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 | 31 | 31 | 25 | 20 | 19 | 24 | 29 | 19 | 23 | 21 |
N.S. |
1 | 1.00 | 0.81 | 0.65 | 0.61 | 0.77 | 0.94 | 0.61 | 0.74 | 0.68 |
time (sec) |
N/A | 0.272 | 0.016 | 0.072 | 0.027 | 0.060 | 0.219 | 0.134 | 0.247 | 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 | 31 | 31 | 25 | 20 | 19 | 22 | 29 | 19 | 21 | 21 |
N.S. |
1 | 1.00 | 0.81 | 0.65 | 0.61 | 0.71 | 0.94 | 0.61 | 0.68 | 0.68 |
time (sec) |
N/A | 0.272 | 0.016 | 0.069 | 0.028 | 0.060 | 0.435 | 0.097 | 0.184 | 0.035 |
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 | 29 | 25 | 20 | 19 | 21 | 27 | 19 | 20 | 21 |
N.S. |
1 | 1.00 | 0.86 | 0.69 | 0.66 | 0.72 | 0.93 | 0.66 | 0.69 | 0.72 |
time (sec) |
N/A | 0.274 | 0.016 | 0.070 | 0.036 | 0.063 | 0.130 | 0.109 | 0.165 | 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 | 29 | 29 | 25 | 20 | 19 | 21 | 27 | 19 | 22 | 21 |
N.S. |
1 | 1.00 | 0.86 | 0.69 | 0.66 | 0.72 | 0.93 | 0.66 | 0.76 | 0.72 |
time (sec) |
N/A | 0.269 | 0.020 | 0.080 | 0.040 | 0.065 | 0.200 | 0.110 | 0.158 | 17.253 |
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 | 29 | 25 | 20 | 19 | 21 | 27 | 19 | 25 | 21 |
N.S. |
1 | 1.00 | 0.86 | 0.69 | 0.66 | 0.72 | 0.93 | 0.66 | 0.86 | 0.72 |
time (sec) |
N/A | 0.275 | 0.021 | 0.081 | 0.034 | 0.069 | 0.219 | 0.109 | 0.149 | 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 | 29 | 29 | 25 | 20 | 20 | 21 | 27 | 20 | 25 | 21 |
N.S. |
1 | 1.00 | 0.86 | 0.69 | 0.69 | 0.72 | 0.93 | 0.69 | 0.86 | 0.72 |
time (sec) |
N/A | 0.270 | 0.024 | 0.087 | 0.039 | 0.064 | 0.268 | 0.110 | 0.151 | 17.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 62 | 45 | 44 | 49 | 70 | 46 | 50 | 45 |
N.S. |
1 | 1.00 | 0.97 | 0.70 | 0.69 | 0.77 | 1.09 | 0.72 | 0.78 | 0.70 |
time (sec) |
N/A | 0.330 | 0.034 | 0.209 | 0.027 | 0.066 | 0.766 | 0.103 | 0.154 | 17.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 57 | 45 | 44 | 49 | 70 | 46 | 50 | 45 |
N.S. |
1 | 1.00 | 0.89 | 0.70 | 0.69 | 0.77 | 1.09 | 0.72 | 0.78 | 0.70 |
time (sec) |
N/A | 0.347 | 0.032 | 0.142 | 0.033 | 0.065 | 0.518 | 0.103 | 0.156 | 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 | 64 | 64 | 57 | 45 | 44 | 47 | 63 | 46 | 48 | 45 |
N.S. |
1 | 1.00 | 0.89 | 0.70 | 0.69 | 0.73 | 0.98 | 0.72 | 0.75 | 0.70 |
time (sec) |
N/A | 0.342 | 0.032 | 0.176 | 0.026 | 0.062 | 0.674 | 0.124 | 0.168 | 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 | 62 | 62 | 57 | 45 | 48 | 46 | 68 | 46 | 47 | 45 |
N.S. |
1 | 1.00 | 0.92 | 0.73 | 0.77 | 0.74 | 1.10 | 0.74 | 0.76 | 0.73 |
time (sec) |
N/A | 0.317 | 0.030 | 0.088 | 0.029 | 0.066 | 0.351 | 0.105 | 0.153 | 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 | 62 | 62 | 52 | 47 | 44 | 46 | 68 | 46 | 49 | 45 |
N.S. |
1 | 1.00 | 0.84 | 0.76 | 0.71 | 0.74 | 1.10 | 0.74 | 0.79 | 0.73 |
time (sec) |
N/A | 0.322 | 0.034 | 0.100 | 0.031 | 0.064 | 0.437 | 0.109 | 0.153 | 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 | 62 | 62 | 52 | 47 | 44 | 46 | 68 | 46 | 52 | 45 |
N.S. |
1 | 1.00 | 0.84 | 0.76 | 0.71 | 0.74 | 1.10 | 0.74 | 0.84 | 0.73 |
time (sec) |
N/A | 0.321 | 0.037 | 0.100 | 0.027 | 0.068 | 0.487 | 0.106 | 0.149 | 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 | 62 | 62 | 52 | 47 | 45 | 46 | 68 | 47 | 52 | 48 |
N.S. |
1 | 1.00 | 0.84 | 0.76 | 0.73 | 0.74 | 1.10 | 0.76 | 0.84 | 0.77 |
time (sec) |
N/A | 0.320 | 0.041 | 0.109 | 0.037 | 0.067 | 0.592 | 0.107 | 0.160 | 0.046 |
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 | 103 | 103 | 111 | 90 | 81 | 86 | 129 | 87 | 91 | 76 |
N.S. |
1 | 1.00 | 1.08 | 0.87 | 0.79 | 0.83 | 1.25 | 0.84 | 0.88 | 0.74 |
time (sec) |
N/A | 0.391 | 0.052 | 0.389 | 0.029 | 0.066 | 1.571 | 0.110 | 0.155 | 0.043 |
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 | 103 | 103 | 111 | 90 | 81 | 86 | 129 | 87 | 91 | 76 |
N.S. |
1 | 1.00 | 1.08 | 0.87 | 0.79 | 0.83 | 1.25 | 0.84 | 0.88 | 0.74 |
time (sec) |
N/A | 0.380 | 0.052 | 0.159 | 0.032 | 0.061 | 1.174 | 0.108 | 0.153 | 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 | 103 | 103 | 107 | 90 | 81 | 84 | 112 | 87 | 89 | 76 |
N.S. |
1 | 1.00 | 1.04 | 0.87 | 0.79 | 0.82 | 1.09 | 0.84 | 0.86 | 0.74 |
time (sec) |
N/A | 0.379 | 0.053 | 0.194 | 0.030 | 0.065 | 1.246 | 0.114 | 0.161 | 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 | 101 | 101 | 97 | 89 | 88 | 83 | 128 | 87 | 88 | 76 |
N.S. |
1 | 1.00 | 0.96 | 0.88 | 0.87 | 0.82 | 1.27 | 0.86 | 0.87 | 0.75 |
time (sec) |
N/A | 0.373 | 0.057 | 0.104 | 0.033 | 0.064 | 0.839 | 0.104 | 0.151 | 0.035 |
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 | 93 | 88 | 81 | 83 | 126 | 87 | 90 | 76 |
N.S. |
1 | 1.00 | 0.94 | 0.89 | 0.82 | 0.84 | 1.27 | 0.88 | 0.91 | 0.77 |
time (sec) |
N/A | 0.380 | 0.063 | 0.115 | 0.036 | 0.063 | 0.922 | 0.131 | 0.151 | 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 | 101 | 101 | 93 | 88 | 81 | 83 | 128 | 87 | 93 | 76 |
N.S. |
1 | 1.00 | 0.92 | 0.87 | 0.80 | 0.82 | 1.27 | 0.86 | 0.92 | 0.75 |
time (sec) |
N/A | 0.390 | 0.059 | 0.116 | 0.032 | 0.066 | 1.017 | 0.109 | 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 | 99 | 99 | 93 | 88 | 82 | 83 | 124 | 88 | 93 | 79 |
N.S. |
1 | 1.00 | 0.94 | 0.89 | 0.83 | 0.84 | 1.25 | 0.89 | 0.94 | 0.80 |
time (sec) |
N/A | 0.364 | 0.068 | 0.125 | 0.031 | 0.064 | 1.205 | 0.112 | 0.150 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 389 | 364 | 80 | 65 | 0 | 7019 | 0 | 0 | 20 | 12789 |
N.S. |
1 | 0.94 | 0.21 | 0.17 | 0.00 | 18.04 | 0.00 | 0.00 | 0.05 | 32.88 |
time (sec) |
N/A | 1.130 | 0.096 | 0.213 | 0.000 | 1.125 | 0.000 | 0.000 | 200.017 | 19.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 359 | 80 | 61 | 0 | 4023 | 0 | 0 | 20 | 10449 |
N.S. |
1 | 0.93 | 0.21 | 0.16 | 0.00 | 10.45 | 0.00 | 0.00 | 0.05 | 27.14 |
time (sec) |
N/A | 0.927 | 0.059 | 0.135 | 0.000 | 0.268 | 0.000 | 0.000 | 200.021 | 19.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 332 | 48 | 45 | 0 | 4449 | 0 | 0 | 20 | 8093 |
N.S. |
1 | 1.00 | 0.15 | 0.14 | 0.00 | 13.44 | 0.00 | 0.00 | 0.06 | 24.45 |
time (sec) |
N/A | 0.813 | 0.057 | 0.149 | 0.000 | 0.135 | 0.000 | 0.000 | 200.049 | 20.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 330 | 46 | 45 | 0 | 2157 | 0 | 0 | 20 | 8229 |
N.S. |
1 | 1.00 | 0.14 | 0.14 | 0.00 | 6.52 | 0.00 | 0.00 | 0.06 | 24.86 |
time (sec) |
N/A | 0.779 | 0.052 | 0.106 | 0.000 | 0.104 | 0.000 | 0.000 | 200.028 | 19.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 327 | 47 | 45 | 0 | 3209 | 0 | 0 | 20 | 6133 |
N.S. |
1 | 0.99 | 0.14 | 0.14 | 0.00 | 9.69 | 0.00 | 0.00 | 0.06 | 18.53 |
time (sec) |
N/A | 0.758 | 0.055 | 0.100 | 0.000 | 0.108 | 0.000 | 0.000 | 200.024 | 18.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 318 | 49 | 42 | 0 | 3137 | 0 | 0 | 20 | 10401 |
N.S. |
1 | 0.96 | 0.15 | 0.13 | 0.00 | 9.48 | 0.00 | 0.00 | 0.06 | 31.42 |
time (sec) |
N/A | 0.726 | 0.039 | 0.125 | 0.000 | 0.162 | 0.000 | 0.000 | 200.038 | 19.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 350 | 78 | 65 | 0 | 5778 | 0 | 0 | 20 | 10573 |
N.S. |
1 | 0.94 | 0.21 | 0.18 | 0.00 | 15.57 | 0.00 | 0.00 | 0.05 | 28.50 |
time (sec) |
N/A | 0.885 | 0.088 | 0.109 | 0.000 | 0.968 | 0.000 | 0.000 | 200.015 | 20.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 350 | 82 | 61 | 0 | 5046 | 0 | 0 | 20 | 16557 |
N.S. |
1 | 0.94 | 0.22 | 0.16 | 0.00 | 13.60 | 0.00 | 0.00 | 0.05 | 44.63 |
time (sec) |
N/A | 0.858 | 0.062 | 0.114 | 0.000 | 0.716 | 0.000 | 0.000 | 200.019 | 22.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 383 | 106 | 81 | 0 | 8376 | 0 | 0 | 20 | 15149 |
N.S. |
1 | 0.93 | 0.26 | 0.20 | 0.00 | 20.33 | 0.00 | 0.00 | 0.05 | 36.77 |
time (sec) |
N/A | 1.074 | 0.112 | 0.125 | 0.000 | 6.697 | 0.000 | 0.000 | 200.016 | 19.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 536 | 441 | 232 | 149 | 0 | 14601 | 0 | 0 | 20 | 28774 |
N.S. |
1 | 0.82 | 0.43 | 0.28 | 0.00 | 27.24 | 0.00 | 0.00 | 0.04 | 53.68 |
time (sec) |
N/A | 1.200 | 0.512 | 0.519 | 0.000 | 20.295 | 0.000 | 0.000 | 200.015 | 20.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 535 | 431 | 237 | 146 | 0 | 9180 | 0 | 0 | 20 | 31964 |
N.S. |
1 | 0.81 | 0.44 | 0.27 | 0.00 | 17.16 | 0.00 | 0.00 | 0.04 | 59.75 |
time (sec) |
N/A | 1.191 | 0.425 | 0.505 | 0.000 | 1.980 | 0.000 | 0.000 | 200.019 | 26.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 471 | 405 | 189 | 121 | 0 | 11817 | 0 | 0 | 20 | 23808 |
N.S. |
1 | 0.86 | 0.40 | 0.26 | 0.00 | 25.09 | 0.00 | 0.00 | 0.04 | 50.55 |
time (sec) |
N/A | 1.042 | 0.353 | 0.498 | 0.000 | 4.694 | 0.000 | 0.000 | 200.020 | 19.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 483 | 409 | 194 | 118 | 0 | 7244 | 0 | 0 | 20 | 26432 |
N.S. |
1 | 0.85 | 0.40 | 0.24 | 0.00 | 15.00 | 0.00 | 0.00 | 0.04 | 54.72 |
time (sec) |
N/A | 1.039 | 0.301 | 0.500 | 0.000 | 0.454 | 0.000 | 0.000 | 200.031 | 23.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 393 | 109 | 121 | 0 | 10601 | 0 | 0 | 20 | 21913 |
N.S. |
1 | 0.87 | 0.24 | 0.27 | 0.00 | 23.56 | 0.00 | 0.00 | 0.04 | 48.70 |
time (sec) |
N/A | 1.039 | 0.227 | 0.499 | 0.000 | 1.883 | 0.000 | 0.000 | 200.031 | 19.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 442 | 385 | 110 | 118 | 0 | 8211 | 0 | 0 | 20 | 28713 |
N.S. |
1 | 0.87 | 0.25 | 0.27 | 0.00 | 18.58 | 0.00 | 0.00 | 0.05 | 64.96 |
time (sec) |
N/A | 0.997 | 0.199 | 0.148 | 0.000 | 0.950 | 0.000 | 0.000 | 200.024 | 23.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 489 | 416 | 136 | 149 | 0 | 13225 | 0 | 0 | 20 | 26373 |
N.S. |
1 | 0.85 | 0.28 | 0.30 | 0.00 | 27.04 | 0.00 | 0.00 | 0.04 | 53.93 |
time (sec) |
N/A | 1.151 | 0.268 | 0.152 | 0.000 | 8.481 | 0.000 | 0.000 | 200.019 | 20.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 431 | 140 | 144 | 0 | 10274 | 0 | 0 | 20 | 35171 |
N.S. |
1 | 0.86 | 0.28 | 0.29 | 0.00 | 20.43 | 0.00 | 0.00 | 0.04 | 69.92 |
time (sec) |
N/A | 1.157 | 0.232 | 0.151 | 0.000 | 4.173 | 0.000 | 0.000 | 200.022 | 20.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 573 | 487 | 265 | 172 | 0 | 16004 | 0 | 0 | 20 | 31145 |
N.S. |
1 | 0.85 | 0.46 | 0.30 | 0.00 | 27.93 | 0.00 | 0.00 | 0.03 | 54.35 |
time (sec) |
N/A | 1.472 | 0.486 | 0.238 | 0.000 | 80.482 | 0.000 | 0.000 | 200.027 | 25.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 525 | 506 | 275 | 0 | 14789 | 0 | 0 | 20 | 50970 |
N.S. |
1 | 0.85 | 0.82 | 0.45 | 0.00 | 23.97 | 0.00 | 0.00 | 0.03 | 82.61 |
time (sec) |
N/A | 1.429 | 0.859 | 2.523 | 0.000 | 8.919 | 0.000 | 0.000 | 200.046 | 22.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 569 | 494 | 392 | 242 | 0 | 19805 | 0 | 0 | 20 | 39697 |
N.S. |
1 | 0.87 | 0.69 | 0.43 | 0.00 | 34.81 | 0.00 | 0.00 | 0.04 | 69.77 |
time (sec) |
N/A | 1.296 | 0.758 | 2.477 | 0.000 | 42.023 | 0.000 | 0.000 | 200.020 | 21.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 569 | 490 | 397 | 241 | 0 | 12814 | 0 | 0 | 20 | 45495 |
N.S. |
1 | 0.86 | 0.70 | 0.42 | 0.00 | 22.52 | 0.00 | 0.00 | 0.04 | 79.96 |
time (sec) |
N/A | 1.236 | 0.638 | 2.476 | 0.000 | 3.089 | 0.000 | 0.000 | 200.020 | 21.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 480 | 339 | 244 | 0 | 18451 | 0 | 0 | 20 | 37678 |
N.S. |
1 | 0.90 | 0.64 | 0.46 | 0.00 | 34.62 | 0.00 | 0.00 | 0.04 | 70.69 |
time (sec) |
N/A | 1.271 | 0.692 | 2.475 | 0.000 | 24.475 | 0.000 | 0.000 | 200.026 | 21.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 472 | 345 | 237 | 0 | 13878 | 0 | 0 | 20 | 47803 |
N.S. |
1 | 0.89 | 0.65 | 0.44 | 0.00 | 26.04 | 0.00 | 0.00 | 0.04 | 89.69 |
time (sec) |
N/A | 1.251 | 0.609 | 2.476 | 0.000 | 6.002 | 0.000 | 0.000 | 200.033 | 22.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 594 | 518 | 214 | 281 | 0 | 21124 | 0 | 0 | 20 | 42197 |
N.S. |
1 | 0.87 | 0.36 | 0.47 | 0.00 | 35.56 | 0.00 | 0.00 | 0.03 | 71.04 |
time (sec) |
N/A | 1.354 | 0.370 | 2.506 | 0.000 | 62.227 | 0.000 | 0.000 | 200.024 | 22.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 594 | 516 | 215 | 270 | 0 | 15770 | 0 | 0 | 20 | 54027 |
N.S. |
1 | 0.87 | 0.36 | 0.45 | 0.00 | 26.55 | 0.00 | 0.00 | 0.03 | 90.95 |
time (sec) |
N/A | 1.316 | 0.319 | 0.243 | 0.000 | 15.976 | 0.000 | 0.000 | 200.022 | 23.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 658 | 576 | 255 | 321 | 0 | 23877 | 0 | 0 | 20 | 46948 |
N.S. |
1 | 0.88 | 0.39 | 0.49 | 0.00 | 36.29 | 0.00 | 0.00 | 0.03 | 71.35 |
time (sec) |
N/A | 2.378 | 0.471 | 0.250 | 0.000 | 162.849 | 0.000 | 0.000 | 200.022 | 23.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 658 | 573 | 259 | 316 | 0 | 17801 | 0 | 0 | 20 | 60099 |
N.S. |
1 | 0.87 | 0.39 | 0.48 | 0.00 | 27.05 | 0.00 | 0.00 | 0.03 | 91.34 |
time (sec) |
N/A | 2.388 | 0.399 | 0.247 | 0.000 | 44.143 | 0.000 | 0.000 | 200.023 | 23.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 180 | 166 | 154 | 0 | 367 | 0 | 170 | 4009 | 315 |
N.S. |
1 | 1.05 | 0.97 | 0.90 | 0.00 | 2.15 | 0.00 | 0.99 | 23.44 | 1.84 |
time (sec) |
N/A | 0.557 | 0.316 | 0.283 | 0.000 | 0.092 | 0.000 | 0.122 | 0.264 | 18.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 163 | 132 | 122 | 0 | 303 | 0 | 132 | 2818 | 193 |
N.S. |
1 | 1.07 | 0.86 | 0.80 | 0.00 | 1.98 | 0.00 | 0.86 | 18.42 | 1.26 |
time (sec) |
N/A | 0.543 | 0.234 | 0.205 | 0.000 | 0.081 | 0.000 | 0.129 | 0.215 | 18.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 119 | 103 | 91 | 0 | 237 | 0 | 96 | 1536 | 87 |
N.S. |
1 | 1.10 | 0.95 | 0.84 | 0.00 | 2.19 | 0.00 | 0.89 | 14.22 | 0.81 |
time (sec) |
N/A | 0.427 | 0.201 | 0.171 | 0.000 | 0.093 | 0.000 | 0.121 | 0.195 | 19.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 87 | 73 | 0 | 197 | 0 | 74 | 816 | 72 |
N.S. |
1 | 1.05 | 1.05 | 0.88 | 0.00 | 2.37 | 0.00 | 0.89 | 9.83 | 0.87 |
time (sec) |
N/A | 0.368 | 0.283 | 0.171 | 0.000 | 0.106 | 0.000 | 0.117 | 0.177 | 19.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 104 | 91 | 0 | 566 | 0 | 0 | 369 | 88 |
N.S. |
1 | 1.00 | 0.95 | 0.83 | 0.00 | 5.19 | 0.00 | 0.00 | 3.39 | 0.81 |
time (sec) |
N/A | 0.493 | 0.174 | 0.151 | 0.000 | 0.101 | 0.000 | 0.000 | 0.251 | 18.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 115 | 107 | 94 | 0 | 601 | 0 | 148 | 111 | 91 |
N.S. |
1 | 1.03 | 0.96 | 0.84 | 0.00 | 5.37 | 0.00 | 1.32 | 0.99 | 0.81 |
time (sec) |
N/A | 0.495 | 0.171 | 0.181 | 0.000 | 0.101 | 0.000 | 0.135 | 0.283 | 18.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 88 | 81 | 0 | 215 | 0 | 241 | 123 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.92 | 0.00 | 2.44 | 0.00 | 2.74 | 1.40 | 0.00 |
time (sec) |
N/A | 0.381 | 0.248 | 0.155 | 0.000 | 0.090 | 0.000 | 0.128 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 127 | 108 | 101 | 0 | 261 | 0 | 359 | 168 | 0 |
N.S. |
1 | 1.09 | 0.93 | 0.87 | 0.00 | 2.25 | 0.00 | 3.09 | 1.45 | 0.00 |
time (sec) |
N/A | 0.450 | 0.410 | 0.197 | 0.000 | 0.099 | 0.000 | 0.134 | 23.583 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 171 | 141 | 130 | 0 | 325 | 0 | 617 | 20 | 0 |
N.S. |
1 | 1.06 | 0.88 | 0.81 | 0.00 | 2.02 | 0.00 | 3.83 | 0.12 | 0.00 |
time (sec) |
N/A | 0.570 | 0.521 | 0.230 | 0.000 | 0.121 | 0.000 | 0.130 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 216 | 176 | 160 | 0 | 389 | 0 | 842 | 20 | 0 |
N.S. |
1 | 1.09 | 0.88 | 0.80 | 0.00 | 1.95 | 0.00 | 4.23 | 0.10 | 0.00 |
time (sec) |
N/A | 0.685 | 0.692 | 0.245 | 0.000 | 0.157 | 0.000 | 0.158 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 400 | 538 | 476 | 0 | 402 | 0 | 0 | 232 | 0 |
N.S. |
1 | 1.02 | 1.37 | 1.21 | 0.00 | 1.02 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.958 | 8.221 | 3.523 | 0.000 | 0.082 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 341 | 479 | 406 | 0 | 355 | 0 | 0 | 150 | 0 |
N.S. |
1 | 0.99 | 1.40 | 1.18 | 0.00 | 1.03 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.707 | 6.889 | 3.019 | 0.000 | 0.081 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 312 | 445 | 379 | 0 | 301 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.01 | 1.44 | 1.23 | 0.00 | 0.97 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.630 | 6.329 | 2.106 | 0.000 | 0.078 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 305 | 435 | 381 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.01 | 1.44 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.637 | 10.539 | 2.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 345 | 459 | 398 | 0 | 303 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.10 | 1.47 | 1.27 | 0.00 | 0.97 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.735 | 10.598 | 2.832 | 0.000 | 0.075 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 402 | 530 | 428 | 0 | 357 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.11 | 1.46 | 1.18 | 0.00 | 0.98 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.913 | 10.901 | 3.754 | 0.000 | 0.080 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 227 | 220 | 241 | 0 | 535 | 0 | 663 | 7599 | 0 |
N.S. |
1 | 1.02 | 0.99 | 1.08 | 0.00 | 2.40 | 0.00 | 2.97 | 34.08 | 0.00 |
time (sec) |
N/A | 0.612 | 0.690 | 0.355 | 0.000 | 0.097 | 0.000 | 0.167 | 0.605 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 210 | 194 | 199 | 0 | 451 | 0 | 529 | 5920 | 0 |
N.S. |
1 | 1.03 | 0.95 | 0.98 | 0.00 | 2.21 | 0.00 | 2.59 | 29.02 | 0.00 |
time (sec) |
N/A | 0.585 | 0.526 | 0.299 | 0.000 | 0.091 | 0.000 | 0.165 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 166 | 140 | 152 | 0 | 361 | 0 | 408 | 3844 | 223 |
N.S. |
1 | 1.11 | 0.93 | 1.01 | 0.00 | 2.41 | 0.00 | 2.72 | 25.63 | 1.49 |
time (sec) |
N/A | 0.481 | 0.358 | 0.240 | 0.000 | 0.089 | 0.000 | 0.158 | 0.221 | 17.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 134 | 114 | 120 | 0 | 297 | 0 | 311 | 2869 | 115 |
N.S. |
1 | 1.08 | 0.92 | 0.97 | 0.00 | 2.40 | 0.00 | 2.51 | 23.14 | 0.93 |
time (sec) |
N/A | 0.424 | 0.640 | 0.208 | 0.000 | 0.085 | 0.000 | 0.146 | 0.194 | 17.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 169 | 148 | 192 | 0 | 727 | 0 | 0 | 693 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.24 | 0.00 | 4.69 | 0.00 | 0.00 | 4.47 | 0.00 |
time (sec) |
N/A | 0.649 | 0.452 | 0.187 | 0.000 | 0.160 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 157 | 132 | 170 | 0 | 713 | 0 | 184 | 652 | 0 |
N.S. |
1 | 1.05 | 0.88 | 1.13 | 0.00 | 4.75 | 0.00 | 1.23 | 4.35 | 0.00 |
time (sec) |
N/A | 0.680 | 0.464 | 0.250 | 0.000 | 0.131 | 0.000 | 0.170 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 159 | 131 | 150 | 0 | 713 | 0 | 304 | 633 | 0 |
N.S. |
1 | 1.05 | 0.87 | 0.99 | 0.00 | 4.72 | 0.00 | 2.01 | 4.19 | 0.00 |
time (sec) |
N/A | 0.606 | 0.496 | 0.244 | 0.000 | 0.131 | 0.000 | 0.180 | 0.501 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 177 | 148 | 142 | 0 | 771 | 0 | 398 | 233 | 0 |
N.S. |
1 | 1.09 | 0.91 | 0.87 | 0.00 | 4.73 | 0.00 | 2.44 | 1.43 | 0.00 |
time (sec) |
N/A | 0.655 | 0.670 | 0.243 | 0.000 | 0.148 | 0.000 | 0.201 | 17.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 143 | 120 | 123 | 0 | 319 | 0 | 606 | 20 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.92 | 0.00 | 2.40 | 0.00 | 4.56 | 0.15 | 0.00 |
time (sec) |
N/A | 0.473 | 0.672 | 0.236 | 0.000 | 0.111 | 0.000 | 0.167 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 178 | 160 | 153 | 0 | 383 | 0 | 832 | 20 | 0 |
N.S. |
1 | 1.10 | 0.99 | 0.94 | 0.00 | 2.36 | 0.00 | 5.14 | 0.12 | 0.00 |
time (sec) |
N/A | 0.533 | 0.980 | 0.264 | 0.000 | 0.168 | 0.000 | 0.195 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 222 | 201 | 189 | 0 | 473 | 0 | 1235 | 757 | 0 |
N.S. |
1 | 1.03 | 0.93 | 0.88 | 0.00 | 2.19 | 0.00 | 5.72 | 3.50 | 0.00 |
time (sec) |
N/A | 0.656 | 1.345 | 0.319 | 0.000 | 0.249 | 0.000 | 0.202 | 12.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 493 | 498 | 657 | 674 | 0 | 528 | 0 | 0 | 435 | 0 |
N.S. |
1 | 1.01 | 1.33 | 1.37 | 0.00 | 1.07 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.232 | 11.441 | 3.700 | 0.000 | 0.082 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 436 | 602 | 545 | 0 | 472 | 0 | 0 | 323 | 0 |
N.S. |
1 | 0.98 | 1.35 | 1.22 | 0.00 | 1.06 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.968 | 10.968 | 4.046 | 0.000 | 0.082 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 383 | 533 | 471 | 0 | 396 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.01 | 1.40 | 1.24 | 0.00 | 1.04 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.833 | 9.705 | 2.910 | 0.000 | 0.077 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 359 | 505 | 405 | 0 | 0 | 0 | 0 | 200 | 0 |
N.S. |
1 | 0.99 | 1.40 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.791 | 10.833 | 2.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 355 | 473 | 428 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.01 | 1.34 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.755 | 10.606 | 3.470 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 401 | 527 | 424 | 0 | 0 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.10 | 1.44 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.924 | 10.881 | 3.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 455 | 572 | 495 | 0 | 403 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.11 | 1.39 | 1.20 | 0.00 | 0.98 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.081 | 11.066 | 4.322 | 0.000 | 0.083 | 0.000 | 0.000 | 0.474 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 133 | 101 | 91 | 0 | 241 | 0 | 101 | 1548 | 0 |
N.S. |
1 | 1.10 | 0.83 | 0.75 | 0.00 | 1.99 | 0.00 | 0.83 | 12.79 | 0.00 |
time (sec) |
N/A | 0.464 | 0.218 | 0.198 | 0.000 | 0.080 | 0.000 | 0.121 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 114 | 91 | 75 | 0 | 203 | 0 | 80 | 862 | 0 |
N.S. |
1 | 1.10 | 0.88 | 0.72 | 0.00 | 1.95 | 0.00 | 0.77 | 8.29 | 0.00 |
time (sec) |
N/A | 0.445 | 0.189 | 0.160 | 0.000 | 0.080 | 0.000 | 0.111 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 69 | 68 | 56 | 0 | 161 | 0 | 59 | 249 | 55 |
N.S. |
1 | 1.01 | 1.00 | 0.82 | 0.00 | 2.37 | 0.00 | 0.87 | 3.66 | 0.81 |
time (sec) |
N/A | 0.359 | 0.126 | 0.130 | 0.000 | 0.077 | 0.000 | 0.118 | 0.185 | 17.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 41 | 35 | 0 | 118 | 0 | 38 | 47 | 34 |
N.S. |
1 | 1.00 | 0.95 | 0.81 | 0.00 | 2.74 | 0.00 | 0.88 | 1.09 | 0.79 |
time (sec) |
N/A | 0.285 | 0.078 | 0.100 | 0.000 | 0.076 | 0.000 | 0.115 | 0.183 | 18.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 41 | 39 | 0 | 124 | 0 | 38 | 131 | 44 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.00 | 2.82 | 0.00 | 0.86 | 2.98 | 1.00 |
time (sec) |
N/A | 0.297 | 0.077 | 0.101 | 0.000 | 0.078 | 0.000 | 0.114 | 0.194 | 17.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 74 | 72 | 63 | 0 | 179 | 0 | 114 | 21 | 56 |
N.S. |
1 | 1.03 | 1.00 | 0.88 | 0.00 | 2.49 | 0.00 | 1.58 | 0.29 | 0.78 |
time (sec) |
N/A | 0.359 | 0.148 | 0.141 | 0.000 | 0.083 | 0.000 | 0.120 | 0.228 | 17.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 118 | 91 | 82 | 0 | 221 | 0 | 221 | 21 | 0 |
N.S. |
1 | 1.09 | 0.84 | 0.76 | 0.00 | 2.05 | 0.00 | 2.05 | 0.19 | 0.00 |
time (sec) |
N/A | 0.449 | 0.242 | 0.156 | 0.000 | 0.094 | 0.000 | 0.128 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 163 | 110 | 101 | 0 | 265 | 0 | 335 | 0 | 0 |
N.S. |
1 | 1.12 | 0.76 | 0.70 | 0.00 | 1.83 | 0.00 | 2.31 | 0.00 | 0.00 |
time (sec) |
N/A | 0.600 | 0.352 | 0.203 | 0.000 | 0.101 | 0.000 | 0.132 | 24.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 317 | 444 | 388 | 0 | 305 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.01 | 1.42 | 1.24 | 0.00 | 0.97 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.678 | 10.611 | 2.830 | 0.000 | 0.080 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 270 | 278 | 216 | 0 | 273 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.01 | 1.04 | 0.81 | 0.00 | 1.02 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.536 | 10.089 | 0.962 | 0.000 | 0.073 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 186 | 144 | 0 | 121 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.63 | 1.26 | 0.00 | 1.06 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.321 | 0.052 | 0.645 | 0.000 | 0.080 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 300 | 298 | 239 | 0 | 269 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.02 | 1.01 | 0.81 | 0.00 | 0.91 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.641 | 10.329 | 1.310 | 0.000 | 0.074 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 350 | 459 | 399 | 0 | 306 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.10 | 1.45 | 1.26 | 0.00 | 0.97 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.766 | 10.592 | 2.845 | 0.000 | 0.079 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 136 | 107 | 93 | 153 | 249 | 0 | 112 | 178 | 0 |
N.S. |
1 | 1.10 | 0.86 | 0.75 | 1.23 | 2.01 | 0.00 | 0.90 | 1.44 | 0.00 |
time (sec) |
N/A | 0.470 | 0.351 | 0.663 | 0.119 | 0.176 | 0.000 | 0.119 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 117 | 91 | 77 | 105 | 211 | 0 | 91 | 101 | 0 |
N.S. |
1 | 1.09 | 0.85 | 0.72 | 0.98 | 1.97 | 0.00 | 0.85 | 0.94 | 0.00 |
time (sec) |
N/A | 0.443 | 0.256 | 0.190 | 0.111 | 0.081 | 0.000 | 0.122 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 72 | 57 | 50 | 169 | 0 | 70 | 49 | 62 |
N.S. |
1 | 1.03 | 1.03 | 0.81 | 0.71 | 2.41 | 0.00 | 1.00 | 0.70 | 0.89 |
time (sec) |
N/A | 0.348 | 0.175 | 0.227 | 0.153 | 0.080 | 0.000 | 0.113 | 0.157 | 18.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 35 | 28 | 124 | 0 | 45 | 28 | 40 |
N.S. |
1 | 1.00 | 0.98 | 0.80 | 0.64 | 2.82 | 0.00 | 1.02 | 0.64 | 0.91 |
time (sec) |
N/A | 0.289 | 0.124 | 0.123 | 0.111 | 0.072 | 0.000 | 0.123 | 0.152 | 19.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 44 | 45 | 36 | 129 | 0 | 36 | 40 | 52 |
N.S. |
1 | 1.00 | 0.94 | 0.96 | 0.77 | 2.74 | 0.00 | 0.77 | 0.85 | 1.11 |
time (sec) |
N/A | 0.301 | 0.094 | 0.140 | 0.113 | 0.074 | 0.000 | 0.118 | 0.166 | 17.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 78 | 76 | 74 | 62 | 188 | 0 | 111 | 23 | 64 |
N.S. |
1 | 1.01 | 0.99 | 0.96 | 0.81 | 2.44 | 0.00 | 1.44 | 0.30 | 0.83 |
time (sec) |
N/A | 0.357 | 0.141 | 0.151 | 0.123 | 0.088 | 0.000 | 0.121 | 0.182 | 17.802 |