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 | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 47 | 37 | 34 | 13 | 13 | 0 | 30 | 15 | 33 |
N.S. |
1 | 0.61 | 0.48 | 0.44 | 0.17 | 0.17 | 0.00 | 0.39 | 0.19 | 0.43 |
time (sec) |
N/A | 0.317 | 1.008 | 1.538 | 0.026 | 0.082 | 0.000 | 0.116 | 0.176 | 17.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 35 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.44 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.326 | 1.008 | 2.191 | 0.025 | 0.102 | 0.000 | 0.128 | 0.173 | 18.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 35 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.44 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.316 | 1.007 | 3.117 | 0.024 | 0.094 | 0.000 | 0.111 | 0.173 | 18.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 35 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.44 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.327 | 1.009 | 4.326 | 0.031 | 0.140 | 0.000 | 0.127 | 0.175 | 18.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 78 | 113 | 46 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.47 | 0.68 | 0.28 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.384 | 0.620 | 0.174 | 0.031 | 0.172 | 0.000 | 0.112 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 78 | 113 | 46 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.47 | 0.68 | 0.28 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.381 | 0.552 | 0.165 | 0.033 | 0.158 | 0.000 | 0.119 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 78 | 113 | 46 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.74 | 1.07 | 0.43 | 0.33 | 0.33 | 0.00 | 0.63 | 0.35 | 0.00 |
time (sec) |
N/A | 0.380 | 0.523 | 0.170 | 0.027 | 0.196 | 0.000 | 0.139 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 113 | 46 | 35 | 35 | 0 | 45 | 37 | 46 |
N.S. |
1 | 1.06 | 1.64 | 0.67 | 0.51 | 0.51 | 0.00 | 0.65 | 0.54 | 0.67 |
time (sec) |
N/A | 0.348 | 0.460 | 0.149 | 0.026 | 0.126 | 0.000 | 0.121 | 0.173 | 17.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 24 | 35 | 35 | 0 | 44 | 36 | 36 |
N.S. |
1 | 1.00 | 0.71 | 0.63 | 0.92 | 0.92 | 0.00 | 1.16 | 0.95 | 0.95 |
time (sec) |
N/A | 0.290 | 0.011 | 0.148 | 0.027 | 0.091 | 0.000 | 0.132 | 0.177 | 17.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 74 | 60 | 47 | 33 | 33 | 0 | 68 | 33 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.29 | 0.20 | 0.20 | 0.00 | 0.42 | 0.20 | 0.00 |
time (sec) |
N/A | 0.346 | 1.018 | 0.125 | 0.025 | 0.078 | 0.000 | 0.136 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 73 | 62 | 48 | 34 | 38 | 0 | 87 | 38 | 0 |
N.S. |
1 | 0.45 | 0.38 | 0.29 | 0.21 | 0.23 | 0.00 | 0.53 | 0.23 | 0.00 |
time (sec) |
N/A | 0.374 | 1.019 | 0.150 | 0.034 | 0.091 | 0.000 | 0.111 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 72 | 612 | 48 | 34 | 39 | 0 | 87 | 39 | 0 |
N.S. |
1 | 0.44 | 3.73 | 0.29 | 0.21 | 0.24 | 0.00 | 0.53 | 0.24 | 0.00 |
time (sec) |
N/A | 0.367 | 0.828 | 0.130 | 0.026 | 0.082 | 0.000 | 0.108 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 74 | 266 | 50 | 33 | 39 | 0 | 87 | 39 | 0 |
N.S. |
1 | 0.45 | 1.63 | 0.31 | 0.20 | 0.24 | 0.00 | 0.53 | 0.24 | 0.00 |
time (sec) |
N/A | 0.371 | 0.324 | 0.134 | 0.026 | 0.089 | 0.000 | 0.124 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 59 | 41 | 35 | 35 | 0 | 68 | 37 | 151 |
N.S. |
1 | 1.00 | 1.44 | 1.00 | 0.85 | 0.85 | 0.00 | 1.66 | 0.90 | 3.68 |
time (sec) |
N/A | 0.290 | 1.016 | 0.129 | 0.028 | 0.181 | 0.000 | 0.123 | 0.172 | 17.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 75 | 61 | 44 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.89 | 0.73 | 0.52 | 0.42 | 0.44 | 0.00 | 0.82 | 0.44 | 1.80 |
time (sec) |
N/A | 0.314 | 1.015 | 0.125 | 0.028 | 0.177 | 0.000 | 0.122 | 0.165 | 17.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 78 | 61 | 44 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.47 | 0.37 | 0.26 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.363 | 1.016 | 0.132 | 0.036 | 0.137 | 0.000 | 0.110 | 0.168 | 17.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 78 | 61 | 46 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.47 | 0.37 | 0.28 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.377 | 1.016 | 0.141 | 0.030 | 0.083 | 0.000 | 0.117 | 0.172 | 17.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 78 | 61 | 44 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.47 | 0.37 | 0.26 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.375 | 1.016 | 0.137 | 0.028 | 0.102 | 0.000 | 0.112 | 0.173 | 17.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.365 | 1.015 | 3.154 | 0.027 | 0.102 | 0.000 | 0.104 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.362 | 1.011 | 2.258 | 0.027 | 0.122 | 0.000 | 0.134 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.361 | 1.013 | 1.641 | 0.025 | 0.084 | 0.000 | 0.150 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.349 | 1.011 | 1.075 | 0.026 | 0.087 | 0.000 | 0.110 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 75 | 59 | 56 | 31 | 31 | 0 | 63 | 35 | 0 |
N.S. |
1 | 0.47 | 0.37 | 0.35 | 0.19 | 0.19 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.358 | 1.009 | 0.639 | 0.027 | 0.087 | 0.000 | 0.111 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 66 | 60 | 58 | 32 | 36 | 0 | 64 | 36 | 0 |
N.S. |
1 | 0.42 | 0.38 | 0.37 | 0.20 | 0.23 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.361 | 1.013 | 0.979 | 0.030 | 0.130 | 0.000 | 0.104 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 69 | 59 | 56 | 33 | 36 | 0 | 67 | 36 | 0 |
N.S. |
1 | 0.43 | 0.37 | 0.35 | 0.20 | 0.22 | 0.00 | 0.42 | 0.22 | 0.00 |
time (sec) |
N/A | 0.357 | 1.012 | 1.515 | 0.031 | 0.137 | 0.000 | 0.104 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 66 | 59 | 56 | 32 | 37 | 0 | 66 | 37 | 0 |
N.S. |
1 | 0.42 | 0.37 | 0.35 | 0.20 | 0.23 | 0.00 | 0.42 | 0.23 | 0.00 |
time (sec) |
N/A | 0.358 | 1.015 | 2.214 | 0.025 | 0.090 | 0.000 | 0.114 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 71 | 61 | 57 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.44 | 0.37 | 0.35 | 0.21 | 0.23 | 0.00 | 0.42 | 0.23 | 0.93 |
time (sec) |
N/A | 0.353 | 1.012 | 3.113 | 0.033 | 0.129 | 0.000 | 0.142 | 0.169 | 18.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 57 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.45 | 0.37 | 0.34 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.350 | 1.011 | 4.263 | 0.032 | 0.147 | 0.000 | 0.108 | 0.165 | 18.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 57 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.45 | 0.37 | 0.34 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.362 | 1.015 | 5.825 | 0.026 | 0.115 | 0.000 | 0.115 | 0.171 | 17.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 57 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.45 | 0.37 | 0.34 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.365 | 1.011 | 7.834 | 0.026 | 0.150 | 0.000 | 0.114 | 0.175 | 17.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 75 | 61 | 57 | 35 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.45 | 0.37 | 0.34 | 0.21 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.372 | 1.014 | 10.311 | 0.031 | 0.122 | 0.000 | 0.105 | 0.167 | 17.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 66 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.26 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.430 | 1.020 | 0.432 | 0.033 | 0.100 | 0.000 | 0.127 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 104 | 135 | 66 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.41 | 0.53 | 0.26 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.433 | 0.981 | 0.311 | 0.027 | 0.090 | 0.000 | 0.146 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 104 | 135 | 68 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.41 | 0.53 | 0.27 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.438 | 0.995 | 0.265 | 0.026 | 0.087 | 0.000 | 0.113 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 107 | 135 | 66 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.67 | 0.84 | 0.41 | 0.36 | 0.36 | 0.00 | 0.66 | 0.37 | 0.00 |
time (sec) |
N/A | 0.420 | 0.865 | 0.208 | 0.026 | 0.139 | 0.000 | 0.143 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 88 | 135 | 66 | 56 | 56 | 0 | 104 | 59 | 0 |
N.S. |
1 | 0.74 | 1.13 | 0.55 | 0.47 | 0.47 | 0.00 | 0.87 | 0.50 | 0.00 |
time (sec) |
N/A | 0.400 | 0.777 | 0.191 | 0.026 | 0.101 | 0.000 | 0.111 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 135 | 66 | 56 | 56 | 0 | 67 | 59 | 0 |
N.S. |
1 | 1.06 | 1.96 | 0.96 | 0.81 | 0.81 | 0.00 | 0.97 | 0.86 | 0.00 |
time (sec) |
N/A | 0.348 | 0.721 | 0.161 | 0.033 | 0.123 | 0.000 | 0.104 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 24 | 57 | 57 | 0 | 66 | 58 | 36 |
N.S. |
1 | 1.00 | 0.71 | 0.63 | 1.50 | 1.50 | 0.00 | 1.74 | 1.53 | 0.95 |
time (sec) |
N/A | 0.287 | 0.014 | 0.167 | 0.033 | 0.117 | 0.000 | 0.125 | 0.177 | 17.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 98 | 82 | 69 | 55 | 55 | 0 | 106 | 55 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.27 | 0.22 | 0.22 | 0.00 | 0.42 | 0.22 | 0.00 |
time (sec) |
N/A | 0.389 | 1.022 | 0.137 | 0.028 | 0.093 | 0.000 | 0.139 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 97 | 85 | 70 | 56 | 61 | 0 | 125 | 61 | 0 |
N.S. |
1 | 0.39 | 0.34 | 0.28 | 0.22 | 0.24 | 0.00 | 0.50 | 0.24 | 0.00 |
time (sec) |
N/A | 0.393 | 1.021 | 0.153 | 0.030 | 0.157 | 0.000 | 0.131 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 99 | 276 | 70 | 56 | 61 | 0 | 127 | 61 | 0 |
N.S. |
1 | 0.40 | 1.10 | 0.28 | 0.22 | 0.24 | 0.00 | 0.51 | 0.24 | 0.00 |
time (sec) |
N/A | 0.411 | 0.864 | 0.155 | 0.035 | 0.179 | 0.000 | 0.134 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 99 | 279 | 70 | 56 | 61 | 0 | 128 | 61 | 0 |
N.S. |
1 | 0.40 | 1.12 | 0.28 | 0.22 | 0.24 | 0.00 | 0.51 | 0.24 | 0.00 |
time (sec) |
N/A | 0.413 | 0.741 | 0.194 | 0.033 | 0.198 | 0.000 | 0.132 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 96 | 696 | 70 | 56 | 61 | 0 | 126 | 61 | 0 |
N.S. |
1 | 0.38 | 2.78 | 0.28 | 0.22 | 0.24 | 0.00 | 0.50 | 0.24 | 0.00 |
time (sec) |
N/A | 0.403 | 1.022 | 0.206 | 0.032 | 0.102 | 0.000 | 0.112 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 98 | 268 | 70 | 55 | 61 | 0 | 125 | 61 | 0 |
N.S. |
1 | 0.39 | 1.07 | 0.28 | 0.22 | 0.24 | 0.00 | 0.50 | 0.24 | 0.00 |
time (sec) |
N/A | 0.404 | 0.521 | 0.256 | 0.026 | 0.153 | 0.000 | 0.110 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 81 | 58 | 57 | 57 | 0 | 106 | 59 | 231 |
N.S. |
1 | 1.00 | 1.98 | 1.41 | 1.39 | 1.39 | 0.00 | 2.59 | 1.44 | 5.63 |
time (sec) |
N/A | 0.286 | 1.016 | 0.349 | 0.026 | 0.176 | 0.000 | 0.126 | 0.169 | 18.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 75 | 83 | 68 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.89 | 0.99 | 0.81 | 0.68 | 0.70 | 0.00 | 1.27 | 0.70 | 2.75 |
time (sec) |
N/A | 0.316 | 1.019 | 0.522 | 0.034 | 0.201 | 0.000 | 0.103 | 0.175 | 17.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 103 | 83 | 66 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.80 | 0.65 | 0.52 | 0.45 | 0.46 | 0.00 | 0.84 | 0.46 | 1.80 |
time (sec) |
N/A | 0.352 | 1.016 | 0.769 | 0.032 | 0.081 | 0.000 | 0.104 | 0.170 | 17.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 102 | 83 | 66 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.26 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.409 | 1.020 | 1.182 | 0.030 | 0.086 | 0.000 | 0.120 | 0.169 | 18.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 104 | 83 | 66 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.41 | 0.33 | 0.26 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.400 | 1.022 | 1.843 | 0.030 | 0.090 | 0.000 | 0.150 | 0.169 | 17.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 104 | 83 | 66 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.41 | 0.33 | 0.26 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.410 | 1.025 | 2.712 | 0.032 | 0.080 | 0.000 | 0.129 | 0.172 | 18.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 102 | 83 | 66 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.26 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.408 | 1.026 | 4.033 | 0.030 | 0.089 | 0.000 | 0.107 | 0.171 | 18.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 80 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.406 | 1.022 | 5.989 | 0.035 | 0.078 | 0.000 | 0.106 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 80 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.407 | 1.015 | 4.385 | 0.027 | 0.071 | 0.000 | 0.125 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 80 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.404 | 1.017 | 3.164 | 0.027 | 0.072 | 0.000 | 0.110 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 80 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.389 | 1.017 | 2.211 | 0.027 | 0.079 | 0.000 | 0.131 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 80 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.390 | 1.015 | 1.522 | 0.035 | 0.074 | 0.000 | 0.153 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 98 | 83 | 80 | 56 | 56 | 0 | 104 | 59 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.32 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.392 | 1.016 | 1.054 | 0.031 | 0.077 | 0.000 | 0.150 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 102 | 81 | 78 | 54 | 54 | 0 | 102 | 57 | 0 |
N.S. |
1 | 0.41 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.405 | 1.014 | 0.638 | 0.029 | 0.067 | 0.000 | 0.134 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 93 | 83 | 80 | 55 | 59 | 0 | 103 | 59 | 0 |
N.S. |
1 | 0.38 | 0.34 | 0.32 | 0.22 | 0.24 | 0.00 | 0.42 | 0.24 | 0.00 |
time (sec) |
N/A | 0.402 | 1.021 | 1.003 | 0.031 | 0.065 | 0.000 | 0.118 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 92 | 83 | 80 | 54 | 59 | 0 | 104 | 59 | 0 |
N.S. |
1 | 0.37 | 0.34 | 0.33 | 0.22 | 0.24 | 0.00 | 0.42 | 0.24 | 0.00 |
time (sec) |
N/A | 0.404 | 1.017 | 1.461 | 0.026 | 0.075 | 0.000 | 0.125 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 95 | 83 | 80 | 55 | 59 | 0 | 106 | 59 | 0 |
N.S. |
1 | 0.38 | 0.33 | 0.32 | 0.22 | 0.24 | 0.00 | 0.43 | 0.24 | 0.00 |
time (sec) |
N/A | 0.393 | 1.017 | 2.148 | 0.031 | 0.084 | 0.000 | 0.136 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 93 | 83 | 80 | 55 | 59 | 0 | 106 | 59 | 0 |
N.S. |
1 | 0.38 | 0.34 | 0.32 | 0.22 | 0.24 | 0.00 | 0.43 | 0.24 | 0.00 |
time (sec) |
N/A | 0.402 | 1.015 | 3.112 | 0.025 | 0.075 | 0.000 | 0.134 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 92 | 83 | 80 | 54 | 59 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.37 | 0.34 | 0.33 | 0.22 | 0.24 | 0.00 | 0.43 | 0.24 | 0.00 |
time (sec) |
N/A | 0.400 | 1.016 | 4.307 | 0.033 | 0.069 | 0.000 | 0.138 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 97 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.39 | 0.33 | 0.31 | 0.23 | 0.24 | 0.00 | 0.43 | 0.24 | 0.92 |
time (sec) |
N/A | 0.399 | 1.016 | 5.860 | 0.035 | 0.076 | 0.000 | 0.126 | 0.172 | 19.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 99 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.39 | 0.33 | 0.31 | 0.23 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.396 | 1.014 | 7.861 | 0.027 | 0.084 | 0.000 | 0.110 | 0.172 | 18.961 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.404 | 1.014 | 10.395 | 0.031 | 0.074 | 0.000 | 0.110 | 0.165 | 20.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.397 | 1.018 | 13.645 | 0.032 | 0.064 | 0.000 | 0.112 | 0.170 | 18.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.401 | 1.017 | 22.323 | 0.028 | 0.064 | 0.000 | 0.119 | 0.163 | 17.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.401 | 1.015 | 27.442 | 0.027 | 0.063 | 0.000 | 0.153 | 0.164 | 17.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 101 | 83 | 79 | 57 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.23 | 0.00 | 0.42 | 0.23 | 0.91 |
time (sec) |
N/A | 0.399 | 1.014 | 33.045 | 0.041 | 0.071 | 0.000 | 0.108 | 0.170 | 18.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 68 | 167 | 42 | 34 | 33 | 0 | 59 | 33 | 0 |
N.S. |
1 | 0.54 | 1.31 | 0.33 | 0.27 | 0.26 | 0.00 | 0.46 | 0.26 | 0.00 |
time (sec) |
N/A | 0.376 | 0.372 | 0.204 | 0.031 | 0.073 | 0.000 | 0.151 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 113 | 31 | 23 | 22 | 0 | 33 | 22 | 64 |
N.S. |
1 | 0.99 | 1.51 | 0.41 | 0.31 | 0.29 | 0.00 | 0.44 | 0.29 | 0.85 |
time (sec) |
N/A | 0.351 | 0.302 | 0.158 | 0.035 | 0.067 | 0.000 | 0.107 | 0.167 | 19.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 49 | 22 | 13 | 13 | 0 | 22 | 13 | 33 |
N.S. |
1 | 1.00 | 1.11 | 0.50 | 0.30 | 0.30 | 0.00 | 0.50 | 0.30 | 0.75 |
time (sec) |
N/A | 0.288 | 0.109 | 0.148 | 0.026 | 0.069 | 0.000 | 0.105 | 0.164 | 18.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 55 | 134 | 29 | 23 | 18 | 0 | 33 | 20 | 40 |
N.S. |
1 | 0.69 | 1.68 | 0.36 | 0.29 | 0.22 | 0.00 | 0.41 | 0.25 | 0.50 |
time (sec) |
N/A | 0.304 | 0.181 | 0.167 | 0.032 | 0.070 | 0.000 | 0.136 | 0.161 | 18.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 65 | 175 | 42 | 33 | 33 | 0 | 52 | 33 | 75 |
N.S. |
1 | 0.52 | 1.40 | 0.34 | 0.26 | 0.26 | 0.00 | 0.42 | 0.26 | 0.60 |
time (sec) |
N/A | 0.365 | 0.190 | 0.177 | 0.026 | 0.071 | 0.000 | 0.113 | 0.172 | 18.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 72 | 66 | 64 | 37 | 99 | 0 | 64 | 37 | 0 |
N.S. |
1 | 0.56 | 0.51 | 0.50 | 0.29 | 0.77 | 0.00 | 0.50 | 0.29 | 0.00 |
time (sec) |
N/A | 0.343 | 1.023 | 1.511 | 0.111 | 0.073 | 0.000 | 0.111 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 61 | 54 | 48 | 26 | 82 | 0 | 42 | 26 | 0 |
N.S. |
1 | 0.69 | 0.61 | 0.54 | 0.29 | 0.92 | 0.00 | 0.47 | 0.29 | 0.00 |
time (sec) |
N/A | 0.323 | 1.012 | 1.023 | 0.109 | 0.079 | 0.000 | 0.140 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 44 | 34 | 15 | 67 | 0 | 23 | 23 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.64 | 0.28 | 1.26 | 0.00 | 0.43 | 0.43 | 0.00 |
time (sec) |
N/A | 0.293 | 1.011 | 0.717 | 0.106 | 0.078 | 0.000 | 0.139 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 64 | 56 | 50 | 29 | 82 | 0 | 37 | 30 | 0 |
N.S. |
1 | 0.70 | 0.61 | 0.54 | 0.32 | 0.89 | 0.00 | 0.40 | 0.33 | 0.00 |
time (sec) |
N/A | 0.310 | 1.013 | 1.067 | 0.104 | 0.070 | 0.000 | 0.141 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 81 | 70 | 68 | 40 | 106 | 0 | 50 | 43 | 0 |
N.S. |
1 | 0.61 | 0.53 | 0.51 | 0.30 | 0.80 | 0.00 | 0.38 | 0.32 | 0.00 |
time (sec) |
N/A | 0.326 | 1.019 | 1.535 | 0.104 | 0.077 | 0.000 | 0.116 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 91 | 81 | 74 | 66 | 91 | 0 | 92 | 95 | 0 |
N.S. |
1 | 0.58 | 0.51 | 0.47 | 0.42 | 0.58 | 0.00 | 0.58 | 0.60 | 0.00 |
time (sec) |
N/A | 0.410 | 1.027 | 0.148 | 0.033 | 0.065 | 0.000 | 0.112 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 80 | 192 | 54 | 55 | 69 | 0 | 62 | 81 | 0 |
N.S. |
1 | 0.71 | 1.70 | 0.48 | 0.49 | 0.61 | 0.00 | 0.55 | 0.72 | 0.00 |
time (sec) |
N/A | 0.394 | 0.468 | 0.130 | 0.036 | 0.071 | 0.000 | 0.125 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 71 | 119 | 31 | 36 | 36 | 0 | 32 | 28 | 42 |
N.S. |
1 | 1.73 | 2.90 | 0.76 | 0.88 | 0.88 | 0.00 | 0.78 | 0.68 | 1.02 |
time (sec) |
N/A | 0.345 | 0.298 | 0.116 | 0.027 | 0.072 | 0.000 | 0.106 | 0.171 | 18.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 23 | 26 | 26 | 0 | 24 | 25 | 34 |
N.S. |
1 | 1.00 | 0.71 | 0.61 | 0.68 | 0.68 | 0.00 | 0.63 | 0.66 | 0.89 |
time (sec) |
N/A | 0.285 | 0.006 | 0.102 | 0.033 | 0.064 | 0.000 | 0.108 | 0.161 | 18.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 84 | 790 | 68 | 57 | 90 | 0 | 89 | 109 | 0 |
N.S. |
1 | 0.57 | 5.37 | 0.46 | 0.39 | 0.61 | 0.00 | 0.61 | 0.74 | 0.00 |
time (sec) |
N/A | 0.390 | 1.213 | 0.150 | 0.026 | 0.075 | 0.000 | 0.107 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 98 | 901 | 90 | 75 | 119 | 0 | 122 | 133 | 0 |
N.S. |
1 | 0.52 | 4.77 | 0.48 | 0.40 | 0.63 | 0.00 | 0.65 | 0.70 | 0.00 |
time (sec) |
N/A | 0.424 | 1.439 | 0.161 | 0.036 | 0.065 | 0.000 | 0.146 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 115 | 89 | 116 | 68 | 202 | 0 | 84 | 118 | 0 |
N.S. |
1 | 0.70 | 0.54 | 0.71 | 0.41 | 1.23 | 0.00 | 0.51 | 0.72 | 0.00 |
time (sec) |
N/A | 0.386 | 1.036 | 2.102 | 0.116 | 0.078 | 0.000 | 0.142 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 102 | 84 | 97 | 59 | 188 | 0 | 65 | 113 | 0 |
N.S. |
1 | 0.80 | 0.66 | 0.76 | 0.46 | 1.47 | 0.00 | 0.51 | 0.88 | 0.00 |
time (sec) |
N/A | 0.356 | 1.023 | 1.454 | 0.113 | 0.075 | 0.000 | 0.138 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 100 | 81 | 99 | 62 | 190 | 0 | 70 | 110 | 0 |
N.S. |
1 | 0.78 | 0.63 | 0.77 | 0.48 | 1.47 | 0.00 | 0.54 | 0.85 | 0.00 |
time (sec) |
N/A | 0.360 | 1.025 | 1.005 | 0.115 | 0.080 | 0.000 | 0.110 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 112 | 83 | 97 | 58 | 188 | 0 | 65 | 113 | 0 |
N.S. |
1 | 0.89 | 0.66 | 0.77 | 0.46 | 1.49 | 0.00 | 0.52 | 0.90 | 0.00 |
time (sec) |
N/A | 0.358 | 1.021 | 0.668 | 0.113 | 0.074 | 0.000 | 0.132 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 118 | 93 | 110 | 71 | 202 | 0 | 87 | 121 | 0 |
N.S. |
1 | 0.72 | 0.56 | 0.67 | 0.43 | 1.22 | 0.00 | 0.53 | 0.73 | 0.00 |
time (sec) |
N/A | 0.382 | 1.026 | 1.006 | 0.114 | 0.099 | 0.000 | 0.130 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 135 | 105 | 127 | 86 | 238 | 0 | 101 | 137 | 0 |
N.S. |
1 | 0.65 | 0.50 | 0.61 | 0.41 | 1.14 | 0.00 | 0.48 | 0.66 | 0.00 |
time (sec) |
N/A | 0.423 | 1.030 | 1.481 | 0.116 | 0.091 | 0.000 | 0.150 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 127 | 103 | 96 | 110 | 157 | 0 | 114 | 175 | 0 |
N.S. |
1 | 0.53 | 0.43 | 0.40 | 0.46 | 0.66 | 0.00 | 0.48 | 0.74 | 0.00 |
time (sec) |
N/A | 0.475 | 1.033 | 0.164 | 0.036 | 0.076 | 0.000 | 0.123 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 116 | 261 | 76 | 99 | 135 | 0 | 84 | 163 | 0 |
N.S. |
1 | 0.59 | 1.33 | 0.39 | 0.51 | 0.69 | 0.00 | 0.43 | 0.83 | 0.00 |
time (sec) |
N/A | 0.461 | 0.782 | 0.148 | 0.036 | 0.077 | 0.000 | 0.110 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 161 | 50 | 80 | 80 | 0 | 54 | 50 | 144 |
N.S. |
1 | 1.00 | 3.93 | 1.22 | 1.95 | 1.95 | 0.00 | 1.32 | 1.22 | 3.51 |
time (sec) |
N/A | 0.289 | 0.525 | 0.135 | 0.054 | 0.079 | 0.000 | 0.117 | 0.164 | 19.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 86 | 206 | 42 | 69 | 69 | 0 | 43 | 68 | 53 |
N.S. |
1 | 1.16 | 2.78 | 0.57 | 0.93 | 0.93 | 0.00 | 0.58 | 0.92 | 0.72 |
time (sec) |
N/A | 0.392 | 0.466 | 0.128 | 0.037 | 0.078 | 0.000 | 0.106 | 0.167 | 18.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 232 | 31 | 58 | 58 | 0 | 32 | 57 | 42 |
N.S. |
1 | 1.06 | 3.36 | 0.45 | 0.84 | 0.84 | 0.00 | 0.46 | 0.83 | 0.61 |
time (sec) |
N/A | 0.343 | 0.479 | 0.121 | 0.028 | 0.075 | 0.000 | 0.174 | 0.235 | 17.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 23 | 48 | 48 | 0 | 24 | 47 | 34 |
N.S. |
1 | 1.00 | 0.71 | 0.61 | 1.26 | 1.26 | 0.00 | 0.63 | 1.24 | 0.89 |
time (sec) |
N/A | 0.283 | 0.008 | 0.110 | 0.033 | 0.067 | 0.000 | 0.107 | 0.223 | 18.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 116 | 96 | 90 | 101 | 178 | 0 | 111 | 215 | 0 |
N.S. |
1 | 0.52 | 0.43 | 0.40 | 0.45 | 0.80 | 0.00 | 0.50 | 0.96 | 0.00 |
time (sec) |
N/A | 0.448 | 1.035 | 0.168 | 0.037 | 0.080 | 0.000 | 0.143 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 132 | 119 | 112 | 119 | 207 | 0 | 144 | 241 | 0 |
N.S. |
1 | 0.49 | 0.45 | 0.42 | 0.45 | 0.78 | 0.00 | 0.54 | 0.90 | 0.00 |
time (sec) |
N/A | 0.475 | 1.037 | 0.180 | 0.038 | 0.075 | 0.000 | 0.139 | 0.226 | 0.000 |