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 | 25 | 25 | 25 | 20 | 17 | 63 | 19 | 22 | 53 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.68 | 2.52 | 0.76 | 0.88 | 2.12 | 0.76 |
time (sec) |
N/A | 0.143 | 0.018 | 0.333 | 0.026 | 0.069 | 0.546 | 0.126 | 0.241 | 0.431 |
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 | 18 | 17 | 17 | 19 | 30 | 23 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 1.00 | 1.58 | 1.21 | 0.89 |
time (sec) |
N/A | 0.130 | 0.027 | 0.329 | 0.025 | 0.062 | 0.376 | 0.125 | 0.242 | 0.174 |
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 | 49 | 50 | 43 | 36 | 108 | 42 | 48 | 79 | 38 |
N.S. |
1 | 0.98 | 1.00 | 0.86 | 0.72 | 2.16 | 0.84 | 0.96 | 1.58 | 0.76 |
time (sec) |
N/A | 0.154 | 0.041 | 0.388 | 0.030 | 0.078 | 1.286 | 0.121 | 0.238 | 0.461 |
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 | 44 | 44 | 31 | 26 | 36 | 27 | 46 | 55 | 42 | 25 |
N.S. |
1 | 1.00 | 0.70 | 0.59 | 0.82 | 0.61 | 1.05 | 1.25 | 0.95 | 0.57 |
time (sec) |
N/A | 0.148 | 0.037 | 0.339 | 0.035 | 0.066 | 0.523 | 0.131 | 0.255 | 0.329 |
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 | 74 | 79 | 62 | 60 | 56 | 138 | 97 | 75 | 101 | 57 |
N.S. |
1 | 1.07 | 0.84 | 0.81 | 0.76 | 1.86 | 1.31 | 1.01 | 1.36 | 0.77 |
time (sec) |
N/A | 0.172 | 0.069 | 0.361 | 0.042 | 0.079 | 2.669 | 0.123 | 0.229 | 0.483 |
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 | 55 | 59 | 38 | 35 | 53 | 46 | 68 | 57 | 42 | 41 |
N.S. |
1 | 1.07 | 0.69 | 0.64 | 0.96 | 0.84 | 1.24 | 1.04 | 0.76 | 0.75 |
time (sec) |
N/A | 0.173 | 0.025 | 0.384 | 0.026 | 0.066 | 0.231 | 0.126 | 0.185 | 0.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 66 | 54 | 49 | 159 | 71 | 51 | 114 | 0 |
N.S. |
1 | 1.09 | 0.97 | 0.79 | 0.72 | 2.34 | 1.04 | 0.75 | 1.68 | 0.00 |
time (sec) |
N/A | 0.174 | 0.152 | 0.387 | 0.029 | 0.078 | 1.841 | 0.129 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 38 | 24 | 23 | 32 | 34 | 41 | 32 | 30 | 22 |
N.S. |
1 | 1.19 | 0.75 | 0.72 | 1.00 | 1.06 | 1.28 | 1.00 | 0.94 | 0.69 |
time (sec) |
N/A | 0.162 | 0.021 | 0.365 | 0.027 | 0.068 | 0.185 | 0.126 | 0.262 | 0.368 |
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 | 54 | 37 | 29 | 130 | 37 | 39 | 88 | 36 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 0.67 | 3.02 | 0.86 | 0.91 | 2.05 | 0.84 |
time (sec) |
N/A | 0.151 | 0.075 | 0.374 | 0.028 | 0.074 | 0.952 | 0.134 | 0.223 | 0.101 |
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 | 15 | 14 | 24 | 24 | 14 | 22 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.50 | 1.50 | 0.88 | 1.38 | 0.88 |
time (sec) |
N/A | 0.129 | 0.002 | 0.330 | 0.026 | 0.075 | 0.102 | 0.121 | 0.219 | 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 | 16 | 16 | 16 | 15 | 14 | 23 | 17 | 14 | 39 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.44 | 1.06 | 0.88 | 2.44 | 0.88 |
time (sec) |
N/A | 0.125 | 0.001 | 0.324 | 0.033 | 0.066 | 0.365 | 0.131 | 0.192 | 0.031 |
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 | 41 | 46 | 41 | 34 | 31 | 129 | 184 | 39 | 136 | 33 |
N.S. |
1 | 1.12 | 1.00 | 0.83 | 0.76 | 3.15 | 4.49 | 0.95 | 3.32 | 0.80 |
time (sec) |
N/A | 0.157 | 0.031 | 0.358 | 0.027 | 0.079 | 0.983 | 0.126 | 0.249 | 0.445 |
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 | 38 | 38 | 28 | 26 | 34 | 35 | 46 | 50 | 56 | 35 |
N.S. |
1 | 1.00 | 0.74 | 0.68 | 0.89 | 0.92 | 1.21 | 1.32 | 1.47 | 0.92 |
time (sec) |
N/A | 0.146 | 0.040 | 0.371 | 0.029 | 0.070 | 0.483 | 0.132 | 0.219 | 0.313 |
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 | 69 | 74 | 60 | 54 | 51 | 174 | 73 | 72 | 172 | 53 |
N.S. |
1 | 1.07 | 0.87 | 0.78 | 0.74 | 2.52 | 1.06 | 1.04 | 2.49 | 0.77 |
time (sec) |
N/A | 0.173 | 0.061 | 0.402 | 0.029 | 0.079 | 1.879 | 0.127 | 0.218 | 0.533 |
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 | 62 | 68 | 42 | 37 | 54 | 50 | 233 | 106 | 81 | 38 |
N.S. |
1 | 1.10 | 0.68 | 0.60 | 0.87 | 0.81 | 3.76 | 1.71 | 1.31 | 0.61 |
time (sec) |
N/A | 0.161 | 0.054 | 0.415 | 0.031 | 0.071 | 0.744 | 0.144 | 0.223 | 0.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 103 | 78 | 70 | 89 | 227 | 367 | 65 | 189 | 0 |
N.S. |
1 | 1.13 | 0.86 | 0.77 | 0.98 | 2.49 | 4.03 | 0.71 | 2.08 | 0.00 |
time (sec) |
N/A | 0.187 | 0.216 | 0.490 | 0.034 | 0.083 | 2.856 | 0.122 | 0.207 | 0.000 |
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 | 54 | 59 | 39 | 36 | 52 | 58 | 138 | 49 | 54 | 38 |
N.S. |
1 | 1.09 | 0.72 | 0.67 | 0.96 | 1.07 | 2.56 | 0.91 | 1.00 | 0.70 |
time (sec) |
N/A | 0.174 | 0.026 | 0.366 | 0.033 | 0.069 | 0.346 | 0.122 | 0.209 | 0.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 69 | 66 | 57 | 65 | 199 | 303 | 51 | 138 | 0 |
N.S. |
1 | 1.08 | 1.03 | 0.89 | 1.02 | 3.11 | 4.73 | 0.80 | 2.16 | 0.00 |
time (sec) |
N/A | 0.168 | 0.148 | 0.367 | 0.036 | 0.077 | 1.626 | 0.135 | 0.188 | 0.000 |
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 | 40 | 28 | 25 | 33 | 47 | 92 | 24 | 43 | 24 |
N.S. |
1 | 1.11 | 0.78 | 0.69 | 0.92 | 1.31 | 2.56 | 0.67 | 1.19 | 0.67 |
time (sec) |
N/A | 0.160 | 0.022 | 0.376 | 0.025 | 0.067 | 0.349 | 0.117 | 0.249 | 0.345 |
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 | 21 | 21 | 21 | 18 | 34 | 37 | 44 | 17 | 68 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.62 | 1.76 | 2.10 | 0.81 | 3.24 | 0.81 |
time (sec) |
N/A | 0.127 | 0.043 | 0.421 | 0.035 | 0.104 | 0.444 | 0.121 | 0.227 | 0.330 |
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 | 18 | 18 | 18 | 15 | 14 | 35 | 46 | 14 | 33 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.94 | 2.56 | 0.78 | 1.83 | 0.78 |
time (sec) |
N/A | 0.127 | 0.002 | 0.335 | 0.029 | 0.069 | 0.321 | 0.119 | 0.200 | 0.207 |
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 | 39 | 39 | 29 | 26 | 31 | 47 | 95 | 27 | 84 | 28 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.79 | 1.21 | 2.44 | 0.69 | 2.15 | 0.72 |
time (sec) |
N/A | 0.136 | 0.003 | 0.335 | 0.032 | 0.067 | 0.521 | 0.127 | 0.341 | 0.190 |
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 | 69 | 54 | 54 | 45 | 200 | 740 | 50 | 238 | 47 |
N.S. |
1 | 1.17 | 0.92 | 0.92 | 0.76 | 3.39 | 12.54 | 0.85 | 4.03 | 0.80 |
time (sec) |
N/A | 0.167 | 0.054 | 0.421 | 0.028 | 0.081 | 1.585 | 0.120 | 0.233 | 0.444 |
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 | 64 | 65 | 42 | 37 | 50 | 59 | 165 | 64 | 100 | 42 |
N.S. |
1 | 1.02 | 0.66 | 0.58 | 0.78 | 0.92 | 2.58 | 1.00 | 1.56 | 0.66 |
time (sec) |
N/A | 0.159 | 0.057 | 0.404 | 0.025 | 0.071 | 0.763 | 0.130 | 0.208 | 0.349 |
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 | 88 | 97 | 71 | 72 | 66 | 244 | 864 | 73 | 272 | 73 |
N.S. |
1 | 1.10 | 0.81 | 0.82 | 0.75 | 2.77 | 9.82 | 0.83 | 3.09 | 0.83 |
time (sec) |
N/A | 0.181 | 0.076 | 0.754 | 0.041 | 0.081 | 2.913 | 0.125 | 0.196 | 0.482 |
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 | 84 | 93 | 53 | 45 | 72 | 72 | 354 | 121 | 124 | 78 |
N.S. |
1 | 1.11 | 0.63 | 0.54 | 0.86 | 0.86 | 4.21 | 1.44 | 1.48 | 0.93 |
time (sec) |
N/A | 0.176 | 0.063 | 0.431 | 0.027 | 0.074 | 1.014 | 0.136 | 0.250 | 0.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 161 | 100 | 94 | 285 | 359 | 3181 | 91 | 339 | 0 |
N.S. |
1 | 1.23 | 0.76 | 0.72 | 2.18 | 2.74 | 24.28 | 0.69 | 2.59 | 0.00 |
time (sec) |
N/A | 0.226 | 0.348 | 0.556 | 0.058 | 0.104 | 8.550 | 0.135 | 0.254 | 0.000 |
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 | 94 | 99 | 61 | 58 | 92 | 102 | 454 | 77 | 98 | 80 |
N.S. |
1 | 1.05 | 0.65 | 0.62 | 0.98 | 1.09 | 4.83 | 0.82 | 1.04 | 0.85 |
time (sec) |
N/A | 0.195 | 0.032 | 0.427 | 0.050 | 0.076 | 0.777 | 0.115 | 0.214 | 0.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 121 | 88 | 79 | 255 | 331 | 2980 | 78 | 314 | 0 |
N.S. |
1 | 1.14 | 0.83 | 0.75 | 2.41 | 3.12 | 28.11 | 0.74 | 2.96 | 0.00 |
time (sec) |
N/A | 0.204 | 0.287 | 0.394 | 0.059 | 0.092 | 4.782 | 0.134 | 0.218 | 0.000 |
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 | 75 | 80 | 50 | 47 | 73 | 91 | 364 | 55 | 87 | 63 |
N.S. |
1 | 1.07 | 0.67 | 0.63 | 0.97 | 1.21 | 4.85 | 0.73 | 1.16 | 0.84 |
time (sec) |
N/A | 0.181 | 0.031 | 0.352 | 0.038 | 0.075 | 0.771 | 0.122 | 0.243 | 0.466 |
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 | 21 | 21 | 21 | 18 | 103 | 59 | 95 | 17 | 116 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 4.90 | 2.81 | 4.52 | 0.81 | 5.52 | 3.24 |
time (sec) |
N/A | 0.131 | 0.075 | 0.347 | 0.033 | 0.073 | 0.707 | 0.131 | 0.242 | 0.484 |
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 | 39 | 36 | 53 | 80 | 272 | 41 | 76 | 41 |
N.S. |
1 | 1.07 | 0.66 | 0.61 | 0.90 | 1.36 | 4.61 | 0.69 | 1.29 | 0.69 |
time (sec) |
N/A | 0.168 | 0.028 | 0.341 | 0.031 | 0.076 | 0.760 | 0.121 | 0.225 | 0.451 |
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 | 43 | 44 | 31 | 28 | 85 | 71 | 199 | 29 | 136 | 68 |
N.S. |
1 | 1.02 | 0.72 | 0.65 | 1.98 | 1.65 | 4.63 | 0.67 | 3.16 | 1.58 |
time (sec) |
N/A | 0.146 | 0.075 | 0.332 | 0.026 | 0.076 | 0.800 | 0.137 | 0.234 | 0.443 |
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 | 38 | 42 | 28 | 25 | 33 | 69 | 180 | 24 | 65 | 24 |
N.S. |
1 | 1.11 | 0.74 | 0.66 | 0.87 | 1.82 | 4.74 | 0.63 | 1.71 | 0.63 |
time (sec) |
N/A | 0.160 | 0.024 | 0.320 | 0.027 | 0.074 | 0.763 | 0.126 | 0.215 | 0.418 |
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 | 64 | 74 | 42 | 39 | 70 | 82 | 517 | 43 | 155 | 70 |
N.S. |
1 | 1.16 | 0.66 | 0.61 | 1.09 | 1.28 | 8.08 | 0.67 | 2.42 | 1.09 |
time (sec) |
N/A | 0.163 | 0.067 | 0.352 | 0.032 | 0.073 | 1.001 | 0.132 | 0.245 | 0.393 |
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 | 18 | 18 | 18 | 15 | 14 | 57 | 90 | 14 | 55 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 3.17 | 5.00 | 0.78 | 3.06 | 0.78 |
time (sec) |
N/A | 0.128 | 0.003 | 0.341 | 0.031 | 0.072 | 0.736 | 0.121 | 0.193 | 0.225 |
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 | 77 | 93 | 51 | 48 | 61 | 91 | 1265 | 55 | 170 | 61 |
N.S. |
1 | 1.21 | 0.66 | 0.62 | 0.79 | 1.18 | 16.43 | 0.71 | 2.21 | 0.79 |
time (sec) |
N/A | 0.167 | 0.005 | 0.341 | 0.024 | 0.079 | 1.178 | 0.137 | 0.238 | 0.232 |
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 | 95 | 115 | 76 | 76 | 73 | 332 | 5250 | 81 | 438 | 75 |
N.S. |
1 | 1.21 | 0.80 | 0.80 | 0.77 | 3.49 | 55.26 | 0.85 | 4.61 | 0.79 |
time (sec) |
N/A | 0.193 | 0.063 | 0.353 | 0.033 | 0.089 | 4.126 | 0.123 | 0.245 | 0.465 |
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 | 119 | 64 | 59 | 82 | 103 | 400 | 90 | 186 | 76 |
N.S. |
1 | 1.12 | 0.60 | 0.56 | 0.77 | 0.97 | 3.77 | 0.85 | 1.75 | 0.72 |
time (sec) |
N/A | 0.183 | 0.084 | 0.415 | 0.035 | 0.081 | 1.595 | 0.133 | 0.199 | 0.479 |
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 | 143 | 93 | 94 | 96 | 376 | 5540 | 104 | 472 | 113 |
N.S. |
1 | 1.13 | 0.74 | 0.75 | 0.76 | 2.98 | 43.97 | 0.83 | 3.75 | 0.90 |
time (sec) |
N/A | 0.212 | 0.080 | 0.471 | 0.035 | 0.100 | 7.612 | 0.124 | 0.455 | 0.622 |
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 | 128 | 149 | 75 | 70 | 108 | 116 | 668 | 147 | 210 | 97 |
N.S. |
1 | 1.16 | 0.59 | 0.55 | 0.84 | 0.91 | 5.22 | 1.15 | 1.64 | 0.76 |
time (sec) |
N/A | 0.202 | 0.093 | 0.411 | 0.036 | 0.098 | 1.928 | 0.139 | 0.212 | 0.458 |
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 | 50 | 27 | 23 | 40 | 23 | 44 | 34 | 22 | 21 |
N.S. |
1 | 1.09 | 0.59 | 0.50 | 0.87 | 0.50 | 0.96 | 0.74 | 0.48 | 0.46 |
time (sec) |
N/A | 0.157 | 0.014 | 0.343 | 0.106 | 0.063 | 0.215 | 0.114 | 0.193 | 0.030 |
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 | 50 | 44 | 27 | 33 | 37 | 39 | 36 | 42 | 25 |
N.S. |
1 | 1.11 | 0.98 | 0.60 | 0.73 | 0.82 | 0.87 | 0.80 | 0.93 | 0.56 |
time (sec) |
N/A | 0.150 | 0.034 | 0.383 | 0.103 | 0.063 | 0.158 | 0.122 | 0.256 | 0.050 |
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 | 31 | 35 | 22 | 18 | 26 | 18 | 27 | 23 | 17 | 15 |
N.S. |
1 | 1.13 | 0.71 | 0.58 | 0.84 | 0.58 | 0.87 | 0.74 | 0.55 | 0.48 |
time (sec) |
N/A | 0.150 | 0.012 | 0.331 | 0.104 | 0.062 | 0.126 | 0.119 | 0.203 | 0.179 |
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 | 37 | 20 | 19 | 29 | 22 | 29 | 29 | 17 |
N.S. |
1 | 1.00 | 1.37 | 0.74 | 0.70 | 1.07 | 0.81 | 1.07 | 1.07 | 0.63 |
time (sec) |
N/A | 0.131 | 0.024 | 0.386 | 0.106 | 0.062 | 0.090 | 0.119 | 0.223 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 10 | 11 | 10 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 0.67 | 0.73 | 0.67 | 0.60 |
time (sec) |
N/A | 0.127 | 0.001 | 0.324 | 0.029 | 0.061 | 0.073 | 0.118 | 0.204 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 20 | 7 | 6 | 16 | 7 | 29 | 17 | 6 |
N.S. |
1 | 1.00 | 2.00 | 0.70 | 0.60 | 1.60 | 0.70 | 2.90 | 1.70 | 0.60 |
time (sec) |
N/A | 0.118 | 0.000 | 0.333 | 0.106 | 0.062 | 0.065 | 0.121 | 0.238 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 9 | 35 | 8 | 29 | 37 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.45 | 1.75 | 0.40 | 1.45 | 1.85 | 0.60 |
time (sec) |
N/A | 0.135 | 0.014 | 0.341 | 0.104 | 0.064 | 0.547 | 0.114 | 0.207 | 0.188 |
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 | 15 | 14 | 18 | 15 | 23 | 19 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.00 | 0.83 | 1.28 | 1.06 | 0.67 |
time (sec) |
N/A | 0.128 | 0.019 | 0.329 | 0.104 | 0.063 | 0.427 | 0.119 | 0.232 | 0.024 |
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 | 43 | 39 | 30 | 24 | 57 | 44 | 43 | 58 | 25 |
N.S. |
1 | 1.10 | 1.00 | 0.77 | 0.62 | 1.46 | 1.13 | 1.10 | 1.49 | 0.64 |
time (sec) |
N/A | 0.145 | 0.028 | 0.432 | 0.104 | 0.063 | 1.322 | 0.121 | 0.233 | 0.032 |
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 | 37 | 37 | 25 | 22 | 29 | 28 | 32 | 42 | 34 | 19 |
N.S. |
1 | 1.00 | 0.68 | 0.59 | 0.78 | 0.76 | 0.86 | 1.14 | 0.92 | 0.51 |
time (sec) |
N/A | 0.137 | 0.027 | 0.346 | 0.101 | 0.064 | 0.629 | 0.123 | 0.244 | 0.025 |
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 | 66 | 46 | 41 | 38 | 64 | 63 | 55 | 71 | 33 |
N.S. |
1 | 1.16 | 0.81 | 0.72 | 0.67 | 1.12 | 1.11 | 0.96 | 1.25 | 0.58 |
time (sec) |
N/A | 0.154 | 0.035 | 0.425 | 0.103 | 0.067 | 2.613 | 0.116 | 0.208 | 0.175 |
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 | 50 | 27 | 23 | 40 | 23 | 46 | 43 | 22 | 23 |
N.S. |
1 | 1.09 | 0.59 | 0.50 | 0.87 | 0.50 | 1.00 | 0.93 | 0.48 | 0.50 |
time (sec) |
N/A | 0.155 | 0.015 | 0.357 | 0.104 | 0.063 | 0.288 | 0.124 | 0.193 | 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 | 50 | 47 | 34 | 33 | 40 | 39 | 26 | 31 | 27 |
N.S. |
1 | 1.11 | 1.04 | 0.76 | 0.73 | 0.89 | 0.87 | 0.58 | 0.69 | 0.60 |
time (sec) |
N/A | 0.146 | 0.062 | 0.407 | 0.103 | 0.065 | 0.177 | 0.128 | 0.238 | 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 | 31 | 35 | 22 | 18 | 26 | 18 | 29 | 23 | 17 | 18 |
N.S. |
1 | 1.13 | 0.71 | 0.58 | 0.84 | 0.58 | 0.94 | 0.74 | 0.55 | 0.58 |
time (sec) |
N/A | 0.148 | 0.012 | 0.352 | 0.102 | 0.062 | 0.136 | 0.121 | 0.243 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 40 | 20 | 19 | 32 | 22 | 19 | 18 | 19 |
N.S. |
1 | 1.00 | 1.48 | 0.74 | 0.70 | 1.19 | 0.81 | 0.70 | 0.67 | 0.70 |
time (sec) |
N/A | 0.132 | 0.039 | 0.401 | 0.109 | 0.065 | 0.121 | 0.129 | 0.221 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 12 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 0.80 | 0.73 | 0.67 | 0.73 |
time (sec) |
N/A | 0.123 | 0.001 | 0.332 | 0.026 | 0.064 | 0.079 | 0.120 | 0.217 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 19 | 7 | 6 | 19 | 7 | 19 | 6 | 6 |
N.S. |
1 | 1.00 | 1.90 | 0.70 | 0.60 | 1.90 | 0.70 | 1.90 | 0.60 | 0.60 |
time (sec) |
N/A | 0.115 | 0.000 | 0.345 | 0.104 | 0.064 | 0.082 | 0.125 | 0.254 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 25 | 18 | 26 | 31 | 10 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.25 | 0.90 | 1.30 | 1.55 | 0.50 | 1.00 |
time (sec) |
N/A | 0.137 | 0.012 | 0.487 | 0.103 | 0.063 | 0.591 | 0.123 | 0.221 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 14 | 36 | 33 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 2.00 | 1.83 | 0.72 | 0.78 |
time (sec) |
N/A | 0.129 | 0.021 | 0.342 | 0.106 | 0.059 | 0.514 | 0.123 | 0.222 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 39 | 30 | 40 | 38 | 99 | 45 | 29 | 35 |
N.S. |
1 | 1.10 | 1.00 | 0.77 | 1.03 | 0.97 | 2.54 | 1.15 | 0.74 | 0.90 |
time (sec) |
N/A | 0.143 | 0.027 | 0.436 | 0.102 | 0.065 | 1.284 | 0.121 | 0.229 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 25 | 22 | 29 | 21 | 80 | 73 | 20 | 22 |
N.S. |
1 | 1.00 | 0.68 | 0.59 | 0.78 | 0.57 | 2.16 | 1.97 | 0.54 | 0.59 |
time (sec) |
N/A | 0.139 | 0.028 | 0.277 | 0.103 | 0.069 | 0.678 | 0.124 | 0.236 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 66 | 46 | 41 | 54 | 45 | 136 | 57 | 42 | 49 |
N.S. |
1 | 1.16 | 0.81 | 0.72 | 0.95 | 0.79 | 2.39 | 1.00 | 0.74 | 0.86 |
time (sec) |
N/A | 0.153 | 0.031 | 0.341 | 0.105 | 0.066 | 2.754 | 0.123 | 0.236 | 0.176 |
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 | 50 | 27 | 23 | 40 | 23 | 44 | 34 | 22 | 22 |
N.S. |
1 | 1.09 | 0.59 | 0.50 | 0.87 | 0.50 | 0.96 | 0.74 | 0.48 | 0.48 |
time (sec) |
N/A | 0.156 | 0.014 | 0.283 | 0.106 | 0.061 | 0.213 | 0.119 | 0.189 | 0.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 59 | 44 | 39 | 45 | 37 | 48 | 37 | 42 | 0 |
N.S. |
1 | 1.09 | 0.81 | 0.72 | 0.83 | 0.69 | 0.89 | 0.69 | 0.78 | 0.00 |
time (sec) |
N/A | 0.154 | 0.033 | 0.404 | 0.105 | 0.066 | 0.161 | 0.128 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 22 | 18 | 26 | 18 | 27 | 23 | 17 | 18 |
N.S. |
1 | 1.13 | 0.71 | 0.58 | 0.84 | 0.58 | 0.87 | 0.74 | 0.55 | 0.58 |
time (sec) |
N/A | 0.151 | 0.012 | 0.339 | 0.102 | 0.063 | 0.125 | 0.124 | 0.211 | 0.361 |
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 | 36 | 37 | 30 | 31 | 29 | 31 | 30 | 29 | 29 |
N.S. |
1 | 1.00 | 1.03 | 0.83 | 0.86 | 0.81 | 0.86 | 0.83 | 0.81 | 0.81 |
time (sec) |
N/A | 0.140 | 0.025 | 0.401 | 0.116 | 0.065 | 0.095 | 0.125 | 0.230 | 0.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 10 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 0.67 | 0.73 | 0.67 | 0.73 |
time (sec) |
N/A | 0.121 | 0.001 | 0.327 | 0.032 | 0.063 | 0.090 | 0.125 | 0.206 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 43 | 19 | 18 | 16 | 15 | 30 | 17 | 16 |
N.S. |
1 | 1.00 | 2.26 | 1.00 | 0.95 | 0.84 | 0.79 | 1.58 | 0.89 | 0.84 |
time (sec) |
N/A | 0.127 | 0.000 | 0.340 | 0.103 | 0.066 | 0.081 | 0.128 | 0.253 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 9 | 18 | 26 | 14 | 17 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.45 | 0.90 | 1.30 | 0.70 | 0.85 | 1.00 |
time (sec) |
N/A | 0.132 | 0.012 | 0.378 | 0.107 | 0.066 | 0.621 | 0.111 | 0.208 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 18 | 37 | 23 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.00 | 2.06 | 1.28 | 0.94 | 0.78 |
time (sec) |
N/A | 0.121 | 0.020 | 0.533 | 0.103 | 0.064 | 0.466 | 0.130 | 0.189 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 39 | 30 | 24 | 38 | 99 | 29 | 36 | 29 |
N.S. |
1 | 1.10 | 1.00 | 0.77 | 0.62 | 0.97 | 2.54 | 0.74 | 0.92 | 0.74 |
time (sec) |
N/A | 0.145 | 0.023 | 0.458 | 0.103 | 0.066 | 1.251 | 0.122 | 0.185 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 25 | 22 | 29 | 28 | 68 | 42 | 34 | 31 |
N.S. |
1 | 1.00 | 0.68 | 0.59 | 0.78 | 0.76 | 1.84 | 1.14 | 0.92 | 0.84 |
time (sec) |
N/A | 0.135 | 0.025 | 0.394 | 0.103 | 0.067 | 0.686 | 0.130 | 0.245 | 0.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 66 | 46 | 42 | 38 | 45 | 136 | 41 | 49 | 57 |
N.S. |
1 | 1.16 | 0.81 | 0.74 | 0.67 | 0.79 | 2.39 | 0.72 | 0.86 | 1.00 |
time (sec) |
N/A | 0.152 | 0.031 | 0.490 | 0.111 | 0.068 | 2.757 | 0.120 | 0.200 | 0.358 |
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 | 46 | 50 | 27 | 23 | 40 | 23 | 49 | 34 | 22 | 23 |
N.S. |
1 | 1.09 | 0.59 | 0.50 | 0.87 | 0.50 | 1.07 | 0.74 | 0.48 | 0.50 |
time (sec) |
N/A | 0.151 | 0.014 | 0.334 | 0.103 | 0.064 | 0.239 | 0.119 | 0.222 | 0.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 59 | 43 | 39 | 33 | 67 | 53 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 0.80 | 0.72 | 0.61 | 1.24 | 0.98 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.153 | 0.070 | 0.388 | 0.104 | 0.066 | 0.274 | 0.000 | 0.219 | 0.000 |
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 | 31 | 35 | 22 | 18 | 26 | 18 | 31 | 23 | 17 | 18 |
N.S. |
1 | 1.13 | 0.71 | 0.58 | 0.84 | 0.58 | 1.00 | 0.74 | 0.55 | 0.58 |
time (sec) |
N/A | 0.146 | 0.013 | 0.328 | 0.102 | 0.064 | 0.136 | 0.126 | 0.215 | 0.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 29 | 19 | 59 | 36 | 0 | 19 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.53 | 1.64 | 1.00 | 0.00 | 0.53 | 0.86 |
time (sec) |
N/A | 0.139 | 0.057 | 0.373 | 0.105 | 0.066 | 0.188 | 0.000 | 0.196 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 14 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 0.93 | 0.73 | 0.67 | 0.73 |
time (sec) |
N/A | 0.123 | 0.001 | 0.346 | 0.032 | 0.062 | 0.085 | 0.118 | 0.188 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 8 | 6 | 47 | 17 | 0 | 7 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.42 | 0.32 | 2.47 | 0.89 | 0.00 | 0.37 | 0.79 |
time (sec) |
N/A | 0.126 | 0.000 | 0.333 | 0.108 | 0.064 | 0.209 | 0.000 | 0.238 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 25 | 43 | 8 | 14 | 40 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.25 | 2.15 | 0.40 | 0.70 | 2.00 | 0.70 |
time (sec) |
N/A | 0.137 | 0.021 | 0.351 | 0.105 | 0.064 | 0.724 | 0.121 | 0.194 | 0.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 14 | 15 | 0 | 20 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 0.83 | 0.00 | 1.11 | 0.78 |
time (sec) |
N/A | 0.124 | 0.040 | 0.345 | 0.102 | 0.060 | 0.461 | 0.000 | 0.206 | 0.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 39 | 30 | 40 | 65 | 46 | 29 | 62 | 29 |
N.S. |
1 | 1.10 | 1.00 | 0.77 | 1.03 | 1.67 | 1.18 | 0.74 | 1.59 | 0.74 |
time (sec) |
N/A | 0.141 | 0.021 | 0.419 | 0.103 | 0.070 | 1.274 | 0.118 | 0.190 | 0.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 25 | 22 | 29 | 21 | 36 | 0 | 35 | 31 |
N.S. |
1 | 1.00 | 0.68 | 0.59 | 0.78 | 0.57 | 0.97 | 0.00 | 0.95 | 0.84 |
time (sec) |
N/A | 0.136 | 0.044 | 0.332 | 0.104 | 0.059 | 0.667 | 0.000 | 0.243 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 66 | 46 | 42 | 54 | 72 | 65 | 43 | 75 | 60 |
N.S. |
1 | 1.16 | 0.81 | 0.74 | 0.95 | 1.26 | 1.14 | 0.75 | 1.32 | 1.05 |
time (sec) |
N/A | 0.158 | 0.025 | 0.404 | 0.106 | 0.072 | 2.863 | 0.122 | 0.197 | 0.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 209 | 103 | 152 | 0 | 76 | 46 | 0 | 90 | 0 |
N.S. |
1 | 1.14 | 0.56 | 0.83 | 0.00 | 0.41 | 0.25 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.266 | 10.044 | 0.635 | 0.000 | 0.077 | 14.085 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 171 | 85 | 138 | 0 | 57 | 46 | 0 | 67 | 0 |
N.S. |
1 | 1.12 | 0.56 | 0.90 | 0.00 | 0.37 | 0.30 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.240 | 8.947 | 0.408 | 0.000 | 0.078 | 1.391 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 139 | 54 | 119 | 0 | 42 | 46 | 0 | 45 | 0 |
N.S. |
1 | 1.10 | 0.43 | 0.94 | 0.00 | 0.33 | 0.37 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.211 | 6.240 | 0.391 | 0.000 | 0.075 | 0.582 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 139 | 56 | 120 | 0 | 44 | 49 | 0 | 54 | 0 |
N.S. |
1 | 1.10 | 0.44 | 0.95 | 0.00 | 0.35 | 0.39 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.213 | 10.013 | 0.461 | 0.000 | 0.071 | 1.485 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 176 | 56 | 137 | 0 | 57 | 53 | 0 | 56 | 0 |
N.S. |
1 | 1.14 | 0.36 | 0.88 | 0.00 | 0.37 | 0.34 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.244 | 10.012 | 0.585 | 0.000 | 0.068 | 15.744 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 216 | 56 | 151 | 0 | 70 | 53 | 0 | 56 | 0 |
N.S. |
1 | 1.16 | 0.30 | 0.81 | 0.00 | 0.38 | 0.28 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.270 | 10.011 | 0.734 | 0.000 | 0.075 | 157.360 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 378 | 103 | 232 | 0 | 86 | 46 | 0 | 89 | 0 |
N.S. |
1 | 1.14 | 0.31 | 0.70 | 0.00 | 0.26 | 0.14 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.402 | 10.043 | 0.546 | 0.000 | 0.100 | 41.500 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 340 | 85 | 221 | 0 | 71 | 46 | 0 | 68 | 0 |
N.S. |
1 | 1.13 | 0.28 | 0.73 | 0.00 | 0.24 | 0.15 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.367 | 10.028 | 0.457 | 0.000 | 0.072 | 5.784 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 307 | 56 | 205 | 0 | 48 | 46 | 0 | 41 | 0 |
N.S. |
1 | 1.14 | 0.21 | 0.76 | 0.00 | 0.18 | 0.17 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.342 | 7.109 | 0.419 | 0.000 | 0.071 | 0.662 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 303 | 54 | 194 | 0 | 49 | 49 | 0 | 50 | 0 |
N.S. |
1 | 1.15 | 0.21 | 0.74 | 0.00 | 0.19 | 0.19 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.341 | 10.011 | 0.469 | 0.000 | 0.074 | 0.788 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 343 | 56 | 219 | 0 | 63 | 53 | 0 | 56 | 0 |
N.S. |
1 | 1.13 | 0.18 | 0.72 | 0.00 | 0.21 | 0.17 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.373 | 10.013 | 0.561 | 0.000 | 0.070 | 5.307 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 383 | 56 | 234 | 0 | 78 | 53 | 0 | 56 | 0 |
N.S. |
1 | 1.15 | 0.17 | 0.70 | 0.00 | 0.23 | 0.16 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.398 | 10.014 | 0.690 | 0.000 | 0.070 | 47.102 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 240 | 102 | 163 | 0 | 90 | 46 | 0 | 111 | 0 |
N.S. |
1 | 1.13 | 0.48 | 0.77 | 0.00 | 0.42 | 0.22 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.274 | 10.053 | 1.239 | 0.000 | 0.091 | 24.730 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 202 | 89 | 150 | 0 | 69 | 46 | 0 | 88 | 0 |
N.S. |
1 | 1.12 | 0.49 | 0.83 | 0.00 | 0.38 | 0.25 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.258 | 10.041 | 0.786 | 0.000 | 0.079 | 2.542 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 170 | 55 | 134 | 0 | 55 | 46 | 0 | 65 | 0 |
N.S. |
1 | 1.12 | 0.36 | 0.88 | 0.00 | 0.36 | 0.30 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.235 | 9.094 | 0.648 | 0.000 | 0.075 | 1.090 | 0.000 | 0.231 | 0.000 |