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 | C | A | F | F(-1) | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 324 | 48 | 159 | 0 | 0 | 0 | 207 | -1 |
N.S. |
1 | 1.00 | 0.15 | 0.49 | 0.00 | 0.00 | 0.00 | 0.64 | -0.00 |
time (sec) |
N/A | 0.387 | 10.068 | 0.334 | 0.000 | 0.000 | 0.000 | 1.781 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | F(-1) | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 412 | 48 | 192 | 0 | 0 | 0 | 258 | -1 |
N.S. |
1 | 1.00 | 0.12 | 0.47 | 0.00 | 0.00 | 0.00 | 0.63 | -0.00 |
time (sec) |
N/A | 0.539 | 10.064 | 0.342 | 0.000 | 0.000 | 0.000 | 2.407 | 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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.007 | 0.001 | 0.036 | 0.288 | 2.515 | 0.010 | 1.638 | 0.022 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.006 | 0.001 | 0.019 | 0.277 | 2.973 | 0.007 | 1.281 | 0.022 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.002 | 0.000 | 0.020 | 0.274 | 3.556 | 0.007 | 1.460 | 0.022 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.004 | 0.001 | 0.019 | 0.284 | 1.138 | 0.006 | 1.118 | 0.020 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. | 1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.003 | 0.001 | 0.018 | 0.271 | 2.593 | 0.006 | 1.471 | 0.017 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.023 | 0.002 | 0.430 | 0.283 | 1.282 | 0.009 | 1.439 | 0.040 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 24 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A | 0.013 | 0.002 | 0.345 | 0.277 | 1.135 | 0.009 | 1.440 | 0.033 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.011 | 0.001 | 0.334 | 0.286 | 1.316 | 0.008 | 1.419 | 0.031 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 24 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A | 0.012 | 0.001 | 0.339 | 0.290 | 1.214 | 0.008 | 1.380 | 0.034 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.012 | 0.001 | 0.330 | 0.267 | 1.147 | 0.009 | 0.983 | 0.032 |
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 | 57 | 57 | 57 | 52 | 52 | 52 | 49 | 53 | 51 |
N.S. | 1 | 1.00 | 1.00 | 0.91 | 0.91 | 0.91 | 0.86 | 0.93 | 0.89 |
time (sec) |
N/A | 0.026 | 0.003 | 0.389 | 0.298 | 1.164 | 0.053 | 0.917 | 5.093 |
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 | 44 | 44 | 44 | 41 | 42 | 41 | 37 | 43 | 40 |
N.S. | 1 | 1.00 | 1.00 | 0.93 | 0.95 | 0.93 | 0.84 | 0.98 | 0.91 |
time (sec) |
N/A | 0.018 | 0.003 | 0.354 | 0.291 | 1.430 | 0.043 | 1.743 | 0.042 |
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 | 31 | 31 | 31 | 30 | 29 | 29 | 26 | 30 | 29 |
N.S. | 1 | 1.00 | 1.00 | 0.97 | 0.94 | 0.94 | 0.84 | 0.97 | 0.94 |
time (sec) |
N/A | 0.015 | 0.003 | 0.347 | 0.270 | 1.365 | 0.038 | 1.371 | 0.041 |
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 | 18 | 18 | 18 | 19 | 18 | 17 | 14 | 19 | 18 |
N.S. | 1 | 1.00 | 1.00 | 1.06 | 1.00 | 0.94 | 0.78 | 1.06 | 1.00 |
time (sec) |
N/A | 0.011 | 0.002 | 0.354 | 0.290 | 1.348 | 0.031 | 1.032 | 0.036 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 |
N.S. | 1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 |
time (sec) |
N/A | 0.005 | 0.001 | 0.337 | 0.285 | 1.583 | 0.010 | 2.611 | 0.022 |
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 | 18 | 18 | 18 | 19 | 18 | 16 | 10 | 20 | 15 |
N.S. | 1 | 1.00 | 1.00 | 1.06 | 1.00 | 0.89 | 0.56 | 1.11 | 0.83 |
time (sec) |
N/A | 0.005 | 0.003 | 0.342 | 0.294 | 1.495 | 0.062 | 1.902 | 5.120 |
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 | 28 | 28 | 28 | 29 | 28 | 26 | 19 | 30 | 25 |
N.S. | 1 | 1.00 | 1.00 | 1.04 | 1.00 | 0.93 | 0.68 | 1.07 | 0.89 |
time (sec) |
N/A | 0.011 | 0.003 | 0.360 | 0.269 | 2.324 | 0.084 | 1.261 | 0.052 |
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 | 42 | 42 | 42 | 41 | 40 | 41 | 31 | 45 | 38 |
N.S. | 1 | 1.00 | 1.00 | 0.98 | 0.95 | 0.98 | 0.74 | 1.07 | 0.90 |
time (sec) |
N/A | 0.015 | 0.004 | 0.343 | 0.269 | 1.895 | 0.085 | 1.617 | 0.059 |
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 | 56 | 56 | 56 | 53 | 51 | 54 | 44 | 56 | 48 |
N.S. | 1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.96 | 0.79 | 1.00 | 0.86 |
time (sec) |
N/A | 0.020 | 0.004 | 0.366 | 0.268 | 1.326 | 0.126 | 1.085 | 0.061 |
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 | 58 | 58 | 54 | 57 | 59 | 73 | 54 | 62 | 62 |
N.S. | 1 | 1.00 | 0.93 | 0.98 | 1.02 | 1.26 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.028 | 0.015 | 0.368 | 0.279 | 1.386 | 0.081 | 1.117 | 0.038 |
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 | 46 | 46 | 43 | 46 | 47 | 62 | 44 | 48 | 50 |
N.S. | 1 | 1.00 | 0.93 | 1.00 | 1.02 | 1.35 | 0.96 | 1.04 | 1.09 |
time (sec) |
N/A | 0.022 | 0.010 | 0.350 | 0.286 | 1.428 | 0.073 | 1.624 | 0.045 |
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 | 33 | 33 | 29 | 34 | 36 | 47 | 31 | 34 | 36 |
N.S. | 1 | 1.00 | 0.88 | 1.03 | 1.09 | 1.42 | 0.94 | 1.03 | 1.09 |
time (sec) |
N/A | 0.016 | 0.010 | 0.358 | 0.267 | 1.470 | 0.066 | 1.670 | 0.040 |
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 | 23 | 23 | 20 | 24 | 26 | 28 | 20 | 24 | 23 |
N.S. | 1 | 1.00 | 0.87 | 1.04 | 1.13 | 1.22 | 0.87 | 1.04 | 1.00 |
time (sec) |
N/A | 0.013 | 0.005 | 0.362 | 0.280 | 1.390 | 0.048 | 1.705 | 0.037 |
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 | 12 | 12 | 12 | 13 | 13 | 13 | 10 | 12 | 12 |
N.S. | 1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.08 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.005 | 0.002 | 0.406 | 0.282 | 1.430 | 0.045 | 1.672 | 5.169 |
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 | 24 | 30 | 28 | 39 | 22 | 31 | 26 |
N.S. | 1 | 1.00 | 0.83 | 1.03 | 0.97 | 1.34 | 0.76 | 1.07 | 0.90 |
time (sec) |
N/A | 0.014 | 0.010 | 0.358 | 0.285 | 1.081 | 0.086 | 1.277 | 0.045 |
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 | 42 | 42 | 35 | 43 | 45 | 63 | 37 | 45 | 41 |
N.S. | 1 | 1.00 | 0.83 | 1.02 | 1.07 | 1.50 | 0.88 | 1.07 | 0.98 |
time (sec) |
N/A | 0.017 | 0.027 | 0.356 | 0.270 | 1.767 | 0.116 | 1.112 | 5.343 |
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 | 58 | 58 | 53 | 57 | 64 | 86 | 54 | 64 | 57 |
N.S. | 1 | 1.00 | 0.91 | 0.98 | 1.10 | 1.48 | 0.93 | 1.10 | 0.98 |
time (sec) |
N/A | 0.022 | 0.035 | 0.369 | 0.290 | 1.236 | 0.133 | 1.770 | 5.315 |
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 | 69 | 69 | 66 | 68 | 73 | 95 | 66 | 73 | 69 |
N.S. | 1 | 1.00 | 0.96 | 0.99 | 1.06 | 1.38 | 0.96 | 1.06 | 1.00 |
time (sec) |
N/A | 0.026 | 0.038 | 0.372 | 0.273 | 1.579 | 0.146 | 1.093 | 0.071 |
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 | 84 | 84 | 79 | 79 | 86 | 108 | 80 | 86 | 79 |
N.S. | 1 | 1.00 | 0.94 | 0.94 | 1.02 | 1.29 | 0.95 | 1.02 | 0.94 |
time (sec) |
N/A | 0.034 | 0.030 | 0.381 | 0.279 | 1.681 | 0.187 | 1.219 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 53 | 57 | 53 | 62 | 0 | 131 | 62 |
N.S. | 1 | 1.00 | 0.50 | 0.54 | 0.50 | 0.59 | 0.00 | 1.25 | 0.59 |
time (sec) |
N/A | 0.079 | 0.025 | 0.362 | 0.303 | 1.200 | 0.000 | 1.412 | 5.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 42 | 46 | 42 | 51 | 0 | 108 | 51 |
N.S. | 1 | 1.00 | 0.52 | 0.58 | 0.52 | 0.64 | 0.00 | 1.35 | 0.64 |
time (sec) |
N/A | 0.049 | 0.022 | 0.366 | 0.276 | 1.406 | 0.000 | 1.252 | 5.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 41 | 35 | 30 | 39 | 0 | 81 | 39 |
N.S. | 1 | 1.00 | 0.79 | 0.67 | 0.58 | 0.75 | 0.00 | 1.56 | 0.75 |
time (sec) |
N/A | 0.028 | 0.016 | 0.376 | 0.289 | 1.558 | 0.000 | 1.665 | 5.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 27 | 12 | 26 | 0 | 50 | -1 |
N.S. | 1 | 1.00 | 0.92 | 1.08 | 0.48 | 1.04 | 0.00 | 2.00 | -0.04 |
time (sec) |
N/A | 0.025 | 0.010 | 0.362 | 0.270 | 1.354 | 0.000 | 1.525 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 53 | 51 | 0 | 111 | 0 | 67 | 73 |
N.S. | 1 | 1.00 | 1.04 | 1.00 | 0.00 | 2.18 | 0.00 | 1.31 | 1.43 |
time (sec) |
N/A | 0.033 | 0.035 | 0.371 | 0.000 | 1.796 | 0.000 | 1.264 | 5.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 64 | 56 | 0 | 127 | 0 | 45 | -1 |
N.S. | 1 | 1.00 | 1.23 | 1.08 | 0.00 | 2.44 | 0.00 | 0.87 | -0.02 |
time (sec) |
N/A | 0.033 | 0.054 | 0.508 | 0.000 | 1.425 | 0.000 | 0.959 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 81 | 73 | 0 | 149 | 0 | 72 | -1 |
N.S. | 1 | 1.00 | 0.96 | 0.87 | 0.00 | 1.77 | 0.00 | 0.86 | -0.01 |
time (sec) |
N/A | 0.065 | 0.089 | 0.424 | 0.000 | 1.737 | 0.000 | 1.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 93 | 89 | 0 | 175 | 0 | 92 | -1 |
N.S. | 1 | 1.00 | 0.83 | 0.79 | 0.00 | 1.56 | 0.00 | 0.82 | -0.01 |
time (sec) |
N/A | 0.092 | 0.109 | 0.392 | 0.000 | 1.328 | 0.000 | 1.495 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 80 | 79 | 86 | 95 | 0 | 282 | 80 |
N.S. | 1 | 1.00 | 0.50 | 0.49 | 0.53 | 0.59 | 0.00 | 1.75 | 0.50 |
time (sec) |
N/A | 0.156 | 0.033 | 0.369 | 0.296 | 1.768 | 0.000 | 1.281 | 5.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 69 | 68 | 75 | 84 | 0 | 246 | 69 |
N.S. | 1 | 1.00 | 0.51 | 0.50 | 0.55 | 0.62 | 0.00 | 1.81 | 0.51 |
time (sec) |
N/A | 0.114 | 0.030 | 0.373 | 0.295 | 1.284 | 0.000 | 1.491 | 5.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 58 | 57 | 64 | 73 | 0 | 210 | 58 |
N.S. | 1 | 1.00 | 0.54 | 0.53 | 0.59 | 0.68 | 0.00 | 1.94 | 0.54 |
time (sec) |
N/A | 0.093 | 0.027 | 0.360 | 0.284 | 1.461 | 0.000 | 1.388 | 5.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 47 | 46 | 53 | 62 | 0 | 173 | 47 |
N.S. | 1 | 1.00 | 0.59 | 0.58 | 0.66 | 0.78 | 0.00 | 2.16 | 0.59 |
time (sec) |
N/A | 0.089 | 0.025 | 0.365 | 0.295 | 1.242 | 0.000 | 1.873 | 5.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 31 | 35 | 41 | 50 | 0 | 136 | 36 |
N.S. | 1 | 1.00 | 0.60 | 0.67 | 0.79 | 0.96 | 0.00 | 2.62 | 0.69 |
time (sec) |
N/A | 0.059 | 0.022 | 0.363 | 0.290 | 1.100 | 0.000 | 1.336 | 5.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 27 | 28 | 37 | 0 | 89 | 28 |
N.S. | 1 | 1.00 | 0.92 | 1.08 | 1.12 | 1.48 | 0.00 | 3.56 | 1.12 |
time (sec) |
N/A | 0.029 | 0.012 | 0.359 | 0.281 | 2.046 | 0.000 | 1.561 | 5.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 68 | 61 | 0 | 130 | 0 | 85 | -1 |
N.S. | 1 | 1.00 | 0.92 | 0.82 | 0.00 | 1.76 | 0.00 | 1.15 | -0.01 |
time (sec) |
N/A | 0.066 | 0.049 | 0.371 | 0.000 | 2.751 | 0.000 | 1.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 66 | 72 | 0 | 136 | 0 | 62 | -1 |
N.S. | 1 | 1.00 | 0.90 | 0.99 | 0.00 | 1.86 | 0.00 | 0.85 | -0.01 |
time (sec) |
N/A | 0.063 | 0.072 | 0.375 | 0.000 | 2.039 | 0.000 | 1.669 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 82 | 74 | 0 | 154 | 0 | 70 | -1 |
N.S. | 1 | 1.00 | 1.01 | 0.91 | 0.00 | 1.90 | 0.00 | 0.86 | -0.01 |
time (sec) |
N/A | 0.063 | 0.103 | 0.375 | 0.000 | 1.098 | 0.000 | 1.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 94 | 87 | 0 | 175 | 0 | 92 | -1 |
N.S. | 1 | 1.00 | 0.86 | 0.80 | 0.00 | 1.61 | 0.00 | 0.84 | -0.01 |
time (sec) |
N/A | 0.090 | 0.123 | 0.371 | 0.000 | 1.814 | 0.000 | 1.561 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 104 | 101 | 0 | 197 | 0 | 109 | -1 |
N.S. | 1 | 1.00 | 0.76 | 0.74 | 0.00 | 1.44 | 0.00 | 0.80 | -0.01 |
time (sec) |
N/A | 0.121 | 0.141 | 0.508 | 0.000 | 0.940 | 0.000 | 2.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 116 | 113 | 0 | 219 | 0 | 126 | -1 |
N.S. | 1 | 1.00 | 0.70 | 0.68 | 0.00 | 1.33 | 0.00 | 0.76 | -0.01 |
time (sec) |
N/A | 0.157 | 0.153 | 0.434 | 0.000 | 1.939 | 0.000 | 1.584 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 53 | 55 | 53 | 51 | 0 | 64 | 51 |
N.S. | 1 | 1.00 | 0.51 | 0.53 | 0.51 | 0.50 | 0.00 | 0.62 | 0.50 |
time (sec) |
N/A | 0.101 | 0.025 | 0.366 | 0.286 | 1.229 | 0.000 | 1.752 | 5.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 42 | 44 | 42 | 40 | 0 | 52 | 40 |
N.S. | 1 | 1.00 | 0.56 | 0.59 | 0.56 | 0.53 | 0.00 | 0.69 | 0.53 |
time (sec) |
N/A | 0.066 | 0.022 | 0.356 | 0.287 | 2.168 | 0.000 | 1.781 | 5.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 30 | 33 | 30 | 28 | 0 | 38 | 31 |
N.S. | 1 | 1.00 | 0.61 | 0.67 | 0.61 | 0.57 | 0.00 | 0.78 | 0.63 |
time (sec) |
N/A | 0.037 | 0.016 | 0.349 | 0.282 | 2.877 | 0.000 | 1.145 | 5.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 25 | 12 | 21 | 0 | 27 | 17 |
N.S. | 1 | 1.00 | 0.91 | 1.09 | 0.52 | 0.91 | 0.00 | 1.17 | 0.74 |
time (sec) |
N/A | 0.007 | 0.009 | 0.358 | 0.283 | 1.354 | 0.000 | 1.371 | 5.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 46 | 39 | 0 | 74 | 0 | 45 | -1 |
N.S. | 1 | 1.00 | 1.53 | 1.30 | 0.00 | 2.47 | 0.00 | 1.50 | -0.03 |
time (sec) |
N/A | 0.007 | 0.020 | 0.364 | 0.000 | 1.359 | 0.000 | 1.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 60 | 55 | 0 | 127 | 0 | 51 | -1 |
N.S. | 1 | 1.00 | 1.11 | 1.02 | 0.00 | 2.35 | 0.00 | 0.94 | -0.02 |
time (sec) |
N/A | 0.035 | 0.053 | 0.372 | 0.000 | 1.993 | 0.000 | 1.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 83 | 77 | 0 | 153 | 0 | 73 | 44 |
N.S. | 1 | 1.00 | 0.95 | 0.89 | 0.00 | 1.76 | 0.00 | 0.84 | 0.51 |
time (sec) |
N/A | 0.061 | 0.076 | 0.382 | 0.000 | 1.286 | 0.000 | 1.114 | 5.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 96 | 95 | 0 | 175 | 0 | 88 | -1 |
N.S. | 1 | 1.00 | 0.83 | 0.83 | 0.00 | 1.52 | 0.00 | 0.77 | -0.01 |
time (sec) |
N/A | 0.092 | 0.072 | 0.390 | 0.000 | 2.033 | 0.000 | 0.956 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 50 | 56 | 41 | 60 | 0 | 79 | 57 |
N.S. | 1 | 1.00 | 0.51 | 0.57 | 0.42 | 0.61 | 0.00 | 0.81 | 0.58 |
time (sec) |
N/A | 0.096 | 0.025 | 0.372 | 0.286 | 1.101 | 0.000 | 1.654 | 5.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 39 | 46 | 30 | 49 | 0 | 64 | 47 |
N.S. | 1 | 1.00 | 0.54 | 0.64 | 0.42 | 0.68 | 0.00 | 0.89 | 0.65 |
time (sec) |
N/A | 0.068 | 0.023 | 0.367 | 0.305 | 1.865 | 0.000 | 1.135 | 5.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 26 | 34 | 19 | 38 | 0 | 48 | 35 |
N.S. | 1 | 1.00 | 0.55 | 0.72 | 0.40 | 0.81 | 0.00 | 1.02 | 0.74 |
time (sec) |
N/A | 0.041 | 0.016 | 0.371 | 0.292 | 1.451 | 0.000 | 0.884 | 5.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 27 | 12 | 29 | 0 | 27 | 28 |
N.S. | 1 | 1.00 | 0.90 | 1.29 | 0.57 | 1.38 | 0.00 | 1.29 | 1.33 |
time (sec) |
N/A | 0.012 | 0.010 | 0.362 | 0.314 | 1.667 | 0.000 | 1.321 | 5.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 54 | 54 | 0 | 156 | 0 | 77 | -1 |
N.S. | 1 | 1.00 | 1.04 | 1.04 | 0.00 | 3.00 | 0.00 | 1.48 | -0.02 |
time (sec) |
N/A | 0.041 | 0.030 | 0.370 | 0.000 | 1.473 | 0.000 | 1.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 62 | 62 | 0 | 189 | 0 | 72 | -1 |
N.S. | 1 | 1.00 | 0.83 | 0.83 | 0.00 | 2.52 | 0.00 | 0.96 | -0.01 |
time (sec) |
N/A | 0.057 | 0.063 | 0.404 | 0.000 | 1.603 | 0.000 | 1.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 84 | 76 | 0 | 219 | 0 | 92 | 42 |
N.S. | 1 | 1.00 | 0.76 | 0.69 | 0.00 | 1.99 | 0.00 | 0.84 | 0.38 |
time (sec) |
N/A | 0.074 | 0.095 | 0.395 | 0.000 | 1.518 | 0.000 | 1.437 | 5.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 96 | 86 | 0 | 241 | 0 | 107 | -1 |
N.S. | 1 | 1.00 | 0.70 | 0.62 | 0.00 | 1.75 | 0.00 | 0.78 | -0.01 |
time (sec) |
N/A | 0.154 | 0.112 | 0.456 | 0.000 | 1.926 | 0.000 | 1.432 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 106 | 100 | 0 | 263 | 0 | 122 | 44 |
N.S. | 1 | 1.00 | 0.64 | 0.60 | 0.00 | 1.58 | 0.00 | 0.73 | 0.27 |
time (sec) |
N/A | 0.284 | 0.148 | 0.459 | 0.000 | 1.599 | 0.000 | 1.126 | 5.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 102 | 103 | 0 | 180 | 0 | 83 | -1 |
N.S. | 1 | 1.00 | 0.82 | 0.82 | 0.00 | 1.44 | 0.00 | 0.66 | -0.01 |
time (sec) |
N/A | 0.260 | 0.085 | 0.392 | 0.000 | 1.528 | 0.000 | 1.817 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 91 | 92 | 0 | 159 | 0 | 71 | -1 |
N.S. | 1 | 1.00 | 0.96 | 0.97 | 0.00 | 1.67 | 0.00 | 0.75 | -0.01 |
time (sec) |
N/A | 0.200 | 0.073 | 0.380 | 0.000 | 1.332 | 0.000 | 1.956 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 71 | 79 | 0 | 131 | 0 | 55 | -1 |
N.S. | 1 | 1.00 | 1.18 | 1.32 | 0.00 | 2.18 | 0.00 | 0.92 | -0.02 |
time (sec) |
N/A | 0.106 | 0.056 | 0.386 | 0.000 | 2.896 | 0.000 | 1.625 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 53 | 58 | 0 | 77 | 0 | 37 | -1 |
N.S. | 1 | 1.00 | 1.56 | 1.71 | 0.00 | 2.26 | 0.00 | 1.09 | -0.03 |
time (sec) |
N/A | 0.030 | 0.036 | 0.372 | 0.000 | 2.841 | 0.000 | 2.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 27 | 0 | 21 | 0 | 34 | -1 |
N.S. | 1 | 1.00 | 0.92 | 1.08 | 0.00 | 0.84 | 0.00 | 1.36 | -0.04 |
time (sec) |
N/A | 0.024 | 0.020 | 0.365 | 0.000 | 2.860 | 0.000 | 1.810 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 31 | 33 | 0 | 29 | 0 | 54 | -1 |
N.S. | 1 | 1.00 | 0.55 | 0.59 | 0.00 | 0.52 | 0.00 | 0.96 | -0.02 |
time (sec) |
N/A | 0.056 | 0.061 | 0.372 | 0.000 | 1.725 | 0.000 | 1.537 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 44 | 46 | 0 | 40 | 0 | 81 | -1 |
N.S. | 1 | 1.00 | 0.51 | 0.53 | 0.00 | 0.47 | 0.00 | 0.94 | -0.01 |
time (sec) |
N/A | 0.079 | 0.069 | 0.375 | 0.000 | 2.140 | 0.000 | 1.541 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 55 | 57 | 0 | 51 | 0 | 107 | -1 |
N.S. | 1 | 1.00 | 0.47 | 0.49 | 0.00 | 0.44 | 0.00 | 0.92 | -0.01 |
time (sec) |
N/A | 0.111 | 0.078 | 0.364 | 0.000 | 1.840 | 0.000 | 2.174 | 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 | 61 | 61 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.029 | 0.031 | 0.070 | 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 | 48 | 61 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.27 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.028 | 0.025 | 0.074 | 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 | 54 | 54 | 52 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.027 | 0.024 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 30 | 36 | 0 | 38 | 0 | 0 | 54 |
N.S. | 1 | 1.00 | 0.94 | 1.12 | 0.00 | 1.19 | 0.00 | 0.00 | 1.69 |
time (sec) |
N/A | 0.018 | 0.028 | 0.405 | 0.000 | 1.592 | 0.000 | 0.000 | 5.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 44 | 50 | 0 | 70 | 0 | 0 | 98 |
N.S. | 1 | 1.00 | 0.63 | 0.71 | 0.00 | 1.00 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A | 0.039 | 0.045 | 0.396 | 0.000 | 2.060 | 0.000 | 0.000 | 5.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 72 | 84 | 0 | 111 | 0 | 0 | 157 |
N.S. | 1 | 1.00 | 0.62 | 0.72 | 0.00 | 0.96 | 0.00 | 0.00 | 1.35 |
time (sec) |
N/A | 0.066 | 0.038 | 0.401 | 0.000 | 2.294 | 0.000 | 0.000 | 5.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 24 | 31 | 36 | 36 | 36 | 22 | 37 |
N.S. | 1 | 1.00 | 1.26 | 1.63 | 1.89 | 1.89 | 1.89 | 1.16 | 1.95 |
time (sec) |
N/A | 0.007 | 0.006 | 0.372 | 0.282 | 1.978 | 0.157 | 0.936 | 5.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 46 | 48 | 46 | 42 | 0 | 65 | 42 |
N.S. | 1 | 1.00 | 0.58 | 0.60 | 0.58 | 0.52 | 0.00 | 0.81 | 0.52 |
time (sec) |
N/A | 0.079 | 0.029 | 0.372 | 0.298 | 1.226 | 0.000 | 1.863 | 5.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 34 | 37 | 34 | 30 | 0 | 48 | 33 |
N.S. | 1 | 1.00 | 0.65 | 0.71 | 0.65 | 0.58 | 0.00 | 0.92 | 0.63 |
time (sec) |
N/A | 0.045 | 0.023 | 0.372 | 0.303 | 3.074 | 0.000 | 1.948 | 5.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 27 | 14 | 21 | 0 | 29 | 21 |
N.S. | 1 | 1.00 | 1.00 | 1.08 | 0.56 | 0.84 | 0.00 | 1.16 | 0.84 |
time (sec) |
N/A | 0.013 | 0.015 | 0.388 | 0.288 | 1.525 | 0.000 | 1.774 | 5.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 54 | 43 | 0 | 75 | 0 | 47 | -1 |
N.S. | 1 | 1.00 | 1.69 | 1.34 | 0.00 | 2.34 | 0.00 | 1.47 | -0.03 |
time (sec) |
N/A | 0.009 | 0.022 | 0.386 | 0.000 | 1.326 | 0.000 | 1.730 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 76 | 66 | 0 | 127 | 0 | 55 | -1 |
N.S. | 1 | 1.00 | 1.29 | 1.12 | 0.00 | 2.15 | 0.00 | 0.93 | -0.02 |
time (sec) |
N/A | 0.037 | 0.059 | 0.429 | 0.000 | 1.781 | 0.000 | 2.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 68 | 248 | 0 | 37 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.29 | 1.04 | 0.00 | 0.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.092 | 10.026 | 0.431 | 0.000 | 0.439 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 52 | 231 | 0 | 14 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.25 | 1.09 | 0.00 | 0.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.049 | 10.017 | 0.370 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 243 | 55 | 248 | 0 | 38 | 0 | 0 | 44 |
N.S. | 1 | 1.00 | 0.23 | 1.02 | 0.00 | 0.16 | 0.00 | 0.00 | 0.18 |
time (sec) |
N/A | 0.087 | 10.021 | 0.387 | 0.000 | 0.348 | 0.000 | 0.000 | 5.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 514 | 514 | 68 | 676 | 0 | 45 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.13 | 1.32 | 0.00 | 0.09 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.216 | 10.030 | 0.405 | 0.000 | 0.506 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 484 | 484 | 55 | 394 | 0 | 22 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.11 | 0.81 | 0.00 | 0.05 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.132 | 10.016 | 0.455 | 0.000 | 0.675 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 510 | 50 | 673 | 0 | 46 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.10 | 1.32 | 0.00 | 0.09 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.238 | 10.017 | 0.375 | 0.000 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | C | F | F | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 265 | 86 | 2017 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.32 | 7.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.207 | 10.036 | 0.476 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 525 | 525 | 70 | 2586 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.13 | 4.93 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.367 | 10.033 | 0.469 | 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 | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 81 | 3347 | 0 | 148 | 0 | 52 | -1 |
N.S. | 1 | 1.00 | 1.25 | 51.49 | 0.00 | 2.28 | 0.00 | 0.80 | -0.02 |
time (sec) |
N/A | 0.064 | 0.022 | 0.580 | 0.000 | 2.026 | 0.000 | 0.681 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 237 | 70 | 1793 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.30 | 7.57 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.161 | 10.039 | 0.591 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | C | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 492 | 57 | 2374 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.12 | 4.83 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.306 | 10.024 | 0.508 | 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 | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 59 | 480 | 0 | 101 | 0 | 40 | -1 |
N.S. | 1 | 1.00 | 1.64 | 13.33 | 0.00 | 2.81 | 0.00 | 1.11 | -0.03 |
time (sec) |
N/A | 0.032 | 0.008 | 0.524 | 0.000 | 2.765 | 0.000 | 0.532 | 0.000 |