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 | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 1539 | 1572 | 1581 | 1581 | 1775 | 1833 | 1834 | 1549 |
N.S. |
1 | 1.00 | 5.52 | 5.63 | 5.67 | 5.67 | 6.36 | 6.57 | 6.57 | 5.55 |
time (sec) |
N/A | 1.149 | 0.100 | 0.223 | 0.223 | 0.229 | 0.124 | 0.320 | 0.003 | 0.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 250 | 1397 | 1423 | 1437 | 1437 | 1598 | 1656 | 1657 | 1404 |
N.S. |
1 | 1.00 | 5.59 | 5.69 | 5.75 | 5.75 | 6.39 | 6.62 | 6.63 | 5.62 |
time (sec) |
N/A | 1.060 | 0.114 | 0.608 | 0.221 | 0.226 | 0.118 | 0.285 | 0.002 | 1.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 1241 | 1273 | 1283 | 1283 | 1428 | 1478 | 1480 | 1253 |
N.S. |
1 | 1.00 | 5.52 | 5.66 | 5.70 | 5.70 | 6.35 | 6.57 | 6.58 | 5.57 |
time (sec) |
N/A | 0.938 | 0.092 | 0.208 | 0.219 | 0.228 | 0.107 | 0.282 | 0.002 | 0.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 1105 | 1125 | 1135 | 1135 | 1280 | 1302 | 1303 | 1106 |
N.S. |
1 | 1.00 | 5.52 | 5.62 | 5.68 | 5.68 | 6.40 | 6.51 | 6.52 | 5.53 |
time (sec) |
N/A | 0.840 | 0.080 | 0.408 | 0.216 | 0.225 | 0.097 | 0.301 | 0.002 | 0.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 939 | 975 | 977 | 977 | 1088 | 1124 | 1126 | 953 |
N.S. |
1 | 1.00 | 5.52 | 5.74 | 5.75 | 5.75 | 6.40 | 6.61 | 6.62 | 5.61 |
time (sec) |
N/A | 0.781 | 0.074 | 0.203 | 0.227 | 0.224 | 0.091 | 0.289 | 0.002 | 0.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 811 | 827 | 835 | 835 | 940 | 948 | 949 | 806 |
N.S. |
1 | 1.00 | 5.55 | 5.66 | 5.72 | 5.72 | 6.44 | 6.49 | 6.50 | 5.52 |
time (sec) |
N/A | 0.634 | 0.057 | 0.201 | 0.230 | 0.217 | 0.084 | 0.297 | 0.001 | 0.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 660 | 678 | 686 | 686 | 748 | 771 | 772 | 664 |
N.S. |
1 | 1.00 | 5.55 | 5.70 | 5.76 | 5.76 | 6.29 | 6.48 | 6.49 | 5.58 |
time (sec) |
N/A | 0.545 | 0.047 | 0.203 | 0.204 | 0.222 | 0.070 | 0.294 | 0.001 | 0.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 511 | 529 | 535 | 535 | 586 | 594 | 595 | 495 |
N.S. |
1 | 1.00 | 5.55 | 5.75 | 5.82 | 5.82 | 6.37 | 6.46 | 6.47 | 5.38 |
time (sec) |
N/A | 0.461 | 0.035 | 0.206 | 0.203 | 0.220 | 0.061 | 0.307 | 0.002 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 358 | 380 | 384 | 384 | 415 | 417 | 418 | 348 |
N.S. |
1 | 1.00 | 5.51 | 5.85 | 5.91 | 5.91 | 6.38 | 6.42 | 6.43 | 5.35 |
time (sec) |
N/A | 0.366 | 0.024 | 0.198 | 0.202 | 0.214 | 0.054 | 0.294 | 0.001 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 220 | 232 | 240 | 240 | 248 | 241 | 241 | 208 |
N.S. |
1 | 1.00 | 5.79 | 6.11 | 6.32 | 6.32 | 6.53 | 6.34 | 6.34 | 5.47 |
time (sec) |
N/A | 0.182 | 0.014 | 0.193 | 0.210 | 0.216 | 0.046 | 0.300 | 0.000 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 108 | 114 | 12 | 109 | 108 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 7.71 | 8.14 | 0.86 | 7.79 | 7.71 |
time (sec) |
N/A | 0.131 | 0.001 | 0.196 | 0.199 | 0.226 | 0.031 | 0.341 | 0.000 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 241 | 591 | 827 | 866 | 868 | 799 | 961 | 1021 | 979 |
N.S. |
1 | 1.00 | 2.45 | 3.43 | 3.59 | 3.60 | 3.32 | 3.99 | 4.24 | 4.06 |
time (sec) |
N/A | 0.367 | 0.161 | 0.280 | 0.220 | 0.229 | 0.820 | 0.403 | 0.002 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 708 | 840 | 874 | 1124 | 816 | 1012 | 1255 | 3475 |
N.S. |
1 | 1.00 | 2.74 | 3.26 | 3.39 | 4.36 | 3.16 | 3.92 | 4.86 | 13.47 |
time (sec) |
N/A | 0.632 | 0.135 | 0.225 | 0.218 | 0.242 | 1.419 | 0.413 | 0.003 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 262 | 708 | 838 | 881 | 1233 | 843 | 924 | 1420 | 3299 |
N.S. |
1 | 1.00 | 2.70 | 3.20 | 3.36 | 4.71 | 3.22 | 3.53 | 5.42 | 12.59 |
time (sec) |
N/A | 0.623 | 0.140 | 0.225 | 0.225 | 0.240 | 6.417 | 0.396 | 0.003 | 0.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 427 | 841 | 891 | 1316 | 0 | 907 | 1524 | 2219 |
N.S. |
1 | 1.00 | 1.66 | 3.26 | 3.45 | 5.10 | 0.00 | 3.52 | 5.91 | 8.60 |
time (sec) |
N/A | 0.598 | 0.104 | 0.225 | 0.260 | 0.233 | 0.000 | 0.396 | 0.003 | 0.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 262 | 359 | 844 | 903 | 1365 | 0 | 1168 | 1604 | 1494 |
N.S. |
1 | 1.00 | 1.37 | 3.22 | 3.45 | 5.21 | 0.00 | 4.46 | 6.12 | 5.70 |
time (sec) |
N/A | 0.615 | 0.112 | 0.226 | 0.242 | 0.230 | 0.000 | 0.337 | 0.003 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 260 | 305 | 847 | 912 | 1395 | 0 | 883 | 1638 | 1141 |
N.S. |
1 | 1.00 | 1.17 | 3.26 | 3.51 | 5.37 | 0.00 | 3.40 | 6.30 | 4.39 |
time (sec) |
N/A | 0.606 | 0.127 | 0.223 | 0.258 | 0.234 | 0.000 | 0.369 | 0.004 | 0.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 262 | 265 | 850 | 925 | 1386 | 0 | 878 | 1626 | 997 |
N.S. |
1 | 1.00 | 1.01 | 3.24 | 3.53 | 5.29 | 0.00 | 3.35 | 6.21 | 3.81 |
time (sec) |
N/A | 0.580 | 0.127 | 0.240 | 0.256 | 0.240 | 0.000 | 0.367 | 0.004 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 239 | 854 | 934 | 1362 | 0 | 872 | 1568 | 950 |
N.S. |
1 | 1.00 | 0.93 | 3.31 | 3.62 | 5.28 | 0.00 | 3.38 | 6.08 | 3.68 |
time (sec) |
N/A | 0.568 | 0.145 | 0.240 | 0.272 | 0.250 | 0.000 | 0.365 | 0.004 | 0.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 712 | 854 | 945 | 1296 | 0 | 871 | 1464 | 946 |
N.S. |
1 | 1.00 | 2.76 | 3.31 | 3.66 | 5.02 | 0.00 | 3.38 | 5.67 | 3.67 |
time (sec) |
N/A | 0.568 | 0.183 | 0.228 | 0.279 | 0.233 | 0.000 | 0.333 | 0.005 | 0.288 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 708 | 848 | 957 | 1216 | 0 | 867 | 1314 | 955 |
N.S. |
1 | 1.00 | 2.75 | 3.30 | 3.72 | 4.73 | 0.00 | 3.37 | 5.11 | 3.72 |
time (sec) |
N/A | 0.547 | 0.245 | 0.227 | 0.268 | 0.236 | 0.000 | 0.302 | 0.004 | 0.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 591 | 843 | 975 | 1107 | 0 | 874 | 1160 | 866 |
N.S. |
1 | 1.00 | 2.18 | 3.11 | 3.60 | 4.08 | 0.00 | 3.23 | 4.28 | 3.20 |
time (sec) |
N/A | 0.521 | 0.221 | 0.231 | 0.247 | 0.234 | 0.000 | 0.298 | 0.002 | 0.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 665 | 776 | 920 | 920 | 0 | 951 | 969 | 1066 |
N.S. |
1 | 1.00 | 23.75 | 27.71 | 32.86 | 32.86 | 0.00 | 33.96 | 34.61 | 38.07 |
time (sec) |
N/A | 0.146 | 0.174 | 0.237 | 0.237 | 0.226 | 0.000 | 0.321 | 0.002 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 684 | 831 | 986 | 986 | 0 | 961 | 1083 | 39 |
N.S. |
1 | 1.00 | 11.79 | 14.33 | 17.00 | 17.00 | 0.00 | 16.57 | 18.67 | 0.67 |
time (sec) |
N/A | 0.165 | 0.166 | 0.230 | 0.256 | 0.235 | 0.000 | 0.339 | 0.002 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 102 | 690 | 831 | 997 | 997 | 0 | 961 | 1094 | 1098 |
N.S. |
1 | 1.15 | 7.75 | 9.34 | 11.20 | 11.20 | 0.00 | 10.80 | 12.29 | 12.34 |
time (sec) |
N/A | 0.191 | 0.176 | 0.231 | 0.249 | 0.237 | 0.000 | 0.295 | 0.002 | 0.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 146 | 692 | 831 | 1008 | 1008 | 0 | 961 | 1105 | 1109 |
N.S. |
1 | 1.22 | 5.77 | 6.92 | 8.40 | 8.40 | 0.00 | 8.01 | 9.21 | 9.24 |
time (sec) |
N/A | 0.209 | 0.176 | 0.252 | 0.251 | 0.235 | 0.000 | 0.329 | 0.002 | 1.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 190 | 690 | 831 | 1019 | 1019 | 0 | 961 | 1116 | 1120 |
N.S. |
1 | 1.26 | 4.57 | 5.50 | 6.75 | 6.75 | 0.00 | 6.36 | 7.39 | 7.42 |
time (sec) |
N/A | 0.244 | 0.172 | 0.246 | 0.245 | 0.228 | 0.000 | 0.315 | 0.003 | 3.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 234 | 694 | 831 | 1030 | 1030 | 0 | 961 | 1127 | 1131 |
N.S. |
1 | 1.29 | 3.81 | 4.57 | 5.66 | 5.66 | 0.00 | 5.28 | 6.19 | 6.21 |
time (sec) |
N/A | 0.265 | 0.175 | 0.251 | 0.251 | 0.239 | 0.000 | 0.315 | 0.002 | 0.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 278 | 690 | 831 | 1041 | 1041 | 0 | 961 | 1138 | 1142 |
N.S. |
1 | 1.31 | 3.24 | 3.90 | 4.89 | 4.89 | 0.00 | 4.51 | 5.34 | 5.36 |
time (sec) |
N/A | 0.295 | 0.179 | 0.254 | 0.261 | 0.228 | 0.000 | 0.298 | 0.002 | 0.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 322 | 694 | 831 | 1052 | 1052 | 0 | 961 | 1149 | 1153 |
N.S. |
1 | 1.32 | 2.84 | 3.41 | 4.31 | 4.31 | 0.00 | 3.94 | 4.71 | 4.73 |
time (sec) |
N/A | 0.324 | 0.172 | 0.256 | 0.281 | 0.235 | 0.000 | 0.323 | 0.003 | 12.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 273 | 692 | 831 | 1063 | 1063 | 0 | 961 | 1160 | 1164 |
N.S. |
1 | 1.00 | 2.53 | 3.04 | 3.89 | 3.89 | 0.00 | 3.52 | 4.25 | 4.26 |
time (sec) |
N/A | 0.520 | 0.170 | 0.251 | 0.271 | 0.234 | 0.000 | 0.297 | 0.002 | 25.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 692 | 831 | 1074 | 1074 | 0 | 961 | 1171 | 1175 |
N.S. |
1 | 1.00 | 2.48 | 2.98 | 3.85 | 3.85 | 0.00 | 3.44 | 4.20 | 4.21 |
time (sec) |
N/A | 0.526 | 0.177 | 0.267 | 0.276 | 0.234 | 0.000 | 0.316 | 0.002 | 0.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 692 | 831 | 1085 | 1085 | 0 | 961 | 1182 | 1186 |
N.S. |
1 | 1.00 | 2.48 | 2.98 | 3.89 | 3.89 | 0.00 | 3.44 | 4.24 | 4.25 |
time (sec) |
N/A | 0.502 | 0.178 | 0.250 | 0.300 | 0.233 | 0.000 | 0.298 | 0.002 | 1.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 167 | 244 | 258 | 259 | 209 | 273 | 301 | 280 |
N.S. |
1 | 1.00 | 1.37 | 2.00 | 2.11 | 2.12 | 1.71 | 2.24 | 2.47 | 2.30 |
time (sec) |
N/A | 0.258 | 0.042 | 0.226 | 0.213 | 0.210 | 0.314 | 0.313 | 0.000 | 0.094 |
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 | 98 | 98 | 115 | 168 | 177 | 179 | 136 | 184 | 208 | 189 |
N.S. |
1 | 1.00 | 1.17 | 1.71 | 1.81 | 1.83 | 1.39 | 1.88 | 2.12 | 1.93 |
time (sec) |
N/A | 0.234 | 0.027 | 0.235 | 0.210 | 0.229 | 0.228 | 0.337 | 0.000 | 0.256 |
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 | 74 | 74 | 74 | 107 | 114 | 115 | 83 | 116 | 132 | 118 |
N.S. |
1 | 1.00 | 1.00 | 1.45 | 1.54 | 1.55 | 1.12 | 1.57 | 1.78 | 1.59 |
time (sec) |
N/A | 0.207 | 0.019 | 0.222 | 0.215 | 0.217 | 0.173 | 0.306 | 0.001 | 0.077 |
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 | 50 | 50 | 43 | 56 | 60 | 62 | 44 | 60 | 72 | 62 |
N.S. |
1 | 1.00 | 0.86 | 1.12 | 1.20 | 1.24 | 0.88 | 1.20 | 1.44 | 1.24 |
time (sec) |
N/A | 0.187 | 0.011 | 0.217 | 0.200 | 0.219 | 0.127 | 0.305 | 0.000 | 0.387 |
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 | 26 | 25 | 26 | 26 | 25 | 20 | 27 | 28 | 25 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 1.00 | 0.96 | 0.77 | 1.04 | 1.08 | 0.96 |
time (sec) |
N/A | 0.170 | 0.006 | 0.636 | 0.199 | 0.223 | 0.080 | 0.292 | 0.000 | 0.222 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 | 1.00 |
time (sec) |
N/A | 0.134 | 0.000 | 0.211 | 0.207 | 0.219 | 0.019 | 0.298 | 0.001 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 26 | 28 | 36 | 26 | 128 | 46 | 26 | 25 |
N.S. |
1 | 1.00 | 0.72 | 0.78 | 1.00 | 0.72 | 3.56 | 1.28 | 0.72 | 0.69 |
time (sec) |
N/A | 0.153 | 0.008 | 0.463 | 0.196 | 0.221 | 0.198 | 0.282 | 0.000 | 0.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 53 | 57 | 92 | 93 | 233 | 78 | 115 | 46 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 1.61 | 1.63 | 4.09 | 1.37 | 2.02 | 0.81 |
time (sec) |
N/A | 0.206 | 0.017 | 0.474 | 0.202 | 0.239 | 0.391 | 0.285 | 0.000 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 67 | 81 | 202 | 242 | 381 | 165 | 288 | 182 |
N.S. |
1 | 1.00 | 0.82 | 0.99 | 2.46 | 2.95 | 4.65 | 2.01 | 3.51 | 2.22 |
time (sec) |
N/A | 0.227 | 0.038 | 0.488 | 0.194 | 0.232 | 0.656 | 0.304 | 0.001 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 228 | 256 | 264 | 373 | 231 | 339 | 415 | 327 |
N.S. |
1 | 1.00 | 1.75 | 1.97 | 2.03 | 2.87 | 1.78 | 2.61 | 3.19 | 2.52 |
time (sec) |
N/A | 0.319 | 0.044 | 0.651 | 0.213 | 0.225 | 0.529 | 0.296 | 0.001 | 0.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 165 | 175 | 183 | 267 | 155 | 245 | 297 | 203 |
N.S. |
1 | 1.00 | 1.59 | 1.68 | 1.76 | 2.57 | 1.49 | 2.36 | 2.86 | 1.95 |
time (sec) |
N/A | 0.272 | 0.034 | 0.224 | 0.215 | 0.219 | 0.394 | 0.314 | 0.001 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 114 | 108 | 117 | 172 | 102 | 166 | 197 | 123 |
N.S. |
1 | 1.00 | 1.52 | 1.44 | 1.56 | 2.29 | 1.36 | 2.21 | 2.63 | 1.64 |
time (sec) |
N/A | 0.238 | 0.023 | 0.226 | 0.218 | 0.217 | 0.309 | 0.291 | 0.001 | 0.086 |
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 | 51 | 51 | 47 | 63 | 67 | 92 | 60 | 98 | 112 | 71 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.31 | 1.80 | 1.18 | 1.92 | 2.20 | 1.39 |
time (sec) |
N/A | 0.199 | 0.024 | 0.221 | 0.224 | 0.217 | 0.192 | 0.288 | 0.000 | 0.258 |
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 | 31 | 31 | 31 | 33 | 34 | 37 | 27 | 57 | 49 | 32 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.10 | 1.19 | 0.87 | 1.84 | 1.58 | 1.03 |
time (sec) |
N/A | 0.173 | 0.007 | 0.220 | 0.216 | 0.216 | 0.107 | 0.287 | 0.000 | 0.077 |
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 | 12 | 12 | 12 | 13 | 12 | 13 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.08 | 0.83 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.133 | 0.001 | 0.426 | 0.209 | 0.216 | 0.055 | 0.301 | 0.000 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 53 | 58 | 90 | 92 | 233 | 77 | 115 | 47 |
N.S. |
1 | 1.00 | 0.95 | 1.04 | 1.61 | 1.64 | 4.16 | 1.38 | 2.05 | 0.84 |
time (sec) |
N/A | 0.202 | 0.016 | 0.261 | 0.206 | 0.221 | 0.387 | 0.313 | 0.000 | 0.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 66 | 82 | 208 | 241 | 406 | 153 | 459 | 74 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.57 | 2.98 | 5.01 | 1.89 | 5.67 | 0.91 |
time (sec) |
N/A | 0.228 | 0.042 | 0.272 | 0.202 | 0.232 | 0.653 | 0.291 | 0.002 | 0.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 98 | 109 | 386 | 494 | 634 | 216 | 821 | 330 |
N.S. |
1 | 1.00 | 0.90 | 1.00 | 3.54 | 4.53 | 5.82 | 1.98 | 7.53 | 3.03 |
time (sec) |
N/A | 0.269 | 0.045 | 0.301 | 0.226 | 0.229 | 0.990 | 0.311 | 0.002 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 303 | 343 | 364 | 548 | 340 | 362 | 625 | 441 |
N.S. |
1 | 1.00 | 1.92 | 2.17 | 2.30 | 3.47 | 2.15 | 2.29 | 3.96 | 2.79 |
time (sec) |
N/A | 0.391 | 0.066 | 0.231 | 0.236 | 0.224 | 1.276 | 0.323 | 0.002 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 230 | 254 | 271 | 416 | 258 | 264 | 470 | 291 |
N.S. |
1 | 1.00 | 1.73 | 1.91 | 2.04 | 3.13 | 1.94 | 1.98 | 3.53 | 2.19 |
time (sec) |
N/A | 0.312 | 0.041 | 0.226 | 0.201 | 0.216 | 0.960 | 0.287 | 0.001 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 167 | 172 | 191 | 291 | 185 | 183 | 330 | 196 |
N.S. |
1 | 1.00 | 1.62 | 1.67 | 1.85 | 2.83 | 1.80 | 1.78 | 3.20 | 1.90 |
time (sec) |
N/A | 0.263 | 0.033 | 0.224 | 0.193 | 0.230 | 0.688 | 0.313 | 0.001 | 0.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 114 | 114 | 125 | 188 | 128 | 112 | 209 | 130 |
N.S. |
1 | 1.00 | 1.46 | 1.46 | 1.60 | 2.41 | 1.64 | 1.44 | 2.68 | 1.67 |
time (sec) |
N/A | 0.231 | 0.025 | 0.224 | 0.204 | 0.226 | 0.505 | 0.299 | 0.000 | 0.113 |
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 | 59 | 59 | 48 | 66 | 80 | 100 | 80 | 69 | 113 | 77 |
N.S. |
1 | 1.00 | 0.81 | 1.12 | 1.36 | 1.69 | 1.36 | 1.17 | 1.92 | 1.31 |
time (sec) |
N/A | 0.205 | 0.016 | 0.223 | 0.210 | 0.219 | 0.253 | 0.281 | 0.001 | 0.289 |
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 | 28 | 26 | 25 | 38 | 38 | 39 | 24 | 37 | 39 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.36 | 1.36 | 1.39 | 0.86 | 1.32 | 1.39 |
time (sec) |
N/A | 0.142 | 0.006 | 0.217 | 0.191 | 0.223 | 0.162 | 0.300 | 0.000 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 24 | 26 | 12 | 23 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.71 | 1.86 | 0.86 | 1.64 | 1.86 |
time (sec) |
N/A | 0.136 | 0.001 | 0.443 | 0.208 | 0.216 | 0.088 | 0.309 | 0.000 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 67 | 81 | 202 | 242 | 381 | 165 | 289 | 183 |
N.S. |
1 | 1.00 | 0.82 | 0.99 | 2.46 | 2.95 | 4.65 | 2.01 | 3.52 | 2.23 |
time (sec) |
N/A | 0.231 | 0.031 | 0.482 | 0.210 | 0.223 | 0.590 | 0.307 | 0.001 | 0.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 97 | 108 | 386 | 495 | 632 | 217 | 821 | 329 |
N.S. |
1 | 1.00 | 0.88 | 0.98 | 3.51 | 4.50 | 5.75 | 1.97 | 7.46 | 2.99 |
time (sec) |
N/A | 0.272 | 0.060 | 0.719 | 0.235 | 0.244 | 0.948 | 0.309 | 0.002 | 0.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 128 | 140 | 594 | 760 | 881 | 345 | 1202 | 542 |
N.S. |
1 | 1.00 | 0.90 | 0.98 | 4.15 | 5.31 | 6.16 | 2.41 | 8.41 | 3.79 |
time (sec) |
N/A | 0.311 | 0.065 | 0.305 | 0.211 | 0.236 | 1.437 | 0.310 | 0.003 | 0.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 232 | 584 | 705 | 786 | 1093 | 0 | 723 | 1231 | 784 |
N.S. |
1 | 1.00 | 2.52 | 3.04 | 3.39 | 4.71 | 0.00 | 3.12 | 5.31 | 3.38 |
time (sec) |
N/A | 0.543 | 0.152 | 0.238 | 0.250 | 0.229 | 0.000 | 0.291 | 0.003 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 474 | 570 | 649 | 852 | 0 | 581 | 911 | 649 |
N.S. |
1 | 1.00 | 2.27 | 2.73 | 3.11 | 4.08 | 0.00 | 2.78 | 4.36 | 3.11 |
time (sec) |
N/A | 0.475 | 0.119 | 0.234 | 0.237 | 0.225 | 0.000 | 0.290 | 0.002 | 0.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 308 | 446 | 535 | 625 | 0 | 467 | 638 | 460 |
N.S. |
1 | 1.00 | 1.59 | 2.30 | 2.76 | 3.22 | 0.00 | 2.41 | 3.29 | 2.37 |
time (sec) |
N/A | 0.417 | 0.092 | 0.230 | 0.222 | 0.224 | 0.000 | 0.312 | 0.002 | 0.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 271 | 314 | 398 | 398 | 0 | 369 | 383 | 378 |
N.S. |
1 | 1.00 | 9.68 | 11.21 | 14.21 | 14.21 | 0.00 | 13.18 | 13.68 | 13.50 |
time (sec) |
N/A | 0.142 | 0.058 | 0.232 | 0.208 | 0.214 | 0.000 | 0.312 | 0.001 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 205 | 246 | 326 | 326 | 0 | 271 | 338 | 39 |
N.S. |
1 | 1.00 | 3.53 | 4.24 | 5.62 | 5.62 | 0.00 | 4.67 | 5.83 | 0.67 |
time (sec) |
N/A | 0.174 | 0.036 | 0.230 | 0.233 | 0.222 | 0.000 | 0.294 | 0.001 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 102 | 144 | 171 | 247 | 247 | 267 | 184 | 251 | 237 |
N.S. |
1 | 1.15 | 1.62 | 1.92 | 2.78 | 2.78 | 3.00 | 2.07 | 2.82 | 2.66 |
time (sec) |
N/A | 0.188 | 0.031 | 0.228 | 0.203 | 0.220 | 114.475 | 0.288 | 0.001 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 94 | 110 | 182 | 182 | 196 | 114 | 181 | 176 |
N.S. |
1 | 1.00 | 1.02 | 1.20 | 1.98 | 1.98 | 2.13 | 1.24 | 1.97 | 1.91 |
time (sec) |
N/A | 0.247 | 0.020 | 0.228 | 0.225 | 0.213 | 1.943 | 0.288 | 0.000 | 0.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 55 | 62 | 131 | 131 | 139 | 61 | 128 | 129 |
N.S. |
1 | 1.00 | 0.85 | 0.95 | 2.02 | 2.02 | 2.14 | 0.94 | 1.97 | 1.98 |
time (sec) |
N/A | 0.208 | 0.017 | 0.227 | 0.207 | 0.218 | 0.819 | 0.308 | 0.001 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 26 | 94 | 94 | 100 | 25 | 92 | 96 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 2.47 | 2.47 | 2.63 | 0.66 | 2.42 | 2.53 |
time (sec) |
N/A | 0.186 | 0.007 | 0.225 | 0.240 | 0.222 | 0.437 | 0.294 | 0.000 | 0.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 79 | 85 | 12 | 78 | 81 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 5.64 | 6.07 | 0.86 | 5.57 | 5.79 |
time (sec) |
N/A | 0.131 | 0.001 | 0.442 | 0.208 | 0.215 | 0.224 | 0.313 | 0.001 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 196 | 192 | 1418 | 1589 | 1776 | 703 | 1877 | 1299 |
N.S. |
1 | 1.00 | 0.97 | 0.95 | 7.02 | 7.87 | 8.79 | 3.48 | 9.29 | 6.43 |
time (sec) |
N/A | 0.396 | 0.054 | 0.344 | 0.287 | 0.268 | 8.345 | 0.327 | 0.006 | 1.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 213 | 223 | 1881 | 2264 | 2336 | 714 | 3377 | 1738 |
N.S. |
1 | 1.00 | 0.92 | 0.97 | 8.14 | 9.80 | 10.11 | 3.09 | 14.62 | 7.52 |
time (sec) |
N/A | 0.498 | 0.136 | 0.368 | 0.328 | 0.285 | 27.861 | 0.337 | 0.011 | 1.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 276 | 254 | 265 | 2399 | 3016 | 0 | 1029 | 4422 | 2224 |
N.S. |
1 | 1.00 | 0.92 | 0.96 | 8.69 | 10.93 | 0.00 | 3.73 | 16.02 | 8.06 |
time (sec) |
N/A | 0.583 | 0.111 | 0.387 | 0.420 | 0.307 | 0.000 | 0.313 | 0.014 | 2.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 217 | 121 | 259 | 338 | 335 | 641 | 359 | 137 |
N.S. |
1 | 1.00 | 1.39 | 0.78 | 1.66 | 2.17 | 2.15 | 4.11 | 2.30 | 0.88 |
time (sec) |
N/A | 0.280 | 0.108 | 0.515 | 0.197 | 0.220 | 0.940 | 0.301 | 0.001 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 154 | 100 | 181 | 245 | 243 | 470 | 255 | 112 |
N.S. |
1 | 1.00 | 1.19 | 0.78 | 1.40 | 1.90 | 1.88 | 3.64 | 1.98 | 0.87 |
time (sec) |
N/A | 0.256 | 0.081 | 0.268 | 0.198 | 0.221 | 0.897 | 0.324 | 0.001 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 102 | 78 | 118 | 164 | 167 | 322 | 168 | 87 |
N.S. |
1 | 1.00 | 1.02 | 0.78 | 1.18 | 1.64 | 1.67 | 3.22 | 1.68 | 0.87 |
time (sec) |
N/A | 0.221 | 0.062 | 0.266 | 0.202 | 0.218 | 0.785 | 0.338 | 0.001 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 61 | 54 | 68 | 99 | 105 | 200 | 98 | 68 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.96 | 1.39 | 1.48 | 2.82 | 1.38 | 0.96 |
time (sec) |
N/A | 0.195 | 0.037 | 0.239 | 0.218 | 0.225 | 0.728 | 0.294 | 0.000 | 0.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 30 | 27 | 33 | 46 | 51 | 100 | 44 | 29 |
N.S. |
1 | 1.00 | 0.71 | 0.64 | 0.79 | 1.10 | 1.21 | 2.38 | 1.05 | 0.69 |
time (sec) |
N/A | 0.172 | 0.021 | 0.251 | 0.191 | 0.218 | 0.532 | 0.307 | 0.001 | 0.044 |
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 | 16 | 16 | 16 | 13 | 12 | 12 | 12 | 12 | 16 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.131 | 0.002 | 0.219 | 0.190 | 0.215 | 0.017 | 0.306 | 0.000 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 62 | 58 | 0 | 143 | 78 | 62 | 51 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 2.31 | 1.26 | 1.00 | 0.82 | 0.81 |
time (sec) |
N/A | 0.197 | 0.076 | 0.724 | 0.000 | 0.236 | 1.789 | 0.283 | 0.001 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 69 | 58 | 0 | 232 | 0 | 72 | 129 | 61 |
N.S. |
1 | 1.00 | 0.99 | 0.83 | 0.00 | 3.31 | 0.00 | 1.03 | 1.84 | 0.87 |
time (sec) |
N/A | 0.182 | 0.168 | 0.714 | 0.000 | 0.232 | 0.000 | 0.287 | 0.001 | 0.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 108 | 99 | 87 | 0 | 456 | 0 | 126 | 301 | 135 |
N.S. |
1 | 0.98 | 0.90 | 0.79 | 0.00 | 4.15 | 0.00 | 1.15 | 2.74 | 1.23 |
time (sec) |
N/A | 0.207 | 0.372 | 0.507 | 0.000 | 0.239 | 0.000 | 0.296 | 0.001 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 154 | 131 | 118 | 0 | 785 | 0 | 207 | 536 | 207 |
N.S. |
1 | 1.05 | 0.90 | 0.81 | 0.00 | 5.38 | 0.00 | 1.42 | 3.67 | 1.42 |
time (sec) |
N/A | 0.230 | 0.570 | 0.528 | 0.000 | 0.243 | 0.000 | 0.296 | 0.003 | 0.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 200 | 170 | 170 | 0 | 1176 | 0 | 311 | 821 | 297 |
N.S. |
1 | 1.10 | 0.93 | 0.93 | 0.00 | 6.46 | 0.00 | 1.71 | 4.51 | 1.63 |
time (sec) |
N/A | 0.260 | 0.916 | 0.333 | 0.000 | 0.254 | 0.000 | 0.312 | 0.004 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 246 | 224 | 220 | 0 | 1673 | 0 | 432 | 1167 | 401 |
N.S. |
1 | 1.13 | 1.03 | 1.01 | 0.00 | 7.67 | 0.00 | 1.98 | 5.35 | 1.84 |
time (sec) |
N/A | 0.284 | 1.279 | 0.376 | 0.000 | 0.273 | 0.000 | 0.316 | 0.007 | 0.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 217 | 122 | 259 | 418 | 335 | 1084 | 451 | 137 |
N.S. |
1 | 1.00 | 1.37 | 0.77 | 1.64 | 2.65 | 2.12 | 6.86 | 2.85 | 0.87 |
time (sec) |
N/A | 0.262 | 0.122 | 0.289 | 0.200 | 0.220 | 0.988 | 0.319 | 0.002 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 154 | 100 | 181 | 311 | 243 | 807 | 330 | 112 |
N.S. |
1 | 1.00 | 1.19 | 0.78 | 1.40 | 2.41 | 1.88 | 6.26 | 2.56 | 0.87 |
time (sec) |
N/A | 0.236 | 0.086 | 0.270 | 0.189 | 0.219 | 0.930 | 0.326 | 0.001 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 102 | 78 | 118 | 216 | 167 | 566 | 226 | 87 |
N.S. |
1 | 1.00 | 1.02 | 0.78 | 1.18 | 2.16 | 1.67 | 5.66 | 2.26 | 0.87 |
time (sec) |
N/A | 0.222 | 0.066 | 0.261 | 0.190 | 0.231 | 0.831 | 0.312 | 0.001 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 61 | 54 | 68 | 137 | 105 | 360 | 139 | 68 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.96 | 1.93 | 1.48 | 5.07 | 1.96 | 0.96 |
time (sec) |
N/A | 0.191 | 0.042 | 0.261 | 0.203 | 0.223 | 0.718 | 0.316 | 0.001 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 30 | 27 | 33 | 69 | 146 | 192 | 68 | 29 |
N.S. |
1 | 1.00 | 0.71 | 0.64 | 0.79 | 1.64 | 3.48 | 4.57 | 1.62 | 0.69 |
time (sec) |
N/A | 0.165 | 0.024 | 0.254 | 0.208 | 0.224 | 0.223 | 0.302 | 0.000 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 28 | 12 | 58 | 27 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.75 | 0.75 | 3.62 | 1.69 | 0.75 |
time (sec) |
N/A | 0.128 | 0.002 | 0.222 | 0.196 | 0.219 | 0.018 | 0.293 | 0.000 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 91 | 77 | 88 | 0 | 188 | 105 | 105 | 119 | 93 |
N.S. |
1 | 1.06 | 0.90 | 1.02 | 0.00 | 2.19 | 1.22 | 1.22 | 1.38 | 1.08 |
time (sec) |
N/A | 0.199 | 0.135 | 0.733 | 0.000 | 0.233 | 1.320 | 0.314 | 0.001 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 92 | 83 | 93 | 0 | 210 | 0 | 113 | 127 | 109 |
N.S. |
1 | 1.08 | 0.98 | 1.09 | 0.00 | 2.47 | 0.00 | 1.33 | 1.49 | 1.28 |
time (sec) |
N/A | 0.195 | 0.219 | 0.552 | 0.000 | 0.247 | 0.000 | 0.305 | 0.001 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 102 | 90 | 79 | 0 | 383 | 0 | 108 | 259 | 135 |
N.S. |
1 | 1.02 | 0.90 | 0.79 | 0.00 | 3.83 | 0.00 | 1.08 | 2.59 | 1.35 |
time (sec) |
N/A | 0.189 | 0.322 | 0.287 | 0.000 | 0.241 | 0.000 | 0.310 | 0.001 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 140 | 129 | 119 | 0 | 666 | 0 | 185 | 470 | 209 |
N.S. |
1 | 1.03 | 0.95 | 0.88 | 0.00 | 4.90 | 0.00 | 1.36 | 3.46 | 1.54 |
time (sec) |
N/A | 0.212 | 0.534 | 0.306 | 0.000 | 0.249 | 0.000 | 0.340 | 0.003 | 0.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 186 | 171 | 145 | 0 | 1043 | 0 | 285 | 742 | 296 |
N.S. |
1 | 1.08 | 0.99 | 0.84 | 0.00 | 6.06 | 0.00 | 1.66 | 4.31 | 1.72 |
time (sec) |
N/A | 0.249 | 0.830 | 0.327 | 0.000 | 0.260 | 0.000 | 0.349 | 0.004 | 0.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 232 | 223 | 219 | 0 | 1492 | 0 | 410 | 1068 | 398 |
N.S. |
1 | 1.12 | 1.07 | 1.05 | 0.00 | 7.17 | 0.00 | 1.97 | 5.13 | 1.91 |
time (sec) |
N/A | 0.271 | 1.556 | 0.368 | 0.000 | 0.266 | 0.000 | 0.315 | 0.006 | 0.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 217 | 122 | 259 | 497 | 335 | 1599 | 543 | 137 |
N.S. |
1 | 1.00 | 1.37 | 0.77 | 1.64 | 3.15 | 2.12 | 10.12 | 3.44 | 0.87 |
time (sec) |
N/A | 0.269 | 0.127 | 0.816 | 0.198 | 0.226 | 1.156 | 0.335 | 0.002 | 0.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 154 | 100 | 181 | 377 | 243 | 1204 | 405 | 112 |
N.S. |
1 | 1.00 | 1.19 | 0.78 | 1.40 | 2.92 | 1.88 | 9.33 | 3.14 | 0.87 |
time (sec) |
N/A | 0.243 | 0.091 | 0.300 | 0.215 | 0.229 | 1.102 | 0.311 | 0.001 | 0.236 |