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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, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 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, 220 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 15, 18, 20, 21, 23, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 71, 73, 74, 75, 76, 77, 78, 83, 84, 86, 88, 89, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 159, 161, 163, 165, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 182, 183, 184, 185, 186, 187, 188, 190, 192, 193, 194, 195, 197, 201, 202, 203, 204, 208, 209, 210, 211, 212, 214, 216, 217, 219, 220 }

B grade: { 5, 7, 13, 14, 16, 17, 19, 22, 24, 25, 27, 30, 32, 35, 38, 40, 41, 43, 48, 70, 72, 79, 80, 81, 82, 85, 87, 90, 91, 92, 96, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 158, 160, 162, 164, 180, 181, 191, 196, 198, 199, 200, 205, 206, 207, 213, 215, 218 }

C grade: { 26, 28, 29, 31, 33, 34, 36, 37, 39, 42, 44, 45, 46, 47, 66, 68, 69, 108, 110, 166, 168, 169, 189 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 28, 29, 31, 36, 44, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 123, 125, 127, 128, 129, 130, 131, 133, 136, 137, 142, 152, 163, 180, 189, 198, 207, 216 }

B grade: { 22, 24, 25, 26, 27, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 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, 110, 112, 114, 120, 121, 122, 124, 126, 132, 134, 135, 138, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

C grade: { }

F grade: { 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220 }

2.1.4 Maxima

A grade: { 3, 4, 6, 12, 20, 49, 51, 52, 57, 59, 60, 65, 103, 104, 105, 106, 115, 118, 127, 138, 140, 170, 171, 172 }

B grade: { 1, 2, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 30, 32, 33, 35, 38, 40, 41, 43, 46, 48, 50, 53, 54, 55, 56, 58, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 75, 78, 80, 82, 84, 87, 89, 91, 93, 96, 98, 100, 102, 107, 108, 109, 110, 111, 112, 113, 114, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169 }

C grade: { 173, 174, 175 }

F grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 74, 76, 77, 79, 81, 83, 85, 86, 88, 90, 92, 94, 95, 97, 99, 101, 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, 220 }

2.1.5 FriCAS

A grade: { 1, 3, 4, 49, 50, 51, 57, 59, 65, 171, 172, 173, 174, 175 }

B grade: { 2, 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, 52, 53, 54, 55, 56, 58, 60, 61, 62, 63, 64, 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, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 213, 214, 215, 216, 217, 219 }

C grade: { }

F grade: { 47, 48, 168, 169, 186, 193, 211, 218, 220 }

2.1.6 Sympy

A grade: { 51, 103, 105, 113, 115, 125, 127, 142, 207, 216 }

B grade: { }

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, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 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, 104, 106, 107, 108, 109, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 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, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220 }

2.1.7 Giac

A grade: { 4, 6, 8, 12, 16, 17, 20, 30, 32, 33, 35, 52, 56, 57, 58, 75, 78, 80, 82, 87, 89, 106, 107, 108, 118, 143, 151, 153 }

B grade: { 1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 18, 19, 21, 22, 23, 24, 25, 27, 38, 40, 41, 43, 46, 48, 49, 50, 51, 53, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 84, 91, 93, 96, 98, 100, 102, 103, 104, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 148, 149, 150, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 191, 192 }

C grade: { 173, 174, 175 }

F grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 74, 76, 77, 79, 81, 83, 85, 86, 88, 90, 92, 94, 95, 97, 99, 101, 138, 139, 140, 141, 142, 145, 146, 147, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 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, 220 }

2.1.8 Mupad

A grade: { }

B 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, 36, 44, 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, 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, 152, 163, 180, 189, 198, 207, 216 }

C grade: { }

F grade: { 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 148, 149, 150, 151, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220 }

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 B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 54 78 129 114 0 130 73
normalized size 1 1.00 0.77 1.11 1.84 1.63 0.00 1.86 1.04
time (sec) N/A 0.081 0.333 0.327 0.313 0.400 0.000 1.103 1.609
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 53 56 111 85 0 85 44
normalized size 1 1.00 1.20 1.27 2.52 1.93 0.00 1.93 1.00
time (sec) N/A 0.056 0.052 0.312 0.338 0.441 0.000 0.133 0.177
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 57 45 62 67 0 92 55
normalized size 1 1.00 1.33 1.05 1.44 1.56 0.00 2.14 1.28
time (sec) N/A 0.056 0.194 0.176 0.327 0.405 0.000 0.164 1.428
Problem 4 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 24 24 35 26 36 38 0 45 26
normalized size 1 1.00 1.46 1.08 1.50 1.58 0.00 1.88 1.08
time (sec) N/A 0.033 0.022 0.090 0.321 0.428 0.000 0.125 0.083
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 67 36 80 180 0 72 79
normalized size 1 1.00 2.48 1.33 2.96 6.67 0.00 2.67 2.93
time (sec) N/A 0.045 0.048 0.196 0.325 0.418 0.000 0.126 1.412
Problem 6 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 27 27 37 44 39 91 0 34 34
normalized size 1 1.00 1.37 1.63 1.44 3.37 0.00 1.26 1.26
time (sec) N/A 0.046 0.073 0.381 0.333 0.400 0.000 0.143 1.376
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 131 70 198 924 0 142 160
normalized size 1 1.00 2.43 1.30 3.67 17.11 0.00 2.63 2.96
time (sec) N/A 0.071 0.049 0.382 0.342 0.431 0.000 0.154 0.166
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 84 73 187 246 0 80 172
normalized size 1 1.00 1.87 1.62 4.16 5.47 0.00 1.78 3.82
time (sec) N/A 0.058 0.054 0.437 0.339 0.384 0.000 0.135 1.401
Problem 9 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 114 114 153 109 211 342 0 231 269
normalized size 1 1.00 1.34 0.96 1.85 3.00 0.00 2.03 2.36
time (sec) N/A 0.138 1.663 0.343 0.338 0.417 0.000 0.177 0.270
Problem 10 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 72 72 83 93 266 212 0 140 201
normalized size 1 1.00 1.15 1.29 3.69 2.94 0.00 1.94 2.79
time (sec) N/A 0.087 0.526 0.329 0.340 0.394 0.000 0.189 1.496
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 126 90 160 252 0 144 236
normalized size 1 1.00 1.73 1.23 2.19 3.45 0.00 1.97 3.23
time (sec) N/A 0.107 0.952 0.336 0.332 0.409 0.000 0.177 0.159
Problem 12 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 45 45 59 43 65 133 0 75 45
normalized size 1 1.00 1.31 0.96 1.44 2.96 0.00 1.67 1.00
time (sec) N/A 0.046 0.173 0.096 0.321 0.403 0.000 0.142 1.466
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 108 72 197 1148 0 139 232
normalized size 1 1.00 2.08 1.38 3.79 22.08 0.00 2.67 4.46
time (sec) N/A 0.077 0.577 0.215 0.337 0.425 0.000 0.140 1.503
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 109 91 140 284 0 111 215
normalized size 1 1.00 2.18 1.82 2.80 5.68 0.00 2.22 4.30
time (sec) N/A 0.062 1.767 0.490 0.337 0.416 0.000 0.151 1.487
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 144 126 354 2930 0 228 316
normalized size 1 1.00 1.38 1.21 3.40 28.17 0.00 2.19 3.04
time (sec) N/A 0.136 1.645 0.425 0.339 0.453 0.000 0.157 1.655
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 151 138 285 408 0 115 115
normalized size 1 1.00 2.01 1.84 3.80 5.44 0.00 1.53 1.53
time (sec) N/A 0.083 1.320 0.549 0.343 0.400 0.000 0.175 0.213
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 651 182 422 727 0 339 686
normalized size 1 1.00 3.58 1.00 2.32 3.99 0.00 1.86 3.77
time (sec) N/A 0.232 2.515 0.440 0.345 0.453 0.000 0.218 0.367
Problem 18 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 99 99 119 130 489 403 0 193 348
normalized size 1 1.00 1.20 1.31 4.94 4.07 0.00 1.95 3.52
time (sec) N/A 0.111 1.253 0.371 0.342 0.415 0.000 0.209 0.330
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 143 480 145 443 595 0 278 592
normalized size 1 1.28 4.29 1.29 3.96 5.31 0.00 2.48 5.29
time (sec) N/A 0.193 1.916 0.418 0.339 0.429 0.000 0.202 0.230
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 93 58 94 276 0 101 288
normalized size 1 1.00 1.45 0.91 1.47 4.31 0.00 1.58 4.50
time (sec) N/A 0.059 0.257 0.130 0.322 0.394 0.000 0.191 1.497
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 134 118 358 3443 0 228 434
normalized size 1 1.00 1.61 1.42 4.31 41.48 0.00 2.75 5.23
time (sec) N/A 0.100 1.281 0.245 0.329 0.445 0.000 0.168 1.532
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 380 148 358 622 0 249 644
normalized size 1 1.00 5.43 2.11 5.11 8.89 0.00 3.56 9.20
time (sec) N/A 0.073 2.793 0.591 0.335 0.470 0.000 0.181 1.479
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 224 192 556 6717 0 341 536
normalized size 1 1.00 1.56 1.33 3.86 46.65 0.00 2.37 3.72
time (sec) N/A 0.178 3.887 0.443 0.338 0.596 0.000 0.197 1.644
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 213 213 664 955 0 355 745
normalized size 1 1.00 2.05 2.05 6.38 9.18 0.00 3.41 7.16
time (sec) N/A 0.105 2.466 0.659 0.344 0.587 0.000 0.189 1.602
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 294 708 526 1681 0 220 328
normalized size 1 1.00 2.51 6.05 4.50 14.37 0.00 1.88 2.80
time (sec) N/A 0.196 2.483 0.411 0.462 0.593 0.000 2.883 2.426
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 372 261 0 1246 0 0 473
normalized size 1 1.00 5.24 3.68 0.00 17.55 0.00 0.00 6.66
time (sec) N/A 0.105 2.226 0.336 0.000 0.492 0.000 0.000 1.841
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 236 383 352 805 0 132 276
normalized size 1 1.00 3.15 5.11 4.69 10.73 0.00 1.76 3.68
time (sec) N/A 0.110 0.997 0.319 0.424 0.483 0.000 1.603 2.029
Problem 28 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 47 47 328 44 0 595 0 0 42
normalized size 1 1.00 6.98 0.94 0.00 12.66 0.00 0.00 0.89
time (sec) N/A 0.048 1.015 0.079 0.000 0.512 0.000 0.000 0.145
Problem 29 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 55 55 232 67 0 533 0 0 616
normalized size 1 1.00 4.22 1.22 0.00 9.69 0.00 0.00 11.20
time (sec) N/A 0.082 0.928 0.250 0.000 0.507 0.000 0.000 2.181
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 179 147 100 588 0 75 847
normalized size 1 1.00 3.38 2.77 1.89 11.09 0.00 1.42 15.98
time (sec) N/A 0.071 0.752 0.300 0.426 0.557 0.000 0.633 2.467
Problem 31 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 87 87 338 134 0 1881 0 0 1586
normalized size 1 1.00 3.89 1.54 0.00 21.62 0.00 0.00 18.23
time (sec) N/A 0.118 2.050 0.325 0.000 0.464 0.000 0.000 3.070
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 216 258 195 1753 0 123 248
normalized size 1 1.00 2.88 3.44 2.60 23.37 0.00 1.64 3.31
time (sec) N/A 0.099 2.082 0.357 0.456 0.524 0.000 0.669 2.170
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F(-1) A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 1330 1034 1299 5169 0 323 -1
normalized size 1 1.00 6.86 5.33 6.70 26.64 0.00 1.66 -0.01
time (sec) N/A 0.273 14.252 0.395 0.514 0.562 0.000 3.728 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 114 114 861 561 0 3804 0 0 -1
normalized size 1 1.00 7.55 4.92 0.00 33.37 0.00 0.00 -0.01
time (sec) N/A 0.144 4.819 0.368 0.000 0.486 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 131 131 791 543 696 2925 0 234 -1
normalized size 1 1.00 6.04 4.15 5.31 22.33 0.00 1.79 -0.01
time (sec) N/A 0.196 11.332 0.371 0.459 0.502 0.000 2.051 0.000
Problem 36 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 84 84 479 74 0 1780 0 0 71
normalized size 1 1.00 5.70 0.88 0.00 21.19 0.00 0.00 0.85
time (sec) N/A 0.065 2.763 0.172 0.000 0.544 0.000 0.000 1.645
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 377 431 0 2376 0 0 -1
normalized size 1 1.00 3.81 4.35 0.00 24.00 0.00 0.00 -0.01
time (sec) N/A 0.130 1.251 0.336 0.000 0.580 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 220 313 262 2407 0 239 -1
normalized size 1 1.00 2.39 3.40 2.85 26.16 0.00 2.60 -0.01
time (sec) N/A 0.084 2.625 0.394 0.461 0.623 0.000 0.732 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 462 496 0 6878 0 0 -1
normalized size 1 1.00 3.14 3.37 0.00 46.79 0.00 0.00 -0.01
time (sec) N/A 0.206 2.227 0.423 0.000 0.733 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 295 577 430 6143 0 253 -1
normalized size 1 1.00 2.40 4.69 3.50 49.94 0.00 2.06 -0.01
time (sec) N/A 0.195 6.078 0.504 0.520 0.525 0.000 0.772 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 242 242 3080 1668 2468 12353 0 518 -1
normalized size 1 1.00 12.73 6.89 10.20 51.05 0.00 2.14 -0.00
time (sec) N/A 0.399 27.316 0.426 0.603 0.637 0.000 6.128 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) B F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 154 154 1217 1296 0 8667 0 0 -1
normalized size 1 1.00 7.90 8.42 0.00 56.28 0.00 0.00 -0.01
time (sec) N/A 0.218 10.382 0.381 0.000 0.564 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 187 187 2544 1329 1373 9730 0 370 -1
normalized size 1 1.00 13.60 7.11 7.34 52.03 0.00 1.98 -0.01
time (sec) N/A 0.292 17.845 0.389 0.533 0.596 0.000 3.702 0.000
Problem 44 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 NO TBD TBD TBD TBD TBD TBD
size 116 116 453 107 0 4829 0 0 103
normalized size 1 1.00 3.91 0.92 0.00 41.63 0.00 0.00 0.89
time (sec) N/A 0.084 9.604 0.168 0.000 0.514 0.000 0.000 1.607
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 440 1476 0 8742 0 0 -1
normalized size 1 1.00 2.86 9.58 0.00 56.77 0.00 0.00 -0.01
time (sec) N/A 0.223 2.498 0.359 0.000 0.637 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 126 126 981 816 533 7275 0 347 -1
normalized size 1 1.00 7.79 6.48 4.23 57.74 0.00 2.75 -0.01
time (sec) N/A 0.100 6.920 0.406 0.528 0.549 0.000 1.761 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 524 1555 0 0 0 0 -1
normalized size 1 1.00 2.46 7.30 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.342 4.117 0.447 0.000 0.000 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B F(-1) F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 165 165 985 1443 782 0 0 406 -1
normalized size 1 1.00 5.97 8.75 4.74 0.00 0.00 2.46 -0.01
time (sec) N/A 0.273 5.530 0.483 0.595 0.000 0.000 1.664 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 45 66 97 61 0 116 50
normalized size 1 1.00 0.74 1.08 1.59 1.00 0.00 1.90 0.82
time (sec) N/A 0.046 0.093 0.457 0.308 0.397 0.000 0.137 0.129
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 50 34 85 41 0 72 34
normalized size 1 1.00 1.67 1.13 2.83 1.37 0.00 2.40 1.13
time (sec) N/A 0.050 0.018 0.426 0.309 0.394 0.000 0.157 0.085
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 33 37 38 28 60 66 23
normalized size 1 1.00 1.06 1.19 1.23 0.90 1.94 2.13 0.74
time (sec) N/A 0.031 0.030 0.306 0.310 0.405 11.245 0.146 0.077
Problem 52 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 24 24 35 26 28 93 0 36 62
normalized size 1 1.00 1.46 1.08 1.17 3.88 0.00 1.50 2.58
time (sec) N/A 0.030 0.018 0.286 0.412 0.450 0.000 0.146 1.436
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 48 45 81 321 0 84 124
normalized size 1 1.00 1.20 1.12 2.02 8.02 0.00 2.10 3.10
time (sec) N/A 0.027 0.024 0.300 0.403 0.409 0.000 0.124 0.159
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 43 39 34 112 158 0 61 61
normalized size 1 1.43 1.30 1.13 3.73 5.27 0.00 2.03 2.03
time (sec) N/A 0.040 0.012 0.336 0.317 0.383 0.000 0.124 1.382
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 60 83 184 1112 0 156 283
normalized size 1 1.00 0.86 1.19 2.63 15.89 0.00 2.23 4.04
time (sec) N/A 0.050 0.105 0.417 0.410 0.422 0.000 0.158 1.383
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 65 71 56 300 343 0 85 292
normalized size 1 1.30 1.42 1.12 6.00 6.86 0.00 1.70 5.84
time (sec) N/A 0.046 0.014 0.366 0.321 0.384 0.000 0.145 1.435
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 58 79 105 78 0 151 66
normalized size 1 1.00 0.71 0.96 1.28 0.95 0.00 1.84 0.80
time (sec) N/A 0.093 0.131 0.397 0.306 0.399 0.000 0.155 1.371
Problem 58 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 49 49 72 66 105 414 0 94 114
normalized size 1 1.00 1.47 1.35 2.14 8.45 0.00 1.92 2.33
time (sec) N/A 0.059 0.024 0.364 0.412 0.409 0.000 0.151 0.166
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 52 51 63 80 0 128 65
normalized size 1 1.00 1.11 1.09 1.34 1.70 0.00 2.72 1.38
time (sec) N/A 0.078 0.149 0.355 0.322 0.392 0.000 0.173 0.164
Problem 60 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 56 56 80 63 101 653 0 112 172
normalized size 1 1.00 1.43 1.12 1.80 11.66 0.00 2.00 3.07
time (sec) N/A 0.068 0.041 0.365 0.420 0.418 0.000 0.139 1.439
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 71 106 201 1372 0 170 303
normalized size 1 1.00 0.79 1.18 2.23 15.24 0.00 1.89 3.37
time (sec) N/A 0.084 0.133 0.385 0.423 0.429 0.000 0.141 1.518
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 93 70 324 404 0 156 452
normalized size 1 1.00 1.75 1.32 6.11 7.62 0.00 2.94 8.53
time (sec) N/A 0.066 0.031 0.418 0.335 0.406 0.000 0.173 1.465
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 104 169 348 2946 0 293 569
normalized size 1 1.00 0.81 1.32 2.72 23.02 0.00 2.29 4.45
time (sec) N/A 0.149 0.244 0.460 0.420 0.432 0.000 0.160 1.570
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 144 102 671 677 0 197 692
normalized size 1 1.00 1.80 1.28 8.39 8.46 0.00 2.46 8.65
time (sec) N/A 0.076 0.024 0.445 0.329 0.390 0.000 0.159 1.416
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 70 93 130 153 0 177 117
normalized size 1 1.00 0.83 1.11 1.55 1.82 0.00 2.11 1.39
time (sec) N/A 0.111 0.427 0.479 0.324 0.395 0.000 0.214 1.529
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F(-1) B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 81 81 483 103 179 1409 0 163 218
normalized size 1 1.00 5.96 1.27 2.21 17.40 0.00 2.01 2.69
time (sec) N/A 0.093 6.882 0.454 0.415 0.423 0.000 0.213 0.223
Problem 67 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 72 72 64 77 160 270 0 152 221
normalized size 1 1.00 0.89 1.07 2.22 3.75 0.00 2.11 3.07
time (sec) N/A 0.092 0.508 0.461 0.319 0.427 0.000 0.195 0.167
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 575 125 221 1992 0 199 344
normalized size 1 1.00 6.18 1.34 2.38 21.42 0.00 2.14 3.70
time (sec) N/A 0.103 7.875 0.507 0.412 0.466 0.000 0.191 0.191
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 147 147 1430 193 365 3465 0 310 535
normalized size 1 1.00 9.73 1.31 2.48 23.57 0.00 2.11 3.64
time (sec) N/A 0.143 9.836 0.460 0.414 0.473 0.000 0.189 1.472
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 319 116 695 816 0 302 978
normalized size 1 1.00 4.31 1.57 9.39 11.03 0.00 4.08 13.22
time (sec) N/A 0.080 1.486 0.571 0.329 0.437 0.000 0.191 1.495
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 297 280 556 6114 0 485 931
normalized size 1 1.00 1.52 1.43 2.84 31.19 0.00 2.47 4.75
time (sec) N/A 0.232 9.396 0.472 0.421 0.505 0.000 0.177 1.599
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 348 158 1245 1190 0 360 1333
normalized size 1 1.00 3.22 1.46 11.53 11.02 0.00 3.33 12.34
time (sec) N/A 0.094 1.756 0.520 0.343 0.417 0.000 0.182 1.473
Problem 73 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 117 117 95 493 526 1713 0 208 260
normalized size 1 1.00 0.81 4.21 4.50 14.64 0.00 1.78 2.22
time (sec) N/A 0.189 0.495 0.541 0.457 0.458 0.000 2.623 1.998
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 79 256 0 1616 0 0 332
normalized size 1 1.00 1.04 3.37 0.00 21.26 0.00 0.00 4.37
time (sec) N/A 0.090 0.274 0.489 0.000 0.465 0.000 0.000 2.213
Problem 75 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 75 75 67 278 352 829 0 125 206
normalized size 1 1.00 0.89 3.71 4.69 11.05 0.00 1.67 2.75
time (sec) N/A 0.116 0.235 0.464 0.424 0.457 0.000 1.574 1.968
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 52 128 0 718 0 0 277
normalized size 1 1.00 1.00 2.46 0.00 13.81 0.00 0.00 5.33
time (sec) N/A 0.061 0.124 0.402 0.000 0.459 0.000 0.000 1.739
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 36 82 0 487 0 0 108
normalized size 1 1.00 1.00 2.28 0.00 13.53 0.00 0.00 3.00
time (sec) N/A 0.042 0.066 0.278 0.000 0.423 0.000 0.000 1.896
Problem 78 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 36 36 36 104 66 411 0 47 125
normalized size 1 1.00 1.00 2.89 1.83 11.42 0.00 1.31 3.47
time (sec) N/A 0.061 0.080 0.252 0.417 0.429 0.000 0.639 0.570
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 194 108 0 526 0 0 307
normalized size 1 1.00 3.53 1.96 0.00 9.56 0.00 0.00 5.58
time (sec) N/A 0.069 0.712 0.252 0.000 0.437 0.000 0.000 1.815
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 182 141 91 645 0 72 166
normalized size 1 1.00 3.50 2.71 1.75 12.40 0.00 1.38 3.19
time (sec) N/A 0.070 0.632 0.217 0.426 0.426 0.000 0.622 0.475
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 213 189 0 1518 0 0 946
normalized size 1 1.00 2.48 2.20 0.00 17.65 0.00 0.00 11.00
time (sec) N/A 0.103 1.836 0.281 0.000 0.489 0.000 0.000 3.500
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 214 316 160 1905 0 118 334
normalized size 1 1.00 2.78 4.10 2.08 24.74 0.00 1.53 4.34
time (sec) N/A 0.089 2.178 0.282 0.461 0.488 0.000 0.639 1.990
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 113 517 0 5842 0 0 -1
normalized size 1 1.00 0.90 4.14 0.00 46.74 0.00 0.00 -0.01
time (sec) N/A 0.154 0.919 0.533 0.000 0.539 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 103 557 696 3739 0 323 -1
normalized size 1 1.00 0.72 3.87 4.83 25.97 0.00 2.24 -0.01
time (sec) N/A 0.235 1.379 0.513 0.466 0.492 0.000 2.018 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 234 385 0 3154 0 0 -1
normalized size 1 1.00 2.34 3.85 0.00 31.54 0.00 0.00 -0.01
time (sec) N/A 0.132 1.812 0.514 0.000 0.487 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 124 331 0 1856 0 0 -1
normalized size 1 1.00 1.51 4.04 0.00 22.63 0.00 0.00 -0.01
time (sec) N/A 0.066 0.314 0.345 0.000 0.453 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 187 263 150 1489 0 130 -1
normalized size 1 1.00 2.53 3.55 2.03 20.12 0.00 1.76 -0.01
time (sec) N/A 0.074 1.015 0.253 0.456 0.444 0.000 0.744 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 108 241 0 1570 0 0 -1
normalized size 1 1.00 1.48 3.30 0.00 21.51 0.00 0.00 -0.01
time (sec) N/A 0.071 0.228 0.270 0.000 0.475 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 88 374 165 1569 0 139 -1
normalized size 1 1.00 1.06 4.51 1.99 18.90 0.00 1.67 -0.01
time (sec) N/A 0.090 0.216 0.294 0.478 0.451 0.000 0.769 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 282 361 0 2069 0 0 -1
normalized size 1 1.00 2.79 3.57 0.00 20.49 0.00 0.00 -0.01
time (sec) N/A 0.117 2.529 0.272 0.000 0.498 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 229 419 244 2958 0 225 -1
normalized size 1 1.00 2.27 4.15 2.42 29.29 0.00 2.23 -0.01
time (sec) N/A 0.142 3.813 0.276 0.554 0.480 0.000 0.789 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 489 448 0 6499 0 0 -1
normalized size 1 1.00 3.20 2.93 0.00 42.48 0.00 0.00 -0.01
time (sec) N/A 0.200 5.193 0.288 0.000 0.581 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 204 204 156 1435 1373 11740 0 395 -1
normalized size 1 1.00 0.76 7.03 6.73 57.55 0.00 1.94 -0.00
time (sec) N/A 0.377 4.229 0.591 0.546 0.655 0.000 3.671 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 292 1238 0 9856 0 0 -1
normalized size 1 1.00 1.90 8.04 0.00 64.00 0.00 0.00 -0.01
time (sec) N/A 0.185 3.653 0.559 0.000 0.639 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 214 1172 0 6806 0 0 -1
normalized size 1 1.00 1.51 8.25 0.00 47.93 0.00 0.00 -0.01
time (sec) N/A 0.137 2.936 0.398 0.000 0.541 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 258 615 353 5109 0 282 -1
normalized size 1 1.00 2.39 5.69 3.27 47.31 0.00 2.61 -0.01
time (sec) N/A 0.090 2.169 0.344 0.514 0.508 0.000 1.754 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 159 1038 0 6037 0 0 -1
normalized size 1 1.00 1.29 8.44 0.00 49.08 0.00 0.00 -0.01
time (sec) N/A 0.108 0.789 0.342 0.000 0.526 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 250 1084 369 5447 0 274 -1
normalized size 1 1.00 2.00 8.67 2.95 43.58 0.00 2.19 -0.01
time (sec) N/A 0.107 3.386 0.284 0.535 0.519 0.000 1.734 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 125 592 0 5006 0 0 -1
normalized size 1 1.00 1.18 5.58 0.00 47.23 0.00 0.00 -0.01
time (sec) N/A 0.092 0.287 0.320 0.000 0.512 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 125 1245 395 5887 0 302 -1
normalized size 1 1.00 0.87 8.65 2.74 40.88 0.00 2.10 -0.01
time (sec) N/A 0.142 1.012 0.345 1.367 0.528 0.000 1.751 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 247 1201 0 7993 0 0 -1
normalized size 1 1.00 1.61 7.85 0.00 52.24 0.00 0.00 -0.01
time (sec) N/A 0.205 4.721 0.299 0.000 0.624 0.000 0.000 0.000
Problem 102 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 48 48 57 98 92 327 0 105 433
normalized size 1 1.00 1.19 2.04 1.92 6.81 0.00 2.19 9.02
time (sec) N/A 0.064 0.030 0.329 0.615 0.421 0.000 0.202 1.545
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 45 64 78 1072 80 116 173
normalized size 1 1.00 0.92 1.31 1.59 21.88 1.63 2.37 3.53
time (sec) N/A 0.056 0.022 0.201 0.747 0.430 1.662 0.179 0.125
Problem 104 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 32 32 41 60 42 155 0 69 163
normalized size 1 1.00 1.28 1.88 1.31 4.84 0.00 2.16 5.09
time (sec) N/A 0.057 0.017 0.328 0.405 0.398 0.000 0.161 1.503
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 29 27 359 42 80 72
normalized size 1 1.00 1.00 1.00 0.93 12.38 1.45 2.76 2.48
time (sec) N/A 0.028 0.021 0.138 0.331 0.419 0.487 0.134 1.470
Problem 106 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 15 15 15 16 23 36 0 23 23
normalized size 1 1.00 1.00 1.07 1.53 2.40 0.00 1.53 1.53
time (sec) N/A 0.013 0.003 0.269 0.370 0.403 0.000 0.121 1.395
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 44 26 65 69 0 56 167
normalized size 1 1.00 1.57 0.93 2.32 2.46 0.00 2.00 5.96
time (sec) N/A 0.051 0.041 0.256 0.534 0.420 0.000 0.153 0.172
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 41 30 47 39 0 27 25
normalized size 1 1.00 2.28 1.67 2.61 2.17 0.00 1.50 1.39
time (sec) N/A 0.059 0.031 0.333 0.336 0.414 0.000 0.146 0.111
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 52 42 108 378 0 81 76
normalized size 1 1.00 1.68 1.35 3.48 12.19 0.00 2.61 2.45
time (sec) N/A 0.057 0.179 0.329 0.333 0.419 0.000 0.208 1.414
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 49 70 170 140 0 67 161
normalized size 1 1.00 1.44 2.06 5.00 4.12 0.00 1.97 4.74
time (sec) N/A 0.063 0.023 0.389 0.344 0.414 0.000 0.214 1.492
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 62 78 251 1099 0 117 179
normalized size 1 1.00 1.22 1.53 4.92 21.55 0.00 2.29 3.51
time (sec) N/A 0.078 0.263 0.313 0.512 0.426 0.000 0.232 0.110
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 395 181 649 721 0 275 1022
normalized size 1 1.00 5.13 2.35 8.43 9.36 0.00 3.57 13.27
time (sec) N/A 0.105 1.185 0.437 0.548 0.417 0.000 0.249 0.183
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 107 110 333 2591 129 241 349
normalized size 1 1.00 1.39 1.43 4.32 33.65 1.68 3.13 4.53
time (sec) N/A 0.095 0.290 0.242 0.439 0.450 5.089 0.202 1.522
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 281 115 325 435 0 193 513
normalized size 1 1.00 4.76 1.95 5.51 7.37 0.00 3.27 8.69
time (sec) N/A 0.098 0.864 0.405 0.524 0.423 0.000 0.171 0.142
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 81 48 55 1180 63 159 182
normalized size 1 1.00 1.69 1.00 1.15 24.58 1.31 3.31 3.79
time (sec) N/A 0.050 0.145 0.158 0.482 0.418 1.665 0.142 1.689
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 106 47 120 176 0 79 163
normalized size 1 1.00 2.65 1.18 3.00 4.40 0.00 1.98 4.08
time (sec) N/A 0.034 0.377 0.365 0.457 0.396 0.000 0.144 1.458
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 84 60 161 665 0 171 308
normalized size 1 1.00 1.58 1.13 3.04 12.55 0.00 3.23 5.81
time (sec) N/A 0.080 0.246 0.262 0.698 0.458 0.000 0.171 0.296
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 82 64 71 106 0 65 60
normalized size 1 1.00 2.28 1.78 1.97 2.94 0.00 1.81 1.67
time (sec) N/A 0.085 0.741 0.388 0.545 0.438 0.000 0.201 1.422
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 82 78 206 637 0 161 240
normalized size 1 1.00 1.49 1.42 3.75 11.58 0.00 2.93 4.36
time (sec) N/A 0.089 0.200 0.311 0.480 0.449 0.000 0.252 0.220
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 160 96 268 201 0 97 183
normalized size 1 1.00 3.48 2.09 5.83 4.37 0.00 2.11 3.98
time (sec) N/A 0.092 0.810 0.360 0.427 0.427 0.000 0.272 1.424
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 77 102 282 1252 0 147 207
normalized size 1 1.00 1.48 1.96 5.42 24.08 0.00 2.83 3.98
time (sec) N/A 0.094 0.232 0.321 0.449 0.444 0.000 0.337 1.466
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 256 163 613 425 0 167 511
normalized size 1 1.00 4.00 2.55 9.58 6.64 0.00 2.61 7.98
time (sec) N/A 0.097 1.101 0.445 0.542 0.422 0.000 0.374 1.439
Problem 123 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 86 86 107 164 696 2548 0 216 377
normalized size 1 1.00 1.24 1.91 8.09 29.63 0.00 2.51 4.38
time (sec) N/A 0.125 0.516 0.337 0.408 0.478 0.000 0.459 1.530
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 301 274 1453 1323 0 472 1834
normalized size 1 1.00 2.74 2.49 13.21 12.03 0.00 4.29 16.67
time (sec) N/A 0.118 5.936 0.554 0.385 0.435 0.000 0.305 1.623
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 128 156 652 4658 178 384 573
normalized size 1 1.00 1.24 1.51 6.33 45.22 1.73 3.73 5.56
time (sec) N/A 0.098 0.754 0.298 0.462 0.513 13.795 0.273 1.638
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 479 180 788 881 0 356 1133
normalized size 1 1.00 5.21 1.96 8.57 9.58 0.00 3.87 12.32
time (sec) N/A 0.110 1.790 0.515 0.442 0.417 0.000 0.197 0.213
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 100 67 85 2519 87 268 347
normalized size 1 1.00 1.41 0.94 1.20 35.48 1.23 3.77 4.89
time (sec) N/A 0.058 0.301 0.161 0.431 0.441 4.911 0.186 0.215
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 268 83 332 470 0 182 502
normalized size 1 1.00 3.67 1.14 4.55 6.44 0.00 2.49 6.88
time (sec) N/A 0.047 0.928 0.420 0.411 0.425 0.000 0.154 1.442
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 114 111 300 2376 0 325 360
normalized size 1 1.00 1.36 1.32 3.57 28.29 0.00 3.87 4.29
time (sec) N/A 0.107 0.663 0.308 0.469 0.457 0.000 0.183 1.638
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 126 111 172 359 0 132 234
normalized size 1 1.00 2.07 1.82 2.82 5.89 0.00 2.16 3.84
time (sec) N/A 0.103 1.799 0.573 0.413 0.413 0.000 0.211 0.142
Problem 131 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 81 81 110 137 314 1701 0 292 324
normalized size 1 1.00 1.36 1.69 3.88 21.00 0.00 3.60 4.00
time (sec) N/A 0.116 1.242 0.359 0.470 0.443 0.000 0.289 1.723
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 343 149 366 354 0 155 260
normalized size 1 1.00 5.72 2.48 6.10 5.90 0.00 2.58 4.33
time (sec) N/A 0.101 1.726 0.483 0.521 0.401 0.000 0.343 1.479
Problem 133 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 81 81 101 153 422 1830 0 248 384
normalized size 1 1.00 1.25 1.89 5.21 22.59 0.00 3.06 4.74
time (sec) N/A 0.121 0.907 0.318 0.497 0.449 0.000 0.410 1.636
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 303 199 826 521 0 210 547
normalized size 1 1.00 4.39 2.88 11.97 7.55 0.00 3.04 7.93
time (sec) N/A 0.109 1.087 0.425 0.361 0.408 0.000 0.427 1.603
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 98 189 727 2632 0 239 411
normalized size 1 1.00 1.27 2.45 9.44 34.18 0.00 3.10 5.34
time (sec) N/A 0.121 0.797 0.363 0.420 0.464 0.000 0.586 1.614
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 455 129 703 941 0 334 1083
normalized size 1 1.00 4.10 1.16 6.33 8.48 0.00 3.01 9.76
time (sec) N/A 0.070 1.666 0.525 0.567 0.424 0.000 0.151 0.196
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 724 185 1277 1652 0 537 1952
normalized size 1 1.00 4.44 1.13 7.83 10.13 0.00 3.29 11.98
time (sec) N/A 0.095 6.567 0.606 0.349 0.427 0.000 0.167 0.317
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 98 331 131 736 0 0 421
normalized size 1 1.00 1.40 4.73 1.87 10.51 0.00 0.00 6.01
time (sec) N/A 0.112 0.307 0.316 0.459 0.485 0.000 0.000 1.812
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 196 386 637 683 0 0 183
normalized size 1 1.00 3.32 6.54 10.80 11.58 0.00 0.00 3.10
time (sec) N/A 0.178 1.086 0.349 0.636 0.449 0.000 0.000 1.873
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 41 196 77 112 0 0 238
normalized size 1 1.00 0.91 4.36 1.71 2.49 0.00 0.00 5.29
time (sec) N/A 0.088 0.117 0.333 0.474 0.460 0.000 0.000 1.650
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 174 251 291 419 0 0 105
normalized size 1 1.00 3.78 5.46 6.33 9.11 0.00 0.00 2.28
time (sec) N/A 0.140 0.304 0.358 0.497 0.455 0.000 0.000 0.426
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 26 38 51 76 124 0 51
normalized size 1 1.00 1.13 1.65 2.22 3.30 5.39 0.00 2.22
time (sec) N/A 0.035 0.183 0.146 0.378 0.421 7.035 0.000 0.345
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 172 149 83 436 0 64 470
normalized size 1 1.00 3.74 3.24 1.80 9.48 0.00 1.39 10.22
time (sec) N/A 0.046 0.250 0.277 0.467 0.441 0.000 0.390 2.161
Problem 144 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 46 46 42 133 100 115 0 97 228
normalized size 1 1.00 0.91 2.89 2.17 2.50 0.00 2.11 4.96
time (sec) N/A 0.087 0.092 0.375 0.421 0.461 0.000 0.334 1.817
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 193 189 429 749 0 0 977
normalized size 1 1.00 3.11 3.05 6.92 12.08 0.00 0.00 15.76
time (sec) N/A 0.180 1.161 0.457 0.477 0.457 0.000 0.000 3.389
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 100 199 187 862 0 0 523
normalized size 1 1.00 1.37 2.73 2.56 11.81 0.00 0.00 7.16
time (sec) N/A 0.122 0.236 0.476 0.435 0.524 0.000 0.000 2.069
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 380 298 1435 2705 0 0 779
normalized size 1 1.00 4.37 3.43 16.49 31.09 0.00 0.00 8.95
time (sec) N/A 0.286 3.325 0.493 0.627 0.465 0.000 0.000 4.146
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 109 351 154 853 0 208 -1
normalized size 1 1.00 1.43 4.62 2.03 11.22 0.00 2.74 -0.01
time (sec) N/A 0.117 0.454 0.372 0.446 0.495 0.000 1.376 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 228 676 1053 1479 0 187 -1
normalized size 1 1.00 2.51 7.43 11.57 16.25 0.00 2.05 -0.01
time (sec) N/A 0.194 2.133 0.402 0.837 0.450 0.000 1.162 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 81 186 108 485 0 121 -1
normalized size 1 1.00 1.59 3.65 2.12 9.51 0.00 2.37 -0.02
time (sec) N/A 0.090 0.760 0.351 0.375 0.416 0.000 0.889 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 326 411 597 1846 0 147 -1
normalized size 1 1.00 3.84 4.84 7.02 21.72 0.00 1.73 -0.01
time (sec) N/A 0.169 4.629 0.351 0.547 0.473 0.000 0.718 0.000
Problem 152 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 49 49 79 60 106 476 0 121 53
normalized size 1 1.00 1.61 1.22 2.16 9.71 0.00 2.47 1.08
time (sec) N/A 0.062 0.593 0.185 0.423 0.418 0.000 0.423 1.730
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 221 423 187 1690 0 163 -1
normalized size 1 1.00 2.38 4.55 2.01 18.17 0.00 1.75 -0.01
time (sec) N/A 0.096 2.042 0.382 0.694 0.461 0.000 0.435 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 115 292 209 1031 0 246 -1
normalized size 1 1.00 1.39 3.52 2.52 12.42 0.00 2.96 -0.01
time (sec) N/A 0.129 0.295 0.423 0.351 0.551 0.000 0.556 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 121 121 268 481 1070 3624 0 282 -1
normalized size 1 1.00 2.21 3.98 8.84 29.95 0.00 2.33 -0.01
time (sec) N/A 0.284 2.824 0.457 0.917 0.508 0.000 0.955 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 130 367 384 3624 0 383 -1
normalized size 1 1.00 1.18 3.34 3.49 32.95 0.00 3.48 -0.01
time (sec) N/A 0.175 1.276 0.530 0.473 0.716 0.000 1.318 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 161 161 350 634 2961 9849 0 302 -1
normalized size 1 1.00 2.17 3.94 18.39 61.17 0.00 1.88 -0.01
time (sec) N/A 0.411 5.093 0.520 1.414 0.612 0.000 1.604 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 148 148 515 1713 3239 5463 0 371 -1
normalized size 1 1.00 3.48 11.57 21.89 36.91 0.00 2.51 -0.01
time (sec) N/A 0.320 5.782 0.446 1.993 0.524 0.000 2.251 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 136 579 206 1741 0 187 -1
normalized size 1 1.00 1.77 7.52 2.68 22.61 0.00 2.43 -0.01
time (sec) N/A 0.120 2.168 0.417 0.420 0.459 0.000 1.883 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 139 139 1457 1306 2201 6464 0 295 -1
normalized size 1 1.00 10.48 9.40 15.83 46.50 0.00 2.12 -0.01
time (sec) N/A 0.294 13.087 0.481 1.020 0.573 0.000 1.614 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 131 672 209 1753 0 175 -1
normalized size 1 1.00 1.62 8.30 2.58 21.64 0.00 2.16 -0.01
time (sec) N/A 0.126 1.568 0.405 0.336 0.447 0.000 1.221 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 139 139 1457 1173 1255 7158 0 309 -1
normalized size 1 1.00 10.48 8.44 9.03 51.50 0.00 2.22 -0.01
time (sec) N/A 0.246 12.056 0.430 0.927 0.568 0.000 0.966 0.000
Problem 163 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 73 73 129 82 193 1666 0 187 94
normalized size 1 1.00 1.77 1.12 2.64 22.82 0.00 2.56 1.29
time (sec) N/A 0.082 2.010 0.207 0.420 0.454 0.000 0.526 1.604
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 146 146 301 1283 402 6538 0 327 -1
normalized size 1 1.00 2.06 8.79 2.75 44.78 0.00 2.24 -0.01
time (sec) N/A 0.181 6.209 0.411 0.528 0.570 0.000 0.856 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 155 1046 419 4132 0 475 -1
normalized size 1 1.00 1.19 8.05 3.22 31.78 0.00 3.65 -0.01
time (sec) N/A 0.186 1.056 0.473 0.721 0.847 0.000 0.716 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 182 182 2083 1433 1971 11606 0 402 -1
normalized size 1 1.00 11.45 7.87 10.83 63.77 0.00 2.21 -0.01
time (sec) N/A 0.403 7.228 0.507 0.941 0.630 0.000 1.272 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 172 1128 692 10255 0 766 -1
normalized size 1 1.00 1.13 7.42 4.55 67.47 0.00 5.04 -0.01
time (sec) N/A 0.243 1.922 0.570 0.538 1.341 0.000 2.475 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B F(-1) F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 232 232 3334 1610 4920 0 0 482 -1
normalized size 1 1.00 14.37 6.94 21.21 0.00 0.00 2.08 -0.00
time (sec) N/A 0.514 7.738 0.567 1.838 0.000 0.000 2.587 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B F(-1) F(-1) B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 207 207 1405 2880 718 0 0 594 -1
normalized size 1 1.00 6.79 13.91 3.47 0.00 0.00 2.87 -0.00
time (sec) N/A 0.346 6.926 0.446 0.840 0.000 0.000 0.853 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 25 120 33 183 0 72 -1
normalized size 1 1.00 0.86 4.14 1.14 6.31 0.00 2.48 -0.03
time (sec) N/A 0.031 0.023 0.284 0.460 0.671 0.000 0.126 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 79 13 18 0 26 -1
normalized size 1 1.00 1.00 5.64 0.93 1.29 0.00 1.86 -0.07
time (sec) N/A 0.022 0.006 0.299 0.606 0.773 0.000 0.117 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 79 22 18 0 31 -1
normalized size 1 1.00 1.00 5.64 1.57 1.29 0.00 2.21 -0.07
time (sec) N/A 0.024 0.010 0.258 0.670 0.534 0.000 0.134 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 27 123 33 1 0 83 -1
normalized size 1 1.00 0.79 3.62 0.97 0.03 0.00 2.44 -0.03
time (sec) N/A 0.029 0.014 0.316 0.489 0.679 0.000 0.142 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 81 13 1 0 31 -1
normalized size 1 1.00 1.00 5.06 0.81 0.06 0.00 1.94 -0.06
time (sec) N/A 0.020 0.006 0.321 0.545 0.513 0.000 0.125 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 81 22 1 0 37 -1
normalized size 1 1.00 1.00 5.06 1.38 0.06 0.00 2.31 -0.06
time (sec) N/A 0.022 0.010 0.299 0.439 0.492 0.000 0.141 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 114 0 0 4594 0 0 -1
normalized size 1 1.00 1.37 0.00 0.00 55.35 0.00 0.00 -0.01
time (sec) N/A 0.147 0.749 0.453 0.000 1.326 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 192 0 0 8852 0 0 -1
normalized size 1 1.00 1.54 0.00 0.00 70.82 0.00 0.00 -0.01
time (sec) N/A 0.313 0.470 0.397 0.000 1.218 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 90 0 0 2394 0 0 -1
normalized size 1 1.00 1.53 0.00 0.00 40.58 0.00 0.00 -0.02
time (sec) N/A 0.107 0.397 0.319 0.000 0.730 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 150 0 0 4316 0 0 -1
normalized size 1 1.00 1.72 0.00 0.00 49.61 0.00 0.00 -0.01
time (sec) N/A 0.218 0.287 0.273 0.000 0.889 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 90 43 0 1608 0 0 32
normalized size 1 1.00 2.25 1.08 0.00 40.20 0.00 0.00 0.80
time (sec) N/A 0.063 0.274 0.067 0.000 0.486 0.000 0.000 1.710
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 134 0 0 2949 0 0 -1
normalized size 1 1.00 2.27 0.00 0.00 49.98 0.00 0.00 -0.02
time (sec) N/A 0.045 0.741 0.308 0.000 0.584 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 111 0 0 3597 0 0 -1
normalized size 1 1.00 1.98 0.00 0.00 64.23 0.00 0.00 -0.02
time (sec) N/A 0.108 0.130 0.381 0.000 0.616 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 75 0 0 1303 0 0 -1
normalized size 1 1.00 1.56 0.00 0.00 27.15 0.00 0.00 -0.02
time (sec) N/A 0.178 0.521 0.388 0.000 0.523 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 156 0 0 5247 0 0 -1
normalized size 1 1.00 1.88 0.00 0.00 63.22 0.00 0.00 -0.01
time (sec) N/A 0.143 0.594 0.411 0.000 0.634 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 149 0 0 2341 0 0 -1
normalized size 1 1.00 1.77 0.00 0.00 27.87 0.00 0.00 -0.01
time (sec) N/A 0.248 0.625 0.412 0.000 0.622 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 191 0 0 0 0 0 -1
normalized size 1 1.00 1.53 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.221 1.022 0.419 0.000 0.000 0.000 0.000 0.000
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 129 0 0 4226 0 0 -1
normalized size 1 1.00 1.70 0.00 0.00 55.61 0.00 0.00 -0.01
time (sec) N/A 0.128 0.971 0.302 0.000 2.146 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 197 0 0 8582 0 0 -1
normalized size 1 1.00 1.58 0.00 0.00 68.66 0.00 0.00 -0.01
time (sec) N/A 0.361 0.853 0.293 0.000 1.153 0.000 0.000 0.000
Problem 189 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 57 57 65 56 0 2312 0 0 45
normalized size 1 1.00 1.14 0.98 0.00 40.56 0.00 0.00 0.79
time (sec) N/A 0.084 0.116 0.049 0.000 0.842 0.000 0.000 3.359
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 152 0 0 4140 0 0 -1
normalized size 1 1.00 1.73 0.00 0.00 47.05 0.00 0.00 -0.01
time (sec) N/A 0.091 0.275 0.283 0.000 1.851 0.000 0.000 0.000
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 159 0 0 4123 0 134 -1
normalized size 1 1.00 2.27 0.00 0.00 58.90 0.00 1.91 -0.01
time (sec) N/A 0.132 0.517 0.365 0.000 1.307 0.000 0.473 0.000
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 144 0 0 3349 0 222 -1
normalized size 1 1.00 1.78 0.00 0.00 41.35 0.00 2.74 -0.01
time (sec) N/A 0.232 0.350 0.375 0.000 4.041 0.000 0.523 0.000
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 280 0 0 0 0 0 -1
normalized size 1 1.00 1.65 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.194 9.281 0.620 0.000 0.000 0.000 0.000 0.000
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 109 0 0 2678 0 0 -1
normalized size 1 1.00 1.65 0.00 0.00 40.58 0.00 0.00 -0.02
time (sec) N/A 0.131 0.520 0.414 0.000 0.613 0.000 0.000 0.000
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 169 0 0 4569 0 0 -1
normalized size 1 1.00 1.88 0.00 0.00 50.77 0.00 0.00 -0.01
time (sec) N/A 0.228 0.530 0.401 0.000 0.658 0.000 0.000 0.000
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 105 0 0 1650 0 0 -1
normalized size 1 1.00 2.50 0.00 0.00 39.29 0.00 0.00 -0.02
time (sec) N/A 0.093 0.225 0.358 0.000 0.524 0.000 0.000 0.000
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 107 0 0 2856 0 0 -1
normalized size 1 1.00 1.78 0.00 0.00 47.60 0.00 0.00 -0.02
time (sec) N/A 0.193 0.181 0.352 0.000 0.562 0.000 0.000 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 70 30 0 1430 0 0 19
normalized size 1 1.00 2.80 1.20 0.00 57.20 0.00 0.00 0.76
time (sec) N/A 0.053 0.083 0.118 0.000 0.465 0.000 0.000 1.667
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 62 0 0 1059 0 0 -1
normalized size 1 1.00 2.14 0.00 0.00 36.52 0.00 0.00 -0.03
time (sec) N/A 0.025 0.041 0.369 0.000 0.453 0.000 0.000 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 124 0 0 3663 0 0 -1
normalized size 1 1.00 2.21 0.00 0.00 65.41 0.00 0.00 -0.02
time (sec) N/A 0.103 0.261 0.402 0.000 0.574 0.000 0.000 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 94 0 0 1365 0 0 -1
normalized size 1 1.00 1.77 0.00 0.00 25.75 0.00 0.00 -0.02
time (sec) N/A 0.188 0.112 0.470 0.000 0.510 0.000 0.000 0.000
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 159 0 0 6475 0 0 -1
normalized size 1 1.00 1.77 0.00 0.00 71.94 0.00 0.00 -0.01
time (sec) N/A 0.161 0.848 0.411 0.000 0.734 0.000 0.000 0.000
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 129 0 0 3360 0 0 -1
normalized size 1 1.00 1.90 0.00 0.00 49.41 0.00 0.00 -0.01
time (sec) N/A 0.147 0.531 0.382 0.000 0.676 0.000 0.000 0.000
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 169 0 0 5170 0 0 -1
normalized size 1 1.00 1.97 0.00 0.00 60.12 0.00 0.00 -0.01
time (sec) N/A 0.252 0.409 0.378 0.000 0.700 0.000 0.000 0.000
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 103 0 0 2194 0 0 -1
normalized size 1 1.00 2.10 0.00 0.00 44.78 0.00 0.00 -0.02
time (sec) N/A 0.115 0.234 0.335 0.000 0.537 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 128 0 0 1733 0 0 -1
normalized size 1 1.00 2.51 0.00 0.00 33.98 0.00 0.00 -0.02
time (sec) N/A 0.218 0.755 0.334 0.000 0.542 0.000 0.000 0.000
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 98 46 0 2034 44 0 35
normalized size 1 1.00 2.28 1.07 0.00 47.30 1.02 0.00 0.81
time (sec) N/A 0.073 0.396 0.099 0.000 0.519 5.925 0.000 1.741
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 107 0 0 2095 0 0 -1
normalized size 1 1.00 1.88 0.00 0.00 36.75 0.00 0.00 -0.02
time (sec) N/A 0.045 0.841 0.280 0.000 0.550 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(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 155 0 0 6939 0 0 -1
normalized size 1 1.00 1.96 0.00 0.00 87.84 0.00 0.00 -0.01
time (sec) N/A 0.140 0.686 0.393 0.000 0.738 0.000 0.000 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 120 0 0 3941 0 0 -1
normalized size 1 1.00 1.36 0.00 0.00 44.78 0.00 0.00 -0.01
time (sec) N/A 0.274 0.458 0.399 0.000 0.670 0.000 0.000 0.000
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 178 0 0 0 0 0 -1
normalized size 1 1.00 1.51 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.339 0.747 0.395 0.000 0.000 0.000 0.000 0.000
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 126 0 0 5184 0 0 -1
normalized size 1 1.00 1.66 0.00 0.00 68.21 0.00 0.00 -0.01
time (sec) N/A 0.158 0.564 0.377 0.000 0.764 0.000 0.000 0.000
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 290 0 0 3559 0 0 -1
normalized size 1 1.00 3.22 0.00 0.00 39.54 0.00 0.00 -0.01
time (sec) N/A 0.262 2.168 0.382 0.000 0.696 0.000 0.000 0.000
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 124 0 0 4644 0 0 -1
normalized size 1 1.00 1.82 0.00 0.00 68.29 0.00 0.00 -0.01
time (sec) N/A 0.124 0.999 0.385 0.000 0.726 0.000 0.000 0.000
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 290 0 0 4989 0 0 -1
normalized size 1 1.00 3.30 0.00 0.00 56.69 0.00 0.00 -0.01
time (sec) N/A 0.248 1.199 0.334 0.000 0.770 0.000 0.000 0.000
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 112 61 0 3994 65 0 50
normalized size 1 1.00 1.81 0.98 0.00 64.42 1.05 0.00 0.81
time (sec) N/A 0.087 0.718 0.106 0.000 0.703 12.680 0.000 3.069
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 130 0 0 6299 0 0 -1
normalized size 1 1.00 1.37 0.00 0.00 66.31 0.00 0.00 -0.01
time (sec) N/A 0.090 0.451 0.285 0.000 0.801 0.000 0.000 0.000
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 242 0 0 0 0 0 -1
normalized size 1 1.00 2.22 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.200 1.114 0.381 0.000 0.000 0.000 0.000 0.000
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 155 0 0 11205 0 0 -1
normalized size 1 1.00 1.17 0.00 0.00 84.25 0.00 0.00 -0.01
time (sec) N/A 0.376 0.829 0.401 0.000 4.182 0.000 0.000 0.000
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 330 0 0 0 0 0 -1
normalized size 1 1.00 1.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.191 7.985 0.604 0.000 0.000 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 [190] had the largest ratio of [.5833]

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 5 5 1.00 21 0.238
2 A 3 2 1.00 21 0.095
3 A 4 4 1.00 21 0.190
4 A 3 2 1.00 19 0.105
5 A 3 3 1.00 19 0.158
6 A 3 2 1.00 21 0.095
7 A 4 4 1.00 21 0.190
8 A 3 2 1.00 21 0.095
9 A 6 5 1.00 23 0.217
10 A 3 2 1.00 23 0.087
11 A 5 5 1.00 23 0.217
12 A 3 2 1.00 21 0.095
13 A 4 3 1.00 21 0.143
14 A 3 2 1.00 23 0.087
15 A 5 5 1.00 23 0.217
16 A 3 2 1.00 23 0.087
17 A 6 5 1.00 23 0.217
18 A 3 2 1.00 23 0.087
19 A 6 5 1.28 23 0.217
20 A 3 2 1.00 21 0.095
21 A 4 3 1.00 21 0.143
22 A 3 2 1.00 23 0.087
23 A 5 4 1.00 23 0.174
24 A 3 2 1.00 23 0.087
25 A 6 6 1.00 23 0.261
26 A 4 4 1.00 23 0.174
27 A 5 5 1.00 23 0.217
28 A 3 3 1.00 21 0.143
29 A 4 4 1.00 21 0.190
30 A 3 3 1.00 23 0.130
31 A 5 5 1.00 23 0.217
32 A 4 4 1.00 23 0.174
33 A 7 6 1.00 23 0.261
34 A 5 4 1.00 23 0.174
35 A 6 6 1.00 23 0.261
36 A 4 4 1.00 21 0.190
37 A 5 5 1.00 21 0.238
38 A 4 4 1.00 23 0.174
39 A 6 6 1.00 23 0.261
40 A 5 4 1.00 23 0.174
41 A 8 6 1.00 23 0.261
42 A 6 5 1.00 23 0.217
43 A 7 6 1.00 23 0.261
44 A 5 4 1.00 21 0.190
45 A 6 6 1.00 21 0.286
46 A 5 4 1.00 23 0.174
47 A 7 7 1.00 23 0.304
48 A 6 5 1.00 23 0.217
49 A 3 3 1.00 21 0.143
50 A 3 2 1.00 21 0.095
51 A 2 2 1.00 21 0.095
52 A 2 2 1.00 19 0.105
53 A 2 2 1.00 19 0.105
54 A 3 3 1.43 21 0.143
55 A 3 3 1.00 21 0.143
56 A 3 2 1.30 21 0.095
57 A 4 4 1.00 23 0.174
58 A 4 3 1.00 23 0.130
59 A 5 4 1.00 23 0.174
60 A 5 4 1.00 21 0.190
61 A 4 4 1.00 21 0.190
62 A 3 2 1.00 23 0.087
63 A 5 5 1.00 23 0.217
64 A 3 2 1.00 23 0.087
65 A 6 5 1.00 23 0.217
66 A 5 4 1.00 23 0.174
67 A 5 4 1.00 23 0.174
68 A 6 5 1.00 21 0.238
69 A 5 5 1.00 21 0.238
70 A 3 2 1.00 23 0.087
71 A 6 6 1.00 23 0.261
72 A 3 2 1.00 23 0.087
73 A 6 6 1.00 23 0.261
74 A 4 3 1.00 23 0.130
75 A 5 5 1.00 23 0.217
76 A 3 3 1.00 21 0.143
77 A 2 2 1.00 21 0.095
78 A 2 2 1.00 23 0.087
79 A 4 4 1.00 23 0.174
80 A 3 3 1.00 23 0.130
81 A 5 5 1.00 23 0.217
82 A 4 3 1.00 23 0.130
83 A 5 4 1.00 23 0.174
84 A 6 6 1.00 23 0.261
85 A 5 4 1.00 21 0.190
86 A 3 3 1.00 21 0.143
87 A 3 3 1.00 23 0.130
88 A 3 3 1.00 23 0.130
89 A 3 3 1.00 23 0.130
90 A 5 5 1.00 23 0.217
91 A 5 4 1.00 23 0.174
92 A 6 6 1.00 23 0.261
93 A 7 6 1.00 23 0.261
94 A 6 5 1.00 21 0.238
95 A 4 4 1.00 21 0.190
96 A 4 3 1.00 23 0.130
97 A 4 4 1.00 23 0.174
98 A 4 4 1.00 23 0.174
99 A 4 3 1.00 23 0.130
100 A 4 4 1.00 23 0.174
101 A 6 6 1.00 23 0.261
102 A 4 3 1.00 21 0.143
103 A 4 3 1.00 21 0.143
104 A 4 3 1.00 21 0.143
105 A 3 2 1.00 19 0.105
106 A 3 2 1.00 12 0.167
107 A 4 3 1.00 19 0.158
108 A 4 3 1.00 21 0.143
109 A 4 3 1.00 21 0.143
110 A 4 3 1.00 21 0.143
111 A 4 3 1.00 21 0.143
112 A 4 3 1.00 23 0.130
113 A 4 3 1.00 23 0.130
114 A 4 3 1.00 23 0.130
115 A 4 3 1.00 21 0.143
116 A 4 3 1.00 14 0.214
117 A 4 3 1.00 21 0.143
118 A 4 3 1.00 23 0.130
119 A 4 3 1.00 23 0.130
120 A 4 3 1.00 23 0.130
121 A 4 3 1.00 23 0.130
122 A 4 3 1.00 23 0.130
123 A 5 4 1.00 23 0.174
124 A 4 3 1.00 23 0.130
125 A 5 4 1.00 23 0.174
126 A 4 3 1.00 23 0.130
127 A 4 3 1.00 21 0.143
128 A 4 3 1.00 14 0.214
129 A 4 3 1.00 21 0.143
130 A 4 3 1.00 23 0.130
131 A 4 3 1.00 23 0.130
132 A 4 3 1.00 23 0.130
133 A 4 3 1.00 23 0.130
134 A 4 3 1.00 23 0.130
135 A 4 3 1.00 23 0.130
136 A 4 3 1.00 14 0.214
137 A 4 3 1.00 14 0.214
138 A 4 3 1.00 23 0.130
139 A 6 6 1.00 23 0.261
140 A 4 3 1.00 23 0.130
141 A 5 5 1.00 23 0.217
142 A 2 2 1.00 21 0.095
143 A 3 3 1.00 14 0.214
144 A 4 3 1.00 21 0.143
145 A 6 6 1.00 23 0.261
146 A 4 3 1.00 23 0.130
147 A 7 7 1.00 23 0.304
148 A 4 3 1.00 23 0.130
149 A 6 6 1.00 23 0.261
150 A 4 3 1.00 23 0.130
151 A 6 6 1.00 23 0.261
152 A 4 3 1.00 21 0.143
153 A 5 5 1.00 14 0.357
154 A 4 3 1.00 21 0.143
155 A 7 7 1.00 23 0.304
156 A 4 3 1.00 23 0.130
157 A 8 7 1.00 23 0.304
158 A 7 7 1.00 23 0.304
159 A 4 3 1.00 23 0.130
160 A 7 7 1.00 23 0.304
161 A 4 3 1.00 23 0.130
162 A 7 7 1.00 23 0.304
163 A 4 3 1.00 21 0.143
164 A 6 6 1.00 14 0.429
165 A 4 3 1.00 21 0.143
166 A 8 8 1.00 23 0.348
167 A 4 3 1.00 23 0.130
168 A 9 8 1.00 23 0.348
169 A 7 6 1.00 14 0.429
170 A 4 4 1.00 12 0.333
171 A 3 3 1.00 12 0.250
172 A 3 3 1.00 12 0.250
173 A 4 4 1.00 10 0.400
174 A 3 3 1.00 10 0.300
175 A 3 3 1.00 10 0.300
176 A 7 6 1.00 17 0.353
177 A 9 9 1.00 17 0.529
178 A 6 6 1.00 17 0.353
179 A 8 8 1.00 17 0.471
180 A 5 5 1.00 15 0.333
181 A 6 6 1.00 12 0.500
182 A 7 5 1.00 15 0.333
183 A 6 6 1.00 17 0.353
184 A 8 6 1.00 17 0.353
185 A 7 7 1.00 17 0.412
186 A 9 7 1.00 17 0.412
187 A 7 6 1.00 17 0.353
188 A 9 9 1.00 17 0.529
189 A 6 5 1.00 15 0.333
190 A 7 7 1.00 12 0.583
191 A 8 6 1.00 15 0.400
192 A 8 8 1.00 17 0.471
193 A 8 8 1.00 16 0.500
194 A 6 5 1.00 17 0.294
195 A 8 8 1.00 17 0.471
196 A 5 5 1.00 17 0.294
197 A 7 7 1.00 17 0.412
198 A 4 4 1.00 15 0.267
199 A 3 3 1.00 12 0.250
200 A 7 5 1.00 15 0.333
201 A 6 6 1.00 17 0.353
202 A 8 6 1.00 17 0.353
203 A 6 5 1.00 17 0.294
204 A 8 8 1.00 17 0.471
205 A 5 5 1.00 17 0.294
206 A 5 5 1.00 17 0.294
207 A 5 5 1.00 15 0.333
208 A 4 4 1.00 12 0.333
209 A 8 6 1.00 15 0.400
210 A 7 7 1.00 17 0.412
211 A 9 9 1.00 17 0.529
212 A 6 5 1.00 17 0.294
213 A 7 7 1.00 17 0.412
214 A 6 6 1.00 17 0.353
215 A 7 7 1.00 17 0.412
216 A 6 5 1.00 15 0.333
217 A 6 6 1.00 12 0.500
218 A 9 7 1.00 15 0.467
219 A 8 8 1.00 17 0.471
220 A 7 6 1.00 16 0.375

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