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 | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 16 | 22 | 12 | 16 | 30 | 14 | 11 | 30 | 11 |
N.S. |
1 | 0.94 | 1.29 | 0.71 | 0.94 | 1.76 | 0.82 | 0.65 | 1.76 | 0.65 |
time (sec) |
N/A | 0.241 | 0.008 | 0.108 | 0.039 | 0.060 | 0.068 | 0.112 | 0.208 | 0.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 133 | 127 | 155 | 158 | 201 | 170 | 149 | 212 | 268 |
N.S. |
1 | 5.78 | 5.52 | 6.74 | 6.87 | 8.74 | 7.39 | 6.48 | 9.22 | 11.65 |
time (sec) |
N/A | 0.711 | 0.074 | 0.707 | 0.052 | 0.068 | 3.288 | 0.114 | 0.247 | 0.755 |
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 | 17 | 13 | 12 | 11 | 11 | 12 | 12 | 11 | 11 |
N.S. |
1 | 0.89 | 0.68 | 0.63 | 0.58 | 0.58 | 0.63 | 0.63 | 0.58 | 0.58 |
time (sec) |
N/A | 0.163 | 0.001 | 0.058 | 0.034 | 0.061 | 0.034 | 0.117 | 0.233 | 0.018 |
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 | 23 | 32 | 28 | 28 | 27 | 29 | 26 | 24 |
N.S. |
1 | 1.00 | 0.92 | 1.28 | 1.12 | 1.12 | 1.08 | 1.16 | 1.04 | 0.96 |
time (sec) |
N/A | 0.444 | 0.026 | 1.112 | 0.152 | 0.069 | 0.172 | 0.126 | 0.250 | 0.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 29 | 73 | 71 | 70 | 71 | 0 | 1594 | 80 |
N.S. |
1 | 0.00 | 1.26 | 3.17 | 3.09 | 3.04 | 3.09 | 0.00 | 69.30 | 3.48 |
time (sec) |
N/A | 0.000 | 0.148 | 2.339 | 0.415 | 0.075 | 0.298 | 0.000 | 5.491 | 1.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 49 | 125 | 49 | 42 | 55 | 95 | 132 |
N.S. |
1 | 0.00 | 0.00 | 1.48 | 3.79 | 1.48 | 1.27 | 1.67 | 2.88 | 4.00 |
time (sec) |
N/A | 0.000 | 0.000 | 5.727 | 0.205 | 0.082 | 0.305 | 0.674 | 0.297 | 0.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 148 | 31 | 34 | 117 | 44 | 49 | 44 | 41 | 30 |
N.S. |
1 | 4.62 | 0.97 | 1.06 | 3.66 | 1.38 | 1.53 | 1.38 | 1.28 | 0.94 |
time (sec) |
N/A | 1.649 | 4.267 | 0.465 | 0.139 | 0.075 | 0.140 | 0.122 | 0.244 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 34 | 14 | 22 | 187 | 21 | 19 | 56 | 22 | 62 |
N.S. |
1 | 2.27 | 0.93 | 1.47 | 12.47 | 1.40 | 1.27 | 3.73 | 1.47 | 4.13 |
time (sec) |
N/A | 0.379 | 0.039 | 0.517 | 0.113 | 0.070 | 0.090 | 0.123 | 0.251 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 119 | 41 | 53 | 0 | 46 | 73 | 87 | 54 | 32 |
N.S. |
1 | 3.97 | 1.37 | 1.77 | 0.00 | 1.53 | 2.43 | 2.90 | 1.80 | 1.07 |
time (sec) |
N/A | 0.759 | 0.141 | 12.313 | 0.000 | 0.069 | 0.196 | 0.109 | 0.219 | 0.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 127 | 65 | 71 | 121 | 92 | 83 | 114 | 126 | 84 |
N.S. |
1 | 4.88 | 2.50 | 2.73 | 4.65 | 3.54 | 3.19 | 4.38 | 4.85 | 3.23 |
time (sec) |
N/A | 1.716 | 0.350 | 28.855 | 0.087 | 0.076 | 0.112 | 0.127 | 0.212 | 0.645 |
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 | 13 | 10 | 10 | 14 | 10 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.67 | 0.67 | 0.93 | 0.67 | 0.87 | 0.60 |
time (sec) |
N/A | 0.255 | 0.009 | 0.108 | 0.027 | 0.062 | 0.055 | 0.114 | 0.221 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 70 | 25 | 66 | 29 | 24 | 32 | 25 | 26 |
N.S. |
1 | 1.42 | 3.68 | 1.32 | 3.47 | 1.53 | 1.26 | 1.68 | 1.32 | 1.37 |
time (sec) |
N/A | 0.376 | 0.039 | 2.795 | 0.041 | 0.075 | 0.106 | 0.119 | 0.223 | 0.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 29 | 32 | 47 | 84 | 34 | 0 | 390 | 46 |
N.S. |
1 | 0.00 | 1.07 | 1.19 | 1.74 | 3.11 | 1.26 | 0.00 | 14.44 | 1.70 |
time (sec) |
N/A | 0.000 | 5.108 | 2.934 | 0.427 | 0.076 | 1.864 | 0.000 | 0.267 | 0.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 51 | 59 | 45 | 53 | 39 | 29 | 31 | 46 | 28 |
N.S. |
1 | 2.12 | 2.46 | 1.88 | 2.21 | 1.62 | 1.21 | 1.29 | 1.92 | 1.17 |
time (sec) |
N/A | 0.841 | 0.063 | 0.864 | 0.090 | 0.066 | 0.121 | 0.116 | 0.219 | 0.604 |
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 | 25 | 25 | 26 | 24 | 25 | 19 | 29 | 36 | 23 |
N.S. |
1 | 0.86 | 0.86 | 0.90 | 0.83 | 0.86 | 0.66 | 1.00 | 1.24 | 0.79 |
time (sec) |
N/A | 0.446 | 0.088 | 0.444 | 0.093 | 0.066 | 0.144 | 0.114 | 1.010 | 0.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | B | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 203 | 197 | 37 | 98 | 33 | 31 | 0 | 41 | 34 |
N.S. |
1 | 7.25 | 7.04 | 1.32 | 3.50 | 1.18 | 1.11 | 0.00 | 1.46 | 1.21 |
time (sec) |
N/A | 2.182 | 0.074 | 0.554 | 0.041 | 0.068 | 0.132 | 0.000 | 0.216 | 1.345 |
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 | 17 | 17 | 19 | 15 | 17 | 18 | 12 | 18 | 15 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 1.06 | 0.71 | 1.06 | 0.88 | 0.94 |
time (sec) |
N/A | 0.206 | 0.014 | 0.211 | 0.036 | 0.073 | 0.234 | 0.113 | 0.226 | 0.562 |
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 | 19 | 17 | 18 | 18 | 17 | 18 | 44 | 18 |
N.S. |
1 | 1.00 | 0.70 | 0.63 | 0.67 | 0.67 | 0.63 | 0.67 | 1.63 | 0.67 |
time (sec) |
N/A | 0.181 | 0.025 | 0.174 | 0.031 | 0.068 | 0.062 | 0.111 | 0.246 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | F(-1) | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 34 | 64 | 33 | 0 | 33 | 36 | 33 |
N.S. |
1 | 0.00 | 0.00 | 1.26 | 2.37 | 1.22 | 0.00 | 1.22 | 1.33 | 1.22 |
time (sec) |
N/A | 0.000 | 0.000 | 1.782 | 0.094 | 0.076 | 0.000 | 3.466 | 0.238 | 0.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 22 | 21 | 25 | 22 | 19 | 20 | 22 | 20 |
N.S. |
1 | 0.88 | 0.88 | 0.84 | 1.00 | 0.88 | 0.76 | 0.80 | 0.88 | 0.80 |
time (sec) |
N/A | 1.028 | 0.052 | 18.104 | 0.159 | 0.074 | 0.397 | 0.171 | 0.222 | 1.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 37 | 47 | 60 | 50 | 76 | 73 | 42 | 1650 |
N.S. |
1 | 0.00 | 1.09 | 1.38 | 1.76 | 1.47 | 2.24 | 2.15 | 1.24 | 48.53 |
time (sec) |
N/A | 0.000 | 5.040 | 1.836 | 0.168 | 0.074 | 0.206 | 0.129 | 0.230 | 1.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 49 | 35 | 37 | 46 | 31 | 58 | 44 | 0 |
N.S. |
1 | 0.00 | 1.48 | 1.06 | 1.12 | 1.39 | 0.94 | 1.76 | 1.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.058 | 0.671 | 0.197 | 0.071 | 5.321 | 0.133 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 295 | 27 | 121 | 102 | 83 | 94 | 102 | 132 | 115 |
N.S. |
1 | 10.54 | 0.96 | 4.32 | 3.64 | 2.96 | 3.36 | 3.64 | 4.71 | 4.11 |
time (sec) |
N/A | 4.228 | 11.029 | 0.028 | 0.559 | 0.116 | 0.210 | 0.321 | 5.111 | 0.903 |
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 | 17 | 10 | 10 | 9 | 8 | 8 | 10 | 9 | 8 | 8 |
N.S. |
1 | 0.59 | 0.59 | 0.53 | 0.47 | 0.47 | 0.59 | 0.53 | 0.47 | 0.47 |
time (sec) |
N/A | 0.232 | 0.002 | 0.060 | 0.026 | 0.060 | 0.030 | 0.112 | 0.216 | 0.011 |
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 | 15 | 15 | 16 | 15 | 15 | 12 | 15 | 15 | 15 |
N.S. |
1 | 0.79 | 0.79 | 0.84 | 0.79 | 0.79 | 0.63 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.552 | 0.011 | 0.372 | 0.062 | 0.060 | 0.049 | 0.112 | 0.203 | 0.671 |
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 | 24 | 35 | 16 | 14 | 25 | 13 | 14 | 13 | 13 | 13 |
N.S. |
1 | 1.46 | 0.67 | 0.58 | 1.04 | 0.54 | 0.58 | 0.54 | 0.54 | 0.54 |
time (sec) |
N/A | 0.290 | 0.025 | 0.120 | 0.031 | 0.061 | 0.092 | 0.108 | 0.212 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 118 | 81 | 74 | 80 | 64 | 80 | 70 | 79 | 67 |
N.S. |
1 | 4.54 | 3.12 | 2.85 | 3.08 | 2.46 | 3.08 | 2.69 | 3.04 | 2.58 |
time (sec) |
N/A | 0.607 | 0.047 | 1.750 | 0.039 | 0.074 | 0.152 | 0.127 | 0.236 | 0.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 459 | 86 | 324 | 296 | 296 | 323 | 296 | 446 | 416 |
N.S. |
1 | 15.30 | 2.87 | 10.80 | 9.87 | 9.87 | 10.77 | 9.87 | 14.87 | 13.87 |
time (sec) |
N/A | 4.237 | 11.680 | 219.083 | 0.045 | 0.077 | 0.296 | 0.119 | 0.208 | 3.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 19 | 19 | 49 | 38 | 38 | 54 | 50 | 50 | 48 |
N.S. |
1 | 0.79 | 0.79 | 2.04 | 1.58 | 1.58 | 2.25 | 2.08 | 2.08 | 2.00 |
time (sec) |
N/A | 0.493 | 0.025 | 1.077 | 0.069 | 0.073 | 0.296 | 0.130 | 0.212 | 1.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 23 | 24 | 24 | 20 | 46 | 24 | 24 |
N.S. |
1 | 0.00 | 1.04 | 0.92 | 0.96 | 0.96 | 0.80 | 1.84 | 0.96 | 0.96 |
time (sec) |
N/A | 0.000 | 0.287 | 0.590 | 0.080 | 0.071 | 0.108 | 0.214 | 0.263 | 0.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 177 | 131 | 68 | 227 | 330 | 423 | 0 | 209 | 236 |
N.S. |
1 | 4.78 | 3.54 | 1.84 | 6.14 | 8.92 | 11.43 | 0.00 | 5.65 | 6.38 |
time (sec) |
N/A | 0.839 | 0.134 | 0.685 | 0.038 | 0.068 | 1.335 | 0.000 | 0.230 | 1.061 |
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 | 36 | 18 | 20 | 23 | 23 | 19 | 29 | 18 | 23 |
N.S. |
1 | 2.00 | 1.00 | 1.11 | 1.28 | 1.28 | 1.06 | 1.61 | 1.00 | 1.28 |
time (sec) |
N/A | 0.434 | 0.013 | 0.144 | 0.028 | 0.057 | 0.257 | 0.108 | 0.223 | 0.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 25 | 0 | 0 | 0 | 0 | 0 | 123 | 23 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.92 | 0.92 |
time (sec) |
N/A | 3.724 | 0.136 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 1.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 50 | 64 | 73 | 50 | 46 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.47 | 1.88 | 2.15 | 1.47 | 1.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.151 | 98.381 | 0.558 | 0.071 | 0.439 | 0.000 | 0.446 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | F(-2) | A | F(-2) | F | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 58 | 0 | 29 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.23 | 0.00 | 1.12 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 58.120 | 0.000 | 0.069 | 0.000 | 0.000 | 0.338 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 14 | 14 | 13 | 12 | 18 | 12 | 12 | 14 | 12 |
N.S. |
1 | 0.70 | 0.70 | 0.65 | 0.60 | 0.90 | 0.60 | 0.60 | 0.70 | 0.60 |
time (sec) |
N/A | 0.234 | 0.064 | 0.061 | 0.041 | 0.068 | 0.068 | 0.103 | 0.369 | 0.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | A | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 40 | 8222 | 38 | 77 | 37 | 36 | 41 | 90 | 42 |
N.S. |
1 | 1.25 | 256.94 | 1.19 | 2.41 | 1.16 | 1.12 | 1.28 | 2.81 | 1.31 |
time (sec) |
N/A | 6.408 | 7.160 | 1.196 | 1.370 | 0.069 | 0.129 | 0.159 | 0.333 | 0.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 61 | 86 | 322 | 94 | 90 | 427 | 147 | 419 |
N.S. |
1 | 0.00 | 3.05 | 4.30 | 16.10 | 4.70 | 4.50 | 21.35 | 7.35 | 20.95 |
time (sec) |
N/A | 0.000 | 0.279 | 3.923 | 0.398 | 0.068 | 0.519 | 1.887 | 0.387 | 0.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 27 | 24 | 25 | 41 | 39 | 25 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 0.96 | 1.00 | 1.64 | 1.56 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.300 | 25.988 | 0.154 | 0.085 | 0.202 | 0.135 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | C | A | A | F | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 35 | 195 | 47 | 53 | 39 | 0 | 44 | 82 |
N.S. |
1 | 0.00 | 0.97 | 5.42 | 1.31 | 1.47 | 1.08 | 0.00 | 1.22 | 2.28 |
time (sec) |
N/A | 0.000 | 0.175 | 0.119 | 0.230 | 0.070 | 1.594 | 0.000 | 0.438 | 1.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 21 | 20 | 20 | 19 | 20 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.00 | 1.00 | 0.95 | 1.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.486 | 5.964 | 0.194 | 0.073 | 0.189 | 0.167 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 36 | 39 | 78 | 78 | 37 | 44 | 0 | 0 |
N.S. |
1 | 0.00 | 1.29 | 1.39 | 2.79 | 2.79 | 1.32 | 1.57 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.066 | 18.360 | 0.095 | 0.074 | 0.110 | 0.147 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 24 | 0 | 25 | 24 | 38 | 27 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 0.00 | 1.00 | 0.96 | 1.52 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.101 | 0.649 | 0.000 | 0.068 | 1.047 | 0.123 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 36 | 33 | 26 | 39 | 29 | 24 | 30 | 34 | 25 |
N.S. |
1 | 1.64 | 1.50 | 1.18 | 1.77 | 1.32 | 1.09 | 1.36 | 1.55 | 1.14 |
time (sec) |
N/A | 0.238 | 0.073 | 0.376 | 0.031 | 0.067 | 0.100 | 0.110 | 0.319 | 0.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 21 | 23 | 36 | 24 | 73 | 66 | 23 |
N.S. |
1 | 0.00 | 0.96 | 0.81 | 0.88 | 1.38 | 0.92 | 2.81 | 2.54 | 0.88 |
time (sec) |
N/A | 0.000 | 0.116 | 0.228 | 0.154 | 0.069 | 7.415 | 0.161 | 0.321 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 1168 | 25 | 116 | 587 | 65 | 63 | 125 | 239 | 46 |
N.S. |
1 | 43.26 | 0.93 | 4.30 | 21.74 | 2.41 | 2.33 | 4.63 | 8.85 | 1.70 |
time (sec) |
N/A | 4.725 | 0.055 | 0.338 | 0.107 | 0.067 | 0.165 | 0.281 | 0.296 | 1.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 30 | 28 | 30 | 27 | 26 | 27 | 30 | 27 |
N.S. |
1 | 0.00 | 1.15 | 1.08 | 1.15 | 1.04 | 1.00 | 1.04 | 1.15 | 1.04 |
time (sec) |
N/A | 0.000 | 5.053 | 0.413 | 0.090 | 0.069 | 0.116 | 0.131 | 0.302 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 39 | 25 | 23 | 31 | 19 | 0 | 49 | 26 |
N.S. |
1 | 0.00 | 1.50 | 0.96 | 0.88 | 1.19 | 0.73 | 0.00 | 1.88 | 1.00 |
time (sec) |
N/A | 0.000 | 0.115 | 1.841 | 0.085 | 0.071 | 0.154 | 0.000 | 0.399 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 71 | 27 | 24 | 36 | 28 | 24 | 41 | 60 | 25 |
N.S. |
1 | 2.63 | 1.00 | 0.89 | 1.33 | 1.04 | 0.89 | 1.52 | 2.22 | 0.93 |
time (sec) |
N/A | 0.920 | 5.313 | 3.476 | 0.128 | 0.068 | 0.101 | 0.138 | 0.382 | 0.191 |
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 | 17 | 21 | 21 | 24 | 16 | 17 | 19 | 16 | 20 | 15 |
N.S. |
1 | 1.24 | 1.24 | 1.41 | 0.94 | 1.00 | 1.12 | 0.94 | 1.18 | 0.88 |
time (sec) |
N/A | 0.154 | 0.002 | 0.370 | 0.029 | 0.063 | 0.065 | 0.110 | 0.339 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 26 | 50 | 25 | 26 | 25 | 32 | 25 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 1.92 | 0.96 | 1.00 | 0.96 | 1.23 | 0.96 |
time (sec) |
N/A | 0.000 | 0.194 | 4.636 | 0.165 | 0.075 | 0.596 | 0.134 | 0.392 | 0.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-2) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 911 | 22 | 28 | 0 | 48 | 0 | 87 | 0 | 738 |
N.S. |
1 | 39.61 | 0.96 | 1.22 | 0.00 | 2.09 | 0.00 | 3.78 | 0.00 | 32.09 |
time (sec) |
N/A | 2.375 | 0.248 | 1.422 | 0.000 | 0.070 | 0.000 | 0.150 | 0.997 | 0.883 |
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 | 39 | 22 | 29 | 39 | 29 | 20 | 25 | 53 | 25 |
N.S. |
1 | 1.44 | 0.81 | 1.07 | 1.44 | 1.07 | 0.74 | 0.93 | 1.96 | 0.93 |
time (sec) |
N/A | 0.458 | 0.039 | 0.640 | 0.167 | 0.066 | 0.069 | 0.116 | 0.288 | 0.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 24 | 162 | 35 | 27 | 0 | 35 | 23 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 6.75 | 1.46 | 1.12 | 0.00 | 1.46 | 0.96 |
time (sec) |
N/A | 0.000 | 0.298 | 1.138 | 0.188 | 0.070 | 0.088 | 0.000 | 0.310 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | A | B | F | F | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 166 | 0 | 0 | 43 | 51 | 0 | 266 | 36 |
N.S. |
1 | 0.00 | 6.15 | 0.00 | 0.00 | 1.59 | 1.89 | 0.00 | 9.85 | 1.33 |
time (sec) |
N/A | 0.000 | 0.197 | 0.000 | 0.000 | 0.077 | 1.253 | 0.000 | 0.465 | 0.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 33 | 28 | 32 | 26 | 0 | 29 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.00 | 1.14 | 0.93 | 0.00 | 1.04 | 0.93 |
time (sec) |
N/A | 0.756 | 0.069 | 44.776 | 0.141 | 0.074 | 1.476 | 0.000 | 0.362 | 0.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 48 | 28 | 25 | 40 | 23 | 22 | 34 | 30 | 24 |
N.S. |
1 | 1.78 | 1.04 | 0.93 | 1.48 | 0.85 | 0.81 | 1.26 | 1.11 | 0.89 |
time (sec) |
N/A | 0.319 | 0.030 | 0.165 | 0.036 | 0.067 | 0.107 | 0.111 | 0.345 | 0.082 |
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 | 13 | 11 | 12 | 11 | 11 | 8 | 11 | 12 | 11 |
N.S. |
1 | 0.81 | 0.69 | 0.75 | 0.69 | 0.69 | 0.50 | 0.69 | 0.75 | 0.69 |
time (sec) |
N/A | 0.290 | 0.021 | 0.301 | 0.060 | 0.059 | 0.042 | 0.115 | 0.409 | 0.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 43 | 37 | 35 | 37 | 0 | 44 | 37 |
N.S. |
1 | 0.00 | 1.00 | 2.05 | 1.76 | 1.67 | 1.76 | 0.00 | 2.10 | 1.76 |
time (sec) |
N/A | 0.000 | 0.811 | 0.073 | 0.254 | 0.081 | 82.430 | 0.000 | 0.421 | 0.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 62 | 53 | 45 | 44 | 25 | 31 | 46 | 41 | 45 |
N.S. |
1 | 2.48 | 2.12 | 1.80 | 1.76 | 1.00 | 1.24 | 1.84 | 1.64 | 1.80 |
time (sec) |
N/A | 0.284 | 0.018 | 0.612 | 0.037 | 0.069 | 0.098 | 0.111 | 0.280 | 0.590 |
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 | 20 | 16 | 18 | 16 | 28 | 14 | 17 | 27 | 16 |
N.S. |
1 | 0.80 | 0.64 | 0.72 | 0.64 | 1.12 | 0.56 | 0.68 | 1.08 | 0.64 |
time (sec) |
N/A | 0.251 | 0.009 | 0.114 | 0.029 | 0.061 | 0.101 | 0.110 | 0.353 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 20 | 15 | 14 | 14 | 14 | 14 | 16 | 14 |
N.S. |
1 | 1.05 | 1.05 | 0.79 | 0.74 | 0.74 | 0.74 | 0.74 | 0.84 | 0.74 |
time (sec) |
N/A | 0.156 | 0.013 | 0.105 | 0.032 | 0.060 | 0.060 | 0.114 | 0.281 | 0.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 48 | 54 | 89 | 48 | 78 | 109 | 0 | 0 |
N.S. |
1 | 0.00 | 1.66 | 1.86 | 3.07 | 1.66 | 2.69 | 3.76 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.068 | 3.758 | 0.289 | 0.074 | 0.301 | 9.402 | 0.350 | 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 | 14 | 16 | 12 | 13 | 12 | 12 | 14 | 16 | 12 | 12 |
N.S. |
1 | 1.14 | 0.86 | 0.93 | 0.86 | 0.86 | 1.00 | 1.14 | 0.86 | 0.86 |
time (sec) |
N/A | 0.340 | 0.026 | 0.489 | 0.065 | 0.059 | 0.088 | 0.108 | 0.369 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 30 | 20 | 21 | 25 | 20 | 20 | 20 | 27 | 25 |
N.S. |
1 | 1.30 | 0.87 | 0.91 | 1.09 | 0.87 | 0.87 | 0.87 | 1.17 | 1.09 |
time (sec) |
N/A | 0.849 | 0.743 | 0.668 | 0.093 | 0.065 | 0.090 | 0.117 | 0.321 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 35 | 21 | 40 | 21 | 29 | 30 | 319 | 30 |
N.S. |
1 | 0.00 | 1.40 | 0.84 | 1.60 | 0.84 | 1.16 | 1.20 | 12.76 | 1.20 |
time (sec) |
N/A | 0.000 | 1.991 | 0.350 | 0.079 | 0.080 | 0.239 | 0.121 | 0.308 | 0.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 173 | 118 | 48 | 148 | 148 | 199 | 148 | 113 | 163 |
N.S. |
1 | 6.18 | 4.21 | 1.71 | 5.29 | 5.29 | 7.11 | 5.29 | 4.04 | 5.82 |
time (sec) |
N/A | 0.355 | 0.024 | 0.423 | 0.033 | 0.066 | 0.049 | 0.108 | 0.297 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 1290 | 55 | 52 | 161 | 40 | 53 | 51 | 48 | 55 |
N.S. |
1 | 37.94 | 1.62 | 1.53 | 4.74 | 1.18 | 1.56 | 1.50 | 1.41 | 1.62 |
time (sec) |
N/A | 6.328 | 0.353 | 1.334 | 0.195 | 0.072 | 0.159 | 0.124 | 0.329 | 0.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 59 | 52 | 49 | 44 | 44 | 41 | 44 | 59 | 54 |
N.S. |
1 | 2.27 | 2.00 | 1.88 | 1.69 | 1.69 | 1.58 | 1.69 | 2.27 | 2.08 |
time (sec) |
N/A | 0.631 | 0.251 | 0.431 | 0.048 | 0.066 | 0.065 | 0.112 | 0.291 | 0.595 |
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 | 18 | 18 | 18 | 17 | 17 | 19 | 17 | 20 | 20 |
N.S. |
1 | 1.29 | 1.29 | 1.29 | 1.21 | 1.21 | 1.36 | 1.21 | 1.43 | 1.43 |
time (sec) |
N/A | 0.420 | 0.404 | 0.270 | 0.109 | 0.067 | 0.113 | 0.110 | 0.320 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 52 | 52 | 17 | 41 | 22 | 19 | 19 | 25 | 21 |
N.S. |
1 | 2.17 | 2.17 | 0.71 | 1.71 | 0.92 | 0.79 | 0.79 | 1.04 | 0.88 |
time (sec) |
N/A | 0.263 | 0.011 | 0.233 | 0.040 | 0.063 | 0.074 | 0.115 | 0.342 | 0.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 37 | 82 | 57 | 59 | 49 | 56 | 83 | 303 |
N.S. |
1 | 0.00 | 1.37 | 3.04 | 2.11 | 2.19 | 1.81 | 2.07 | 3.07 | 11.22 |
time (sec) |
N/A | 0.000 | 45.735 | 21.652 | 0.083 | 0.073 | 0.075 | 0.117 | 0.346 | 0.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 18 | 15 | 14 | 15 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.00 | 0.78 | 0.65 | 0.61 | 0.65 | 0.65 | 0.70 | 0.74 | 0.70 |
time (sec) |
N/A | 0.186 | 0.005 | 0.285 | 0.037 | 0.061 | 0.060 | 0.112 | 0.354 | 0.567 |
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 | 24 | 35 | 34 | 36 | 52 | 34 | 24 | 70 | 26 |
N.S. |
1 | 0.89 | 1.30 | 1.26 | 1.33 | 1.93 | 1.26 | 0.89 | 2.59 | 0.96 |
time (sec) |
N/A | 0.545 | 0.016 | 0.258 | 0.034 | 0.067 | 0.194 | 0.120 | 0.356 | 0.138 |
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 | 11 | 12 | 12 | 10 | 12 | 15 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.75 | 0.75 | 0.62 | 0.75 | 0.94 | 0.69 |
time (sec) |
N/A | 0.136 | 0.002 | 0.197 | 0.030 | 0.065 | 0.039 | 0.110 | 0.326 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 37 | 40 | 72 | 72 | 27 | 177 | 144 | 32 |
N.S. |
1 | 0.00 | 1.19 | 1.29 | 2.32 | 2.32 | 0.87 | 5.71 | 4.65 | 1.03 |
time (sec) |
N/A | 0.000 | 0.087 | 0.351 | 0.145 | 0.075 | 0.218 | 0.220 | 0.345 | 0.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 45 | 20 | 80 | 80 | 36 | 6825 | 142 | 0 |
N.S. |
1 | 0.00 | 2.05 | 0.91 | 3.64 | 3.64 | 1.64 | 310.23 | 6.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.119 | 0.819 | 0.156 | 0.075 | 0.184 | 0.466 | 0.363 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 23 | 22 | 21 | 17 | 22 | 22 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.28 | 1.22 | 1.17 | 0.94 | 1.22 | 1.22 | 1.39 |
time (sec) |
N/A | 0.000 | 0.123 | 0.194 | 0.158 | 0.068 | 0.147 | 0.147 | 0.381 | 0.626 |
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 | 17 | 26 | 19 | 17 | 18 | 18 | 19 | 18 | 15 | 14 |
N.S. |
1 | 1.53 | 1.12 | 1.00 | 1.06 | 1.06 | 1.12 | 1.06 | 0.88 | 0.82 |
time (sec) |
N/A | 0.172 | 0.006 | 0.151 | 0.038 | 0.065 | 0.055 | 0.110 | 0.305 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 20 | 16 | 13 | 12 | 17 | 14 | 12 | 25 | 14 |
N.S. |
1 | 0.95 | 0.76 | 0.62 | 0.57 | 0.81 | 0.67 | 0.57 | 1.19 | 0.67 |
time (sec) |
N/A | 0.156 | 0.014 | 0.132 | 0.034 | 0.063 | 0.055 | 0.109 | 0.294 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 64 | 143 | 455 | 143 | 146 | 0 | 135 | 29280 |
N.S. |
1 | 0.00 | 1.78 | 3.97 | 12.64 | 3.97 | 4.06 | 0.00 | 3.75 | 813.33 |
time (sec) |
N/A | 0.000 | 0.101 | 11.978 | 23.466 | 0.076 | 1.415 | 0.000 | 0.391 | 31.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 59 | 58 | 52 | 70 | 42 | 56 | 846 | 0 |
N.S. |
1 | 0.00 | 1.79 | 1.76 | 1.58 | 2.12 | 1.27 | 1.70 | 25.64 | 0.00 |
time (sec) |
N/A | 0.000 | 0.103 | 0.034 | 0.097 | 0.108 | 0.481 | 0.361 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 20 | 28 | 24 | 26 | 24 | 18 | 31 |
N.S. |
1 | 0.00 | 0.95 | 0.91 | 1.27 | 1.09 | 1.18 | 1.09 | 0.82 | 1.41 |
time (sec) |
N/A | 0.000 | 0.188 | 1.733 | 0.184 | 0.068 | 0.439 | 0.240 | 0.355 | 0.691 |
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 | 34 | 30 | 27 | 26 | 25 | 24 | 27 | 29 | 26 |
N.S. |
1 | 1.10 | 0.97 | 0.87 | 0.84 | 0.81 | 0.77 | 0.87 | 0.94 | 0.84 |
time (sec) |
N/A | 0.495 | 0.018 | 0.285 | 0.033 | 0.069 | 0.445 | 0.115 | 0.427 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 24 | 20 | 19 | 19 | 22 | 19 | 24 | 23 |
N.S. |
1 | 0.00 | 1.14 | 0.95 | 0.90 | 0.90 | 1.05 | 0.90 | 1.14 | 1.10 |
time (sec) |
N/A | 0.000 | 0.136 | 0.216 | 0.077 | 0.072 | 0.099 | 0.124 | 0.305 | 0.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F(-1) | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 0 | 198 | 460 | 223 | 81 | 634 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 8.25 | 19.17 | 9.29 | 3.38 | 26.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.080 | 0.086 | 69.484 | 0.141 | 160.989 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 33 | 29 | 29 | 32 | 34 | 101 | 34 |
N.S. |
1 | 0.00 | 1.11 | 1.22 | 1.07 | 1.07 | 1.19 | 1.26 | 3.74 | 1.26 |
time (sec) |
N/A | 0.000 | 0.049 | 6.183 | 0.096 | 0.063 | 0.486 | 0.272 | 200.029 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 33 | 32 | 26 | 0 | 34 | 27 | 67 | 43 | 38 |
N.S. |
1 | 1.22 | 1.19 | 0.96 | 0.00 | 1.26 | 1.00 | 2.48 | 1.59 | 1.41 |
time (sec) |
N/A | 0.851 | 0.025 | 19.698 | 0.000 | 0.072 | 0.146 | 0.120 | 0.207 | 0.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 23 | 23 | 24 | 23 | 23 | 19 | 23 | 23 | 23 |
N.S. |
1 | 1.05 | 1.05 | 1.09 | 1.05 | 1.05 | 0.86 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 1.054 | 0.104 | 1.071 | 0.075 | 0.068 | 0.090 | 0.114 | 0.196 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 69 | 0 | 144 | 141 | 82 | 168 | 0 | 0 |
N.S. |
1 | 0.00 | 1.82 | 0.00 | 3.79 | 3.71 | 2.16 | 4.42 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.167 | 180.000 | 0.219 | 0.089 | 0.554 | 1.392 | 0.833 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 24 | 68 | 23 | 22 | 33 | 648 | 83 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 2.72 | 0.92 | 0.88 | 1.32 | 25.92 | 3.32 |
time (sec) |
N/A | 0.000 | 0.062 | 1.892 | 0.443 | 0.077 | 0.749 | 0.981 | 0.327 | 0.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 27 | 34 | 25 | 22 | 22 | 24 | 22 | 27 | 24 |
N.S. |
1 | 2.25 | 2.83 | 2.08 | 1.83 | 1.83 | 2.00 | 1.83 | 2.25 | 2.00 |
time (sec) |
N/A | 0.206 | 0.023 | 0.156 | 0.032 | 0.066 | 0.055 | 0.107 | 0.211 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | B | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 40 | 2581 | 41 | 122 | 0 | 0 | 140 | 119 |
N.S. |
1 | 0.00 | 1.29 | 83.26 | 1.32 | 3.94 | 0.00 | 0.00 | 4.52 | 3.84 |
time (sec) |
N/A | 0.000 | 0.145 | 0.201 | 64.107 | 0.077 | 0.000 | 0.000 | 0.283 | 2.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 23 | 16 | 17 | 31 | 17 | 14 | 20 | 18 | 15 |
N.S. |
1 | 1.28 | 0.89 | 0.94 | 1.72 | 0.94 | 0.78 | 1.11 | 1.00 | 0.83 |
time (sec) |
N/A | 0.243 | 0.052 | 0.201 | 0.055 | 0.075 | 0.179 | 0.112 | 0.250 | 0.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 105 | 57 | 64 | 58 | 58 | 73 | 63 | 60 | 53 |
N.S. |
1 | 4.20 | 2.28 | 2.56 | 2.32 | 2.32 | 2.92 | 2.52 | 2.40 | 2.12 |
time (sec) |
N/A | 0.488 | 0.249 | 8.738 | 0.033 | 0.074 | 0.206 | 0.114 | 0.215 | 0.714 |
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 | 25 | 19 | 19 | 16 | 16 | 19 | 16 | 22 | 29 |
N.S. |
1 | 1.39 | 1.06 | 1.06 | 0.89 | 0.89 | 1.06 | 0.89 | 1.22 | 1.61 |
time (sec) |
N/A | 0.314 | 0.004 | 0.251 | 0.039 | 0.071 | 0.214 | 0.110 | 0.205 | 0.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 19 | 19 | 16 | 56 | 19 | 0 | 21 | 17 |
N.S. |
1 | 0.00 | 1.06 | 1.06 | 0.89 | 3.11 | 1.06 | 0.00 | 1.17 | 0.94 |
time (sec) |
N/A | 0.000 | 0.837 | 2.014 | 0.171 | 0.075 | 0.546 | 0.000 | 0.502 | 0.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 26 | 22 | 20 | 22 | 40 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.30 | 1.10 | 1.00 | 1.10 | 2.00 | 1.10 |
time (sec) |
N/A | 0.592 | 0.020 | 1.006 | 0.182 | 0.061 | 0.170 | 0.114 | 0.228 | 1.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 61 | 47 | 58 | 36 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.65 | 1.27 | 1.57 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.302 | 0.065 | 0.330 | 0.075 | 0.000 | 0.000 | 0.919 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 32 | 20 | 15 | 0 | 15 | 14 | 0 | 31 | 15 |
N.S. |
1 | 1.33 | 0.83 | 0.62 | 0.00 | 0.62 | 0.58 | 0.00 | 1.29 | 0.62 |
time (sec) |
N/A | 0.252 | 0.039 | 0.173 | 0.000 | 0.066 | 0.216 | 0.000 | 0.215 | 0.908 |