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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, 68, 71, 72, 73, 74, 75, 76, 79, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 120, 127, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 147, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 199, 206, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243 }

B grade: { 65, 67, 69, 77, 78, 117, 119, 121, 123, 124, 125, 126, 144, 146, 148, 155, 172, 174 }

C grade: { 64, 66, 70, 116, 118, 122, 143, 145, 149, 171, 175 }

F grade: { 80, 81, 90, 91, 92, 93, 128, 129, 150, 151, 152, 153, 156, 195, 196, 197, 198, 200, 201, 202, 203, 204, 205, 207, 208, 221, 223 }

2.1.2 Mathematica

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, 32, 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, 73, 74, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 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, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 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, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241, 242, 243 }

B grade: { }

C grade: { 31, 33, 80, 128, 151, 153, 227, 236 }

F grade: { 71, 72, 75, 76, 90, 91, 92, 93, 176, 177, 180, 181 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 18, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 119, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 148, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 174, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 194, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 231, 232, 234, 235, 238, 239, 240, 242, 243 }

B grade: { 7, 13, 14, 15, 16, 17, 20, 21, 22, 23, 29, 54, 66, 70, 78, 118, 122, 126, 139, 143, 144, 145, 146, 149, 155, 161, 191, 195, 196, 197, 198, 200, 201, 217, 221, 227, 236 }

C grade: { 19, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 77, 103, 125, 147, 150, 151, 152, 153, 154, 156, 199, 202, 203, 204, 205, 206, 207, 208, 222, 233, 237 }

F grade: { 45, 64, 65, 68, 69, 71, 72, 73, 74, 75, 76, 79, 80, 81, 90, 91, 92, 93, 96, 116, 117, 120, 121, 123, 124, 127, 128, 129, 132, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 184, 223, 224, 225, 226, 228, 229, 230, 241 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 145, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 231, 232, 234, 235, 238, 239, 240, 242, 243 }

B grade: { 17, 21, 23, 66, 70, 118, 122, 149, 175, 191, 197, 198, 200, 201, 202, 203, 204, 207, 208, 217, 221, 223, 236, 237 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 45, 54, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 90, 91, 92, 93, 96, 103, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 132, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 176, 177, 178, 179, 180, 181, 184, 199, 205, 206, 222, 224, 225, 226, 227, 228, 229, 230, 233, 241 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 66, 70, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 122, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 145, 149, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 175, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 201, 209, 210, 211, 212, 214, 218, 219, 220, 231, 232, 234, 235, 238, 239, 240, 242, 243 }

B grade: { 60, 198, 200, 221, 223, 227, 236 }

C grade: { 213, 215, 216 }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 45, 54, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 90, 91, 92, 93, 96, 103, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 132, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 176, 177, 178, 179, 180, 181, 184, 191, 199, 202, 203, 204, 205, 206, 207, 208, 217, 222, 224, 225, 226, 228, 229, 230, 233, 237, 241 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 43, 44, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 70, 94, 95, 97, 135, 136, 137, 138, 140, 141, 142, 143, 145, 149, 157, 159, 162, 163, 164, 165, 166, 167, 168, 169, 170, 175, 182, 183, 185, 192, 193, 200, 201, 210, 231, 232, 234, 235, 238, 242 }

B grade: { 209, 211, 212 }

C grade: { 37, 158, 160, 171 }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 45, 49, 54, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 96, 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, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 176, 177, 178, 179, 180, 181, 184, 186, 187, 188, 189, 190, 191, 194, 195, 196, 197, 198, 199, 202, 203, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 233, 236, 237, 239, 240, 241, 243 }

2.1.7 Giac

A grade: { 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 55, 56, 57, 58, 59, 62, 63, 64, 94, 95, 97, 98, 99, 100, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 130, 131, 133, 134, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 182, 183, 185, 186, 216, 218, 219, 220, 231, 232, 234, 235, 239, 240, 242, 243 }

B grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 52, 53, 60, 61, 66, 85, 86, 87, 88, 89, 101, 102, 118, 135, 136, 137, 138, 140, 141, 142, 143, 145, 149, 159, 160, 171, 187, 188, 189, 190, 192, 193, 194, 209, 210, 211, 212, 214, 238 }

C grade: { 213 }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 45, 54, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 90, 91, 92, 93, 96, 103, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 191, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 215, 217, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 233, 236, 237, 241 }

2.1.8 Mupad

A grade: { 43, 44, 46, 47, 48, 49, 94, 95, 97, 98, 130, 131, 133, 134, 182, 183, 185, 186, 231, 232, 234, 235, 239, 240, 242, 243 }

B grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 70, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 122, 135, 136, 137, 138, 140, 141, 142, 143, 145, 149, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 175, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198, 200, 201, 209, 211, 212, 213, 214, 215, 216, 218, 219, 220, 221, 223, 238 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 45, 54, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 96, 103, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 132, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 176, 177, 178, 179, 180, 181, 184, 191, 199, 202, 203, 204, 205, 206, 207, 208, 210, 217, 222, 224, 225, 226, 227, 228, 229, 230, 233, 236, 237, 241 }

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 A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 81 67 70 67 63 442 52
normalized size 1 1.00 1.37 1.14 1.19 1.14 1.07 7.49 0.88
time (sec) N/A 0.033 0.011 0.008 0.313 1.333 1.621 0.312 0.839
Problem 2 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 57 57 62 60 55 69 68 403 53
normalized size 1 1.00 1.09 1.05 0.96 1.21 1.19 7.07 0.93
time (sec) N/A 0.043 0.009 0.009 0.307 1.347 1.267 0.251 0.821
Problem 3 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 48 48 70 58 61 58 53 296 43
normalized size 1 1.00 1.46 1.21 1.27 1.21 1.10 6.17 0.90
time (sec) N/A 0.029 0.010 0.008 0.308 0.802 0.914 0.165 0.773
Problem 4 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 46 46 51 51 44 58 58 258 44
normalized size 1 1.00 1.11 1.11 0.96 1.26 1.26 5.61 0.96
time (sec) N/A 0.035 0.009 0.008 0.309 0.580 0.726 0.229 0.744
Problem 5 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 37 37 59 49 50 48 42 148 35
normalized size 1 1.00 1.59 1.32 1.35 1.30 1.14 4.00 0.95
time (sec) N/A 0.017 0.008 0.007 0.303 0.580 0.492 0.291 0.727
Problem 6 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 30 30 30 29 30 42 27 156 27
normalized size 1 1.00 1.00 0.97 1.00 1.40 0.90 5.20 0.90
time (sec) N/A 0.013 0.004 0.003 0.326 0.562 0.331 0.185 0.684
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 24 47 0 0 0 0 -1
normalized size 1 1.00 0.92 1.81 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.015 0.011 0.014 0.000 0.562 0.000 0.000 0.000
Problem 8 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 36 36 39 45 39 47 41 94 33
normalized size 1 1.00 1.08 1.25 1.08 1.31 1.14 2.61 0.92
time (sec) N/A 0.026 0.008 0.010 0.321 0.696 0.726 0.133 0.700
Problem 9 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 37 37 59 49 45 43 36 135 46
normalized size 1 1.00 1.59 1.32 1.22 1.16 0.97 3.65 1.24
time (sec) N/A 0.022 0.009 0.011 0.320 1.301 0.578 0.148 0.728
Problem 10 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 54 54 59 59 49 59 70 251 46
normalized size 1 1.00 1.09 1.09 0.91 1.09 1.30 4.65 0.85
time (sec) N/A 0.036 0.010 0.012 0.317 0.592 1.219 0.144 0.730
Problem 11 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 48 48 70 58 60 52 46 292 59
normalized size 1 1.00 1.46 1.21 1.25 1.08 0.96 6.08 1.23
time (sec) N/A 0.027 0.009 0.013 0.317 1.212 0.896 0.130 1.053
Problem 12 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 65 65 70 68 61 70 80 397 71
normalized size 1 1.00 1.08 1.05 0.94 1.08 1.23 6.11 1.09
time (sec) N/A 0.041 0.010 0.013 0.327 0.628 1.911 0.158 0.911
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 164 314 215 193 211 889 171
normalized size 1 1.00 1.13 2.17 1.48 1.33 1.46 6.13 1.18
time (sec) N/A 0.327 0.073 0.032 0.368 1.181 2.737 0.177 1.042
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 162 162 161 306 0 0 0 0 -1
normalized size 1 1.00 0.99 1.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.302 0.500 0.018 0.000 0.600 0.000 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 132 278 189 160 168 603 134
normalized size 1 1.00 1.17 2.46 1.67 1.42 1.49 5.34 1.19
time (sec) N/A 0.223 0.064 0.017 0.331 0.574 1.679 0.168 0.916
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 130 130 122 270 0 0 0 0 -1
normalized size 1 1.00 0.94 2.08 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.201 0.276 0.013 0.000 0.444 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 90 239 158 122 114 301 89
normalized size 1 1.00 1.20 3.19 2.11 1.63 1.52 4.01 1.19
time (sec) N/A 0.114 0.067 0.016 0.325 0.613 0.840 0.161 0.785
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 74 74 82 123 0 0 0 0 -1
normalized size 1 1.00 1.11 1.66 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.101 0.149 0.189 0.000 0.528 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 120 701 0 0 0 0 -1
normalized size 1 1.00 1.03 5.99 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.264 0.075 0.280 0.000 0.618 0.000 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 71 71 94 248 0 0 0 0 -1
normalized size 1 1.00 1.32 3.49 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.145 0.153 0.023 0.000 0.652 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 101 253 151 135 126 278 246
normalized size 1 1.00 1.26 3.16 1.89 1.69 1.58 3.48 3.08
time (sec) N/A 0.133 0.072 0.019 0.323 0.707 1.144 0.158 1.490
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 130 130 145 339 0 0 0 0 -1
normalized size 1 1.00 1.12 2.61 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.231 0.379 0.023 0.000 0.460 0.000 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 164 290 224 173 184 612 303
normalized size 1 1.00 1.40 2.48 1.91 1.48 1.57 5.23 2.59
time (sec) N/A 0.228 0.076 0.027 0.337 0.900 1.996 0.153 1.903
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 247 247 305 1330 0 0 0 0 -1
normalized size 1 1.00 1.23 5.38 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.964 0.782 2.326 0.000 0.514 0.000 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 262 262 383 1275 0 0 0 0 -1
normalized size 1 1.00 1.46 4.87 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.774 0.809 2.219 0.000 0.692 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 185 185 245 1245 0 0 0 0 -1
normalized size 1 1.00 1.32 6.73 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.569 0.600 1.412 0.000 1.143 0.000 0.000 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 197 197 250 1177 0 0 0 0 -1
normalized size 1 1.00 1.27 5.97 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.449 0.561 1.411 0.000 0.649 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 123 123 161 6097 0 0 0 0 -1
normalized size 1 1.00 1.31 49.57 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.250 0.302 0.636 0.000 0.519 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 108 108 161 261 0 0 0 0 -1
normalized size 1 1.00 1.49 2.42 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.217 0.288 0.243 0.000 0.642 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 184 178 1470 0 0 0 0 -1
normalized size 1 1.00 0.97 7.99 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.449 0.137 0.263 0.000 0.822 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 196 1583 0 0 0 0 -1
normalized size 1 1.00 1.92 15.52 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.268 0.344 0.535 0.000 1.595 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 123 123 192 5098 0 0 0 0 -1
normalized size 1 1.00 1.56 41.45 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.294 0.293 0.710 0.000 0.550 0.000 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 200 200 323 1838 0 0 0 0 -1
normalized size 1 1.00 1.62 9.19 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.498 0.937 1.943 0.000 0.627 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 187 187 295 1281 0 0 0 0 -1
normalized size 1 1.00 1.58 6.85 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.626 0.699 1.707 0.000 1.051 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 128 107 134 296 0 0 -1
normalized size 1 1.00 1.03 0.86 1.08 2.39 0.00 0.00 -0.01
time (sec) N/A 0.086 0.078 0.045 0.424 0.579 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 115 93 118 255 0 0 -1
normalized size 1 1.00 1.08 0.88 1.11 2.41 0.00 0.00 -0.01
time (sec) N/A 0.067 0.061 0.036 0.430 0.664 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 114 89 119 223 685 0 -1
normalized size 1 1.00 1.08 0.84 1.12 2.10 6.46 0.00 -0.01
time (sec) N/A 0.061 0.053 0.034 0.430 0.750 11.725 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 98 70 103 211 0 88 -1
normalized size 1 1.00 1.15 0.82 1.21 2.48 0.00 1.04 -0.01
time (sec) N/A 0.052 0.035 0.035 0.428 0.553 0.000 0.152 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 99 78 94 221 0 93 -1
normalized size 1 1.00 1.16 0.92 1.11 2.60 0.00 1.09 -0.01
time (sec) N/A 0.055 0.046 0.031 0.434 0.654 0.000 0.172 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 107 94 101 243 0 117 -1
normalized size 1 1.00 1.00 0.88 0.94 2.27 0.00 1.09 -0.01
time (sec) N/A 0.063 0.066 0.037 0.427 1.265 0.000 0.186 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 108 94 112 253 0 117 -1
normalized size 1 1.00 1.01 0.88 1.05 2.36 0.00 1.09 -0.01
time (sec) N/A 0.066 0.053 0.034 0.434 0.647 0.000 0.202 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 122 108 130 272 0 135 -1
normalized size 1 1.00 0.98 0.86 1.04 2.18 0.00 1.08 -0.01
time (sec) N/A 0.078 0.073 0.038 0.415 1.482 0.000 0.204 0.000
Problem 43 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 19 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 -0.05
time (sec) N/A 0.024 3.831 1.756 0.000 1.079 0.000 0.000 0.000
Problem 44 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 19 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 -0.05
time (sec) N/A 0.023 2.519 1.411 0.000 0.564 0.000 0.000 0.000
Problem 45 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 72 72 59 0 0 0 0 0 -1
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.032 0.071 1.470 0.000 0.739 0.000 0.000 0.000
Problem 46 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 19 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 -0.05
time (sec) N/A 0.027 0.273 0.883 0.000 1.538 0.000 0.000 0.000
Problem 47 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 19 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 -0.05
time (sec) N/A 0.026 0.547 0.900 0.000 1.368 0.000 0.000 0.000
Problem 48 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 13 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 -0.08
time (sec) N/A 0.005 0.477 0.303 0.000 2.140 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 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 -0.05
time (sec) N/A 0.024 0.355 0.565 0.000 1.056 0.000 0.000 0.000
Problem 50 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 54 54 78 66 69 64 58 78 69
normalized size 1 1.00 1.44 1.22 1.28 1.19 1.07 1.44 1.28
time (sec) N/A 0.039 0.018 0.030 0.315 0.713 17.367 0.161 1.064
Problem 51 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 48 48 53 45 46 62 85 57 61
normalized size 1 1.00 1.10 0.94 0.96 1.29 1.77 1.19 1.27
time (sec) N/A 0.035 0.016 0.025 0.318 1.071 12.461 0.132 0.791
Problem 52 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 43 43 67 57 58 54 48 181 60
normalized size 1 1.00 1.56 1.33 1.35 1.26 1.12 4.21 1.40
time (sec) N/A 0.030 0.014 0.031 0.337 1.466 8.412 0.162 0.939
Problem 53 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 37 37 42 37 37 50 71 188 52
normalized size 1 1.00 1.14 1.00 1.00 1.35 1.92 5.08 1.41
time (sec) N/A 0.015 0.008 0.021 0.315 0.843 6.943 0.151 0.765
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 124 0 0 0 0 -1
normalized size 1 1.00 0.93 4.13 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.033 0.014 0.055 0.000 0.412 0.000 0.000 0.000
Problem 55 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 40 40 45 49 41 55 80 51 55
normalized size 1 1.00 1.12 1.22 1.02 1.38 2.00 1.28 1.38
time (sec) N/A 0.026 0.012 0.032 0.312 0.698 11.509 0.148 0.855
Problem 56 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 41 41 65 55 51 49 41 67 52
normalized size 1 1.00 1.59 1.34 1.24 1.20 1.00 1.63 1.27
time (sec) N/A 0.027 0.013 0.033 0.322 1.104 8.073 0.138 0.999
Problem 57 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 56 56 61 63 51 65 97 65 67
normalized size 1 1.00 1.09 1.12 0.91 1.16 1.73 1.16 1.20
time (sec) N/A 0.034 0.013 0.033 0.310 0.892 22.255 0.150 0.884
Problem 58 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 65 65 93 53 69 197 238 73 72
normalized size 1 1.00 1.43 0.82 1.06 3.03 3.66 1.12 1.11
time (sec) N/A 0.035 0.026 0.030 0.411 0.879 11.708 0.394 0.984
Problem 59 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 91 51 66 186 559 75 70
normalized size 1 1.00 1.44 0.81 1.05 2.95 8.87 1.19 1.11
time (sec) N/A 0.033 0.020 0.032 0.408 0.921 8.538 0.296 0.851
Problem 60 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 44 44 57 37 55 160 178 83 55
normalized size 1 1.00 1.30 0.84 1.25 3.64 4.05 1.89 1.25
time (sec) N/A 0.024 0.022 0.030 0.402 0.877 5.614 0.129 0.790
Problem 61 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 46 46 75 42 61 157 1292 79 62
normalized size 1 1.00 1.63 0.91 1.33 3.41 28.09 1.72 1.35
time (sec) N/A 0.026 0.019 0.030 0.413 1.162 10.148 0.170 0.921
Problem 62 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 91 51 65 181 1822 93 71
normalized size 1 1.00 1.44 0.81 1.03 2.87 28.92 1.48 1.13
time (sec) N/A 0.033 0.029 0.033 0.409 0.976 14.518 0.182 0.995
Problem 63 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 91 51 66 187 1867 91 71
normalized size 1 1.00 1.44 0.81 1.05 2.97 29.63 1.44 1.13
time (sec) N/A 0.032 0.030 0.034 0.405 1.017 20.466 0.219 1.026
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A F(-2) A A A A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 125 636 146 0 217 176 206 175 335
normalized size 1 5.09 1.17 0.00 1.74 1.41 1.65 1.40 2.68
time (sec) N/A 1.547 0.080 180.000 0.332 0.861 23.145 0.280 1.733
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 146 536 132 0 0 0 0 0 -1
normalized size 1 3.67 0.90 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.296 0.303 180.000 0.000 0.882 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B B A A B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 91 524 106 247 186 138 163 361 275
normalized size 1 5.76 1.16 2.71 2.04 1.52 1.79 3.97 3.02
time (sec) N/A 0.965 0.062 0.264 0.325 0.796 11.526 0.191 1.262
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 94 207 99 144 0 0 0 0 -1
normalized size 1 2.20 1.05 1.53 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.514 0.163 0.178 0.000 0.957 0.000 0.000 0.000
Problem 68 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 137 137 183 0 0 0 0 0 -1
normalized size 1 1.00 1.34 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.336 0.076 0.216 0.000 0.843 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 87 237 119 0 0 0 0 0 -1
normalized size 1 2.72 1.37 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.632 0.164 180.000 0.000 0.733 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B B A A F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 88 360 111 257 175 151 175 0 278
normalized size 1 4.09 1.26 2.92 1.99 1.72 1.99 0.00 3.16
time (sec) N/A 1.057 0.097 0.273 0.328 0.844 17.023 0.000 1.498
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1173 1173 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.334 5.620 0.383 0.000 0.000 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1129 1129 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.061 3.305 0.344 0.000 0.882 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 958 958 566 0 0 0 0 0 -1
normalized size 1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.468 2.741 0.288 0.000 0.990 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 942 942 566 0 0 0 0 0 -1
normalized size 1 1.00 0.60 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.335 3.723 0.342 0.000 0.465 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1102 1102 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.842 2.769 0.290 0.000 2.145 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1176 1176 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.990 3.269 0.296 0.000 0.677 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A C F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 141 479 185 748 0 0 0 0 -1
normalized size 1 3.40 1.31 5.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 4.216 0.499 0.390 0.000 0.660 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 134 390 213 298 0 0 0 0 -1
normalized size 1 2.91 1.59 2.22 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.323 0.086 0.200 0.000 0.904 0.000 0.000 0.000
Problem 79 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 207 207 211 0 0 0 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.560 0.210 0.214 0.000 1.121 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 125 0 222 0 0 0 0 0 -1
normalized size 1 0.00 1.78 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.780 0.433 0.289 0.000 1.286 0.000 0.000 0.000
Problem 81 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 139 0 218 0 0 0 0 0 -1
normalized size 1 0.00 1.57 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.558 0.295 0.338 0.000 1.157 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 241 302 316 57 0 0 -1
normalized size 1 1.00 0.76 0.95 1.00 0.18 0.00 0.00 -0.00
time (sec) N/A 0.334 0.131 0.056 0.422 1.309 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 240 292 310 49 0 0 -1
normalized size 1 1.00 0.76 0.92 0.98 0.15 0.00 0.00 -0.00
time (sec) N/A 0.300 0.100 0.038 0.427 2.031 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 301 301 227 280 301 34 0 0 -1
normalized size 1 1.00 0.75 0.93 1.00 0.11 0.00 0.00 -0.00
time (sec) N/A 0.251 0.080 0.039 0.422 1.292 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 285 285 227 273 296 34 0 493 -1
normalized size 1 1.00 0.80 0.96 1.04 0.12 0.00 1.73 -0.00
time (sec) N/A 0.242 0.065 0.038 0.419 1.961 0.000 0.164 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 285 285 268 272 296 38 0 505 -1
normalized size 1 1.00 0.94 0.95 1.04 0.13 0.00 1.77 -0.00
time (sec) N/A 0.248 0.111 0.034 0.411 1.829 0.000 0.851 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 301 301 268 280 277 38 0 516 -1
normalized size 1 1.00 0.89 0.93 0.92 0.13 0.00 1.71 -0.00
time (sec) N/A 0.250 0.112 0.037 0.437 0.891 0.000 0.732 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 275 292 298 45 0 532 -1
normalized size 1 1.00 0.87 0.92 0.94 0.14 0.00 1.68 -0.00
time (sec) N/A 0.278 0.094 0.040 0.425 1.122 0.000 2.613 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 281 302 297 46 0 519 -1
normalized size 1 1.00 0.89 0.95 0.94 0.15 0.00 1.64 -0.00
time (sec) N/A 0.287 0.109 0.038 0.413 0.702 0.000 7.783 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F F F F F F(-1) F F
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 6327 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 -0.00
time (sec) N/A 0.026 63.715 0.465 0.000 1.081 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F F F F F F F F
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 6177 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 -0.00
time (sec) N/A 0.026 62.666 0.386 0.000 0.645 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F F F F F F F F
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 6334 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 -0.00
time (sec) N/A 0.029 99.105 0.474 0.000 0.433 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F F F F F F F F
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 6520 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 -0.00
time (sec) N/A 0.030 52.225 0.476 0.000 0.583 0.000 0.000 0.000
Problem 94 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 21 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 -0.05
time (sec) N/A 0.024 1.854 0.183 0.000 0.545 0.000 0.000 0.000
Problem 95 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 21 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 -0.05
time (sec) N/A 0.024 1.250 0.179 0.000 0.495 0.000 0.000 0.000
Problem 96 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 74 74 64 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.040 0.059 0.179 0.000 0.563 0.000 0.000 0.000
Problem 97 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 21 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 -0.05
time (sec) N/A 0.029 0.356 0.110 0.000 1.024 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.027 0.372 0.114 0.000 0.928 0.000 0.000 0.000
Problem 99 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 54 54 78 66 69 64 0 78 69
normalized size 1 1.00 1.44 1.22 1.28 1.19 0.00 1.44 1.28
time (sec) N/A 0.038 0.018 0.031 0.304 0.595 0.000 0.143 1.108
Problem 100 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 48 48 53 45 46 62 0 57 61
normalized size 1 1.00 1.10 0.94 0.96 1.29 0.00 1.19 1.27
time (sec) N/A 0.036 0.015 0.023 0.306 0.568 0.000 0.158 0.824
Problem 101 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 43 43 67 57 58 54 0 181 60
normalized size 1 1.00 1.56 1.33 1.35 1.26 0.00 4.21 1.40
time (sec) N/A 0.030 0.014 0.029 0.305 0.710 0.000 0.145 0.957
Problem 102 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 37 37 42 37 37 50 0 188 52
normalized size 1 1.00 1.14 1.00 1.00 1.35 0.00 5.08 1.41
time (sec) N/A 0.020 0.008 0.021 0.300 0.659 0.000 0.160 0.780
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 92 0 0 0 0 -1
normalized size 1 1.00 0.93 3.07 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.034 0.014 0.098 0.000 0.733 0.000 0.000 0.000
Problem 104 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 40 40 45 49 41 55 0 51 55
normalized size 1 1.00 1.12 1.22 1.02 1.38 0.00 1.28 1.38
time (sec) N/A 0.027 0.012 0.033 0.307 0.637 0.000 0.154 0.853
Problem 105 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 41 41 65 55 51 49 0 67 52
normalized size 1 1.00 1.59 1.34 1.24 1.20 0.00 1.63 1.27
time (sec) N/A 0.027 0.012 0.033 0.306 0.562 0.000 0.148 1.022
Problem 106 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 56 56 61 63 51 65 0 65 67
normalized size 1 1.00 1.09 1.12 0.91 1.16 0.00 1.16 1.20
time (sec) N/A 0.036 0.012 0.036 0.300 0.684 0.000 0.135 0.901
Problem 107 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 174 174 196 184 162 981 0 207 125
normalized size 1 1.00 1.13 1.06 0.93 5.64 0.00 1.19 0.72
time (sec) N/A 0.220 0.044 0.035 0.402 0.753 0.000 0.199 1.574
Problem 108 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 101 101 136 99 90 260 0 109 107
normalized size 1 1.00 1.35 0.98 0.89 2.57 0.00 1.08 1.06
time (sec) N/A 0.097 0.043 0.030 0.403 1.004 0.000 0.129 2.757
Problem 109 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 165 165 187 159 155 228 0 165 118
normalized size 1 1.00 1.13 0.96 0.94 1.38 0.00 1.00 0.72
time (sec) N/A 0.197 0.056 0.032 0.405 0.652 0.000 0.211 1.470
Problem 110 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 115 115 196 172 100 151 0 125 135
normalized size 1 1.00 1.70 1.50 0.87 1.31 0.00 1.09 1.17
time (sec) N/A 0.095 0.051 0.035 0.424 0.967 0.000 0.165 3.119
Problem 111 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 176 176 198 186 164 248 0 208 127
normalized size 1 1.00 1.12 1.06 0.93 1.41 0.00 1.18 0.72
time (sec) N/A 0.284 0.031 0.032 0.414 0.644 0.000 0.288 1.259
Problem 112 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 117 117 198 114 103 166 0 126 124
normalized size 1 1.00 1.69 0.97 0.88 1.42 0.00 1.08 1.06
time (sec) N/A 0.097 0.029 0.026 0.414 0.772 0.000 0.155 2.438
Problem 113 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 165 165 187 177 155 238 0 179 118
normalized size 1 1.00 1.13 1.07 0.94 1.44 0.00 1.08 0.72
time (sec) N/A 0.249 0.026 0.031 0.412 0.614 0.000 0.440 1.248
Problem 114 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 104 104 183 105 94 117 0 106 117
normalized size 1 1.00 1.76 1.01 0.90 1.12 0.00 1.02 1.12
time (sec) N/A 0.083 0.027 0.026 0.412 0.728 0.000 0.149 2.387
Problem 115 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 174 174 196 172 160 196 0 187 125
normalized size 1 1.00 1.13 0.99 0.92 1.13 0.00 1.07 0.72
time (sec) N/A 0.267 0.053 0.035 0.418 0.578 0.000 0.436 1.276
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A F(-2) A A F(-1) A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 125 636 146 0 217 176 0 175 335
normalized size 1 5.09 1.17 0.00 1.74 1.41 0.00 1.40 2.68
time (sec) N/A 1.546 0.080 180.000 0.324 0.572 0.000 0.298 1.596
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 146 536 132 0 0 0 0 0 -1
normalized size 1 3.67 0.90 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.309 0.287 180.000 0.000 0.660 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B B A F(-1) B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 91 524 106 247 186 138 0 361 275
normalized size 1 5.76 1.16 2.71 2.04 1.52 0.00 3.97 3.02
time (sec) N/A 0.985 0.059 0.276 0.322 0.554 0.000 0.245 1.247
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 96 207 99 145 0 0 0 0 -1
normalized size 1 2.16 1.03 1.51 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.592 0.159 0.179 0.000 0.620 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 183 0 0 0 0 0 -1
normalized size 1 1.00 1.31 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.335 0.072 0.220 0.000 0.756 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 90 237 117 0 0 0 0 0 -1
normalized size 1 2.63 1.30 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.619 0.163 180.000 0.000 1.247 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B B A F(-1) F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 88 360 111 257 175 151 0 0 278
normalized size 1 4.09 1.26 2.92 1.99 1.72 0.00 0.00 3.16
time (sec) N/A 1.060 0.088 0.283 0.329 1.363 0.000 0.000 1.543
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 144 420 159 0 0 0 0 0 -1
normalized size 1 2.92 1.10 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.311 0.382 0.273 0.000 0.626 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 231 1421 334 0 0 0 0 0 -1
normalized size 1 6.15 1.45 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 6.350 0.496 0.343 0.000 0.578 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A C F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 139 479 185 750 0 0 0 0 -1
normalized size 1 3.45 1.33 5.40 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 4.204 0.316 0.436 0.000 0.951 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 130 390 208 295 0 0 0 0 -1
normalized size 1 3.00 1.60 2.27 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.467 0.257 0.205 0.000 0.764 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 210 214 0 0 0 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.565 0.190 0.222 0.000 0.692 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C F F F F(-1) F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 120 0 223 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 0.779 0.409 0.312 0.000 0.526 0.000 0.000 0.000
Problem 129 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 136 0 218 0 0 0 0 0 -1
normalized size 1 0.00 1.60 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.575 0.298 0.327 0.000 0.556 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.025 1.876 0.192 0.000 0.635 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.025 1.245 0.193 0.000 1.056 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 64 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.043 0.061 0.183 0.000 0.545 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.028 0.363 0.113 0.000 0.669 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.027 0.376 0.118 0.000 1.069 0.000 0.000 0.000
Problem 135 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 50 50 67 62 57 48 46 262 45
normalized size 1 1.00 1.34 1.24 1.14 0.96 0.92 5.24 0.90
time (sec) N/A 0.032 0.011 0.041 0.312 0.667 0.561 0.174 0.779
Problem 136 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 45 45 50 67 42 49 49 227 42
normalized size 1 1.00 1.11 1.49 0.93 1.09 1.09 5.04 0.93
time (sec) N/A 0.033 0.008 0.040 0.318 0.679 0.448 0.199 0.719
Problem 137 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 39 39 56 53 44 39 36 130 36
normalized size 1 1.00 1.44 1.36 1.13 1.00 0.92 3.33 0.92
time (sec) N/A 0.020 0.008 0.037 0.319 0.617 0.336 0.377 0.735
Problem 138 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 29 29 29 48 29 35 24 150 27
normalized size 1 1.00 1.00 1.66 1.00 1.21 0.83 5.17 0.93
time (sec) N/A 0.013 0.003 0.034 0.314 0.556 0.247 0.214 0.679
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 63 0 0 0 0 -1
normalized size 1 1.00 0.93 2.10 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.032 0.013 0.043 0.000 0.651 0.000 0.000 0.000
Problem 140 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 35 35 38 37 37 48 39 87 43
normalized size 1 1.00 1.09 1.06 1.06 1.37 1.11 2.49 1.23
time (sec) N/A 0.021 0.009 0.023 0.314 0.657 0.792 0.198 0.745
Problem 141 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 43 43 60 57 52 46 44 123 49
normalized size 1 1.00 1.40 1.33 1.21 1.07 1.02 2.86 1.14
time (sec) N/A 0.027 0.009 0.030 0.320 0.509 0.953 0.169 0.709
Problem 142 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 57 57 62 57 55 62 68 234 59
normalized size 1 1.00 1.09 1.00 0.96 1.09 1.19 4.11 1.04
time (sec) N/A 0.041 0.010 0.034 0.317 1.118 1.288 0.310 0.750
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B A A A B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 123 812 131 328 189 149 158 552 142
normalized size 1 6.60 1.07 2.67 1.54 1.21 1.28 4.49 1.15
time (sec) N/A 1.703 0.064 0.064 0.336 0.594 0.957 0.175 0.892
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 142 695 145 391 0 0 0 0 -1
normalized size 1 4.89 1.02 2.75 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.389 0.327 0.069 0.000 0.558 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B A A A B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 83 574 92 287 136 111 104 268 101
normalized size 1 6.92 1.11 3.46 1.64 1.34 1.25 3.23 1.22
time (sec) N/A 1.041 0.050 0.062 0.331 0.641 0.518 0.581 0.782
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 74 370 97 282 0 0 0 0 -1
normalized size 1 5.00 1.31 3.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.402 0.126 0.059 0.000 1.695 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 133 133 114 780 0 0 0 0 -1
normalized size 1 1.00 0.86 5.86 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.314 0.095 0.201 0.000 0.665 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 87 205 101 144 0 0 0 0 -1
normalized size 1 2.36 1.16 1.66 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.507 0.188 0.181 0.000 0.965 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A B B A A B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 87 707 119 284 165 130 124 255 235
normalized size 1 8.13 1.37 3.26 1.90 1.49 1.43 2.93 2.70
time (sec) N/A 1.247 0.072 0.051 0.329 0.700 1.173 0.177 1.284
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 203 0 286 1410 0 0 0 0 -1
normalized size 1 0.00 1.41 6.95 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.390 0.675 0.707 0.000 0.615 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 217 0 316 2033 0 0 0 0 -1
normalized size 1 0.00 1.46 9.37 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.302 0.792 0.871 0.000 0.522 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 135 0 193 5536 0 0 0 0 -1
normalized size 1 0.00 1.43 41.01 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.245 0.336 0.596 0.000 0.487 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 108 0 198 1756 0 0 0 0 -1
normalized size 1 0.00 1.83 16.26 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.701 0.279 0.363 0.000 0.889 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 208 208 171 1631 0 0 0 0 -1
normalized size 1 1.00 0.82 7.84 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.509 0.199 0.129 0.000 0.719 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 126 387 206 298 0 0 0 0 -1
normalized size 1 3.07 1.63 2.37 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.237 0.117 0.209 0.000 0.542 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 139 0 195 6645 0 0 0 0 -1
normalized size 1 0.00 1.40 47.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.102 0.352 0.565 0.000 0.625 0.000 0.000 0.000
Problem 157 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 54 54 73 64 62 53 51 71 66
normalized size 1 1.00 1.35 1.19 1.15 0.98 0.94 1.31 1.22
time (sec) N/A 0.042 0.015 0.043 0.319 0.532 9.895 0.152 1.010
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 50 65 42 52 75 52 56
normalized size 1 1.00 1.11 1.44 0.93 1.16 1.67 1.16 1.24
time (sec) N/A 0.033 0.011 0.061 0.318 0.574 6.845 0.154 0.814
Problem 159 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 43 43 62 55 49 44 41 162 57
normalized size 1 1.00 1.44 1.28 1.14 1.02 0.95 3.77 1.33
time (sec) N/A 0.030 0.011 0.040 0.315 0.549 4.599 0.180 0.865
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 39 52 34 43 61 184 47
normalized size 1 1.00 1.15 1.53 1.00 1.26 1.79 5.41 1.38
time (sec) N/A 0.018 0.007 0.057 0.324 0.683 3.200 0.169 0.789
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 154 0 0 0 0 -1
normalized size 1 1.00 0.93 5.13 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.033 0.014 0.058 0.000 0.515 0.000 0.000 0.000
Problem 162 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 37 37 42 37 37 55 76 52 56
normalized size 1 1.00 1.14 1.00 1.00 1.49 2.05 1.41 1.51
time (sec) N/A 0.020 0.010 0.023 0.318 0.554 11.523 0.189 0.842
Problem 163 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 45 45 64 57 56 52 49 66 59
normalized size 1 1.00 1.42 1.27 1.24 1.16 1.09 1.47 1.31
time (sec) N/A 0.032 0.012 0.038 0.305 0.691 15.088 0.699 0.995
Problem 164 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 57 57 62 45 55 67 94 65 66
normalized size 1 1.00 1.09 0.79 0.96 1.18 1.65 1.14 1.16
time (sec) N/A 0.040 0.013 0.037 0.322 0.637 23.618 0.239 0.894
Problem 165 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 88 53 62 170 717 67 67
normalized size 1 1.00 1.40 0.84 0.98 2.70 11.38 1.06 1.06
time (sec) N/A 0.035 0.022 0.042 0.413 0.625 11.515 0.303 0.983
Problem 166 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 61 61 86 51 61 162 702 69 65
normalized size 1 1.00 1.41 0.84 1.00 2.66 11.51 1.13 1.07
time (sec) N/A 0.033 0.019 0.040 0.420 0.646 7.790 0.207 0.895
Problem 167 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 44 44 54 39 51 138 520 57 52
normalized size 1 1.00 1.23 0.89 1.16 3.14 11.82 1.30 1.18
time (sec) N/A 0.024 0.017 0.036 0.422 0.585 5.143 0.361 0.819
Problem 168 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 46 46 72 44 57 159 620 62 59
normalized size 1 1.00 1.57 0.96 1.24 3.46 13.48 1.35 1.28
time (sec) N/A 0.031 0.018 0.037 0.423 0.534 9.307 0.224 0.960
Problem 169 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 65 65 90 55 64 189 733 72 69
normalized size 1 1.00 1.38 0.85 0.98 2.91 11.28 1.11 1.06
time (sec) N/A 0.037 0.032 0.039 0.414 0.649 13.689 0.252 0.992
Problem 170 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 65 65 90 55 65 196 797 74 69
normalized size 1 1.00 1.38 0.85 1.00 3.02 12.26 1.14 1.06
time (sec) N/A 0.038 0.025 0.040 0.416 0.530 20.045 0.183 1.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A F(-2) A A C B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 94 599 104 0 157 126 151 327 247
normalized size 1 6.37 1.11 0.00 1.67 1.34 1.61 3.48 2.63
time (sec) N/A 1.296 0.064 180.000 0.334 0.424 6.124 0.290 1.209
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 94 404 107 0 0 0 0 0 -1
normalized size 1 4.30 1.14 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.696 0.141 180.000 0.000 0.729 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 144 144 183 0 0 0 0 0 -1
normalized size 1 1.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.324 0.070 0.711 0.000 0.485 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 99 207 114 144 0 0 0 0 -1
normalized size 1 2.09 1.15 1.45 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.529 0.184 0.193 0.000 0.556 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A F(-1) B A A F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 97 770 131 0 183 143 172 0 262
normalized size 1 7.94 1.35 0.00 1.89 1.47 1.77 0.00 2.70
time (sec) N/A 1.530 0.085 180.000 0.328 0.500 16.628 0.000 1.541
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1214 1214 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.712 5.895 1.013 0.000 0.571 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1172 1172 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.208 3.172 0.843 0.000 0.642 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1549 1549 565 0 0 0 0 0 -1
normalized size 1 1.00 0.36 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.249 3.480 0.767 0.000 0.602 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1117 1117 568 0 0 0 0 0 -1
normalized size 1 1.00 0.51 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.150 3.006 0.888 0.000 0.897 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1263 1263 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.585 2.906 0.832 0.000 0.616 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 1337 1337 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.790 2.773 0.932 0.000 0.656 0.000 0.000 0.000
Problem 182 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 21 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 -0.05
time (sec) N/A 0.025 2.668 0.921 0.000 0.966 0.000 0.000 0.000
Problem 183 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 21 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 -0.05
time (sec) N/A 0.025 1.721 0.405 0.000 0.515 0.000 0.000 0.000
Problem 184 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 75 75 68 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.056 0.064 0.311 0.000 0.541 0.000 0.000 0.000
Problem 185 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 21 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 -0.05
time (sec) N/A 0.028 0.409 0.181 0.000 0.857 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.026 0.411 0.203 0.000 0.720 0.000 0.000 0.000
Problem 187 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 88 88 114 84 86 89 0 359 86
normalized size 1 1.00 1.30 0.95 0.98 1.01 0.00 4.08 0.98
time (sec) N/A 0.042 0.034 0.030 0.318 0.639 0.000 0.205 1.434
Problem 188 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 75 75 101 75 78 80 0 301 58
normalized size 1 1.00 1.35 1.00 1.04 1.07 0.00 4.01 0.77
time (sec) N/A 0.035 0.024 0.030 0.318 0.678 0.000 0.197 1.217
Problem 189 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 62 62 88 66 69 70 0 239 49
normalized size 1 1.00 1.42 1.06 1.11 1.13 0.00 3.85 0.79
time (sec) N/A 0.024 0.021 0.029 0.314 0.611 0.000 0.212 1.170
Problem 190 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 39 39 42 50 53 56 0 174 32
normalized size 1 1.00 1.08 1.28 1.36 1.44 0.00 4.46 0.82
time (sec) N/A 0.020 0.026 0.027 0.317 1.213 0.000 0.197 0.901
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 63 61 0 0 0 -1
normalized size 1 1.00 1.00 2.17 2.10 0.00 0.00 0.00 -0.03
time (sec) N/A 0.032 0.012 0.042 0.464 0.528 0.000 0.000 0.000
Problem 192 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 40 40 67 55 51 53 231 168 52
normalized size 1 1.00 1.68 1.38 1.28 1.32 5.78 4.20 1.30
time (sec) N/A 0.023 0.025 0.033 0.318 0.798 21.867 0.431 1.117
Problem 193 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 60 60 86 64 64 64 342 356 61
normalized size 1 1.00 1.43 1.07 1.07 1.07 5.70 5.93 1.02
time (sec) N/A 0.026 0.028 0.035 0.310 0.563 89.354 0.195 1.363
Problem 194 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 73 73 99 73 72 74 0 534 69
normalized size 1 1.00 1.36 1.00 0.99 1.01 0.00 7.32 0.95
time (sec) N/A 0.034 0.031 0.036 0.315 0.774 0.000 0.219 1.386
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B A A F F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 211 0 224 396 265 273 0 0 453
normalized size 1 0.00 1.06 1.88 1.26 1.29 0.00 0.00 2.15
time (sec) N/A 0.025 0.117 0.060 0.336 1.521 0.000 0.000 4.867
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B A A F F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 173 0 194 358 241 241 0 0 185
normalized size 1 0.00 1.12 2.07 1.39 1.39 0.00 0.00 1.07
time (sec) N/A 0.024 0.108 0.059 0.336 1.214 0.000 0.000 1.565
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B B A F F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 129 0 160 317 215 207 0 0 143
normalized size 1 0.00 1.24 2.46 1.67 1.60 0.00 0.00 1.11
time (sec) N/A 0.014 0.092 0.052 0.330 0.919 0.000 0.000 1.281
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B B B F F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 85 0 115 272 175 165 0 0 94
normalized size 1 0.00 1.35 3.20 2.06 1.94 0.00 0.00 1.11
time (sec) N/A 0.006 0.065 0.053 0.339 1.132 0.000 0.000 1.058
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 164 742 0 0 0 0 -1
normalized size 1 1.00 1.13 5.12 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.317 0.089 0.227 0.000 1.157 0.000 0.000 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B B B A F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 85 0 129 292 174 157 680 0 278
normalized size 1 0.00 1.52 3.44 2.05 1.85 8.00 0.00 3.27
time (sec) N/A 0.024 0.114 0.067 0.335 0.716 22.586 0.000 1.792
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B B A A F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 133 0 178 332 234 201 972 0 341
normalized size 1 0.00 1.34 2.50 1.76 1.51 7.31 0.00 2.56
time (sec) N/A 0.024 0.132 0.071 0.335 0.736 91.043 0.000 2.707
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 374 0 418 1518 1972 0 0 0 -1
normalized size 1 0.00 1.12 4.06 5.27 0.00 0.00 0.00 -0.00
time (sec) N/A 0.023 1.267 3.658 1.281 0.609 0.000 0.000 0.000
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 304 0 351 1423 1579 0 0 0 -1
normalized size 1 0.00 1.15 4.68 5.19 0.00 0.00 0.00 -0.00
time (sec) N/A 0.024 0.861 0.579 1.143 1.716 0.000 0.000 0.000
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 234 0 285 1339 1184 0 0 0 -1
normalized size 1 0.00 1.22 5.72 5.06 0.00 0.00 0.00 -0.00
time (sec) N/A 0.014 0.559 0.419 1.040 0.710 0.000 0.000 0.000
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 142 0 201 6235 0 0 0 0 -1
normalized size 1 0.00 1.42 43.91 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.006 0.287 0.320 0.000 1.347 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 248 1542 0 0 0 0 -1
normalized size 1 1.00 1.11 6.88 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.512 0.207 0.183 0.000 1.224 0.000 0.000 0.000
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 142 0 230 5199 528 0 0 0 -1
normalized size 1 0.00 1.62 36.61 3.72 0.00 0.00 0.00 -0.01
time (sec) N/A 0.022 0.323 0.634 1.730 0.628 0.000 0.000 0.000
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 234 0 333 1365 703 0 0 0 -1
normalized size 1 0.00 1.42 5.83 3.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.023 0.724 0.593 1.959 0.728 0.000 0.000 0.000
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 31 35 24 36 121 170 24
normalized size 1 1.00 0.82 0.92 0.63 0.95 3.18 4.47 0.63
time (sec) N/A 0.016 0.016 0.025 0.307 0.785 5.349 0.204 0.862
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 25 30 19 31 39 121 -1
normalized size 1 1.00 0.81 0.97 0.61 1.00 1.26 3.90 -0.03
time (sec) N/A 0.013 0.012 0.024 0.316 1.005 1.065 0.154 0.000
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 17 16 25 87 72 14
normalized size 1 1.00 1.00 0.85 0.80 1.25 4.35 3.60 0.70
time (sec) N/A 0.009 0.008 0.025 0.309 0.579 0.539 0.242 0.801
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 29 18 37 126 72 22
normalized size 1 1.00 1.00 1.21 0.75 1.54 5.25 3.00 0.92
time (sec) N/A 0.010 0.020 0.031 0.308 0.960 1.375 0.177 0.786
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A C F(-1) C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 190 190 222 194 172 1803 0 227 231
normalized size 1 1.00 1.17 1.02 0.91 9.49 0.00 1.19 1.22
time (sec) N/A 0.301 0.057 0.036 0.425 3.706 0.000 0.369 13.380
Problem 214 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 49 49 75 57 58 64 0 97 110
normalized size 1 1.00 1.53 1.16 1.18 1.31 0.00 1.98 2.24
time (sec) N/A 0.034 0.027 0.025 0.316 0.674 0.000 0.165 1.757
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A C F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 190 190 222 194 172 1848 0 0 247
normalized size 1 1.00 1.17 1.02 0.91 9.73 0.00 0.00 1.30
time (sec) N/A 0.238 0.036 0.036 0.421 3.947 0.000 0.000 11.967
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A C F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 141 179 158 1682 0 186 107
normalized size 1 1.00 0.83 1.05 0.93 9.89 0.00 1.09 0.63
time (sec) N/A 0.287 0.106 0.033 0.421 3.596 0.000 0.249 5.100
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 32 63 62 0 0 0 -1
normalized size 1 1.00 0.94 1.85 1.82 0.00 0.00 0.00 -0.03
time (sec) N/A 0.033 0.020 0.042 0.509 0.930 0.000 0.000 0.000
Problem 218 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 172 172 205 167 163 234 0 172 220
normalized size 1 1.00 1.19 0.97 0.95 1.36 0.00 1.00 1.28
time (sec) N/A 0.221 0.035 0.036 0.421 0.745 0.000 0.329 7.456
Problem 219 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 188 188 220 180 168 214 0 194 228
normalized size 1 1.00 1.17 0.96 0.89 1.14 0.00 1.03 1.21
time (sec) N/A 0.287 0.060 0.040 0.421 0.634 0.000 0.342 7.375
Problem 220 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 47 47 73 55 51 59 0 67 114
normalized size 1 1.00 1.55 1.17 1.09 1.26 0.00 1.43 2.43
time (sec) N/A 0.032 0.030 0.035 0.307 0.705 0.000 0.233 1.358
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B B B F(-1) F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 101 0 122 284 186 179 0 0 105
normalized size 1 0.00 1.21 2.81 1.84 1.77 0.00 0.00 1.04
time (sec) N/A 0.024 0.100 0.054 0.335 0.837 0.000 0.000 1.307
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 167 785 0 0 0 0 -1
normalized size 1 1.00 1.07 5.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.320 0.137 0.248 0.000 0.698 0.000 0.000 0.000
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F B B F(-1) F B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 96 0 123 0 175 173 0 0 281
normalized size 1 0.00 1.28 0.00 1.82 1.80 0.00 0.00 2.93
time (sec) N/A 0.024 0.142 0.432 0.332 1.459 0.000 0.000 2.037
Problem 224 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 66 66 73 0 0 0 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.031 0.056 0.138 0.000 0.973 0.000 0.000 0.000
Problem 225 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 67 67 73 0 0 0 0 0 -1
normalized size 1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.024 0.047 0.277 0.000 0.664 0.000 0.000 0.000
Problem 226 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 58 58 58 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 0.028 0.032 0.220 0.000 0.503 0.000 0.000 0.000
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 39 76 0 141 0 0 -1
normalized size 1 1.00 1.08 2.11 0.00 3.92 0.00 0.00 -0.03
time (sec) N/A 0.035 0.080 0.045 0.000 0.669 0.000 0.000 0.000
Problem 228 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 67 67 66 0 0 0 0 0 -1
normalized size 1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.032 0.065 0.122 0.000 0.766 0.000 0.000 0.000
Problem 229 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 70 70 73 0 0 0 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.031 0.044 0.127 0.000 0.733 0.000 0.000 0.000
Problem 230 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 72 72 73 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.034 0.044 0.131 0.000 0.699 0.000 0.000 0.000
Problem 231 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 17 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 -0.06
time (sec) N/A 0.015 13.830 0.194 0.000 0.637 0.000 0.000 0.000
Problem 232 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 15 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 -0.07
time (sec) N/A 0.006 1.973 0.233 0.000 0.980 0.000 0.000 0.000
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 183 880 0 0 0 0 -1
normalized size 1 1.00 1.24 5.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.313 0.097 0.241 0.000 1.252 0.000 0.000 0.000
Problem 234 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 19 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 -0.05
time (sec) N/A 0.023 17.796 0.123 0.000 1.136 0.000 0.000 0.000
Problem 235 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 19 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 -0.05
time (sec) N/A 0.023 17.653 0.129 0.000 1.180 0.000 0.000 0.000
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 33 61 147 129 0 0 -1
normalized size 1 1.00 1.10 2.03 4.90 4.30 0.00 0.00 -0.03
time (sec) N/A 0.021 0.043 0.042 0.416 1.316 0.000 0.000 0.000
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 22 85 104 0 0 0 -1
normalized size 1 1.00 0.92 3.54 4.33 0.00 0.00 0.00 -0.04
time (sec) N/A 0.021 0.013 0.104 0.311 0.512 0.000 0.000 0.000
Problem 238 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 19 19 17 30 15 22 15 101 15
normalized size 1 1.00 0.89 1.58 0.79 1.16 0.79 5.32 0.79
time (sec) N/A 0.006 0.002 0.046 0.309 0.635 0.194 0.164 0.071
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.024 8.422 0.246 0.000 0.685 0.000 0.000 0.000
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.024 5.973 0.234 0.000 0.527 0.000 0.000 0.000
Problem 241 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 84 88 77 0 0 0 0 0 -1
normalized size 1 1.05 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.044 0.090 0.286 0.000 0.812 0.000 0.000 0.000
Problem 242 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 21 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 -0.05
time (sec) N/A 0.027 0.382 0.064 0.000 1.074 0.000 0.000 0.000
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 -0.05
time (sec) N/A 0.026 1.830 0.296 0.000 0.588 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 [178] had the largest ratio of [2.417]

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 4 3 1.00 12 0.250
2 A 4 3 1.00 12 0.250
3 A 4 3 1.00 12 0.250
4 A 4 3 1.00 12 0.250
5 A 3 3 1.00 10 0.300
6 A 3 2 1.00 8 0.250
7 A 1 1 1.00 12 0.083
8 A 5 5 1.00 12 0.417
9 A 3 3 1.00 12 0.250
10 A 4 3 1.00 12 0.250
11 A 4 3 1.00 12 0.250
12 A 4 3 1.00 12 0.250
13 A 16 7 1.00 14 0.500
14 A 14 9 1.00 14 0.643
15 A 11 7 1.00 14 0.500
16 A 9 8 1.00 14 0.571
17 A 6 5 1.00 12 0.417
18 A 5 5 1.00 10 0.500
19 A 6 5 1.00 14 0.357
20 A 4 4 1.00 14 0.286
21 A 8 7 1.00 14 0.500
22 A 8 7 1.00 14 0.500
23 A 13 8 1.00 14 0.571
24 A 33 11 1.00 14 0.786
25 A 24 11 1.00 14 0.786
26 A 18 10 1.00 14 0.714
27 A 12 9 1.00 14 0.643
28 A 8 8 1.00 12 0.667
29 A 5 6 1.00 10 0.600
30 A 8 6 1.00 14 0.429
31 A 5 6 1.00 14 0.429
32 A 7 6 1.00 14 0.429
33 A 14 11 1.00 14 0.786
34 A 16 8 1.00 14 0.571
35 A 7 6 1.00 16 0.375
36 A 6 6 1.00 16 0.375
37 A 6 6 1.00 16 0.375
38 A 5 5 1.00 16 0.312
39 A 5 5 1.00 16 0.312
40 A 6 6 1.00 16 0.375
41 A 6 6 1.00 16 0.375
42 A 7 6 1.00 16 0.375
43 A 0 0 0.00 0 0.000
44 A 0 0 0.00 0 0.000
45 A 2 2 1.00 14 0.143
46 A 0 0 0.00 0 0.000
47 A 0 0 0.00 0 0.000
48 A 0 0 0.00 0 0.000
49 A 0 0 0.00 0 0.000
50 A 5 4 1.00 14 0.286
51 A 4 3 1.00 14 0.214
52 A 4 4 1.00 14 0.286
53 A 2 2 1.00 12 0.167
54 A 2 2 1.00 14 0.143
55 A 5 5 1.00 14 0.357
56 A 4 4 1.00 14 0.286
57 A 4 3 1.00 14 0.214
58 A 5 5 1.00 14 0.357
59 A 5 5 1.00 14 0.357
60 A 5 4 1.00 10 0.400
61 A 4 4 1.00 14 0.286
62 A 5 5 1.00 14 0.357
63 A 5 5 1.00 14 0.357
64 C 62 19 5.09 16 1.187
65 B 53 19 3.67 16 1.187
66 C 44 16 5.76 16 1.000
67 B 28 12 2.20 14 0.857
68 A 7 6 1.00 16 0.375
69 B 24 13 2.72 16 0.812
70 C 46 23 4.09 16 1.438
71 A 102 26 1.00 16 1.625
72 A 86 26 1.00 16 1.625
73 A 69 21 1.00 12 1.750
74 A 47 21 1.00 16 1.313
75 A 64 24 1.00 16 1.500
76 A 77 24 1.00 16 1.500
77 B 155 30 3.40 16 1.875
78 B 82 23 2.91 14 1.643
79 A 9 7 1.00 16 0.438
80 F 0 0 N/A 0 N/A
81 F 0 0 N/A 0 N/A
82 A 17 14 1.00 18 0.778
83 A 17 14 1.00 18 0.778
84 A 16 13 1.00 18 0.722
85 A 16 13 1.00 18 0.722
86 A 16 13 1.00 18 0.722
87 A 16 13 1.00 18 0.722
88 A 17 14 1.00 18 0.778
89 A 17 14 1.00 18 0.778
90 F 0 0 N/A 0 N/A
91 F 0 0 N/A 0 N/A
92 F 0 0 N/A 0 N/A
93 F 0 0 N/A 0 N/A
94 A 0 0 0.00 0 0.000
95 A 0 0 0.00 0 0.000
96 A 3 3 1.00 16 0.188
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 5 4 1.00 14 0.286
100 A 4 3 1.00 14 0.214
101 A 4 4 1.00 14 0.286
102 A 2 2 1.00 14 0.143
103 A 2 2 1.00 14 0.143
104 A 5 5 1.00 14 0.357
105 A 4 4 1.00 14 0.286
106 A 4 3 1.00 14 0.214
107 A 12 8 1.00 14 0.571
108 A 9 8 1.00 10 0.800
109 A 11 7 1.00 14 0.500
110 A 9 9 1.00 14 0.643
111 A 12 8 1.00 14 0.571
112 A 9 9 1.00 14 0.643
113 A 11 7 1.00 12 0.583
114 A 8 8 1.00 14 0.571
115 A 12 8 1.00 14 0.571
116 C 62 19 5.09 16 1.187
117 B 53 19 3.67 16 1.187
118 C 44 16 5.76 16 1.000
119 B 28 12 2.16 16 0.750
120 A 7 6 1.00 16 0.375
121 B 24 13 2.63 16 0.812
122 C 46 23 4.09 16 1.438
123 B 59 24 2.92 16 1.500
124 B 239 32 6.15 16 2.000
125 B 155 30 3.45 16 1.875
126 B 82 23 3.00 16 1.438
127 A 9 7 1.00 16 0.438
128 F 0 0 N/A 0 N/A
129 F 0 0 N/A 0 N/A
130 A 0 0 0.00 0 0.000
131 A 0 0 0.00 0 0.000
132 A 3 3 1.00 16 0.188
133 A 0 0 0.00 0 0.000
134 A 0 0 0.00 0 0.000
135 A 5 4 1.00 14 0.286
136 A 5 4 1.00 14 0.286
137 A 4 4 1.00 12 0.333
138 A 4 3 1.00 10 0.300
139 A 2 2 1.00 14 0.143
140 A 2 2 1.00 14 0.143
141 A 4 4 1.00 14 0.286
142 A 5 4 1.00 14 0.286
143 C 88 34 6.60 16 2.125
144 B 73 34 4.89 16 2.125
145 C 58 32 6.92 14 2.286
146 B 31 14 5.00 12 1.167
147 A 7 6 1.00 16 0.375
148 B 28 12 2.36 16 0.750
149 C 66 23 8.13 16 1.438
150 F 0 0 N/A 0 N/A
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 A 9 7 1.00 16 0.438
155 B 82 23 3.07 16 1.438
156 F 0 0 N/A 0 N/A
157 A 6 5 1.00 14 0.357
158 A 5 4 1.00 14 0.286
159 A 5 5 1.00 14 0.357
160 A 3 3 1.00 12 0.250
161 A 2 2 1.00 14 0.143
162 A 2 2 1.00 14 0.143
163 A 5 5 1.00 14 0.357
164 A 5 4 1.00 14 0.286
165 A 6 6 1.00 14 0.429
166 A 6 6 1.00 14 0.429
167 A 6 5 1.00 10 0.500
168 A 5 5 1.00 14 0.357
169 A 6 6 1.00 14 0.429
170 A 6 6 1.00 14 0.429
171 C 59 33 6.37 16 2.063
172 B 34 19 4.30 14 1.357
173 A 7 6 1.00 16 0.375
174 B 28 12 2.09 16 0.750
175 C 67 23 7.94 16 1.438
176 A 97 33 1.00 16 2.063
177 A 79 33 1.00 16 2.063
178 A 99 29 1.00 12 2.417
179 A 71 29 1.00 16 1.812
180 A 104 30 1.00 16 1.875
181 A 129 30 1.00 16 1.875
182 A 0 0 0.00 0 0.000
183 A 0 0 0.00 0 0.000
184 A 4 4 1.00 16 0.250
185 A 0 0 0.00 0 0.000
186 A 0 0 0.00 0 0.000
187 A 7 4 1.00 16 0.250
188 A 6 4 1.00 16 0.250
189 A 5 4 1.00 14 0.286
190 A 5 4 1.00 12 0.333
191 A 2 2 1.00 16 0.125
192 A 4 4 1.00 16 0.250
193 A 5 4 1.00 16 0.250
194 A 6 4 1.00 16 0.250
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 18 0.333
200 F 0 0 N/A 0 N/A
201 F 0 0 N/A 0 N/A
202 F 0 0 N/A 0 N/A
203 F 0 0 N/A 0 N/A
204 F 0 0 N/A 0 N/A
205 F 0 0 N/A 0 N/A
206 A 9 7 1.00 18 0.389
207 F 0 0 N/A 0 N/A
208 F 0 0 N/A 0 N/A
209 A 3 2 1.00 12 0.167
210 A 3 2 1.00 12 0.167
211 A 2 2 1.00 12 0.167
212 A 4 4 1.00 12 0.333
213 A 13 9 1.00 16 0.562
214 A 5 5 1.00 16 0.312
215 A 13 9 1.00 14 0.643
216 A 13 8 1.00 12 0.667
217 A 2 2 1.00 16 0.125
218 A 12 8 1.00 16 0.500
219 A 13 9 1.00 16 0.562
220 A 5 5 1.00 16 0.312
221 F 0 0 N/A 0 N/A
222 A 7 6 1.00 18 0.333
223 F 0 0 N/A 0 N/A
224 A 2 2 1.00 14 0.143
225 A 2 2 1.00 12 0.167
226 A 3 2 1.00 10 0.200
227 A 2 2 1.00 14 0.143
228 A 2 2 1.00 14 0.143
229 A 2 2 1.00 14 0.143
230 A 2 2 1.00 14 0.143
231 A 0 0 0.00 0 0.000
232 A 0 0 0.00 0 0.000
233 A 7 6 1.00 16 0.375
234 A 0 0 0.00 0 0.000
235 A 0 0 0.00 0 0.000
236 A 2 2 1.00 10 0.200
237 A 2 2 1.00 10 0.200
238 A 3 3 1.00 4 0.750
239 A 0 0 0.00 0 0.000
240 A 0 0 0.00 0 0.000
241 A 3 3 1.05 16 0.188
242 A 0 0 0.00 0 0.000
243 A 0 0 0.00 0 0.000

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