Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F(-1) | C | A | B | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 141 | 18 | 0 | 114 | 21 | 128 | 0 | 21 | 17 |
N.S. |
1 | 7.83 | 1.00 | 0.00 | 6.33 | 1.17 | 7.11 | 0.00 | 1.17 | 0.94 |
time (sec) |
N/A | 0.585 | 0.085 | 0.000 | 0.150 | 0.068 | 2.417 | 0.000 | 0.256 | 0.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 23 | 104 | 22 | 19 | 0 | 30 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 4.33 | 0.92 | 0.79 | 0.00 | 1.25 | 0.96 |
time (sec) |
N/A | 0.000 | 0.067 | 38.971 | 0.145 | 0.067 | 0.975 | 0.000 | 0.236 | 1.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 7 | 9 | 7 | 6 | 8 | 5 | 6 | 7 | 6 |
N.S. |
1 | 0.39 | 0.50 | 0.39 | 0.33 | 0.44 | 0.28 | 0.33 | 0.39 | 0.33 |
time (sec) |
N/A | 0.140 | 0.000 | 0.013 | 0.036 | 0.056 | 0.017 | 0.107 | 0.217 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 36 | 43 | 36 | 40 | 39 | 41 | 90 | 42 |
N.S. |
1 | 0.00 | 1.24 | 1.48 | 1.24 | 1.38 | 1.34 | 1.41 | 3.10 | 1.45 |
time (sec) |
N/A | 0.000 | 0.027 | 0.458 | 0.030 | 0.067 | 1.648 | 0.118 | 0.220 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 56 | 49 | 62 | 53 | 54 | 49 | 207 | 0 |
N.S. |
1 | 0.00 | 1.87 | 1.63 | 2.07 | 1.77 | 1.80 | 1.63 | 6.90 | 0.00 |
time (sec) |
N/A | 0.000 | 0.111 | 0.411 | 0.084 | 0.083 | 0.411 | 3.822 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 35 | 41 | 33 | 32 | 32 | 32 | 32 | 34 | 31 |
N.S. |
1 | 1.75 | 2.05 | 1.65 | 1.60 | 1.60 | 1.60 | 1.60 | 1.70 | 1.55 |
time (sec) |
N/A | 0.218 | 0.004 | 0.098 | 0.068 | 0.058 | 0.065 | 0.123 | 0.217 | 0.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 24 | 14 | 16 | 27 | 15 | 17 | 15 | 13 | 13 |
N.S. |
1 | 0.92 | 0.54 | 0.62 | 1.04 | 0.58 | 0.65 | 0.58 | 0.50 | 0.50 |
time (sec) |
N/A | 0.172 | 0.006 | 0.062 | 0.034 | 0.068 | 0.059 | 0.106 | 0.230 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 84 | 79 | 26 | 130 | 58 | 66 | 75 | 79 | 67 |
N.S. |
1 | 3.36 | 3.16 | 1.04 | 5.20 | 2.32 | 2.64 | 3.00 | 3.16 | 2.68 |
time (sec) |
N/A | 0.399 | 0.034 | 12.710 | 0.048 | 0.080 | 0.141 | 0.114 | 0.242 | 0.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 70 | 47 | 55 | 0 | 45 | 49 | 70 | 80 | 55 |
N.S. |
1 | 2.12 | 1.42 | 1.67 | 0.00 | 1.36 | 1.48 | 2.12 | 2.42 | 1.67 |
time (sec) |
N/A | 0.728 | 2.229 | 0.326 | 0.000 | 0.075 | 0.136 | 0.120 | 0.244 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 27 | 46 | 46 | 20 | 46 | 55 | 26 |
N.S. |
1 | 0.00 | 0.90 | 0.93 | 1.59 | 1.59 | 0.69 | 1.59 | 1.90 | 0.90 |
time (sec) |
N/A | 0.000 | 3.609 | 1.122 | 0.080 | 0.073 | 0.074 | 0.136 | 0.261 | 0.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 9 | 10 | 9 | 9 | 7 | 9 | 14 | 9 |
N.S. |
1 | 0.00 | 0.39 | 0.43 | 0.39 | 0.39 | 0.30 | 0.39 | 0.61 | 0.39 |
time (sec) |
N/A | 0.000 | 0.019 | 0.145 | 0.063 | 0.059 | 0.049 | 0.113 | 0.245 | 0.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 26 | 26 | 14 | 13 | 12 | 14 | 13 | 14 | 12 |
N.S. |
1 | 2.00 | 2.00 | 1.08 | 1.00 | 0.92 | 1.08 | 1.00 | 1.08 | 0.92 |
time (sec) |
N/A | 0.438 | 0.021 | 0.654 | 0.083 | 0.069 | 0.131 | 0.113 | 0.251 | 0.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 50 | 36 | 50 | 49 | 46 | 54 | 57 | 99 |
N.S. |
1 | 0.00 | 1.79 | 1.29 | 1.79 | 1.75 | 1.64 | 1.93 | 2.04 | 3.54 |
time (sec) |
N/A | 0.000 | 0.067 | 0.092 | 0.088 | 0.072 | 0.225 | 0.140 | 0.241 | 0.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 64 | 32 | 35 | 44 | 33 | 44 | 33 | 35 | 41 |
N.S. |
1 | 1.83 | 0.91 | 1.00 | 1.26 | 0.94 | 1.26 | 0.94 | 1.00 | 1.17 |
time (sec) |
N/A | 0.763 | 0.096 | 0.249 | 0.079 | 0.067 | 0.471 | 0.115 | 0.218 | 0.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 28 | 26 | 29 | 29 | 29 | 31 | 29 |
N.S. |
1 | 0.00 | 1.14 | 1.27 | 1.18 | 1.32 | 1.32 | 1.32 | 1.41 | 1.32 |
time (sec) |
N/A | 0.000 | 0.040 | 3.198 | 0.104 | 0.071 | 0.242 | 12.818 | 0.222 | 1.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 34 | 34 | 61 | 37 | 70 | 70 | 71 | 78 | 71 |
N.S. |
1 | 1.36 | 1.36 | 2.44 | 1.48 | 2.80 | 2.80 | 2.84 | 3.12 | 2.84 |
time (sec) |
N/A | 1.333 | 5.555 | 0.783 | 0.197 | 0.073 | 0.380 | 0.542 | 0.245 | 1.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 20 | 26 | 20 | 20 | 0 | 32 | 26 | 0 |
N.S. |
1 | 0.00 | 0.83 | 1.08 | 0.83 | 0.83 | 0.00 | 1.33 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.258 | 0.204 | 0.084 | 0.071 | 0.000 | 0.123 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 24 | 25 | 43 | 26 | 20 | 24 | 26 | 21 |
N.S. |
1 | 0.89 | 0.89 | 0.93 | 1.59 | 0.96 | 0.74 | 0.89 | 0.96 | 0.78 |
time (sec) |
N/A | 0.221 | 0.008 | 0.218 | 0.025 | 0.063 | 0.072 | 0.115 | 0.219 | 0.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 19 | 17 | 13 | 14 | 14 | 24 | 14 | 15 | 14 |
N.S. |
1 | 1.06 | 0.94 | 0.72 | 0.78 | 0.78 | 1.33 | 0.78 | 0.83 | 0.78 |
time (sec) |
N/A | 0.156 | 0.004 | 0.077 | 0.046 | 0.059 | 0.074 | 0.106 | 0.276 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 18 | 19 | 17 | 17 | 19 | 17 | 19 | 16 |
N.S. |
1 | 1.00 | 1.20 | 1.27 | 1.13 | 1.13 | 1.27 | 1.13 | 1.27 | 1.07 |
time (sec) |
N/A | 0.153 | 0.004 | 0.057 | 0.035 | 0.063 | 0.046 | 0.115 | 0.211 | 0.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 118 | 39 | 46 | 73 | 45 | 66 | 0 | 84 | 37 |
N.S. |
1 | 4.07 | 1.34 | 1.59 | 2.52 | 1.55 | 2.28 | 0.00 | 2.90 | 1.28 |
time (sec) |
N/A | 4.156 | 0.076 | 1.945 | 0.127 | 0.077 | 5.245 | 0.000 | 0.306 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 46 | 24 | 23 | 73 | 25 | 22 | 43 | 22 | 22 |
N.S. |
1 | 2.19 | 1.14 | 1.10 | 3.48 | 1.19 | 1.05 | 2.05 | 1.05 | 1.05 |
time (sec) |
N/A | 0.527 | 0.078 | 0.169 | 0.087 | 0.060 | 0.073 | 0.113 | 0.210 | 0.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 34 | 37 | 38 | 37 | 29 | 37 | 60 | 35 |
N.S. |
1 | 0.00 | 1.06 | 1.16 | 1.19 | 1.16 | 0.91 | 1.16 | 1.88 | 1.09 |
time (sec) |
N/A | 0.000 | 0.048 | 0.769 | 0.187 | 0.062 | 0.140 | 0.236 | 0.245 | 0.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 25 | 24 | 18 | 68 | 17 | 14 | 17 | 21 | 19 |
N.S. |
1 | 1.25 | 1.20 | 0.90 | 3.40 | 0.85 | 0.70 | 0.85 | 1.05 | 0.95 |
time (sec) |
N/A | 0.260 | 0.037 | 0.075 | 0.032 | 0.064 | 0.054 | 0.106 | 0.223 | 0.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 35 | 26 | 34 | 44 | 29 | 34 | 26 | 40 | 15 |
N.S. |
1 | 1.59 | 1.18 | 1.55 | 2.00 | 1.32 | 1.55 | 1.18 | 1.82 | 0.68 |
time (sec) |
N/A | 0.216 | 0.028 | 0.131 | 0.031 | 0.063 | 0.140 | 0.113 | 0.229 | 0.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 19 | 19 | 14 | 20 | 14 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.27 | 1.27 | 0.93 | 1.33 | 0.93 | 0.73 |
time (sec) |
N/A | 0.141 | 0.001 | 0.057 | 0.028 | 0.060 | 0.027 | 0.111 | 0.237 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 47 | 47 | 46 | 61 | 44 | 51 | 45 | 47 | 51 |
N.S. |
1 | 1.52 | 1.52 | 1.48 | 1.97 | 1.42 | 1.65 | 1.45 | 1.52 | 1.65 |
time (sec) |
N/A | 0.271 | 0.021 | 0.467 | 0.026 | 0.066 | 0.139 | 0.111 | 0.217 | 0.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 36 | 39 | 32 | 42 | 37 | 0 | 318 | 133 |
N.S. |
1 | 0.00 | 1.33 | 1.44 | 1.19 | 1.56 | 1.37 | 0.00 | 11.78 | 4.93 |
time (sec) |
N/A | 0.000 | 1.718 | 1.791 | 0.229 | 0.070 | 0.666 | 0.000 | 200.022 | 0.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 21 | 17 | 16 | 15 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 0.88 | 0.71 | 0.67 | 0.62 | 0.62 | 0.62 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.622 | 0.053 | 0.079 | 0.083 | 0.066 | 0.098 | 0.105 | 0.211 | 0.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 19 | 18 | 24 | 19 | 18 | 24 | 18 |
N.S. |
1 | 0.90 | 0.90 | 0.95 | 0.90 | 1.20 | 0.95 | 0.90 | 1.20 | 0.90 |
time (sec) |
N/A | 0.596 | 0.007 | 0.106 | 0.022 | 0.067 | 0.061 | 0.107 | 0.229 | 0.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 50 | 44 | 24 | 41 | 32 | 31 | 166 | 68 | 44 |
N.S. |
1 | 1.79 | 1.57 | 0.86 | 1.46 | 1.14 | 1.11 | 5.93 | 2.43 | 1.57 |
time (sec) |
N/A | 0.681 | 1.201 | 0.528 | 0.029 | 0.073 | 0.111 | 0.152 | 0.211 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 29 | 38 | 36 | 37 | 36 | 44 | 41 | 37 |
N.S. |
1 | 1.11 | 1.04 | 1.36 | 1.29 | 1.32 | 1.29 | 1.57 | 1.46 | 1.32 |
time (sec) |
N/A | 2.932 | 0.063 | 1.170 | 0.167 | 0.073 | 0.307 | 0.175 | 0.215 | 1.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 58 | 28 | 35 | 417 | 35 | 31 | 32 | 39 | 35 |
N.S. |
1 | 2.32 | 1.12 | 1.40 | 16.68 | 1.40 | 1.24 | 1.28 | 1.56 | 1.40 |
time (sec) |
N/A | 3.097 | 0.193 | 1.735 | 0.043 | 0.068 | 0.085 | 0.115 | 0.225 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 16 | 14 | 15 | 15 | 15 | 15 | 119 | 15 |
N.S. |
1 | 0.95 | 0.84 | 0.74 | 0.79 | 0.79 | 0.79 | 0.79 | 6.26 | 0.79 |
time (sec) |
N/A | 0.376 | 0.332 | 0.139 | 0.164 | 0.068 | 0.128 | 0.125 | 0.238 | 0.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 28 | 34 | 53 | 134 | 51 | 22 | 147 | 55 |
N.S. |
1 | 2.04 | 1.12 | 1.36 | 2.12 | 5.36 | 2.04 | 0.88 | 5.88 | 2.20 |
time (sec) |
N/A | 0.872 | 0.017 | 0.084 | 0.033 | 0.069 | 0.115 | 0.116 | 0.229 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 36 | 19 | 35 | 27 | 33 | 34 | 34 | 61 | 32 |
N.S. |
1 | 2.00 | 1.06 | 1.94 | 1.50 | 1.83 | 1.89 | 1.89 | 3.39 | 1.78 |
time (sec) |
N/A | 0.614 | 0.087 | 0.293 | 0.469 | 0.063 | 0.133 | 0.128 | 41.185 | 0.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 43 | 165 | 29 | 23 | 24 | 29 | 28 | 23 |
N.S. |
1 | 0.00 | 1.79 | 6.88 | 1.21 | 0.96 | 1.00 | 1.21 | 1.17 | 0.96 |
time (sec) |
N/A | 0.000 | 0.518 | 0.038 | 0.095 | 0.073 | 0.506 | 0.218 | 0.234 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 33 | 37 | 62 | 55 | 34 | 39 | 79 | 37 |
N.S. |
1 | 0.00 | 1.14 | 1.28 | 2.14 | 1.90 | 1.17 | 1.34 | 2.72 | 1.28 |
time (sec) |
N/A | 0.000 | 0.039 | 1.722 | 0.087 | 0.064 | 0.089 | 0.315 | 0.206 | 0.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 14 | 14 | 13 | 12 | 12 | 10 | 14 | 12 | 12 |
N.S. |
1 | 0.54 | 0.54 | 0.50 | 0.46 | 0.46 | 0.38 | 0.54 | 0.46 | 0.46 |
time (sec) |
N/A | 0.190 | 0.004 | 0.053 | 0.044 | 0.060 | 0.061 | 0.112 | 0.237 | 0.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 42 | 37 | 43 | 447 | 47 | 46 | 0 |
N.S. |
1 | 0.00 | 1.13 | 1.35 | 1.19 | 1.39 | 14.42 | 1.52 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.088 | 1.341 | 0.157 | 0.087 | 0.697 | 0.188 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 26 | 56 | 24 | 0 | 30 | 63 | 178 |
N.S. |
1 | 0.00 | 0.96 | 1.13 | 2.43 | 1.04 | 0.00 | 1.30 | 2.74 | 7.74 |
time (sec) |
N/A | 0.000 | 5.066 | 1.030 | 0.153 | 0.068 | 0.000 | 0.246 | 0.237 | 0.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 34 | 25 | 40 | 34 | 31 | 0 | 218 | 56 |
N.S. |
1 | 0.00 | 1.21 | 0.89 | 1.43 | 1.21 | 1.11 | 0.00 | 7.79 | 2.00 |
time (sec) |
N/A | 0.000 | 0.177 | 27.838 | 0.320 | 0.070 | 0.838 | 0.000 | 200.031 | 1.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 38 | 30 | 53 | 31 | 31 | 31 | 32 | 31 |
N.S. |
1 | 0.00 | 1.19 | 0.94 | 1.66 | 0.97 | 0.97 | 0.97 | 1.00 | 0.97 |
time (sec) |
N/A | 0.000 | 10.271 | 0.142 | 0.077 | 0.070 | 0.101 | 0.120 | 0.328 | 0.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 38 | 32 | 29 | 59 | 28 | 32 | 30 | 33 | 30 |
N.S. |
1 | 2.11 | 1.78 | 1.61 | 3.28 | 1.56 | 1.78 | 1.67 | 1.83 | 1.67 |
time (sec) |
N/A | 0.267 | 0.024 | 0.692 | 0.060 | 0.068 | 0.100 | 0.116 | 0.241 | 0.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 |
time (sec) |
N/A | 0.125 | 0.000 | 0.015 | 0.031 | 0.065 | 0.019 | 0.107 | 0.261 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 24 | 22 | 21 | 21 | 22 | 23 | 22 | 21 |
N.S. |
1 | 0.89 | 0.89 | 0.81 | 0.78 | 0.78 | 0.81 | 0.85 | 0.81 | 0.78 |
time (sec) |
N/A | 1.052 | 0.325 | 157.293 | 0.160 | 0.068 | 0.482 | 0.150 | 0.371 | 0.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 55 | 51 | 40 | 48 | 38 | 48 | 39 | 26 | 14 |
N.S. |
1 | 2.50 | 2.32 | 1.82 | 2.18 | 1.73 | 2.18 | 1.77 | 1.18 | 0.64 |
time (sec) |
N/A | 0.238 | 0.010 | 0.243 | 0.032 | 0.072 | 0.072 | 0.108 | 0.235 | 0.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 9 | 8 | 9 | 8 | 8 | 8 | 8 | 10 | 8 |
N.S. |
1 | 0.47 | 0.42 | 0.47 | 0.42 | 0.42 | 0.42 | 0.42 | 0.53 | 0.42 |
time (sec) |
N/A | 0.150 | 0.004 | 0.027 | 0.037 | 0.062 | 0.035 | 0.113 | 0.246 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 23 | 22 | 24 | 34 | 15 | 24 | 35 | 21 |
N.S. |
1 | 0.00 | 0.74 | 0.71 | 0.77 | 1.10 | 0.48 | 0.77 | 1.13 | 0.68 |
time (sec) |
N/A | 0.000 | 0.578 | 0.140 | 0.176 | 0.072 | 0.100 | 0.115 | 0.219 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 38 | 22 | 0 | 38 | 19 | 38 | 38 | 23 |
N.S. |
1 | 1.00 | 1.36 | 0.79 | 0.00 | 1.36 | 0.68 | 1.36 | 1.36 | 0.82 |
time (sec) |
N/A | 0.451 | 0.129 | 0.454 | 0.000 | 0.074 | 0.067 | 0.113 | 0.252 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 15 | 15 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 1.06 | 0.88 |
time (sec) |
N/A | 0.273 | 0.013 | 0.241 | 0.078 | 0.066 | 0.091 | 0.116 | 0.263 | 0.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 21 | 19 | 18 | 25 | 14 | 18 | 24 | 18 |
N.S. |
1 | 1.05 | 1.00 | 0.90 | 0.86 | 1.19 | 0.67 | 0.86 | 1.14 | 0.86 |
time (sec) |
N/A | 0.199 | 0.006 | 0.102 | 0.024 | 0.061 | 0.044 | 0.114 | 0.232 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 10 | 10 | 15 | 15 | 12 | 9 | 9 | 9 |
N.S. |
1 | 0.00 | 0.62 | 0.62 | 0.94 | 0.94 | 0.75 | 0.56 | 0.56 | 0.56 |
time (sec) |
N/A | 0.000 | 0.031 | 0.057 | 0.057 | 0.067 | 0.071 | 0.117 | 0.237 | 0.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 41 | 48 | 37 | 37 | 31 | 37 | 57 | 34 |
N.S. |
1 | 0.00 | 1.95 | 2.29 | 1.76 | 1.76 | 1.48 | 1.76 | 2.71 | 1.62 |
time (sec) |
N/A | 0.000 | 0.145 | 0.741 | 0.080 | 0.071 | 0.085 | 0.149 | 0.229 | 0.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 62 | 20 | 18 | 17 | 18 | 19 | 0 | 26 | 20 |
N.S. |
1 | 3.10 | 1.00 | 0.90 | 0.85 | 0.90 | 0.95 | 0.00 | 1.30 | 1.00 |
time (sec) |
N/A | 0.499 | 0.090 | 0.303 | 0.113 | 0.070 | 0.117 | 0.000 | 0.267 | 0.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 0 | 25 | 25 | 22 | 24 | 25 | 170 |
N.S. |
1 | 0.00 | 0.92 | 0.00 | 1.04 | 1.04 | 0.92 | 1.00 | 1.04 | 7.08 |
time (sec) |
N/A | 0.000 | 0.053 | 0.000 | 0.081 | 0.072 | 0.107 | 0.346 | 0.219 | 1.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 15 | 16 | 14 | 17 | 14 | 12 | 17 | 12 | 12 |
N.S. |
1 | 1.07 | 1.14 | 1.00 | 1.21 | 1.00 | 0.86 | 1.21 | 0.86 | 0.86 |
time (sec) |
N/A | 0.146 | 0.000 | 0.033 | 0.024 | 0.061 | 0.019 | 0.111 | 0.234 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 24 | 22 | 24 | 48 | 31 | 247 | 35 | 54 |
N.S. |
1 | 0.00 | 0.73 | 0.67 | 0.73 | 1.45 | 0.94 | 7.48 | 1.06 | 1.64 |
time (sec) |
N/A | 0.000 | 0.241 | 3.675 | 0.085 | 0.067 | 0.097 | 0.149 | 0.444 | 0.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 36 | 22 | 108 | 21 | 22 | 19 | 55 | 21 |
N.S. |
1 | 1.71 | 1.71 | 1.05 | 5.14 | 1.00 | 1.05 | 0.90 | 2.62 | 1.00 |
time (sec) |
N/A | 0.299 | 0.024 | 0.250 | 0.029 | 0.066 | 0.068 | 0.121 | 0.206 | 0.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 33 | 37 | 57 | 53 | 29 | 33 | 66 | 57 |
N.S. |
1 | 0.00 | 0.97 | 1.09 | 1.68 | 1.56 | 0.85 | 0.97 | 1.94 | 1.68 |
time (sec) |
N/A | 0.000 | 0.063 | 30.595 | 0.169 | 0.074 | 0.118 | 0.158 | 0.237 | 1.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 79 | 67 | 27 | 33 | 34 | 32 | 33 | 24 | 33 |
N.S. |
1 | 3.04 | 2.58 | 1.04 | 1.27 | 1.31 | 1.23 | 1.27 | 0.92 | 1.27 |
time (sec) |
N/A | 0.449 | 0.044 | 0.188 | 0.029 | 0.070 | 0.361 | 0.113 | 0.260 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 37 | 36 | 28 | 35 | 34 | 32 | 35 | 32 | 34 |
N.S. |
1 | 1.48 | 1.44 | 1.12 | 1.40 | 1.36 | 1.28 | 1.40 | 1.28 | 1.36 |
time (sec) |
N/A | 0.232 | 0.012 | 0.197 | 0.033 | 0.071 | 0.115 | 0.116 | 0.245 | 0.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 14 | 14 | 15 | 14 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 1.00 | 0.88 |
time (sec) |
N/A | 0.338 | 0.028 | 0.214 | 0.026 | 0.069 | 0.154 | 0.122 | 0.249 | 0.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 19 | 19 | 18 | 21 | 23 | 17 | 17 | 23 | 17 |
N.S. |
1 | 0.95 | 0.95 | 0.90 | 1.05 | 1.15 | 0.85 | 0.85 | 1.15 | 0.85 |
time (sec) |
N/A | 0.672 | 0.072 | 0.168 | 0.079 | 0.072 | 0.119 | 0.124 | 0.227 | 0.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 14 | 15 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.042 | 0.072 | 0.060 | 0.063 | 0.076 | 0.109 | 0.245 | 0.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 63 | 78 | 107 | 107 | 82 | 110 | 134 | 314 |
N.S. |
1 | 0.00 | 2.74 | 3.39 | 4.65 | 4.65 | 3.57 | 4.78 | 5.83 | 13.65 |
time (sec) |
N/A | 0.000 | 0.053 | 15.211 | 0.071 | 0.078 | 0.144 | 0.129 | 0.234 | 0.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 13 | 13 | 14 | 11 | 11 | 12 | 11 | 11 | 11 |
N.S. |
1 | 0.87 | 0.87 | 0.93 | 0.73 | 0.73 | 0.80 | 0.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.144 | 0.001 | 0.027 | 0.025 | 0.058 | 0.019 | 0.104 | 0.238 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 37 | 18 | 22 | 19 | 14 | 19 | 26 | 19 |
N.S. |
1 | 0.00 | 1.76 | 0.86 | 1.05 | 0.90 | 0.67 | 0.90 | 1.24 | 0.90 |
time (sec) |
N/A | 0.000 | 2.640 | 0.200 | 0.082 | 0.068 | 0.075 | 0.130 | 0.240 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 23 | 24 | 24 | 27 | 22 | 23 | 27 | 24 |
N.S. |
1 | 1.14 | 1.10 | 1.14 | 1.14 | 1.29 | 1.05 | 1.10 | 1.29 | 1.14 |
time (sec) |
N/A | 0.334 | 0.004 | 0.060 | 0.027 | 0.060 | 0.040 | 0.116 | 0.232 | 0.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 14 | 19 | 14 | 13 | 13 | 10 | 14 | 14 | 13 |
N.S. |
1 | 0.61 | 0.83 | 0.61 | 0.57 | 0.57 | 0.43 | 0.61 | 0.61 | 0.57 |
time (sec) |
N/A | 0.292 | 0.006 | 0.099 | 0.031 | 0.060 | 0.047 | 0.110 | 0.243 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 39 | 119 | 586 | 178 | 170 | 0 | 429 | 83 |
N.S. |
1 | 0.00 | 1.22 | 3.72 | 18.31 | 5.56 | 5.31 | 0.00 | 13.41 | 2.59 |
time (sec) |
N/A | 0.000 | 0.207 | 0.065 | 0.166 | 0.086 | 0.489 | 0.000 | 0.237 | 1.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 27 | 43 | 26 | 26 | 49 | 29 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.54 | 0.93 | 0.93 | 1.75 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.035 | 3.226 | 0.156 | 0.070 | 0.138 | 0.144 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 12 | 8 | 7 | 6 | 6 | 7 | 7 | 6 | 6 |
N.S. |
1 | 0.92 | 0.62 | 0.54 | 0.46 | 0.46 | 0.54 | 0.54 | 0.46 | 0.46 |
time (sec) |
N/A | 0.150 | 0.001 | 0.022 | 0.022 | 0.058 | 0.032 | 0.114 | 0.221 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 22 | 22 | 25 | 22 | 26 | 20 | 24 | 26 | 19 |
N.S. |
1 | 0.85 | 0.85 | 0.96 | 0.85 | 1.00 | 0.77 | 0.92 | 1.00 | 0.73 |
time (sec) |
N/A | 0.460 | 0.078 | 1.369 | 0.159 | 0.072 | 0.079 | 0.123 | 0.226 | 1.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-2) | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 52 | 30 | 19 | 123 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 2.00 | 1.15 | 0.73 | 4.73 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.580 | 0.277 | 1.526 | 0.205 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 40 | 23 | 25 | 678 | 37 | 24 | 40 | 62 | 0 |
N.S. |
1 | 1.48 | 0.85 | 0.93 | 25.11 | 1.37 | 0.89 | 1.48 | 2.30 | 0.00 |
time (sec) |
N/A | 1.059 | 0.105 | 0.425 | 0.045 | 0.081 | 0.120 | 0.125 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 22 | 21 | 21 | 20 | 21 | 38 | 21 |
N.S. |
1 | 0.00 | 0.79 | 0.79 | 0.75 | 0.75 | 0.71 | 0.75 | 1.36 | 0.75 |
time (sec) |
N/A | 0.000 | 3.156 | 0.200 | 0.070 | 0.076 | 0.108 | 0.131 | 0.679 | 1.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 39 | 36 | 35 | 35 | 32 | 35 | 41 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.16 | 1.13 | 1.13 | 1.03 | 1.13 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 2.898 | 0.241 | 0.110 | 0.069 | 0.112 | 0.221 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 28 | 16 | 35 | 29 | 16 | 20 | 17 |
N.S. |
1 | 0.00 | 1.00 | 1.40 | 0.80 | 1.75 | 1.45 | 0.80 | 1.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.111 | 20.200 | 0.313 | 0.071 | 0.117 | 0.120 | 0.250 | 1.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 34 | 31 | 33 | 41 | 31 | 32 | 33 | 36 | 27 |
N.S. |
1 | 0.89 | 0.82 | 0.87 | 1.08 | 0.82 | 0.84 | 0.87 | 0.95 | 0.71 |
time (sec) |
N/A | 0.297 | 0.039 | 0.282 | 0.062 | 0.070 | 0.095 | 0.113 | 0.239 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 35 | 23 | 31 | 0 | 29 | 19 | 43 | 24 | 21 |
N.S. |
1 | 1.40 | 0.92 | 1.24 | 0.00 | 1.16 | 0.76 | 1.72 | 0.96 | 0.84 |
time (sec) |
N/A | 0.424 | 0.055 | 0.269 | 0.000 | 0.073 | 0.100 | 0.117 | 0.260 | 1.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 8 | 9 | 9 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.89 | 1.00 | 1.00 | 1.11 |
time (sec) |
N/A | 0.145 | 0.002 | 0.095 | 0.031 | 0.065 | 0.045 | 0.109 | 0.224 | 1.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 17 | 15 | 16 | 14 | 12 | 16 | 18 | 14 |
N.S. |
1 | 0.90 | 0.81 | 0.71 | 0.76 | 0.67 | 0.57 | 0.76 | 0.86 | 0.67 |
time (sec) |
N/A | 0.147 | 0.000 | 0.031 | 0.028 | 0.059 | 0.016 | 0.108 | 0.233 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 31 | 42 | 42 | 49 | 57 | 57 | 22 |
N.S. |
1 | 0.00 | 0.79 | 1.11 | 1.50 | 1.50 | 1.75 | 2.04 | 2.04 | 0.79 |
time (sec) |
N/A | 0.000 | 0.345 | 18.185 | 0.108 | 0.077 | 0.138 | 0.269 | 0.235 | 1.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 22 | 23 | 22 | 21 | 21 | 17 | 28 | 23 | 21 |
N.S. |
1 | 0.73 | 0.77 | 0.73 | 0.70 | 0.70 | 0.57 | 0.93 | 0.77 | 0.70 |
time (sec) |
N/A | 0.195 | 0.007 | 0.130 | 0.025 | 0.064 | 0.053 | 0.119 | 0.242 | 1.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 12 | 27 | 11 | 12 | 27 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.93 | 0.79 | 0.86 | 1.93 | 0.86 | 0.79 |
time (sec) |
N/A | 0.157 | 0.003 | 0.072 | 0.027 | 0.062 | 0.049 | 0.112 | 0.248 | 1.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 66 | 67 | 235 | 71 | 63 | 71 | 134 | 113 |
N.S. |
1 | 0.00 | 1.83 | 1.86 | 6.53 | 1.97 | 1.75 | 1.97 | 3.72 | 3.14 |
time (sec) |
N/A | 0.000 | 0.219 | 5.741 | 0.230 | 0.084 | 0.343 | 0.763 | 0.523 | 1.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 18 | 14 | 19 | 69 | 11 | 20 | 18 | 10 | 11 |
N.S. |
1 | 1.50 | 1.17 | 1.58 | 5.75 | 0.92 | 1.67 | 1.50 | 0.83 | 0.92 |
time (sec) |
N/A | 0.324 | 0.013 | 0.108 | 0.032 | 0.073 | 0.058 | 0.110 | 0.223 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 11 | 9 | 7 | 6 | 6 | 7 | 6 | 9 | 7 |
N.S. |
1 | 1.22 | 1.00 | 0.78 | 0.67 | 0.67 | 0.78 | 0.67 | 1.00 | 0.78 |
time (sec) |
N/A | 0.151 | 0.014 | 0.026 | 0.025 | 0.063 | 0.033 | 0.111 | 0.238 | 0.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 23 | 41 | 28 | 33 | 31 | 29 | 39 | 50 |
N.S. |
1 | 0.00 | 0.62 | 1.11 | 0.76 | 0.89 | 0.84 | 0.78 | 1.05 | 1.35 |
time (sec) |
N/A | 0.000 | 5.091 | 4.210 | 0.156 | 0.074 | 0.431 | 0.273 | 0.211 | 1.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 18 | 15 | 14 | 14 | 14 | 27 | 16 | 14 |
N.S. |
1 | 0.00 | 0.82 | 0.68 | 0.64 | 0.64 | 0.64 | 1.23 | 0.73 | 0.64 |
time (sec) |
N/A | 0.000 | 0.014 | 0.079 | 0.079 | 0.074 | 0.080 | 0.115 | 0.249 | 1.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | A | F | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 29 | 25 | 87 | 27 | 0 | 551 | 30 |
N.S. |
1 | 0.00 | 0.00 | 1.16 | 1.00 | 3.48 | 1.08 | 0.00 | 22.04 | 1.20 |
time (sec) |
N/A | 0.000 | 0.000 | 0.964 | 0.381 | 0.081 | 0.558 | 0.000 | 1.337 | 1.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 22 | 22 | 20 | 21 | 21 | 22 | 21 | 20 | 20 |
N.S. |
1 | 0.85 | 0.85 | 0.77 | 0.81 | 0.81 | 0.85 | 0.81 | 0.77 | 0.77 |
time (sec) |
N/A | 0.179 | 0.004 | 0.068 | 0.038 | 0.059 | 0.021 | 0.112 | 0.251 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 10 | 10 | 12 | 11 | 14 | 7 | 11 | 13 | 11 |
N.S. |
1 | 0.50 | 0.50 | 0.60 | 0.55 | 0.70 | 0.35 | 0.55 | 0.65 | 0.55 |
time (sec) |
N/A | 0.155 | 0.001 | 0.034 | 0.030 | 0.058 | 0.030 | 0.114 | 0.216 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 43 | 43 | 33 | 37 | 37 | 31 | 37 | 35 | 35 |
N.S. |
1 | 1.95 | 1.95 | 1.50 | 1.68 | 1.68 | 1.41 | 1.68 | 1.59 | 1.59 |
time (sec) |
N/A | 0.186 | 0.003 | 0.058 | 0.033 | 0.060 | 0.024 | 0.119 | 0.220 | 1.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 36 | 38 | 39 | 39 | 34 | 43 | 36 | 32 |
N.S. |
1 | 0.00 | 1.64 | 1.73 | 1.77 | 1.77 | 1.55 | 1.95 | 1.64 | 1.45 |
time (sec) |
N/A | 0.000 | 2.111 | 0.183 | 0.079 | 0.074 | 0.138 | 0.123 | 0.221 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 23 | 29 | 28 | 32 | 32 | 36 | 40 | 36 |
N.S. |
1 | 0.00 | 0.82 | 1.04 | 1.00 | 1.14 | 1.14 | 1.29 | 1.43 | 1.29 |
time (sec) |
N/A | 0.000 | 0.872 | 0.224 | 0.085 | 0.081 | 0.161 | 0.218 | 0.228 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 24 | 29 | 34 | 17 | 55 | 23 | 20 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 1.12 | 1.31 | 0.65 | 2.12 | 0.88 | 0.77 |
time (sec) |
N/A | 0.000 | 0.141 | 6.982 | 0.180 | 0.067 | 0.098 | 0.118 | 0.239 | 1.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 15 | 27 | 14 | 15 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.42 | 0.74 | 0.79 | 1.11 | 0.95 |
time (sec) |
N/A | 0.484 | 0.098 | 0.114 | 0.037 | 0.073 | 0.121 | 0.110 | 0.263 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 57 | 45 | 49 | 42 | 60 | 59 | 0 |
N.S. |
1 | 0.00 | 1.16 | 2.28 | 1.80 | 1.96 | 1.68 | 2.40 | 2.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.386 | 1.968 | 0.158 | 0.072 | 0.206 | 0.143 | 0.226 | 0.000 |