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 | 56 | 55 | 85 | 74 | 73 | 73 | 85 | 73 | 73 | 73 |
N.S. |
1 | 0.98 | 1.52 | 1.32 | 1.30 | 1.30 | 1.52 | 1.30 | 1.30 | 1.30 |
time (sec) |
N/A | 0.180 | 0.002 | 0.516 | 0.029 | 0.066 | 0.022 | 0.123 | 0.146 | 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 | 45 | 45 | 60 | 51 | 50 | 50 | 58 | 50 | 51 | 50 |
N.S. |
1 | 1.00 | 1.33 | 1.13 | 1.11 | 1.11 | 1.29 | 1.11 | 1.13 | 1.11 |
time (sec) |
N/A | 0.172 | 0.002 | 0.563 | 0.032 | 0.065 | 0.023 | 0.126 | 0.148 | 0.026 |
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 | 32 | 32 | 27 | 26 | 26 | 29 | 26 | 29 | 26 |
N.S. |
1 | 1.03 | 1.03 | 0.87 | 0.84 | 0.84 | 0.94 | 0.84 | 0.94 | 0.84 |
time (sec) |
N/A | 0.159 | 0.001 | 0.118 | 0.028 | 0.061 | 0.017 | 0.124 | 0.149 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 12 | 11 | 10 | 10 | 8 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 0.86 | 0.79 | 0.71 | 0.71 | 0.57 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.131 | 0.000 | 0.023 | 0.036 | 0.035 | 0.017 | 0.119 | 0.147 | 0.020 |
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 | 42 | 42 | 42 | 32 | 31 | 98 | 124 | 31 | 34 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.74 | 2.33 | 2.95 | 0.74 | 0.81 | 0.76 |
time (sec) |
N/A | 0.159 | 0.015 | 0.566 | 0.117 | 0.079 | 0.121 | 0.133 | 0.146 | 0.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 49 | 48 | 140 | 90 | 47 | 68 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 2.46 | 1.58 | 0.82 | 1.19 | 0.77 |
time (sec) |
N/A | 0.164 | 0.019 | 0.458 | 0.111 | 0.074 | 0.143 | 0.124 | 0.161 | 0.059 |
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 | 75 | 82 | 71 | 70 | 74 | 212 | 124 | 60 | 119 | 64 |
N.S. |
1 | 1.09 | 0.95 | 0.93 | 0.99 | 2.83 | 1.65 | 0.80 | 1.59 | 0.85 |
time (sec) |
N/A | 0.181 | 0.034 | 0.457 | 0.112 | 0.078 | 0.213 | 0.126 | 0.157 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 90 | 87 | 70 | 61 | 176 | 119 | 76 | 111 | 54 |
N.S. |
1 | 1.03 | 1.00 | 0.80 | 0.70 | 2.02 | 1.37 | 0.87 | 1.28 | 0.62 |
time (sec) |
N/A | 0.192 | 0.217 | 0.491 | 0.036 | 0.085 | 0.389 | 0.129 | 0.183 | 0.585 |
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 | 67 | 68 | 68 | 54 | 45 | 128 | 90 | 55 | 73 | 52 |
N.S. |
1 | 1.01 | 1.01 | 0.81 | 0.67 | 1.91 | 1.34 | 0.82 | 1.09 | 0.78 |
time (sec) |
N/A | 0.172 | 0.130 | 0.470 | 0.037 | 0.083 | 0.320 | 0.125 | 0.167 | 0.524 |
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 | 46 | 37 | 29 | 92 | 71 | 39 | 38 | 36 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.67 | 2.14 | 1.65 | 0.91 | 0.88 | 0.84 |
time (sec) |
N/A | 0.167 | 0.121 | 0.484 | 0.034 | 0.081 | 0.298 | 0.122 | 0.154 | 0.532 |
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 | 28 | 28 | 27 | 26 | 31 | 35 | 46 | 23 | 47 | 24 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 1.11 | 1.25 | 1.64 | 0.82 | 1.68 | 0.86 |
time (sec) |
N/A | 0.148 | 0.192 | 0.591 | 0.039 | 0.072 | 2.006 | 0.130 | 0.170 | 0.343 |
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 | 51 | 51 | 43 | 40 | 48 | 62 | 146 | 37 | 96 | 41 |
N.S. |
1 | 1.00 | 0.84 | 0.78 | 0.94 | 1.22 | 2.86 | 0.73 | 1.88 | 0.80 |
time (sec) |
N/A | 0.162 | 0.313 | 0.599 | 0.029 | 0.076 | 3.759 | 0.131 | 0.161 | 0.363 |
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 | 71 | 78 | 55 | 52 | 64 | 85 | 486 | 52 | 141 | 59 |
N.S. |
1 | 1.10 | 0.77 | 0.73 | 0.90 | 1.20 | 6.85 | 0.73 | 1.99 | 0.83 |
time (sec) |
N/A | 0.171 | 0.405 | 0.587 | 0.030 | 0.081 | 6.648 | 0.126 | 0.252 | 0.399 |
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 | 91 | 105 | 67 | 64 | 80 | 108 | 1360 | 67 | 184 | 74 |
N.S. |
1 | 1.15 | 0.74 | 0.70 | 0.88 | 1.19 | 14.95 | 0.74 | 2.02 | 0.81 |
time (sec) |
N/A | 0.185 | 0.496 | 0.472 | 0.031 | 0.089 | 11.765 | 0.126 | 5.256 | 0.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 310 | 105 | 0 | 0 | 0 | 332 | 0 | 95 | 54 |
N.S. |
1 | 1.01 | 0.34 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 | 0.31 | 0.18 |
time (sec) |
N/A | 0.313 | 6.168 | 0.000 | 0.000 | 0.000 | 1.652 | 0.000 | 0.232 | 0.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 288 | 83 | 0 | 0 | 0 | 54 | 0 | 57 | 54 |
N.S. |
1 | 1.00 | 0.29 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 | 0.20 | 0.19 |
time (sec) |
N/A | 0.278 | 4.601 | 0.000 | 0.000 | 0.000 | 0.836 | 0.000 | 0.202 | 0.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 267 | 68 | 0 | 0 | 0 | 53 | 0 | 25 | 54 |
N.S. |
1 | 1.00 | 0.25 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 | 0.09 | 0.20 |
time (sec) |
N/A | 0.258 | 8.093 | 0.000 | 0.000 | 0.000 | 0.758 | 0.000 | 0.176 | 0.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 68 | 0 | 0 | 0 | 54 | 0 | 67 | 54 |
N.S. |
1 | 1.00 | 0.24 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 | 0.24 | 0.19 |
time (sec) |
N/A | 0.269 | 10.032 | 0.000 | 0.000 | 0.000 | 2.234 | 0.000 | 0.193 | 0.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 573 | 614 | 83 | 0 | 0 | 0 | 54 | 0 | 57 | 54 |
N.S. |
1 | 1.07 | 0.14 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.10 | 0.09 |
time (sec) |
N/A | 0.501 | 5.355 | 0.000 | 0.000 | 0.000 | 0.921 | 0.000 | 0.204 | 0.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 551 | 595 | 68 | 0 | 0 | 0 | 53 | 0 | 29 | 54 |
N.S. |
1 | 1.08 | 0.12 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 | 0.05 | 0.10 |
time (sec) |
N/A | 0.489 | 8.422 | 0.000 | 0.000 | 0.000 | 0.754 | 0.000 | 0.177 | 0.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 566 | 609 | 69 | 0 | 0 | 0 | 54 | 0 | 67 | 54 |
N.S. |
1 | 1.08 | 0.12 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 | 0.12 | 0.10 |
time (sec) |
N/A | 0.516 | 9.707 | 0.000 | 0.000 | 0.000 | 2.009 | 0.000 | 0.178 | 0.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 98 | 0 | 0 | 0 | 61 | 0 | 213 | 65 |
N.S. |
1 | 1.00 | 1.40 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 3.04 | 0.93 |
time (sec) |
N/A | 0.180 | 0.108 | 0.000 | 0.000 | 0.000 | 2.384 | 0.000 | 0.165 | 1.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 100 | 109 | 108 | 108 | 122 | 111 | 111 | 103 |
N.S. |
1 | 1.00 | 1.15 | 1.25 | 1.24 | 1.24 | 1.40 | 1.28 | 1.28 | 1.18 |
time (sec) |
N/A | 0.263 | 0.023 | 0.434 | 0.032 | 0.067 | 0.025 | 0.118 | 0.155 | 0.315 |
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 | 67 | 67 | 69 | 75 | 74 | 74 | 83 | 76 | 77 | 74 |
N.S. |
1 | 1.00 | 1.03 | 1.12 | 1.10 | 1.10 | 1.24 | 1.13 | 1.15 | 1.10 |
time (sec) |
N/A | 0.233 | 0.015 | 0.562 | 0.027 | 0.061 | 0.023 | 0.122 | 0.155 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 39 | 38 | 38 | 42 | 40 | 43 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.91 | 0.87 | 0.93 | 0.85 |
time (sec) |
N/A | 0.209 | 0.006 | 0.174 | 0.033 | 0.063 | 0.019 | 0.123 | 0.162 | 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 | 20 | 20 | 20 | 17 | 16 | 16 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.85 | 0.80 |
time (sec) |
N/A | 0.152 | 0.000 | 0.031 | 0.028 | 0.061 | 0.015 | 0.118 | 0.157 | 0.027 |
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 | 55 | 55 | 56 | 47 | 48 | 125 | 156 | 48 | 61 | 56 |
N.S. |
1 | 1.00 | 1.02 | 0.85 | 0.87 | 2.27 | 2.84 | 0.87 | 1.11 | 1.02 |
time (sec) |
N/A | 0.225 | 0.028 | 0.520 | 0.112 | 0.075 | 0.233 | 0.123 | 0.159 | 0.317 |
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 | 69 | 68 | 65 | 62 | 195 | 116 | 60 | 120 | 60 |
N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.90 | 2.83 | 1.68 | 0.87 | 1.74 | 0.87 |
time (sec) |
N/A | 0.206 | 0.042 | 0.467 | 0.112 | 0.078 | 0.319 | 0.127 | 0.160 | 0.089 |
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 | 98 | 98 | 90 | 83 | 98 | 314 | 156 | 84 | 212 | 88 |
N.S. |
1 | 1.00 | 0.92 | 0.85 | 1.00 | 3.20 | 1.59 | 0.86 | 2.16 | 0.90 |
time (sec) |
N/A | 0.226 | 0.050 | 0.469 | 0.120 | 0.079 | 0.547 | 0.124 | 0.164 | 0.352 |
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 | 126 | 123 | 112 | 100 | 133 | 430 | 196 | 109 | 304 | 116 |
N.S. |
1 | 0.98 | 0.89 | 0.79 | 1.06 | 3.41 | 1.56 | 0.87 | 2.41 | 0.92 |
time (sec) |
N/A | 0.241 | 0.064 | 0.576 | 0.114 | 0.082 | 0.890 | 0.122 | 0.159 | 0.386 |
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 | 137 | 123 | 117 | 112 | 131 | 259 | 209 | 125 | 194 | 0 |
N.S. |
1 | 0.90 | 0.85 | 0.82 | 0.96 | 1.89 | 1.53 | 0.91 | 1.42 | 0.00 |
time (sec) |
N/A | 0.249 | 0.395 | 0.527 | 0.036 | 0.088 | 0.364 | 0.133 | 0.168 | 0.000 |
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 | 106 | 101 | 87 | 76 | 96 | 187 | 124 | 84 | 136 | 0 |
N.S. |
1 | 0.95 | 0.82 | 0.72 | 0.91 | 1.76 | 1.17 | 0.79 | 1.28 | 0.00 |
time (sec) |
N/A | 0.231 | 0.228 | 0.503 | 0.035 | 0.087 | 0.314 | 0.130 | 0.171 | 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 | 74 | 77 | 70 | 53 | 61 | 121 | 92 | 56 | 81 | 107 |
N.S. |
1 | 1.04 | 0.95 | 0.72 | 0.82 | 1.64 | 1.24 | 0.76 | 1.09 | 1.45 |
time (sec) |
N/A | 0.218 | 0.325 | 0.492 | 0.030 | 0.083 | 0.276 | 0.128 | 0.158 | 0.647 |
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 | 61 | 61 | 62 | 70 | 61 | 179 | 87 | 61 | 133 | 68 |
N.S. |
1 | 1.00 | 1.02 | 1.15 | 1.00 | 2.93 | 1.43 | 1.00 | 2.18 | 1.11 |
time (sec) |
N/A | 0.210 | 0.351 | 0.518 | 0.034 | 0.083 | 2.737 | 0.133 | 0.160 | 0.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 50 | 47 | 83 | 68 | 194 | 48 | 146 | 59 |
N.S. |
1 | 1.00 | 0.75 | 0.70 | 1.24 | 1.01 | 2.90 | 0.72 | 2.18 | 0.88 |
time (sec) |
N/A | 0.217 | 0.441 | 0.494 | 0.033 | 0.078 | 5.102 | 0.131 | 0.160 | 0.389 |
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 | 97 | 94 | 71 | 72 | 118 | 103 | 638 | 80 | 226 | 93 |
N.S. |
1 | 0.97 | 0.73 | 0.74 | 1.22 | 1.06 | 6.58 | 0.82 | 2.33 | 0.96 |
time (sec) |
N/A | 0.229 | 0.525 | 0.500 | 0.027 | 0.086 | 11.556 | 0.132 | 0.167 | 0.442 |
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 | 127 | 121 | 92 | 96 | 153 | 137 | 1880 | 112 | 303 | 115 |
N.S. |
1 | 0.95 | 0.72 | 0.76 | 1.20 | 1.08 | 14.80 | 0.88 | 2.39 | 0.91 |
time (sec) |
N/A | 0.246 | 0.633 | 0.506 | 0.038 | 0.085 | 25.958 | 0.134 | 0.166 | 0.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 321 | 81 | 0 | 0 | 0 | 87 | 0 | 114 | 0 |
N.S. |
1 | 0.98 | 0.25 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.362 | 6.045 | 0.000 | 0.000 | 0.000 | 1.092 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 300 | 81 | 0 | 0 | 0 | 83 | 0 | 42 | 0 |
N.S. |
1 | 1.01 | 0.27 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.330 | 9.512 | 0.000 | 0.000 | 0.000 | 0.969 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 296 | 78 | 0 | 0 | 0 | 85 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 0.26 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.321 | 10.048 | 0.000 | 0.000 | 0.000 | 2.682 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 631 | 647 | 81 | 0 | 0 | 0 | 87 | 0 | 114 | 0 |
N.S. |
1 | 1.03 | 0.13 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.552 | 7.039 | 0.000 | 0.000 | 0.000 | 1.097 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 602 | 628 | 81 | 0 | 0 | 0 | 83 | 0 | 46 | 0 |
N.S. |
1 | 1.04 | 0.13 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.545 | 9.416 | 0.000 | 0.000 | 0.000 | 0.938 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 596 | 623 | 79 | 0 | 0 | 0 | 85 | 0 | 103 | 0 |
N.S. |
1 | 1.05 | 0.13 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.555 | 10.047 | 0.000 | 0.000 | 0.000 | 2.506 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 633 | 652 | 111 | 0 | 0 | 0 | 105 | 0 | 163 | 0 |
N.S. |
1 | 1.03 | 0.18 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.601 | 10.076 | 0.000 | 0.000 | 0.000 | 5.359 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 121 | 114 | 0 | 0 | 0 | 90 | 0 | 778 | 0 |
N.S. |
1 | 1.11 | 1.05 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 | 7.14 | 0.00 |
time (sec) |
N/A | 0.263 | 0.185 | 0.000 | 0.000 | 0.000 | 4.393 | 0.000 | 0.173 | 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 | 133 | 133 | 121 | 144 | 142 | 142 | 158 | 149 | 149 | 149 |
N.S. |
1 | 1.00 | 0.91 | 1.08 | 1.07 | 1.07 | 1.19 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.366 | 0.055 | 0.372 | 0.035 | 0.062 | 0.027 | 0.126 | 0.168 | 0.690 |
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 | 99 | 99 | 88 | 99 | 98 | 98 | 107 | 102 | 103 | 105 |
N.S. |
1 | 1.00 | 0.89 | 1.00 | 0.99 | 0.99 | 1.08 | 1.03 | 1.04 | 1.06 |
time (sec) |
N/A | 0.300 | 0.030 | 0.370 | 0.030 | 0.061 | 0.024 | 0.118 | 0.169 | 0.505 |
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 | 60 | 60 | 60 | 51 | 50 | 50 | 56 | 54 | 57 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.93 | 0.90 | 0.95 | 0.90 |
time (sec) |
N/A | 0.221 | 0.006 | 0.106 | 0.036 | 0.063 | 0.018 | 0.125 | 0.158 | 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 | 28 | 28 | 28 | 23 | 22 | 22 | 22 | 22 | 23 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.79 | 0.79 | 0.79 | 0.79 | 0.82 | 0.79 |
time (sec) |
N/A | 0.156 | 0.000 | 0.031 | 0.038 | 0.060 | 0.016 | 0.122 | 0.161 | 0.383 |
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 | 73 | 73 | 68 | 65 | 64 | 157 | 219 | 66 | 79 | 79 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.88 | 2.15 | 3.00 | 0.90 | 1.08 | 1.08 |
time (sec) |
N/A | 0.239 | 0.035 | 0.446 | 0.116 | 0.077 | 0.400 | 0.118 | 0.168 | 0.612 |
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 | 93 | 99 | 83 | 88 | 89 | 257 | 233 | 88 | 156 | 110 |
N.S. |
1 | 1.06 | 0.89 | 0.95 | 0.96 | 2.76 | 2.51 | 0.95 | 1.68 | 1.18 |
time (sec) |
N/A | 0.242 | 0.068 | 0.448 | 0.120 | 0.081 | 0.902 | 0.121 | 0.165 | 0.566 |
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 | 116 | 127 | 104 | 98 | 122 | 346 | 184 | 106 | 222 | 163 |
N.S. |
1 | 1.09 | 0.90 | 0.84 | 1.05 | 2.98 | 1.59 | 0.91 | 1.91 | 1.41 |
time (sec) |
N/A | 0.252 | 0.078 | 0.449 | 0.113 | 0.082 | 3.064 | 0.117 | 0.162 | 0.695 |
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 | 20 | 22 | 20 | 19 | 18 | 24 | 15 | 25 | 35 | 20 |
N.S. |
1 | 1.10 | 1.00 | 0.95 | 0.90 | 1.20 | 0.75 | 1.25 | 1.75 | 1.00 |
time (sec) |
N/A | 0.185 | 0.007 | 0.508 | 0.035 | 0.063 | 0.037 | 0.122 | 0.160 | 0.037 |
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 | 163 | 159 | 141 | 180 | 165 | 327 | 303 | 180 | 261 | 0 |
N.S. |
1 | 0.98 | 0.87 | 1.10 | 1.01 | 2.01 | 1.86 | 1.10 | 1.60 | 0.00 |
time (sec) |
N/A | 0.337 | 0.603 | 0.523 | 0.039 | 0.102 | 0.454 | 0.134 | 0.174 | 0.000 |
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 | 132 | 137 | 108 | 148 | 130 | 231 | 160 | 121 | 183 | 0 |
N.S. |
1 | 1.04 | 0.82 | 1.12 | 0.98 | 1.75 | 1.21 | 0.92 | 1.39 | 0.00 |
time (sec) |
N/A | 0.321 | 0.471 | 0.601 | 0.038 | 0.090 | 0.424 | 0.124 | 0.174 | 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 | 100 | 113 | 78 | 112 | 95 | 147 | 116 | 77 | 109 | 149 |
N.S. |
1 | 1.13 | 0.78 | 1.12 | 0.95 | 1.47 | 1.16 | 0.77 | 1.09 | 1.49 |
time (sec) |
N/A | 0.305 | 0.379 | 0.605 | 0.036 | 0.089 | 0.366 | 0.136 | 0.160 | 0.959 |
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 | 85 | 90 | 75 | 104 | 94 | 210 | 131 | 88 | 159 | 91 |
N.S. |
1 | 1.06 | 0.88 | 1.22 | 1.11 | 2.47 | 1.54 | 1.04 | 1.87 | 1.07 |
time (sec) |
N/A | 0.239 | 0.421 | 0.519 | 0.037 | 0.087 | 3.905 | 0.133 | 0.160 | 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 | 85 | 85 | 66 | 68 | 117 | 91 | 289 | 72 | 176 | 89 |
N.S. |
1 | 1.00 | 0.78 | 0.80 | 1.38 | 1.07 | 3.40 | 0.85 | 2.07 | 1.05 |
time (sec) |
N/A | 0.231 | 0.582 | 0.513 | 0.037 | 0.080 | 6.746 | 0.135 | 0.168 | 1.050 |
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 | 115 | 123 | 89 | 93 | 152 | 126 | 777 | 103 | 258 | 125 |
N.S. |
1 | 1.07 | 0.77 | 0.81 | 1.32 | 1.10 | 6.76 | 0.90 | 2.24 | 1.09 |
time (sec) |
N/A | 0.257 | 0.753 | 0.509 | 0.037 | 0.086 | 13.649 | 0.138 | 0.171 | 1.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 150 | 110 | 117 | 187 | 160 | 2064 | 138 | 335 | 178 |
N.S. |
1 | 1.03 | 0.76 | 0.81 | 1.29 | 1.10 | 14.23 | 0.95 | 2.31 | 1.23 |
time (sec) |
N/A | 0.284 | 1.257 | 0.511 | 0.040 | 0.101 | 28.819 | 0.134 | 0.180 | 1.062 |
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 | 23 | 29 | 18 | 15 | 22 | 14 | 22 | 17 | 13 | 14 |
N.S. |
1 | 1.26 | 0.78 | 0.65 | 0.96 | 0.61 | 0.96 | 0.74 | 0.57 | 0.61 |
time (sec) |
N/A | 0.180 | 0.049 | 0.435 | 0.034 | 0.069 | 0.102 | 0.126 | 0.158 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 357 | 96 | 0 | 0 | 0 | 321 | 0 | 174 | 0 |
N.S. |
1 | 1.01 | 0.27 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.437 | 8.168 | 0.000 | 0.000 | 0.000 | 1.604 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 335 | 96 | 0 | 0 | 0 | 272 | 0 | 59 | 0 |
N.S. |
1 | 1.04 | 0.30 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.420 | 5.163 | 0.000 | 0.000 | 0.000 | 1.433 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 328 | 93 | 0 | 0 | 0 | 134 | 0 | 139 | 0 |
N.S. |
1 | 1.02 | 0.29 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.351 | 10.061 | 0.000 | 0.000 | 0.000 | 4.030 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 357 | 124 | 0 | 0 | 0 | 201 | 0 | 219 | 0 |
N.S. |
1 | 1.03 | 0.36 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.385 | 10.093 | 0.000 | 0.000 | 0.000 | 8.812 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 384 | 150 | 0 | 0 | 0 | 267 | 0 | 299 | 0 |
N.S. |
1 | 1.02 | 0.40 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.390 | 10.119 | 0.000 | 0.000 | 0.000 | 19.518 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 657 | 683 | 96 | 0 | 0 | 0 | 156 | 0 | 174 | 0 |
N.S. |
1 | 1.04 | 0.15 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.660 | 8.157 | 0.000 | 0.000 | 0.000 | 1.358 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 628 | 663 | 95 | 0 | 0 | 0 | 272 | 0 | 63 | 0 |
N.S. |
1 | 1.06 | 0.15 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.626 | 5.059 | 0.000 | 0.000 | 0.000 | 1.396 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 621 | 658 | 98 | 0 | 0 | 0 | 134 | 0 | 139 | 0 |
N.S. |
1 | 1.06 | 0.16 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.588 | 10.062 | 0.000 | 0.000 | 0.000 | 3.678 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 651 | 683 | 126 | 0 | 0 | 0 | 201 | 0 | 219 | 0 |
N.S. |
1 | 1.05 | 0.19 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.617 | 10.083 | 0.000 | 0.000 | 0.000 | 7.229 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 682 | 710 | 150 | 0 | 0 | 0 | 267 | 0 | 299 | 0 |
N.S. |
1 | 1.04 | 0.22 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.625 | 10.102 | 0.000 | 0.000 | 0.000 | 13.954 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 171 | 142 | 0 | 0 | 0 | 427 | 0 | 1220 | 0 |
N.S. |
1 | 1.22 | 1.01 | 0.00 | 0.00 | 0.00 | 3.05 | 0.00 | 8.71 | 0.00 |
time (sec) |
N/A | 0.417 | 0.342 | 0.000 | 0.000 | 0.000 | 5.616 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 136 | 166 | 329 | 252 | 399 | 5005 | 556 | 398 | 0 |
N.S. |
1 | 0.94 | 1.15 | 2.28 | 1.75 | 2.77 | 34.76 | 3.86 | 2.76 | 0.00 |
time (sec) |
N/A | 0.398 | 0.314 | 0.535 | 0.049 | 0.083 | 24.546 | 0.149 | 0.167 | 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 | 25 | 33 | 25 | 21 | 20 | 20 | 20 | 20 | 21 | 20 |
N.S. |
1 | 1.32 | 1.00 | 0.84 | 0.80 | 0.80 | 0.80 | 0.80 | 0.84 | 0.80 |
time (sec) |
N/A | 0.179 | 0.034 | 0.648 | 0.118 | 0.067 | 0.039 | 0.122 | 0.156 | 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 | 30 | 30 | 30 | 25 | 24 | 24 | 22 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.73 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.185 | 0.006 | 0.505 | 0.111 | 0.070 | 0.044 | 0.126 | 0.152 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 61 | 34 | 33 | 50 | 50 | 48 | 28 | 47 | 48 |
N.S. |
1 | 1.15 | 0.64 | 0.62 | 0.94 | 0.94 | 0.91 | 0.53 | 0.89 | 0.91 |
time (sec) |
N/A | 0.351 | 0.011 | 0.469 | 0.033 | 0.063 | 0.063 | 0.125 | 0.166 | 0.041 |
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 | 53 | 61 | 34 | 33 | 50 | 50 | 48 | 28 | 47 | 48 |
N.S. |
1 | 1.15 | 0.64 | 0.62 | 0.94 | 0.94 | 0.91 | 0.53 | 0.89 | 0.91 |
time (sec) |
N/A | 0.319 | 0.007 | 0.411 | 0.030 | 0.061 | 0.060 | 0.121 | 0.153 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 61 | 34 | 33 | 50 | 50 | 48 | 28 | 47 | 48 |
N.S. |
1 | 1.15 | 0.64 | 0.62 | 0.94 | 0.94 | 0.91 | 0.53 | 0.89 | 0.91 |
time (sec) |
N/A | 0.348 | 0.005 | 0.406 | 0.034 | 0.062 | 0.056 | 0.124 | 0.162 | 0.027 |
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 | 94 | 94 | 94 | 95 | 96 | 96 | 107 | 98 | 57 | 88 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.02 | 1.02 | 1.14 | 1.04 | 0.61 | 0.94 |
time (sec) |
N/A | 0.250 | 0.015 | 0.558 | 0.035 | 0.061 | 0.033 | 0.116 | 0.154 | 0.051 |
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 | 70 | 70 | 70 | 71 | 70 | 70 | 76 | 73 | 46 | 65 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.00 | 1.00 | 1.09 | 1.04 | 0.66 | 0.93 |
time (sec) |
N/A | 0.219 | 0.010 | 0.457 | 0.037 | 0.059 | 0.027 | 0.120 | 0.168 | 0.301 |
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 | 50 | 50 | 49 | 48 | 48 | 53 | 50 | 35 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.06 | 1.00 | 0.70 | 0.96 |
time (sec) |
N/A | 0.194 | 0.006 | 0.381 | 0.029 | 0.060 | 0.020 | 0.122 | 0.158 | 0.048 |
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 | 28 | 28 | 28 | 25 | 24 | 24 | 26 | 26 | 24 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 0.93 | 0.93 | 0.86 | 0.89 |
time (sec) |
N/A | 0.170 | 0.004 | 0.121 | 0.038 | 0.060 | 0.018 | 0.122 | 0.155 | 0.297 |
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 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.148 | 0.000 | 0.046 | 0.026 | 0.061 | 0.017 | 0.122 | 0.156 | 0.022 |
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 | 40 | 34 | 34 | 99 | 82 | 34 | 1 | 31 |
N.S. |
1 | 1.00 | 1.03 | 0.87 | 0.87 | 2.54 | 2.10 | 0.87 | 0.03 | 0.79 |
time (sec) |
N/A | 0.158 | 0.023 | 0.467 | 0.110 | 0.075 | 0.135 | 0.123 | 0.160 | 0.360 |
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 | 63 | 63 | 63 | 57 | 57 | 182 | 112 | 57 | 23 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 2.89 | 1.78 | 0.90 | 0.37 | 0.81 |
time (sec) |
N/A | 0.169 | 0.034 | 0.464 | 0.122 | 0.078 | 0.202 | 0.123 | 0.163 | 0.356 |
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 | 92 | 92 | 84 | 77 | 92 | 300 | 150 | 78 | 61 | 82 |
N.S. |
1 | 1.00 | 0.91 | 0.84 | 1.00 | 3.26 | 1.63 | 0.85 | 0.66 | 0.89 |
time (sec) |
N/A | 0.186 | 0.050 | 0.478 | 0.117 | 0.079 | 0.280 | 0.118 | 0.158 | 0.373 |
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 | 120 | 117 | 105 | 94 | 127 | 416 | 189 | 103 | 113 | 110 |
N.S. |
1 | 0.98 | 0.88 | 0.78 | 1.06 | 3.47 | 1.58 | 0.86 | 0.94 | 0.92 |
time (sec) |
N/A | 0.210 | 0.064 | 0.477 | 0.132 | 0.082 | 0.341 | 0.114 | 0.155 | 0.405 |
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 | 149 | 127 | 123 | 106 | 151 | 257 | 279 | 134 | 99 | 0 |
N.S. |
1 | 0.85 | 0.83 | 0.71 | 1.01 | 1.72 | 1.87 | 0.90 | 0.66 | 0.00 |
time (sec) |
N/A | 0.213 | 0.206 | 0.562 | 0.048 | 0.098 | 0.392 | 0.140 | 0.170 | 0.000 |
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 | 118 | 105 | 99 | 88 | 116 | 207 | 175 | 102 | 80 | 0 |
N.S. |
1 | 0.89 | 0.84 | 0.75 | 0.98 | 1.75 | 1.48 | 0.86 | 0.68 | 0.00 |
time (sec) |
N/A | 0.200 | 0.140 | 0.536 | 0.036 | 0.090 | 0.337 | 0.125 | 0.160 | 0.000 |
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 | 87 | 83 | 74 | 63 | 81 | 155 | 104 | 69 | 61 | 0 |
N.S. |
1 | 0.95 | 0.85 | 0.72 | 0.93 | 1.78 | 1.20 | 0.79 | 0.70 | 0.00 |
time (sec) |
N/A | 0.188 | 0.093 | 0.569 | 0.040 | 0.083 | 0.264 | 0.130 | 0.159 | 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 | 58 | 58 | 65 | 48 | 47 | 110 | 82 | 48 | 40 | 86 |
N.S. |
1 | 1.00 | 1.12 | 0.83 | 0.81 | 1.90 | 1.41 | 0.83 | 0.69 | 1.48 |
time (sec) |
N/A | 0.171 | 0.153 | 0.535 | 0.037 | 0.087 | 0.230 | 0.132 | 0.156 | 0.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 58 | 51 | 46 | 168 | 60 | 51 | 25 | 53 |
N.S. |
1 | 1.00 | 1.07 | 0.94 | 0.85 | 3.11 | 1.11 | 0.94 | 0.46 | 0.98 |
time (sec) |
N/A | 0.172 | 0.086 | 0.513 | 0.044 | 0.083 | 2.020 | 0.135 | 0.160 | 0.605 |
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 | 47 | 37 | 34 | 68 | 54 | 144 | 40 | 39 | 33 |
N.S. |
1 | 0.77 | 0.61 | 0.56 | 1.11 | 0.89 | 2.36 | 0.66 | 0.64 | 0.54 |
time (sec) |
N/A | 0.157 | 0.081 | 0.516 | 0.039 | 0.079 | 3.869 | 0.132 | 0.166 | 0.414 |
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 | 91 | 88 | 60 | 52 | 103 | 87 | 566 | 72 | 84 | 87 |
N.S. |
1 | 0.97 | 0.66 | 0.57 | 1.13 | 0.96 | 6.22 | 0.79 | 0.92 | 0.96 |
time (sec) |
N/A | 0.186 | 0.128 | 0.506 | 0.030 | 0.081 | 9.890 | 0.139 | 0.158 | 0.487 |
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 | 121 | 115 | 80 | 71 | 138 | 121 | 1787 | 104 | 127 | 105 |
N.S. |
1 | 0.95 | 0.66 | 0.59 | 1.14 | 1.00 | 14.77 | 0.86 | 1.05 | 0.87 |
time (sec) |
N/A | 0.204 | 0.135 | 0.552 | 0.041 | 0.095 | 24.521 | 0.133 | 0.159 | 0.486 |
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 | 13 | 13 | 13 | 14 | 19 | 19 | 24 | 27 | 18 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.46 | 1.46 | 1.85 | 2.08 | 1.38 | 1.00 |
time (sec) |
N/A | 0.138 | 0.072 | 0.597 | 0.081 | 0.072 | 1.518 | 0.125 | 0.158 | 0.352 |
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 | 11 | 42 | 42 | 12 | 42 | 42 | 42 | 42 | 42 | 42 |
N.S. |
1 | 3.82 | 3.82 | 1.09 | 3.82 | 3.82 | 3.82 | 3.82 | 3.82 | 3.82 |
time (sec) |
N/A | 0.192 | 0.003 | 0.544 | 0.030 | 0.062 | 0.021 | 0.114 | 0.165 | 0.030 |
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 | 11 | 31 | 31 | 12 | 31 | 31 | 31 | 31 | 31 | 31 |
N.S. |
1 | 2.82 | 2.82 | 1.09 | 2.82 | 2.82 | 2.82 | 2.82 | 2.82 | 2.82 |
time (sec) |
N/A | 0.181 | 0.001 | 0.532 | 0.034 | 0.057 | 0.019 | 0.120 | 0.161 | 0.044 |
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 | 11 | 20 | 20 | 12 | 20 | 20 | 19 | 20 | 20 | 11 |
N.S. |
1 | 1.82 | 1.82 | 1.09 | 1.82 | 1.82 | 1.73 | 1.82 | 1.82 | 1.00 |
time (sec) |
N/A | 0.168 | 0.002 | 0.152 | 0.038 | 0.060 | 0.019 | 0.123 | 0.169 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 11 | 7 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.64 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.139 | 0.006 | 0.470 | 0.057 | 0.059 | 0.085 | 0.125 | 0.167 | 0.040 |