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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
  2.1.8 Mupad
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 155, 162, 181, 188, 191, 192, 193, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224 }

B grade: { }

C grade: { }

F grade: { 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198 }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 10, 12, 15, 16, 17, 18, 19, 20, 21, 22, 24, 28, 29, 30, 35, 36, 37, 38, 39, 42, 43, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 64, 65, 66, 67, 68, 69, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 155, 157, 158, 165, 166, 167, 169, 170, 171, 172, 173, 181, 184, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 198, 199, 200, 201, 202, 205, 206, 208, 209, 211, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224 }

B grade: { 151, 168, 174, 175, 176, 177, 178, 179, 180, 182, 183, 197, 207, 210 }

C grade: { 6, 7, 8, 9, 11, 13, 14, 23, 25, 26, 27, 31, 32, 33, 34, 40, 41, 44, 46, 47, 48, 49, 61, 62, 63, 70, 71, 72, 73, 74, 75, 76, 87, 113, 132, 133, 134, 135, 136, 137, 138, 139, 152, 154, 156, 159, 160, 161, 162, 163, 164, 188, 192, 203, 204, 212 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 29, 30, 31, 32, 40, 41, 42, 43, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 81, 82, 83, 84, 85, 86, 87, 88, 93, 94, 98, 100, 101, 102, 109, 115, 116, 117, 118, 119, 122, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 164, 191, 192, 193, 199, 200, 201, 202, 203, 204, 205, 206, 207, 211, 212, 217, 218, 219, 220, 221, 222, 223, 224 }

B grade: { 33, 34, 35, 36, 37, 38, 77, 78, 79, 80, 89, 90, 91, 92, 95, 96, 97, 99, 103, 104, 105, 106, 107, 108, 110, 111, 112, 114, 120, 121, 123, 124, 125, 126, 140, 141, 152, 154, 155, 156, 162, 181, 188, 213 }

C grade: { 163, 210, 214, 215, 216 }

F grade: { 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 113, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 208, 209 }

2.1.4 Maxima

A grade: { 18, 19, 20, 21, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 64, 65, 66, 67, 68, 69, 80, 81, 82, 85, 86, 89, 90, 91, 92, 93, 94, 97, 99, 102, 105, 106, 107, 108, 109, 110, 114, 116, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 181, 188, 211, 212, 213, 214, 215, 216, 220, 224 }

B grade: { 61, 62, 63, 77, 78, 79, 83, 84, 95, 96, 104, 111, 112, 191, 192, 193 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 70, 71, 72, 73, 74, 75, 76, 87, 88, 98, 100, 101, 103, 113, 115, 117, 118, 120, 132, 133, 134, 135, 136, 137, 138, 139, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 217, 218, 219, 221, 222, 223 }

2.1.5 FriCAS

A grade: { 9, 10, 46, 81, 85, 86, 91, 92, 93, 101, 107, 108, 118, 122, 143, 144, 145, 146, 151, 152, 153, 155, 156, 158, 163, 164, 213, 214, 218, 220, 222, 224 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 87, 88, 89, 90, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 147, 148, 149, 150, 154, 157, 159, 160, 161, 162, 181, 188, 191, 192, 193, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 219, 221, 223 }

C grade: { }

F grade: { 15, 16, 17, 27, 28, 39, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198 }

2.1.6 Sympy

A grade: { 34, 61, 62, 63, 64, 77, 78, 79, 80, 81, 85, 86, 144, 145, 146, 147, 148, 149, 162, 220, 224 }

B grade: { 65, 66, 67, 68, 69, 127, 128, 129, 130, 131, 155 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 70, 71, 72, 73, 74, 75, 76, 82, 83, 84, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223 }

2.1.7 Giac

A grade: { 18, 19, 21, 40, 41, 42, 43, 61, 62, 63, 64, 65, 66, 67, 68, 69, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 103, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 188, 192, 211, 212, 213, 214, 215, 216, 220, 224 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 20, 29, 30, 31, 32, 70, 71, 72, 73, 74, 75, 76, 95, 102, 104, 113, 119, 121, 132, 133, 134, 135, 136, 137, 138, 139, 150, 155, 181, 191, 193 }

C grade: { }

F grade: { 9, 10, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 87, 88, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 217, 218, 219, 221, 222, 223 }

2.1.8 Mupad

A grade: { 220, 224 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 181, 188, 191, 192, 193, 199, 200, 201, 202, 203, 204 }

C grade: { }

F grade: { 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 113, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 83 80 0 1574 0 379 83
normalized size 1 1.00 0.86 0.82 0.00 16.23 0.00 3.91 0.86
time (sec) N/A 0.070 0.238 0.129 0.000 0.469 0.000 0.421 1.580
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 68 63 0 988 0 224 62
normalized size 1 1.00 0.87 0.81 0.00 12.67 0.00 2.87 0.79
time (sec) N/A 0.049 0.222 0.113 0.000 0.466 0.000 0.356 1.372
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 61 62 0 637 0 168 61
normalized size 1 1.00 0.81 0.83 0.00 8.49 0.00 2.24 0.81
time (sec) N/A 0.050 0.093 0.133 0.000 0.439 0.000 0.255 1.275
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 51 47 0 594 0 101 41
normalized size 1 1.00 0.88 0.81 0.00 10.24 0.00 1.74 0.71
time (sec) N/A 0.036 0.041 0.128 0.000 0.436 0.000 0.191 1.215
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 49 46 0 598 0 102 38
normalized size 1 1.00 0.86 0.81 0.00 10.49 0.00 1.79 0.67
time (sec) N/A 0.031 0.035 0.125 0.000 0.428 0.000 0.277 1.294
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 36 65 0 923 0 196 64
normalized size 1 1.00 0.46 0.83 0.00 11.83 0.00 2.51 0.82
time (sec) N/A 0.051 0.077 0.101 0.000 0.437 0.000 0.585 1.390
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 38 64 0 1428 0 239 63
normalized size 1 1.00 0.48 0.81 0.00 18.08 0.00 3.03 0.80
time (sec) N/A 0.050 0.072 0.095 0.000 0.457 0.000 0.607 1.491
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 38 83 0 2132 0 359 80
normalized size 1 1.00 0.38 0.83 0.00 21.32 0.00 3.59 0.80
time (sec) N/A 0.071 0.100 0.104 0.000 0.487 0.000 0.634 1.596
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 236 236 36 209 0 292 0 0 249
normalized size 1 1.00 0.15 0.89 0.00 1.24 0.00 0.00 1.06
time (sec) N/A 0.282 0.027 0.110 0.000 0.437 0.000 0.000 1.881
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 218 218 149 193 0 310 0 0 233
normalized size 1 1.00 0.68 0.89 0.00 1.42 0.00 0.00 1.07
time (sec) N/A 0.294 0.186 0.108 0.000 0.431 0.000 0.000 1.499
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 38 115 0 291 0 217 146
normalized size 1 1.00 0.29 0.87 0.00 2.20 0.00 1.64 1.11
time (sec) N/A 0.109 0.043 0.102 0.000 0.406 0.000 0.370 1.516
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 98 115 0 1598 0 216 147
normalized size 1 1.00 0.74 0.87 0.00 12.11 0.00 1.64 1.11
time (sec) N/A 0.104 0.126 0.088 0.000 0.448 0.000 0.641 1.652
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 218 218 36 193 0 356 0 0 197
normalized size 1 1.00 0.17 0.89 0.00 1.63 0.00 0.00 0.90
time (sec) N/A 0.235 0.031 0.090 0.000 0.458 0.000 0.000 1.386
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 36 211 0 3348 0 0 165
normalized size 1 1.00 0.15 0.89 0.00 14.07 0.00 0.00 0.69
time (sec) N/A 0.316 0.061 0.095 0.000 0.514 0.000 0.000 1.419
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 45 0 0 0 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.068 0.443 0.000 0.417 0.000 0.000 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 51 0 0 0 0 0 -1
normalized size 1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.027 0.042 0.471 0.000 0.434 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 47 0 0 0 0 0 -1
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.040 0.051 0.627 0.000 0.439 0.000 0.000 0.000
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 56 53 97 823 0 90 -1
normalized size 1 1.00 0.92 0.87 1.59 13.49 0.00 1.48 -0.02
time (sec) N/A 0.037 0.129 0.154 0.466 0.435 0.000 0.180 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 39 45 54 125 0 54 -1
normalized size 1 1.00 1.26 1.45 1.74 4.03 0.00 1.74 -0.03
time (sec) N/A 0.020 0.047 0.156 0.468 0.423 0.000 0.122 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 52 34 128 0 60 30
normalized size 1 1.00 1.00 1.68 1.10 4.13 0.00 1.94 0.97
time (sec) N/A 0.020 0.063 0.158 0.434 0.415 0.000 0.149 1.264
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 48 79 84 817 0 104 -1
normalized size 1 1.00 0.74 1.22 1.29 12.57 0.00 1.60 -0.02
time (sec) N/A 0.036 0.150 0.125 0.429 0.454 0.000 0.731 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 297 297 166 0 0 1994 0 0 -1
normalized size 1 1.00 0.56 0.00 0.00 6.71 0.00 0.00 -0.00
time (sec) N/A 0.284 0.352 0.357 0.000 0.463 0.000 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 289 289 43 0 0 2037 0 0 -1
normalized size 1 1.00 0.15 0.00 0.00 7.05 0.00 0.00 -0.00
time (sec) N/A 0.180 0.041 0.337 0.000 0.466 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 264 264 151 0 0 1618 0 0 -1
normalized size 1 1.00 0.57 0.00 0.00 6.13 0.00 0.00 -0.00
time (sec) N/A 0.212 0.109 0.378 0.000 0.493 0.000 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 264 264 41 0 0 8338 0 0 -1
normalized size 1 1.00 0.16 0.00 0.00 31.58 0.00 0.00 -0.00
time (sec) N/A 0.169 0.056 0.395 0.000 0.616 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 289 289 41 0 0 2066 0 0 -1
normalized size 1 1.00 0.14 0.00 0.00 7.15 0.00 0.00 -0.00
time (sec) N/A 0.222 0.066 0.353 0.000 0.455 0.000 0.000 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 309 309 43 0 0 0 0 0 -1
normalized size 1 1.00 0.14 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.182 0.157 0.362 0.000 0.000 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 53 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.042 0.627 0.000 0.666 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 82 107 0 2152 0 788 -1
normalized size 1 1.00 0.61 0.80 0.00 16.06 0.00 5.88 -0.01
time (sec) N/A 0.060 0.531 0.203 0.000 1.815 0.000 0.650 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 63 89 0 633 0 269 -1
normalized size 1 1.00 0.61 0.86 0.00 6.09 0.00 2.59 -0.01
time (sec) N/A 0.047 0.103 0.167 0.000 1.587 0.000 0.286 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 41 92 0 907 0 279 -1
normalized size 1 1.00 0.39 0.88 0.00 8.64 0.00 2.66 -0.01
time (sec) N/A 0.048 0.032 0.157 0.000 1.211 0.000 0.500 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 43 106 0 3022 0 521 -1
normalized size 1 1.00 0.30 0.75 0.00 21.43 0.00 3.70 -0.01
time (sec) N/A 0.061 0.069 0.135 0.000 1.583 0.000 2.332 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 43 145 87 1046 0 0 -1
normalized size 1 1.00 0.58 1.96 1.18 14.14 0.00 0.00 -0.01
time (sec) N/A 0.034 0.065 0.400 0.417 1.448 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 41 119 34 392 90 0 -1
normalized size 1 1.00 0.82 2.38 0.68 7.84 1.80 0.00 -0.02
time (sec) N/A 0.024 0.033 0.396 0.418 0.657 23.764 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 39 192 51 148 0 0 -1
normalized size 1 1.00 1.26 6.19 1.65 4.77 0.00 0.00 -0.03
time (sec) N/A 0.020 0.029 0.385 0.513 0.568 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 192 32 187 0 0 -1
normalized size 1 1.00 1.00 6.19 1.03 6.03 0.00 0.00 -0.03
time (sec) N/A 0.020 0.031 0.414 0.827 1.534 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 40 119 37 287 0 0 -1
normalized size 1 1.00 0.80 2.38 0.74 5.74 0.00 0.00 -0.02
time (sec) N/A 0.024 0.064 0.395 1.055 0.596 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 51 149 89 1579 0 0 -1
normalized size 1 1.00 0.64 1.86 1.11 19.74 0.00 0.00 -0.01
time (sec) N/A 0.035 0.096 0.390 0.419 0.557 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 51 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.045 0.665 0.000 0.609 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 43 77 137 3421 0 77 -1
normalized size 1 1.00 0.39 0.70 1.25 31.10 0.00 0.70 -0.01
time (sec) N/A 0.045 0.067 0.165 0.425 0.908 0.000 0.179 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 41 55 34 415 0 27 -1
normalized size 1 1.00 0.82 1.10 0.68 8.30 0.00 0.54 -0.02
time (sec) N/A 0.023 0.035 0.157 0.416 1.097 0.000 0.155 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 40 59 36 422 0 32 -1
normalized size 1 1.00 0.80 1.18 0.72 8.44 0.00 0.64 -0.02
time (sec) N/A 0.023 0.071 0.180 0.424 1.301 0.000 0.151 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 68 84 155 3473 0 99 -1
normalized size 1 1.00 0.58 0.71 1.31 29.43 0.00 0.84 -0.01
time (sec) N/A 0.046 0.258 0.130 0.450 0.556 0.000 3.385 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 353 353 68 0 0 2864 0 0 -1
normalized size 1 1.00 0.19 0.00 0.00 8.11 0.00 0.00 -0.00
time (sec) N/A 0.196 0.143 0.367 0.000 1.325 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 166 0 0 618 0 0 -1
normalized size 1 1.00 0.57 0.00 0.00 2.12 0.00 0.00 -0.00
time (sec) N/A 0.215 0.416 0.370 0.000 1.793 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 289 289 43 0 0 288 0 0 -1
normalized size 1 1.00 0.15 0.00 0.00 1.00 0.00 0.00 -0.00
time (sec) N/A 0.176 0.028 0.371 0.000 3.085 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 289 289 41 0 0 3316 0 0 -1
normalized size 1 1.00 0.14 0.00 0.00 11.47 0.00 0.00 -0.00
time (sec) N/A 0.218 0.053 0.371 0.000 0.831 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 43 0 0 1159 0 0 -1
normalized size 1 1.00 0.15 0.00 0.00 3.98 0.00 0.00 -0.00
time (sec) N/A 0.185 0.055 0.379 0.000 0.485 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 369 369 43 0 0 0 0 0 -1
normalized size 1 1.00 0.12 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.245 0.044 0.380 0.000 0.000 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 55 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.042 0.052 5.401 0.000 0.424 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 58 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.045 0.077 1.567 0.000 0.000 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.041 0.041 0.551 0.000 0.000 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 58 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.049 0.662 0.000 0.000 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 58 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.048 0.069 0.566 0.000 0.000 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 60 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.045 0.073 0.391 0.000 0.000 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 60 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.043 0.044 0.418 0.000 0.000 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.044 0.041 0.394 0.000 0.000 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 58 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.043 0.041 0.451 0.000 0.000 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 60 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.045 0.042 0.457 0.000 0.000 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 60 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.070 0.423 0.000 0.000 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 94 31 140 448 48 41 88
normalized size 1 1.00 2.29 0.76 3.41 10.93 1.17 1.00 2.15
time (sec) N/A 0.039 0.249 0.012 0.326 0.395 1.223 0.112 1.126
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 84 25 95 273 37 35 60
normalized size 1 1.00 2.71 0.81 3.06 8.81 1.19 1.13 1.94
time (sec) N/A 0.031 0.187 0.013 0.322 0.405 0.915 0.110 1.144
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 61 19 55 142 31 29 36
normalized size 1 1.00 2.65 0.83 2.39 6.17 1.35 1.26 1.57
time (sec) N/A 0.021 0.155 0.011 0.316 0.391 0.682 0.112 0.041
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 13 19 53 22 21 20
normalized size 1 1.00 1.00 1.00 1.46 4.08 1.69 1.62 1.54
time (sec) N/A 0.013 0.005 0.013 0.308 0.413 0.369 0.127 1.143
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 24 10 26 27 10 14
normalized size 1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.88
time (sec) N/A 0.009 0.031 0.047 0.307 0.427 0.444 0.128 0.051
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 30 32 16 52 88 18 16
normalized size 1 1.00 1.15 1.23 0.62 2.00 3.38 0.69 0.62
time (sec) N/A 0.017 0.061 0.050 0.307 0.382 0.809 0.107 0.046
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 44 40 22 86 182 24 22
normalized size 1 1.00 1.22 1.11 0.61 2.39 5.06 0.67 0.61
time (sec) N/A 0.027 0.092 0.051 0.306 0.385 1.054 0.132 0.056
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 53 48 28 121 299 30 28
normalized size 1 1.00 1.15 1.04 0.61 2.63 6.50 0.65 0.61
time (sec) N/A 0.036 0.127 0.054 0.317 0.386 1.419 0.132 1.145
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 62 56 34 159 444 36 34
normalized size 1 1.00 1.11 1.00 0.61 2.84 7.93 0.64 0.61
time (sec) N/A 0.046 0.145 0.054 0.320 0.389 1.803 0.117 1.149
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 101 43 0 438 0 160 44
normalized size 1 1.00 1.77 0.75 0.00 7.68 0.00 2.81 0.77
time (sec) N/A 0.042 0.270 0.076 0.000 0.401 0.000 0.150 1.265
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 92 35 0 259 0 112 54
normalized size 1 1.00 2.04 0.78 0.00 5.76 0.00 2.49 1.20
time (sec) N/A 0.032 0.159 0.063 0.000 0.407 0.000 0.150 1.195
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 69 27 0 131 0 63 26
normalized size 1 1.00 2.09 0.82 0.00 3.97 0.00 1.91 0.79
time (sec) N/A 0.022 0.110 0.065 0.000 0.402 0.000 0.146 1.185
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 45 17 0 50 0 37 16
normalized size 1 1.00 2.14 0.81 0.00 2.38 0.00 1.76 0.76
time (sec) N/A 0.012 0.077 0.082 0.000 0.390 0.000 0.145 1.204
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 51 27 0 85 0 66 26
normalized size 1 1.00 1.59 0.84 0.00 2.66 0.00 2.06 0.81
time (sec) N/A 0.023 0.305 0.079 0.000 0.406 0.000 0.146 1.243
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 86 35 0 168 0 131 32
normalized size 1 1.00 1.76 0.71 0.00 3.43 0.00 2.67 0.65
time (sec) N/A 0.031 0.324 0.072 0.000 0.397 0.000 0.161 1.200
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 94 43 0 266 0 179 40
normalized size 1 1.00 1.54 0.70 0.00 4.36 0.00 2.93 0.66
time (sec) N/A 0.042 0.797 0.072 0.000 0.404 0.000 0.152 1.200
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 141 322 348 2748 325 226 244
normalized size 1 1.00 0.99 2.27 2.45 19.35 2.29 1.59 1.72
time (sec) N/A 0.209 0.818 0.016 0.331 0.456 13.420 0.167 1.282
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 109 246 219 1396 233 153 158
normalized size 1 1.00 1.08 2.44 2.17 13.82 2.31 1.51 1.56
time (sec) N/A 0.123 0.923 0.017 0.333 0.422 6.235 0.144 1.238
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 86 173 136 654 175 99 97
normalized size 1 1.00 1.25 2.51 1.97 9.48 2.54 1.43 1.41
time (sec) N/A 0.064 0.416 0.016 0.325 0.426 2.850 0.135 0.109
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 65 116 49 205 104 57 51
normalized size 1 1.00 1.71 3.05 1.29 5.39 2.74 1.50 1.34
time (sec) N/A 0.024 0.132 0.019 0.305 0.407 1.355 0.121 0.104
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 64 76 52 62 236 62 55
normalized size 1 1.00 1.28 1.52 1.04 1.24 4.72 1.24 1.10
time (sec) N/A 0.054 0.083 0.107 0.354 0.449 2.557 0.145 1.225
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 100 101 124 426 0 130 104
normalized size 1 1.00 1.18 1.19 1.46 5.01 0.00 1.53 1.22
time (sec) N/A 0.095 1.559 0.122 0.326 0.425 0.000 0.133 1.300
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 134 166 322 1431 0 203 195
normalized size 1 1.00 1.04 1.29 2.50 11.09 0.00 1.57 1.51
time (sec) N/A 0.180 3.621 0.124 0.342 0.436 0.000 0.179 1.399
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 214 230 522 3698 0 303 310
normalized size 1 1.00 1.27 1.36 3.09 21.88 0.00 1.79 1.83
time (sec) N/A 0.264 6.221 0.128 0.373 0.503 0.000 0.176 1.386
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 53 46 28 49 42 29 22
normalized size 1 1.00 1.71 1.48 0.90 1.58 1.35 0.94 0.71
time (sec) N/A 0.044 0.043 0.110 0.311 0.406 0.811 0.139 0.045
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 53 46 29 48 42 24 22
normalized size 1 1.00 1.71 1.48 0.94 1.55 1.35 0.77 0.71
time (sec) N/A 0.042 0.040 0.108 0.302 0.403 0.805 0.117 0.044
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 128 63 0 2231 0 0 151
normalized size 1 1.00 1.73 0.85 0.00 30.15 0.00 0.00 2.04
time (sec) N/A 0.070 3.285 0.194 0.000 0.509 0.000 0.000 1.408
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 73 62 0 2307 0 0 242
normalized size 1 1.00 0.99 0.84 0.00 31.18 0.00 0.00 3.27
time (sec) N/A 0.068 0.154 0.114 0.000 0.498 0.000 0.000 1.471
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 42 110 36 93 0 42 34
normalized size 1 1.00 0.70 1.83 0.60 1.55 0.00 0.70 0.57
time (sec) N/A 0.063 0.111 0.092 0.318 0.389 0.000 0.130 1.377
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 36 80 33 60 0 31 29
normalized size 1 1.00 1.24 2.76 1.14 2.07 0.00 1.07 1.00
time (sec) N/A 0.047 0.081 0.093 0.314 0.398 0.000 0.113 1.267
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 30 70 22 50 0 30 22
normalized size 1 1.00 0.79 1.84 0.58 1.32 0.00 0.79 0.58
time (sec) N/A 0.052 0.054 0.092 0.306 0.395 0.000 0.143 1.245
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 21 40 17 25 0 19 17
normalized size 1 1.00 1.11 2.11 0.89 1.32 0.00 1.00 0.89
time (sec) N/A 0.036 0.051 0.088 0.306 0.393 0.000 0.125 1.242
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 7 11 6 9 0 6 6
normalized size 1 1.00 0.70 1.10 0.60 0.90 0.00 0.60 0.60
time (sec) N/A 0.022 0.004 0.012 0.302 0.429 0.000 0.114 1.197
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 7 7 7 8 7 18 0 12 11
normalized size 1 1.00 1.00 1.14 1.00 2.57 0.00 1.71 1.57
time (sec) N/A 0.036 0.003 0.073 0.302 0.412 0.000 0.128 1.176
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 14 23 31 77 0 26 29
normalized size 1 1.00 1.75 2.88 3.88 9.62 0.00 3.25 3.62
time (sec) N/A 0.040 0.038 0.088 0.304 0.389 0.000 0.128 0.079
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 32 41 55 0 10 16
normalized size 1 1.00 1.00 2.91 3.73 5.00 0.00 0.91 1.45
time (sec) N/A 0.034 0.026 0.100 0.304 0.399 0.000 0.129 1.176
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 156 354 166 1279 0 229 143
normalized size 1 1.00 1.01 2.28 1.07 8.25 0.00 1.48 0.92
time (sec) N/A 0.240 0.294 0.132 0.320 0.428 0.000 0.129 1.629
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 171 197 0 1859 0 163 172
normalized size 1 1.00 1.28 1.47 0.00 13.87 0.00 1.22 1.28
time (sec) N/A 0.237 0.826 0.128 0.000 0.455 0.000 0.130 1.865
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 75 175 83 331 0 114 85
normalized size 1 1.00 0.82 1.90 0.90 3.60 0.00 1.24 0.92
time (sec) N/A 0.142 0.170 0.126 0.329 0.406 0.000 0.119 1.469
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 80 93 0 431 0 72 156
normalized size 1 1.00 1.10 1.27 0.00 5.90 0.00 0.99 2.14
time (sec) N/A 0.107 0.464 0.116 0.000 0.437 0.000 0.139 1.496
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 46 39 0 147 0 35 35
normalized size 1 1.00 1.21 1.03 0.00 3.87 0.00 0.92 0.92
time (sec) N/A 0.036 0.036 0.073 0.000 0.403 0.000 0.113 0.172
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 20 13 12 43 0 46 51
normalized size 1 1.00 1.67 1.08 1.00 3.58 0.00 3.83 4.25
time (sec) N/A 0.044 0.063 0.089 0.310 0.406 0.000 0.113 0.156
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 65 115 0 384 0 85 230
normalized size 1 1.00 1.14 2.02 0.00 6.74 0.00 1.49 4.04
time (sec) N/A 0.109 0.115 0.114 0.000 0.450 0.000 0.121 1.457
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 50 116 110 434 0 106 88
normalized size 1 1.00 1.25 2.90 2.75 10.85 0.00 2.65 2.20
time (sec) N/A 0.067 0.168 0.124 0.333 0.417 0.000 0.117 1.442
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 42 118 36 92 0 42 34
normalized size 1 1.00 0.70 1.97 0.60 1.53 0.00 0.70 0.57
time (sec) N/A 0.067 0.091 0.099 0.335 0.407 0.000 0.116 1.422
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 34 82 27 56 0 25 23
normalized size 1 1.00 1.36 3.28 1.08 2.24 0.00 1.00 0.92
time (sec) N/A 0.177 0.058 0.093 0.306 0.372 0.000 0.109 1.315
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 24 78 22 51 0 30 22
normalized size 1 1.00 0.63 2.05 0.58 1.34 0.00 0.79 0.58
time (sec) N/A 0.059 0.050 0.094 0.301 0.402 0.000 0.129 0.107
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 19 42 11 23 0 11 11
normalized size 1 1.00 1.12 2.47 0.65 1.35 0.00 0.65 0.65
time (sec) N/A 0.113 0.018 0.091 0.301 0.410 0.000 0.128 1.186
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 16 19 12 23 0 10 10
normalized size 1 1.00 1.60 1.90 1.20 2.30 0.00 1.00 1.00
time (sec) N/A 0.114 0.024 0.095 0.501 0.387 0.000 0.115 1.281
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 9 36 18 78 0 27 21
normalized size 1 1.00 0.60 2.40 1.20 5.20 0.00 1.80 1.40
time (sec) N/A 0.041 0.032 0.106 0.404 0.415 0.000 0.110 1.189
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 45 33 140 0 25 22
normalized size 1 1.00 1.00 2.25 1.65 7.00 0.00 1.25 1.10
time (sec) N/A 0.167 0.040 0.106 0.416 0.380 0.000 0.116 1.255
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 38 75 84 0 18 18
normalized size 1 1.00 1.00 2.24 4.41 4.94 0.00 1.06 1.06
time (sec) N/A 0.045 0.052 0.105 0.302 0.367 0.000 0.111 0.074
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 160 0 0 231 0 149 -1
normalized size 1 1.00 7.62 0.00 0.00 11.00 0.00 7.10 -0.05
time (sec) N/A 0.046 5.271 0.378 0.000 0.435 0.000 0.130 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 144 319 154 1229 0 216 135
normalized size 1 1.00 0.98 2.17 1.05 8.36 0.00 1.47 0.92
time (sec) N/A 0.339 0.570 0.132 0.335 0.425 0.000 0.120 1.743
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 167 200 0 1873 0 164 262
normalized size 1 1.00 1.24 1.48 0.00 13.87 0.00 1.21 1.94
time (sec) N/A 0.251 1.483 0.131 0.000 0.444 0.000 0.141 2.044
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 73 146 80 334 0 104 82
normalized size 1 1.00 0.86 1.72 0.94 3.93 0.00 1.22 0.96
time (sec) N/A 0.164 0.258 0.125 0.325 0.410 0.000 0.116 1.398
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 79 92 0 431 0 71 158
normalized size 1 1.00 1.10 1.28 0.00 5.99 0.00 0.99 2.19
time (sec) N/A 0.112 0.308 0.117 0.000 0.423 0.000 0.119 1.529
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 60 54 0 200 0 48 164
normalized size 1 1.00 1.20 1.08 0.00 4.00 0.00 0.96 3.28
time (sec) N/A 0.138 0.123 0.125 0.000 0.464 0.000 0.117 3.223
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 27 59 46 117 0 76 323
normalized size 1 1.00 0.93 2.03 1.59 4.03 0.00 2.62 11.14
time (sec) N/A 0.055 0.097 0.135 0.420 0.437 0.000 0.134 1.584
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 85 187 0 856 0 102 166
normalized size 1 1.00 1.02 2.25 0.00 10.31 0.00 1.23 2.00
time (sec) N/A 0.237 0.200 0.175 0.000 0.469 0.000 0.124 3.938
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 68 257 133 909 0 201 123
normalized size 1 1.00 0.86 3.25 1.68 11.51 0.00 2.54 1.56
time (sec) N/A 0.100 0.309 0.155 0.414 0.422 0.000 0.126 1.450
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 38 41 42 41 0 26 65
normalized size 1 1.00 1.23 1.32 1.35 1.32 0.00 0.84 2.10
time (sec) N/A 0.103 0.053 0.173 0.428 0.415 0.000 0.127 0.513
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 40 96 55 571 0 47 69
normalized size 1 1.00 0.93 2.23 1.28 13.28 0.00 1.09 1.60
time (sec) N/A 0.115 0.101 0.110 0.408 0.422 0.000 0.131 1.303
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 33 80 43 354 0 39 35
normalized size 1 1.00 0.89 2.16 1.16 9.57 0.00 1.05 0.95
time (sec) N/A 0.099 0.056 0.108 0.408 0.410 0.000 0.128 1.206
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 27 65 29 186 0 35 29
normalized size 1 1.00 0.93 2.24 1.00 6.41 0.00 1.21 1.00
time (sec) N/A 0.074 0.049 0.097 0.421 0.437 0.000 0.117 1.216
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 23 47 17 73 0 17 17
normalized size 1 1.00 1.21 2.47 0.89 3.84 0.00 0.89 0.89
time (sec) N/A 0.042 0.029 0.100 0.416 0.407 0.000 0.126 1.170
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 24 10 26 27 10 14
normalized size 1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.88
time (sec) N/A 0.008 0.027 0.049 0.307 0.408 0.445 0.127 0.002
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 24 10 26 27 10 12
normalized size 1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.75
time (sec) N/A 0.022 0.017 0.050 0.305 0.397 0.479 0.127 0.049
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 23 24 24 73 92 18 21
normalized size 1 1.00 1.21 1.26 1.26 3.84 4.84 0.95 1.11
time (sec) N/A 0.038 0.028 0.051 0.304 0.418 0.621 0.117 0.059
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 28 38 196 160 36 21
normalized size 1 1.00 0.87 0.90 1.23 6.32 5.16 1.16 0.68
time (sec) N/A 0.055 0.043 0.058 0.354 0.422 0.934 0.118 1.164
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 33 32 54 357 197 40 29
normalized size 1 1.00 0.89 0.86 1.46 9.65 5.32 1.08 0.78
time (sec) N/A 0.068 0.060 0.067 0.307 0.410 1.183 0.134 0.066
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 90 35 0 259 0 135 34
normalized size 1 1.00 2.00 0.78 0.00 5.76 0.00 3.00 0.76
time (sec) N/A 0.052 0.139 0.050 0.000 0.387 0.000 0.151 1.238
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 53 26 0 131 0 71 25
normalized size 1 1.00 1.66 0.81 0.00 4.09 0.00 2.22 0.78
time (sec) N/A 0.038 0.122 0.061 0.000 0.397 0.000 0.159 1.197
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 97 25 0 85 0 88 24
normalized size 1 1.00 3.23 0.83 0.00 2.83 0.00 2.93 0.80
time (sec) N/A 0.039 0.199 0.077 0.000 0.396 0.000 0.173 1.230
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 84 35 0 166 0 107 32
normalized size 1 1.00 1.71 0.71 0.00 3.39 0.00 2.18 0.65
time (sec) N/A 0.051 0.348 0.077 0.000 0.403 0.000 0.217 1.218
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 70 35 0 436 0 197 34
normalized size 1 1.00 1.56 0.78 0.00 9.69 0.00 4.38 0.76
time (sec) N/A 0.063 0.263 0.066 0.000 0.404 0.000 0.174 1.248
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 61 26 0 242 0 133 25
normalized size 1 1.00 1.79 0.76 0.00 7.12 0.00 3.91 0.74
time (sec) N/A 0.048 0.180 0.076 0.000 0.398 0.000 0.159 1.195
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 81 35 0 189 0 88 36
normalized size 1 1.00 1.93 0.83 0.00 4.50 0.00 2.10 0.86
time (sec) N/A 0.059 0.374 0.089 0.000 0.403 0.000 0.177 1.256
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 86 35 0 166 0 135 31
normalized size 1 1.00 1.76 0.71 0.00 3.39 0.00 2.76 0.63
time (sec) N/A 0.082 0.367 0.075 0.000 0.410 0.000 0.186 1.232
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 105 283 146 1294 0 141 163
normalized size 1 1.00 1.08 2.92 1.51 13.34 0.00 1.45 1.68
time (sec) N/A 0.525 0.358 0.151 0.414 0.453 0.000 0.143 1.612
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 88 167 94 637 0 97 111
normalized size 1 1.00 1.16 2.20 1.24 8.38 0.00 1.28 1.46
time (sec) N/A 0.326 0.326 0.144 0.411 0.435 0.000 0.119 1.511
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 64 110 67 264 0 74 73
normalized size 1 1.00 1.07 1.83 1.12 4.40 0.00 1.23 1.22
time (sec) N/A 0.193 0.145 0.139 0.464 0.440 0.000 0.116 1.450
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 46 88 50 73 0 57 58
normalized size 1 1.00 0.90 1.73 0.98 1.43 0.00 1.12 1.14
time (sec) N/A 0.082 0.094 0.121 0.420 0.454 0.000 0.133 0.324
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 29 55 37 42 148 43 42
normalized size 1 1.00 0.74 1.41 0.95 1.08 3.79 1.10 1.08
time (sec) N/A 0.046 0.062 0.048 0.300 0.402 0.911 0.112 0.084
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 29 55 36 43 134 43 42
normalized size 1 1.00 0.74 1.41 0.92 1.10 3.44 1.10 1.08
time (sec) N/A 0.058 0.059 0.049 0.631 0.439 0.927 0.111 0.064
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 49 60 63 76 372 59 57
normalized size 1 1.00 0.78 0.95 1.00 1.21 5.90 0.94 0.90
time (sec) N/A 0.092 0.087 0.054 0.650 0.440 1.630 0.133 1.480
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 64 67 82 271 636 76 74
normalized size 1 1.00 1.00 1.05 1.28 4.23 9.94 1.19 1.16
time (sec) N/A 0.130 0.137 0.073 0.313 0.446 2.398 0.118 1.509
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 88 76 119 648 882 100 110
normalized size 1 1.00 1.16 1.00 1.57 8.53 11.61 1.32 1.45
time (sec) N/A 0.221 0.229 0.063 0.984 0.450 3.399 0.140 1.627
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 108 96 169 1299 1013 143 164
normalized size 1 1.00 1.15 1.02 1.80 13.82 10.78 1.52 1.74
time (sec) N/A 0.392 0.322 0.079 0.525 0.457 5.020 0.118 1.631
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 49 73 68 184 0 169 68
normalized size 1 1.00 0.91 1.35 1.26 3.41 0.00 3.13 1.26
time (sec) N/A 0.085 0.178 0.303 0.915 0.403 0.000 0.154 1.282
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B A A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 30 0 64 24 36 28 0 24 23
normalized size 1 0.00 2.13 0.80 1.20 0.93 0.00 0.80 0.77
time (sec) N/A 0.029 0.031 0.104 0.381 0.388 0.000 0.126 1.251
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C B A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 45 0 64 83 48 62 0 54 39
normalized size 1 0.00 1.42 1.84 1.07 1.38 0.00 1.20 0.87
time (sec) N/A 0.021 0.242 0.148 1.074 0.402 0.000 0.138 1.213
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A A A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 23 0 26 37 36 33 0 37 25
normalized size 1 0.00 1.13 1.61 1.57 1.43 0.00 1.61 1.09
time (sec) N/A 0.016 0.188 0.109 0.307 0.429 0.000 0.138 1.226
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C B A B F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 40 0 58 71 45 58 0 51 36
normalized size 1 0.00 1.45 1.78 1.12 1.45 0.00 1.28 0.90
time (sec) N/A 0.007 0.187 0.140 0.596 0.407 0.000 0.138 1.186
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 21 26 10 18 27 21 18
normalized size 1 1.00 1.75 2.17 0.83 1.50 2.25 1.75 1.50
time (sec) N/A 0.014 0.030 0.014 0.300 0.424 0.976 0.133 1.212
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C B A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 41 0 62 93 47 54 0 52 37
normalized size 1 0.00 1.51 2.27 1.15 1.32 0.00 1.27 0.90
time (sec) N/A 0.022 0.172 0.126 1.218 0.418 0.000 0.135 1.205
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A A A B F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 21 0 27 35 30 38 0 33 25
normalized size 1 0.00 1.29 1.67 1.43 1.81 0.00 1.57 1.19
time (sec) N/A 0.021 0.163 0.099 0.499 0.407 0.000 0.133 1.214
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A A A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 47 0 86 41 53 61 0 40 40
normalized size 1 0.00 1.83 0.87 1.13 1.30 0.00 0.85 0.85
time (sec) N/A 0.066 0.110 0.096 0.328 0.389 0.000 0.109 1.247
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C A A B F A B
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 68 0 154 100 66 104 0 72 60
normalized size 1 0.00 2.26 1.47 0.97 1.53 0.00 1.06 0.88
time (sec) N/A 0.048 2.945 0.125 0.419 0.414 0.000 0.112 1.237
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C A A B F A B
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 41 0 163 54 53 74 0 54 42
normalized size 1 0.00 3.98 1.32 1.29 1.80 0.00 1.32 1.02
time (sec) N/A 0.030 3.065 0.091 0.316 0.401 0.000 0.132 1.226
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C A A B F A B
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 60 0 153 86 60 97 0 66 54
normalized size 1 0.00 2.55 1.43 1.00 1.62 0.00 1.10 0.90
time (sec) N/A 0.010 2.239 0.128 0.416 0.408 0.000 0.138 1.205
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 28 35 19 28 32 21 28
normalized size 1 1.00 2.00 2.50 1.36 2.00 2.29 1.50 2.00
time (sec) N/A 0.024 0.054 0.014 0.311 0.432 7.362 0.125 1.188
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C C A A F A B
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 86 0 153 114 69 97 0 77 60
normalized size 1 0.00 1.78 1.33 0.80 1.13 0.00 0.90 0.70
time (sec) N/A 0.045 2.851 0.128 0.415 0.413 0.000 0.115 1.212
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C A A A F A B
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 60 0 155 55 50 82 0 57 48
normalized size 1 0.00 2.58 0.92 0.83 1.37 0.00 0.95 0.80
time (sec) N/A 0.046 3.250 0.086 0.332 0.396 0.000 0.138 1.230
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 59 0 46 0 0 0 0 0 -1
normalized size 1 0.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.102 0.108 0.000 0.405 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 79 0 77 0 0 0 0 0 -1
normalized size 1 0.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.068 0.177 0.092 0.000 0.404 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 177 0 108 0 0 0 0 0 -1
normalized size 1 0.00 0.61 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.233 0.149 0.000 0.399 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 79 0 259 0 0 0 0 0 -1
normalized size 1 0.00 3.28 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.022 2.058 0.270 0.000 0.407 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 99 0 126 0 0 0 0 0 -1
normalized size 1 0.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.116 3.230 0.114 0.000 0.407 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 52 0 83 0 0 0 0 0 -1
normalized size 1 0.00 1.60 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.046 0.432 0.138 0.000 0.409 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 108 0 125 0 0 0 0 0 -1
normalized size 1 0.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.051 0.560 0.162 0.000 0.442 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 162 0 142 0 0 0 0 0 -1
normalized size 1 0.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.050 0.599 0.154 0.000 0.857 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 194 0 223 0 0 0 0 0 -1
normalized size 1 0.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.051 0.947 0.153 0.000 1.749 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0 -1
normalized size 1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.015 1.757 0.176 0.000 0.415 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0 -1
normalized size 1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.011 1.949 0.209 0.000 0.406 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0 -1
normalized size 1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.018 2.009 0.188 0.000 0.422 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 58 0 198 0 0 0 0 0 -1
normalized size 1 0.00 3.41 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 7.164 1.252 0.000 0.403 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 62 0 207 0 0 0 0 0 -1
normalized size 1 0.00 3.34 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.030 4.999 1.147 0.000 0.437 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 54 0 193 0 0 0 0 0 -1
normalized size 1 0.00 3.57 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.024 6.986 1.140 0.000 0.442 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 52 0 198 0 0 0 0 0 -1
normalized size 1 0.00 3.81 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.011 8.363 1.013 0.000 0.402 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 40 56 24 76 0 74 34
normalized size 1 1.00 1.60 2.24 0.96 3.04 0.00 2.96 1.36
time (sec) N/A 0.021 0.066 0.016 0.313 0.415 0.000 0.307 1.193
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 58 0 197 0 0 0 0 0 -1
normalized size 1 0.00 3.40 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.031 3.793 1.094 0.000 0.411 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 55 0 191 0 0 0 0 0 -1
normalized size 1 0.00 3.47 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.030 3.763 1.133 0.000 0.415 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 132 0 155 0 0 0 0 0 -1
normalized size 1 0.00 1.17 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.086 6.724 1.159 0.000 0.411 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 136 0 165 0 0 0 0 0 -1
normalized size 1 0.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 4.623 1.117 0.000 0.422 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 130 0 151 0 0 0 0 0 -1
normalized size 1 0.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.043 6.625 1.118 0.000 0.412 0.000 0.000 0.000
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 126 0 160 0 0 0 0 0 -1
normalized size 1 0.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.014 7.879 1.092 0.000 0.417 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 49 80 37 72 0 37 34
normalized size 1 1.00 1.75 2.86 1.32 2.57 0.00 1.32 1.21
time (sec) N/A 0.029 0.107 0.018 0.828 0.431 0.000 0.302 1.189
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 134 0 158 0 0 0 0 0 -1
normalized size 1 0.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.051 3.630 1.125 0.000 0.416 0.000 0.000 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F(-1) F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 135 0 156 0 0 0 0 0 -1
normalized size 1 0.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.053 3.593 1.152 0.000 0.535 0.000 0.000 0.000
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 52 67 330 572 0 127 95
normalized size 1 1.00 1.21 1.56 7.67 13.30 0.00 2.95 2.21
time (sec) N/A 0.040 0.217 0.023 0.429 0.632 0.000 0.296 1.225
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 44 86 499 171 0 67 163
normalized size 1 1.00 0.98 1.91 11.09 3.80 0.00 1.49 3.62
time (sec) N/A 0.037 0.118 0.021 0.453 0.512 0.000 0.314 1.208
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 67 88 855 1576 0 161 229
normalized size 1 1.00 1.02 1.33 12.95 23.88 0.00 2.44 3.47
time (sec) N/A 0.057 0.289 0.021 0.500 0.423 0.000 0.336 1.199
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 87 0 158 0 0 0 0 0 -1
normalized size 1 0.00 1.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.046 13.477 1.582 0.000 0.528 0.000 0.000 0.000
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 168 0 312 0 0 0 0 0 -1
normalized size 1 0.00 1.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 14.881 1.560 0.000 0.575 0.000 0.000 0.000
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 306 0 600 0 0 0 0 0 -1
normalized size 1 0.00 1.96 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.069 16.828 1.688 0.000 0.464 0.000 0.000 0.000
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 115 0 387 0 0 0 0 0 -1
normalized size 1 0.00 3.37 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.015 3.973 0.281 0.000 0.403 0.000 0.000 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F(-1) F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 135 0 174 0 0 0 0 0 -1
normalized size 1 0.00 1.29 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.097 5.420 0.260 0.000 0.431 0.000 0.000 0.000
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 64 93 0 626 0 0 65
normalized size 1 1.00 0.88 1.27 0.00 8.58 0.00 0.00 0.89
time (sec) N/A 0.051 0.287 0.222 0.000 0.454 0.000 0.000 2.241
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 57 92 0 334 0 0 51
normalized size 1 1.00 0.81 1.31 0.00 4.77 0.00 0.00 0.73
time (sec) N/A 0.050 0.149 0.127 0.000 0.473 0.000 0.000 1.860
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 48 72 0 305 0 0 39
normalized size 1 1.00 1.00 1.50 0.00 6.35 0.00 0.00 0.81
time (sec) N/A 0.039 0.079 0.129 0.000 0.450 0.000 0.000 1.505
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 44 0 303 0 0 36
normalized size 1 1.00 1.00 0.94 0.00 6.45 0.00 0.00 0.77
time (sec) N/A 0.040 0.115 0.137 0.000 0.490 0.000 0.000 1.644
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 44 93 0 625 0 0 65
normalized size 1 1.00 0.62 1.31 0.00 8.80 0.00 0.00 0.92
time (sec) N/A 0.052 0.152 0.138 0.000 0.460 0.000 0.000 1.742
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F(-1) F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 46 92 0 1104 0 0 64
normalized size 1 1.00 0.64 1.28 0.00 15.33 0.00 0.00 0.89
time (sec) N/A 0.051 0.206 0.136 0.000 0.525 0.000 0.000 2.391
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 266 149 0 8951 0 0 -1
normalized size 1 1.00 1.97 1.10 0.00 66.30 0.00 0.00 -0.01
time (sec) N/A 0.353 9.076 0.225 0.000 2.028 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 199 90 0 6695 0 0 -1
normalized size 1 1.00 1.90 0.86 0.00 63.76 0.00 0.00 -0.01
time (sec) N/A 0.217 26.602 0.197 0.000 1.416 0.000 0.000 0.000
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 141 52 0 1752 0 0 -1
normalized size 1 1.00 2.43 0.90 0.00 30.21 0.00 0.00 -0.02
time (sec) N/A 0.117 18.601 0.158 0.000 1.097 0.000 0.000 0.000
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 203 0 0 6705 0 0 -1
normalized size 1 1.00 1.92 0.00 0.00 63.25 0.00 0.00 -0.01
time (sec) N/A 0.240 7.737 0.656 0.000 1.395 0.000 0.000 0.000
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 278 0 0 9148 0 0 -1
normalized size 1 1.00 1.52 0.00 0.00 49.99 0.00 0.00 -0.01
time (sec) N/A 0.332 11.079 0.626 0.000 1.920 0.000 0.000 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 304 559 0 7964 0 0 -1
normalized size 1 1.00 2.30 4.23 0.00 60.33 0.00 0.00 -0.01
time (sec) N/A 0.231 8.419 0.153 0.000 2.308 0.000 0.000 0.000
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 319 319 164 320 167 1617 0 181 -1
normalized size 1 1.00 0.51 1.00 0.52 5.07 0.00 0.57 -0.00
time (sec) N/A 0.912 10.276 0.982 0.428 0.440 0.000 1.067 0.000
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F(-1) A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 197 197 334 298 112 613 0 155 -1
normalized size 1 1.00 1.70 1.51 0.57 3.11 0.00 0.79 -0.01
time (sec) N/A 0.284 3.818 0.848 0.424 0.406 0.000 0.988 0.000
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 51 213 56 70 0 94 -1
normalized size 1 1.00 0.61 2.57 0.67 0.84 0.00 1.13 -0.01
time (sec) N/A 0.144 0.062 0.976 0.423 0.408 0.000 0.370 0.000
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 51 218 35 53 0 60 -1
normalized size 1 1.00 0.61 2.63 0.42 0.64 0.00 0.72 -0.01
time (sec) N/A 0.194 0.126 0.931 0.427 0.392 0.000 1.329 0.000
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 104 301 90 458 0 130 -1
normalized size 1 1.00 0.54 1.56 0.47 2.37 0.00 0.67 -0.01
time (sec) N/A 0.864 0.306 0.877 0.420 0.426 0.000 0.332 0.000
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 311 311 133 324 145 1226 0 185 -1
normalized size 1 1.00 0.43 1.04 0.47 3.94 0.00 0.59 -0.00
time (sec) N/A 1.743 0.482 0.873 0.421 0.491 0.000 0.688 0.000
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 124 118 0 296 0 0 -1
normalized size 1 1.00 0.79 0.75 0.00 1.89 0.00 0.00 -0.01
time (sec) N/A 0.375 0.263 0.134 0.000 0.437 0.000 0.000 0.000
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 88 102 0 155 0 0 -1
normalized size 1 1.00 0.77 0.89 0.00 1.35 0.00 0.00 -0.01
time (sec) N/A 0.262 0.174 0.139 0.000 0.476 0.000 0.000 0.000
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 59 58 0 149 0 0 -1
normalized size 1 1.00 0.77 0.75 0.00 1.94 0.00 0.00 -0.01
time (sec) N/A 0.144 0.137 0.132 0.000 0.439 0.000 0.000 0.000
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 67 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 3.546 0.582 0.000 0.443 0.000 0.000 0.000
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 124 118 0 298 0 0 -1
normalized size 1 1.00 0.79 0.75 0.00 1.90 0.00 0.00 -0.01
time (sec) N/A 0.373 0.261 0.143 0.000 0.482 0.000 0.000 0.000
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 88 102 0 155 0 0 -1
normalized size 1 1.00 0.77 0.89 0.00 1.35 0.00 0.00 -0.01
time (sec) N/A 0.251 0.180 0.137 0.000 0.459 0.000 0.000 0.000
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 62 58 0 151 0 0 -1
normalized size 1 1.00 0.81 0.75 0.00 1.96 0.00 0.00 -0.01
time (sec) N/A 0.140 0.114 0.143 0.000 0.468 0.000 0.000 0.000
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 67 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 6.631 0.506 0.000 0.423 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [109] had the largest ratio of [.7778]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 7 6 1.00 12 0.500
2 A 6 6 1.00 12 0.500
3 A 6 6 1.00 12 0.500
4 A 5 5 1.00 12 0.417
5 A 5 5 1.00 12 0.417
6 A 6 6 1.00 12 0.500
7 A 6 6 1.00 12 0.500
8 A 7 6 1.00 12 0.500
9 A 13 9 1.00 12 0.750
10 A 12 8 1.00 12 0.667
11 A 9 9 1.00 12 0.750
12 A 9 9 1.00 12 0.750
13 A 12 8 1.00 12 0.667
14 A 13 9 1.00 12 0.750
15 A 2 2 1.00 8 0.250
16 A 2 2 1.00 10 0.200
17 A 3 3 1.00 12 0.250
18 A 3 3 1.00 14 0.214
19 A 2 2 1.00 14 0.143
20 A 2 2 1.00 14 0.143
21 A 3 3 1.00 14 0.214
22 A 14 10 1.00 14 0.714
23 A 14 10 1.00 14 0.714
24 A 13 9 1.00 14 0.643
25 A 13 9 1.00 14 0.643
26 A 14 10 1.00 14 0.714
27 A 14 10 1.00 14 0.714
28 A 3 3 1.00 12 0.250
29 A 8 7 1.00 14 0.500
30 A 7 7 1.00 14 0.500
31 A 7 7 1.00 14 0.500
32 A 8 7 1.00 14 0.500
33 A 4 3 1.00 14 0.214
34 A 3 3 1.00 14 0.214
35 A 2 2 1.00 14 0.143
36 A 2 2 1.00 14 0.143
37 A 3 3 1.00 14 0.214
38 A 4 3 1.00 14 0.214
39 A 3 3 1.00 12 0.250
40 A 5 3 1.00 14 0.214
41 A 3 3 1.00 14 0.214
42 A 3 3 1.00 14 0.214
43 A 5 3 1.00 14 0.214
44 A 16 10 1.00 14 0.714
45 A 14 10 1.00 14 0.714
46 A 14 10 1.00 14 0.714
47 A 14 10 1.00 14 0.714
48 A 14 10 1.00 14 0.714
49 A 16 10 1.00 14 0.714
50 A 3 3 1.00 12 0.250
51 A 3 3 1.00 14 0.214
52 A 3 3 1.00 14 0.214
53 A 3 3 1.00 14 0.214
54 A 3 3 1.00 14 0.214
55 A 3 3 1.00 14 0.214
56 A 3 3 1.00 14 0.214
57 A 3 3 1.00 14 0.214
58 A 3 3 1.00 14 0.214
59 A 3 3 1.00 14 0.214
60 A 3 3 1.00 14 0.214
61 A 5 3 1.00 6 0.500
62 A 4 3 1.00 6 0.500
63 A 3 3 1.00 6 0.500
64 A 2 2 1.00 6 0.333
65 A 2 2 1.00 6 0.333
66 A 3 2 1.00 6 0.333
67 A 4 2 1.00 6 0.333
68 A 5 2 1.00 6 0.333
69 A 6 2 1.00 6 0.333
70 A 5 3 1.00 8 0.375
71 A 4 3 1.00 8 0.375
72 A 3 3 1.00 8 0.375
73 A 2 2 1.00 8 0.250
74 A 3 3 1.00 8 0.375
75 A 4 3 1.00 8 0.375
76 A 5 3 1.00 8 0.375
77 A 5 4 1.00 12 0.333
78 A 4 4 1.00 12 0.333
79 A 3 3 1.00 12 0.250
80 A 2 2 1.00 12 0.167
81 A 2 2 1.00 12 0.167
82 A 3 3 1.00 12 0.250
83 A 4 4 1.00 12 0.333
84 A 5 4 1.00 12 0.333
85 A 2 2 1.00 12 0.167
86 A 2 2 1.00 12 0.167
87 A 5 4 1.00 14 0.286
88 A 5 4 1.00 14 0.286
89 A 4 3 1.00 11 0.273
90 A 3 2 1.00 11 0.182
91 A 4 3 1.00 11 0.273
92 A 2 2 1.00 9 0.222
93 A 1 1 1.00 9 0.111
94 A 2 2 1.00 11 0.182
95 A 2 2 1.00 11 0.182
96 A 2 1 1.00 11 0.091
97 A 5 4 1.00 13 0.308
98 A 9 6 1.00 13 0.462
99 A 4 3 1.00 13 0.231
100 A 5 5 1.00 11 0.454
101 A 2 2 1.00 11 0.182
102 A 2 2 1.00 13 0.154
103 A 5 5 1.00 13 0.385
104 A 3 2 1.00 13 0.154
105 A 5 4 1.00 11 0.364
106 A 9 7 1.00 11 0.636
107 A 5 4 1.00 11 0.364
108 A 8 6 1.00 9 0.667
109 A 8 7 1.00 9 0.778
110 A 3 2 1.00 11 0.182
111 A 8 7 1.00 11 0.636
112 A 4 3 1.00 11 0.273
113 A 4 4 1.00 13 0.308
114 A 5 3 1.00 13 0.231
115 A 10 9 1.00 13 0.692
116 A 4 3 1.00 13 0.231
117 A 6 6 1.00 11 0.546
118 A 6 5 1.00 11 0.454
119 A 3 2 1.00 13 0.154
120 A 9 7 1.00 13 0.538
121 A 3 2 1.00 13 0.154
122 A 6 5 1.00 13 0.385
123 A 6 4 1.00 11 0.364
124 A 5 4 1.00 11 0.364
125 A 4 4 1.00 11 0.364
126 A 4 4 1.00 9 0.444
127 A 2 2 1.00 6 0.333
128 A 2 2 1.00 9 0.222
129 A 3 2 1.00 11 0.182
130 A 3 3 1.00 11 0.273
131 A 4 4 1.00 11 0.364
132 A 4 4 1.00 11 0.364
133 A 3 3 1.00 11 0.273
134 A 3 3 1.00 11 0.273
135 A 4 4 1.00 11 0.364
136 A 4 4 1.00 13 0.308
137 A 3 3 1.00 13 0.231
138 A 4 4 1.00 13 0.308
139 A 4 4 1.00 13 0.308
140 A 6 6 1.00 13 0.462
141 A 5 5 1.00 13 0.385
142 A 4 4 1.00 13 0.308
143 A 3 3 1.00 11 0.273
144 A 2 2 1.00 8 0.250
145 A 2 2 1.00 11 0.182
146 A 4 4 1.00 13 0.308
147 A 5 5 1.00 13 0.385
148 A 6 6 1.00 13 0.462
149 A 7 7 1.00 13 0.538
150 A 3 3 1.00 14 0.214
151 F 0 0 N/A 0 N/A
152 F 0 0 N/A 0 N/A
153 F 0 0 N/A 0 N/A
154 F 0 0 N/A 0 N/A
155 A 2 1 1.00 11 0.091
156 F 0 0 N/A 0 N/A
157 F 0 0 N/A 0 N/A
158 F 0 0 N/A 0 N/A
159 F 0 0 N/A 0 N/A
160 F 0 0 N/A 0 N/A
161 F 0 0 N/A 0 N/A
162 A 3 2 1.00 13 0.154
163 F 0 0 N/A 0 N/A
164 F 0 0 N/A 0 N/A
165 F 0 0 N/A 0 N/A
166 F 0 0 N/A 0 N/A
167 F 0 0 N/A 0 N/A
168 F 0 0 N/A 0 N/A
169 F 0 0 N/A 0 N/A
170 F 0 0 N/A 0 N/A
171 F 0 0 N/A 0 N/A
172 F 0 0 N/A 0 N/A
173 F 0 0 N/A 0 N/A
174 F 0 0 N/A 0 N/A
175 F 0 0 N/A 0 N/A
176 F 0 0 N/A 0 N/A
177 F 0 0 N/A 0 N/A
178 F 0 0 N/A 0 N/A
179 F 0 0 N/A 0 N/A
180 F 0 0 N/A 0 N/A
181 A 2 1 1.00 17 0.059
182 F 0 0 N/A 0 N/A
183 F 0 0 N/A 0 N/A
184 F 0 0 N/A 0 N/A
185 F 0 0 N/A 0 N/A
186 F 0 0 N/A 0 N/A
187 F 0 0 N/A 0 N/A
188 A 3 2 1.00 19 0.105
189 F 0 0 N/A 0 N/A
190 F 0 0 N/A 0 N/A
191 A 3 2 1.00 17 0.118
192 A 4 2 1.00 17 0.118
193 A 4 2 1.00 17 0.118
194 F 0 0 N/A 0 N/A
195 F 0 0 N/A 0 N/A
196 F 0 0 N/A 0 N/A
197 F 0 0 N/A 0 N/A
198 F 0 0 N/A 0 N/A
199 A 7 6 1.00 19 0.316
200 A 7 6 1.00 19 0.316
201 A 6 5 1.00 19 0.263
202 A 6 5 1.00 19 0.263
203 A 7 6 1.00 19 0.316
204 A 7 6 1.00 19 0.316
205 A 8 7 1.00 23 0.304
206 A 7 6 1.00 23 0.261
207 A 4 4 1.00 21 0.190
208 A 8 5 1.00 21 0.238
209 A 11 6 1.00 23 0.261
210 A 8 7 1.00 21 0.333
211 A 9 7 1.00 25 0.280
212 A 8 7 1.00 25 0.280
213 A 4 4 1.00 25 0.160
214 A 4 4 1.00 25 0.160
215 A 8 7 1.00 25 0.280
216 A 9 7 1.00 25 0.280
217 A 19 5 1.00 9 0.556
218 A 13 5 1.00 9 0.556
219 A 9 4 1.00 7 0.571
220 A 0 0 0.00 0 0.000
221 A 19 5 1.00 9 0.556
222 A 13 5 1.00 9 0.556
223 A 9 4 1.00 7 0.571
224 A 0 0 0.00 0 0.000

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