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 | 11 | 11 | 22 | 12 | 11 | 11 | 14 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 2.00 | 1.09 | 1.00 | 1.00 | 1.27 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.257 | 0.011 | 2.368 | 0.032 | 0.073 | 0.054 | 0.112 | 0.197 | 0.021 |
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 | 25 | 25 | 23 | 19 | 24 | 23 | 46 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 0.92 | 0.76 | 0.96 | 0.92 | 1.84 | 0.72 | 0.92 | 0.72 |
time (sec) |
N/A | 0.277 | 0.037 | 3.589 | 0.026 | 0.099 | 0.080 | 0.120 | 0.257 | 25.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 29 | 22 | 22 | 22 | 37 | 25 | 31 | 24 |
N.S. |
1 | 0.89 | 1.07 | 0.81 | 0.81 | 0.81 | 1.37 | 0.93 | 1.15 | 0.89 |
time (sec) |
N/A | 0.296 | 0.025 | 6.322 | 0.027 | 0.088 | 0.103 | 0.118 | 0.169 | 0.043 |
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 | 46 | 51 | 33 | 31 | 33 | 36 | 95 | 32 | 40 | 50 |
N.S. |
1 | 1.11 | 0.72 | 0.67 | 0.72 | 0.78 | 2.07 | 0.70 | 0.87 | 1.09 |
time (sec) |
N/A | 0.378 | 0.062 | 6.619 | 0.032 | 0.075 | 0.155 | 0.129 | 0.151 | 25.438 |
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 | 36 | 44 | 32 | 34 | 34 | 60 | 38 | 47 | 32 |
N.S. |
1 | 0.86 | 1.05 | 0.76 | 0.81 | 0.81 | 1.43 | 0.90 | 1.12 | 0.76 |
time (sec) |
N/A | 0.312 | 0.029 | 8.895 | 0.030 | 0.082 | 0.209 | 0.119 | 0.168 | 0.056 |
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 | 67 | 77 | 45 | 44 | 48 | 47 | 139 | 46 | 56 | 43 |
N.S. |
1 | 1.15 | 0.67 | 0.66 | 0.72 | 0.70 | 2.07 | 0.69 | 0.84 | 0.64 |
time (sec) |
N/A | 0.515 | 0.066 | 9.667 | 0.032 | 0.095 | 0.327 | 0.123 | 0.152 | 25.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 46 | 59 | 42 | 44 | 44 | 80 | 50 | 63 | 43 |
N.S. |
1 | 0.85 | 1.09 | 0.78 | 0.81 | 0.81 | 1.48 | 0.93 | 1.17 | 0.80 |
time (sec) |
N/A | 0.348 | 0.025 | 12.771 | 0.038 | 0.084 | 0.443 | 0.120 | 0.149 | 0.064 |
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 | 88 | 103 | 55 | 55 | 59 | 56 | 184 | 60 | 72 | 90 |
N.S. |
1 | 1.17 | 0.62 | 0.62 | 0.67 | 0.64 | 2.09 | 0.68 | 0.82 | 1.02 |
time (sec) |
N/A | 0.678 | 0.080 | 14.104 | 0.028 | 0.099 | 0.640 | 0.118 | 0.171 | 26.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 65 | 45 | 84 | 0 | 66 | 0 | 0 | 14 | 34 |
N.S. |
1 | 1.08 | 0.75 | 1.40 | 0.00 | 1.10 | 0.00 | 0.00 | 0.23 | 0.57 |
time (sec) |
N/A | 0.475 | 0.098 | 2.428 | 0.000 | 0.120 | 0.000 | 0.000 | 0.163 | 25.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 35 | 118 | 0 | 61 | 0 | 0 | 14 | 34 |
N.S. |
1 | 1.00 | 0.85 | 2.88 | 0.00 | 1.49 | 0.00 | 0.00 | 0.34 | 0.83 |
time (sec) |
N/A | 0.367 | 0.058 | 2.175 | 0.000 | 0.109 | 0.000 | 0.000 | 0.149 | 25.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 33 | 72 | 0 | 55 | 0 | 0 | 12 | 34 |
N.S. |
1 | 1.00 | 0.80 | 1.76 | 0.00 | 1.34 | 0.00 | 0.00 | 0.29 | 0.83 |
time (sec) |
N/A | 0.359 | 0.052 | 2.020 | 0.000 | 0.103 | 0.000 | 0.000 | 0.165 | 25.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 77 | 0 | 50 | 0 | 0 | 7 | 15 |
N.S. |
1 | 1.00 | 1.11 | 4.05 | 0.00 | 2.63 | 0.00 | 0.00 | 0.37 | 0.79 |
time (sec) |
N/A | 0.271 | 0.037 | 2.988 | 0.000 | 0.088 | 0.000 | 0.000 | 0.232 | 25.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 57 | 0 | 42 | 0 | 0 | 14 | 15 |
N.S. |
1 | 1.00 | 1.11 | 3.00 | 0.00 | 2.21 | 0.00 | 0.00 | 0.74 | 0.79 |
time (sec) |
N/A | 0.273 | 0.039 | 1.744 | 0.000 | 0.085 | 0.000 | 0.000 | 0.253 | 25.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 32 | 110 | 0 | 75 | 0 | 0 | 14 | 34 |
N.S. |
1 | 1.00 | 0.86 | 2.97 | 0.00 | 2.03 | 0.00 | 0.00 | 0.38 | 0.92 |
time (sec) |
N/A | 0.369 | 0.076 | 2.341 | 0.000 | 0.103 | 0.000 | 0.000 | 0.151 | 25.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 33 | 72 | 0 | 80 | 0 | 0 | 14 | 34 |
N.S. |
1 | 1.00 | 0.80 | 1.76 | 0.00 | 1.95 | 0.00 | 0.00 | 0.34 | 0.83 |
time (sec) |
N/A | 0.365 | 0.069 | 2.020 | 0.000 | 0.089 | 0.000 | 0.000 | 0.158 | 25.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 61 | 51 | 132 | 0 | 117 | 0 | 0 | 14 | 34 |
N.S. |
1 | 1.02 | 0.85 | 2.20 | 0.00 | 1.95 | 0.00 | 0.00 | 0.23 | 0.57 |
time (sec) |
N/A | 0.468 | 0.070 | 2.125 | 0.000 | 0.100 | 0.000 | 0.000 | 0.174 | 25.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 75 | 55 | 104 | 0 | 80 | 0 | 0 | 18 | 42 |
N.S. |
1 | 1.07 | 0.79 | 1.49 | 0.00 | 1.14 | 0.00 | 0.00 | 0.26 | 0.60 |
time (sec) |
N/A | 0.501 | 0.134 | 2.484 | 0.000 | 0.095 | 0.000 | 0.000 | 0.150 | 25.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 44 | 142 | 0 | 73 | 0 | 0 | 18 | 42 |
N.S. |
1 | 1.00 | 0.94 | 3.02 | 0.00 | 1.55 | 0.00 | 0.00 | 0.38 | 0.89 |
time (sec) |
N/A | 0.396 | 0.099 | 2.377 | 0.000 | 0.086 | 0.000 | 0.000 | 0.158 | 25.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 40 | 88 | 0 | 67 | 0 | 0 | 16 | 42 |
N.S. |
1 | 1.00 | 0.85 | 1.87 | 0.00 | 1.43 | 0.00 | 0.00 | 0.34 | 0.89 |
time (sec) |
N/A | 0.389 | 0.044 | 2.281 | 0.000 | 0.140 | 0.000 | 0.000 | 0.163 | 25.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 24 | 91 | 0 | 58 | 0 | 0 | 9 | 18 |
N.S. |
1 | 1.00 | 1.14 | 4.33 | 0.00 | 2.76 | 0.00 | 0.00 | 0.43 | 0.86 |
time (sec) |
N/A | 0.281 | 0.016 | 2.746 | 0.000 | 0.101 | 0.000 | 0.000 | 0.152 | 25.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 24 | 69 | 0 | 50 | 0 | 0 | 18 | 18 |
N.S. |
1 | 1.00 | 1.14 | 3.29 | 0.00 | 2.38 | 0.00 | 0.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.281 | 0.024 | 1.735 | 0.000 | 0.087 | 0.000 | 0.000 | 0.179 | 25.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 39 | 132 | 0 | 93 | 0 | 0 | 18 | 42 |
N.S. |
1 | 1.00 | 0.91 | 3.07 | 0.00 | 2.16 | 0.00 | 0.00 | 0.42 | 0.98 |
time (sec) |
N/A | 0.383 | 0.094 | 2.306 | 0.000 | 0.101 | 0.000 | 0.000 | 0.225 | 25.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 43 | 88 | 0 | 98 | 0 | 0 | 18 | 42 |
N.S. |
1 | 1.00 | 0.91 | 1.87 | 0.00 | 2.09 | 0.00 | 0.00 | 0.38 | 0.89 |
time (sec) |
N/A | 0.382 | 0.127 | 2.203 | 0.000 | 0.104 | 0.000 | 0.000 | 0.159 | 26.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 71 | 55 | 160 | 0 | 143 | 0 | 0 | 18 | 42 |
N.S. |
1 | 1.01 | 0.79 | 2.29 | 0.00 | 2.04 | 0.00 | 0.00 | 0.26 | 0.60 |
time (sec) |
N/A | 0.516 | 0.347 | 2.265 | 0.000 | 0.093 | 0.000 | 0.000 | 0.165 | 26.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 109 | 80 | 108 | 0 | 98 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.06 | 0.78 | 1.05 | 0.00 | 0.95 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.717 | 0.209 | 3.659 | 0.000 | 0.095 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 66 | 152 | 0 | 94 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.03 | 0.00 | 1.25 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.526 | 0.138 | 3.326 | 0.000 | 0.100 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 62 | 97 | 0 | 76 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.29 | 0.00 | 1.01 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.530 | 0.076 | 2.941 | 0.000 | 0.111 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 98 | 0 | 62 | 0 | 0 | 12 | 36 |
N.S. |
1 | 1.00 | 0.98 | 2.28 | 0.00 | 1.44 | 0.00 | 0.00 | 0.28 | 0.84 |
time (sec) |
N/A | 0.391 | 0.042 | 3.749 | 0.000 | 0.089 | 0.000 | 0.000 | 0.160 | 28.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 74 | 0 | 57 | 0 | 0 | 24 | 36 |
N.S. |
1 | 1.00 | 0.98 | 1.72 | 0.00 | 1.33 | 0.00 | 0.00 | 0.56 | 0.84 |
time (sec) |
N/A | 0.390 | 0.047 | 2.260 | 0.000 | 0.103 | 0.000 | 0.000 | 0.166 | 28.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 54 | 141 | 0 | 102 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.93 | 0.00 | 1.40 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.536 | 0.076 | 3.096 | 0.000 | 0.085 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 55 | 105 | 0 | 110 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.71 | 1.36 | 0.00 | 1.43 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.516 | 0.103 | 2.971 | 0.000 | 0.100 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 109 | 68 | 168 | 0 | 155 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.04 | 0.65 | 1.60 | 0.00 | 1.48 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.717 | 0.211 | 3.071 | 0.000 | 0.100 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.325 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.332 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 517 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.11 | 0.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.320 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.23 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.323 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 56 | 53 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.21 | 0.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.331 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 53 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.329 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 10 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.86 |
time (sec) |
N/A | 0.337 | 0.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 26.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.341 | 0.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 76 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.427 | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 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 | 15 | 15 | 15 | 14 | 13 | 13 | 22 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.47 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.309 | 0.006 | 4.773 | 0.031 | 0.099 | 0.142 | 0.119 | 0.234 | 0.057 |
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 | 14 | 13 | 13 | 22 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.47 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.311 | 0.005 | 4.444 | 0.031 | 0.098 | 0.099 | 0.121 | 0.149 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 37 | 14 | 13 | 13 | 20 | 13 | 13 | 28 |
N.S. |
1 | 1.00 | 2.47 | 0.93 | 0.87 | 0.87 | 1.33 | 0.87 | 0.87 | 1.87 |
time (sec) |
N/A | 0.289 | 0.020 | 2.598 | 0.028 | 0.082 | 0.072 | 0.123 | 0.154 | 25.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 17 | 11 | 18 | 19 | 13 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 0.92 | 1.50 | 1.58 | 1.08 | 1.33 | 1.33 |
time (sec) |
N/A | 0.276 | 0.010 | 0.789 | 0.027 | 0.108 | 0.055 | 0.124 | 0.172 | 25.777 |
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 | 10 | 10 | 10 | 11 | 12 | 12 | 15 | 12 | 10 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.20 | 1.20 | 1.50 | 1.20 | 1.00 | 2.00 |
time (sec) |
N/A | 0.286 | 0.011 | 1.067 | 0.028 | 0.099 | 0.087 | 0.125 | 0.142 | 26.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 20 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.33 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.305 | 0.014 | 1.211 | 0.033 | 0.072 | 0.117 | 0.121 | 0.153 | 25.806 |
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 | 14 | 13 | 13 | 20 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.33 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.306 | 0.012 | 1.866 | 0.027 | 0.091 | 0.170 | 0.126 | 0.150 | 25.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 53 | 47 | 47 | 46 | 53 | 88 | 46 | 45 | 45 |
N.S. |
1 | 0.87 | 0.77 | 0.77 | 0.75 | 0.87 | 1.44 | 0.75 | 0.74 | 0.74 |
time (sec) |
N/A | 0.375 | 0.203 | 17.695 | 0.028 | 0.080 | 0.903 | 0.133 | 0.149 | 25.853 |
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 | 41 | 37 | 36 | 36 | 43 | 66 | 36 | 35 | 36 |
N.S. |
1 | 0.89 | 0.80 | 0.78 | 0.78 | 0.93 | 1.43 | 0.78 | 0.76 | 0.78 |
time (sec) |
N/A | 0.366 | 0.102 | 11.905 | 0.028 | 0.094 | 0.445 | 0.122 | 0.154 | 25.472 |
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 | 29 | 27 | 37 | 26 | 33 | 44 | 26 | 25 | 26 |
N.S. |
1 | 0.94 | 0.87 | 1.19 | 0.84 | 1.06 | 1.42 | 0.84 | 0.81 | 0.84 |
time (sec) |
N/A | 0.352 | 0.060 | 9.525 | 0.033 | 0.076 | 0.209 | 0.130 | 0.153 | 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 | 15 | 15 | 15 | 14 | 13 | 21 | 20 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.40 | 1.33 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.306 | 0.005 | 4.420 | 0.026 | 0.080 | 0.099 | 0.120 | 0.216 | 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 | 14 | 14 | 23 | 15 | 18 | 17 | 15 | 21 | 15 | 14 |
N.S. |
1 | 1.00 | 1.64 | 1.07 | 1.29 | 1.21 | 1.07 | 1.50 | 1.07 | 1.00 |
time (sec) |
N/A | 0.291 | 0.011 | 0.733 | 0.104 | 0.083 | 0.066 | 0.142 | 0.264 | 25.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 29 | 22 | 13 | 33 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.93 | 1.47 | 0.87 | 2.20 | 0.87 |
time (sec) |
N/A | 0.321 | 0.008 | 1.535 | 0.025 | 0.081 | 0.466 | 0.170 | 0.156 | 25.369 |
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 | 31 | 29 | 56 | 26 | 26 | 39 | 0 | 26 | 55 | 25 |
N.S. |
1 | 0.94 | 1.81 | 0.84 | 0.84 | 1.26 | 0.00 | 0.84 | 1.77 | 0.81 |
time (sec) |
N/A | 0.359 | 0.190 | 4.460 | 0.029 | 0.082 | 0.000 | 0.183 | 0.158 | 25.392 |
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 | 46 | 41 | 77 | 36 | 36 | 51 | 0 | 36 | 75 | 35 |
N.S. |
1 | 0.89 | 1.67 | 0.78 | 0.78 | 1.11 | 0.00 | 0.78 | 1.63 | 0.76 |
time (sec) |
N/A | 0.371 | 0.156 | 15.566 | 0.043 | 0.090 | 0.000 | 0.211 | 0.168 | 25.397 |
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 | 61 | 53 | 98 | 46 | 46 | 61 | 0 | 46 | 95 | 45 |
N.S. |
1 | 0.87 | 1.61 | 0.75 | 0.75 | 1.00 | 0.00 | 0.75 | 1.56 | 0.74 |
time (sec) |
N/A | 0.368 | 0.159 | 54.680 | 0.033 | 0.085 | 0.000 | 0.217 | 0.148 | 25.502 |
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 | 88 | 103 | 52 | 55 | 48 | 57 | 189 | 60 | 72 | 89 |
N.S. |
1 | 1.17 | 0.59 | 0.62 | 0.55 | 0.65 | 2.15 | 0.68 | 0.82 | 1.01 |
time (sec) |
N/A | 0.714 | 0.188 | 15.714 | 0.032 | 0.101 | 0.654 | 0.125 | 0.151 | 26.735 |
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 | 67 | 77 | 40 | 44 | 37 | 47 | 136 | 46 | 56 | 43 |
N.S. |
1 | 1.15 | 0.60 | 0.66 | 0.55 | 0.70 | 2.03 | 0.69 | 0.84 | 0.64 |
time (sec) |
N/A | 0.566 | 0.091 | 10.247 | 0.051 | 0.081 | 0.330 | 0.129 | 0.164 | 25.855 |
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 | 46 | 51 | 23 | 19 | 24 | 36 | 92 | 18 | 39 | 50 |
N.S. |
1 | 1.11 | 0.50 | 0.41 | 0.52 | 0.78 | 2.00 | 0.39 | 0.85 | 1.09 |
time (sec) |
N/A | 0.434 | 0.090 | 4.331 | 0.027 | 0.093 | 0.157 | 0.125 | 0.170 | 25.712 |
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 | 25 | 25 | 23 | 19 | 24 | 23 | 46 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 0.92 | 0.76 | 0.96 | 0.92 | 1.84 | 0.72 | 0.92 | 0.72 |
time (sec) |
N/A | 0.290 | 0.019 | 3.480 | 0.037 | 0.081 | 0.081 | 0.130 | 0.170 | 0.004 |
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 | 23 | 20 | 23 | 28 | 34 | 36 | 0 | 42 | 39 | 27 |
N.S. |
1 | 0.87 | 1.00 | 1.22 | 1.48 | 1.57 | 0.00 | 1.83 | 1.70 | 1.17 |
time (sec) |
N/A | 0.301 | 0.015 | 2.200 | 0.037 | 0.095 | 0.000 | 0.130 | 0.166 | 25.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 48 | 46 | 61 | 0 | 48 | 95 | 69 |
N.S. |
1 | 1.00 | 1.00 | 1.41 | 1.35 | 1.79 | 0.00 | 1.41 | 2.79 | 2.03 |
time (sec) |
N/A | 0.401 | 0.020 | 1.504 | 0.043 | 0.101 | 0.000 | 0.179 | 0.171 | 26.134 |
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 | 55 | 60 | 55 | 66 | 65 | 71 | 0 | 82 | 155 | 125 |
N.S. |
1 | 1.09 | 1.00 | 1.20 | 1.18 | 1.29 | 0.00 | 1.49 | 2.82 | 2.27 |
time (sec) |
N/A | 0.560 | 0.021 | 3.053 | 0.048 | 0.089 | 0.000 | 0.207 | 0.279 | 28.553 |
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 | 76 | 86 | 76 | 84 | 91 | 84 | 0 | 73 | 226 | 177 |
N.S. |
1 | 1.13 | 1.00 | 1.11 | 1.20 | 1.11 | 0.00 | 0.96 | 2.97 | 2.33 |
time (sec) |
N/A | 0.724 | 0.023 | 8.760 | 0.038 | 0.119 | 0.000 | 0.224 | 0.250 | 29.282 |
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 | 31 | 30 | 48 | 26 | 36 | 26 | 63 | 26 | 35 | 25 |
N.S. |
1 | 0.97 | 1.55 | 0.84 | 1.16 | 0.84 | 2.03 | 0.84 | 1.13 | 0.81 |
time (sec) |
N/A | 0.352 | 0.154 | 14.457 | 0.037 | 0.082 | 0.623 | 0.125 | 0.162 | 0.059 |
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 | 31 | 30 | 27 | 26 | 26 | 26 | 46 | 26 | 63 | 26 |
N.S. |
1 | 0.97 | 0.87 | 0.84 | 0.84 | 0.84 | 1.48 | 0.84 | 2.03 | 0.84 |
time (sec) |
N/A | 0.362 | 0.117 | 12.029 | 0.040 | 0.078 | 0.441 | 0.126 | 0.167 | 0.052 |
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 | 29 | 35 | 26 | 26 | 26 | 42 | 26 | 25 | 37 |
N.S. |
1 | 0.94 | 1.13 | 0.84 | 0.84 | 0.84 | 1.35 | 0.84 | 0.81 | 1.19 |
time (sec) |
N/A | 0.353 | 0.067 | 7.030 | 0.034 | 0.108 | 0.308 | 0.121 | 0.180 | 25.514 |
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 | 31 | 30 | 27 | 34 | 26 | 26 | 46 | 26 | 47 | 26 |
N.S. |
1 | 0.97 | 0.87 | 1.10 | 0.84 | 0.84 | 1.48 | 0.84 | 1.52 | 0.84 |
time (sec) |
N/A | 0.357 | 0.057 | 7.708 | 0.048 | 0.071 | 0.209 | 0.120 | 0.167 | 0.031 |
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 | 14 | 13 | 24 | 20 | 24 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.60 | 1.33 | 1.60 | 0.87 | 0.87 |
time (sec) |
N/A | 0.309 | 0.004 | 4.753 | 0.044 | 0.090 | 0.142 | 0.119 | 0.183 | 25.262 |
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 | 28 | 25 | 25 | 25 | 25 | 25 | 0 | 27 | 60 | 30 |
N.S. |
1 | 0.89 | 0.89 | 0.89 | 0.89 | 0.89 | 0.00 | 0.96 | 2.14 | 1.07 |
time (sec) |
N/A | 0.345 | 0.022 | 2.471 | 0.044 | 0.087 | 0.000 | 0.127 | 0.158 | 25.274 |
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 | 21 | 22 | 21 | 40 | 19 | 22 | 0 | 23 | 31 | 20 |
N.S. |
1 | 1.05 | 1.00 | 1.90 | 0.90 | 1.05 | 0.00 | 1.10 | 1.48 | 0.95 |
time (sec) |
N/A | 0.347 | 0.108 | 3.974 | 0.045 | 0.107 | 0.000 | 0.150 | 0.161 | 25.400 |
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 | 27 | 27 | 25 | 28 | 31 | 27 | 32 | 30 | 27 | 30 |
N.S. |
1 | 1.00 | 0.93 | 1.04 | 1.15 | 1.00 | 1.19 | 1.11 | 1.00 | 1.11 |
time (sec) |
N/A | 0.390 | 0.069 | 0.828 | 0.035 | 0.102 | 0.078 | 0.137 | 0.155 | 25.252 |
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 | 25 | 27 | 24 | 25 | 25 | 39 | 25 | 21 | 23 |
N.S. |
1 | 0.93 | 1.00 | 0.89 | 0.93 | 0.93 | 1.44 | 0.93 | 0.78 | 0.85 |
time (sec) |
N/A | 0.334 | 0.116 | 1.224 | 0.042 | 0.094 | 0.176 | 0.138 | 0.153 | 25.508 |
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 | 15 | 15 | 15 | 14 | 13 | 25 | 42 | 25 | 23 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.67 | 2.80 | 1.67 | 1.53 | 0.87 |
time (sec) |
N/A | 0.322 | 0.007 | 1.945 | 0.033 | 0.100 | 0.251 | 0.143 | 0.168 | 25.322 |
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 | 29 | 31 | 26 | 25 | 25 | 44 | 25 | 25 | 25 |
N.S. |
1 | 0.94 | 1.00 | 0.84 | 0.81 | 0.81 | 1.42 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.363 | 0.178 | 3.533 | 0.048 | 0.077 | 0.393 | 0.139 | 0.218 | 25.394 |
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 | 29 | 31 | 34 | 49 | 25 | 42 | 25 | 25 | 25 |
N.S. |
1 | 0.94 | 1.00 | 1.10 | 1.58 | 0.81 | 1.35 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.360 | 0.027 | 6.685 | 0.039 | 0.083 | 0.565 | 0.141 | 0.262 | 25.241 |
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 | 29 | 31 | 26 | 25 | 25 | 44 | 25 | 25 | 27 |
N.S. |
1 | 0.94 | 1.00 | 0.84 | 0.81 | 0.81 | 1.42 | 0.81 | 0.81 | 0.87 |
time (sec) |
N/A | 0.363 | 0.135 | 11.602 | 0.037 | 0.110 | 0.816 | 0.141 | 0.162 | 25.597 |
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 | 31 | 29 | 31 | 34 | 59 | 25 | 42 | 25 | 25 | 35 |
N.S. |
1 | 0.94 | 1.00 | 1.10 | 1.90 | 0.81 | 1.35 | 0.81 | 0.81 | 1.13 |
time (sec) |
N/A | 0.353 | 0.026 | 21.747 | 0.031 | 0.106 | 1.153 | 0.147 | 0.163 | 25.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 53 | 47 | 47 | 46 | 63 | 88 | 46 | 45 | 45 |
N.S. |
1 | 0.87 | 0.77 | 0.77 | 0.75 | 1.03 | 1.44 | 0.75 | 0.74 | 0.74 |
time (sec) |
N/A | 0.379 | 0.218 | 54.112 | 0.041 | 0.098 | 1.763 | 0.129 | 0.205 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 37 | 36 | 36 | 53 | 66 | 36 | 35 | 36 |
N.S. |
1 | 0.89 | 0.80 | 0.78 | 0.78 | 1.15 | 1.43 | 0.78 | 0.76 | 0.78 |
time (sec) |
N/A | 0.368 | 0.107 | 21.329 | 0.029 | 0.081 | 0.896 | 0.122 | 0.165 | 25.445 |
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 | 31 | 29 | 27 | 26 | 26 | 41 | 44 | 26 | 25 | 26 |
N.S. |
1 | 0.94 | 0.87 | 0.84 | 0.84 | 1.32 | 1.42 | 0.84 | 0.81 | 0.84 |
time (sec) |
N/A | 0.355 | 0.067 | 10.422 | 0.041 | 0.106 | 0.441 | 0.119 | 0.171 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 31 | 20 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.07 | 1.33 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.308 | 0.004 | 3.891 | 0.044 | 0.078 | 0.202 | 0.118 | 0.162 | 0.038 |
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 | 35 | 49 | 31 | 54 | 41 | 42 | 0 | 44 | 51 | 38 |
N.S. |
1 | 1.40 | 0.89 | 1.54 | 1.17 | 1.20 | 0.00 | 1.26 | 1.46 | 1.09 |
time (sec) |
N/A | 0.356 | 0.258 | 2.326 | 0.122 | 0.083 | 0.000 | 0.149 | 0.166 | 25.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 38 | 27 | 29 | 26 | 27 | 39 | 26 | 24 |
N.S. |
1 | 1.00 | 1.36 | 0.96 | 1.04 | 0.93 | 0.96 | 1.39 | 0.93 | 0.86 |
time (sec) |
N/A | 0.382 | 0.016 | 0.435 | 0.115 | 0.075 | 0.089 | 0.151 | 0.169 | 25.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 39 | 22 | 13 | 43 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.60 | 1.47 | 0.87 | 2.87 | 0.87 |
time (sec) |
N/A | 0.314 | 0.009 | 1.394 | 0.033 | 0.080 | 0.709 | 0.183 | 0.169 | 25.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 77 | 26 | 26 | 49 | 0 | 26 | 65 | 25 |
N.S. |
1 | 0.94 | 2.48 | 0.84 | 0.84 | 1.58 | 0.00 | 0.84 | 2.10 | 0.81 |
time (sec) |
N/A | 0.346 | 0.190 | 4.694 | 0.040 | 0.091 | 0.000 | 0.204 | 0.168 | 25.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 98 | 36 | 36 | 61 | 0 | 36 | 85 | 35 |
N.S. |
1 | 0.89 | 2.13 | 0.78 | 0.78 | 1.33 | 0.00 | 0.78 | 1.85 | 0.76 |
time (sec) |
N/A | 0.367 | 0.164 | 15.803 | 0.037 | 0.122 | 0.000 | 0.220 | 0.169 | 25.346 |
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 | 111 | 131 | 62 | 66 | 48 | 66 | 231 | 74 | 88 | 109 |
N.S. |
1 | 1.18 | 0.56 | 0.59 | 0.43 | 0.59 | 2.08 | 0.67 | 0.79 | 0.98 |
time (sec) |
N/A | 0.926 | 0.211 | 21.421 | 0.047 | 0.095 | 1.276 | 0.127 | 0.162 | 26.864 |
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 | 90 | 105 | 33 | 31 | 33 | 56 | 189 | 32 | 72 | 90 |
N.S. |
1 | 1.17 | 0.37 | 0.34 | 0.37 | 0.62 | 2.10 | 0.36 | 0.80 | 1.00 |
time (sec) |
N/A | 0.745 | 0.100 | 7.570 | 0.032 | 0.081 | 0.646 | 0.126 | 0.232 | 26.450 |
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 | 69 | 79 | 40 | 42 | 37 | 46 | 136 | 46 | 56 | 43 |
N.S. |
1 | 1.14 | 0.58 | 0.61 | 0.54 | 0.67 | 1.97 | 0.67 | 0.81 | 0.62 |
time (sec) |
N/A | 0.595 | 0.062 | 5.237 | 0.045 | 0.090 | 0.326 | 0.132 | 0.259 | 25.423 |
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 | 46 | 51 | 33 | 31 | 33 | 36 | 95 | 32 | 40 | 50 |
N.S. |
1 | 1.11 | 0.72 | 0.67 | 0.72 | 0.78 | 2.07 | 0.70 | 0.87 | 1.09 |
time (sec) |
N/A | 0.399 | 0.038 | 4.098 | 0.051 | 0.076 | 0.152 | 0.126 | 0.170 | 0.076 |
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 | 38 | 32 | 38 | 38 | 46 | 48 | 0 | 60 | 52 | 53 |
N.S. |
1 | 0.84 | 1.00 | 1.00 | 1.21 | 1.26 | 0.00 | 1.58 | 1.37 | 1.39 |
time (sec) |
N/A | 0.350 | 0.019 | 1.762 | 0.056 | 0.089 | 0.000 | 0.126 | 0.163 | 25.435 |
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 | 51 | 53 | 58 | 56 | 74 | 0 | 64 | 71 | 98 |
N.S. |
1 | 1.16 | 1.20 | 1.32 | 1.27 | 1.68 | 0.00 | 1.45 | 1.61 | 2.23 |
time (sec) |
N/A | 0.339 | 0.021 | 1.396 | 0.037 | 0.097 | 0.000 | 0.138 | 0.182 | 27.471 |
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 | 55 | 60 | 73 | 76 | 71 | 74 | 0 | 63 | 162 | 126 |
N.S. |
1 | 1.09 | 1.33 | 1.38 | 1.29 | 1.35 | 0.00 | 1.15 | 2.95 | 2.29 |
time (sec) |
N/A | 0.571 | 0.026 | 1.238 | 0.037 | 0.098 | 0.000 | 0.203 | 0.176 | 29.005 |
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 | 78 | 88 | 99 | 94 | 91 | 84 | 0 | 73 | 226 | 177 |
N.S. |
1 | 1.13 | 1.27 | 1.21 | 1.17 | 1.08 | 0.00 | 0.94 | 2.90 | 2.27 |
time (sec) |
N/A | 0.749 | 0.029 | 2.986 | 0.053 | 0.117 | 0.000 | 0.230 | 0.169 | 29.717 |
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 | 99 | 114 | 120 | 112 | 111 | 94 | 0 | 107 | 290 | 229 |
N.S. |
1 | 1.15 | 1.21 | 1.13 | 1.12 | 0.95 | 0.00 | 1.08 | 2.93 | 2.31 |
time (sec) |
N/A | 0.946 | 0.030 | 9.269 | 0.047 | 0.096 | 0.000 | 0.252 | 0.177 | 30.397 |
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 | 46 | 44 | 68 | 47 | 46 | 36 | 83 | 36 | 45 | 35 |
N.S. |
1 | 0.96 | 1.48 | 1.02 | 1.00 | 0.78 | 1.80 | 0.78 | 0.98 | 0.76 |
time (sec) |
N/A | 0.380 | 0.404 | 43.957 | 0.051 | 0.130 | 2.458 | 0.123 | 0.166 | 0.087 |
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 | 42 | 37 | 37 | 36 | 36 | 68 | 36 | 95 | 36 |
N.S. |
1 | 0.91 | 0.80 | 0.80 | 0.78 | 0.78 | 1.48 | 0.78 | 2.07 | 0.78 |
time (sec) |
N/A | 0.363 | 0.289 | 34.793 | 0.033 | 0.106 | 1.757 | 0.125 | 0.157 | 25.795 |
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 | 44 | 50 | 36 | 36 | 36 | 63 | 36 | 35 | 36 |
N.S. |
1 | 0.96 | 1.09 | 0.78 | 0.78 | 0.78 | 1.37 | 0.78 | 0.76 | 0.78 |
time (sec) |
N/A | 0.367 | 0.084 | 17.375 | 0.037 | 0.107 | 1.278 | 0.121 | 0.171 | 25.860 |