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 | A | A | B | F | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 1322 | 0 | 0 | 0 | 0 | 11 | 826 |
N.S. |
1 | 1.00 | 1.00 | 52.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 33.04 |
time (sec) |
N/A | 0.176 | 0.003 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.283 | 2.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 46 | 0 | 0 | 54 | 0 | 11 | 44 |
N.S. |
1 | 1.00 | 1.00 | 1.84 | 0.00 | 0.00 | 2.16 | 0.00 | 0.44 | 1.76 |
time (sec) |
N/A | 0.178 | 0.002 | 0.720 | 0.000 | 0.000 | 0.306 | 0.000 | 0.188 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 34 | 0 | 0 | 39 | 0 | 9 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.36 | 0.00 | 0.00 | 1.56 | 0.00 | 0.36 | 1.40 |
time (sec) |
N/A | 0.173 | 0.002 | 0.429 | 0.000 | 0.000 | 0.228 | 0.000 | 0.201 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 19 | 10 | 0 | 19 | 0 | 7 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.53 | 0.00 | 1.00 | 0.00 | 0.37 | 0.89 |
time (sec) |
N/A | 0.160 | 0.007 | 0.289 | 0.030 | 0.000 | 0.169 | 0.000 | 0.212 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 66 | 56 | 0 | 0 | 24 | 0 | 11 | 10 |
N.S. |
1 | 1.00 | 2.06 | 1.75 | 0.00 | 0.00 | 0.75 | 0.00 | 0.34 | 0.31 |
time (sec) |
N/A | 0.186 | 0.091 | 0.223 | 0.000 | 0.000 | 0.417 | 0.000 | 0.203 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 27 | 0 | 0 | 20 | 0 | 11 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 0.00 | 0.00 | 1.11 | 0.00 | 0.61 | 1.44 |
time (sec) |
N/A | 0.186 | 0.003 | 0.638 | 0.000 | 0.000 | 0.187 | 0.000 | 0.186 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 40 | 0 | 0 | 41 | 0 | 11 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.60 | 0.00 | 0.00 | 1.64 | 0.00 | 0.44 | 0.68 |
time (sec) |
N/A | 0.184 | 0.003 | 0.647 | 0.000 | 0.000 | 0.246 | 0.000 | 0.216 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 54 | 0 | 0 | 54 | 0 | 11 | 17 |
N.S. |
1 | 1.00 | 1.00 | 2.16 | 0.00 | 0.00 | 2.16 | 0.00 | 0.44 | 0.68 |
time (sec) |
N/A | 0.187 | 0.003 | 0.695 | 0.000 | 0.000 | 0.303 | 0.000 | 0.252 | 0.016 |
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 | 52 | 64 | 32 | 32 | 31 | 31 | 37 | 31 | 33 | 31 |
N.S. |
1 | 1.23 | 0.62 | 0.62 | 0.60 | 0.60 | 0.71 | 0.60 | 0.63 | 0.60 |
time (sec) |
N/A | 0.274 | 0.018 | 0.149 | 0.036 | 0.101 | 0.052 | 0.112 | 0.208 | 0.043 |
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 | 38 | 44 | 24 | 24 | 23 | 23 | 29 | 23 | 25 | 23 |
N.S. |
1 | 1.16 | 0.63 | 0.63 | 0.61 | 0.61 | 0.76 | 0.61 | 0.66 | 0.61 |
time (sec) |
N/A | 0.227 | 0.017 | 0.111 | 0.043 | 0.095 | 0.046 | 0.110 | 0.204 | 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 | 24 | 24 | 16 | 16 | 15 | 15 | 20 | 15 | 17 | 15 |
N.S. |
1 | 1.00 | 0.67 | 0.67 | 0.62 | 0.62 | 0.83 | 0.62 | 0.71 | 0.62 |
time (sec) |
N/A | 0.176 | 0.014 | 0.116 | 0.035 | 0.094 | 0.041 | 0.107 | 0.201 | 0.039 |
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 | 11 | 11 | 11 | 11 | 10 | 10 | 10 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.91 | 0.91 | 1.09 | 0.91 |
time (sec) |
N/A | 0.145 | 0.008 | 0.094 | 0.039 | 0.080 | 0.036 | 0.108 | 0.228 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 8 | 5 | 5 | 8 | 5 | 5 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.60 | 1.00 | 1.00 | 1.60 | 1.00 | 1.00 | 1.20 |
time (sec) |
N/A | 0.153 | 0.012 | 0.216 | 0.084 | 0.078 | 0.378 | 0.110 | 0.200 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 8 | 19 | 20 | 19 | 27 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.40 | 0.95 | 1.00 | 0.95 | 1.35 | 0.85 |
time (sec) |
N/A | 0.186 | 0.025 | 0.271 | 0.083 | 0.074 | 0.573 | 0.114 | 0.210 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 39 | 36 | 33 | 10 | 29 | 36 | 33 | 34 | 36 |
N.S. |
1 | 0.98 | 0.90 | 0.82 | 0.25 | 0.72 | 0.90 | 0.82 | 0.85 | 0.90 |
time (sec) |
N/A | 0.223 | 0.020 | 0.267 | 0.079 | 0.091 | 0.851 | 0.119 | 0.263 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 58 | 43 | 46 | 10 | 37 | 49 | 46 | 43 | 45 |
N.S. |
1 | 1.04 | 0.77 | 0.82 | 0.18 | 0.66 | 0.88 | 0.82 | 0.77 | 0.80 |
time (sec) |
N/A | 0.270 | 0.021 | 0.282 | 0.091 | 0.081 | 1.223 | 0.108 | 0.208 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 816 | 0 | 838 | 877 | 0 | 817 | 814 |
N.S. |
1 | 1.00 | 1.00 | 32.64 | 0.00 | 33.52 | 35.08 | 0.00 | 32.68 | 32.56 |
time (sec) |
N/A | 0.177 | 0.003 | 75.899 | 0.000 | 0.148 | 0.497 | 0.000 | 0.192 | 2.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 32 | 0 | 54 | 44 | 0 | 33 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.28 | 0.00 | 2.16 | 1.76 | 0.00 | 1.32 | 1.24 |
time (sec) |
N/A | 0.187 | 0.003 | 0.211 | 0.000 | 0.082 | 0.052 | 0.000 | 0.184 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 24 | 0 | 46 | 36 | 0 | 25 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.00 | 1.84 | 1.44 | 0.00 | 1.00 | 0.92 |
time (sec) |
N/A | 0.179 | 0.002 | 0.152 | 0.000 | 0.105 | 0.059 | 0.000 | 0.246 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 30 | 16 | 20 | 33 | 20 | 0 | 17 | 15 |
N.S. |
1 | 1.00 | 1.67 | 0.89 | 1.11 | 1.83 | 1.11 | 0.00 | 0.94 | 0.83 |
time (sec) |
N/A | 0.175 | 0.011 | 0.145 | 0.059 | 0.081 | 0.044 | 0.000 | 0.220 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 41 | 16 | 0 | 0 | 19 | 0 | 21 | 13 |
N.S. |
1 | 1.00 | 2.93 | 1.14 | 0.00 | 0.00 | 1.36 | 0.00 | 1.50 | 0.93 |
time (sec) |
N/A | 0.212 | 0.014 | 0.214 | 0.000 | 0.000 | 1.827 | 0.000 | 0.210 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 11 | 0 | 20 | 8 | 0 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.58 | 0.00 | 1.05 | 0.42 | 0.00 | 0.63 | 0.53 |
time (sec) |
N/A | 0.179 | 0.005 | 0.261 | 0.000 | 0.102 | 0.045 | 0.000 | 0.213 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 33 | 0 | 23 | 17 | 0 | 36 | 33 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 0.00 | 0.92 | 0.68 | 0.00 | 1.44 | 1.32 |
time (sec) |
N/A | 0.184 | 0.003 | 0.288 | 0.000 | 0.094 | 0.399 | 0.000 | 0.227 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 46 | 0 | 37 | 19 | 0 | 42 | 46 |
N.S. |
1 | 1.00 | 1.00 | 1.84 | 0.00 | 1.48 | 0.76 | 0.00 | 1.68 | 1.84 |
time (sec) |
N/A | 0.254 | 0.003 | 0.306 | 0.000 | 0.119 | 0.413 | 0.000 | 0.194 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 824 | 0 | 846 | 896 | 0 | 825 | 821 |
N.S. |
1 | 1.00 | 1.00 | 32.96 | 0.00 | 33.84 | 35.84 | 0.00 | 33.00 | 32.84 |
time (sec) |
N/A | 0.270 | 0.003 | 81.734 | 0.000 | 0.098 | 0.607 | 0.000 | 0.203 | 2.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 40 | 0 | 62 | 63 | 0 | 41 | 39 |
N.S. |
1 | 1.00 | 1.00 | 1.60 | 0.00 | 2.48 | 2.52 | 0.00 | 1.64 | 1.56 |
time (sec) |
N/A | 0.301 | 0.003 | 0.232 | 0.000 | 0.083 | 0.063 | 0.000 | 0.236 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 32 | 0 | 54 | 53 | 0 | 33 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.28 | 0.00 | 2.16 | 2.12 | 0.00 | 1.32 | 1.24 |
time (sec) |
N/A | 0.286 | 0.002 | 0.195 | 0.000 | 0.085 | 0.052 | 0.000 | 0.186 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 38 | 24 | 20 | 41 | 37 | 0 | 25 | 23 |
N.S. |
1 | 1.00 | 2.11 | 1.33 | 1.11 | 2.28 | 2.06 | 0.00 | 1.39 | 1.28 |
time (sec) |
N/A | 0.278 | 0.011 | 0.218 | 0.050 | 0.077 | 0.071 | 0.000 | 0.187 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 56 | 25 | 0 | 0 | 22 | 0 | 26 | 24 |
N.S. |
1 | 1.04 | 2.43 | 1.09 | 0.00 | 0.00 | 0.96 | 0.00 | 1.13 | 1.04 |
time (sec) |
N/A | 0.443 | 0.018 | 0.231 | 0.000 | 0.000 | 3.045 | 0.000 | 0.213 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 0 | 29 | 12 | 0 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.00 | 1.61 | 0.67 | 0.00 | 0.94 | 0.83 |
time (sec) |
N/A | 0.308 | 0.003 | 0.274 | 0.000 | 0.082 | 0.060 | 0.000 | 0.253 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 16 | 0 | 25 | 14 | 0 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.62 | 0.00 | 0.96 | 0.54 | 0.00 | 0.65 | 0.58 |
time (sec) |
N/A | 0.318 | 0.007 | 0.346 | 0.000 | 0.073 | 0.063 | 0.000 | 0.201 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 46 | 0 | 23 | 32 | 0 | 44 | 46 |
N.S. |
1 | 1.00 | 1.00 | 1.84 | 0.00 | 0.92 | 1.28 | 0.00 | 1.76 | 1.84 |
time (sec) |
N/A | 0.311 | 0.003 | 0.358 | 0.000 | 0.086 | 0.628 | 0.000 | 0.209 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 866 | 0 | 814 | 0 | 0 | 15 | 822 |
N.S. |
1 | 1.00 | 1.00 | 34.64 | 0.00 | 32.56 | 0.00 | 0.00 | 0.60 | 32.88 |
time (sec) |
N/A | 0.200 | 0.003 | 0.068 | 0.000 | 0.111 | 0.000 | 0.000 | 0.241 | 2.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 84 | 0 | 38 | 73 | 0 | 15 | 46 |
N.S. |
1 | 1.00 | 1.00 | 3.36 | 0.00 | 1.52 | 2.92 | 0.00 | 0.60 | 1.84 |
time (sec) |
N/A | 0.242 | 0.003 | 0.221 | 0.000 | 0.085 | 2.982 | 0.000 | 0.208 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 76 | 0 | 30 | 60 | 0 | 13 | 37 |
N.S. |
1 | 1.00 | 1.00 | 3.04 | 0.00 | 1.20 | 2.40 | 0.00 | 0.52 | 1.48 |
time (sec) |
N/A | 0.189 | 0.002 | 0.223 | 0.000 | 0.077 | 1.678 | 0.000 | 0.183 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 68 | 0 | 25 | 46 | 0 | 11 | 22 |
N.S. |
1 | 1.00 | 1.00 | 2.62 | 0.00 | 0.96 | 1.77 | 0.00 | 0.42 | 0.85 |
time (sec) |
N/A | 0.178 | 0.006 | 0.259 | 0.000 | 0.101 | 0.982 | 0.000 | 0.189 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 55 | 18 | 32 | 37 | 0 | 15 | 26 |
N.S. |
1 | 1.00 | 0.94 | 3.06 | 1.00 | 1.78 | 2.06 | 0.00 | 0.83 | 1.44 |
time (sec) |
N/A | 0.171 | 0.005 | 0.252 | 0.053 | 0.085 | 0.855 | 0.000 | 0.255 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 103 | 77 | 0 | 0 | 42 | 0 | 15 | 14 |
N.S. |
1 | 1.00 | 2.64 | 1.97 | 0.00 | 0.00 | 1.08 | 0.00 | 0.38 | 0.36 |
time (sec) |
N/A | 0.252 | 0.322 | 0.259 | 0.000 | 0.000 | 0.476 | 0.000 | 0.183 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 106 | 0 | 34 | 58 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 5.89 | 0.00 | 1.89 | 3.22 | 0.00 | 0.83 | 1.17 |
time (sec) |
N/A | 0.186 | 0.003 | 0.280 | 0.000 | 0.085 | 0.906 | 0.000 | 0.183 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 141 | 0 | 39 | 78 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 5.64 | 0.00 | 1.56 | 3.12 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.188 | 0.003 | 0.305 | 0.000 | 0.090 | 1.692 | 0.000 | 0.198 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 165 | 0 | 47 | 92 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 6.60 | 0.00 | 1.88 | 3.68 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.183 | 0.003 | 0.311 | 0.000 | 0.081 | 3.099 | 0.000 | 0.221 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 866 | 0 | 806 | 0 | 0 | 15 | 814 |
N.S. |
1 | 1.00 | 1.00 | 34.64 | 0.00 | 32.24 | 0.00 | 0.00 | 0.60 | 32.56 |
time (sec) |
N/A | 0.184 | 0.003 | 0.064 | 0.000 | 0.120 | 0.000 | 0.000 | 0.190 | 2.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 84 | 0 | 30 | 76 | 0 | 13 | 37 |
N.S. |
1 | 1.00 | 1.00 | 3.36 | 0.00 | 1.20 | 3.04 | 0.00 | 0.52 | 1.48 |
time (sec) |
N/A | 0.184 | 0.003 | 0.224 | 0.000 | 0.087 | 3.238 | 0.000 | 0.199 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 76 | 0 | 25 | 63 | 0 | 11 | 22 |
N.S. |
1 | 1.00 | 1.00 | 2.92 | 0.00 | 0.96 | 2.42 | 0.00 | 0.42 | 0.85 |
time (sec) |
N/A | 0.185 | 0.006 | 0.217 | 0.000 | 0.096 | 1.932 | 0.000 | 0.234 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 82 | 0 | 43 | 63 | 0 | 15 | 17 |
N.S. |
1 | 1.00 | 1.00 | 3.28 | 0.00 | 1.72 | 2.52 | 0.00 | 0.60 | 0.68 |
time (sec) |
N/A | 0.179 | 0.002 | 0.253 | 0.000 | 0.103 | 1.338 | 0.000 | 0.207 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 32 | 98 | 20 | 37 | 60 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.78 | 5.44 | 1.11 | 2.06 | 3.33 | 0.00 | 0.83 | 1.17 |
time (sec) |
N/A | 0.174 | 0.013 | 0.247 | 0.058 | 0.104 | 0.957 | 0.000 | 0.193 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 51 | 121 | 85 | 0 | 0 | 61 | 0 | 15 | 14 |
N.S. |
1 | 0.93 | 2.20 | 1.55 | 0.00 | 0.00 | 1.11 | 0.00 | 0.27 | 0.25 |
time (sec) |
N/A | 0.359 | 0.507 | 0.243 | 0.000 | 0.000 | 0.648 | 0.000 | 0.186 | 1.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 135 | 0 | 38 | 80 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 7.50 | 0.00 | 2.11 | 4.44 | 0.00 | 0.83 | 1.17 |
time (sec) |
N/A | 0.180 | 0.003 | 0.286 | 0.000 | 0.081 | 1.357 | 0.000 | 0.255 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 165 | 0 | 43 | 99 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 6.60 | 0.00 | 1.72 | 3.96 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.182 | 0.003 | 0.300 | 0.000 | 0.091 | 2.628 | 0.000 | 0.190 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 189 | 0 | 51 | 112 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 7.56 | 0.00 | 2.04 | 4.48 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.185 | 0.003 | 0.295 | 0.000 | 0.089 | 4.936 | 0.000 | 0.197 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 866 | 0 | 798 | 0 | 0 | 15 | 805 |
N.S. |
1 | 1.00 | 1.00 | 34.64 | 0.00 | 31.92 | 0.00 | 0.00 | 0.60 | 32.20 |
time (sec) |
N/A | 0.175 | 0.003 | 0.073 | 0.000 | 0.102 | 0.000 | 0.000 | 0.229 | 2.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 84 | 0 | 25 | 76 | 0 | 11 | 22 |
N.S. |
1 | 1.00 | 1.00 | 3.23 | 0.00 | 0.96 | 2.92 | 0.00 | 0.42 | 0.85 |
time (sec) |
N/A | 0.179 | 0.006 | 0.263 | 0.000 | 0.098 | 3.956 | 0.000 | 0.226 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 90 | 0 | 51 | 76 | 0 | 15 | 17 |
N.S. |
1 | 1.00 | 1.00 | 3.60 | 0.00 | 2.04 | 3.04 | 0.00 | 0.60 | 0.68 |
time (sec) |
N/A | 0.178 | 0.003 | 0.271 | 0.000 | 0.086 | 2.744 | 0.000 | 0.196 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 131 | 0 | 43 | 76 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 5.24 | 0.00 | 1.72 | 3.04 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.168 | 0.002 | 0.309 | 0.000 | 0.081 | 1.946 | 0.000 | 0.198 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 40 | 127 | 20 | 37 | 76 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 2.22 | 7.06 | 1.11 | 2.06 | 4.22 | 0.00 | 0.83 | 1.17 |
time (sec) |
N/A | 0.166 | 0.018 | 0.271 | 0.058 | 0.086 | 1.461 | 0.000 | 0.225 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 67 | 145 | 94 | 0 | 0 | 71 | 0 | 15 | 14 |
N.S. |
1 | 1.05 | 2.27 | 1.47 | 0.00 | 0.00 | 1.11 | 0.00 | 0.23 | 0.22 |
time (sec) |
N/A | 0.383 | 0.475 | 0.270 | 0.000 | 0.000 | 1.218 | 0.000 | 0.193 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 159 | 0 | 38 | 94 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 8.83 | 0.00 | 2.11 | 5.22 | 0.00 | 0.83 | 1.17 |
time (sec) |
N/A | 0.180 | 0.003 | 0.305 | 0.000 | 0.079 | 2.248 | 0.000 | 0.184 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 189 | 0 | 43 | 114 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 7.56 | 0.00 | 1.72 | 4.56 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.191 | 0.002 | 0.317 | 0.000 | 0.093 | 4.508 | 0.000 | 0.185 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 213 | 0 | 51 | 128 | 0 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 8.52 | 0.00 | 2.04 | 5.12 | 0.00 | 0.60 | 0.84 |
time (sec) |
N/A | 0.187 | 0.003 | 0.339 | 0.000 | 0.100 | 9.173 | 0.000 | 0.243 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 1346 | 755 | 848 | 0 | 1362 | 1266 | 0 |
N.S. |
1 | 1.00 | 1.00 | 46.41 | 26.03 | 29.24 | 0.00 | 46.97 | 43.66 | 0.00 |
time (sec) |
N/A | 0.185 | 0.003 | 0.187 | 0.038 | 0.512 | 0.000 | 0.124 | 2.591 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 72 | 69 | 64 | 110 | 88 | 90 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.48 | 2.38 | 2.21 | 3.79 | 3.03 | 3.10 | 0.00 |
time (sec) |
N/A | 0.185 | 0.003 | 0.127 | 0.041 | 0.116 | 0.614 | 0.122 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 58 | 62 | 56 | 83 | 75 | 78 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 2.14 | 1.93 | 2.86 | 2.59 | 2.69 | 0.00 |
time (sec) |
N/A | 0.180 | 0.003 | 0.121 | 0.047 | 0.116 | 0.379 | 0.110 | 0.221 | 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 | 22 | 22 | 50 | 43 | 46 | 42 | 46 | 53 | 61 | 47 |
N.S. |
1 | 1.00 | 2.27 | 1.95 | 2.09 | 1.91 | 2.09 | 2.41 | 2.77 | 2.14 |
time (sec) |
N/A | 0.178 | 0.041 | 0.104 | 0.043 | 0.117 | 0.242 | 0.117 | 0.192 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 56 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.192 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 44 | 29 | 38 | 46 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.32 | 1.73 | 2.09 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.191 | 0.003 | 0.132 | 0.075 | 0.107 | 0.274 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 59 | 32 | 49 | 78 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.03 | 1.10 | 1.69 | 2.69 | 0.00 | 2.45 | 0.00 |
time (sec) |
N/A | 0.191 | 0.003 | 0.150 | 0.089 | 0.112 | 0.429 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 72 | 32 | 57 | 107 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.48 | 1.10 | 1.97 | 3.69 | 0.00 | 3.10 | 0.00 |
time (sec) |
N/A | 0.195 | 0.003 | 0.131 | 0.093 | 0.124 | 0.687 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 2679 | 0 | 848 | 0 | 2693 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 92.38 | 0.00 | 29.24 | 0.00 | 92.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.191 | 0.003 | 0.796 | 0.000 | 0.477 | 0.000 | 0.141 | 2.700 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 71 | 0 | 64 | 107 | 145 | 114 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.45 | 0.00 | 2.21 | 3.69 | 5.00 | 3.93 | 0.00 |
time (sec) |
N/A | 0.186 | 0.002 | 0.325 | 0.000 | 0.122 | 1.027 | 0.120 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 59 | 0 | 56 | 85 | 119 | 102 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.03 | 0.00 | 1.93 | 2.93 | 4.10 | 3.52 | 0.00 |
time (sec) |
N/A | 0.174 | 0.003 | 0.244 | 0.000 | 0.121 | 0.598 | 0.120 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 54 | 43 | 0 | 42 | 83 | 82 | 85 | 77 |
N.S. |
1 | 1.00 | 2.45 | 1.95 | 0.00 | 1.91 | 3.77 | 3.73 | 3.86 | 3.50 |
time (sec) |
N/A | 0.176 | 0.071 | 0.117 | 0.000 | 0.110 | 0.758 | 0.111 | 0.231 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 78 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.179 | 0.227 | 0.000 | 0.000 | 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 | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 50 | 0 | 37 | 44 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.27 | 0.00 | 1.68 | 2.00 | 0.00 | 3.82 | 0.00 |
time (sec) |
N/A | 0.252 | 0.002 | 0.218 | 0.000 | 0.110 | 0.276 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 70 | 0 | 49 | 66 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.41 | 0.00 | 1.69 | 2.28 | 0.00 | 2.72 | 0.00 |
time (sec) |
N/A | 0.293 | 0.003 | 0.293 | 0.000 | 0.114 | 0.429 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 86 | 0 | 57 | 95 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.97 | 0.00 | 1.97 | 3.28 | 0.00 | 3.10 | 0.00 |
time (sec) |
N/A | 0.301 | 0.003 | 0.368 | 0.000 | 0.107 | 0.751 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 228 | 0 | 100 | 185 | 0 | 135 | 0 |
N.S. |
1 | 1.00 | 0.76 | 4.47 | 0.00 | 1.96 | 3.63 | 0.00 | 2.65 | 0.00 |
time (sec) |
N/A | 0.345 | 0.014 | 0.721 | 0.000 | 0.096 | 3.008 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 133 | 0 | 74 | 116 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 0.76 | 2.61 | 0.00 | 1.45 | 2.27 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.358 | 0.013 | 0.444 | 0.000 | 0.099 | 2.058 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 39 | 19 | 21 | 54 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 0.79 | 0.88 | 2.25 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.283 | 0.013 | 0.339 | 0.055 | 0.088 | 0.430 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-2) | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 86 | 0 | 0 | 2358 | 0 | 15 | 12 |
N.S. |
1 | 1.00 | 0.76 | 1.69 | 0.00 | 0.00 | 46.24 | 0.00 | 0.29 | 0.24 |
time (sec) |
N/A | 0.336 | 0.013 | 0.149 | 0.000 | 0.000 | 1.336 | 0.000 | 0.215 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 37 | 97 | 0 | 52 | 4357 | 0 | 21 | 19 |
N.S. |
1 | 1.00 | 0.76 | 1.98 | 0.00 | 1.06 | 88.92 | 0.00 | 0.43 | 0.39 |
time (sec) |
N/A | 0.350 | 0.013 | 0.139 | 0.000 | 0.095 | 1.286 | 0.000 | 0.217 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 116 | 0 | 82 | 8162 | 0 | 21 | 19 |
N.S. |
1 | 1.00 | 0.76 | 2.27 | 0.00 | 1.61 | 160.04 | 0.00 | 0.41 | 0.37 |
time (sec) |
N/A | 0.320 | 0.012 | 0.162 | 0.000 | 0.117 | 2.428 | 0.000 | 0.212 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 24 | 61 | 0 | 40 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 0.86 | 2.18 | 0.00 | 1.43 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.197 | 0.028 | 0.165 | 0.000 | 0.093 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 38 | 81 | 0 | 62 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.80 | 0.00 | 1.38 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.248 | 0.011 | 0.155 | 0.000 | 0.103 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 34 | 72 | 0 | 56 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 0.79 | 1.67 | 0.00 | 1.30 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.203 | 0.028 | 0.135 | 0.000 | 0.095 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 40 | 91 | 0 | 83 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.75 | 0.00 | 1.60 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.208 | 0.010 | 0.142 | 0.000 | 0.099 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 64 | 0 | 41441 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.37 | 0.00 | 1534.85 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.191 | 0.003 | 0.109 | 0.000 | 3.028 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 64 | 0 | 85 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.37 | 0.00 | 3.15 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.190 | 0.003 | 0.294 | 0.000 | 0.095 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 64 | 0 | 57 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.37 | 0.00 | 2.11 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.180 | 0.002 | 0.244 | 0.000 | 0.100 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 106 | 22 | 35 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.30 | 1.10 | 1.75 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.181 | 0.021 | 0.242 | 0.072 | 0.115 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 41 | 61 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.191 | 0.084 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 148 | 0 | 41 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 7.40 | 0.00 | 2.05 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.179 | 0.003 | 0.319 | 0.000 | 0.117 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 79 | 0 | 70 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.93 | 0.00 | 2.59 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.184 | 0.003 | 0.398 | 0.000 | 0.111 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 79 | 0 | 101 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.93 | 0.00 | 3.74 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.185 | 0.003 | 0.634 | 0.000 | 0.114 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 54 | 0 | 26081 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.25 | 0.00 | 1086.71 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.188 | 0.003 | 0.092 | 0.000 | 2.635 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 54 | 0 | 62 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.25 | 0.00 | 2.58 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.179 | 0.003 | 0.304 | 0.000 | 0.094 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 54 | 0 | 42 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.25 | 0.00 | 1.75 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.176 | 0.002 | 0.280 | 0.000 | 0.092 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 97 | 17 | 27 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.11 | 0.89 | 1.42 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.165 | 0.008 | 0.250 | 0.051 | 0.112 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 43 | 60 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.39 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.183 | 0.069 | 0.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 133 | 0 | 37 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 6.65 | 0.00 | 1.85 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.179 | 0.003 | 0.322 | 0.000 | 0.101 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 69 | 0 | 59 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.14 | 0.00 | 2.68 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.180 | 0.003 | 0.424 | 0.000 | 0.093 | 0.000 | 0.000 | 0.202 | 0.000 |