81 | 81 |
N.S. |
1 | 1.15 | 0.81 | 1.63 | 1.75 | 1.15 | 0.00 | 2.75 | 1.56 | 1.56 |
time (sec) |
N/A | 0.394 | 0.054 | 0.084 | 0.111 | 0.092 | 0.000 | 0.135 | 0.154 | 23.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 90 | 51 | 93 | 136 | 68 | 0 | 148 | 110 | 105 |
N.S. |
1 | 1.14 | 0.65 | 1.18 | 1.72 | 0.86 | 0.00 | 1.87 | 1.39 | 1.33 |
time (sec) |
N/A | 0.461 | 0.096 | 0.092 | 0.116 | 0.084 | 0.000 | 0.119 | 0.169 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 120 | 59 | 101 | 172 | 76 | 0 | 226 | 130 | 129 |
N.S. |
1 | 1.17 | 0.57 | 0.98 | 1.67 | 0.74 | 0.00 | 2.19 | 1.26 | 1.25 |
time (sec) |
N/A | 0.518 | 0.111 | 0.098 | 0.106 | 0.077 | 0.000 | 0.150 | 0.163 | 23.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 39 | 43 | 42 | 37 | 47 | 42 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.00 | 0.98 | 0.86 | 1.09 | 0.98 | 0.88 |
time (sec) |
N/A | 0.530 | 0.025 | 0.114 | 0.025 | 0.079 | 0.053 | 0.131 | 0.158 | 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 | 33 | 33 | 33 | 31 | 34 | 33 | 27 | 38 | 33 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.03 | 1.00 | 0.82 | 1.15 | 1.00 | 0.91 |
time (sec) |
N/A | 0.460 | 0.021 | 0.117 | 0.028 | 0.069 | 0.047 | 0.111 | 0.150 | 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 | 26 | 26 | 26 | 24 | 26 | 25 | 20 | 30 | 25 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.00 | 0.96 | 0.77 | 1.15 | 0.96 | 0.88 |
time (sec) |
N/A | 0.431 | 0.018 | 0.109 | 0.030 | 0.076 | 0.042 | 0.136 | 0.158 | 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 | 14 | 14 | 14 | 14 | 13 | 16 | 10 | 14 | 16 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 1.14 | 0.71 | 1.00 | 1.14 | 0.93 |
time (sec) |
N/A | 0.385 | 0.020 | 0.111 | 0.033 | 0.071 | 0.037 | 0.107 | 0.152 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 14 | 13 | 13 | 10 | 15 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.71 | 1.07 | 0.93 | 1.00 |
time (sec) |
N/A | 0.428 | 0.014 | 0.119 | 0.026 | 0.068 | 0.062 | 0.115 | 0.157 | 23.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 19 | 18 | 22 | 15 | 20 | 22 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 1.16 | 0.79 | 1.05 | 1.16 | 0.74 |
time (sec) |
N/A | 0.430 | 0.017 | 0.127 | 0.029 | 0.069 | 0.078 | 0.130 | 0.157 | 23.557 |
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 | 33 | 33 | 30 | 30 | 35 | 26 | 32 | 35 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 1.06 | 0.79 | 0.97 | 1.06 | 0.70 |
time (sec) |
N/A | 0.463 | 0.019 | 0.135 | 0.024 | 0.078 | 0.092 | 0.121 | 0.157 | 0.044 |
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 | 40 | 40 | 40 | 37 | 38 | 43 | 34 | 40 | 43 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.95 | 1.08 | 0.85 | 1.00 | 1.08 | 0.75 |
time (sec) |
N/A | 0.474 | 0.023 | 0.138 | 0.034 | 0.099 | 0.102 | 0.114 | 0.152 | 23.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 75 | 151 | 182 | 112 | 0 | 0 | 95 | 154 |
N.S. |
1 | 1.00 | 0.64 | 1.28 | 1.54 | 0.95 | 0.00 | 0.00 | 0.81 | 1.31 |
time (sec) |
N/A | 1.028 | 0.102 | 0.111 | 0.036 | 0.103 | 0.000 | 0.000 | 0.160 | 23.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 66 | 142 | 145 | 103 | 0 | 0 | 80 | 117 |
N.S. |
1 | 1.00 | 0.72 | 1.54 | 1.58 | 1.12 | 0.00 | 0.00 | 0.87 | 1.27 |
time (sec) |
N/A | 0.975 | 0.080 | 0.101 | 0.027 | 0.082 | 0.000 | 0.000 | 0.153 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 54 | 133 | 110 | 92 | 0 | 0 | 67 | 59 |
N.S. |
1 | 1.00 | 0.87 | 2.15 | 1.77 | 1.48 | 0.00 | 0.00 | 1.08 | 0.95 |
time (sec) |
N/A | 0.866 | 0.065 | 0.089 | 0.034 | 0.077 | 0.000 | 0.000 | 0.159 | 23.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 83 | 53 | 372 | 90 | 104 | 0 | 0 | 98 | 54 |
N.S. |
1 | 1.80 | 1.15 | 8.09 | 1.96 | 2.26 | 0.00 | 0.00 | 2.13 | 1.17 |
time (sec) |
N/A | 0.978 | 0.075 | 0.089 | 0.111 | 0.072 | 0.000 | 0.000 | 0.162 | 23.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 57 | 41 | 116 | 72 | 74 | 0 | 0 | 89 | 57 |
N.S. |
1 | 1.08 | 0.77 | 2.19 | 1.36 | 1.40 | 0.00 | 0.00 | 1.68 | 1.08 |
time (sec) |
N/A | 0.457 | 0.103 | 0.104 | 0.114 | 0.074 | 0.000 | 0.000 | 0.157 | 23.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 99 | 56 | 125 | 110 | 88 | 0 | 0 | 116 | 83 |
N.S. |
1 | 1.22 | 0.69 | 1.54 | 1.36 | 1.09 | 0.00 | 0.00 | 1.43 | 1.02 |
time (sec) |
N/A | 1.191 | 0.109 | 0.115 | 0.122 | 0.075 | 0.000 | 0.000 | 0.155 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 129 | 66 | 135 | 154 | 96 | 0 | 0 | 132 | 152 |
N.S. |
1 | 1.24 | 0.63 | 1.30 | 1.48 | 0.92 | 0.00 | 0.00 | 1.27 | 1.46 |
time (sec) |
N/A | 1.544 | 0.128 | 0.112 | 0.119 | 0.104 | 0.000 | 0.000 | 0.168 | 23.588 |
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 | 57 | 57 | 57 | 52 | 58 | 66 | 49 | 78 | 67 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.02 | 1.16 | 0.86 | 1.37 | 1.18 | 1.00 |
time (sec) |
N/A | 0.517 | 0.078 | 0.139 | 0.024 | 0.062 | 0.092 | 0.115 | 0.153 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 44 | 49 | 57 | 39 | 69 | 58 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.04 | 1.21 | 0.83 | 1.47 | 1.23 | 1.04 |
time (sec) |
N/A | 0.497 | 0.060 | 0.131 | 0.034 | 0.085 | 0.088 | 0.120 | 0.150 | 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 | 39 | 39 | 39 | 36 | 41 | 49 | 31 | 64 | 50 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.05 | 1.26 | 0.79 | 1.64 | 1.28 | 0.97 |
time (sec) |
N/A | 0.447 | 0.046 | 0.129 | 0.027 | 0.069 | 0.082 | 0.134 | 0.152 | 0.040 |
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 | 27 | 26 | 26 | 26 | 38 | 19 | 46 | 41 | 25 |
N.S. |
1 | 1.00 | 0.96 | 0.96 | 0.96 | 1.41 | 0.70 | 1.70 | 1.52 | 0.93 |
time (sec) |
N/A | 0.396 | 0.034 | 0.125 | 0.025 | 0.060 | 0.080 | 0.128 | 0.148 | 23.336 |
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 | 13 | 13 | 13 | 13 | 12 | 18 | 8 | 57 | 22 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 1.38 | 0.62 | 4.38 | 1.69 | 0.92 |
time (sec) |
N/A | 0.433 | 0.016 | 0.140 | 0.030 | 0.075 | 0.092 | 0.127 | 0.147 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 31 | 34 | 55 | 26 | 40 | 61 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.06 | 1.72 | 0.81 | 1.25 | 1.91 | 0.88 |
time (sec) |
N/A | 0.458 | 0.037 | 0.145 | 0.024 | 0.076 | 0.126 | 0.118 | 0.160 | 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 | 46 | 46 | 46 | 43 | 48 | 73 | 41 | 62 | 74 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.04 | 1.59 | 0.89 | 1.35 | 1.61 | 0.89 |
time (sec) |
N/A | 0.489 | 0.050 | 0.156 | 0.034 | 0.072 | 0.155 | 0.138 | 0.160 | 23.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 51 | 56 | 81 | 49 | 74 | 82 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.04 | 1.50 | 0.91 | 1.37 | 1.52 | 0.91 |
time (sec) |
N/A | 0.489 | 0.067 | 0.161 | 0.031 | 0.074 | 0.166 | 0.134 | 0.150 | 23.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 125 | 68 | 117 | 203 | 91 | 0 | 0 | 97 | 172 |
N.S. |
1 | 1.10 | 0.60 | 1.03 | 1.78 | 0.80 | 0.00 | 0.00 | 0.85 | 1.51 |
time (sec) |
N/A | 0.577 | 0.114 | 0.085 | 0.033 | 0.100 | 0.000 | 0.000 | 0.156 | 23.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 60 | 109 | 166 | 83 | 0 | 86 | 77 | 134 |
N.S. |
1 | 1.06 | 0.67 | 1.21 | 1.84 | 0.92 | 0.00 | 0.96 | 0.86 | 1.49 |
time (sec) |
N/A | 0.500 | 0.063 | 0.077 | 0.032 | 0.095 | 0.000 | 0.131 | 0.147 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 63 | 49 | 100 | 130 | 73 | 0 | 71 | 56 | 97 |
N.S. |
1 | 0.98 | 0.77 | 1.56 | 2.03 | 1.14 | 0.00 | 1.11 | 0.88 | 1.52 |
time (sec) |
N/A | 0.468 | 0.048 | 0.076 | 0.026 | 0.077 | 0.000 | 0.135 | 0.151 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 42 | 91 | 90 | 64 | 0 | 52 | 39 | 58 |
N.S. |
1 | 1.00 | 1.14 | 2.46 | 2.43 | 1.73 | 0.00 | 1.41 | 1.05 | 1.57 |
time (sec) |
N/A | 0.392 | 0.034 | 0.063 | 0.026 | 0.094 | 0.000 | 0.143 | 0.148 | 23.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 24 | 34 | 133 | 70 | 57 | 0 | 59 | 56 | 37 |
N.S. |
1 | 1.20 | 1.70 | 6.65 | 3.50 | 2.85 | 0.00 | 2.95 | 2.80 | 1.85 |
time (sec) |
N/A | 0.392 | 0.020 | 0.071 | 0.112 | 0.073 | 0.000 | 0.132 | 0.144 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 26 | 77 | 55 | 47 | 0 | 0 | 61 | 55 |
N.S. |
1 | 1.16 | 1.04 | 3.08 | 2.20 | 1.88 | 0.00 | 0.00 | 2.44 | 2.20 |
time (sec) |
N/A | 0.350 | 0.039 | 0.082 | 0.109 | 0.097 | 0.000 | 0.000 | 0.148 | 24.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 59 | 41 | 85 | 93 | 60 | 0 | 157 | 82 | 82 |
N.S. |
1 | 1.13 | 0.79 | 1.63 | 1.79 | 1.15 | 0.00 | 3.02 | 1.58 | 1.58 |
time (sec) |
N/A | 0.400 | 0.060 | 0.092 | 0.108 | 0.067 | 0.000 | 0.148 | 0.152 | 24.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 90 | 52 | 93 | 137 | 68 | 0 | 0 | 110 | 105 |
N.S. |
1 | 1.14 | 0.66 | 1.18 | 1.73 | 0.86 | 0.00 | 0.00 | 1.39 | 1.33 |
time (sec) |
N/A | 0.471 | 0.095 | 0.092 | 0.112 | 0.082 | 0.000 | 0.000 | 0.143 | 23.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 120 | 59 | 101 | 173 | 77 | 0 | 258 | 130 | 129 |
N.S. |
1 | 1.17 | 0.57 | 0.98 | 1.68 | 0.75 | 0.00 | 2.50 | 1.26 | 1.25 |
time (sec) |
N/A | 0.554 | 0.109 | 0.093 | 0.110 | 0.094 | 0.000 | 0.127 | 0.156 | 23.707 |
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 | 42 | 39 | 43 | 42 | 37 | 47 | 42 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.02 | 1.00 | 0.88 | 1.12 | 1.00 | 0.90 |
time (sec) |
N/A | 0.483 | 0.026 | 0.118 | 0.027 | 0.076 | 0.056 | 0.148 | 0.143 | 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 | 33 | 33 | 33 | 32 | 34 | 33 | 27 | 38 | 33 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.03 | 1.00 | 0.82 | 1.15 | 1.00 | 0.94 |
time (sec) |
N/A | 0.477 | 0.019 | 0.120 | 0.031 | 0.075 | 0.049 | 0.133 | 0.143 | 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 | 25 | 25 | 25 | 24 | 26 | 25 | 20 | 30 | 25 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.04 | 1.00 | 0.80 | 1.20 | 1.00 | 0.92 |
time (sec) |
N/A | 0.439 | 0.016 | 0.113 | 0.029 | 0.064 | 0.049 | 0.133 | 0.147 | 23.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 13 | 16 | 10 | 14 | 16 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.23 | 0.77 | 1.08 | 1.23 | 1.00 |
time (sec) |
N/A | 0.392 | 0.017 | 0.108 | 0.025 | 0.066 | 0.046 | 0.119 | 0.148 | 23.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 13 | 13 | 10 | 15 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 0.77 | 1.15 | 1.00 | 1.08 |
time (sec) |
N/A | 0.422 | 0.011 | 0.121 | 0.030 | 0.101 | 0.069 | 0.115 | 0.145 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 23 | 15 | 20 | 22 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.28 | 0.83 | 1.11 | 1.22 | 0.78 |
time (sec) |
N/A | 0.434 | 0.014 | 0.130 | 0.029 | 0.070 | 0.073 | 0.125 | 0.152 | 0.040 |
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 | 32 | 30 | 30 | 35 | 26 | 32 | 35 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 1.09 | 0.81 | 1.00 | 1.09 | 0.75 |
time (sec) |
N/A | 0.461 | 0.016 | 0.138 | 0.028 | 0.114 | 0.084 | 0.115 | 0.147 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 38 | 38 | 43 | 34 | 40 | 43 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.95 | 1.08 | 0.85 | 1.00 | 1.08 | 0.78 |
time (sec) |
N/A | 0.472 | 0.019 | 0.138 | 0.030 | 0.069 | 0.094 | 0.107 | 0.154 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 83 | 153 | 223 | 92 | 0 | 0 | 152 | 192 |
N.S. |
1 | 1.00 | 0.61 | 1.12 | 1.64 | 0.68 | 0.00 | 0.00 | 1.12 | 1.41 |
time (sec) |
N/A | 1.100 | 0.119 | 0.105 | 0.042 | 0.082 | 0.000 | 0.000 | 0.157 | 23.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 75 | 145 | 186 | 84 | 0 | 0 | 132 | 156 |
N.S. |
1 | 1.00 | 0.65 | 1.25 | 1.60 | 0.72 | 0.00 | 0.00 | 1.14 | 1.34 |
time (sec) |
N/A | 1.023 | 0.101 | 0.093 | 0.032 | 0.073 | 0.000 | 0.000 | 0.153 | 24.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 66 | 136 | 151 | 75 | 0 | 0 | 111 | 120 |
N.S. |
1 | 1.00 | 0.73 | 1.51 | 1.68 | 0.83 | 0.00 | 0.00 | 1.23 | 1.33 |
time (sec) |
N/A | 0.968 | 0.085 | 0.099 | 0.036 | 0.080 | 0.000 | 0.000 | 0.158 | 23.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 60 | 54 | 127 | 111 | 66 | 0 | 0 | 92 | 78 |
N.S. |
1 | 0.95 | 0.86 | 2.02 | 1.76 | 1.05 | 0.00 | 0.00 | 1.46 | 1.24 |
time (sec) |
N/A | 0.868 | 0.066 | 0.086 | 0.036 | 0.101 | 0.000 | 0.000 | 0.142 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 81 | 55 | 369 | 89 | 74 | 0 | 0 | 139 | 54 |
N.S. |
1 | 1.69 | 1.15 | 7.69 | 1.85 | 1.54 | 0.00 | 0.00 | 2.90 | 1.12 |
time (sec) |
N/A | 0.959 | 0.075 | 0.089 | 0.114 | 0.097 | 0.000 | 0.000 | 0.165 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 54 | 41 | 109 | 72 | 49 | 0 | 0 | 137 | 59 |
N.S. |
1 | 1.15 | 0.87 | 2.32 | 1.53 | 1.04 | 0.00 | 0.00 | 2.91 | 1.26 |
time (sec) |
N/A | 0.453 | 0.116 | 0.102 | 0.105 | 0.088 | 0.000 | 0.000 | 0.157 | 23.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 96 | 56 | 119 | 112 | 61 | 0 | 0 | 170 | 118 |
N.S. |
1 | 1.19 | 0.69 | 1.47 | 1.38 | 0.75 | 0.00 | 0.00 | 2.10 | 1.46 |
time (sec) |
N/A | 1.184 | 0.155 | 0.108 | 0.113 | 0.072 | 0.000 | 0.000 | 0.155 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 127 | 66 | 129 | 157 | 69 | 0 | 0 | 191 | 153 |
N.S. |
1 | 1.25 | 0.65 | 1.26 | 1.54 | 0.68 | 0.00 | 0.00 | 1.87 | 1.50 |
time (sec) |
N/A | 1.519 | 0.136 | 0.110 | 0.113 | 0.081 | 0.000 | 0.000 | 0.162 | 23.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 155 | 75 | 137 | 193 | 77 | 0 | 0 | 211 | 190 |
N.S. |
1 | 1.28 | 0.62 | 1.13 | 1.60 | 0.64 | 0.00 | 0.00 | 1.74 | 1.57 |
time (sec) |
N/A | 1.696 | 0.064 | 0.109 | 0.109 | 0.132 | 0.000 | 0.000 | 0.167 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 272 | 173 | 0 | 259 | 119 | 0 | 234 | 20 | 229 |
N.S. |
1 | 1.08 | 0.68 | 0.00 | 1.02 | 0.47 | 0.00 | 0.92 | 0.08 | 0.91 |
time (sec) |
N/A | 0.690 | 5.302 | 0.000 | 0.116 | 0.089 | 0.000 | 0.136 | 0.213 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 229 | 149 | 0 | 224 | 111 | 0 | 203 | 20 | 192 |
N.S. |
1 | 1.06 | 0.69 | 0.00 | 1.04 | 0.51 | 0.00 | 0.94 | 0.09 | 0.89 |
time (sec) |
N/A | 0.605 | 5.213 | 0.000 | 0.110 | 0.082 | 0.000 | 0.139 | 0.230 | 23.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 186 | 125 | 0 | 187 | 103 | 0 | 172 | 20 | 157 |
N.S. |
1 | 1.04 | 0.70 | 0.00 | 1.04 | 0.58 | 0.00 | 0.96 | 0.11 | 0.88 |
time (sec) |
N/A | 0.531 | 5.175 | 0.000 | 0.109 | 0.087 | 0.000 | 0.147 | 0.212 | 23.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 145 | 66 | 0 | 149 | 93 | 0 | 139 | 18 | 120 |
N.S. |
1 | 1.02 | 0.46 | 0.00 | 1.05 | 0.65 | 0.00 | 0.98 | 0.13 | 0.85 |
time (sec) |
N/A | 0.437 | 0.201 | 0.000 | 0.109 | 0.092 | 0.000 | 0.139 | 0.204 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 102 | 51 | 0 | 111 | 84 | 0 | 108 | 17 | 78 |
N.S. |
1 | 1.06 | 0.53 | 0.00 | 1.16 | 0.88 | 0.00 | 1.12 | 0.18 | 0.81 |
time (sec) |
N/A | 0.376 | 0.105 | 0.000 | 0.110 | 0.087 | 0.000 | 0.132 | 0.170 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 258 | 30 | 0 | 224 | 194 | 0 | 232 | 20 | 101 |
N.S. |
1 | 1.16 | 0.14 | 0.00 | 1.01 | 0.87 | 0.00 | 1.05 | 0.09 | 0.45 |
time (sec) |
N/A | 0.752 | 0.057 | 0.000 | 0.121 | 0.086 | 0.000 | 0.147 | 0.185 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 219 | 148 | 0 | 186 | 174 | 0 | 186 | 20 | 87 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.97 | 0.91 | 0.00 | 0.97 | 0.10 | 0.45 |
time (sec) |
N/A | 0.693 | 0.295 | 0.000 | 0.115 | 0.079 | 0.000 | 0.132 | 0.189 | 24.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 260 | 173 | 0 | 226 | 199 | 0 | 223 | 20 | 132 |
N.S. |
1 | 1.07 | 0.71 | 0.00 | 0.93 | 0.82 | 0.00 | 0.91 | 0.08 | 0.54 |
time (sec) |
N/A | 0.761 | 0.231 | 0.000 | 0.109 | 0.099 | 0.000 | 0.141 | 0.205 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 303 | 93 | 0 | 270 | 208 | 0 | 271 | 20 | 168 |
N.S. |
1 | 1.08 | 0.33 | 0.00 | 0.96 | 0.74 | 0.00 | 0.96 | 0.07 | 0.60 |
time (sec) |
N/A | 0.839 | 0.136 | 0.000 | 0.109 | 0.077 | 0.000 | 0.120 | 0.196 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 272 | 173 | 0 | 259 | 119 | 0 | 234 | 20 | 229 |
N.S. |
1 | 1.08 | 0.68 | 0.00 | 1.02 | 0.47 | 0.00 | 0.92 | 0.08 | 0.91 |
time (sec) |
N/A | 0.667 | 5.273 | 0.000 | 0.133 | 0.084 | 0.000 | 0.145 | 0.214 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 227 | 149 | 0 | 224 | 111 | 0 | 203 | 20 | 192 |
N.S. |
1 | 1.05 | 0.69 | 0.00 | 1.04 | 0.51 | 0.00 | 0.94 | 0.09 | 0.89 |
time (sec) |
N/A | 0.599 | 5.214 | 0.000 | 0.113 | 0.099 | 0.000 | 0.136 | 0.191 | 23.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 186 | 125 | 0 | 187 | 103 | 0 | 172 | 20 | 157 |
N.S. |
1 | 1.04 | 0.70 | 0.00 | 1.04 | 0.58 | 0.00 | 0.96 | 0.11 | 0.88 |
time (sec) |
N/A | 0.563 | 5.182 | 0.000 | 0.109 | 0.088 | 0.000 | 0.124 | 0.190 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 145 | 70 | 0 | 152 | 95 | 0 | 141 | 18 | 120 |
N.S. |
1 | 1.02 | 0.49 | 0.00 | 1.07 | 0.67 | 0.00 | 0.99 | 0.13 | 0.85 |
time (sec) |
N/A | 0.437 | 0.197 | 0.000 | 0.110 | 0.082 | 0.000 | 0.148 | 0.184 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 56 | 0 | 112 | 86 | 0 | 109 | 17 | 79 |
N.S. |
1 | 1.04 | 0.57 | 0.00 | 1.14 | 0.88 | 0.00 | 1.11 | 0.17 | 0.81 |
time (sec) |
N/A | 0.385 | 0.092 | 0.000 | 0.109 | 0.106 | 0.000 | 0.140 | 0.167 | 23.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 258 | 30 | 0 | 224 | 194 | 0 | 232 | 20 | 101 |
N.S. |
1 | 1.17 | 0.14 | 0.00 | 1.01 | 0.88 | 0.00 | 1.05 | 0.09 | 0.46 |
time (sec) |
N/A | 0.758 | 0.058 | 0.000 | 0.109 | 0.080 | 0.000 | 0.137 | 0.194 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 219 | 46 | 0 | 187 | 175 | 0 | 187 | 20 | 88 |
N.S. |
1 | 1.13 | 0.24 | 0.00 | 0.97 | 0.91 | 0.00 | 0.97 | 0.10 | 0.46 |
time (sec) |
N/A | 0.667 | 0.086 | 0.000 | 0.114 | 0.087 | 0.000 | 0.143 | 0.180 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 260 | 76 | 0 | 229 | 200 | 0 | 225 | 20 | 132 |
N.S. |
1 | 1.07 | 0.31 | 0.00 | 0.94 | 0.82 | 0.00 | 0.92 | 0.08 | 0.54 |
time (sec) |
N/A | 0.729 | 0.102 | 0.000 | 0.122 | 0.074 | 0.000 | 0.123 | 0.178 | 23.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 303 | 93 | 0 | 277 | 208 | 0 | 271 | 20 | 168 |
N.S. |
1 | 1.08 | 0.33 | 0.00 | 0.99 | 0.74 | 0.00 | 0.96 | 0.07 | 0.60 |
time (sec) |
N/A | 0.812 | 0.152 | 0.000 | 0.117 | 0.082 | 0.000 | 0.138 | 0.185 | 23.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 311 | 198 | 0 | 275 | 152 | 0 | 254 | 73 | 248 |
N.S. |
1 | 1.09 | 0.69 | 0.00 | 0.96 | 0.53 | 0.00 | 0.89 | 0.26 | 0.87 |
time (sec) |
N/A | 0.739 | 5.283 | 0.000 | 0.110 | 0.080 | 0.000 | 0.147 | 0.249 | 23.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 268 | 161 | 0 | 238 | 144 | 0 | 223 | 73 | 211 |
N.S. |
1 | 1.08 | 0.65 | 0.00 | 0.96 | 0.58 | 0.00 | 0.90 | 0.29 | 0.85 |
time (sec) |
N/A | 0.669 | 5.248 | 0.000 | 0.119 | 0.080 | 0.000 | 0.157 | 0.255 | 23.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 225 | 137 | 0 | 203 | 136 | 0 | 192 | 73 | 176 |
N.S. |
1 | 1.07 | 0.65 | 0.00 | 0.96 | 0.64 | 0.00 | 0.91 | 0.35 | 0.83 |
time (sec) |
N/A | 0.597 | 5.229 | 0.000 | 0.112 | 0.085 | 0.000 | 0.127 | 0.213 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 179 | 80 | 0 | 166 | 128 | 0 | 161 | 71 | 139 |
N.S. |
1 | 1.02 | 0.45 | 0.00 | 0.94 | 0.73 | 0.00 | 0.91 | 0.40 | 0.79 |
time (sec) |
N/A | 0.487 | 0.244 | 0.000 | 0.111 | 0.080 | 0.000 | 0.131 | 0.217 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 136 | 67 | 0 | 131 | 117 | 0 | 141 | 68 | 98 |
N.S. |
1 | 1.05 | 0.52 | 0.00 | 1.01 | 0.90 | 0.00 | 1.08 | 0.52 | 0.75 |
time (sec) |
N/A | 0.435 | 0.186 | 0.000 | 0.112 | 0.078 | 0.000 | 0.146 | 0.195 | 23.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 287 | 30 | 0 | 244 | 263 | 0 | 252 | 70 | 118 |
N.S. |
1 | 1.15 | 0.12 | 0.00 | 0.98 | 1.05 | 0.00 | 1.01 | 0.28 | 0.47 |
time (sec) |
N/A | 0.817 | 0.107 | 0.000 | 0.121 | 0.074 | 0.000 | 0.131 | 0.249 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 253 | 173 | 0 | 204 | 232 | 0 | 217 | 75 | 107 |
N.S. |
1 | 1.13 | 0.77 | 0.00 | 0.91 | 1.04 | 0.00 | 0.97 | 0.33 | 0.48 |
time (sec) |
N/A | 0.755 | 0.517 | 0.000 | 0.113 | 0.083 | 0.000 | 0.135 | 0.220 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 293 | 186 | 0 | 244 | 258 | 0 | 243 | 77 | 152 |
N.S. |
1 | 1.06 | 0.67 | 0.00 | 0.88 | 0.93 | 0.00 | 0.88 | 0.28 | 0.55 |
time (sec) |
N/A | 0.806 | 0.335 | 0.000 | 0.120 | 0.099 | 0.000 | 0.125 | 0.246 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 332 | 104 | 0 | 288 | 266 | 0 | 291 | 77 | 188 |
N.S. |
1 | 1.07 | 0.34 | 0.00 | 0.93 | 0.86 | 0.00 | 0.94 | 0.25 | 0.61 |
time (sec) |
N/A | 0.872 | 0.198 | 0.000 | 0.127 | 0.075 | 0.000 | 0.140 | 0.236 | 23.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 272 | 173 | 0 | 259 | 119 | 0 | 234 | 20 | 229 |
N.S. |
1 | 1.08 | 0.68 | 0.00 | 1.02 | 0.47 | 0.00 | 0.92 | 0.08 | 0.91 |
time (sec) |
N/A | 0.665 | 5.329 | 0.000 | 0.117 | 0.087 | 0.000 | 0.128 | 0.214 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 229 | 149 | 0 | 224 | 111 | 0 | 203 | 20 | 193 |
N.S. |
1 | 1.06 | 0.69 | 0.00 | 1.04 | 0.51 | 0.00 | 0.94 | 0.09 | 0.89 |
time (sec) |
N/A | 0.618 | 5.271 | 0.000 | 0.109 | 0.082 | 0.000 | 0.146 | 0.220 | 23.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 186 | 125 | 0 | 187 | 102 | 0 | 172 | 20 | 157 |
N.S. |
1 | 1.04 | 0.70 | 0.00 | 1.04 | 0.57 | 0.00 | 0.96 | 0.11 | 0.88 |
time (sec) |
N/A | 0.532 | 5.221 | 0.000 | 0.114 | 0.117 | 0.000 | 0.126 | 0.189 | 23.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 145 | 66 | 0 | 151 | 93 | 0 | 140 | 18 | 121 |
N.S. |
1 | 1.02 | 0.46 | 0.00 | 1.06 | 0.65 | 0.00 | 0.99 | 0.13 | 0.85 |
time (sec) |
N/A | 0.430 | 0.191 | 0.000 | 0.121 | 0.104 | 0.000 | 0.143 | 0.177 | 23.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 102 | 33 | 0 | 111 | 84 | 0 | 108 | 17 | 79 |
N.S. |
1 | 1.05 | 0.34 | 0.00 | 1.14 | 0.87 | 0.00 | 1.11 | 0.18 | 0.81 |
time (sec) |
N/A | 0.385 | 0.063 | 0.000 | 0.125 | 0.082 | 0.000 | 0.129 | 0.181 | 23.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 258 | 30 | 0 | 224 | 196 | 0 | 232 | 20 | 101 |
N.S. |
1 | 1.16 | 0.14 | 0.00 | 1.01 | 0.88 | 0.00 | 1.05 | 0.09 | 0.45 |
time (sec) |
N/A | 0.751 | 0.057 | 0.000 | 0.120 | 0.097 | 0.000 | 0.145 | 0.172 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 220 | 33 | 0 | 186 | 174 | 0 | 186 | 20 | 88 |
N.S. |
1 | 1.15 | 0.17 | 0.00 | 0.97 | 0.91 | 0.00 | 0.97 | 0.10 | 0.46 |
time (sec) |
N/A | 0.662 | 0.064 | 0.000 | 0.121 | 0.085 | 0.000 | 0.141 | 0.181 | 0.058 |