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 | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 27 | 24 | 26 | 26 | 26 | 28 | 53 |
N.S. |
1 | 0.92 | 1.08 | 0.96 | 1.04 | 1.04 | 1.04 | 1.12 | 2.12 |
time (sec) |
N/A | 0.461 | 0.622 | 0.138 | 0.313 | 0.261 | 0.228 | 0.265 | 8.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 43 | 49 | 28 | 37 | 32 | 32 | 33 | 32 |
N.S. |
1 | 2.15 | 2.45 | 1.40 | 1.85 | 1.60 | 1.60 | 1.65 | 1.60 |
time (sec) |
N/A | 0.024 | 0.016 | 0.054 | 0.202 | 0.229 | 0.040 | 0.250 | 7.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | B | F(-1) | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 55 | 77 | 81 | 76 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.72 | 2.41 | 2.53 | 2.38 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.170 | 0.357 | 0.281 | 0.865 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 36 | 0 | 33 | 29 | 54 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.24 | 0.00 | 1.14 | 1.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.000 | 5.050 | 16.222 | 0.000 | 0.241 | 52.822 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 37 | 32 | 0 | 36 | 32 | 84 | 95 |
N.S. |
1 | 0.00 | 1.12 | 0.97 | 0.00 | 1.09 | 0.97 | 2.55 | 2.88 |
time (sec) |
N/A | 0.000 | 0.231 | 2.700 | 0.000 | 0.256 | 1.513 | 1.090 | 7.913 |
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 | 17 | 24 | 14 | 26 | 26 | 22 | 13 | 31 |
N.S. |
1 | 1.13 | 1.60 | 0.93 | 1.73 | 1.73 | 1.47 | 0.87 | 2.07 |
time (sec) |
N/A | 0.082 | 0.197 | 0.020 | 0.226 | 0.233 | 0.053 | 0.274 | 0.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 30 | 27 | 29 | 0 | 29 | 28 |
N.S. |
1 | 0.00 | 1.03 | 1.03 | 0.93 | 1.00 | 0.00 | 1.00 | 0.97 |
time (sec) |
N/A | 0.000 | 0.116 | 45.343 | 0.252 | 0.245 | 0.000 | 0.348 | 8.059 |
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 | 41 | 39 | 35 | 32 | 32 | 36 | 32 | 34 |
N.S. |
1 | 1.64 | 1.56 | 1.40 | 1.28 | 1.28 | 1.44 | 1.28 | 1.36 |
time (sec) |
N/A | 0.054 | 0.040 | 0.023 | 0.190 | 0.257 | 0.060 | 0.268 | 7.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 76 | 42 | 49 | 79 | 51 | 54 | 69 | 59 |
N.S. |
1 | 2.24 | 1.24 | 1.44 | 2.32 | 1.50 | 1.59 | 2.03 | 1.74 |
time (sec) |
N/A | 0.283 | 2.361 | 0.067 | 0.231 | 0.238 | 0.088 | 0.261 | 7.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 42 | 33 | 57 | 34 | 31 | 34 | 80 |
N.S. |
1 | 0.00 | 1.31 | 1.03 | 1.78 | 1.06 | 0.97 | 1.06 | 2.50 |
time (sec) |
N/A | 0.000 | 0.280 | 13.315 | 0.277 | 0.248 | 0.318 | 0.360 | 8.477 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 445 | 59 | 27 | 127 | 45 | 27 | 45 | 28 |
N.S. |
1 | 15.34 | 2.03 | 0.93 | 4.38 | 1.55 | 0.93 | 1.55 | 0.97 |
time (sec) |
N/A | 1.634 | 0.600 | 0.149 | 0.319 | 0.259 | 0.065 | 0.259 | 7.696 |
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 | 14 | 13 | 11 | 10 | 9 | 9 | 10 | 9 | 10 |
N.S. |
1 | 0.93 | 0.79 | 0.71 | 0.64 | 0.64 | 0.71 | 0.64 | 0.71 |
time (sec) |
N/A | 0.004 | 0.001 | 0.011 | 0.202 | 0.229 | 0.025 | 0.261 | 0.032 |
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 | 33 | 24 | 21 | 23 | 20 | 17 | 22 | 18 |
N.S. |
1 | 1.38 | 1.00 | 0.88 | 0.96 | 0.83 | 0.71 | 0.92 | 0.75 |
time (sec) |
N/A | 0.034 | 0.008 | 0.023 | 0.236 | 0.241 | 0.072 | 0.254 | 7.885 |
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 | 19 | 19 | 17 | 24 | 22 | 14 | 16 | 14 |
N.S. |
1 | 0.66 | 0.66 | 0.59 | 0.83 | 0.76 | 0.48 | 0.55 | 0.48 |
time (sec) |
N/A | 0.073 | 0.045 | 0.019 | 0.180 | 0.243 | 0.047 | 0.249 | 7.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 43 | 45 | 59 | 56 | 41 | 0 | 52 |
N.S. |
1 | 0.00 | 1.23 | 1.29 | 1.69 | 1.60 | 1.17 | 0.00 | 1.49 |
time (sec) |
N/A | 0.000 | 0.208 | 10.566 | 0.253 | 0.241 | 0.143 | 0.000 | 8.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 32 | 37 | 31 | 36 | 34 | 31 | 36 |
N.S. |
1 | 0.00 | 1.28 | 1.48 | 1.24 | 1.44 | 1.36 | 1.24 | 1.44 |
time (sec) |
N/A | 0.000 | 0.219 | 40.124 | 0.266 | 0.252 | 0.735 | 0.394 | 7.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 40 | 34 | 38 | 52 | 49 | 0 | 43 |
N.S. |
1 | 0.00 | 1.14 | 0.97 | 1.09 | 1.49 | 1.40 | 0.00 | 1.23 |
time (sec) |
N/A | 0.000 | 2.149 | 17.244 | 0.457 | 0.243 | 0.314 | 0.000 | 7.922 |
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 | 15 | 15 | 14 | 13 | 13 | 8 | 13 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.81 | 0.81 | 0.50 | 0.81 | 0.81 |
time (sec) |
N/A | 0.047 | 0.040 | 0.365 | 0.202 | 0.250 | 0.061 | 0.248 | 7.532 |
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 | 14 | 9 | 9 | 9 | 9 | 9 | 8 | 9 | 8 |
N.S. |
1 | 0.64 | 0.64 | 0.64 | 0.64 | 0.64 | 0.57 | 0.64 | 0.57 |
time (sec) |
N/A | 0.002 | 0.000 | 0.007 | 0.206 | 0.223 | 0.021 | 0.257 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 31 | 116 | 33 | 29 | 33 | 58 |
N.S. |
1 | 0.00 | 1.00 | 1.29 | 4.83 | 1.38 | 1.21 | 1.38 | 2.42 |
time (sec) |
N/A | 0.000 | 0.056 | 6.375 | 14.689 | 0.230 | 0.116 | 0.347 | 7.752 |
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 | 23 | 43 | 43 | 41 | 43 | 38 | 39 | 41 | 25 |
N.S. |
1 | 1.87 | 1.87 | 1.78 | 1.87 | 1.65 | 1.70 | 1.78 | 1.09 |
time (sec) |
N/A | 0.077 | 0.016 | 0.032 | 0.190 | 0.244 | 0.068 | 0.254 | 7.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 63 | 85 | 186 | 186 | 129 | 274 | 0 |
N.S. |
1 | 0.00 | 2.10 | 2.83 | 6.20 | 6.20 | 4.30 | 9.13 | 0.00 |
time (sec) |
N/A | 0.000 | 19.446 | 0.406 | 0.373 | 0.252 | 0.373 | 0.335 | 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 | 18 | 16 | 16 | 14 | 13 | 13 | 14 | 19 | 12 |
N.S. |
1 | 0.89 | 0.89 | 0.78 | 0.72 | 0.72 | 0.78 | 1.06 | 0.67 |
time (sec) |
N/A | 0.011 | 0.034 | 0.066 | 0.207 | 0.234 | 0.075 | 0.247 | 8.253 |
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 | 19 | 19 | 33 | 15 | 0 | 21 | 22 | 0 | 18 |
N.S. |
1 | 1.00 | 1.74 | 0.79 | 0.00 | 1.11 | 1.16 | 0.00 | 0.95 |
time (sec) |
N/A | 0.964 | 0.453 | 7.257 | 0.000 | 0.243 | 0.302 | 0.000 | 7.719 |
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 | 20 | 23 | 21 | 23 | 23 | 20 | 23 | 22 |
N.S. |
1 | 0.83 | 0.96 | 0.88 | 0.96 | 0.96 | 0.83 | 0.96 | 0.92 |
time (sec) |
N/A | 0.007 | 0.000 | 0.021 | 0.189 | 0.241 | 0.018 | 0.258 | 7.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 167 | 102 | 144 | 175 | 146 | 153 | 170 | 110 |
N.S. |
1 | 6.68 | 4.08 | 5.76 | 7.00 | 5.84 | 6.12 | 6.80 | 4.40 |
time (sec) |
N/A | 0.527 | 0.604 | 0.142 | 0.281 | 0.251 | 0.247 | 0.272 | 8.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 18 | 113 | 17 | 16 | 17 | 17 | 0 |
N.S. |
1 | 0.00 | 0.78 | 4.91 | 0.74 | 0.70 | 0.74 | 0.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.448 | 0.030 | 0.244 | 0.246 | 95.222 | 0.249 | 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 | 29 | 27 | 28 | 20 | 18 | 18 | 19 | 18 | 19 |
N.S. |
1 | 0.93 | 0.97 | 0.69 | 0.62 | 0.62 | 0.66 | 0.62 | 0.66 |
time (sec) |
N/A | 0.201 | 0.050 | 0.188 | 0.184 | 0.237 | 0.160 | 0.266 | 8.302 |
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 | 12 | 10 | 11 | 10 | 10 | 10 | 10 | 11 |
N.S. |
1 | 0.92 | 0.77 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 0.85 |
time (sec) |
N/A | 0.005 | 0.000 | 0.009 | 0.176 | 0.222 | 0.018 | 0.244 | 7.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 16 | 14 | 14 | 0 | 18 | 0 | 18 | 13 |
N.S. |
1 | 1.14 | 1.00 | 1.00 | 0.00 | 1.29 | 0.00 | 1.29 | 0.93 |
time (sec) |
N/A | 0.996 | 0.232 | 14.204 | 0.000 | 0.237 | 0.000 | 0.302 | 7.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 88 | 50 | 50 | 0 | 54 | 65 | 78 | 69 |
N.S. |
1 | 3.03 | 1.72 | 1.72 | 0.00 | 1.86 | 2.24 | 2.69 | 2.38 |
time (sec) |
N/A | 0.505 | 1.142 | 0.101 | 0.000 | 0.253 | 0.223 | 0.253 | 7.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 29 | 29 | 31 | 68 | 72 | 66 | 0 | 65 |
N.S. |
1 | 1.04 | 1.04 | 1.11 | 2.43 | 2.57 | 2.36 | 0.00 | 2.32 |
time (sec) |
N/A | 1.143 | 0.238 | 0.197 | 0.639 | 0.255 | 0.133 | 0.000 | 8.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 108 | 29 | 77 | 74 | 70 | 70 | 0 | 54 |
N.S. |
1 | 3.60 | 0.97 | 2.57 | 2.47 | 2.33 | 2.33 | 0.00 | 1.80 |
time (sec) |
N/A | 0.234 | 0.030 | 6.035 | 0.377 | 0.258 | 0.217 | 0.000 | 8.290 |
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 | 25 | 25 | 20 | 19 | 17 | 20 | 21 | 21 |
N.S. |
1 | 1.47 | 1.47 | 1.18 | 1.12 | 1.00 | 1.18 | 1.24 | 1.24 |
time (sec) |
N/A | 0.016 | 0.005 | 0.018 | 7.662 | 0.236 | 0.054 | 0.258 | 7.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 28 | 28 | 27 | 27 | 27 | 0 |
N.S. |
1 | 0.00 | 1.07 | 0.93 | 0.93 | 0.90 | 0.90 | 0.90 | 0.00 |
time (sec) |
N/A | 0.000 | 0.503 | 0.227 | 0.447 | 0.253 | 0.097 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 33 | 167 | 223 | 324 | 187 | 227 | 0 |
N.S. |
1 | 0.00 | 1.00 | 5.06 | 6.76 | 9.82 | 5.67 | 6.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.171 | 6.820 | 0.291 | 0.248 | 5.615 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 38 | 37 | 38 | 35 | 54 | 37 | 32 |
N.S. |
1 | 0.00 | 1.09 | 1.06 | 1.09 | 1.00 | 1.54 | 1.06 | 0.91 |
time (sec) |
N/A | 0.000 | 0.085 | 1.006 | 0.297 | 0.239 | 0.544 | 0.320 | 9.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 28 | 117 | 119 | 139 | 132 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.93 | 3.90 | 3.97 | 4.63 | 4.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.163 | 6.366 | 0.245 | 0.240 | 0.279 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 102 | 25 | 24 | 23 | 23 | 24 | 0 | 23 |
N.S. |
1 | 3.09 | 0.76 | 0.73 | 0.70 | 0.70 | 0.73 | 0.00 | 0.70 |
time (sec) |
N/A | 7.797 | 4.347 | 3.454 | 0.342 | 0.237 | 0.188 | 0.000 | 8.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 35 | 51 | 33 | 43 | 42 | 118 | 97 |
N.S. |
1 | 0.00 | 1.03 | 1.50 | 0.97 | 1.26 | 1.24 | 3.47 | 2.85 |
time (sec) |
N/A | 0.000 | 0.294 | 0.044 | 0.466 | 0.234 | 1.639 | 4.085 | 8.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 29 | 55 | 26 | 0 | 40 | 45 |
N.S. |
1 | 0.00 | 1.00 | 1.12 | 2.12 | 1.00 | 0.00 | 1.54 | 1.73 |
time (sec) |
N/A | 0.000 | 10.148 | 2.904 | 0.712 | 0.229 | 0.000 | 0.350 | 8.203 |
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 | 51 | 37 | 27 | 38 | 34 | 31 | 39 | 32 |
N.S. |
1 | 1.89 | 1.37 | 1.00 | 1.41 | 1.26 | 1.15 | 1.44 | 1.19 |
time (sec) |
N/A | 1.481 | 0.892 | 0.139 | 0.327 | 0.238 | 0.052 | 0.254 | 0.144 |
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 | 34 | 35 | 35 | 33 | 48 | 36 | 34 | 0 | 34 |
N.S. |
1 | 1.03 | 1.03 | 0.97 | 1.41 | 1.06 | 1.00 | 0.00 | 1.00 |
time (sec) |
N/A | 1.516 | 1.043 | 0.028 | 0.278 | 0.240 | 0.983 | 0.000 | 8.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 16 | 16 | 13 | 20 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.23 | 1.23 | 1.00 | 1.54 | 0.92 | 0.62 | 0.92 | 0.92 |
time (sec) |
N/A | 0.271 | 0.050 | 0.018 | 0.229 | 0.247 | 0.033 | 0.259 | 7.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 63 | 24 | 27 | 21 | 35 | 29 | 0 | 24 |
N.S. |
1 | 2.33 | 0.89 | 1.00 | 0.78 | 1.30 | 1.07 | 0.00 | 0.89 |
time (sec) |
N/A | 0.083 | 0.417 | 0.154 | 0.395 | 0.230 | 11.376 | 0.000 | 8.005 |
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 | 8 | 8 | 8 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.002 | 0.000 | 0.008 | 0.186 | 0.217 | 0.015 | 0.258 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 48 | 50 | 52 | 52 | 61 | 52 | 172 |
N.S. |
1 | 0.00 | 1.55 | 1.61 | 1.68 | 1.68 | 1.97 | 1.68 | 5.55 |
time (sec) |
N/A | 0.000 | 9.799 | 0.454 | 0.239 | 0.240 | 0.124 | 0.493 | 8.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 34 | 25 | 33 | 29 | 0 | 34 |
N.S. |
1 | 0.00 | 0.00 | 1.31 | 0.96 | 1.27 | 1.12 | 0.00 | 1.31 |
time (sec) |
N/A | 0.000 | 0.000 | 0.656 | 0.325 | 0.233 | 0.121 | 0.000 | 9.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 29 | 42 | 0 | 40 | 32 | 72 | 66 |
N.S. |
1 | 0.00 | 0.78 | 1.14 | 0.00 | 1.08 | 0.86 | 1.95 | 1.78 |
time (sec) |
N/A | 0.000 | 0.281 | 3.049 | 0.000 | 0.234 | 0.744 | 0.611 | 9.788 |
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 | 22 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.45 | 0.45 | 0.45 | 0.41 | 0.41 | 0.36 | 0.41 | 0.41 |
time (sec) |
N/A | 0.008 | 0.009 | 0.015 | 0.185 | 0.244 | 0.035 | 0.246 | 9.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 71 | 145 | 67 | 67 | 67 | 68 | 73 | 68 |
N.S. |
1 | 2.37 | 4.83 | 2.23 | 2.23 | 2.23 | 2.27 | 2.43 | 2.27 |
time (sec) |
N/A | 0.610 | 0.302 | 0.356 | 0.195 | 0.305 | 21.510 | 0.285 | 8.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 74 | 29 | 25 | 24 | 24 | 20 | 0 | 24 |
N.S. |
1 | 2.47 | 0.97 | 0.83 | 0.80 | 0.80 | 0.67 | 0.00 | 0.80 |
time (sec) |
N/A | 0.221 | 0.546 | 0.355 | 0.223 | 0.238 | 0.146 | 0.000 | 8.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 20 | 22 | 21 | 21 | 19 | 21 | 23 |
N.S. |
1 | 0.00 | 0.83 | 0.92 | 0.88 | 0.88 | 0.79 | 0.88 | 0.96 |
time (sec) |
N/A | 0.000 | 0.300 | 0.514 | 0.235 | 0.238 | 0.066 | 0.260 | 8.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 12 | 15 | 12 | 12 | 12 | 12 | 11 |
N.S. |
1 | 0.00 | 0.71 | 0.88 | 0.71 | 0.71 | 0.71 | 0.71 | 0.65 |
time (sec) |
N/A | 0.000 | 0.083 | 0.044 | 0.227 | 0.244 | 0.071 | 0.281 | 8.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 44 | 312 | 40 | 46 | 87 | 44 |
N.S. |
1 | 0.00 | 1.00 | 2.20 | 15.60 | 2.00 | 2.30 | 4.35 | 2.20 |
time (sec) |
N/A | 0.000 | 0.862 | 0.629 | 0.227 | 0.248 | 2.626 | 0.291 | 8.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 69 | 81 | 66 | 64 | 75 | 80 | 0 |
N.S. |
1 | 0.00 | 2.46 | 2.89 | 2.36 | 2.29 | 2.68 | 2.86 | 0.00 |
time (sec) |
N/A | 0.000 | 0.082 | 0.704 | 0.290 | 0.254 | 0.267 | 63.860 | 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 | 17 | 16 | 16 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 0.82 | 0.94 | 0.82 |
time (sec) |
N/A | 0.004 | 0.000 | 0.038 | 0.194 | 0.234 | 0.017 | 0.255 | 7.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 30 | 64 | 64 | 36 | 76 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.91 | 1.94 | 1.94 | 1.09 | 2.30 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.059 | 0.389 | 0.256 | 0.223 | 0.580 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 26 | 28 | 23 | 0 | 0 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.18 | 1.27 | 1.05 | 0.00 | 0.00 | 1.27 |
time (sec) |
N/A | 0.000 | 0.215 | 0.237 | 0.214 | 0.234 | 0.000 | 0.000 | 7.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 63 | 48 | 43 | 41 | 40 | 39 | 41 | 48 |
N.S. |
1 | 3.32 | 2.53 | 2.26 | 2.16 | 2.11 | 2.05 | 2.16 | 2.53 |
time (sec) |
N/A | 0.027 | 0.010 | 0.033 | 0.171 | 0.237 | 0.040 | 0.252 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 97 | 46 | 50 | 117 | 73 | 54 | 79 | 59 |
N.S. |
1 | 3.23 | 1.53 | 1.67 | 3.90 | 2.43 | 1.80 | 2.63 | 1.97 |
time (sec) |
N/A | 0.879 | 2.146 | 0.104 | 0.222 | 0.248 | 0.096 | 0.262 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 48 | 38 | 98 | 40 | 41 | 329 | 54 |
N.S. |
1 | 0.00 | 1.78 | 1.41 | 3.63 | 1.48 | 1.52 | 12.19 | 2.00 |
time (sec) |
N/A | 0.000 | 1.150 | 26.285 | 0.331 | 0.239 | 15.548 | 11.644 | 1.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 251 | 114 | 148 | 302 | 141 | 168 | 144 | 217 |
N.S. |
1 | 8.66 | 3.93 | 5.10 | 10.41 | 4.86 | 5.79 | 4.97 | 7.48 |
time (sec) |
N/A | 0.490 | 0.083 | 0.067 | 0.185 | 0.238 | 0.163 | 0.280 | 9.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 209 | 57 | 66 | 0 | 69 | 88 | 99 | 110 |
N.S. |
1 | 8.71 | 2.38 | 2.75 | 0.00 | 2.88 | 3.67 | 4.12 | 4.58 |
time (sec) |
N/A | 0.752 | 6.114 | 0.162 | 0.000 | 0.249 | 0.128 | 0.297 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 27 | 33 | 28 | 24 | 30 | 29 |
N.S. |
1 | 0.00 | 1.09 | 1.17 | 1.43 | 1.22 | 1.04 | 1.30 | 1.26 |
time (sec) |
N/A | 0.000 | 0.229 | 0.227 | 0.319 | 0.232 | 0.134 | 0.277 | 10.600 |
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 | 16 | 16 | 16 | 15 | 35 | 17 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.19 | 1.06 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.038 | 0.008 | 0.020 | 0.195 | 0.232 | 0.046 | 0.277 | 7.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 41 | 27 | 23 | 103 | 14 | 20 | 42 | 14 |
N.S. |
1 | 2.73 | 1.80 | 1.53 | 6.87 | 0.93 | 1.33 | 2.80 | 0.93 |
time (sec) |
N/A | 0.093 | 0.031 | 0.184 | 0.196 | 0.231 | 0.057 | 0.274 | 8.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 302 | 76 | 32 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 10.41 | 2.62 | 1.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.279 | 0.076 | 0.380 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 222 | 44 | 29 | 84 | 35 | 0 | 37 | 0 |
N.S. |
1 | 6.17 | 1.22 | 0.81 | 2.33 | 0.97 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.389 | 0.113 | 35.929 | 0.582 | 0.254 | 0.000 | 0.557 | 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 | 28 | 28 | 28 | 26 | 25 | 25 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.89 | 0.89 | 0.86 | 0.93 | 0.93 |
time (sec) |
N/A | 0.033 | 0.012 | 0.013 | 0.229 | 0.260 | 0.061 | 0.278 | 8.151 |
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 | 21 | 21 | 19 | 32 | 24 | 17 | 18 | 14 |
N.S. |
1 | 0.78 | 0.78 | 0.70 | 1.19 | 0.89 | 0.63 | 0.67 | 0.52 |
time (sec) |
N/A | 0.093 | 0.052 | 0.023 | 0.195 | 0.248 | 0.044 | 0.288 | 0.071 |
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 | 16 | 20 | 19 | 18 | 0 | 17 | 19 | 17 | 13 |
N.S. |
1 | 1.25 | 1.19 | 1.12 | 0.00 | 1.06 | 1.19 | 1.06 | 0.81 |
time (sec) |
N/A | 0.024 | 0.017 | 0.088 | 0.000 | 0.242 | 0.074 | 0.288 | 8.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 232 | 27 | 29 | 73 | 26 | 26 | 56 | 26 |
N.S. |
1 | 6.82 | 0.79 | 0.85 | 2.15 | 0.76 | 0.76 | 1.65 | 0.76 |
time (sec) |
N/A | 1.140 | 0.139 | 2.370 | 0.357 | 0.247 | 0.130 | 0.292 | 0.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 37 | 27 | 0 | 35 | 22 | 0 | 0 |
N.S. |
1 | 0.00 | 1.28 | 0.93 | 0.00 | 1.21 | 0.76 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.433 | 0.921 | 0.000 | 0.251 | 0.131 | 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 | 15 | 15 | 16 | 15 | 23 | 10 | 16 | 15 |
N.S. |
1 | 0.88 | 0.88 | 0.94 | 0.88 | 1.35 | 0.59 | 0.94 | 0.88 |
time (sec) |
N/A | 0.041 | 0.011 | 0.024 | 0.183 | 0.249 | 0.047 | 0.283 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 50 | 51 | 25 | 55 | 44 | 54 | 57 | 51 |
N.S. |
1 | 2.63 | 2.68 | 1.32 | 2.89 | 2.32 | 2.84 | 3.00 | 2.68 |
time (sec) |
N/A | 0.038 | 0.033 | 0.045 | 0.185 | 0.255 | 0.885 | 0.276 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 25 | 44 | 1065 | 263 | 357 | 428 | 428 |
N.S. |
1 | 1.16 | 1.00 | 1.76 | 42.60 | 10.52 | 14.28 | 17.12 | 17.12 |
time (sec) |
N/A | 1.231 | 0.116 | 0.354 | 0.216 | 0.265 | 0.561 | 0.290 | 13.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 20 | 20 | 19 | 17 | 172 | 31 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 0.91 | 0.86 | 0.77 | 7.82 | 1.41 |
time (sec) |
N/A | 0.000 | 0.105 | 1.331 | 0.320 | 0.257 | 0.084 | 0.324 | 9.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | F | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 79 | 82 | 93 | 87 | 205 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.55 | 2.65 | 3.00 | 2.81 | 6.61 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.183 | 0.365 | 0.284 | 0.303 | 3.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 36 | 33 | 32 | 32 | 29 | 0 | 32 |
N.S. |
1 | 0.00 | 1.50 | 1.38 | 1.33 | 1.33 | 1.21 | 0.00 | 1.33 |
time (sec) |
N/A | 0.000 | 0.362 | 0.072 | 0.208 | 0.254 | 0.205 | 0.000 | 0.166 |
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 | 22 | 22 | 22 | 19 | 18 | 18 | 17 | 36 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.82 | 0.77 | 1.64 | 0.82 |
time (sec) |
N/A | 0.078 | 0.050 | 0.042 | 0.177 | 0.267 | 0.079 | 0.266 | 8.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 76 | 28 | 28 | 37 | 33 | 31 | 37 | 40 |
N.S. |
1 | 3.30 | 1.22 | 1.22 | 1.61 | 1.43 | 1.35 | 1.61 | 1.74 |
time (sec) |
N/A | 0.477 | 0.388 | 0.153 | 0.312 | 0.252 | 0.140 | 0.415 | 8.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 17 | 36 | 76 | 20 | 136 | 50 |
N.S. |
1 | 0.00 | 0.95 | 0.77 | 1.64 | 3.45 | 0.91 | 6.18 | 2.27 |
time (sec) |
N/A | 0.000 | 6.236 | 0.338 | 0.756 | 0.267 | 0.237 | 2.032 | 9.404 |
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 | 7 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 |
N.S. |
1 | 0.43 | 0.43 | 0.57 | 0.43 | 0.43 | 0.29 | 0.43 | 0.43 |
time (sec) |
N/A | 0.001 | 0.000 | 0.011 | 0.205 | 0.249 | 0.019 | 0.280 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 32 | 31 | 37 | 31 | 159 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.15 | 1.37 | 1.15 | 5.89 | 0.00 |
time (sec) |
N/A | 0.000 | 0.128 | 155.720 | 0.249 | 0.252 | 0.175 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 16 | 0 | 15 | 10 | 15 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.00 | 0.88 | 0.59 | 0.88 | 0.88 |
time (sec) |
N/A | 0.000 | 0.540 | 0.120 | 0.000 | 0.266 | 0.118 | 0.286 | 8.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 68 | 26 | 39 | 0 | 37 | 41 | 61 | 23 |
N.S. |
1 | 2.96 | 1.13 | 1.70 | 0.00 | 1.61 | 1.78 | 2.65 | 1.00 |
time (sec) |
N/A | 0.591 | 1.140 | 0.076 | 0.000 | 0.269 | 0.101 | 0.291 | 8.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 525 | 21 | 22 | 19 | 21 | 19 | 24 | 21 |
N.S. |
1 | 22.83 | 0.91 | 0.96 | 0.83 | 0.91 | 0.83 | 1.04 | 0.91 |
time (sec) |
N/A | 2.170 | 0.463 | 0.103 | 0.454 | 0.249 | 0.100 | 0.288 | 8.144 |
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 | 19 | 18 | 13 | 13 | 17 | 17 | 12 | 17 | 16 |
N.S. |
1 | 0.95 | 0.68 | 0.68 | 0.89 | 0.89 | 0.63 | 0.89 | 0.84 |
time (sec) |
N/A | 0.007 | 0.002 | 0.011 | 0.205 | 0.236 | 0.024 | 0.273 | 0.317 |
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 | 17 | 17 | 16 | 15 | 15 | 14 | 17 | 15 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.62 | 0.62 | 0.58 | 0.71 | 0.62 |
time (sec) |
N/A | 0.009 | 0.003 | 0.027 | 0.200 | 0.261 | 0.039 | 0.263 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 20 | 20 | 19 | 23 | 17 | 23 | 19 |
N.S. |
1 | 0.00 | 0.77 | 0.77 | 0.73 | 0.88 | 0.65 | 0.88 | 0.73 |
time (sec) |
N/A | 0.000 | 0.122 | 0.046 | 0.259 | 0.257 | 0.084 | 0.296 | 7.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 11 | 32 | 10 | 8 | 27 | 10 |
N.S. |
1 | 1.00 | 0.83 | 0.92 | 2.67 | 0.83 | 0.67 | 2.25 | 0.83 |
time (sec) |
N/A | 0.021 | 0.030 | 0.020 | 0.223 | 0.260 | 0.046 | 0.278 | 7.500 |
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 | 18 | 10 | 21 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 0.56 | 1.17 | 0.56 | 0.50 | 0.50 | 0.39 | 0.50 | 0.50 |
time (sec) |
N/A | 0.009 | 0.017 | 0.020 | 0.186 | 0.248 | 0.032 | 0.268 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 56 | 25 | 46 | 96 | 42 | 48 | 46 | 22 |
N.S. |
1 | 2.43 | 1.09 | 2.00 | 4.17 | 1.83 | 2.09 | 2.00 | 0.96 |
time (sec) |
N/A | 0.344 | 1.538 | 0.041 | 0.307 | 0.256 | 0.085 | 0.288 | 7.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 42 | 0 | 41 | 0 | 0 | 23 |
N.S. |
1 | 0.00 | 1.00 | 1.62 | 0.00 | 1.58 | 0.00 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.197 | 35.034 | 0.000 | 0.261 | 0.000 | 0.000 | 7.651 |
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 | 16 | 13 | 13 | 14 | 38 | 19 | 12 | 13 | 13 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 2.38 | 1.19 | 0.75 | 0.81 | 0.81 |
time (sec) |
N/A | 0.061 | 0.009 | 0.025 | 0.209 | 0.245 | 0.050 | 0.271 | 7.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 427 | 48 | 65 | 43 | 56 | 50 | 256790 |
N.S. |
1 | 0.00 | 12.94 | 1.45 | 1.97 | 1.30 | 1.70 | 1.52 | 7781.52 |
time (sec) |
N/A | 0.000 | 0.763 | 0.117 | 0.188 | 0.242 | 1.956 | 0.306 | 41.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 317 | 37 | 37 | 0 | 39 | 32 |
N.S. |
1 | 0.00 | 1.00 | 10.23 | 1.19 | 1.19 | 0.00 | 1.26 | 1.03 |
time (sec) |
N/A | 0.000 | 0.182 | 0.115 | 0.456 | 0.275 | 0.000 | 0.428 | 8.948 |
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 | 11 | 11 | 11 | 11 | 10 | 10 | 7 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.64 | 0.91 | 0.91 |
time (sec) |
N/A | 0.020 | 0.020 | 0.022 | 0.184 | 0.249 | 0.035 | 0.273 | 0.057 |
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 | 27 | 16 | 14 | 25 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.04 | 0.62 | 0.54 | 0.96 | 0.50 | 0.54 | 0.50 | 0.50 |
time (sec) |
N/A | 0.018 | 0.036 | 0.027 | 0.186 | 0.241 | 0.038 | 0.281 | 0.047 |