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 | C | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 154 | 51 | 113 | 0 | 0 | 42 | 0 | 65 | 41 |
N.S. |
1 | 1.02 | 0.34 | 0.75 | 0.00 | 0.00 | 0.28 | 0.00 | 0.43 | 0.27 |
time (sec) |
N/A | 0.522 | 10.010 | 0.581 | 0.000 | 0.000 | 0.620 | 0.000 | 0.265 | 0.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 154 | 53 | 112 | 0 | 0 | 37 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.35 | 0.73 | 0.00 | 0.00 | 0.24 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.546 | 10.011 | 0.813 | 0.000 | 0.000 | 0.685 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 37 | 35 | 28 | 58 | 29 | 88 | 29 | 117 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.80 | 1.66 | 0.83 | 2.51 | 0.83 | 3.34 | 0.00 |
time (sec) |
N/A | 0.255 | 0.086 | 0.459 | 0.025 | 0.081 | 0.968 | 0.122 | 0.192 | 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 | 62 | 64 | 40 | 37 | 50 | 36 | 70 | 61 | 35 | 38 |
N.S. |
1 | 1.03 | 0.65 | 0.60 | 0.81 | 0.58 | 1.13 | 0.98 | 0.56 | 0.61 |
time (sec) |
N/A | 0.318 | 0.029 | 0.585 | 0.030 | 0.078 | 0.380 | 0.116 | 0.204 | 0.400 |
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 | 40 | 42 | 29 | 25 | 32 | 24 | 44 | 32 | 24 | 24 |
N.S. |
1 | 1.05 | 0.72 | 0.62 | 0.80 | 0.60 | 1.10 | 0.80 | 0.60 | 0.60 |
time (sec) |
N/A | 0.284 | 0.023 | 0.567 | 0.026 | 0.073 | 0.271 | 0.122 | 0.221 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 15 | 15 | 24 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 0.79 | 1.26 | 0.79 | 0.74 | 0.79 |
time (sec) |
N/A | 0.231 | 0.015 | 0.583 | 0.035 | 0.070 | 0.102 | 0.115 | 0.200 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 21 | 39 | 73 | 53 | 24 | 22 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.39 | 2.61 | 1.89 | 0.86 | 0.79 | 0.71 |
time (sec) |
N/A | 0.262 | 0.023 | 0.574 | 0.104 | 0.082 | 0.578 | 0.116 | 0.205 | 0.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 44 | 71 | 119 | 129 | 54 | 46 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.37 | 2.29 | 2.48 | 1.04 | 0.88 | 0.77 |
time (sec) |
N/A | 0.281 | 0.070 | 0.620 | 0.105 | 0.087 | 1.298 | 0.124 | 0.228 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 59 | 61 | 44 | 62 | 105 | 128 | 53 | 39 | 0 |
N.S. |
1 | 1.07 | 1.11 | 0.80 | 1.13 | 1.91 | 2.33 | 0.96 | 0.71 | 0.00 |
time (sec) |
N/A | 0.279 | 0.168 | 0.775 | 0.110 | 0.082 | 1.322 | 0.125 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 37 | 24 | 23 | 65 | 53 | 30 | 17 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.77 | 0.74 | 2.10 | 1.71 | 0.97 | 0.55 | 0.00 |
time (sec) |
N/A | 0.244 | 0.125 | 0.665 | 0.115 | 0.082 | 0.570 | 0.126 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 18 | 51 | 36 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.82 | 2.32 | 1.64 | 0.77 | 0.82 |
time (sec) |
N/A | 0.227 | 0.148 | 0.677 | 0.034 | 0.072 | 0.423 | 0.127 | 0.182 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 32 | 27 | 36 | 26 | 189 | 68 | 27 | 26 |
N.S. |
1 | 1.00 | 0.70 | 0.59 | 0.78 | 0.57 | 4.11 | 1.48 | 0.59 | 0.57 |
time (sec) |
N/A | 0.272 | 0.172 | 0.793 | 0.028 | 0.078 | 0.690 | 0.127 | 0.247 | 0.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 77 | 43 | 40 | 55 | 39 | 609 | 97 | 38 | 39 |
N.S. |
1 | 1.08 | 0.61 | 0.56 | 0.77 | 0.55 | 8.58 | 1.37 | 0.54 | 0.55 |
time (sec) |
N/A | 0.310 | 0.202 | 0.971 | 0.037 | 0.088 | 1.568 | 0.127 | 0.217 | 0.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 80 | 98 | 0 | 58 | 39 | 0 | 61 | 0 |
N.S. |
1 | 1.08 | 0.80 | 0.98 | 0.00 | 0.58 | 0.39 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.351 | 10.020 | 0.865 | 0.000 | 0.081 | 0.551 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 64 | 86 | 0 | 46 | 39 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.12 | 0.00 | 0.60 | 0.51 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.304 | 10.027 | 0.661 | 0.000 | 0.081 | 0.594 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 72 | 64 | 0 | 26 | 37 | 0 | 22 | 38 |
N.S. |
1 | 1.00 | 1.36 | 1.21 | 0.00 | 0.49 | 0.70 | 0.00 | 0.42 | 0.72 |
time (sec) |
N/A | 0.258 | 0.020 | 0.483 | 0.000 | 0.077 | 0.452 | 0.000 | 0.227 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 52 | 88 | 0 | 47 | 42 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.66 | 1.11 | 0.00 | 0.59 | 0.53 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.299 | 10.010 | 0.648 | 0.000 | 0.083 | 0.538 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 110 | 52 | 100 | 0 | 59 | 46 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 0.51 | 0.98 | 0.00 | 0.58 | 0.45 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.358 | 10.010 | 0.906 | 0.000 | 0.076 | 0.699 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 170 | 81 | 117 | 0 | 105 | 39 | 0 | 66 | 0 |
N.S. |
1 | 1.08 | 0.51 | 0.74 | 0.00 | 0.66 | 0.25 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.588 | 10.039 | 1.080 | 0.000 | 0.084 | 0.804 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 139 | 66 | 107 | 0 | 89 | 39 | 0 | 48 | 0 |
N.S. |
1 | 1.03 | 0.49 | 0.79 | 0.00 | 0.66 | 0.29 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.526 | 10.020 | 0.771 | 0.000 | 0.081 | 0.519 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 52 | 88 | 0 | 76 | 39 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.48 | 0.81 | 0.00 | 0.70 | 0.36 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.437 | 10.017 | 0.498 | 0.000 | 0.081 | 0.460 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 135 | 50 | 106 | 0 | 68 | 41 | 0 | 26 | 41 |
N.S. |
1 | 1.05 | 0.39 | 0.83 | 0.00 | 0.53 | 0.32 | 0.00 | 0.20 | 0.32 |
time (sec) |
N/A | 0.509 | 10.013 | 0.597 | 0.000 | 0.079 | 0.497 | 0.000 | 0.202 | 0.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 166 | 52 | 115 | 0 | 84 | 39 | 0 | 26 | 0 |
N.S. |
1 | 1.05 | 0.33 | 0.73 | 0.00 | 0.53 | 0.25 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.576 | 10.010 | 0.819 | 0.000 | 0.082 | 0.654 | 0.000 | 0.247 | 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 | 59 | 62 | 39 | 37 | 49 | 48 | 68 | 55 | 37 | 44 |
N.S. |
1 | 1.05 | 0.66 | 0.63 | 0.83 | 0.81 | 1.15 | 0.93 | 0.63 | 0.75 |
time (sec) |
N/A | 0.319 | 0.039 | 0.601 | 0.037 | 0.070 | 0.409 | 0.121 | 0.202 | 0.545 |
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 | 40 | 40 | 29 | 26 | 32 | 37 | 41 | 35 | 26 | 22 |
N.S. |
1 | 1.00 | 0.72 | 0.65 | 0.80 | 0.92 | 1.02 | 0.88 | 0.65 | 0.55 |
time (sec) |
N/A | 0.289 | 0.032 | 0.621 | 0.032 | 0.074 | 0.267 | 0.124 | 0.224 | 0.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 15 | 26 | 24 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.37 | 1.26 | 0.79 | 0.84 | 0.79 |
time (sec) |
N/A | 0.231 | 0.020 | 0.592 | 0.031 | 0.083 | 0.106 | 0.121 | 0.227 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 48 | 37 | 55 | 149 | 520 | 43 | 58 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 1.15 | 3.10 | 10.83 | 0.90 | 1.21 | 0.75 |
time (sec) |
N/A | 0.281 | 0.056 | 0.582 | 0.107 | 0.082 | 1.085 | 0.122 | 0.223 | 0.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 77 | 62 | 57 | 92 | 193 | 165 | 77 | 81 | 56 |
N.S. |
1 | 1.07 | 0.86 | 0.79 | 1.28 | 2.68 | 2.29 | 1.07 | 1.12 | 0.78 |
time (sec) |
N/A | 0.320 | 0.093 | 0.641 | 0.114 | 0.089 | 1.801 | 0.122 | 0.206 | 0.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 84 | 70 | 63 | 84 | 177 | 163 | 75 | 60 | 0 |
N.S. |
1 | 1.09 | 0.91 | 0.82 | 1.09 | 2.30 | 2.12 | 0.97 | 0.78 | 0.00 |
time (sec) |
N/A | 0.332 | 0.259 | 1.026 | 0.112 | 0.087 | 1.847 | 0.132 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 60 | 43 | 42 | 148 | 100 | 63 | 49 | 0 |
N.S. |
1 | 0.98 | 1.11 | 0.80 | 0.78 | 2.74 | 1.85 | 1.17 | 0.91 | 0.00 |
time (sec) |
N/A | 0.284 | 0.223 | 0.779 | 0.111 | 0.085 | 0.916 | 0.136 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 29 | 53 | 29 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.32 | 2.41 | 1.32 | 0.86 | 0.82 |
time (sec) |
N/A | 0.230 | 0.144 | 0.648 | 0.034 | 0.074 | 0.386 | 0.124 | 0.231 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 30 | 27 | 38 | 41 | 133 | 70 | 29 | 26 |
N.S. |
1 | 1.00 | 0.70 | 0.63 | 0.88 | 0.95 | 3.09 | 1.63 | 0.67 | 0.60 |
time (sec) |
N/A | 0.270 | 0.190 | 0.699 | 0.035 | 0.093 | 0.518 | 0.122 | 0.206 | 0.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 41 | 38 | 58 | 52 | 481 | 145 | 40 | 73 |
N.S. |
1 | 1.09 | 0.60 | 0.56 | 0.85 | 0.76 | 7.07 | 2.13 | 0.59 | 1.07 |
time (sec) |
N/A | 0.311 | 0.294 | 0.795 | 0.025 | 0.087 | 0.919 | 0.136 | 0.201 | 0.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 105 | 52 | 49 | 76 | 63 | 724 | 225 | 51 | 80 |
N.S. |
1 | 1.13 | 0.56 | 0.53 | 0.82 | 0.68 | 7.78 | 2.42 | 0.55 | 0.86 |
time (sec) |
N/A | 0.360 | 0.423 | 0.975 | 0.026 | 0.086 | 6.212 | 0.136 | 0.231 | 0.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 107 | 67 | 108 | 0 | 79 | 39 | 0 | 122 | 0 |
N.S. |
1 | 1.08 | 0.68 | 1.09 | 0.00 | 0.80 | 0.39 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.346 | 10.018 | 1.648 | 0.000 | 0.095 | 0.541 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 57 | 90 | 0 | 64 | 39 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.17 | 0.00 | 0.83 | 0.51 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.302 | 6.400 | 0.566 | 0.000 | 0.099 | 0.501 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 56 | 90 | 0 | 66 | 37 | 0 | 32 | 38 |
N.S. |
1 | 1.00 | 0.73 | 1.17 | 0.00 | 0.86 | 0.48 | 0.00 | 0.42 | 0.49 |
time (sec) |
N/A | 0.291 | 0.007 | 0.483 | 0.000 | 0.075 | 0.496 | 0.000 | 0.217 | 0.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 109 | 55 | 110 | 0 | 80 | 42 | 0 | 36 | 0 |
N.S. |
1 | 1.08 | 0.54 | 1.09 | 0.00 | 0.79 | 0.42 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.341 | 10.011 | 1.360 | 0.000 | 0.091 | 0.575 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 140 | 55 | 133 | 0 | 94 | 46 | 0 | 36 | 0 |
N.S. |
1 | 1.13 | 0.44 | 1.07 | 0.00 | 0.76 | 0.37 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.385 | 10.019 | 1.659 | 0.000 | 0.084 | 0.692 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 169 | 67 | 131 | 0 | 134 | 39 | 0 | 130 | 0 |
N.S. |
1 | 1.08 | 0.43 | 0.83 | 0.00 | 0.85 | 0.25 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.560 | 10.029 | 2.072 | 0.000 | 0.082 | 0.600 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 138 | 55 | 112 | 0 | 117 | 39 | 0 | 111 | 0 |
N.S. |
1 | 1.02 | 0.41 | 0.83 | 0.00 | 0.87 | 0.29 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.498 | 10.019 | 0.660 | 0.000 | 0.081 | 0.503 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 138 | 55 | 112 | 0 | 100 | 39 | 0 | 35 | 0 |
N.S. |
1 | 1.02 | 0.41 | 0.83 | 0.00 | 0.74 | 0.29 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.491 | 6.048 | 0.497 | 0.000 | 0.078 | 0.464 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 165 | 53 | 131 | 0 | 109 | 41 | 0 | 36 | 41 |
N.S. |
1 | 1.05 | 0.34 | 0.83 | 0.00 | 0.69 | 0.26 | 0.00 | 0.23 | 0.26 |
time (sec) |
N/A | 0.558 | 10.011 | 1.431 | 0.000 | 0.087 | 0.536 | 0.000 | 0.226 | 0.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 196 | 55 | 152 | 0 | 132 | 46 | 0 | 36 | 0 |
N.S. |
1 | 1.09 | 0.31 | 0.84 | 0.00 | 0.73 | 0.26 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.628 | 10.011 | 1.786 | 0.000 | 0.080 | 0.688 | 0.000 | 0.208 | 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 | 46 | 48 | 27 | 23 | 34 | 23 | 41 | 41 | 22 | 23 |
N.S. |
1 | 1.04 | 0.59 | 0.50 | 0.74 | 0.50 | 0.89 | 0.89 | 0.48 | 0.50 |
time (sec) |
N/A | 0.274 | 0.020 | 0.476 | 0.031 | 0.069 | 0.192 | 0.121 | 0.225 | 0.390 |
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 | 33 | 22 | 17 | 23 | 16 | 24 | 23 | 17 | 16 |
N.S. |
1 | 1.06 | 0.71 | 0.55 | 0.74 | 0.52 | 0.77 | 0.74 | 0.55 | 0.52 |
time (sec) |
N/A | 0.264 | 0.016 | 0.435 | 0.031 | 0.070 | 0.117 | 0.122 | 0.186 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 10 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 0.67 | 0.73 | 0.67 | 0.73 |
time (sec) |
N/A | 0.225 | 0.013 | 0.435 | 0.031 | 0.071 | 0.066 | 0.120 | 0.202 | 0.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 29 | 29 | 24 | 31 | 10 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 1.81 | 1.81 | 1.50 | 1.94 | 0.62 | 0.75 |
time (sec) |
N/A | 0.237 | 0.018 | 0.447 | 0.030 | 0.072 | 0.481 | 0.122 | 0.200 | 0.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 28 | 43 | 50 | 73 | 45 | 28 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.23 | 1.43 | 2.09 | 1.29 | 0.80 | 0.77 |
time (sec) |
N/A | 0.254 | 0.042 | 0.500 | 0.030 | 0.072 | 1.019 | 0.119 | 0.230 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 54 | 34 | 30 | 74 | 41 | 110 | 28 | 33 | 0 |
N.S. |
1 | 1.20 | 0.76 | 0.67 | 1.64 | 0.91 | 2.44 | 0.62 | 0.73 | 0.00 |
time (sec) |
N/A | 0.272 | 0.136 | 0.461 | 0.120 | 0.074 | 2.112 | 0.125 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 31 | 27 | 22 | 44 | 33 | 61 | 21 | 20 | 0 |
N.S. |
1 | 1.15 | 1.00 | 0.81 | 1.63 | 1.22 | 2.26 | 0.78 | 0.74 | 0.00 |
time (sec) |
N/A | 0.239 | 0.123 | 0.454 | 0.121 | 0.071 | 0.984 | 0.122 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 16 | 18 | 19 | 6 | 6 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 2.00 | 2.25 | 2.38 | 0.75 | 0.75 | 2.00 |
time (sec) |
N/A | 0.218 | 0.094 | 0.426 | 0.113 | 0.072 | 0.465 | 0.119 | 0.181 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 14 | 34 | 35 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 1.89 | 1.94 | 0.72 | 0.78 |
time (sec) |
N/A | 0.221 | 0.116 | 0.431 | 0.026 | 0.072 | 0.353 | 0.125 | 0.220 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 25 | 22 | 29 | 21 | 63 | 73 | 20 | 21 |
N.S. |
1 | 1.00 | 0.68 | 0.59 | 0.78 | 0.57 | 1.70 | 1.97 | 0.54 | 0.57 |
time (sec) |
N/A | 0.253 | 0.133 | 0.440 | 0.024 | 0.072 | 0.474 | 0.128 | 0.196 | 0.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 30 | 27 | 43 | 26 | 104 | 109 | 25 | 26 |
N.S. |
1 | 1.09 | 0.55 | 0.49 | 0.78 | 0.47 | 1.89 | 1.98 | 0.45 | 0.47 |
time (sec) |
N/A | 0.314 | 0.134 | 0.447 | 0.036 | 0.072 | 0.690 | 0.127 | 0.194 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 48 | 42 | 15 | 0 | 29 | 31 | 0 | 45 | 0 |
N.S. |
1 | 1.12 | 0.98 | 0.35 | 0.00 | 0.67 | 0.72 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.273 | 10.032 | 0.771 | 0.000 | 0.085 | 0.453 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 32 | 15 | 0 | 21 | 31 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.60 | 0.00 | 0.84 | 1.24 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.240 | 10.014 | 0.569 | 0.000 | 0.075 | 0.377 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 12 | 0 | 4 | 29 | 0 | 20 | 10 |
N.S. |
1 | 1.00 | 1.00 | 3.00 | 0.00 | 1.00 | 7.25 | 0.00 | 5.00 | 2.50 |
time (sec) |
N/A | 0.213 | 0.006 | 0.430 | 0.000 | 0.073 | 0.357 | 0.000 | 0.220 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 20 | 15 | 0 | 25 | 34 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.56 | 0.00 | 0.93 | 1.26 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.243 | 10.007 | 0.582 | 0.000 | 0.077 | 0.435 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 20 | 15 | 0 | 33 | 37 | 0 | 24 | 0 |
N.S. |
1 | 1.11 | 0.44 | 0.33 | 0.00 | 0.73 | 0.82 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.278 | 10.006 | 0.837 | 0.000 | 0.079 | 0.521 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 57 | 43 | 15 | 0 | 47 | 31 | 0 | 50 | 0 |
N.S. |
1 | 1.08 | 0.81 | 0.28 | 0.00 | 0.89 | 0.58 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.345 | 10.032 | 1.035 | 0.000 | 0.079 | 0.487 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 34 | 15 | 0 | 40 | 31 | 0 | 37 | 0 |
N.S. |
1 | 0.97 | 0.97 | 0.43 | 0.00 | 1.14 | 0.89 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.302 | 10.012 | 0.648 | 0.000 | 0.095 | 0.409 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 20 | 15 | 0 | 34 | 31 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.82 | 1.36 | 0.00 | 3.09 | 2.82 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.258 | 10.022 | 0.488 | 0.000 | 0.077 | 0.371 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 18 | 15 | 0 | 28 | 32 | 0 | 24 | 13 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.00 | 1.04 | 1.19 | 0.00 | 0.89 | 0.48 |
time (sec) |
N/A | 0.298 | 10.012 | 0.563 | 0.000 | 0.080 | 0.429 | 0.000 | 0.279 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 50 | 20 | 15 | 0 | 41 | 37 | 0 | 24 | 0 |
N.S. |
1 | 0.94 | 0.38 | 0.28 | 0.00 | 0.77 | 0.70 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.347 | 10.007 | 0.649 | 0.000 | 0.081 | 0.480 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 46 | 25 | 22 | 32 | 28 | 54 | 32 | 24 | 25 |
N.S. |
1 | 1.10 | 0.60 | 0.52 | 0.76 | 0.67 | 1.29 | 0.76 | 0.57 | 0.60 |
time (sec) |
N/A | 0.285 | 0.025 | 0.440 | 0.025 | 0.072 | 0.286 | 0.123 | 0.238 | 0.371 |
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 | 20 | 17 | 23 | 23 | 34 | 23 | 19 | 16 |
N.S. |
1 | 1.00 | 0.65 | 0.55 | 0.74 | 0.74 | 1.10 | 0.74 | 0.61 | 0.52 |
time (sec) |
N/A | 0.260 | 0.021 | 0.434 | 0.026 | 0.071 | 0.201 | 0.125 | 0.228 | 0.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 18 | 10 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.20 | 0.67 | 0.73 | 0.80 | 0.73 |
time (sec) |
N/A | 0.222 | 0.012 | 0.431 | 0.030 | 0.069 | 0.157 | 0.120 | 0.245 | 0.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 30 | 25 | 40 | 58 | 228 | 42 | 41 | 24 |
N.S. |
1 | 1.00 | 0.94 | 0.78 | 1.25 | 1.81 | 7.12 | 1.31 | 1.28 | 0.75 |
time (sec) |
N/A | 0.250 | 0.034 | 0.480 | 0.025 | 0.077 | 0.767 | 0.113 | 0.218 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 53 | 41 | 35 | 61 | 78 | 95 | 63 | 56 | 38 |
N.S. |
1 | 1.06 | 0.82 | 0.70 | 1.22 | 1.56 | 1.90 | 1.26 | 1.12 | 0.76 |
time (sec) |
N/A | 0.268 | 0.055 | 0.501 | 0.032 | 0.079 | 1.455 | 0.126 | 0.214 | 0.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 49 | 32 | 27 | 60 | 52 | 82 | 33 | 37 | 0 |
N.S. |
1 | 1.09 | 0.71 | 0.60 | 1.33 | 1.16 | 1.82 | 0.73 | 0.82 | 0.00 |
time (sec) |
N/A | 0.266 | 0.183 | 0.484 | 0.107 | 0.079 | 1.514 | 0.124 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 26 | 22 | 31 | 46 | 46 | 28 | 30 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.81 | 1.15 | 1.70 | 1.70 | 1.04 | 1.11 | 0.00 |
time (sec) |
N/A | 0.238 | 0.141 | 0.457 | 0.108 | 0.077 | 0.752 | 0.122 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 21 | 32 | 21 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.17 | 1.78 | 1.17 | 0.83 | 0.78 |
time (sec) |
N/A | 0.216 | 0.109 | 0.428 | 0.042 | 0.076 | 0.340 | 0.127 | 0.220 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 25 | 22 | 29 | 29 | 90 | 56 | 22 | 18 |
N.S. |
1 | 0.97 | 0.71 | 0.63 | 0.83 | 0.83 | 2.57 | 1.60 | 0.63 | 0.51 |
time (sec) |
N/A | 0.248 | 0.141 | 0.435 | 0.029 | 0.073 | 0.426 | 0.121 | 0.198 | 0.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 57 | 30 | 27 | 43 | 34 | 151 | 94 | 27 | 30 |
N.S. |
1 | 1.04 | 0.55 | 0.49 | 0.78 | 0.62 | 2.75 | 1.71 | 0.49 | 0.55 |
time (sec) |
N/A | 0.283 | 0.163 | 0.467 | 0.031 | 0.079 | 0.609 | 0.119 | 0.211 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 71 | 54 | 15 | 0 | 50 | 31 | 0 | 100 | 0 |
N.S. |
1 | 1.16 | 0.89 | 0.25 | 0.00 | 0.82 | 0.51 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.306 | 5.220 | 1.287 | 0.000 | 0.081 | 0.608 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 48 | 49 | 15 | 0 | 45 | 31 | 0 | 87 | 0 |
N.S. |
1 | 1.12 | 1.14 | 0.35 | 0.00 | 1.05 | 0.72 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.271 | 4.595 | 0.793 | 0.000 | 0.078 | 0.449 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 32 | 15 | 0 | 31 | 31 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.60 | 0.00 | 1.24 | 1.24 | 0.00 | 2.84 | 0.00 |
time (sec) |
N/A | 0.242 | 4.129 | 0.597 | 0.000 | 0.072 | 0.413 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 30 | 12 | 0 | 32 | 29 | 0 | 23 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.48 | 0.00 | 1.28 | 1.16 | 0.00 | 0.92 | 0.40 |
time (sec) |
N/A | 0.232 | 0.004 | 0.487 | 0.000 | 0.074 | 0.414 | 0.000 | 0.225 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 20 | 15 | 0 | 47 | 34 | 0 | 25 | 0 |
N.S. |
1 | 1.11 | 0.44 | 0.33 | 0.00 | 1.04 | 0.76 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.285 | 10.005 | 0.566 | 0.000 | 0.078 | 0.497 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 73 | 20 | 15 | 0 | 52 | 37 | 0 | 25 | 0 |
N.S. |
1 | 1.16 | 0.32 | 0.24 | 0.00 | 0.83 | 0.59 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.319 | 10.008 | 0.792 | 0.000 | 0.078 | 0.655 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 80 | 56 | 15 | 0 | 74 | 31 | 0 | 109 | 0 |
N.S. |
1 | 1.13 | 0.79 | 0.21 | 0.00 | 1.04 | 0.44 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.395 | 7.356 | 1.702 | 0.000 | 0.081 | 0.642 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 57 | 49 | 15 | 0 | 69 | 31 | 0 | 95 | 0 |
N.S. |
1 | 1.08 | 0.92 | 0.28 | 0.00 | 1.30 | 0.58 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.328 | 4.789 | 1.016 | 0.000 | 0.082 | 0.586 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 31 | 15 | 0 | 64 | 31 | 0 | 80 | 0 |
N.S. |
1 | 0.97 | 0.89 | 0.43 | 0.00 | 1.83 | 0.89 | 0.00 | 2.29 | 0.00 |
time (sec) |
N/A | 0.304 | 4.386 | 0.656 | 0.000 | 0.080 | 0.414 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 20 | 15 | 0 | 44 | 31 | 0 | 26 | 0 |
N.S. |
1 | 0.97 | 0.57 | 0.43 | 0.00 | 1.26 | 0.89 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.301 | 4.034 | 0.638 | 0.000 | 0.075 | 0.377 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 50 | 18 | 15 | 0 | 55 | 32 | 0 | 25 | 13 |
N.S. |
1 | 0.94 | 0.34 | 0.28 | 0.00 | 1.04 | 0.60 | 0.00 | 0.47 | 0.25 |
time (sec) |
N/A | 0.355 | 9.266 | 0.622 | 0.000 | 0.076 | 0.437 | 0.000 | 0.240 | 0.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 73 | 20 | 15 | 0 | 66 | 37 | 0 | 25 | 0 |
N.S. |
1 | 1.03 | 0.28 | 0.21 | 0.00 | 0.93 | 0.52 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.386 | 10.005 | 0.711 | 0.000 | 0.081 | 0.547 | 0.000 | 0.226 | 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 | 40 | 42 | 25 | 21 | 28 | 21 | 39 | 28 | 131 | 20 |
N.S. |
1 | 1.05 | 0.62 | 0.52 | 0.70 | 0.52 | 0.98 | 0.70 | 3.28 | 0.50 |
time (sec) |
N/A | 0.275 | 0.017 | 0.478 | 0.025 | 0.074 | 0.181 | 0.114 | 0.214 | 0.326 |
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 | 29 | 18 | 15 | 19 | 14 | 22 | 19 | 83 | 14 |
N.S. |
1 | 1.07 | 0.67 | 0.56 | 0.70 | 0.52 | 0.81 | 0.70 | 3.07 | 0.52 |
time (sec) |
N/A | 0.258 | 0.015 | 0.487 | 0.024 | 0.068 | 0.111 | 0.117 | 0.195 | 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 | 13 | 13 | 13 | 10 | 9 | 9 | 8 | 9 | 32 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 0.62 | 0.69 | 2.46 | 0.69 |
time (sec) |
N/A | 0.217 | 0.011 | 0.484 | 0.030 | 0.071 | 0.067 | 0.113 | 0.204 | 0.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 24 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 1.71 | 0.71 | 0.79 | 0.71 |
time (sec) |
N/A | 0.238 | 0.018 | 0.707 | 0.111 | 0.074 | 0.478 | 0.123 | 0.207 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 28 | 28 | 24 | 23 | 25 | 71 | 23 | 109 | 23 |
N.S. |
1 | 0.90 | 0.90 | 0.77 | 0.74 | 0.81 | 2.29 | 0.74 | 3.52 | 0.74 |
time (sec) |
N/A | 0.244 | 0.026 | 0.628 | 0.112 | 0.073 | 1.055 | 0.124 | 0.243 | 0.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 38 | 36 | 48 | 34 | 129 | 35 | 195 | 35 |
N.S. |
1 | 1.04 | 0.81 | 0.77 | 1.02 | 0.72 | 2.74 | 0.74 | 4.15 | 0.74 |
time (sec) |
N/A | 0.262 | 0.039 | 0.555 | 0.124 | 0.077 | 2.111 | 0.120 | 0.219 | 0.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 60 | 42 | 35 | 86 | 37 | 110 | 36 | 186 | 0 |
N.S. |
1 | 1.18 | 0.82 | 0.69 | 1.69 | 0.73 | 2.16 | 0.71 | 3.65 | 0.00 |
time (sec) |
N/A | 0.283 | 0.167 | 0.521 | 0.026 | 0.074 | 2.156 | 0.124 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 39 | 32 | 28 | 58 | 29 | 61 | 29 | 105 | 0 |
N.S. |
1 | 1.11 | 0.91 | 0.80 | 1.66 | 0.83 | 1.74 | 0.83 | 3.00 | 0.00 |
time (sec) |
N/A | 0.255 | 0.114 | 0.475 | 0.026 | 0.073 | 0.986 | 0.125 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 33 | 16 | 19 | 16 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.83 | 0.89 | 1.06 | 0.89 | 0.72 | 0.78 |
time (sec) |
N/A | 0.245 | 0.168 | 0.438 | 0.032 | 0.073 | 0.471 | 0.118 | 0.193 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 16 | 29 | 19 | 35 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.00 | 1.81 | 1.19 | 2.19 | 0.75 |
time (sec) |
N/A | 0.233 | 0.104 | 0.441 | 0.025 | 0.076 | 0.357 | 0.123 | 0.196 | 0.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 23 | 20 | 25 | 26 | 60 | 40 | 55 | 25 |
N.S. |
1 | 1.00 | 0.70 | 0.61 | 0.76 | 0.79 | 1.82 | 1.21 | 1.67 | 0.76 |
time (sec) |
N/A | 0.240 | 0.118 | 0.446 | 0.029 | 0.075 | 0.479 | 0.121 | 0.264 | 0.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 28 | 25 | 37 | 31 | 100 | 57 | 85 | 24 |
N.S. |
1 | 1.10 | 0.57 | 0.51 | 0.76 | 0.63 | 2.04 | 1.16 | 1.73 | 0.49 |
time (sec) |
N/A | 0.272 | 0.125 | 0.461 | 0.033 | 0.079 | 0.706 | 0.123 | 0.227 | 0.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 93 | 52 | 33 | 0 | 27 | 27 | 0 | 39 | 0 |
N.S. |
1 | 1.58 | 0.88 | 0.56 | 0.00 | 0.46 | 0.46 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.303 | 10.022 | 0.953 | 0.000 | 0.076 | 0.440 | 0.000 | 0.199 | 0.000 |