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 | B | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 200 | 37 | 40 | 480 | 73 | 42 | 83 | 135 | 44 |
N.S. |
1 | 8.00 | 1.48 | 1.60 | 19.20 | 2.92 | 1.68 | 3.32 | 5.40 | 1.76 |
time (sec) |
N/A | 1.166 | 2.134 | 3.787 | 0.107 | 0.094 | 0.740 | 0.128 | 0.215 | 2.746 |
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 | 26 | 0 | 26 | 27 | 26 | 26 | 27 | 26 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.00 | 1.00 | 1.04 | 1.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.321 | 0.733 | 0.175 | 0.085 | 0.139 | 0.332 | 0.239 | 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 | 22 | 17 | 20 | 14 | 13 | 13 | 14 | 13 | 18 | 13 |
N.S. |
1 | 0.77 | 0.91 | 0.64 | 0.59 | 0.59 | 0.64 | 0.59 | 0.82 | 0.59 |
time (sec) |
N/A | 0.147 | 0.000 | 0.064 | 0.027 | 0.074 | 0.019 | 0.110 | 0.236 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 65 | 34 | 29 | 29 | 29 | 24 | 36 | 36 | 0 |
N.S. |
1 | 2.03 | 1.06 | 0.91 | 0.91 | 0.91 | 0.75 | 1.12 | 1.12 | 0.00 |
time (sec) |
N/A | 1.016 | 0.283 | 0.470 | 0.094 | 0.090 | 0.593 | 0.127 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 20 | 20 | 19 | 0 | 19 | 22 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.95 | 0.90 | 0.00 | 0.90 | 1.05 | 0.90 |
time (sec) |
N/A | 0.000 | 0.039 | 1.611 | 0.100 | 0.085 | 0.000 | 0.144 | 0.215 | 2.589 |
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 | 9 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 9 | 7 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 1.00 | 0.78 |
time (sec) |
N/A | 0.149 | 0.012 | 0.022 | 0.029 | 0.077 | 0.033 | 0.110 | 0.249 | 2.267 |
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 | 22 | 22 | 36 | 32 | 22 | 19 | 29 | 33 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.64 | 1.45 | 1.00 | 0.86 | 1.32 | 1.50 | 0.91 |
time (sec) |
N/A | 0.393 | 0.013 | 0.820 | 0.146 | 0.095 | 0.071 | 0.114 | 0.213 | 2.544 |
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 | 27 | 25 | 26 | 19 | 25 | 19 | 30 | 38 | 19 |
N.S. |
1 | 1.08 | 1.00 | 1.04 | 0.76 | 1.00 | 0.76 | 1.20 | 1.52 | 0.76 |
time (sec) |
N/A | 0.326 | 0.354 | 0.248 | 0.119 | 0.081 | 0.087 | 0.117 | 1.525 | 2.492 |
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 | 20 | 26 | 17 | 17 | 54 | 19 | 22 | 19 | 18 | 16 |
N.S. |
1 | 1.30 | 0.85 | 0.85 | 2.70 | 0.95 | 1.10 | 0.95 | 0.90 | 0.80 |
time (sec) |
N/A | 0.273 | 0.027 | 0.059 | 0.037 | 0.092 | 0.050 | 0.113 | 0.187 | 2.440 |
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 | 27 | 23 | 18 | 17 | 17 | 19 | 17 | 35 | 31 |
N.S. |
1 | 1.42 | 1.21 | 0.95 | 0.89 | 0.89 | 1.00 | 0.89 | 1.84 | 1.63 |
time (sec) |
N/A | 0.186 | 0.059 | 0.081 | 0.036 | 0.092 | 0.063 | 0.111 | 0.242 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 62 | 23 | 20 | 25 | 27 | 17 | 0 | 28 | 19 |
N.S. |
1 | 2.38 | 0.88 | 0.77 | 0.96 | 1.04 | 0.65 | 0.00 | 1.08 | 0.73 |
time (sec) |
N/A | 0.305 | 0.029 | 0.472 | 0.078 | 0.090 | 0.086 | 0.000 | 0.216 | 2.505 |
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 | 25 | 20 | 16 | 14 | 13 | 13 | 12 | 17 | 14 | 13 |
N.S. |
1 | 0.80 | 0.64 | 0.56 | 0.52 | 0.52 | 0.48 | 0.68 | 0.56 | 0.52 |
time (sec) |
N/A | 0.187 | 0.013 | 0.073 | 0.026 | 0.092 | 0.043 | 0.113 | 0.221 | 2.369 |
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 | 14 | 14 | 14 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 0.61 | 0.61 | 0.61 | 0.57 | 0.57 | 0.52 | 0.57 | 0.61 | 0.57 |
time (sec) |
N/A | 0.151 | 0.002 | 0.045 | 0.033 | 0.081 | 0.036 | 0.111 | 0.257 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 34 | 28 | 53 | 30 | 36 | 0 | 50 | 0 |
N.S. |
1 | 0.00 | 1.17 | 0.97 | 1.83 | 1.03 | 1.24 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.000 | 0.631 | 0.622 | 0.084 | 0.119 | 0.193 | 0.000 | 0.271 | 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 | 17 | 0 | 18 | 18 | 21 | 21 | 19 | 23 | 22 | 16 |
N.S. |
1 | 0.00 | 1.06 | 1.06 | 1.24 | 1.24 | 1.12 | 1.35 | 1.29 | 0.94 |
time (sec) |
N/A | 0.000 | 0.065 | 0.766 | 0.068 | 0.077 | 0.060 | 0.111 | 0.212 | 2.485 |
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 | 26 | 29 | 22 | 18 | 17 | 17 | 17 | 17 | 20 | 22 |
N.S. |
1 | 1.12 | 0.85 | 0.69 | 0.65 | 0.65 | 0.65 | 0.65 | 0.77 | 0.85 |
time (sec) |
N/A | 0.282 | 0.007 | 0.045 | 0.040 | 0.077 | 0.098 | 0.112 | 0.265 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 34 | 49 | 31 | 35 | 31 | 22 | 0 | 823 | 164 |
N.S. |
1 | 1.03 | 1.48 | 0.94 | 1.06 | 0.94 | 0.67 | 0.00 | 24.94 | 4.97 |
time (sec) |
N/A | 2.834 | 0.074 | 4.380 | 0.233 | 0.086 | 0.108 | 0.000 | 0.251 | 3.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | C | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 23 | 0 | 29 | 26 | 1664 | 26 | 0 |
N.S. |
1 | 0.00 | 0.88 | 0.96 | 0.00 | 1.21 | 1.08 | 69.33 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.072 | 229.598 | 0.000 | 0.088 | 0.228 | 0.509 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 27 | 28 | 33 | 33 | 32 | 47 | 30 | 27 |
N.S. |
1 | 1.17 | 1.17 | 1.22 | 1.43 | 1.43 | 1.39 | 2.04 | 1.30 | 1.17 |
time (sec) |
N/A | 0.286 | 0.051 | 0.140 | 0.074 | 0.125 | 0.141 | 0.136 | 0.214 | 2.658 |
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 | 36 | 0 | 51 | 38 | 45 | 34 | 42 | 37 | 38 | 0 |
N.S. |
1 | 0.00 | 1.42 | 1.06 | 1.25 | 0.94 | 1.17 | 1.03 | 1.06 | 0.00 |
time (sec) |
N/A | 0.000 | 0.842 | 0.287 | 0.165 | 0.093 | 0.155 | 0.112 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 67 | 163 | 63 | 27 | 64 | 74 | 483 |
N.S. |
1 | 0.00 | 0.97 | 2.31 | 5.62 | 2.17 | 0.93 | 2.21 | 2.55 | 16.66 |
time (sec) |
N/A | 0.000 | 0.051 | 2.135 | 0.222 | 0.099 | 0.149 | 0.738 | 0.235 | 3.021 |
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 | 28 | 22 | 22 | 22 | 57 | 38 | 17 | 38 | 109 | 21 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 2.04 | 1.36 | 0.61 | 1.36 | 3.89 | 0.75 |
time (sec) |
N/A | 0.927 | 0.049 | 2.005 | 0.186 | 0.113 | 0.078 | 0.173 | 0.241 | 2.520 |
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 | 11 | 11 | 11 | 14 | 14 | 14 | 14 | 11 | 10 |
N.S. |
1 | 0.69 | 0.69 | 0.69 | 0.88 | 0.88 | 0.88 | 0.88 | 0.69 | 0.62 |
time (sec) |
N/A | 0.328 | 0.007 | 0.125 | 0.061 | 0.083 | 0.043 | 0.111 | 0.215 | 2.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 41 | 39 | 68 | 711 | 116 | 148 | 132 | 279 | 724 |
N.S. |
1 | 1.41 | 1.34 | 2.34 | 24.52 | 4.00 | 5.10 | 4.55 | 9.62 | 24.97 |
time (sec) |
N/A | 6.706 | 0.097 | 38.154 | 3.561 | 0.092 | 1.790 | 1.472 | 0.426 | 3.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 28 | 0 | 32 | 51 | 61 | 28 | 32 |
N.S. |
1 | 0.00 | 0.90 | 0.93 | 0.00 | 1.07 | 1.70 | 2.03 | 0.93 | 1.07 |
time (sec) |
N/A | 0.000 | 0.941 | 0.328 | 0.000 | 0.087 | 0.088 | 0.118 | 0.245 | 2.462 |
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 | 36 | 50 | 35 | 36 | 41 | 32 | 36 | 37 | 35 |
N.S. |
1 | 1.20 | 1.67 | 1.17 | 1.20 | 1.37 | 1.07 | 1.20 | 1.23 | 1.17 |
time (sec) |
N/A | 0.166 | 0.000 | 0.066 | 0.033 | 0.085 | 0.014 | 0.114 | 0.204 | 0.002 |
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 | 38 | 194 | 38 | 49 | 67 | 61 | 73 | 435 | 168 | 69 |
N.S. |
1 | 5.11 | 1.00 | 1.29 | 1.76 | 1.61 | 1.92 | 11.45 | 4.42 | 1.82 |
time (sec) |
N/A | 1.454 | 0.204 | 2.590 | 0.584 | 0.087 | 6.330 | 0.140 | 0.219 | 2.808 |
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 | 22 | 0 | 25 | 23 | 80 | 80 | 34 | 301 | 98 | 181 |
N.S. |
1 | 0.00 | 1.14 | 1.05 | 3.64 | 3.64 | 1.55 | 13.68 | 4.45 | 8.23 |
time (sec) |
N/A | 0.000 | 0.077 | 1.539 | 0.083 | 0.092 | 0.191 | 0.233 | 0.221 | 3.011 |
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 | 25 | 0 | 27 | 25 | 41 | 47 | 20 | 37 | 48 | 25 |
N.S. |
1 | 0.00 | 1.08 | 1.00 | 1.64 | 1.88 | 0.80 | 1.48 | 1.92 | 1.00 |
time (sec) |
N/A | 0.000 | 0.395 | 9.531 | 0.099 | 0.089 | 0.097 | 0.138 | 0.246 | 2.537 |
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 | 36 | 36 | 37 | 36 | 31 | 29 | 33 | 37 | 34 |
N.S. |
1 | 1.44 | 1.44 | 1.48 | 1.44 | 1.24 | 1.16 | 1.32 | 1.48 | 1.36 |
time (sec) |
N/A | 0.291 | 0.012 | 0.483 | 0.028 | 0.078 | 0.083 | 0.119 | 0.234 | 2.348 |
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 | 13 | 6 | 6 | 7 | 6 | 6 | 3 | 6 | 6 | 6 |
N.S. |
1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.23 | 0.46 | 0.46 | 0.46 |
time (sec) |
N/A | 0.132 | 0.000 | 0.010 | 0.024 | 0.065 | 0.014 | 0.112 | 0.205 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 44 | 173 | 45 | 48 | 48 | 46 | 0 | 275 | 11837 |
N.S. |
1 | 1.63 | 6.41 | 1.67 | 1.78 | 1.78 | 1.70 | 0.00 | 10.19 | 438.41 |
time (sec) |
N/A | 0.421 | 0.089 | 0.435 | 0.032 | 0.081 | 0.928 | 0.000 | 0.231 | 7.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 27 | 27 | 27 | 26 | 27 | 28 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.35 | 1.35 | 1.35 | 1.30 | 1.35 | 1.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.629 | 0.185 | 0.086 | 0.142 | 0.120 | 0.264 | 0.000 |
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 | 22 | 0 | 22 | 18 | 41 | 18 | 14 | 18 | 24 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.82 | 1.86 | 0.82 | 0.64 | 0.82 | 1.09 | 0.77 |
time (sec) |
N/A | 0.000 | 0.157 | 0.583 | 0.159 | 0.086 | 0.059 | 0.135 | 0.239 | 2.582 |
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 | 29 | 123 | 47 | 64 | 85 | 90 | 82 | 92 | 115 | 47 |
N.S. |
1 | 4.24 | 1.62 | 2.21 | 2.93 | 3.10 | 2.83 | 3.17 | 3.97 | 1.62 |
time (sec) |
N/A | 0.537 | 0.401 | 1.112 | 0.027 | 0.092 | 0.108 | 0.109 | 0.225 | 2.508 |
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 | 18 | 45 | 29 | 38 | 48 | 48 | 46 | 43 | 66 | 58 |
N.S. |
1 | 2.50 | 1.61 | 2.11 | 2.67 | 2.67 | 2.56 | 2.39 | 3.67 | 3.22 |
time (sec) |
N/A | 0.277 | 0.027 | 0.170 | 0.033 | 0.076 | 0.141 | 0.110 | 0.239 | 0.113 |
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 | 20 | 84 | 23 | 31 | 79 | 23 | 24 | 29 | 34 | 22 |
N.S. |
1 | 4.20 | 1.15 | 1.55 | 3.95 | 1.15 | 1.20 | 1.45 | 1.70 | 1.10 |
time (sec) |
N/A | 0.559 | 0.066 | 0.358 | 0.154 | 0.080 | 0.161 | 0.114 | 0.273 | 2.480 |
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 | 24 | 24 | 24 | 23 | 23 | 20 | 23 | 24 | 23 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 0.92 | 0.92 | 0.80 | 0.92 | 0.96 | 0.92 |
time (sec) |
N/A | 0.212 | 0.027 | 0.317 | 0.030 | 0.093 | 0.087 | 0.105 | 0.239 | 2.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 54 | 142 | 44 | 63 | 44 | 51 | 44 | 66 | 27 |
N.S. |
1 | 1.74 | 4.58 | 1.42 | 2.03 | 1.42 | 1.65 | 1.42 | 2.13 | 0.87 |
time (sec) |
N/A | 0.631 | 0.072 | 1.257 | 0.080 | 0.102 | 0.126 | 0.129 | 0.224 | 2.667 |
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 | 26 | 21 | 17 | 22 | 16 | 20 | 16 | 17 | 15 |
N.S. |
1 | 1.37 | 1.11 | 0.89 | 1.16 | 0.84 | 1.05 | 0.84 | 0.89 | 0.79 |
time (sec) |
N/A | 0.167 | 0.053 | 0.105 | 0.032 | 0.080 | 0.062 | 0.115 | 0.227 | 0.049 |
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 | 26 | 31 | 31 | 28 | 29 | 29 | 32 | 29 | 26 | 30 |
N.S. |
1 | 1.19 | 1.19 | 1.08 | 1.12 | 1.12 | 1.23 | 1.12 | 1.00 | 1.15 |
time (sec) |
N/A | 0.171 | 0.000 | 0.057 | 0.024 | 0.068 | 0.022 | 0.117 | 0.255 | 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 | 25 | 22 | 21 | 16 | 16 | 22 | 12 | 16 | 16 | 16 |
N.S. |
1 | 0.88 | 0.84 | 0.64 | 0.64 | 0.88 | 0.48 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.213 | 0.007 | 0.077 | 0.027 | 0.077 | 0.033 | 0.111 | 0.238 | 0.043 |
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 | 26 | 29 | 29 | 27 | 44 | 35 | 31 | 35 | 38 | 32 |
N.S. |
1 | 1.12 | 1.12 | 1.04 | 1.69 | 1.35 | 1.19 | 1.35 | 1.46 | 1.23 |
time (sec) |
N/A | 0.267 | 0.033 | 0.539 | 0.069 | 0.088 | 0.072 | 0.116 | 0.244 | 2.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.75 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.167 | 0.003 | 0.050 | 0.025 | 0.085 | 0.039 | 0.108 | 0.206 | 2.439 |
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 | 22 | 0 | 21 | 24 | 27 | 23 | 22 | 23 | 57 | 25 |
N.S. |
1 | 0.00 | 0.95 | 1.09 | 1.23 | 1.05 | 1.00 | 1.05 | 2.59 | 1.14 |
time (sec) |
N/A | 0.000 | 0.198 | 0.455 | 0.109 | 0.090 | 0.081 | 0.128 | 61.564 | 2.521 |
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 | 18 | 14 | 13 | 12 | 12 | 12 | 12 | 13 | 13 |
N.S. |
1 | 0.78 | 0.61 | 0.57 | 0.52 | 0.52 | 0.52 | 0.52 | 0.57 | 0.57 |
time (sec) |
N/A | 0.155 | 0.001 | 0.022 | 0.024 | 0.071 | 0.017 | 0.112 | 0.195 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 46 | 27 | 26 | 0 | 28 | 44 | 30 | 26 | 23 |
N.S. |
1 | 1.77 | 1.04 | 1.00 | 0.00 | 1.08 | 1.69 | 1.15 | 1.00 | 0.88 |
time (sec) |
N/A | 0.466 | 0.114 | 0.313 | 0.000 | 0.084 | 0.156 | 0.114 | 0.215 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F(-1) | A | F(-1) | F | F | B |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 98 | 39 | 0 | 37 | 0 | 0 | 126 | 79 |
N.S. |
1 | 0.00 | 3.06 | 1.22 | 0.00 | 1.16 | 0.00 | 0.00 | 3.94 | 2.47 |
time (sec) |
N/A | 0.000 | 0.254 | 4.755 | 0.000 | 0.081 | 0.000 | 0.000 | 200.033 | 2.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | F(-1) | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 32 | 60 | 92 | 24 | 0 | 34 | 122 | 24 |
N.S. |
1 | 0.00 | 1.19 | 2.22 | 3.41 | 0.89 | 0.00 | 1.26 | 4.52 | 0.89 |
time (sec) |
N/A | 0.000 | 0.119 | 0.244 | 0.164 | 0.095 | 0.000 | 0.122 | 0.244 | 2.508 |
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 | 22 | 33 | 25 | 18 | 0 | 40 | 20 | 42 | 40 | 24 |
N.S. |
1 | 1.50 | 1.14 | 0.82 | 0.00 | 1.82 | 0.91 | 1.91 | 1.82 | 1.09 |
time (sec) |
N/A | 0.533 | 0.056 | 0.317 | 0.000 | 0.085 | 0.133 | 0.113 | 0.325 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 31 | 29 | 0 | 27 | 27 | 1588 | 72 | 0 |
N.S. |
1 | 1.16 | 1.00 | 0.94 | 0.00 | 0.87 | 0.87 | 51.23 | 2.32 | 0.00 |
time (sec) |
N/A | 1.805 | 0.104 | 39.472 | 0.000 | 0.220 | 0.968 | 96.249 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 53 | 36 | 39 | 31 | 41 | 36 | 41 | 44 | 18 |
N.S. |
1 | 1.96 | 1.33 | 1.44 | 1.15 | 1.52 | 1.33 | 1.52 | 1.63 | 0.67 |
time (sec) |
N/A | 0.355 | 0.063 | 0.728 | 0.090 | 0.079 | 0.080 | 0.130 | 1.885 | 2.342 |
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 | 14 | 0 | 12 | 13 | 12 | 12 | 17 | 67 | 12 | 12 |
N.S. |
1 | 0.00 | 0.86 | 0.93 | 0.86 | 0.86 | 1.21 | 4.79 | 0.86 | 0.86 |
time (sec) |
N/A | 0.000 | 0.154 | 0.569 | 0.068 | 0.156 | 0.282 | 0.631 | 0.233 | 2.606 |
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 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.17 | 0.17 | 0.25 | 0.17 | 0.17 | 0.17 | 0.25 | 0.17 | 0.17 |
time (sec) |
N/A | 0.125 | 0.000 | 0.013 | 0.029 | 0.082 | 0.016 | 0.106 | 0.233 | 0.008 |
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 | 35 | 104 | 32 | 37 | 54 | 51 | 66 | 59 | 55 | 205 |
N.S. |
1 | 2.97 | 0.91 | 1.06 | 1.54 | 1.46 | 1.89 | 1.69 | 1.57 | 5.86 |
time (sec) |
N/A | 0.750 | 0.079 | 0.870 | 0.036 | 0.095 | 34.580 | 0.128 | 0.213 | 6.617 |
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 | 34 | 26 | 26 | 25 | 39 | 39 | 17 | 39 | 43 | 24 |
N.S. |
1 | 0.76 | 0.76 | 0.74 | 1.15 | 1.15 | 0.50 | 1.15 | 1.26 | 0.71 |
time (sec) |
N/A | 0.650 | 0.036 | 0.395 | 0.176 | 0.102 | 0.117 | 0.437 | 0.248 | 2.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 41 | 43 | 103 | 92 | 61 | 57 | 125 | 0 |
N.S. |
1 | 0.00 | 1.32 | 1.39 | 3.32 | 2.97 | 1.97 | 1.84 | 4.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.063 | 0.102 | 0.163 | 0.115 | 0.137 | 0.158 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 167 | 45 | 36 | 24 | 25 | 40 | 55 |
N.S. |
1 | 0.00 | 0.95 | 7.95 | 2.14 | 1.71 | 1.14 | 1.19 | 1.90 | 2.62 |
time (sec) |
N/A | 0.000 | 0.146 | 0.133 | 0.100 | 0.094 | 0.095 | 0.191 | 0.243 | 2.556 |
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 | 18 | 16 | 11 | 14 | 14 | 12 | 14 | 12 | 13 |
N.S. |
1 | 0.75 | 0.67 | 0.46 | 0.58 | 0.58 | 0.50 | 0.58 | 0.50 | 0.54 |
time (sec) |
N/A | 0.144 | 0.000 | 0.033 | 0.032 | 0.086 | 0.018 | 0.109 | 0.233 | 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 | 22 | 26 | 23 | 19 | 28 | 25 | 14 | 18 | 22 | 17 |
N.S. |
1 | 1.18 | 1.05 | 0.86 | 1.27 | 1.14 | 0.64 | 0.82 | 1.00 | 0.77 |
time (sec) |
N/A | 0.538 | 0.063 | 0.159 | 0.060 | 0.091 | 0.046 | 0.116 | 0.263 | 2.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 41 | 35 | 29 | 72 | 31 | 52 | 45 | 46 |
N.S. |
1 | 0.00 | 1.28 | 1.09 | 0.91 | 2.25 | 0.97 | 1.62 | 1.41 | 1.44 |
time (sec) |
N/A | 0.000 | 3.068 | 2.000 | 0.131 | 0.096 | 0.142 | 0.148 | 0.234 | 2.498 |
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 | 10 | 0 | 10 | 9 | 8 | 8 | 14 | 8 | 14 | 9 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 0.80 | 0.80 | 1.40 | 0.80 | 1.40 | 0.90 |
time (sec) |
N/A | 0.000 | 0.033 | 0.072 | 0.091 | 0.089 | 0.089 | 0.107 | 0.221 | 0.070 |
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 | 16 | 0 | 18 | 17 | 19 | 16 | 12 | 19 | 117 | 16 |
N.S. |
1 | 0.00 | 1.12 | 1.06 | 1.19 | 1.00 | 0.75 | 1.19 | 7.31 | 1.00 |
time (sec) |
N/A | 0.000 | 0.254 | 0.099 | 0.070 | 0.082 | 0.060 | 0.117 | 0.247 | 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 | 27 | 23 | 19 | 18 | 18 | 22 | 15 | 17 | 34 | 17 |
N.S. |
1 | 0.85 | 0.70 | 0.67 | 0.67 | 0.81 | 0.56 | 0.63 | 1.26 | 0.63 |
time (sec) |
N/A | 0.853 | 0.015 | 0.176 | 0.190 | 0.099 | 0.120 | 0.123 | 0.262 | 2.638 |
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 | 30 | 20 | 21 | 19 | 21 | 19 | 22 | 23 | 19 |
N.S. |
1 | 1.25 | 0.83 | 0.88 | 0.79 | 0.88 | 0.79 | 0.92 | 0.96 | 0.79 |
time (sec) |
N/A | 0.253 | 0.015 | 0.207 | 0.037 | 0.086 | 0.409 | 0.112 | 0.216 | 0.165 |
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 | 16 | 16 | 24 | 13 | 15 | 13 | 17 | 15 |
N.S. |
1 | 1.39 | 0.89 | 0.89 | 1.33 | 0.72 | 0.83 | 0.72 | 0.94 | 0.83 |
time (sec) |
N/A | 0.190 | 0.022 | 0.057 | 0.030 | 0.102 | 0.052 | 0.115 | 0.218 | 2.277 |
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 | 13 | 13 | 13 | 13 | 12 | 12 | 10 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.77 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.159 | 0.048 | 0.056 | 0.026 | 0.092 | 0.040 | 0.112 | 0.204 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 12 | 0 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 0.00 | 0.79 | 0.71 | 0.79 | 0.86 | 0.79 |
time (sec) |
N/A | 0.309 | 0.026 | 0.176 | 0.000 | 0.094 | 0.071 | 0.111 | 0.219 | 2.322 |
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 | 15 | 0 | 15 | 14 | 15 | 15 | 12 | 15 | 15 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.056 | 0.112 | 0.059 | 0.086 | 0.051 | 0.120 | 0.241 | 2.360 |
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 | 21 | 21 | 22 | 22 | 24 | 22 | 20 | 24 |
N.S. |
1 | 1.05 | 1.11 | 1.11 | 1.16 | 1.16 | 1.26 | 1.16 | 1.05 | 1.26 |
time (sec) |
N/A | 0.161 | 0.004 | 0.026 | 0.030 | 0.075 | 0.019 | 0.102 | 0.221 | 0.510 |
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 | 18 | 0 | 18 | 16 | 15 | 27 | 17 | 0 | 34 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 0.83 | 1.50 | 0.94 | 0.00 | 1.89 | 0.83 |
time (sec) |
N/A | 0.000 | 1.089 | 0.141 | 0.088 | 0.102 | 0.612 | 0.000 | 0.234 | 2.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 25 | 25 | 20 | 25 | 317 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.93 | 0.93 | 0.74 | 0.93 | 11.74 | 0.00 |
time (sec) |
N/A | 2.426 | 0.130 | 259.767 | 0.318 | 0.098 | 1.641 | 0.369 | 60.662 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 48 | 56 | 43 | 44 | 47 | 46 | 44 | 47 | 43 |
N.S. |
1 | 1.60 | 1.87 | 1.43 | 1.47 | 1.57 | 1.53 | 1.47 | 1.57 | 1.43 |
time (sec) |
N/A | 0.233 | 0.003 | 0.041 | 0.031 | 0.087 | 0.054 | 0.115 | 0.188 | 2.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 78 | 97 | 83 | 71 | 59 | 75 | 81 | 0 | 0 |
N.S. |
1 | 2.36 | 2.94 | 2.52 | 2.15 | 1.79 | 2.27 | 2.45 | 0.00 | 0.00 |
time (sec) |
N/A | 1.051 | 0.071 | 2.926 | 0.144 | 0.102 | 0.342 | 0.649 | 0.464 | 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 | 26 | 0 | 26 | 35 | 32 | 32 | 26 | 34 | 159 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.35 | 1.23 | 1.23 | 1.00 | 1.31 | 6.12 | 0.92 |
time (sec) |
N/A | 0.000 | 0.099 | 0.048 | 0.163 | 0.122 | 0.123 | 0.151 | 200.032 | 2.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 37 | 23 | 21 | 0 | 27 | 15 | 28 | 23 | 27 |
N.S. |
1 | 1.54 | 0.96 | 0.88 | 0.00 | 1.12 | 0.62 | 1.17 | 0.96 | 1.12 |
time (sec) |
N/A | 0.705 | 0.053 | 0.312 | 0.000 | 0.104 | 0.060 | 0.119 | 0.211 | 2.381 |
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 | 32 | 0 | 31 | 35 | 26 | 34 | 27 | 31 | 50 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.09 | 0.81 | 1.06 | 0.84 | 0.97 | 1.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.371 | 1.676 | 0.080 | 0.097 | 0.139 | 0.465 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 27 | 24 | 0 | 25 | 1321 | 25 | 24 | 30 |
N.S. |
1 | 0.96 | 1.00 | 0.89 | 0.00 | 0.93 | 48.93 | 0.93 | 0.89 | 1.11 |
time (sec) |
N/A | 0.335 | 0.038 | 1.487 | 0.000 | 0.111 | 38.565 | 0.175 | 0.237 | 2.493 |
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 | 20 | 0 | 19 | 20 | 22 | 19 | 20 | 25 | 21 | 19 |
N.S. |
1 | 0.00 | 0.95 | 1.00 | 1.10 | 0.95 | 1.00 | 1.25 | 1.05 | 0.95 |
time (sec) |
N/A | 0.000 | 0.925 | 0.211 | 0.073 | 0.096 | 0.077 | 0.115 | 0.236 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 102 | 239 | 122 | 130 | 257 | 161 | 0 | 0 |
N.S. |
1 | 0.00 | 3.00 | 7.03 | 3.59 | 3.82 | 7.56 | 4.74 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 9.311 | 3.204 | 0.473 | 0.129 | 1.384 | 10.271 | 0.732 | 0.000 |
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 | 30 | 48 | 32 | 30 | 54 | 29 | 29 | 29 | 26 | 26 |
N.S. |
1 | 1.60 | 1.07 | 1.00 | 1.80 | 0.97 | 0.97 | 0.97 | 0.87 | 0.87 |
time (sec) |
N/A | 0.302 | 0.020 | 0.559 | 0.057 | 0.102 | 0.137 | 0.112 | 0.228 | 2.415 |
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 | 33 | 37 | 28 | 27 | 27 | 31 | 24 | 27 | 32 | 26 |
N.S. |
1 | 1.12 | 0.85 | 0.82 | 0.82 | 0.94 | 0.73 | 0.82 | 0.97 | 0.79 |
time (sec) |
N/A | 0.271 | 0.012 | 0.090 | 0.038 | 0.080 | 0.177 | 0.118 | 0.246 | 0.079 |
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 | 33 | 0 | 32 | 39 | 38 | 38 | 36 | 0 | 40 | 138 |
N.S. |
1 | 0.00 | 0.97 | 1.18 | 1.15 | 1.15 | 1.09 | 0.00 | 1.21 | 4.18 |
time (sec) |
N/A | 0.000 | 0.103 | 2.918 | 0.187 | 0.088 | 0.238 | 0.000 | 0.256 | 3.274 |
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 | 17 | 0 | 17 | 17 | 17 | 16 | 14 | 16 | 17 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.00 | 0.94 | 0.82 | 0.94 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.023 | 22.702 | 0.172 | 0.098 | 0.167 | 0.135 | 0.257 | 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 | 22 | 24 | 24 | 18 | 17 | 34 | 17 | 17 | 28 | 17 |
N.S. |
1 | 1.09 | 1.09 | 0.82 | 0.77 | 1.55 | 0.77 | 0.77 | 1.27 | 0.77 |
time (sec) |
N/A | 0.164 | 0.017 | 0.052 | 0.040 | 0.093 | 0.066 | 0.109 | 0.236 | 2.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 232 | 31 | 91 | 64 | 66 | 124 | 0 | 0 | 67 |
N.S. |
1 | 8.00 | 1.07 | 3.14 | 2.21 | 2.28 | 4.28 | 0.00 | 0.00 | 2.31 |
time (sec) |
N/A | 3.676 | 0.107 | 2.455 | 0.590 | 0.091 | 0.798 | 0.000 | 0.301 | 3.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 135 | 43 | 52 | 0 | 41 | 56 | 81 | 60 | 59 |
N.S. |
1 | 4.22 | 1.34 | 1.62 | 0.00 | 1.28 | 1.75 | 2.53 | 1.88 | 1.84 |
time (sec) |
N/A | 1.845 | 5.034 | 1.812 | 0.000 | 0.087 | 0.235 | 0.116 | 0.206 | 2.538 |
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 | 26 | 26 | 30 | 23 | 22 | 29 | 19 | 24 | 29 | 22 |
N.S. |
1 | 1.00 | 1.15 | 0.88 | 0.85 | 1.12 | 0.73 | 0.92 | 1.12 | 0.85 |
time (sec) |
N/A | 0.237 | 0.008 | 0.076 | 0.036 | 0.069 | 0.060 | 0.117 | 0.234 | 0.049 |
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 | 29 | 33 | 24 | 22 | 30 | 26 | 17 | 32 | 28 | 26 |
N.S. |
1 | 1.14 | 0.83 | 0.76 | 1.03 | 0.90 | 0.59 | 1.10 | 0.97 | 0.90 |
time (sec) |
N/A | 0.449 | 0.430 | 0.267 | 0.062 | 0.077 | 0.056 | 0.117 | 0.241 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 88 | 25 | 25 | 362 | 24 | 48 | 24 | 52 | 7592 |
N.S. |
1 | 3.52 | 1.00 | 1.00 | 14.48 | 0.96 | 1.92 | 0.96 | 2.08 | 303.68 |
time (sec) |
N/A | 2.210 | 0.473 | 1.130 | 0.157 | 0.094 | 0.260 | 0.113 | 0.241 | 7.453 |
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 | 14 | 30 | 19 | 12 | 26 | 11 | 12 | 11 | 12 | 13 |
N.S. |
1 | 2.14 | 1.36 | 0.86 | 1.86 | 0.79 | 0.86 | 0.79 | 0.86 | 0.93 |
time (sec) |
N/A | 0.190 | 0.020 | 0.052 | 0.043 | 0.088 | 0.047 | 0.107 | 0.226 | 0.067 |
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 | 19 | 23 | 18 | 22 | 38 | 30 | 26 | 30 | 20 | 21 |
N.S. |
1 | 1.21 | 0.95 | 1.16 | 2.00 | 1.58 | 1.37 | 1.58 | 1.05 | 1.11 |
time (sec) |
N/A | 0.547 | 0.089 | 0.255 | 0.162 | 0.098 | 0.055 | 0.124 | 0.225 | 2.529 |
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 | 9 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.56 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.137 | 0.001 | 0.020 | 0.027 | 0.083 | 0.028 | 0.114 | 0.219 | 0.015 |
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 | 22 | 55 | 22 | 21 | 20 | 23 | 15 | 23 | 40 | 20 |
N.S. |
1 | 2.50 | 1.00 | 0.95 | 0.91 | 1.05 | 0.68 | 1.05 | 1.82 | 0.91 |
time (sec) |
N/A | 0.313 | 0.074 | 0.169 | 0.144 | 0.087 | 0.077 | 0.126 | 0.217 | 2.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 28682 | 112 | 71 | 20 | 0 | 76 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1103.15 | 4.31 | 2.73 | 0.77 | 0.00 | 2.92 | 0.96 |
time (sec) |
N/A | 1.924 | 0.079 | 13.694 | 0.197 | 0.117 | 2.787 | 0.000 | 1.150 | 3.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 54 | 47 | 70 | 72 | 61 | 95 | 82 | 155 |
N.S. |
1 | 0.00 | 2.08 | 1.81 | 2.69 | 2.77 | 2.35 | 3.65 | 3.15 | 5.96 |
time (sec) |
N/A | 0.000 | 0.065 | 9.314 | 0.097 | 0.093 | 0.103 | 0.272 | 0.228 | 2.460 |
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 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.17 | 0.17 | 0.22 | 0.17 | 0.17 | 0.13 | 0.22 | 0.17 | 0.17 |
time (sec) |
N/A | 0.129 | 0.000 | 0.015 | 0.030 | 0.083 | 0.016 | 0.113 | 0.230 | 0.008 |
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 | 24 | 43 | 23 | 42 | 39 | 36 | 48 | 36 | 40 | 21 |
N.S. |
1 | 1.79 | 0.96 | 1.75 | 1.62 | 1.50 | 2.00 | 1.50 | 1.67 | 0.88 |
time (sec) |
N/A | 0.269 | 0.080 | 0.300 | 0.043 | 0.095 | 0.072 | 0.115 | 0.242 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 71 | 64 | 64 | 90 | 78 | 29 | 0 |
N.S. |
1 | 0.00 | 0.91 | 3.23 | 2.91 | 2.91 | 4.09 | 3.55 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.212 | 51.106 | 0.186 | 0.099 | 0.203 | 0.160 | 0.224 | 0.000 |
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 | 13 | 33 | 13 | 11 | 10 | 10 | 10 | 10 | 18 | 13 |
N.S. |
1 | 2.54 | 1.00 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 1.38 | 1.00 |
time (sec) |
N/A | 0.240 | 0.010 | 0.047 | 0.023 | 0.078 | 0.052 | 0.112 | 0.225 | 2.434 |