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 | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 295 | 43 | 57 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 7.56 | 1.10 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.040 | 0.030 | 1.059 | 0.252 | 0.341 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 454 | 43 | 69 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 12.97 | 1.23 | 1.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.043 | 0.018 | 3.761 | 0.238 | 0.322 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 0 | 47 | 65 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 1.07 | 1.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.042 | 0.023 | 0.000 | 0.236 | 0.307 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 37 | 321 | 32 | 65 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 8.23 | 0.82 | 1.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.039 | 0.035 | 2.759 | 0.306 | 0.322 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 478 | 32 | 77 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 13.66 | 0.91 | 2.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.037 | 0.024 | 5.520 | 0.331 | 0.321 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 0 | 36 | 73 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.82 | 1.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.038 | 0.022 | 0.000 | 0.313 | 0.325 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 35 | 24 | 54 | 101 | 0 | 0 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.62 | 1.38 | 2.59 | 0.00 | 0.00 | 0.51 |
time (sec) |
N/A | 0.033 | 0.007 | 0.500 | 0.324 | 0.359 | 0.000 | 0.000 | 1.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 49 | 76 | 56 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 1.85 | 1.37 | 2.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.035 | 0.009 | 1.066 | 0.280 | 0.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 47 | 47 | 57 | 129 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.27 | 1.27 | 1.54 | 3.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.036 | 0.009 | 1.154 | 0.283 | 0.343 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 55 | 43 | 61 | 116 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.93 | 1.33 | 2.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.035 | 0.010 | 5.638 | 0.281 | 0.311 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 45 | 24 | 49 | 101 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.15 | 0.62 | 1.26 | 2.59 | 0.00 | 0.00 | 0.56 |
time (sec) |
N/A | 0.032 | 0.007 | 0.492 | 0.275 | 0.345 | 0.000 | 0.000 | 1.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 49 | 76 | 51 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 1.85 | 1.24 | 2.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.032 | 0.010 | 1.076 | 0.286 | 0.342 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 47 | 47 | 59 | 127 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.27 | 1.27 | 1.59 | 3.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.033 | 0.010 | 1.138 | 0.284 | 0.330 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 55 | 43 | 61 | 116 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.93 | 1.33 | 2.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.034 | 0.011 | 4.257 | 0.280 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 314 | 31 | 84 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 8.26 | 0.82 | 2.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.037 | 0.012 | 2.588 | 0.315 | 0.346 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 480 | 32 | 106 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 13.71 | 0.91 | 3.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.037 | 0.016 | 3.154 | 0.316 | 0.347 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 0 | 36 | 92 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.84 | 2.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.038 | 0.019 | 0.000 | 0.320 | 0.351 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 293 | 37 | 76 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 7.71 | 0.97 | 2.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.038 | 0.012 | 0.810 | 0.252 | 0.348 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 456 | 45 | 97 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 13.03 | 1.29 | 2.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.036 | 0.017 | 1.439 | 0.238 | 0.322 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 0 | 47 | 84 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.09 | 1.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.038 | 0.020 | 0.000 | 0.237 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 33 | 30 | 112 | 258 | 0 | 94 | 31 |
N.S. |
1 | 1.00 | 0.66 | 0.60 | 2.24 | 5.16 | 0.00 | 1.88 | 0.62 |
time (sec) |
N/A | 0.018 | 0.009 | 9.253 | 0.216 | 0.301 | 0.000 | 0.397 | 1.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 12 | 62 | 14 | 37 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.92 | 4.77 | 1.08 | 2.85 | 0.69 |
time (sec) |
N/A | 0.013 | 0.014 | 141.525 | 0.183 | 0.337 | 0.185 | 0.285 | 1.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 11 | 14 | 13 | 9 | 94 | 13 | 9 |
N.S. |
1 | 1.00 | 0.65 | 0.82 | 0.76 | 0.53 | 5.53 | 0.76 | 0.53 |
time (sec) |
N/A | 0.004 | 0.003 | 0.562 | 0.198 | 0.303 | 0.813 | 0.297 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 25 | 24 | 23 | 27 | 24 | 25 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 0.89 | 0.85 | 1.00 | 0.89 | 0.93 |
time (sec) |
N/A | 0.015 | 0.004 | 0.137 | 0.188 | 0.312 | 0.057 | 0.287 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 22 | 4 | 3 | 20 | 0 | 3 | 3 |
N.S. |
1 | 1.00 | 7.33 | 1.33 | 1.00 | 6.67 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.020 | 0.018 | 0.210 | 0.304 | 0.313 | 0.000 | 0.289 | 1.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 30 | 23 | 17 | 22 | 22 | 22 | 17 |
N.S. |
1 | 1.00 | 1.25 | 0.96 | 0.71 | 0.92 | 0.92 | 0.92 | 0.71 |
time (sec) |
N/A | 0.014 | 0.001 | 0.112 | 0.194 | 0.335 | 0.050 | 0.281 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 26 | 23 | 22 | 29 | 23 | 25 |
N.S. |
1 | 1.00 | 0.92 | 1.04 | 0.92 | 0.88 | 1.16 | 0.92 | 1.00 |
time (sec) |
N/A | 0.006 | 0.013 | 0.164 | 0.204 | 0.346 | 0.074 | 0.290 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 30 | 25 | 24 | 20 | 22 | 30 | 20 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.71 | 0.59 | 0.65 | 0.88 | 0.59 |
time (sec) |
N/A | 0.009 | 0.006 | 0.196 | 0.192 | 0.307 | 0.045 | 0.282 | 1.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 25 | 28 | 24 | 27 | 42 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.62 | 0.70 | 0.60 | 0.68 | 1.05 | 0.55 |
time (sec) |
N/A | 0.012 | 0.008 | 0.254 | 0.185 | 0.378 | 0.061 | 0.288 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 26 | 25 | 25 | 26 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.84 | 0.81 | 0.81 |
time (sec) |
N/A | 0.021 | 0.014 | 0.115 | 0.272 | 0.349 | 0.059 | 0.298 | 1.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.003 | 0.015 | 0.066 | 0.000 | 0.343 | 3.337 | 0.346 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.003 | 0.014 | 0.065 | 0.000 | 0.355 | 2.693 | 0.301 | 1.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.004 | 0.015 | 0.088 | 0.000 | 0.300 | 3.474 | 0.303 | 1.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 52 | 0 | 28 | 0 | 40 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.00 | 0.65 | 0.00 | 0.93 | 0.86 |
time (sec) |
N/A | 0.009 | 0.022 | 0.091 | 0.000 | 0.323 | 0.000 | 0.360 | 2.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 15 | 14 | 13 | 14 | 105 | 13 | 9 |
N.S. |
1 | 1.00 | 0.71 | 0.67 | 0.62 | 0.67 | 5.00 | 0.62 | 0.43 |
time (sec) |
N/A | 0.004 | 0.005 | 0.543 | 0.207 | 0.346 | 1.330 | 0.321 | 1.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 12 | 13 | 24 | 14 | 10 | 14 | 13 |
N.S. |
1 | 1.00 | 0.92 | 1.00 | 1.85 | 1.08 | 0.77 | 1.08 | 1.00 |
time (sec) |
N/A | 0.004 | 0.006 | 0.119 | 0.182 | 0.353 | 0.101 | 0.481 | 1.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 7 | 14 | 6 | 3 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 2.33 | 1.00 | 0.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.007 | 0.002 | 0.083 | 0.198 | 0.306 | 0.042 | 0.354 | 1.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 38 | 28 | 33 | 38 | 184 | 33 | 26 |
N.S. |
1 | 1.00 | 1.19 | 0.88 | 1.03 | 1.19 | 5.75 | 1.03 | 0.81 |
time (sec) |
N/A | 0.137 | 0.013 | 0.171 | 0.184 | 0.385 | 0.411 | 0.317 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.005 | 0.004 | 1.171 | 0.273 | 0.342 | 0.066 | 0.309 | 1.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 22 | 29 | 23 | 34 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.45 | 1.15 | 1.70 | 1.15 | 0.95 |
time (sec) |
N/A | 0.003 | 0.015 | 0.161 | 0.187 | 0.350 | 0.123 | 0.321 | 1.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 31 | 34 | 33 | 33 | 32 | 139 | 29 |
N.S. |
1 | 1.00 | 0.89 | 0.97 | 0.94 | 0.94 | 0.91 | 3.97 | 0.83 |
time (sec) |
N/A | 0.004 | 0.006 | 0.530 | 0.198 | 0.339 | 0.082 | 0.316 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 14 | 12 | 12 | 15 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 |
time (sec) |
N/A | 0.002 | 0.003 | 0.217 | 0.191 | 0.370 | 0.059 | 0.291 | 1.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 27 | 29 | 28 | 28 | 27 | 29 | 40 |
N.S. |
1 | 1.00 | 0.75 | 0.81 | 0.78 | 0.78 | 0.75 | 0.81 | 1.11 |
time (sec) |
N/A | 0.011 | 0.009 | 0.333 | 0.191 | 0.320 | 0.058 | 0.302 | 1.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 43 | 42 | 42 | 48 | 43 | 56 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 0.78 | 0.89 | 0.80 | 1.04 |
time (sec) |
N/A | 0.028 | 0.012 | 0.348 | 0.189 | 0.294 | 0.063 | 0.311 | 1.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 30 | 52 | 42 | 41 | 31 | 46 |
N.S. |
1 | 1.00 | 0.94 | 0.86 | 1.49 | 1.20 | 1.17 | 0.89 | 1.31 |
time (sec) |
N/A | 0.010 | 0.019 | 0.205 | 0.193 | 0.303 | 0.099 | 0.308 | 1.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 44 | 30 | 74 | 64 | 63 | 31 | 73 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 2.11 | 1.83 | 1.80 | 0.89 | 2.09 |
time (sec) |
N/A | 0.016 | 0.015 | 0.796 | 0.200 | 0.321 | 0.109 | 0.302 | 1.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 10 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.87 | 0.87 |
time (sec) |
N/A | 0.012 | 0.001 | 0.806 | 0.187 | 0.321 | 0.048 | 0.299 | 1.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 21 | 26 | 31 | 21 | 26 | 32 | 25 |
N.S. |
1 | 1.00 | 0.68 | 0.84 | 1.00 | 0.68 | 0.84 | 1.03 | 0.81 |
time (sec) |
N/A | 0.014 | 0.003 | 0.859 | 0.185 | 0.282 | 0.091 | 0.287 | 1.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 30 | 61 | 44 | 47 | 185 | 0 | 52 |
N.S. |
1 | 1.00 | 0.68 | 1.39 | 1.00 | 1.07 | 4.20 | 0.00 | 1.18 |
time (sec) |
N/A | 0.022 | 0.013 | 0.829 | 0.185 | 0.364 | 0.428 | 0.000 | 1.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 24 | 19 | 31 | 45 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.33 | 1.06 | 1.72 | 2.50 | 1.00 |
time (sec) |
N/A | 0.008 | 0.003 | 0.339 | 0.209 | 0.300 | 0.402 | 0.304 | 1.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 24 | 0 | 121 | 99 | 26 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.00 | 3.78 | 3.09 | 0.81 | 2.22 |
time (sec) |
N/A | 0.013 | 0.052 | 0.664 | 0.000 | 0.308 | 2.205 | 0.313 | 1.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 112 | 112 | 0 | 480 | 175 | 239 | 153 |
N.S. |
1 | 1.00 | 0.78 | 0.78 | 0.00 | 3.33 | 1.22 | 1.66 | 1.06 |
time (sec) |
N/A | 0.067 | 0.069 | 0.973 | 0.000 | 0.310 | 25.994 | 0.333 | 3.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | A | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 167 | 112 | 0 | 160 | 133 | 170 | 95 |
N.S. |
1 | 1.00 | 0.74 | 0.49 | 0.00 | 0.70 | 0.59 | 0.75 | 0.42 |
time (sec) |
N/A | 0.112 | 0.082 | 1.361 | 0.000 | 0.292 | 13.472 | 0.312 | 3.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 34 | 29 | 33 | 28 | 116 | 53 | 27 |
N.S. |
1 | 1.00 | 1.26 | 1.07 | 1.22 | 1.04 | 4.30 | 1.96 | 1.00 |
time (sec) |
N/A | 0.016 | 0.047 | 0.361 | 0.189 | 0.311 | 1.610 | 0.310 | 1.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 41 | 0 | 143 | 204 | 38 | 45 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.00 | 3.58 | 5.10 | 0.95 | 1.12 |
time (sec) |
N/A | 0.019 | 0.030 | 0.638 | 0.000 | 0.316 | 3.634 | 0.323 | 1.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 129 | 118 | 0 | 149 | 245 | 257 | 174 |
N.S. |
1 | 1.00 | 0.87 | 0.79 | 0.00 | 1.00 | 1.64 | 1.72 | 1.17 |
time (sec) |
N/A | 0.072 | 0.055 | 0.980 | 0.000 | 0.300 | 26.839 | 0.367 | 3.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | A | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 233 | 233 | 208 | 118 | 0 | 156 | 228 | 178 | 176 |
N.S. |
1 | 1.00 | 0.89 | 0.51 | 0.00 | 0.67 | 0.98 | 0.76 | 0.76 |
time (sec) |
N/A | 0.136 | 0.063 | 1.421 | 0.000 | 0.305 | 15.017 | 0.312 | 3.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 20 | 0 | 21 | 22 | 0 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.95 | 1.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.014 | 0.039 | 0.427 | 0.000 | 0.291 | 0.078 | 0.000 | 1.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 42 | 38 | 37 | 39 | 22 | 0 | 37 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 0.90 | 0.95 | 0.54 | 0.00 | 0.90 |
time (sec) |
N/A | 0.039 | 0.065 | 0.186 | 0.272 | 0.300 | 0.086 | 0.000 | 1.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 42 | 38 | 0 | 39 | 22 | 0 | 37 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 0.00 | 0.95 | 0.54 | 0.00 | 0.90 |
time (sec) |
N/A | 0.025 | 0.143 | 0.473 | 0.000 | 0.287 | 0.082 | 0.000 | 1.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 44 | 40 | 0 | 41 | 19 | 0 | 37 |
N.S. |
1 | 1.00 | 1.05 | 0.95 | 0.00 | 0.98 | 0.45 | 0.00 | 0.88 |
time (sec) |
N/A | 0.031 | 0.063 | 0.453 | 0.000 | 0.293 | 0.086 | 0.000 | 1.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 21 | 17 | 21 | 27 | 22 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.66 | 0.53 | 0.66 | 0.84 | 0.69 | 0.66 |
time (sec) |
N/A | 0.014 | 0.003 | 0.193 | 0.205 | 0.280 | 0.056 | 0.295 | 1.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.021 | 0.012 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 60 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.019 | 0.012 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 62 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.021 | 0.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 121 | 102 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.101 | 0.058 | 0.592 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 73 | 109 | 111 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.35 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.072 | 0.030 | 2.762 | 0.195 | 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 | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 5 | 12 | 8 | 10 | 0 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.56 | 1.33 | 0.89 | 1.11 | 0.00 | 0.44 |
time (sec) |
N/A | 0.007 | 0.003 | 0.937 | 0.181 | 0.294 | 0.874 | 0.000 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 35 | 47 | 82 | 0 | 0 | 0 | 59 |
N.S. |
1 | 1.00 | 0.81 | 1.09 | 1.91 | 0.00 | 0.00 | 0.00 | 1.37 |
time (sec) |
N/A | 0.047 | 0.015 | 1.167 | 0.193 | 0.000 | 0.000 | 0.000 | 1.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 31 | 31 | 49 | 0 | 228 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.03 | 1.63 | 0.00 | 7.60 | 0.00 | 0.00 |
time (sec) |
N/A | 0.065 | 0.010 | 0.833 | 0.196 | 0.000 | 58.665 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 8 | 7 | 7 | 0 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.018 | 0.163 | 0.527 | 0.231 | 0.280 | 0.000 | 0.325 | 1.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 57 | 57 | 58 | 46 | 59 | 59 |
N.S. |
1 | 1.00 | 0.93 | 0.84 | 0.84 | 0.85 | 0.68 | 0.87 | 0.87 |
time (sec) |
N/A | 0.157 | 0.027 | 1.994 | 0.283 | 0.321 | 0.111 | 0.367 | 1.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 23 | 31 | 37 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.79 | 1.07 | 1.28 | 0.79 | 0.79 |
time (sec) |
N/A | 0.012 | 0.011 | 0.198 | 0.193 | 0.313 | 2.348 | 0.372 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 18 | 14 | 80 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.78 | 4.44 | 1.00 |
time (sec) |
N/A | 0.003 | 0.003 | 0.504 | 0.191 | 0.297 | 0.048 | 0.338 | 1.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 21 | 22 | 25 | 21 | 15 | 103 | 21 |
N.S. |
1 | 1.00 | 0.78 | 0.81 | 0.93 | 0.78 | 0.56 | 3.81 | 0.78 |
time (sec) |
N/A | 0.003 | 0.004 | 0.506 | 0.188 | 0.305 | 0.052 | 0.326 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 60 | 56 | 54 | 54 | 41 | 56 | 55 |
N.S. |
1 | 1.00 | 1.05 | 0.98 | 0.95 | 0.95 | 0.72 | 0.98 | 0.96 |
time (sec) |
N/A | 0.038 | 0.049 | 2.707 | 0.277 | 0.299 | 0.088 | 0.328 | 1.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 62 | 129 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.054 | 0.009 | 1.381 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 239 | 146 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.92 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.069 | 0.039 | 2.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 373 | 121 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.26 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.131 | 0.158 | 1.680 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 134 | 0 | 0 | 37 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.62 | 0.00 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.022 | 0.534 | 0.000 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 134 | 0 | 0 | 36 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.62 | 0.00 | 0.00 | 1.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.022 | 0.478 | 0.000 | 0.000 | 0.310 | 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 | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 10 | 10 | 8 | 10 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.59 | 0.59 | 0.47 | 0.59 | 1.00 |
time (sec) |
N/A | 0.002 | 0.004 | 0.623 | 0.224 | 0.277 | 0.029 | 0.308 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 25 | 26 | 16 | 20 | 65 | 16 | 49 |
N.S. |
1 | 1.00 | 0.93 | 0.96 | 0.59 | 0.74 | 2.41 | 0.59 | 1.81 |
time (sec) |
N/A | 0.005 | 0.018 | 0.221 | 0.217 | 0.315 | 0.424 | 0.305 | 1.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 31 | 25 | 28 | 26 | 25 | 0 | 26 | 27 |
N.S. |
1 | 1.24 | 1.00 | 1.12 | 1.04 | 1.00 | 0.00 | 1.04 | 1.08 |
time (sec) |
N/A | 0.034 | 0.012 | 0.397 | 0.216 | 0.300 | 0.000 | 0.348 | 1.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 22 | 26 | 24 | 23 | 26 | 24 | 20 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.92 | 0.88 | 1.00 | 0.92 | 0.77 |
time (sec) |
N/A | 0.023 | 0.012 | 0.594 | 0.260 | 0.302 | 3.062 | 0.314 | 1.477 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.026 | 14.590 | 0.470 | 0.263 | 0.273 | 0.256 | 0.307 | 1.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 8 | 10 | 10 | 7 | 10 | 10 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 1.25 | 1.25 | 0.88 | 1.25 | 1.25 |
time (sec) |
N/A | 0.016 | 9.099 | 0.470 | 0.242 | 0.269 | 0.242 | 0.309 | 1.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 8 | 6 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.33 | 1.00 | 1.33 | 1.33 | 1.17 | 1.33 | 1.33 |
time (sec) |
N/A | 0.006 | 0.007 | 0.473 | 0.241 | 0.275 | 0.221 | 0.308 | 1.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.022 | 0.051 | 0.444 | 0.231 | 0.270 | 0.540 | 0.330 | 1.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 14 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.40 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.024 | 17.235 | 0.483 | 0.285 | 0.277 | 0.411 | 0.319 | 1.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.017 | 0.012 | 0.204 | 0.299 | 0.285 | 0.046 | 0.305 | 1.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 10 | 11 | 10 | 10 | 8 | 14 | 10 |
N.S. |
1 | 1.00 | 1.11 | 1.22 | 1.11 | 1.11 | 0.89 | 1.56 | 1.11 |
time (sec) |
N/A | 0.051 | 0.055 | 1.043 | 0.311 | 0.298 | 0.048 | 0.311 | 1.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 20 | 0 | 13 | 15 | 0 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.54 | 0.00 | 1.00 | 1.15 | 0.00 | 1.00 |
time (sec) |
N/A | 0.097 | 0.039 | 1.234 | 0.000 | 0.312 | 1.185 | 0.000 | 1.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 53 | 107 | 67 | 48 | 53 | 88 | 63 |
N.S. |
1 | 1.00 | 0.79 | 1.60 | 1.00 | 0.72 | 0.79 | 1.31 | 0.94 |
time (sec) |
N/A | 0.050 | 0.026 | 0.231 | 0.209 | 0.313 | 45.562 | 0.354 | 1.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 53 | 80 | 68 | 49 | 53 | 53 | 38 |
N.S. |
1 | 1.00 | 1.06 | 1.60 | 1.36 | 0.98 | 1.06 | 1.06 | 0.76 |
time (sec) |
N/A | 0.039 | 0.031 | 0.228 | 0.228 | 0.269 | 47.320 | 0.318 | 1.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 19 | 18 | 18 | 17 | 47 | 18 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 0.86 | 0.86 | 0.81 | 2.24 | 0.86 |
time (sec) |
N/A | 0.005 | 0.004 | 0.474 | 0.218 | 0.276 | 0.043 | 0.313 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 53 | 80 | 68 | 49 | 53 | 53 | 38 |
N.S. |
1 | 1.00 | 1.06 | 1.60 | 1.36 | 0.98 | 1.06 | 1.06 | 0.76 |
time (sec) |
N/A | 0.033 | 0.028 | 0.226 | 0.233 | 0.283 | 47.547 | 0.315 | 1.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 64 | 108 | 67 | 48 | 53 | 88 | 63 |
N.S. |
1 | 1.00 | 0.93 | 1.57 | 0.97 | 0.70 | 0.77 | 1.28 | 0.91 |
time (sec) |
N/A | 0.036 | 0.022 | 0.155 | 0.217 | 0.299 | 46.322 | 0.355 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 10 | 0 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 1.11 | 0.00 | 1.00 |
time (sec) |
N/A | 0.016 | 0.010 | 0.107 | 0.247 | 0.285 | 0.067 | 0.000 | 1.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 0 | 17 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.019 | 0.022 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.000 |