Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 64 | 58 | 57 | 54 | 63 | 0 | 52 |
N.S. | 1 | 1.00 | 1.08 | 0.98 | 0.97 | 0.92 | 1.07 | 0.00 | 0.88 |
time (sec) |
N/A | 0.023 | 0.004 | 0.205 | 0.464 | 3.602 | 0.334 | 0.000 | 0.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 61 | 59 | 56 | 59 | 60 | 0 | 54 |
N.S. | 1 | 1.00 | 1.09 | 1.05 | 1.00 | 1.05 | 1.07 | 0.00 | 0.96 |
time (sec) |
N/A | 0.030 | 0.012 | 0.052 | 0.265 | 2.026 | 0.265 | 0.000 | 0.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 53 | 49 | 48 | 47 | 53 | 0 | 44 |
N.S. | 1 | 1.00 | 1.10 | 1.02 | 1.00 | 0.98 | 1.10 | 0.00 | 0.92 |
time (sec) |
N/A | 0.022 | 0.004 | 0.105 | 0.469 | 6.432 | 0.208 | 0.000 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 50 | 50 | 46 | 49 | 49 | 0 | 42 |
N.S. | 1 | 1.00 | 1.11 | 1.11 | 1.02 | 1.09 | 1.09 | 0.00 | 0.93 |
time (sec) |
N/A | 0.023 | 0.008 | 0.053 | 0.265 | 4.570 | 0.194 | 0.000 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 42 | 40 | 37 | 34 | 42 | 0 | 34 |
N.S. | 1 | 1.00 | 1.14 | 1.08 | 1.00 | 0.92 | 1.14 | 0.00 | 0.92 |
time (sec) |
N/A | 0.011 | 0.004 | 0.112 | 0.463 | 3.426 | 0.138 | 0.000 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 28 | 31 | 33 | 26 | 31 | 27 |
N.S. | 1 | 1.00 | 1.00 | 0.97 | 1.07 | 1.14 | 0.90 | 1.07 | 0.93 |
time (sec) |
N/A | 0.009 | 0.004 | 0.083 | 0.256 | 3.293 | 0.091 | 0.415 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 74 | 0 | 0 | 0 | 0 | 28 |
N.S. | 1 | 1.00 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.022 | 0.004 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 38 | 45 | 39 | 37 | 37 | 0 | 36 |
N.S. | 1 | 1.00 | 1.09 | 1.29 | 1.11 | 1.06 | 1.06 | 0.00 | 1.03 |
time (sec) |
N/A | 0.018 | 0.004 | 0.078 | 0.270 | 0.920 | 0.267 | 0.000 | 0.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 46 | 44 | 31 | 26 | 37 | 0 | 42 |
N.S. | 1 | 1.00 | 1.24 | 1.19 | 0.84 | 0.70 | 1.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.015 | 0.005 | 0.122 | 0.470 | 0.712 | 0.218 | 0.000 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 54 | 57 | 51 | 50 | 61 | 0 | 46 |
N.S. | 1 | 1.00 | 1.02 | 1.08 | 0.96 | 0.94 | 1.15 | 0.00 | 0.87 |
time (sec) |
N/A | 0.025 | 0.013 | 0.082 | 0.266 | 1.259 | 0.377 | 0.000 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 46 | 53 | 46 | 41 | 46 | 0 | 42 |
N.S. | 1 | 1.00 | 0.96 | 1.10 | 0.96 | 0.85 | 0.96 | 0.00 | 0.88 |
time (sec) |
N/A | 0.018 | 0.004 | 0.131 | 0.472 | 0.629 | 0.296 | 0.000 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 64 | 66 | 62 | 59 | 71 | 0 | 56 |
N.S. | 1 | 1.00 | 1.00 | 1.03 | 0.97 | 0.92 | 1.11 | 0.00 | 0.88 |
time (sec) |
N/A | 0.027 | 0.015 | 0.092 | 0.260 | 1.296 | 0.536 | 0.000 | 0.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 138 | 171 | 163 | 152 | 199 | 0 | 171 |
N.S. | 1 | 1.00 | 0.96 | 1.19 | 1.13 | 1.06 | 1.38 | 0.00 | 1.19 |
time (sec) |
N/A | 0.217 | 0.087 | 0.326 | 0.483 | 0.832 | 0.461 | 0.000 | 0.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 169 | 312 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.99 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.206 | 0.358 | 0.471 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 111 | 135 | 136 | 121 | 155 | 0 | 134 |
N.S. | 1 | 1.00 | 0.99 | 1.21 | 1.21 | 1.08 | 1.38 | 0.00 | 1.20 |
time (sec) |
N/A | 0.153 | 0.046 | 0.158 | 0.474 | 0.958 | 0.322 | 0.000 | 0.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 131 | 276 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.95 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.139 | 0.196 | 0.345 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 75 | 97 | 104 | 83 | 107 | 0 | 88 |
N.S. | 1 | 1.00 | 0.99 | 1.28 | 1.37 | 1.09 | 1.41 | 0.00 | 1.16 |
time (sec) |
N/A | 0.076 | 0.035 | 0.193 | 0.474 | 0.768 | 0.194 | 0.000 | 0.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 90 | 123 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.08 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.072 | 0.050 | 0.759 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 144 | 1128 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.09 | 8.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.181 | 0.052 | 8.300 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 102 | 318 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.24 | 3.88 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.107 | 0.097 | 0.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 90 | 115 | 98 | 94 | 119 | 0 | 140 |
N.S. | 1 | 1.00 | 1.14 | 1.46 | 1.24 | 1.19 | 1.51 | 0.00 | 1.77 |
time (sec) |
N/A | 0.091 | 0.036 | 0.239 | 0.474 | 0.782 | 0.341 | 0.000 | 2.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 153 | 365 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.09 | 2.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.166 | 0.268 | 0.840 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 128 | 152 | 152 | 135 | 170 | 0 | 171 |
N.S. | 1 | 1.00 | 1.10 | 1.31 | 1.31 | 1.16 | 1.47 | 0.00 | 1.47 |
time (sec) |
N/A | 0.159 | 0.052 | 0.250 | 0.475 | 1.154 | 0.507 | 0.000 | 2.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 255 | 291 | 494 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.14 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.655 | 0.554 | 0.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 396 | 2951 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.46 | 10.89 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.513 | 0.636 | 18.189 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 225 | 411 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.16 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.383 | 0.414 | 0.535 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 269 | 1921 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.31 | 9.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.313 | 0.420 | 5.489 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 152 | 323 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.16 | 2.47 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.172 | 0.195 | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 192 | 254 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.61 | 2.13 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.152 | 0.058 | 1.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 212 | 2309 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.03 | 11.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.289 | 0.099 | 4.770 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 214 | 2126 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.84 | 18.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.187 | 0.256 | 3.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 176 | 422 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.32 | 3.17 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.199 | 0.218 | 1.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F(-1) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 321 | 5807 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.51 | 27.26 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.331 | 0.618 | 19.816 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-1) | F | F | F(-1) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 265 | 512 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.34 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.412 | 0.489 | 1.583 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A | 0.006 | 0.483 | 1.810 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.11 |
time (sec) |
N/A | 0.002 | 0.011 | 1.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.010 | 0.314 | 1.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A | 0.006 | 0.442 | 2.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.11 |
time (sec) |
N/A | 0.002 | 0.650 | 0.460 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.010 | 0.765 | 1.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.005 | 1.508 | 1.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A | 0.002 | 1.331 | 0.694 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A | 0.009 | 0.927 | 0.840 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.005 | 0.708 | 1.239 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A | 0.003 | 1.606 | 0.685 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A | 0.009 | 0.822 | 0.802 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.005 | 0.937 | 1.360 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A | 0.002 | 0.018 | 0.705 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A | 0.009 | 0.854 | 0.836 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.005 | 1.096 | 1.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A | 0.002 | 1.911 | 0.708 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A | 0.009 | 2.022 | 0.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 108 | 69 | 86 | 118 | 104 | 86 | 49 |
N.S. | 1 | 1.00 | 0.92 | 0.59 | 0.74 | 1.01 | 0.89 | 0.74 | 0.42 |
time (sec) |
N/A | 0.048 | 0.019 | 0.093 | 0.492 | 5.000 | 1.315 | 0.465 | 0.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.016 | 2.712 | 1.527 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.015 | 1.779 | 1.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 60 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.025 | 0.024 | 1.711 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.017 | 0.194 | 0.975 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A | 0.004 | 0.337 | 0.487 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.015 | 0.246 | 1.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 59 | 50 | 54 | 51 | 58 | 60 | 49 |
N.S. | 1 | 1.00 | 1.09 | 0.93 | 1.00 | 0.94 | 1.07 | 1.11 | 0.91 |
time (sec) |
N/A | 0.028 | 0.008 | 0.211 | 0.468 | 2.638 | 28.518 | 0.428 | 0.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 52 | 45 | 48 | 51 | 80 | 47 | 44 |
N.S. | 1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 1.70 | 1.00 | 0.94 |
time (sec) |
N/A | 0.024 | 0.011 | 0.198 | 0.268 | 2.858 | 21.110 | 0.431 | 0.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 48 | 41 | 43 | 38 | 48 | 43 | 40 |
N.S. | 1 | 1.00 | 1.12 | 0.95 | 1.00 | 0.88 | 1.12 | 1.00 | 0.93 |
time (sec) |
N/A | 0.020 | 0.006 | 0.187 | 0.464 | 3.464 | 10.193 | 0.430 | 0.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 41 | 38 | 38 | 39 | 66 | 40 | 35 |
N.S. | 1 | 1.00 | 1.14 | 1.06 | 1.06 | 1.08 | 1.83 | 1.11 | 0.97 |
time (sec) |
N/A | 0.010 | 0.008 | 0.147 | 0.256 | 3.686 | 5.671 | 0.443 | 0.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 63 | 0 | 0 | 0 | 0 | 32 |
N.S. | 1 | 1.00 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.036 | 0.005 | 0.235 | 0.000 | 0.000 | 0.000 | 0.000 | 0.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 44 | 39 | 41 | 43 | 75 | 60 | 38 |
N.S. | 1 | 1.00 | 1.13 | 1.00 | 1.05 | 1.10 | 1.92 | 1.54 | 0.97 |
time (sec) |
N/A | 0.018 | 0.007 | 0.089 | 0.263 | 2.432 | 12.450 | 0.436 | 0.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 48 | 39 | 35 | 30 | 42 | 72 | 41 |
N.S. | 1 | 1.00 | 1.17 | 0.95 | 0.85 | 0.73 | 1.02 | 1.76 | 1.00 |
time (sec) |
N/A | 0.018 | 0.007 | 0.125 | 0.465 | 2.265 | 10.297 | 0.460 | 0.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 60 | 51 | 53 | 54 | 92 | 69 | 50 |
N.S. | 1 | 1.00 | 1.09 | 0.93 | 0.96 | 0.98 | 1.67 | 1.25 | 0.91 |
time (sec) |
N/A | 0.024 | 0.011 | 0.105 | 0.259 | 2.203 | 35.832 | 0.457 | 0.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 179 | 140 | 147 | 372 | 153 | 169 | 64 |
N.S. | 1 | 1.00 | 1.11 | 0.87 | 0.91 | 2.31 | 0.95 | 1.05 | 0.40 |
time (sec) |
N/A | 0.081 | 0.038 | 0.170 | 0.484 | 1.370 | 14.355 | 0.487 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 177 | 138 | 145 | 337 | 143 | 165 | 62 |
N.S. | 1 | 1.00 | 1.11 | 0.87 | 0.91 | 2.12 | 0.90 | 1.04 | 0.39 |
time (sec) |
N/A | 0.072 | 0.028 | 0.085 | 0.487 | 2.398 | 7.254 | 0.461 | 0.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 107 | 125 | 127 | 319 | 617 | 149 | 49 |
N.S. | 1 | 1.00 | 0.76 | 0.89 | 0.91 | 2.28 | 4.41 | 1.06 | 0.35 |
time (sec) |
N/A | 0.077 | 0.030 | 0.082 | 0.466 | 1.387 | 4.139 | 0.410 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 158 | 125 | 132 | 322 | 121 | 138 | 55 |
N.S. | 1 | 1.00 | 1.10 | 0.87 | 0.92 | 2.25 | 0.85 | 0.97 | 0.38 |
time (sec) |
N/A | 0.065 | 0.031 | 0.102 | 0.485 | 2.090 | 8.217 | 0.452 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | C | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 177 | 132 | 142 | 389 | 529 | 159 | 63 |
N.S. | 1 | 1.00 | 1.11 | 0.83 | 0.89 | 2.45 | 3.33 | 1.00 | 0.40 |
time (sec) |
N/A | 0.072 | 0.037 | 0.109 | 0.477 | 1.283 | 16.586 | 0.477 | 0.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 177 | 138 | 138 | 350 | 155 | 150 | 63 |
N.S. | 1 | 1.00 | 1.11 | 0.87 | 0.87 | 2.20 | 0.97 | 0.94 | 0.40 |
time (sec) |
N/A | 0.074 | 0.040 | 0.117 | 0.481 | 1.948 | 27.329 | 0.495 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 121 | 151 | 169 | 137 | 199 | 145 | 150 |
N.S. | 1 | 1.00 | 0.98 | 1.22 | 1.36 | 1.10 | 1.60 | 1.17 | 1.21 |
time (sec) |
N/A | 0.183 | 0.055 | 0.224 | 0.516 | 1.184 | 41.041 | 0.453 | 1.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 141 | 367 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.92 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.169 | 0.234 | 0.432 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 85 | 113 | 126 | 100 | 155 | 100 | 112 |
N.S. | 1 | 1.00 | 0.94 | 1.26 | 1.40 | 1.11 | 1.72 | 1.11 | 1.24 |
time (sec) |
N/A | 0.103 | 0.043 | 0.133 | 0.522 | 1.802 | 14.779 | 0.427 | 0.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 107 | 142 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.06 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.096 | 0.061 | 0.181 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 165 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.213 | 0.072 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 127 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.133 | 0.104 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 98 | 118 | 110 | 115 | 167 | 0 | 152 |
N.S. | 1 | 1.00 | 1.13 | 1.36 | 1.26 | 1.32 | 1.92 | 0.00 | 1.75 |
time (sec) |
N/A | 0.117 | 0.046 | 0.134 | 0.537 | 2.367 | 21.552 | 0.000 | 0.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | F | F | F | F | F | F | F |
verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1393 | 1393 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 1.845 | 4.143 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | F | F | F | F | F | F |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1191 | 1191 | 5293 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 4.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 1.232 | 30.757 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | F | F | F | F | F | F |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1164 | 1164 | 5293 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 4.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 1.151 | 30.545 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | F | F | F | F | F | F | F |
verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1360 | 1360 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 1.549 | 2.000 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | F | F | F | F | F | F | F |
verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1444 | 1444 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 1.690 | 2.033 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 170 | 758 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.14 | 5.09 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.214 | 0.295 | 0.471 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 224 | 289 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.56 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.181 | 0.044 | 0.407 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 245 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.342 | 0.132 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 239 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.218 | 0.288 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 196 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.226 | 0.219 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.015 | 1.271 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.016 | 0.825 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.027 | 0.042 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.018 | 0.221 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.018 | 0.233 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 59 | 50 | 54 | 51 | 58 | 60 | 49 |
N.S. | 1 | 1.00 | 1.09 | 0.93 | 1.00 | 0.94 | 1.07 | 1.11 | 0.91 |
time (sec) |
N/A | 0.025 | 0.007 | 0.047 | 0.487 | 1.468 | 125.815 | 0.420 | 0.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 52 | 45 | 48 | 51 | 117 | 47 | 44 |
N.S. | 1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 2.49 | 1.00 | 0.94 |
time (sec) |
N/A | 0.023 | 0.011 | 0.041 | 0.262 | 1.082 | 69.177 | 0.438 | 0.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 48 | 41 | 43 | 38 | 48 | 43 | 40 |
N.S. | 1 | 1.00 | 1.12 | 0.95 | 1.00 | 0.88 | 1.12 | 1.00 | 0.93 |
time (sec) |
N/A | 0.019 | 0.006 | 0.063 | 0.470 | 1.406 | 35.579 | 0.441 | 0.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 41 | 38 | 38 | 39 | 102 | 40 | 35 |
N.S. | 1 | 1.00 | 1.14 | 1.06 | 1.06 | 1.08 | 2.83 | 1.11 | 0.97 |
time (sec) |
N/A | 0.014 | 0.008 | 0.029 | 0.260 | 1.294 | 19.447 | 0.404 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | F | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 63 | 0 | 0 | 0 | 0 | 32 |
N.S. | 1 | 1.00 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.033 | 0.005 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.351 |