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 | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 41 | 40 | 32 | 31 | 149 | 88 | 31 | 31 | 28 |
N.S. |
1 | 1.02 | 1.00 | 0.80 | 0.78 | 3.72 | 2.20 | 0.78 | 0.78 | 0.70 |
time (sec) |
N/A | 0.232 | 0.027 | 0.371 | 0.107 | 0.072 | 0.329 | 0.124 | 0.180 | 0.107 |
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 | 55 | 57 | 55 | 40 | 40 | 228 | 292 | 39 | 68 | 37 |
N.S. |
1 | 1.04 | 1.00 | 0.73 | 0.73 | 4.15 | 5.31 | 0.71 | 1.24 | 0.67 |
time (sec) |
N/A | 0.244 | 0.072 | 0.369 | 0.110 | 0.087 | 1.898 | 0.122 | 0.204 | 0.049 |
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 | 81 | 88 | 68 | 52 | 64 | 356 | 666 | 52 | 116 | 56 |
N.S. |
1 | 1.09 | 0.84 | 0.64 | 0.79 | 4.40 | 8.22 | 0.64 | 1.43 | 0.69 |
time (sec) |
N/A | 0.270 | 0.134 | 0.391 | 0.107 | 0.083 | 7.452 | 0.120 | 0.220 | 0.144 |
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 | 47 | 41 | 33 | 32 | 32 | 39 | 32 | 35 | 32 |
N.S. |
1 | 1.12 | 0.98 | 0.79 | 0.76 | 0.76 | 0.93 | 0.76 | 0.83 | 0.76 |
time (sec) |
N/A | 0.281 | 0.017 | 0.503 | 0.027 | 0.059 | 0.262 | 0.116 | 0.201 | 0.054 |
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 | 34 | 30 | 22 | 21 | 21 | 27 | 21 | 24 | 21 |
N.S. |
1 | 1.17 | 1.03 | 0.76 | 0.72 | 0.72 | 0.93 | 0.72 | 0.83 | 0.72 |
time (sec) |
N/A | 0.261 | 0.015 | 0.433 | 0.031 | 0.063 | 0.408 | 0.119 | 0.225 | 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 | 14 | 14 | 14 | 11 | 10 | 10 | 12 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.93 | 0.71 |
time (sec) |
N/A | 0.208 | 0.001 | 0.073 | 0.027 | 0.060 | 0.023 | 0.120 | 0.204 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 222 | 101 | 110 | 176 | 132 | 104 | 186 | 120 | 41 |
N.S. |
1 | 1.50 | 0.68 | 0.74 | 1.19 | 0.89 | 0.70 | 1.26 | 0.81 | 0.28 |
time (sec) |
N/A | 0.603 | 0.143 | 0.371 | 0.120 | 0.074 | 1.120 | 0.126 | 0.217 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 249 | 134 | 129 | 196 | 230 | 413 | 201 | 319 | 62 |
N.S. |
1 | 1.49 | 0.80 | 0.77 | 1.17 | 1.38 | 2.47 | 1.20 | 1.91 | 0.37 |
time (sec) |
N/A | 0.661 | 0.331 | 0.379 | 0.113 | 0.080 | 30.580 | 0.132 | 0.187 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 276 | 146 | 150 | 219 | 340 | 0 | 211 | 498 | 84 |
N.S. |
1 | 1.48 | 0.78 | 0.81 | 1.18 | 1.83 | 0.00 | 1.13 | 2.68 | 0.45 |
time (sec) |
N/A | 0.717 | 0.259 | 0.392 | 0.109 | 0.086 | 0.000 | 0.128 | 0.224 | 0.104 |
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 | 36 | 45 | 36 | 31 | 30 | 33 | 36 | 31 | 33 | 33 |
N.S. |
1 | 1.25 | 1.00 | 0.86 | 0.83 | 0.92 | 1.00 | 0.86 | 0.92 | 0.92 |
time (sec) |
N/A | 0.270 | 0.021 | 0.499 | 0.038 | 0.060 | 0.130 | 0.125 | 0.205 | 0.050 |
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 | 15 | 16 | 25 | 14 | 21 | 21 | 24 | 21 | 21 | 21 |
N.S. |
1 | 1.07 | 1.67 | 0.93 | 1.40 | 1.40 | 1.60 | 1.40 | 1.40 | 1.40 |
time (sec) |
N/A | 0.205 | 0.016 | 0.447 | 0.025 | 0.059 | 0.074 | 0.118 | 0.208 | 0.045 |
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 | 11 | 10 | 10 | 12 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.208 | 0.001 | 0.075 | 0.024 | 0.060 | 0.021 | 0.120 | 0.180 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 54 | 51 | 44 | 54 | 43 | 58 | 45 | 43 | 42 |
N.S. |
1 | 1.08 | 1.02 | 0.88 | 1.08 | 0.86 | 1.16 | 0.90 | 0.86 | 0.84 |
time (sec) |
N/A | 0.299 | 0.026 | 0.385 | 0.032 | 0.068 | 0.207 | 0.119 | 0.217 | 0.045 |
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 | 72 | 80 | 62 | 76 | 100 | 165 | 65 | 78 | 65 |
N.S. |
1 | 1.07 | 1.19 | 0.93 | 1.13 | 1.49 | 2.46 | 0.97 | 1.16 | 0.97 |
time (sec) |
N/A | 0.331 | 0.043 | 0.380 | 0.033 | 0.071 | 0.283 | 0.121 | 0.188 | 0.044 |
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 | 90 | 95 | 97 | 79 | 101 | 159 | 362 | 79 | 117 | 87 |
N.S. |
1 | 1.06 | 1.08 | 0.88 | 1.12 | 1.77 | 4.02 | 0.88 | 1.30 | 0.97 |
time (sec) |
N/A | 0.367 | 0.085 | 0.385 | 0.027 | 0.081 | 0.334 | 0.124 | 0.213 | 0.045 |
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 | 36 | 43 | 36 | 33 | 32 | 35 | 32 | 33 | 35 | 33 |
N.S. |
1 | 1.19 | 1.00 | 0.92 | 0.89 | 0.97 | 0.89 | 0.92 | 0.97 | 0.92 |
time (sec) |
N/A | 0.293 | 0.023 | 0.513 | 0.035 | 0.063 | 0.226 | 0.120 | 0.187 | 0.126 |
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 | 30 | 25 | 22 | 21 | 27 | 24 | 21 | 24 | 21 |
N.S. |
1 | 1.20 | 1.00 | 0.88 | 0.84 | 1.08 | 0.96 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.285 | 0.018 | 0.423 | 0.031 | 0.066 | 0.175 | 0.126 | 0.226 | 0.109 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.218 | 0.001 | 0.074 | 0.024 | 0.064 | 0.023 | 0.116 | 0.186 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 46 | 42 | 38 | 161 | 100 | 42 | 38 | 34 |
N.S. |
1 | 1.09 | 1.00 | 0.91 | 0.83 | 3.50 | 2.17 | 0.91 | 0.83 | 0.74 |
time (sec) |
N/A | 0.303 | 0.040 | 0.366 | 0.111 | 0.073 | 0.362 | 0.122 | 0.212 | 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 | 74 | 81 | 76 | 59 | 66 | 285 | 410 | 64 | 87 | 59 |
N.S. |
1 | 1.09 | 1.03 | 0.80 | 0.89 | 3.85 | 5.54 | 0.86 | 1.18 | 0.80 |
time (sec) |
N/A | 0.332 | 0.097 | 0.362 | 0.106 | 0.077 | 1.883 | 0.123 | 0.241 | 0.071 |
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 | 100 | 112 | 89 | 66 | 88 | 403 | 808 | 74 | 138 | 78 |
N.S. |
1 | 1.12 | 0.89 | 0.66 | 0.88 | 4.03 | 8.08 | 0.74 | 1.38 | 0.78 |
time (sec) |
N/A | 0.365 | 0.140 | 0.368 | 0.116 | 0.086 | 7.089 | 0.132 | 0.227 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 40 | 33 | 32 | 37 | 37 | 35 | 37 | 35 |
N.S. |
1 | 1.12 | 1.00 | 0.82 | 0.80 | 0.92 | 0.92 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.305 | 0.027 | 0.496 | 0.024 | 0.065 | 0.391 | 0.123 | 0.195 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 32 | 27 | 22 | 21 | 29 | 26 | 22 | 26 | 24 |
N.S. |
1 | 1.19 | 1.00 | 0.81 | 0.78 | 1.07 | 0.96 | 0.81 | 0.96 | 0.89 |
time (sec) |
N/A | 0.284 | 0.022 | 0.411 | 0.031 | 0.064 | 0.241 | 0.119 | 0.219 | 0.053 |
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 | 12 | 12 | 12 | 11 | 10 | 16 | 10 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.33 | 0.83 | 0.83 | 1.08 | 0.83 |
time (sec) |
N/A | 0.223 | 0.002 | 0.076 | 0.026 | 0.061 | 0.021 | 0.124 | 0.208 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 237 | 124 | 117 | 188 | 161 | 117 | 179 | 153 | 52 |
N.S. |
1 | 1.55 | 0.81 | 0.76 | 1.23 | 1.05 | 0.76 | 1.17 | 1.00 | 0.34 |
time (sec) |
N/A | 0.675 | 0.155 | 0.365 | 0.110 | 0.074 | 1.181 | 0.132 | 0.230 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 268 | 147 | 135 | 213 | 264 | 464 | 195 | 326 | 76 |
N.S. |
1 | 1.55 | 0.85 | 0.78 | 1.23 | 1.53 | 2.68 | 1.13 | 1.88 | 0.44 |
time (sec) |
N/A | 0.728 | 0.302 | 0.369 | 0.120 | 0.081 | 29.947 | 0.131 | 0.188 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 299 | 160 | 144 | 235 | 364 | 0 | 207 | 503 | 96 |
N.S. |
1 | 1.53 | 0.82 | 0.74 | 1.21 | 1.87 | 0.00 | 1.06 | 2.58 | 0.49 |
time (sec) |
N/A | 0.774 | 0.392 | 0.364 | 0.113 | 0.084 | 0.000 | 0.131 | 0.180 | 0.178 |
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 | 15 | 16 | 25 | 14 | 21 | 21 | 24 | 21 | 21 | 21 |
N.S. |
1 | 1.07 | 1.67 | 0.93 | 1.40 | 1.40 | 1.60 | 1.40 | 1.40 | 1.40 |
time (sec) |
N/A | 0.213 | 0.002 | 0.393 | 0.032 | 0.063 | 0.078 | 0.118 | 0.202 | 0.002 |
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 | 15 | 15 | 25 | 14 | 13 | 21 | 24 | 21 | 21 | 21 |
N.S. |
1 | 1.00 | 1.67 | 0.93 | 0.87 | 1.40 | 1.60 | 1.40 | 1.40 | 1.40 |
time (sec) |
N/A | 0.216 | 0.013 | 0.418 | 0.025 | 0.066 | 0.081 | 0.126 | 0.224 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 67 | 45 | 44 | 47 | 55 | 884 | 180 | 54 | 37 |
N.S. |
1 | 1.03 | 0.69 | 0.68 | 0.72 | 0.85 | 13.60 | 2.77 | 0.83 | 0.57 |
time (sec) |
N/A | 0.290 | 0.039 | 0.372 | 0.031 | 0.073 | 1.191 | 0.126 | 0.201 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 67 | 54 | 44 | 47 | 44 | 804 | 107 | 43 | 37 |
N.S. |
1 | 1.06 | 0.86 | 0.70 | 0.75 | 0.70 | 12.76 | 1.70 | 0.68 | 0.59 |
time (sec) |
N/A | 0.284 | 0.033 | 0.369 | 0.032 | 0.070 | 1.020 | 0.123 | 0.182 | 0.138 |
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 | 61 | 65 | 45 | 43 | 47 | 35 | 726 | 43 | 34 | 37 |
N.S. |
1 | 1.07 | 0.74 | 0.70 | 0.77 | 0.57 | 11.90 | 0.70 | 0.56 | 0.61 |
time (sec) |
N/A | 0.293 | 0.027 | 0.368 | 0.034 | 0.071 | 0.945 | 0.119 | 0.210 | 0.173 |
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 | 59 | 63 | 42 | 44 | 47 | 67 | 615 | 57 | 35 | 37 |
N.S. |
1 | 1.07 | 0.71 | 0.75 | 0.80 | 1.14 | 10.42 | 0.97 | 0.59 | 0.63 |
time (sec) |
N/A | 0.281 | 0.029 | 0.395 | 0.027 | 0.078 | 1.025 | 0.124 | 0.209 | 0.301 |
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 | 59 | 63 | 43 | 42 | 47 | 101 | 143 | 49 | 45 | 37 |
N.S. |
1 | 1.07 | 0.73 | 0.71 | 0.80 | 1.71 | 2.42 | 0.83 | 0.76 | 0.63 |
time (sec) |
N/A | 0.284 | 0.031 | 0.379 | 0.025 | 0.105 | 0.826 | 0.118 | 0.190 | 0.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 111 | 98 | 82 | 160 | 0 | 138 | 126 | 82 | 37 |
N.S. |
1 | 1.08 | 0.95 | 0.80 | 1.55 | 0.00 | 1.34 | 1.22 | 0.80 | 0.36 |
time (sec) |
N/A | 0.325 | 0.299 | 0.360 | 0.112 | 0.000 | 3.610 | 0.171 | 0.212 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 87 | 83 | 64 | 120 | 0 | 109 | 54 | 62 | 37 |
N.S. |
1 | 1.06 | 1.01 | 0.78 | 1.46 | 0.00 | 1.33 | 0.66 | 0.76 | 0.45 |
time (sec) |
N/A | 0.294 | 0.200 | 0.357 | 0.111 | 0.000 | 1.961 | 0.153 | 0.192 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 63 | 69 | 43 | 81 | 0 | 54 | 44 | 45 | 67 |
N.S. |
1 | 1.03 | 1.13 | 0.70 | 1.33 | 0.00 | 0.89 | 0.72 | 0.74 | 1.10 |
time (sec) |
N/A | 0.262 | 0.131 | 0.359 | 0.108 | 0.000 | 1.146 | 0.139 | 0.213 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 66 | 42 | 63 | 0 | 49 | 0 | 95 | 37 |
N.S. |
1 | 1.02 | 1.18 | 0.75 | 1.12 | 0.00 | 0.88 | 0.00 | 1.70 | 0.66 |
time (sec) |
N/A | 0.266 | 0.102 | 0.362 | 0.106 | 0.000 | 0.909 | 0.000 | 0.170 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 60 | 14 | 0 | 44 | 14 | 65 | 41 |
N.S. |
1 | 1.00 | 1.00 | 3.33 | 0.78 | 0.00 | 2.44 | 0.78 | 3.61 | 2.28 |
time (sec) |
N/A | 0.206 | 0.056 | 0.365 | 0.026 | 0.000 | 0.670 | 0.134 | 0.218 | 0.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 50 | 33 | 83 | 33 | 0 | 165 | 27 | 110 | 38 |
N.S. |
1 | 1.16 | 0.77 | 1.93 | 0.77 | 0.00 | 3.84 | 0.63 | 2.56 | 0.88 |
time (sec) |
N/A | 0.244 | 0.074 | 0.357 | 0.026 | 0.000 | 1.923 | 0.141 | 0.209 | 0.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 84 | 46 | 106 | 50 | 0 | 573 | 41 | 153 | 38 |
N.S. |
1 | 1.31 | 0.72 | 1.66 | 0.78 | 0.00 | 8.95 | 0.64 | 2.39 | 0.59 |
time (sec) |
N/A | 0.277 | 0.088 | 0.364 | 0.028 | 0.000 | 6.332 | 0.142 | 0.213 | 0.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 295 | 53 | 130 | 0 | 0 | 41 | 0 | 52 | 37 |
N.S. |
1 | 1.03 | 0.18 | 0.45 | 0.00 | 0.00 | 0.14 | 0.00 | 0.18 | 0.13 |
time (sec) |
N/A | 0.520 | 10.013 | 0.424 | 0.000 | 0.000 | 0.617 | 0.000 | 0.270 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 271 | 52 | 114 | 0 | 0 | 41 | 0 | 35 | 37 |
N.S. |
1 | 1.02 | 0.20 | 0.43 | 0.00 | 0.00 | 0.15 | 0.00 | 0.13 | 0.14 |
time (sec) |
N/A | 0.481 | 9.710 | 0.398 | 0.000 | 0.000 | 0.488 | 0.000 | 0.279 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 247 | 52 | 101 | 0 | 0 | 39 | 0 | 20 | 37 |
N.S. |
1 | 1.02 | 0.21 | 0.42 | 0.00 | 0.00 | 0.16 | 0.00 | 0.08 | 0.15 |
time (sec) |
N/A | 0.454 | 10.013 | 0.412 | 0.000 | 0.000 | 0.455 | 0.000 | 0.252 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 276 | 55 | 121 | 0 | 0 | 39 | 0 | 28 | 37 |
N.S. |
1 | 1.02 | 0.20 | 0.45 | 0.00 | 0.00 | 0.14 | 0.00 | 0.10 | 0.14 |
time (sec) |
N/A | 0.488 | 10.011 | 0.518 | 0.000 | 0.000 | 0.484 | 0.000 | 0.212 | 0.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 125 | 83 | 165 | 148 | 0 | 170 | 127 | 108 | 38 |
N.S. |
1 | 1.03 | 0.69 | 1.36 | 1.22 | 0.00 | 1.40 | 1.05 | 0.89 | 0.31 |
time (sec) |
N/A | 0.348 | 0.112 | 0.394 | 0.111 | 0.000 | 16.034 | 0.384 | 0.238 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 105 | 79 | 135 | 131 | 0 | 110 | 122 | 83 | 38 |
N.S. |
1 | 1.05 | 0.79 | 1.35 | 1.31 | 0.00 | 1.10 | 1.22 | 0.83 | 0.38 |
time (sec) |
N/A | 0.333 | 0.101 | 0.374 | 0.111 | 0.000 | 6.481 | 0.186 | 0.202 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 107 | 84 | 135 | 135 | 0 | 139 | 109 | 83 | 38 |
N.S. |
1 | 1.07 | 0.84 | 1.35 | 1.35 | 0.00 | 1.39 | 1.09 | 0.83 | 0.38 |
time (sec) |
N/A | 0.337 | 0.099 | 0.363 | 0.122 | 0.000 | 4.423 | 0.185 | 0.199 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 113 | 84 | 135 | 137 | 0 | 138 | 123 | 83 | 38 |
N.S. |
1 | 1.11 | 0.82 | 1.32 | 1.34 | 0.00 | 1.35 | 1.21 | 0.81 | 0.37 |
time (sec) |
N/A | 0.342 | 0.103 | 0.373 | 0.110 | 0.000 | 4.992 | 0.185 | 0.205 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | A | F(-2) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 119 | 84 | 194 | 137 | 0 | 139 | 0 | 83 | 38 |
N.S. |
1 | 1.13 | 0.80 | 1.85 | 1.30 | 0.00 | 1.32 | 0.00 | 0.79 | 0.36 |
time (sec) |
N/A | 0.364 | 0.108 | 0.560 | 0.112 | 0.000 | 7.431 | 0.000 | 0.199 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | A | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 146 | 103 | 527 | 154 | 0 | 144 | 131 | 103 | 38 |
N.S. |
1 | 1.14 | 0.80 | 4.12 | 1.20 | 0.00 | 1.12 | 1.02 | 0.80 | 0.30 |
time (sec) |
N/A | 0.380 | 0.159 | 0.561 | 0.107 | 0.000 | 13.245 | 0.176 | 0.222 | 0.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | F(-2) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 110 | 110 | 120 | 110 | 0 | 122 | 0 | 116 | 37 |
N.S. |
1 | 1.09 | 1.09 | 1.19 | 1.09 | 0.00 | 1.21 | 0.00 | 1.15 | 0.37 |
time (sec) |
N/A | 0.375 | 5.946 | 0.379 | 0.120 | 0.000 | 7.503 | 0.000 | 0.259 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 77 | 85 | 73 | 72 | 0 | 87 | 126 | 83 | 37 |
N.S. |
1 | 1.10 | 1.21 | 1.04 | 1.03 | 0.00 | 1.24 | 1.80 | 1.19 | 0.53 |
time (sec) |
N/A | 0.353 | 5.221 | 0.368 | 0.106 | 0.000 | 2.609 | 0.139 | 0.233 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 31 | 28 | 14 | 28 | 42 | 40 | 19 | 38 |
N.S. |
1 | 1.00 | 1.72 | 1.56 | 0.78 | 1.56 | 2.33 | 2.22 | 1.06 | 2.11 |
time (sec) |
N/A | 0.230 | 4.321 | 0.375 | 0.032 | 0.409 | 0.705 | 0.124 | 0.207 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 50 | 33 | 37 | 31 | 29 | 48 | 61 | 21 | 38 |
N.S. |
1 | 1.28 | 0.85 | 0.95 | 0.79 | 0.74 | 1.23 | 1.56 | 0.54 | 0.97 |
time (sec) |
N/A | 0.292 | 3.764 | 0.461 | 0.033 | 0.537 | 0.718 | 0.129 | 0.267 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 80 | 57 | 48 | 52 | 79 | 230 | 77 | 41 | 38 |
N.S. |
1 | 1.38 | 0.98 | 0.83 | 0.90 | 1.36 | 3.97 | 1.33 | 0.71 | 0.66 |
time (sec) |
N/A | 0.342 | 4.577 | 0.406 | 0.029 | 0.467 | 1.396 | 0.135 | 0.205 | 0.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | C | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 149 | 53 | 135 | 0 | 0 | 46 | 0 | 59 | 38 |
N.S. |
1 | 1.10 | 0.39 | 0.99 | 0.00 | 0.00 | 0.34 | 0.00 | 0.43 | 0.28 |
time (sec) |
N/A | 0.394 | 10.020 | 1.022 | 0.000 | 0.000 | 3.379 | 0.000 | 0.315 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | C | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 123 | 52 | 133 | 0 | 0 | 46 | 0 | 40 | 38 |
N.S. |
1 | 1.08 | 0.46 | 1.17 | 0.00 | 0.00 | 0.40 | 0.00 | 0.35 | 0.33 |
time (sec) |
N/A | 0.351 | 10.011 | 0.619 | 0.000 | 0.000 | 1.490 | 0.000 | 0.296 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | C | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 52 | 126 | 0 | 0 | 44 | 0 | 46 | 37 |
N.S. |
1 | 1.06 | 0.44 | 1.06 | 0.00 | 0.00 | 0.37 | 0.00 | 0.39 | 0.31 |
time (sec) |
N/A | 0.369 | 10.014 | 0.782 | 0.000 | 0.000 | 1.407 | 0.000 | 0.301 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | C | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 157 | 55 | 134 | 0 | 0 | 44 | 0 | 127 | 37 |
N.S. |
1 | 1.10 | 0.38 | 0.94 | 0.00 | 0.00 | 0.31 | 0.00 | 0.89 | 0.26 |
time (sec) |
N/A | 0.441 | 10.030 | 1.257 | 0.000 | 0.000 | 2.166 | 0.000 | 0.261 | 0.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 0 | 0 | 0 | 37 | 0 | 101 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 | 2.02 | 0.82 |
time (sec) |
N/A | 0.300 | 0.094 | 0.000 | 0.000 | 0.000 | 19.884 | 0.000 | 0.283 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 0 | 0 | 0 | 24 | 0 | 259 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 | 5.18 | 0.82 |
time (sec) |
N/A | 0.277 | 0.055 | 0.000 | 0.000 | 0.000 | 2.077 | 0.000 | 0.225 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 68 | 0 | 71 | 98 | 2628 | 231 | 86 | 41 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.96 | 1.32 | 35.51 | 3.12 | 1.16 | 0.55 |
time (sec) |
N/A | 0.326 | 0.080 | 0.000 | 0.047 | 0.140 | 1.690 | 0.127 | 0.200 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 41 | 0 | 215 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 4.67 | 1.24 |
time (sec) |
N/A | 0.280 | 0.124 | 0.000 | 0.000 | 0.000 | 10.760 | 0.000 | 0.257 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 50 | 0 | 0 | 0 | 27 | 0 | 134 | 41 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 | 2.68 | 0.82 |
time (sec) |
N/A | 0.295 | 0.123 | 0.000 | 0.000 | 0.000 | 14.656 | 0.000 | 0.216 | 0.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 50 | 0 | 0 | 0 | 42 | 0 | 63 | 41 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 1.26 | 0.82 |
time (sec) |
N/A | 0.320 | 0.224 | 0.000 | 0.000 | 0.000 | 81.185 | 0.000 | 0.269 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 16 | 38 | 14 | 32 | 32 | 37 | 32 | 31 | 32 |
N.S. |
1 | 1.07 | 2.53 | 0.93 | 2.13 | 2.13 | 2.47 | 2.13 | 2.07 | 2.13 |
time (sec) |
N/A | 0.222 | 0.017 | 0.494 | 0.030 | 0.111 | 0.583 | 0.118 | 0.280 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 38 | 14 | 13 | 32 | 22 | 32 | 31 | 32 |
N.S. |
1 | 1.00 | 2.53 | 0.93 | 0.87 | 2.13 | 1.47 | 2.13 | 2.07 | 2.13 |
time (sec) |
N/A | 0.222 | 0.014 | 0.502 | 0.030 | 0.080 | 0.538 | 0.121 | 0.202 | 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 | 45 | 45 | 43 | 30 | 42 | 29 | 41 | 29 | 29 | 29 |
N.S. |
1 | 1.00 | 0.96 | 0.67 | 0.93 | 0.64 | 0.91 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.273 | 0.018 | 0.365 | 0.026 | 0.075 | 25.188 | 0.125 | 0.191 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-1) | B | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 31 | 0 | 14 | 0 | 78 | 0 | 13 | 38 |
N.S. |
1 | 1.00 | 1.72 | 0.00 | 0.78 | 0.00 | 4.33 | 0.00 | 0.72 | 2.11 |
time (sec) |
N/A | 0.221 | 6.002 | 0.000 | 0.032 | 0.000 | 3.765 | 0.000 | 0.212 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 54 | 58 | 60 | 130 | 469 | 159 | 146 | 57 |
N.S. |
1 | 1.00 | 0.90 | 0.97 | 1.00 | 2.17 | 7.82 | 2.65 | 2.43 | 0.95 |
time (sec) |
N/A | 0.310 | 0.090 | 0.460 | 0.026 | 0.087 | 0.431 | 0.124 | 0.237 | 0.210 |
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 | 38 | 38 | 34 | 37 | 38 | 65 | 182 | 73 | 66 | 36 |
N.S. |
1 | 1.00 | 0.89 | 0.97 | 1.00 | 1.71 | 4.79 | 1.92 | 1.74 | 0.95 |
time (sec) |
N/A | 0.275 | 0.060 | 0.397 | 0.030 | 0.112 | 0.279 | 0.117 | 0.232 | 0.173 |
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 | 16 | 16 | 16 | 16 | 20 | 17 | 16 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.25 | 1.06 | 1.00 | 1.06 | 0.94 |
time (sec) |
N/A | 0.230 | 0.006 | 0.039 | 0.033 | 0.082 | 0.020 | 0.122 | 0.206 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 0 | 0 | 0 | 44 | 0 | 11 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.83 | 0.00 | 0.46 | 1.04 |
time (sec) |
N/A | 0.231 | 0.019 | 0.000 | 0.000 | 0.000 | 0.478 | 0.000 | 0.241 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 0 | 0 | 0 | 318 | 0 | 24 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 13.25 | 0.00 | 1.00 | 1.04 |
time (sec) |
N/A | 0.229 | 0.014 | 0.000 | 0.000 | 0.000 | 0.684 | 0.000 | 0.222 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 0 | 0 | 0 | 0 | 0 | 128 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.33 | 1.04 |
time (sec) |
N/A | 0.224 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 0 | 49 | 0 | 241 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 4.92 | 0.88 |
time (sec) |
N/A | 0.263 | 0.026 | 0.000 | 0.000 | 0.000 | 0.965 | 0.000 | 0.221 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 48 | 0 | 0 | 0 | 49 | 0 | 91 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 | 1.90 | 0.90 |
time (sec) |
N/A | 0.260 | 0.020 | 0.000 | 0.000 | 0.000 | 0.642 | 0.000 | 0.244 | 0.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 48 | 0 | 0 | 0 | 49 | 0 | 20 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 | 0.42 | 0.90 |
time (sec) |
N/A | 0.261 | 0.023 | 0.000 | 0.000 | 0.000 | 0.588 | 0.000 | 0.203 | 0.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 49 | 0 | 33 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.65 | 0.84 |
time (sec) |
N/A | 0.257 | 0.021 | 0.000 | 0.000 | 0.000 | 0.718 | 0.000 | 0.209 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 49 | 0 | 46 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.90 | 0.84 |
time (sec) |
N/A | 0.258 | 0.026 | 0.000 | 0.000 | 0.000 | 1.186 | 0.000 | 0.256 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 46 | 0 | 96 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 2.09 | 1.02 |
time (sec) |
N/A | 0.258 | 0.020 | 0.000 | 0.000 | 0.000 | 0.930 | 0.000 | 0.194 | 0.941 |
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 | 22 | 22 | 41 | 51 | 0 | 50 | 61 | 0 | 28 | 41 |
N.S. |
1 | 1.00 | 1.86 | 2.32 | 0.00 | 2.27 | 2.77 | 0.00 | 1.27 | 1.86 |
time (sec) |
N/A | 0.223 | 0.087 | 0.469 | 0.000 | 0.100 | 5.416 | 0.000 | 0.216 | 0.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 132 | 55 | 0 | 0 | 192 | 1724 | 0 | 106 | 64 |
N.S. |
1 | 0.90 | 0.38 | 0.00 | 0.00 | 1.32 | 11.81 | 0.00 | 0.73 | 0.44 |
time (sec) |
N/A | 0.408 | 0.049 | 0.000 | 0.000 | 0.086 | 1.139 | 0.000 | 0.216 | 0.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 91 | 55 | 0 | 0 | 126 | 695 | 0 | 82 | 64 |
N.S. |
1 | 0.95 | 0.57 | 0.00 | 0.00 | 1.31 | 7.24 | 0.00 | 0.85 | 0.67 |
time (sec) |
N/A | 0.334 | 0.044 | 0.000 | 0.000 | 0.093 | 0.967 | 0.000 | 0.236 | 0.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 55 | 0 | 0 | 68 | 250 | 0 | 58 | 64 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 1.36 | 5.00 | 0.00 | 1.16 | 1.28 |
time (sec) |
N/A | 0.273 | 0.040 | 0.000 | 0.000 | 0.090 | 0.769 | 0.000 | 0.238 | 0.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 47 | 0 | 31 | 42 | 0 | 34 | 75 |
N.S. |
1 | 1.00 | 1.00 | 2.61 | 0.00 | 1.72 | 2.33 | 0.00 | 1.89 | 4.17 |
time (sec) |
N/A | 0.222 | 0.038 | 0.477 | 0.000 | 0.078 | 0.697 | 0.000 | 0.202 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 39 | 50 | 0 | 0 | 0 | 39 | 0 | 15 | 51 |
N.S. |
1 | 0.78 | 1.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.30 | 1.02 |
time (sec) |
N/A | 0.287 | 0.016 | 0.000 | 0.000 | 0.000 | 6.840 | 0.000 | 0.211 | 0.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 53 | 0 | 0 | 0 | 48 | 0 | 39 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 | 0.74 | 1.02 |
time (sec) |
N/A | 0.274 | 0.022 | 0.000 | 0.000 | 0.000 | 1.673 | 0.000 | 0.255 | 0.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 0 | 0 | 0 | 48 | 0 | 68 | 56 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 1.24 | 1.02 |
time (sec) |
N/A | 0.271 | 0.020 | 0.000 | 0.000 | 0.000 | 1.930 | 0.000 | 0.252 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 132 | 55 | 0 | 0 | 192 | 1911 | 0 | 106 | 64 |
N.S. |
1 | 0.90 | 0.37 | 0.00 | 0.00 | 1.31 | 13.00 | 0.00 | 0.72 | 0.44 |
time (sec) |
N/A | 0.400 | 0.023 | 0.000 | 0.000 | 0.081 | 4.260 | 0.000 | 0.199 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 91 | 55 | 0 | 0 | 126 | 767 | 0 | 82 | 64 |
N.S. |
1 | 0.94 | 0.57 | 0.00 | 0.00 | 1.30 | 7.91 | 0.00 | 0.85 | 0.66 |
time (sec) |
N/A | 0.338 | 0.017 | 0.000 | 0.000 | 0.080 | 4.049 | 0.000 | 0.246 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 55 | 0 | 0 | 68 | 241 | 0 | 58 | 64 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 1.33 | 4.73 | 0.00 | 1.14 | 1.25 |
time (sec) |
N/A | 0.278 | 0.011 | 0.000 | 0.000 | 0.079 | 2.683 | 0.000 | 0.239 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 47 | 0 | 31 | 99 | 0 | 34 | 75 |
N.S. |
1 | 1.00 | 1.00 | 2.61 | 0.00 | 1.72 | 5.50 | 0.00 | 1.89 | 4.17 |
time (sec) |
N/A | 0.215 | 0.009 | 0.497 | 0.000 | 0.076 | 2.375 | 0.000 | 0.186 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 39 | 50 | 0 | 0 | 0 | 39 | 0 | 15 | 51 |
N.S. |
1 | 0.78 | 1.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.30 | 1.02 |
time (sec) |
N/A | 0.275 | 0.000 | 0.000 | 0.000 | 0.000 | 6.698 | 0.000 | 0.195 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 53 | 0 | 0 | 0 | 48 | 0 | 39 | 54 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.66 | 0.92 |
time (sec) |
N/A | 0.287 | 0.001 | 0.000 | 0.000 | 0.000 | 3.469 | 0.000 | 0.276 | 0.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 55 | 0 | 0 | 0 | 48 | 0 | 68 | 56 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 | 1.21 | 1.00 |
time (sec) |
N/A | 0.277 | 0.002 | 0.000 | 0.000 | 0.000 | 2.606 | 0.000 | 0.260 | 0.194 |