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 | 87 | 77 | 74 | 84 | 92 | 62 | 105 | 92 | 82 | 90 |
N.S. |
1 | 0.89 | 0.85 | 0.97 | 1.06 | 0.71 | 1.21 | 1.06 | 0.94 | 1.03 |
time (sec) |
N/A | 0.250 | 0.062 | 10.947 | 0.029 | 0.084 | 0.656 | 0.130 | 0.163 | 0.090 |
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 | 87 | 96 | 57 | 62 | 63 | 62 | 172 | 107 | 114 | 226 |
N.S. |
1 | 1.10 | 0.66 | 0.71 | 0.72 | 0.71 | 1.98 | 1.23 | 1.31 | 2.60 |
time (sec) |
N/A | 0.409 | 0.254 | 7.716 | 0.029 | 0.095 | 0.482 | 0.145 | 0.169 | 30.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 57 | 60 | 63 | 70 | 51 | 83 | 70 | 62 | 68 |
N.S. |
1 | 0.89 | 0.94 | 0.98 | 1.09 | 0.80 | 1.30 | 1.09 | 0.97 | 1.06 |
time (sec) |
N/A | 0.237 | 0.029 | 3.990 | 0.032 | 0.089 | 0.325 | 0.125 | 0.171 | 25.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 70 | 62 | 52 | 48 | 51 | 124 | 77 | 82 | 165 |
N.S. |
1 | 1.08 | 0.95 | 0.80 | 0.74 | 0.78 | 1.91 | 1.18 | 1.26 | 2.54 |
time (sec) |
N/A | 0.334 | 0.149 | 2.682 | 0.028 | 0.084 | 0.226 | 0.139 | 0.159 | 29.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 41 | 44 | 46 | 48 | 39 | 60 | 48 | 42 | 46 |
N.S. |
1 | 0.91 | 0.98 | 1.02 | 1.07 | 0.87 | 1.33 | 1.07 | 0.93 | 1.02 |
time (sec) |
N/A | 0.229 | 0.023 | 1.214 | 0.026 | 0.089 | 0.157 | 0.125 | 0.179 | 0.060 |
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 | 43 | 44 | 46 | 41 | 37 | 37 | 71 | 47 | 50 | 103 |
N.S. |
1 | 1.02 | 1.07 | 0.95 | 0.86 | 0.86 | 1.65 | 1.09 | 1.16 | 2.40 |
time (sec) |
N/A | 0.259 | 0.108 | 0.681 | 0.026 | 0.078 | 0.113 | 0.125 | 0.165 | 28.133 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 39 | 23 | 20 | 25 | 34 | 25 | 25 | 20 |
N.S. |
1 | 1.00 | 1.77 | 1.05 | 0.91 | 1.14 | 1.55 | 1.14 | 1.14 | 0.91 |
time (sec) |
N/A | 0.190 | 0.035 | 0.250 | 0.025 | 0.078 | 0.083 | 0.117 | 0.159 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 18 | 26 | 16 | 15 | 17 | 0 | 16 | 34 | 15 |
N.S. |
1 | 1.06 | 1.53 | 0.94 | 0.88 | 1.00 | 0.00 | 0.94 | 2.00 | 0.88 |
time (sec) |
N/A | 0.196 | 0.020 | 0.075 | 0.032 | 0.120 | 0.000 | 0.123 | 0.172 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 23 | 40 | 0 | 19 | 28 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.00 | 1.74 | 0.00 | 0.83 | 1.22 | 0.83 |
time (sec) |
N/A | 0.259 | 0.021 | 0.116 | 0.033 | 0.079 | 0.000 | 0.137 | 0.178 | 25.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 52 | 50 | 42 | 67 | 0 | 48 | 83 | 30 |
N.S. |
1 | 0.98 | 1.21 | 1.16 | 0.98 | 1.56 | 0.00 | 1.12 | 1.93 | 0.70 |
time (sec) |
N/A | 0.241 | 0.024 | 0.253 | 0.027 | 0.095 | 0.000 | 0.124 | 0.169 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 41 | 38 | 35 | 52 | 0 | 66 | 66 | 63 |
N.S. |
1 | 1.00 | 0.93 | 0.86 | 0.80 | 1.18 | 0.00 | 1.50 | 1.50 | 1.43 |
time (sec) |
N/A | 0.278 | 0.078 | 0.207 | 0.028 | 0.070 | 0.000 | 0.135 | 0.169 | 25.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 81 | 74 | 63 | 86 | 136 | 0 | 79 | 214 | 71 |
N.S. |
1 | 0.84 | 0.77 | 0.66 | 0.90 | 1.42 | 0.00 | 0.82 | 2.23 | 0.74 |
time (sec) |
N/A | 0.265 | 0.029 | 0.423 | 0.028 | 0.113 | 0.000 | 0.127 | 0.163 | 0.094 |
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 | 126 | 131 | 171 | 89 | 115 | 85 | 398 | 123 | 132 | 461 |
N.S. |
1 | 1.04 | 1.36 | 0.71 | 0.91 | 0.67 | 3.16 | 0.98 | 1.05 | 3.66 |
time (sec) |
N/A | 0.559 | 1.684 | 51.221 | 0.040 | 0.119 | 0.721 | 0.174 | 0.176 | 28.519 |
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 | 67 | 60 | 58 | 73 | 95 | 71 | 158 | 95 | 74 | 92 |
N.S. |
1 | 0.90 | 0.87 | 1.09 | 1.42 | 1.06 | 2.36 | 1.42 | 1.10 | 1.37 |
time (sec) |
N/A | 0.252 | 0.084 | 27.402 | 0.034 | 0.081 | 0.481 | 0.132 | 0.176 | 0.073 |
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 | 102 | 105 | 151 | 76 | 89 | 72 | 287 | 106 | 100 | 349 |
N.S. |
1 | 1.03 | 1.48 | 0.75 | 0.87 | 0.71 | 2.81 | 1.04 | 0.98 | 3.42 |
time (sec) |
N/A | 0.470 | 0.594 | 13.477 | 0.034 | 0.091 | 0.393 | 0.148 | 0.166 | 28.114 |
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 | 45 | 41 | 46 | 48 | 56 | 58 | 107 | 56 | 44 | 53 |
N.S. |
1 | 0.91 | 1.02 | 1.07 | 1.24 | 1.29 | 2.38 | 1.24 | 0.98 | 1.18 |
time (sec) |
N/A | 0.237 | 0.095 | 6.094 | 0.033 | 0.079 | 0.236 | 0.120 | 0.170 | 25.640 |
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 | 78 | 79 | 131 | 56 | 65 | 59 | 180 | 72 | 68 | 237 |
N.S. |
1 | 1.01 | 1.68 | 0.72 | 0.83 | 0.76 | 2.31 | 0.92 | 0.87 | 3.04 |
time (sec) |
N/A | 0.374 | 0.316 | 2.537 | 0.032 | 0.081 | 0.191 | 0.135 | 0.167 | 28.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 47 | 21 | 20 | 44 | 53 | 42 | 35 | 32 |
N.S. |
1 | 1.00 | 2.14 | 0.95 | 0.91 | 2.00 | 2.41 | 1.91 | 1.59 | 1.45 |
time (sec) |
N/A | 0.199 | 0.026 | 1.029 | 0.031 | 0.080 | 0.117 | 0.123 | 0.163 | 25.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 30 | 29 | 44 | 30 | 32 | 0 | 33 | 46 | 26 |
N.S. |
1 | 0.88 | 0.85 | 1.29 | 0.88 | 0.94 | 0.00 | 0.97 | 1.35 | 0.76 |
time (sec) |
N/A | 0.225 | 0.024 | 0.121 | 0.027 | 0.083 | 0.000 | 0.125 | 0.183 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 39 | 75 | 30 | 47 | 74 | 0 | 33 | 48 | 28 |
N.S. |
1 | 1.03 | 1.97 | 0.79 | 1.24 | 1.95 | 0.00 | 0.87 | 1.26 | 0.74 |
time (sec) |
N/A | 0.298 | 0.077 | 0.130 | 0.106 | 0.075 | 0.000 | 0.138 | 0.162 | 25.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 19 | 25 | 18 | 19 | 0 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 0.95 | 1.25 | 0.90 | 0.95 | 0.00 | 0.90 | 0.90 | 0.90 |
time (sec) |
N/A | 0.210 | 0.034 | 0.139 | 0.031 | 0.068 | 0.000 | 0.127 | 0.174 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 60 | 58 | 38 | 52 | 97 | 0 | 54 | 60 | 81 |
N.S. |
1 | 0.95 | 0.92 | 0.60 | 0.83 | 1.54 | 0.00 | 0.86 | 0.95 | 1.29 |
time (sec) |
N/A | 0.343 | 0.014 | 0.177 | 0.036 | 0.075 | 0.000 | 0.142 | 0.163 | 25.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 62 | 56 | 100 | 71 | 125 | 0 | 58 | 152 | 58 |
N.S. |
1 | 0.91 | 0.82 | 1.47 | 1.04 | 1.84 | 0.00 | 0.85 | 2.24 | 0.85 |
time (sec) |
N/A | 0.270 | 0.078 | 0.339 | 0.032 | 0.091 | 0.000 | 0.127 | 0.162 | 25.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 61 | 82 | 60 | 77 | 85 | 0 | 106 | 104 | 156 |
N.S. |
1 | 0.95 | 1.28 | 0.94 | 1.20 | 1.33 | 0.00 | 1.66 | 1.62 | 2.44 |
time (sec) |
N/A | 0.330 | 0.015 | 0.311 | 0.034 | 0.072 | 0.000 | 0.147 | 0.175 | 25.840 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 101 | 85 | 160 | 108 | 203 | 0 | 89 | 224 | 94 |
N.S. |
1 | 0.86 | 0.73 | 1.37 | 0.92 | 1.74 | 0.00 | 0.76 | 1.91 | 0.80 |
time (sec) |
N/A | 0.274 | 0.158 | 0.621 | 0.038 | 0.086 | 0.000 | 0.127 | 0.166 | 25.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 73 | 110 | 86 | 98 | 115 | 0 | 171 | 150 | 276 |
N.S. |
1 | 0.89 | 1.34 | 1.05 | 1.20 | 1.40 | 0.00 | 2.09 | 1.83 | 3.37 |
time (sec) |
N/A | 0.314 | 0.036 | 0.433 | 0.033 | 0.088 | 0.000 | 0.152 | 0.168 | 26.262 |
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 | 154 | 165 | 181 | 163 | 141 | 98 | 439 | 157 | 148 | 501 |
N.S. |
1 | 1.07 | 1.18 | 1.06 | 0.92 | 0.64 | 2.85 | 1.02 | 0.96 | 3.25 |
time (sec) |
N/A | 0.718 | 2.154 | 0.123 | 0.035 | 0.102 | 1.310 | 0.189 | 0.162 | 28.482 |
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 | 67 | 60 | 58 | 85 | 108 | 85 | 219 | 108 | 84 | 106 |
N.S. |
1 | 0.90 | 0.87 | 1.27 | 1.61 | 1.27 | 3.27 | 1.61 | 1.25 | 1.58 |
time (sec) |
N/A | 0.249 | 0.097 | 297.548 | 0.033 | 0.142 | 0.895 | 0.138 | 0.164 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 139 | 161 | 85 | 115 | 85 | 335 | 123 | 116 | 389 |
N.S. |
1 | 1.07 | 1.24 | 0.65 | 0.88 | 0.65 | 2.58 | 0.95 | 0.89 | 2.99 |
time (sec) |
N/A | 0.603 | 0.867 | 118.220 | 0.034 | 0.093 | 0.672 | 0.175 | 0.172 | 28.334 |
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 | 45 | 41 | 43 | 68 | 82 | 72 | 146 | 82 | 64 | 80 |
N.S. |
1 | 0.91 | 0.96 | 1.51 | 1.82 | 1.60 | 3.24 | 1.82 | 1.42 | 1.78 |
time (sec) |
N/A | 0.233 | 0.164 | 42.257 | 0.032 | 0.091 | 0.442 | 0.138 | 0.281 | 0.057 |
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 | 106 | 113 | 141 | 67 | 91 | 72 | 226 | 89 | 84 | 277 |
N.S. |
1 | 1.07 | 1.33 | 0.63 | 0.86 | 0.68 | 2.13 | 0.84 | 0.79 | 2.61 |
time (sec) |
N/A | 0.502 | 0.454 | 14.223 | 0.035 | 0.098 | 0.327 | 0.147 | 0.240 | 28.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 65 | 21 | 20 | 57 | 70 | 55 | 45 | 53 |
N.S. |
1 | 1.00 | 2.95 | 0.95 | 0.91 | 2.59 | 3.18 | 2.50 | 2.05 | 2.41 |
time (sec) |
N/A | 0.192 | 0.029 | 4.492 | 0.025 | 0.092 | 0.193 | 0.122 | 0.157 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 49 | 41 | 58 | 43 | 45 | 0 | 50 | 58 | 36 |
N.S. |
1 | 0.94 | 0.79 | 1.12 | 0.83 | 0.87 | 0.00 | 0.96 | 1.12 | 0.69 |
time (sec) |
N/A | 0.227 | 0.033 | 0.182 | 0.030 | 0.132 | 0.000 | 0.131 | 0.173 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 59 | 55 | 54 | 68 | 101 | 0 | 91 | 86 | 138 |
N.S. |
1 | 1.18 | 1.10 | 1.08 | 1.36 | 2.02 | 0.00 | 1.82 | 1.72 | 2.76 |
time (sec) |
N/A | 0.401 | 0.044 | 0.185 | 0.112 | 0.100 | 0.000 | 0.146 | 0.176 | 25.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 36 | 59 | 72 | 33 | 51 | 0 | 36 | 89 | 35 |
N.S. |
1 | 0.92 | 1.51 | 1.85 | 0.85 | 1.31 | 0.00 | 0.92 | 2.28 | 0.90 |
time (sec) |
N/A | 0.235 | 0.052 | 0.213 | 0.032 | 0.082 | 0.000 | 0.132 | 0.163 | 25.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 28 | 37 | 78 | 99 | 0 | 38 | 71 | 55 |
N.S. |
1 | 1.00 | 0.90 | 1.19 | 2.52 | 3.19 | 0.00 | 1.23 | 2.29 | 1.77 |
time (sec) |
N/A | 0.288 | 0.030 | 0.218 | 0.036 | 0.084 | 0.000 | 0.150 | 0.178 | 25.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 28 | 32 | 28 | 30 | 0 | 18 | 28 | 18 |
N.S. |
1 | 1.00 | 1.22 | 1.39 | 1.22 | 1.30 | 0.00 | 0.78 | 1.22 | 0.78 |
time (sec) |
N/A | 0.212 | 0.027 | 0.220 | 0.034 | 0.068 | 0.000 | 0.130 | 0.173 | 25.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 94 | 110 | 55 | 103 | 149 | 0 | 86 | 112 | 135 |
N.S. |
1 | 1.02 | 1.20 | 0.60 | 1.12 | 1.62 | 0.00 | 0.93 | 1.22 | 1.47 |
time (sec) |
N/A | 0.443 | 0.015 | 0.258 | 0.034 | 0.087 | 0.000 | 0.152 | 0.163 | 25.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 82 | 67 | 125 | 96 | 185 | 0 | 71 | 216 | 81 |
N.S. |
1 | 0.86 | 0.71 | 1.32 | 1.01 | 1.95 | 0.00 | 0.75 | 2.27 | 0.85 |
time (sec) |
N/A | 0.271 | 0.125 | 0.534 | 0.033 | 0.086 | 0.000 | 0.131 | 0.175 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 92 | 134 | 84 | 122 | 112 | 0 | 138 | 140 | 228 |
N.S. |
1 | 0.93 | 1.35 | 0.85 | 1.23 | 1.13 | 0.00 | 1.39 | 1.41 | 2.30 |
time (sec) |
N/A | 0.423 | 0.017 | 0.414 | 0.036 | 0.090 | 0.000 | 0.150 | 0.167 | 25.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 60 | 58 | 135 | 173 | 149 | 556 | 173 | 134 | 134 |
N.S. |
1 | 0.90 | 0.87 | 2.01 | 2.58 | 2.22 | 8.30 | 2.58 | 2.00 | 2.00 |
time (sec) |
N/A | 0.272 | 0.456 | 0.040 | 0.034 | 0.110 | 4.736 | 0.157 | 0.171 | 25.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 309 | 211 | 535 | 339 | 150 | 1280 | 208 | 196 | 684 |
N.S. |
1 | 1.08 | 0.74 | 1.87 | 1.19 | 0.52 | 4.48 | 0.73 | 0.69 | 2.39 |
time (sec) |
N/A | 1.540 | 3.302 | 0.069 | 0.042 | 0.174 | 3.468 | 0.191 | 0.170 | 28.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 41 | 43 | 108 | 134 | 136 | 350 | 134 | 104 | 132 |
N.S. |
1 | 0.91 | 0.96 | 2.40 | 2.98 | 3.02 | 7.78 | 2.98 | 2.31 | 2.93 |
time (sec) |
N/A | 0.231 | 1.145 | 0.037 | 0.028 | 0.109 | 2.337 | 0.177 | 0.164 | 0.174 |
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 | 262 | 283 | 191 | 480 | 319 | 137 | 1018 | 174 | 164 | 572 |
N.S. |
1 | 1.08 | 0.73 | 1.83 | 1.22 | 0.52 | 3.89 | 0.66 | 0.63 | 2.18 |
time (sec) |
N/A | 1.363 | 1.590 | 0.061 | 0.042 | 0.121 | 1.975 | 0.239 | 0.179 | 28.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 147 | 21 | 20 | 122 | 148 | 120 | 95 | 118 |
N.S. |
1 | 1.00 | 6.68 | 0.95 | 0.91 | 5.55 | 6.73 | 5.45 | 4.32 | 5.36 |
time (sec) |
N/A | 0.186 | 0.100 | 0.027 | 0.031 | 0.137 | 1.187 | 0.134 | 0.169 | 25.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 139 | 95 | 113 | 109 | 114 | 0 | 135 | 108 | 109 |
N.S. |
1 | 0.86 | 0.59 | 0.70 | 0.67 | 0.70 | 0.00 | 0.83 | 0.67 | 0.67 |
time (sec) |
N/A | 0.271 | 0.189 | 0.839 | 0.032 | 0.100 | 0.000 | 0.134 | 0.175 | 25.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 225 | 55 | 111 | 331 | 231 | 0 | 231 | 220 | 513 |
N.S. |
1 | 1.12 | 0.27 | 0.55 | 1.65 | 1.15 | 0.00 | 1.15 | 1.09 | 2.55 |
time (sec) |
N/A | 1.149 | 0.070 | 0.823 | 0.119 | 0.091 | 0.000 | 0.183 | 0.168 | 30.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 108 | 111 | 128 | 97 | 130 | 0 | 120 | 140 | 97 |
N.S. |
1 | 0.89 | 0.92 | 1.06 | 0.80 | 1.07 | 0.00 | 0.99 | 1.16 | 0.80 |
time (sec) |
N/A | 0.287 | 0.289 | 1.108 | 0.038 | 0.094 | 0.000 | 0.140 | 0.177 | 25.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 201 | 59 | 166 | 311 | 247 | 0 | 200 | 247 | 437 |
N.S. |
1 | 1.12 | 0.33 | 0.93 | 1.74 | 1.38 | 0.00 | 1.12 | 1.38 | 2.44 |
time (sec) |
N/A | 0.972 | 0.062 | 0.956 | 0.117 | 0.124 | 0.000 | 0.197 | 0.178 | 30.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 100 | 73 | 150 | 95 | 139 | 0 | 102 | 188 | 96 |
N.S. |
1 | 0.91 | 0.66 | 1.36 | 0.86 | 1.26 | 0.00 | 0.93 | 1.71 | 0.87 |
time (sec) |
N/A | 0.284 | 0.488 | 0.871 | 0.027 | 0.098 | 0.000 | 0.148 | 0.177 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 74 | 141 | 67 | 258 | 50 | 1355 | 114 | 84 | 107 |
N.S. |
1 | 1.01 | 1.93 | 0.92 | 3.53 | 0.68 | 18.56 | 1.56 | 1.15 | 1.47 |
time (sec) |
N/A | 0.346 | 0.849 | 0.719 | 0.110 | 0.199 | 15.910 | 0.134 | 0.167 | 28.927 |
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 | 47 | 43 | 46 | 45 | 47 | 37 | 530 | 47 | 44 | 54 |
N.S. |
1 | 0.91 | 0.98 | 0.96 | 1.00 | 0.79 | 11.28 | 1.00 | 0.94 | 1.15 |
time (sec) |
N/A | 0.243 | 0.103 | 0.388 | 0.033 | 0.087 | 8.906 | 0.123 | 0.168 | 25.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 48 | 119 | 43 | 156 | 37 | 558 | 75 | 52 | 66 |
N.S. |
1 | 0.98 | 2.43 | 0.88 | 3.18 | 0.76 | 11.39 | 1.53 | 1.06 | 1.35 |
time (sec) |
N/A | 0.272 | 0.300 | 0.307 | 0.108 | 0.106 | 4.774 | 0.132 | 0.163 | 27.696 |
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 | 23 | 23 | 24 | 25 | 25 | 25 | 158 | 25 | 24 | 22 |
N.S. |
1 | 1.00 | 1.04 | 1.09 | 1.09 | 1.09 | 6.87 | 1.09 | 1.04 | 0.96 |
time (sec) |
N/A | 0.215 | 0.046 | 0.140 | 0.032 | 0.098 | 2.547 | 0.117 | 0.177 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 97 | 19 | 52 | 17 | 88 | 34 | 18 | 29 |
N.S. |
1 | 1.00 | 5.11 | 1.00 | 2.74 | 0.89 | 4.63 | 1.79 | 0.95 | 1.53 |
time (sec) |
N/A | 0.206 | 0.141 | 0.145 | 0.110 | 0.083 | 1.529 | 0.129 | 0.184 | 25.358 |
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 | 18 | 16 | 19 | 18 | 16 | 24 | 17 | 16 | 16 |
N.S. |
1 | 1.12 | 1.00 | 1.19 | 1.12 | 1.00 | 1.50 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.196 | 0.016 | 0.070 | 0.031 | 0.117 | 0.348 | 0.123 | 0.192 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 39 | 30 | 43 | 47 | 58 | 0 | 55 | 85 | 33 |
N.S. |
1 | 1.05 | 0.81 | 1.16 | 1.27 | 1.57 | 0.00 | 1.49 | 2.30 | 0.89 |
time (sec) |
N/A | 0.236 | 0.046 | 0.194 | 0.031 | 0.094 | 0.000 | 0.118 | 0.183 | 25.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 45 | 51 | 129 | 49 | 0 | 67 | 68 | 71 |
N.S. |
1 | 1.00 | 1.07 | 1.21 | 3.07 | 1.17 | 0.00 | 1.60 | 1.62 | 1.69 |
time (sec) |
N/A | 0.286 | 0.069 | 0.215 | 0.034 | 0.080 | 0.000 | 0.132 | 0.168 | 25.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 80 | 75 | 67 | 91 | 125 | 0 | 85 | 214 | 74 |
N.S. |
1 | 0.96 | 0.90 | 0.81 | 1.10 | 1.51 | 0.00 | 1.02 | 2.58 | 0.89 |
time (sec) |
N/A | 0.275 | 0.117 | 0.472 | 0.028 | 0.149 | 0.000 | 0.129 | 0.170 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 59 | 66 | 74 | 294 | 75 | 0 | 119 | 138 | 125 |
N.S. |
1 | 0.95 | 1.06 | 1.19 | 4.74 | 1.21 | 0.00 | 1.92 | 2.23 | 2.02 |
time (sec) |
N/A | 0.312 | 0.116 | 0.434 | 0.039 | 0.080 | 0.000 | 0.140 | 0.177 | 26.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 119 | 97 | 91 | 130 | 147 | 0 | 105 | 340 | 115 |
N.S. |
1 | 0.88 | 0.71 | 0.67 | 0.96 | 1.08 | 0.00 | 0.77 | 2.50 | 0.85 |
time (sec) |
N/A | 0.308 | 0.172 | 0.888 | 0.030 | 0.100 | 0.000 | 0.129 | 0.190 | 25.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 113 | 151 | 78 | 393 | 60 | 2531 | 179 | 100 | 172 |
N.S. |
1 | 1.09 | 1.45 | 0.75 | 3.78 | 0.58 | 24.34 | 1.72 | 0.96 | 1.65 |
time (sec) |
N/A | 0.489 | 1.244 | 1.495 | 0.117 | 0.092 | 73.446 | 0.137 | 0.173 | 29.175 |
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 | 47 | 43 | 46 | 46 | 47 | 47 | 1037 | 47 | 44 | 54 |
N.S. |
1 | 0.91 | 0.98 | 0.98 | 1.00 | 1.00 | 22.06 | 1.00 | 0.94 | 1.15 |
time (sec) |
N/A | 0.245 | 0.182 | 1.006 | 0.030 | 0.094 | 46.293 | 0.133 | 0.162 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 87 | 131 | 56 | 267 | 50 | 1243 | 127 | 68 | 65 |
N.S. |
1 | 1.09 | 1.64 | 0.70 | 3.34 | 0.62 | 15.54 | 1.59 | 0.85 | 0.81 |
time (sec) |
N/A | 0.405 | 0.538 | 0.677 | 0.115 | 0.099 | 29.758 | 0.141 | 0.158 | 25.637 |
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 | 23 | 23 | 34 | 19 | 35 | 37 | 394 | 35 | 32 | 32 |
N.S. |
1 | 1.00 | 1.48 | 0.83 | 1.52 | 1.61 | 17.13 | 1.52 | 1.39 | 1.39 |
time (sec) |
N/A | 0.212 | 0.075 | 0.379 | 0.031 | 0.097 | 18.189 | 0.124 | 0.178 | 25.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 58 | 109 | 34 | 140 | 35 | 403 | 73 | 36 | 32 |
N.S. |
1 | 1.04 | 1.95 | 0.61 | 2.50 | 0.62 | 7.20 | 1.30 | 0.64 | 0.57 |
time (sec) |
N/A | 0.320 | 0.186 | 0.328 | 0.114 | 0.085 | 10.202 | 0.142 | 0.160 | 25.683 |
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 | 32 | 31 | 26 | 28 | 30 | 27 | 150 | 33 | 74 | 27 |
N.S. |
1 | 0.97 | 0.81 | 0.88 | 0.94 | 0.84 | 4.69 | 1.03 | 2.31 | 0.84 |
time (sec) |
N/A | 0.228 | 0.040 | 0.269 | 0.031 | 0.103 | 0.637 | 0.129 | 0.170 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 104 | 30 | 56 | 61 | 95 | 33 | 142 | 28 |
N.S. |
1 | 1.00 | 3.06 | 0.88 | 1.65 | 1.79 | 2.79 | 0.97 | 4.18 | 0.82 |
time (sec) |
N/A | 0.215 | 0.190 | 0.213 | 0.112 | 0.104 | 2.922 | 0.133 | 0.162 | 25.422 |
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 | 18 | 21 | 20 | 21 | 32 | 18 | 23 | 18 |
N.S. |
1 | 0.95 | 0.86 | 1.00 | 0.95 | 1.00 | 1.52 | 0.86 | 1.10 | 0.86 |
time (sec) |
N/A | 0.196 | 0.031 | 0.118 | 0.026 | 0.071 | 0.521 | 0.115 | 0.161 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 58 | 38 | 55 | 72 | 105 | 0 | 63 | 150 | 60 |
N.S. |
1 | 0.97 | 0.63 | 0.92 | 1.20 | 1.75 | 0.00 | 1.05 | 2.50 | 1.00 |
time (sec) |
N/A | 0.244 | 0.111 | 0.364 | 0.027 | 0.094 | 0.000 | 0.127 | 0.170 | 0.092 |
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 | 71 | 75 | 53 | 48 | 204 | 79 | 0 | 93 | 101 | 156 |
N.S. |
1 | 1.06 | 0.75 | 0.68 | 2.87 | 1.11 | 0.00 | 1.31 | 1.42 | 2.20 |
time (sec) |
N/A | 0.413 | 0.092 | 0.413 | 0.038 | 0.083 | 0.000 | 0.140 | 0.171 | 25.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 99 | 85 | 79 | 108 | 178 | 0 | 93 | 226 | 93 |
N.S. |
1 | 0.95 | 0.82 | 0.76 | 1.04 | 1.71 | 0.00 | 0.89 | 2.17 | 0.89 |
time (sec) |
N/A | 0.283 | 0.141 | 0.757 | 0.030 | 0.167 | 0.000 | 0.131 | 0.172 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 94 | 78 | 86 | 396 | 103 | 0 | 145 | 150 | 276 |
N.S. |
1 | 1.01 | 0.84 | 0.92 | 4.26 | 1.11 | 0.00 | 1.56 | 1.61 | 2.97 |
time (sec) |
N/A | 0.444 | 0.084 | 0.742 | 0.041 | 0.101 | 0.000 | 0.145 | 0.170 | 26.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 138 | 137 | 103 | 167 | 198 | 0 | 115 | 408 | 151 |
N.S. |
1 | 0.95 | 0.94 | 0.71 | 1.14 | 1.36 | 0.00 | 0.79 | 2.79 | 1.03 |
time (sec) |
N/A | 0.338 | 0.363 | 1.475 | 0.033 | 0.091 | 0.000 | 0.131 | 0.171 | 25.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 112 | 141 | 67 | 310 | 60 | 1717 | 140 | 84 | 81 |
N.S. |
1 | 1.09 | 1.37 | 0.65 | 3.01 | 0.58 | 16.67 | 1.36 | 0.82 | 0.79 |
time (sec) |
N/A | 0.515 | 1.158 | 1.432 | 0.116 | 0.091 | 121.905 | 0.148 | 0.171 | 25.640 |
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 | 23 | 23 | 44 | 19 | 45 | 45 | 654 | 45 | 44 | 53 |
N.S. |
1 | 1.00 | 1.91 | 0.83 | 1.96 | 1.96 | 28.43 | 1.96 | 1.91 | 2.30 |
time (sec) |
N/A | 0.212 | 0.172 | 0.850 | 0.027 | 0.093 | 75.170 | 0.119 | 0.179 | 25.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 82 | 121 | 45 | 184 | 45 | 690 | 88 | 52 | 57 |
N.S. |
1 | 1.06 | 1.57 | 0.58 | 2.39 | 0.58 | 8.96 | 1.14 | 0.68 | 0.74 |
time (sec) |
N/A | 0.397 | 0.470 | 0.687 | 0.112 | 0.093 | 47.173 | 0.136 | 0.236 | 25.471 |
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 | 50 | 50 | 38 | 38 | 41 | 36 | 564 | 53 | 56 | 36 |
N.S. |
1 | 1.00 | 0.76 | 0.76 | 0.82 | 0.72 | 11.28 | 1.06 | 1.12 | 0.72 |
time (sec) |
N/A | 0.239 | 0.067 | 0.465 | 0.027 | 0.098 | 30.325 | 0.124 | 0.225 | 25.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 59 | 54 | 139 | 78 | 478 | 80 | 86 | 69 |
N.S. |
1 | 1.08 | 1.20 | 1.10 | 2.84 | 1.59 | 9.76 | 1.63 | 1.76 | 1.41 |
time (sec) |
N/A | 0.320 | 0.056 | 0.403 | 0.113 | 0.083 | 18.158 | 0.145 | 0.155 | 25.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 58 | 32 | 37 | 41 | 299 | 37 | 95 | 36 |
N.S. |
1 | 1.00 | 1.61 | 0.89 | 1.03 | 1.14 | 8.31 | 1.03 | 2.64 | 1.00 |
time (sec) |
N/A | 0.239 | 0.075 | 0.284 | 0.027 | 0.129 | 0.681 | 0.125 | 0.171 | 25.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 28 | 36 | 99 | 95 | 153 | 36 | 69 | 53 |
N.S. |
1 | 1.00 | 1.04 | 1.33 | 3.67 | 3.52 | 5.67 | 1.33 | 2.56 | 1.96 |
time (sec) |
N/A | 0.217 | 0.023 | 0.275 | 0.035 | 0.085 | 5.990 | 0.145 | 0.157 | 25.589 |
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 | 22 | 22 | 20 | 21 | 20 | 36 | 51 | 18 | 28 | 18 |
N.S. |
1 | 1.00 | 0.91 | 0.95 | 0.91 | 1.64 | 2.32 | 0.82 | 1.27 | 0.82 |
time (sec) |
N/A | 0.200 | 0.031 | 0.192 | 0.025 | 0.093 | 0.696 | 0.123 | 0.185 | 25.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 77 | 61 | 67 | 98 | 154 | 0 | 75 | 216 | 83 |
N.S. |
1 | 0.92 | 0.73 | 0.80 | 1.17 | 1.83 | 0.00 | 0.89 | 2.57 | 0.99 |
time (sec) |
N/A | 0.260 | 0.101 | 0.578 | 0.033 | 0.087 | 0.000 | 0.119 | 0.151 | 25.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 108 | 63 | 74 | 310 | 106 | 0 | 119 | 140 | 228 |
N.S. |
1 | 1.09 | 0.64 | 0.75 | 3.13 | 1.07 | 0.00 | 1.20 | 1.41 | 2.30 |
time (sec) |
N/A | 0.538 | 0.115 | 0.601 | 0.041 | 0.086 | 0.000 | 0.151 | 0.195 | 25.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 118 | 95 | 91 | 146 | 228 | 0 | 105 | 334 | 129 |
N.S. |
1 | 0.91 | 0.73 | 0.70 | 1.12 | 1.75 | 0.00 | 0.81 | 2.57 | 0.99 |
time (sec) |
N/A | 0.300 | 0.181 | 1.171 | 0.033 | 0.129 | 0.000 | 0.131 | 0.180 | 25.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 129 | 85 | 97 | 482 | 130 | 0 | 171 | 212 | 167 |
N.S. |
1 | 1.05 | 0.69 | 0.79 | 3.92 | 1.06 | 0.00 | 1.39 | 1.72 | 1.36 |
time (sec) |
N/A | 0.581 | 0.136 | 1.090 | 0.043 | 0.081 | 0.000 | 0.152 | 0.169 | 26.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 157 | 145 | 115 | 188 | 248 | 0 | 125 | 468 | 173 |
N.S. |
1 | 0.85 | 0.78 | 0.62 | 1.02 | 1.34 | 0.00 | 0.68 | 2.53 | 0.94 |
time (sec) |
N/A | 0.331 | 0.533 | 2.092 | 0.034 | 0.096 | 0.000 | 0.134 | 0.262 | 25.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 142 | 275 | 100 | 295 | 244 | 0 | 99 | 6543 | 91 |
N.S. |
1 | 1.12 | 2.17 | 0.79 | 2.32 | 1.92 | 0.00 | 0.78 | 51.52 | 0.72 |
time (sec) |
N/A | 0.589 | 6.107 | 1.707 | 0.122 | 0.105 | 0.000 | 0.188 | 0.246 | 28.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 35 | 28 | 58 | 74 | 82 | 2006 | 32 | 272 | 64 |
N.S. |
1 | 0.97 | 0.78 | 1.61 | 2.06 | 2.28 | 55.72 | 0.89 | 7.56 | 1.78 |
time (sec) |
N/A | 0.223 | 0.108 | 1.271 | 0.028 | 0.152 | 9.384 | 0.134 | 0.184 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 36 | 107 | 375 | 239 | 0 | 125 | 244 | 118 |
N.S. |
1 | 1.00 | 0.62 | 1.84 | 6.47 | 4.12 | 0.00 | 2.16 | 4.21 | 2.03 |
time (sec) |
N/A | 0.318 | 0.107 | 1.121 | 0.044 | 0.095 | 0.000 | 0.188 | 0.221 | 27.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 57 | 58 | 43 | 93 | 100 | 1120 | 38 | 172 | 54 |
N.S. |
1 | 0.88 | 0.89 | 0.66 | 1.43 | 1.54 | 17.23 | 0.58 | 2.65 | 0.83 |
time (sec) |
N/A | 0.253 | 0.139 | 0.960 | 0.028 | 0.084 | 9.813 | 0.137 | 0.170 | 25.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 128 | 58 | 107 | 461 | 291 | 0 | 151 | 299 | 140 |
N.S. |
1 | 1.08 | 0.49 | 0.91 | 3.91 | 2.47 | 0.00 | 1.28 | 2.53 | 1.19 |
time (sec) |
N/A | 0.560 | 0.096 | 1.028 | 0.046 | 0.075 | 0.000 | 0.178 | 0.170 | 28.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 41 | 43 | 33 | 96 | 105 | 493 | 28 | 108 | 28 |
N.S. |
1 | 0.91 | 0.96 | 0.73 | 2.13 | 2.33 | 10.96 | 0.62 | 2.40 | 0.62 |
time (sec) |
N/A | 0.236 | 0.198 | 0.954 | 0.028 | 0.075 | 9.283 | 0.133 | 0.170 | 25.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 198 | 78 | 107 | 547 | 339 | 3405 | 177 | 351 | 162 |
N.S. |
1 | 1.08 | 0.43 | 0.58 | 2.99 | 1.85 | 18.61 | 0.97 | 1.92 | 0.89 |
time (sec) |
N/A | 0.876 | 0.176 | 1.090 | 0.048 | 0.117 | 98.746 | 0.173 | 0.200 | 30.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 20 | 21 | 20 | 108 | 128 | 18 | 78 | 18 |
N.S. |
1 | 1.00 | 0.91 | 0.95 | 0.91 | 4.91 | 5.82 | 0.82 | 3.55 | 0.82 |
time (sec) |
N/A | 0.196 | 0.069 | 1.094 | 0.034 | 0.080 | 9.946 | 0.126 | 0.216 | 25.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 172 | 122 | 127 | 213 | 374 | 0 | 125 | 536 | 198 |
N.S. |
1 | 0.88 | 0.62 | 0.65 | 1.09 | 1.91 | 0.00 | 0.64 | 2.73 | 1.01 |
time (sec) |
N/A | 0.319 | 0.834 | 2.448 | 0.041 | 0.155 | 0.000 | 0.133 | 0.284 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 273 | 113 | 132 | 740 | 225 | 0 | 249 | 320 | 233 |
N.S. |
1 | 1.11 | 0.46 | 0.54 | 3.02 | 0.92 | 0.00 | 1.02 | 1.31 | 0.95 |
time (sec) |
N/A | 1.429 | 0.401 | 3.710 | 0.070 | 0.097 | 0.000 | 0.199 | 0.175 | 29.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 213 | 175 | 151 | 248 | 446 | 0 | 155 | 610 | 231 |
N.S. |
1 | 0.89 | 0.74 | 0.63 | 1.04 | 1.87 | 0.00 | 0.65 | 2.56 | 0.97 |
time (sec) |
N/A | 0.381 | 1.878 | 5.277 | 0.037 | 0.112 | 0.000 | 0.151 | 0.202 | 0.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 304 | 125 | 143 | 866 | 249 | 0 | 301 | 366 | 277 |
N.S. |
1 | 1.09 | 0.45 | 0.51 | 3.10 | 0.89 | 0.00 | 1.08 | 1.31 | 0.99 |
time (sec) |
N/A | 1.516 | 0.505 | 5.698 | 0.072 | 0.115 | 0.000 | 0.210 | 0.214 | 31.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 252 | 195 | 175 | 305 | 466 | 0 | 175 | 792 | 290 |
N.S. |
1 | 0.89 | 0.69 | 0.62 | 1.07 | 1.64 | 0.00 | 0.62 | 2.79 | 1.02 |
time (sec) |
N/A | 0.416 | 2.876 | 7.692 | 0.039 | 0.130 | 0.000 | 0.155 | 0.232 | 0.866 |