[next] [prev] [prev-tail] [tail] [up]

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, 150, 157, 176, 183, 186, 187, 188, 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, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247 }

B grade: { }

C grade: { }

F grade: { 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193 }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 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, 148, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 176, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 193, 194, 195, 196, 197, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 213, 215, 216, 226, 228, 229, 232, 233, 234, 235, 236, 237, 239, 240, 241, 242, 243, 244, 245, 246, 247 }

B grade: { 41, 42, 146, 163, 169, 170, 171, 172, 173, 174, 175, 177, 178, 190, 192, 230, 231 }

C grade: { 8, 10, 12, 18, 19, 20, 21, 36, 145, 147, 149, 151, 167, 168, 198, 199, 211, 212, 214, 217, 218, 219, 220, 221, 222, 223, 224, 225, 227, 238 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 4, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, 67, 68, 73, 81, 82, 83, 84, 85, 86, 88, 90, 95, 96, 105, 106, 112, 113, 114, 115, 116, 117, 118, 119, 120, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 146, 153, 186, 187, 188, 194, 195, 196, 197, 198, 199, 200, 201, 202, 206, 207, 208, 209, 210, 211, 212, 213, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247 }

B grade: { 3, 5, 6, 7, 8, 10, 45, 57, 58, 59, 60, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 87, 89, 91, 92, 93, 94, 97, 98, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 121, 122, 123, 124, 144, 145, 150, 157, 176, 183, 237 }

C grade: { 147, 148, 149, 151, 152, 154, 155, 156, 158, 159, 205, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 234, 235, 236 }

F grade: { 22, 23, 40, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 203, 204, 228, 229, 230, 231, 232, 233 }

2.1.4 Maxima

A grade: { 5, 6, 7, 8, 24, 25, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50, 56, 59, 60, 61, 62, 65, 66, 69, 70, 71, 72, 73, 74, 80, 82, 90, 91, 92, 93, 94, 95, 96, 105, 106, 107, 108, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 176, 183, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 224, 225, 234, 235, 236, 237, 238, 239, 243, 247 }

B grade: { 1, 2, 3, 4, 9, 10, 11, 12, 26, 41, 42, 43, 51, 52, 53, 54, 55, 57, 58, 63, 64, 75, 76, 77, 78, 79, 85, 87, 89, 97, 98, 99, 100, 101, 102, 103, 104, 186, 187, 188 }

C grade: { 27, 28, 29, 30, 31, 32 }

F grade: { 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 33, 34, 35, 36, 40, 67, 68, 81, 83, 84, 86, 88, 109, 110, 111, 112, 113, 114, 125, 126, 127, 128, 129, 130, 131, 132, 144, 145, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 222, 223, 226, 227, 228, 229, 230, 231, 232, 233, 240, 241, 242, 244, 245, 246 }

2.1.5 FriCAS

A grade: { 61, 65, 66, 71, 72, 84, 90, 93, 94, 95, 106, 112, 136, 137, 138, 139, 146, 147, 148, 149, 150, 152, 153, 154, 155, 159, 209, 215, 218, 219, 220, 224, 236, 237, 241, 243, 245, 247 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 151, 156, 157, 158, 176, 183, 186, 187, 188, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 213, 214, 216, 217, 221, 222, 223, 225, 226, 227, 234, 235, 238, 239, 240, 242, 244, 246 }

C grade: { 27, 28, 29, 30, 31, 32, 145 }

F grade: { 22, 23, 40, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 228, 229, 230, 231, 232, 233 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 41, 42, 43, 44, 45, 46, 47, 48, 49, 57, 58, 59, 60, 61, 62, 65, 66, 95, 106, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 150, 157, 176, 186, 187, 188, 196, 197, 243, 247 }

B grade: { 70, 72, 92, 94, 115, 116, 117, 118, 119, 120, 183 }

C grade: { }

F grade: { 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 50, 51, 52, 53, 54, 55, 56, 63, 64, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 121, 122, 123, 124, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 194, 195, 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, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 16, 17, 24, 26, 33, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100, 101, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 131, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 183, 187, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 234, 235, 236, 237, 238, 239, 243, 247 }

B grade: { 6, 7, 13, 14, 15, 18, 19, 20, 21, 25, 34, 35, 36, 50, 51, 55, 56, 75, 85, 87, 89, 96, 97, 102, 103, 104, 105, 109, 125, 126, 127, 128, 129, 130, 132, 143, 176, 186, 188, 226, 227 }

C grade: { 27, 28, 29, 30, 31, 32 }

F grade: { 22, 23, 40, 67, 68, 144, 145, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 228, 229, 230, 231, 232, 233, 240, 241, 242, 244, 245, 246 }

2.1.8 Mupad

A grade: { 243, 247 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 30, 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, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 176, 183, 186, 187, 188, 194, 195, 196, 197, 198, 199, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

C grade: { }

F grade: { 22, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 144, 145, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 200, 201, 202, 203, 204, 205, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246 }

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 B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 53 67 115 254 39 74 34
normalized size 1 1.00 1.23 1.56 2.67 5.91 0.91 1.72 0.79
time (sec) N/A 0.024 0.022 0.012 0.405 0.652 0.496 0.127 0.109
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 37 56 102 968 42 67 37
normalized size 1 1.00 0.88 1.33 2.43 23.05 1.00 1.60 0.88
time (sec) N/A 0.033 0.095 0.013 1.167 0.631 0.372 0.153 0.117
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 38 54 71 119 27 52 24
normalized size 1 1.00 1.36 1.93 2.54 4.25 0.96 1.86 0.86
time (sec) N/A 0.016 0.010 0.011 0.310 0.507 0.263 0.139 1.010
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 43 61 339 31 48 27
normalized size 1 1.00 1.00 1.59 2.26 12.56 1.15 1.78 1.00
time (sec) N/A 0.017 0.013 0.010 2.371 0.527 0.191 0.124 1.013
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 23 41 25 33 15 24 13
normalized size 1 1.00 1.77 3.15 1.92 2.54 1.15 1.85 1.00
time (sec) N/A 0.009 0.008 0.011 0.300 0.522 0.151 0.123 0.064
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 30 11 37 17 24 16
normalized size 1 1.00 1.00 2.73 1.00 3.36 1.55 2.18 1.45
time (sec) N/A 0.006 0.006 0.010 0.297 0.565 0.133 0.116 1.019
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 19 30 11 37 27 25 21
normalized size 1 1.00 1.73 2.73 1.00 3.36 2.45 2.27 1.91
time (sec) N/A 0.006 0.011 0.010 0.342 0.474 0.356 0.124 0.043
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 27 41 25 33 36 24 13
normalized size 1 1.00 2.08 3.15 1.92 2.54 2.77 1.85 1.00
time (sec) N/A 0.008 0.010 0.010 1.181 0.640 1.256 0.136 1.019
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 34 43 79 346 61 49 68
normalized size 1 1.00 1.26 1.59 2.93 12.81 2.26 1.81 2.52
time (sec) N/A 0.018 0.079 0.010 0.415 0.461 2.485 0.129 0.050
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 31 54 71 108 49 52 24
normalized size 1 1.00 1.11 1.93 2.54 3.86 1.75 1.86 0.86
time (sec) N/A 0.016 0.011 0.009 0.589 0.489 5.485 0.158 0.058
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 44 56 122 978 75 70 159
normalized size 1 1.00 1.05 1.33 2.90 23.29 1.79 1.67 3.79
time (sec) N/A 0.033 0.176 0.012 1.052 0.554 12.170 0.161 0.988
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 31 67 115 239 63 74 34
normalized size 1 1.00 0.72 1.56 2.67 5.56 1.47 1.72 0.79
time (sec) N/A 0.024 0.010 0.010 1.292 0.530 27.109 0.135 0.066
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 83 80 0 1556 0 293 83
normalized size 1 1.00 0.86 0.82 0.00 16.04 0.00 3.02 0.86
time (sec) N/A 0.070 0.245 0.081 0.000 0.906 0.000 0.390 1.515
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 68 63 0 980 0 173 62
normalized size 1 1.00 0.87 0.81 0.00 12.56 0.00 2.22 0.79
time (sec) N/A 0.049 0.223 0.064 0.000 0.518 0.000 0.338 1.254
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 61 62 0 638 0 131 61
normalized size 1 1.00 0.81 0.83 0.00 8.51 0.00 1.75 0.81
time (sec) N/A 0.051 0.090 0.064 0.000 0.520 0.000 0.219 1.164
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 51 47 0 593 0 88 41
normalized size 1 1.00 0.88 0.81 0.00 10.22 0.00 1.52 0.71
time (sec) N/A 0.032 0.042 0.080 0.000 0.902 0.000 0.188 1.083
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 49 46 0 599 0 89 38
normalized size 1 1.00 0.86 0.81 0.00 10.51 0.00 1.56 0.67
time (sec) N/A 0.032 0.036 0.088 0.000 0.578 0.000 0.284 1.123
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 36 65 0 924 0 144 64
normalized size 1 1.00 0.46 0.83 0.00 11.85 0.00 1.85 0.82
time (sec) N/A 0.048 0.079 0.072 0.000 0.694 0.000 0.600 1.201
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 38 64 0 1436 0 187 63
normalized size 1 1.00 0.48 0.81 0.00 18.18 0.00 2.37 0.80
time (sec) N/A 0.049 0.081 0.076 0.000 0.530 0.000 0.622 1.356
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 38 83 0 2144 0 307 80
normalized size 1 1.00 0.38 0.83 0.00 21.44 0.00 3.07 0.80
time (sec) N/A 0.067 0.122 0.079 0.000 0.703 0.000 0.715 1.506
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 26 102 0 179 63 110 71
normalized size 1 1.00 0.38 1.48 0.00 2.59 0.91 1.59 1.03
time (sec) N/A 0.060 0.027 0.036 0.000 0.513 3.699 0.147 1.318
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 45 0 0 0 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.050 0.392 0.000 0.516 0.000 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 51 0 0 0 0 0 -1
normalized size 1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.026 0.047 0.364 0.000 0.786 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 28 30 42 467 0 52 -1
normalized size 1 1.00 0.80 0.86 1.20 13.34 0.00 1.49 -0.03
time (sec) N/A 0.021 0.026 0.077 0.502 0.511 0.000 5.007 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 26 19 72 0 31 -1
normalized size 1 1.00 1.00 1.62 1.19 4.50 0.00 1.94 -0.06
time (sec) N/A 0.015 0.008 0.081 0.447 0.519 0.000 2.903 0.000
Problem 26 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 16 16 16 29 31 76 0 1 14
normalized size 1 1.00 1.00 1.81 1.94 4.75 0.00 0.06 0.88
time (sec) N/A 0.015 0.008 0.089 0.448 0.447 0.000 0.144 1.200
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 56 67 113 177 0 142 -1
normalized size 1 1.00 0.64 0.76 1.28 2.01 0.00 1.61 -0.01
time (sec) N/A 0.049 0.305 0.122 0.456 0.476 0.000 1.891 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 46 53 66 99 0 92 -1
normalized size 1 1.00 0.77 0.88 1.10 1.65 0.00 1.53 -0.02
time (sec) N/A 0.032 0.102 0.107 0.456 0.599 0.000 0.166 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 45 28 23 0 54 -1
normalized size 1 1.00 1.00 1.45 0.90 0.74 0.00 1.74 -0.03
time (sec) N/A 0.018 0.034 0.127 0.418 0.456 0.000 0.153 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 39 52 45 23 0 63 24
normalized size 1 1.00 1.26 1.68 1.45 0.74 0.00 2.03 0.77
time (sec) N/A 0.017 0.085 0.145 0.446 0.504 0.000 0.142 1.224
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 51 79 85 99 0 60 -1
normalized size 1 1.00 0.85 1.32 1.42 1.65 0.00 1.00 -0.02
time (sec) N/A 0.031 0.147 0.122 0.444 0.556 0.000 0.799 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 63 91 131 177 0 83 -1
normalized size 1 1.00 0.72 1.03 1.49 2.01 0.00 0.94 -0.01
time (sec) N/A 0.048 0.252 0.126 0.439 0.691 0.000 1.169 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 38 43 0 106 0 55 -1
normalized size 1 1.00 0.67 0.75 0.00 1.86 0.00 0.96 -0.02
time (sec) N/A 0.038 0.041 0.104 0.000 0.508 0.000 0.147 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 55 76 0 1269 0 342 -1
normalized size 1 1.00 0.64 0.88 0.00 14.76 0.00 3.98 -0.01
time (sec) N/A 0.037 0.063 0.095 0.000 0.828 0.000 0.265 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 40 62 0 376 0 115 -1
normalized size 1 1.00 0.63 0.98 0.00 5.97 0.00 1.83 -0.02
time (sec) N/A 0.030 0.035 0.090 0.000 0.632 0.000 0.193 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 26 65 0 516 0 123 -1
normalized size 1 1.00 0.41 1.02 0.00 8.06 0.00 1.92 -0.02
time (sec) N/A 0.030 0.018 0.103 0.000 0.531 0.000 0.194 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 56 46 82 2114 0 45 -1
normalized size 1 1.00 0.81 0.67 1.19 30.64 0.00 0.65 -0.01
time (sec) N/A 0.026 0.155 0.085 0.420 0.830 0.000 0.136 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 19 32 19 213 0 16 -1
normalized size 1 1.00 0.61 1.03 0.61 6.87 0.00 0.52 -0.03
time (sec) N/A 0.014 0.018 0.089 0.495 0.442 0.000 0.127 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 19 32 23 238 0 19 -1
normalized size 1 1.00 0.61 1.03 0.74 7.68 0.00 0.61 -0.03
time (sec) N/A 0.014 0.035 0.100 0.442 0.564 0.000 0.133 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 55 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.053 6.173 0.000 0.515 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 202 81 302 907 95 85 65
normalized size 1 1.00 2.02 0.81 3.02 9.07 0.95 0.85 0.65
time (sec) N/A 0.072 1.672 0.010 0.424 0.720 0.473 0.137 0.160
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 178 65 196 562 76 71 53
normalized size 1 1.00 2.31 0.84 2.55 7.30 0.99 0.92 0.69
time (sec) N/A 0.053 1.146 0.011 0.433 0.476 0.339 0.129 0.108
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 103 49 116 299 61 57 43
normalized size 1 1.00 1.84 0.88 2.07 5.34 1.09 1.02 0.77
time (sec) N/A 0.036 0.966 0.010 0.415 0.512 0.228 0.128 0.094
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 58 33 50 117 44 39 33
normalized size 1 1.00 1.61 0.92 1.39 3.25 1.22 1.08 0.92
time (sec) N/A 0.021 0.535 0.010 0.312 0.836 0.179 0.123 1.067
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 39 54 31 50 73 30 25
normalized size 1 1.00 1.39 1.93 1.11 1.79 2.61 1.07 0.89
time (sec) N/A 0.013 0.107 0.104 0.309 0.537 0.502 0.125 1.071
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 60 72 43 101 223 42 41
normalized size 1 1.00 1.18 1.41 0.84 1.98 4.37 0.82 0.80
time (sec) N/A 0.028 0.181 0.083 0.313 0.474 0.920 0.142 1.088
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 83 90 56 160 430 53 58
normalized size 1 1.00 1.14 1.23 0.77 2.19 5.89 0.73 0.79
time (sec) N/A 0.044 0.262 0.079 0.327 0.681 1.421 0.142 1.099
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 88 108 67 220 694 64 75
normalized size 1 1.00 0.92 1.12 0.70 2.29 7.23 0.67 0.78
time (sec) N/A 0.062 0.259 0.099 0.334 0.551 2.309 0.120 1.138
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 109 126 78 287 1018 75 92
normalized size 1 1.00 0.90 1.04 0.64 2.37 8.41 0.62 0.76
time (sec) N/A 0.082 0.295 0.095 0.341 0.507 3.658 0.121 1.160
Problem 50 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 57 57 65 43 83 434 0 140 44
normalized size 1 1.00 1.14 0.75 1.46 7.61 0.00 2.46 0.77
time (sec) N/A 0.041 0.207 0.053 0.444 0.700 0.000 0.146 0.192
Problem 51 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 45 45 39 35 70 252 0 96 54
normalized size 1 1.00 0.87 0.78 1.56 5.60 0.00 2.13 1.20
time (sec) N/A 0.031 0.177 0.052 0.418 0.542 0.000 0.146 0.113
Problem 52 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 33 33 33 27 57 129 0 52 26
normalized size 1 1.00 1.00 0.82 1.73 3.91 0.00 1.58 0.79
time (sec) N/A 0.021 0.069 0.048 0.411 0.469 0.000 0.139 1.119
Problem 53 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 21 21 21 17 43 50 0 27 16
normalized size 1 1.00 1.00 0.81 2.05 2.38 0.00 1.29 0.76
time (sec) N/A 0.011 0.049 0.060 0.414 0.567 0.000 0.156 0.132
Problem 54 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 32 32 32 27 57 85 0 50 26
normalized size 1 1.00 1.00 0.84 1.78 2.66 0.00 1.56 0.81
time (sec) N/A 0.023 0.078 0.066 0.407 0.516 0.000 0.142 0.128
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 49 49 53 35 69 166 0 96 32
normalized size 1 1.00 1.08 0.71 1.41 3.39 0.00 1.96 0.65
time (sec) N/A 0.031 0.149 0.058 0.420 0.440 0.000 0.157 0.115
Problem 56 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 61 61 62 43 79 266 0 140 40
normalized size 1 1.00 1.02 0.70 1.30 4.36 0.00 2.30 0.66
time (sec) N/A 0.041 0.234 0.063 0.413 0.701 0.000 0.147 0.121
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 114 322 310 2739 211 224 153
normalized size 1 1.00 0.80 2.27 2.18 19.29 1.49 1.58 1.08
time (sec) N/A 0.211 0.683 0.012 0.448 0.521 0.628 0.187 1.164
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 91 246 201 1389 144 152 113
normalized size 1 1.00 0.90 2.44 1.99 13.75 1.43 1.50 1.12
time (sec) N/A 0.124 0.364 0.014 0.419 0.831 0.419 0.162 1.086
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 67 173 118 646 100 97 77
normalized size 1 1.00 0.97 2.51 1.71 9.36 1.45 1.41 1.12
time (sec) N/A 0.065 0.354 0.014 0.416 0.617 0.287 0.143 0.112
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 54 116 49 201 54 56 44
normalized size 1 1.00 1.42 3.05 1.29 5.29 1.42 1.47 1.16
time (sec) N/A 0.023 0.112 0.012 0.310 0.572 0.189 0.124 1.044
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 64 76 56 62 224 62 60
normalized size 1 1.00 1.28 1.52 1.12 1.24 4.48 1.24 1.20
time (sec) N/A 0.054 0.090 0.089 0.321 0.524 2.132 0.132 1.143
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 94 101 127 422 3597 132 127
normalized size 1 1.00 1.11 1.19 1.49 4.96 42.32 1.55 1.49
time (sec) N/A 0.090 1.176 0.102 0.336 0.495 24.802 0.154 1.429
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 122 166 325 1427 0 205 304
normalized size 1 1.00 0.95 1.29 2.52 11.06 0.00 1.59 2.36
time (sec) N/A 0.178 2.461 0.106 0.346 0.651 0.000 0.174 2.112
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 160 230 525 3693 0 305 452
normalized size 1 1.00 0.95 1.36 3.11 21.85 0.00 1.80 2.67
time (sec) N/A 0.269 3.430 0.123 0.379 0.612 0.000 0.188 2.989
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 53 46 28 49 42 30 34
normalized size 1 1.00 1.71 1.48 0.90 1.58 1.35 0.97 1.10
time (sec) N/A 0.044 0.034 0.088 0.309 0.513 0.542 0.139 0.132
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 53 46 29 48 42 25 33
normalized size 1 1.00 1.71 1.48 0.94 1.55 1.35 0.81 1.06
time (sec) N/A 0.042 0.033 0.088 0.314 0.527 0.521 0.131 0.120
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 63 0 2203 0 0 151
normalized size 1 1.00 1.00 0.85 0.00 29.77 0.00 0.00 2.04
time (sec) N/A 0.072 0.087 0.128 0.000 0.770 0.000 0.000 1.337
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 62 0 2279 0 0 240
normalized size 1 1.00 1.00 0.84 0.00 30.80 0.00 0.00 3.24
time (sec) N/A 0.069 0.072 0.105 0.000 0.666 0.000 0.000 1.393
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 42 98 36 92 0 42 34
normalized size 1 1.00 0.70 1.63 0.60 1.53 0.00 0.70 0.57
time (sec) N/A 0.072 0.080 0.089 0.310 0.493 0.000 0.142 1.312
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 34 72 27 56 134 25 23
normalized size 1 1.00 1.36 2.88 1.08 2.24 5.36 1.00 0.92
time (sec) N/A 0.167 0.063 0.072 0.314 0.760 1.104 0.139 1.179
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 24 68 22 51 0 30 22
normalized size 1 1.00 0.63 1.79 0.58 1.34 0.00 0.79 0.58
time (sec) N/A 0.059 0.039 0.076 0.304 0.555 0.000 0.134 1.145
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 19 42 11 23 48 11 11
normalized size 1 1.00 1.12 2.47 0.65 1.35 2.82 0.65 0.65
time (sec) N/A 0.111 0.019 0.067 0.312 0.568 0.370 0.111 1.119
Problem 73 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 12 12 14 17 21 38 0 18 21
normalized size 1 1.00 1.17 1.42 1.75 3.17 0.00 1.50 1.75
time (sec) N/A 0.110 0.022 0.094 0.299 0.577 0.000 0.110 0.059
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 11 32 29 77 0 29 23
normalized size 1 1.00 0.73 2.13 1.93 5.13 0.00 1.93 1.53
time (sec) N/A 0.039 0.031 0.089 0.309 0.435 0.000 0.116 1.079
Problem 75 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 18 18 20 39 48 209 0 34 48
normalized size 1 1.00 1.11 2.17 2.67 11.61 0.00 1.89 2.67
time (sec) N/A 0.161 0.083 0.101 0.310 0.450 0.000 0.114 1.086
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 20 48 75 84 0 18 18
normalized size 1 1.00 1.18 2.82 4.41 4.94 0.00 1.06 1.06
time (sec) N/A 0.044 0.051 0.105 0.298 0.518 0.000 0.114 1.063
Problem 77 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 34 34 49 55 74 640 0 49 117
normalized size 1 1.00 1.44 1.62 2.18 18.82 0.00 1.44 3.44
time (sec) N/A 0.192 0.124 0.106 0.309 0.548 0.000 0.116 1.093
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 33 33 27 80 149 185 0 24 24
normalized size 1 1.00 0.82 2.42 4.52 5.61 0.00 0.73 0.73
time (sec) N/A 0.054 0.054 0.106 0.309 0.702 0.000 0.114 0.096
Problem 79 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 44 44 68 103 98 1260 0 61 207
normalized size 1 1.00 1.55 2.34 2.23 28.64 0.00 1.39 4.70
time (sec) N/A 0.211 0.282 0.133 0.308 0.650 0.000 0.131 1.166
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 144 320 163 1226 0 214 135
normalized size 1 1.00 0.98 2.18 1.11 8.34 0.00 1.46 0.92
time (sec) N/A 0.346 0.596 0.125 0.333 0.551 0.000 0.142 1.671
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 180 166 0 1861 0 163 261
normalized size 1 1.00 1.31 1.21 0.00 13.58 0.00 1.19 1.91
time (sec) N/A 0.279 1.234 0.118 0.000 0.776 0.000 0.142 1.456
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 73 145 83 334 0 101 81
normalized size 1 1.00 0.87 1.73 0.99 3.98 0.00 1.20 0.96
time (sec) N/A 0.162 0.267 0.115 0.329 0.811 0.000 0.126 1.434
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 79 92 0 427 0 60 157
normalized size 1 1.00 1.10 1.28 0.00 5.93 0.00 0.83 2.18
time (sec) N/A 0.116 0.236 0.106 0.000 0.630 0.000 0.136 1.363
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 59 53 0 237 0 60 177
normalized size 1 1.00 1.13 1.02 0.00 4.56 0.00 1.15 3.40
time (sec) N/A 0.143 0.101 0.112 0.000 0.451 0.000 0.122 1.397
Problem 85 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 29 29 28 56 65 122 0 78 323
normalized size 1 1.00 0.97 1.93 2.24 4.21 0.00 2.69 11.14
time (sec) N/A 0.054 0.099 0.124 0.318 0.867 0.000 0.138 1.509
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 123 110 0 1165 0 125 506
normalized size 1 1.00 1.50 1.34 0.00 14.21 0.00 1.52 6.17
time (sec) N/A 0.293 0.372 0.132 0.000 0.586 0.000 0.121 1.511
Problem 87 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 78 78 70 166 161 912 0 202 123
normalized size 1 1.00 0.90 2.13 2.06 11.69 0.00 2.59 1.58
time (sec) N/A 0.100 0.290 0.135 0.330 0.514 0.000 0.141 1.330
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 255 255 296 311 0 5347 0 273 753
normalized size 1 1.00 1.16 1.22 0.00 20.97 0.00 1.07 2.95
time (sec) N/A 0.548 0.890 0.142 0.000 0.656 0.000 0.128 3.307
Problem 89 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 130 130 119 333 308 2972 0 412 237
normalized size 1 1.00 0.92 2.56 2.37 22.86 0.00 3.17 1.82
time (sec) N/A 0.154 0.688 0.138 0.333 0.595 0.000 0.133 1.326
Problem 90 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 33 33 46 29 34 43 0 28 61
normalized size 1 1.00 1.39 0.88 1.03 1.30 0.00 0.85 1.85
time (sec) N/A 0.102 0.072 0.126 0.410 0.519 0.000 0.148 0.458
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 42 116 36 95 0 42 34
normalized size 1 1.00 0.70 1.93 0.60 1.58 0.00 0.70 0.57
time (sec) N/A 0.061 0.050 0.117 0.311 0.492 0.000 0.110 1.286
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 36 80 33 60 134 31 29
normalized size 1 1.00 1.24 2.76 1.14 2.07 4.62 1.07 1.00
time (sec) N/A 0.042 0.050 0.091 0.310 0.565 1.111 0.115 1.187
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 30 76 22 52 0 30 22
normalized size 1 1.00 0.79 2.00 0.58 1.37 0.00 0.79 0.58
time (sec) N/A 0.049 0.034 0.095 0.310 0.376 0.000 0.135 0.126
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 23 40 17 25 48 19 17
normalized size 1 1.00 1.21 2.11 0.89 1.32 2.53 1.00 0.89
time (sec) N/A 0.030 0.030 0.089 0.310 0.439 0.367 0.130 1.051
Problem 95 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 10 10 7 11 6 9 8 6 6
normalized size 1 1.00 0.70 1.10 0.60 0.90 0.80 0.60 0.60
time (sec) N/A 0.020 0.004 0.007 0.309 0.468 0.302 0.112 0.038
Problem 96 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 5 5 7 6 5 20 0 13 13
normalized size 1 1.00 1.40 1.20 1.00 4.00 0.00 2.60 2.60
time (sec) N/A 0.033 0.004 0.080 0.306 0.572 0.000 0.110 1.047
Problem 97 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 6 6 12 21 22 48 0 18 18
normalized size 1 1.00 2.00 3.50 3.67 8.00 0.00 3.00 3.00
time (sec) N/A 0.035 0.026 0.084 0.414 0.423 0.000 0.140 1.041
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 34 37 53 0 10 16
normalized size 1 1.00 1.00 3.09 3.36 4.82 0.00 0.91 1.45
time (sec) N/A 0.033 0.026 0.085 0.312 0.453 0.000 0.129 1.042
Problem 99 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 24 24 24 41 49 288 0 31 61
normalized size 1 1.00 1.00 1.71 2.04 12.00 0.00 1.29 2.54
time (sec) N/A 0.042 0.030 0.087 0.416 0.469 0.000 0.116 0.091
Problem 100 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 25 25 20 56 93 140 0 18 18
normalized size 1 1.00 0.80 2.24 3.72 5.60 0.00 0.72 0.72
time (sec) N/A 0.041 0.031 0.089 0.309 0.480 0.000 0.129 1.038
Problem 101 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 34 34 34 67 73 670 0 45 137
normalized size 1 1.00 1.00 1.97 2.15 19.71 0.00 1.32 4.03
time (sec) N/A 0.048 0.036 0.089 0.412 0.500 0.000 0.122 0.085
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 140 140 137 925 386 5275 0 593 301
normalized size 1 1.00 0.98 6.61 2.76 37.68 0.00 4.24 2.15
time (sec) N/A 0.158 0.643 0.148 0.432 0.716 0.000 0.150 1.435
Problem 103 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 83 83 92 438 204 1827 0 316 169
normalized size 1 1.00 1.11 5.28 2.46 22.01 0.00 3.81 2.04
time (sec) N/A 0.111 0.406 0.151 0.422 0.586 0.000 0.134 1.290
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 49 143 89 430 0 104 88
normalized size 1 1.00 1.22 3.58 2.22 10.75 0.00 2.60 2.20
time (sec) N/A 0.066 0.190 0.121 0.415 0.611 0.000 0.139 1.266
Problem 105 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 11 11 20 12 11 42 0 45 50
normalized size 1 1.00 1.82 1.09 1.00 3.82 0.00 4.09 4.55
time (sec) N/A 0.042 0.050 0.081 0.309 0.573 0.000 0.120 0.207
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 29 55 41 42 146 43 35
normalized size 1 1.00 0.74 1.41 1.05 1.08 3.74 1.10 0.90
time (sec) N/A 0.046 0.057 0.043 0.316 0.857 0.516 0.117 1.114
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 75 175 86 331 0 111 84
normalized size 1 1.00 0.82 1.92 0.95 3.64 0.00 1.22 0.92
time (sec) N/A 0.146 0.131 0.125 0.324 0.415 0.000 0.123 1.284
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 156 354 165 1281 0 227 143
normalized size 1 1.00 1.01 2.28 1.06 8.26 0.00 1.46 0.92
time (sec) N/A 0.236 0.215 0.129 0.335 0.826 0.000 0.157 1.511
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 187 166 715 0 6509 0 326 447
normalized size 1 1.19 1.06 4.55 0.00 41.46 0.00 2.08 2.85
time (sec) N/A 0.273 0.527 0.142 0.000 0.943 0.000 0.171 7.293
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 109 116 316 0 2043 0 152 265
normalized size 1 1.07 1.14 3.10 0.00 20.03 0.00 1.49 2.60
time (sec) N/A 0.166 0.279 0.156 0.000 0.757 0.000 0.145 5.224
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 65 110 0 309 0 63 119
normalized size 1 1.00 1.16 1.96 0.00 5.52 0.00 1.12 2.12
time (sec) N/A 0.088 0.088 0.113 0.000 0.850 0.000 0.121 3.811
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 46 39 0 148 0 35 35
normalized size 1 1.00 1.24 1.05 0.00 4.00 0.00 0.95 0.95
time (sec) N/A 0.032 0.032 0.075 0.000 0.476 0.000 0.117 0.128
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 80 93 0 435 0 61 157
normalized size 1 1.00 1.10 1.27 0.00 5.96 0.00 0.84 2.15
time (sec) N/A 0.090 0.239 0.122 0.000 0.708 0.000 0.126 1.358
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 258 198 0 1871 0 162 221
normalized size 1 1.00 1.95 1.50 0.00 14.17 0.00 1.23 1.67
time (sec) N/A 0.156 0.477 0.129 0.000 0.711 0.000 0.136 2.254
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 40 40 55 571 104 47 35
normalized size 1 1.00 0.93 0.93 1.28 13.28 2.42 1.09 0.81
time (sec) N/A 0.089 0.104 0.081 0.404 0.804 0.468 0.117 0.099
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 33 32 43 354 85 39 29
normalized size 1 1.00 0.89 0.86 1.16 9.57 2.30 1.05 0.78
time (sec) N/A 0.066 0.057 0.065 0.407 0.469 0.403 0.135 1.045
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 28 29 186 75 35 21
normalized size 1 1.00 0.87 0.90 0.94 6.00 2.42 1.13 0.68
time (sec) N/A 0.051 0.051 0.052 0.408 0.485 0.351 0.135 0.075
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 23 24 17 73 61 17 21
normalized size 1 1.00 1.21 1.26 0.89 3.84 3.21 0.89 1.11
time (sec) N/A 0.038 0.030 0.059 0.414 0.707 0.322 0.115 1.065
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 24 10 26 27 10 10
normalized size 1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.62
time (sec) N/A 0.020 0.027 0.048 0.303 0.651 0.290 0.113 0.066
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 24 10 26 27 10 10
normalized size 1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.62
time (sec) N/A 0.008 0.016 0.044 0.318 0.485 0.297 0.134 1.033
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 23 43 24 73 0 18 17
normalized size 1 1.00 1.21 2.26 1.26 3.84 0.00 0.95 0.89
time (sec) N/A 0.040 0.031 0.080 0.300 0.765 0.000 0.118 0.065
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 27 59 38 196 0 36 29
normalized size 1 1.00 0.93 2.03 1.31 6.76 0.00 1.24 1.00
time (sec) N/A 0.068 0.048 0.091 0.309 0.575 0.000 0.140 1.033
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 33 75 54 357 0 40 35
normalized size 1 1.00 0.89 2.03 1.46 9.65 0.00 1.08 0.95
time (sec) N/A 0.089 0.067 0.098 0.298 0.536 0.000 0.140 0.079
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 42 91 64 582 0 48 69
normalized size 1 1.00 0.98 2.12 1.49 13.53 0.00 1.12 1.60
time (sec) N/A 0.101 0.140 0.099 0.307 0.502 0.000 0.141 1.097
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 39 35 0 252 82 96 34
normalized size 1 1.00 0.87 0.78 0.00 5.60 1.82 2.13 0.76
time (sec) N/A 0.048 0.195 0.039 0.000 0.602 11.025 0.154 0.146
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 32 26 0 129 70 53 25
normalized size 1 1.00 1.00 0.81 0.00 4.03 2.19 1.66 0.78
time (sec) N/A 0.035 0.049 0.052 0.000 0.581 2.121 0.145 1.061
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 25 0 85 66 58 24
normalized size 1 1.00 1.00 0.83 0.00 2.83 2.20 1.93 0.80
time (sec) N/A 0.037 0.060 0.089 0.000 0.465 2.646 0.176 0.129
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 51 35 0 168 82 74 32
normalized size 1 1.00 1.04 0.71 0.00 3.43 1.67 1.51 0.65
time (sec) N/A 0.049 0.132 0.059 0.000 0.481 11.451 0.163 1.088
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 53 35 0 429 82 140 34
normalized size 1 1.00 1.18 0.78 0.00 9.53 1.82 3.11 0.76
time (sec) N/A 0.058 0.210 0.064 0.000 0.690 16.131 0.157 1.111
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 26 0 237 71 96 25
normalized size 1 1.00 1.00 0.76 0.00 6.97 2.09 2.82 0.74
time (sec) N/A 0.044 0.074 0.064 0.000 0.615 3.014 0.165 0.109
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 37 35 0 182 78 54 36
normalized size 1 1.00 0.88 0.83 0.00 4.33 1.86 1.29 0.86
time (sec) N/A 0.056 0.095 0.085 0.000 0.825 3.583 0.180 0.132
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 53 35 0 168 82 101 31
normalized size 1 1.00 1.08 0.71 0.00 3.43 1.67 2.06 0.63
time (sec) N/A 0.080 0.104 0.077 0.000 0.547 12.830 0.158 1.075
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 105 96 150 1296 546 142 85
normalized size 1 1.00 1.12 1.02 1.60 13.79 5.81 1.51 0.90
time (sec) N/A 0.367 0.516 0.065 0.407 0.671 1.571 0.141 0.229
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 88 76 100 644 442 98 68
normalized size 1 1.00 1.16 1.00 1.32 8.47 5.82 1.29 0.89
time (sec) N/A 0.213 0.318 0.062 0.400 0.716 1.196 0.122 0.166
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 65 67 71 264 330 75 59
normalized size 1 1.00 1.02 1.05 1.11 4.12 5.16 1.17 0.92
time (sec) N/A 0.129 0.147 0.068 0.403 1.108 0.841 0.126 1.089
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 49 60 56 76 243 58 46
normalized size 1 1.00 0.78 0.95 0.89 1.21 3.86 0.92 0.73
time (sec) N/A 0.092 0.094 0.048 0.410 0.597 0.645 0.142 0.121
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 29 55 40 43 141 43 36
normalized size 1 1.00 0.74 1.41 1.03 1.10 3.62 1.10 0.92
time (sec) N/A 0.059 0.064 0.046 0.330 0.563 0.510 0.118 1.059
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 29 55 41 42 146 43 35
normalized size 1 1.00 0.74 1.41 1.05 1.08 3.74 1.10 0.90
time (sec) N/A 0.046 0.050 0.047 0.315 0.499 0.517 0.115 0.002
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 46 78 65 73 0 58 58
normalized size 1 1.00 0.90 1.53 1.27 1.43 0.00 1.14 1.14
time (sec) N/A 0.079 0.091 0.134 0.343 0.542 0.000 0.112 0.412
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 64 100 86 271 0 75 73
normalized size 1 1.00 1.07 1.67 1.43 4.52 0.00 1.25 1.22
time (sec) N/A 0.182 0.140 0.120 0.354 0.788 0.000 0.119 1.348
Problem 141 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 76 76 91 134 121 641 0 97 111
normalized size 1 1.00 1.20 1.76 1.59 8.43 0.00 1.28 1.46
time (sec) N/A 0.309 0.205 0.131 0.356 0.486 0.000 0.119 1.416
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 108 185 173 1299 0 142 163
normalized size 1 1.00 1.11 1.91 1.78 13.39 0.00 1.46 1.68
time (sec) N/A 0.494 0.317 0.129 0.355 0.669 0.000 0.137 1.502
Problem 143 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 55 55 49 73 68 182 0 174 69
normalized size 1 1.00 0.89 1.33 1.24 3.31 0.00 3.16 1.25
time (sec) N/A 0.085 0.191 0.278 0.591 0.960 0.000 0.133 1.154
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 231 231 250 953 0 1516 0 0 -1
normalized size 1 1.00 1.08 4.13 0.00 6.56 0.00 0.00 -0.00
time (sec) N/A 0.541 2.790 0.484 0.000 0.571 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 351 351 316 1186 0 2110 0 0 -1
normalized size 1 1.00 0.90 3.38 0.00 6.01 0.00 0.00 -0.00
time (sec) N/A 0.867 2.540 0.513 0.000 0.617 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B A A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 29 0 64 24 23 28 0 23 21
normalized size 1 0.00 2.21 0.83 0.79 0.97 0.00 0.79 0.72
time (sec) N/A 0.029 0.032 0.088 0.323 0.783 0.000 0.133 1.083
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 151 0 64 37 128 158 0 123 47
normalized size 1 0.00 0.42 0.25 0.85 1.05 0.00 0.81 0.31
time (sec) N/A 0.022 0.265 0.105 0.450 0.637 0.000 0.137 1.096
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 23 0 35 41 19 22 0 19 25
normalized size 1 0.00 1.52 1.78 0.83 0.96 0.00 0.83 1.09
time (sec) N/A 0.016 0.187 0.106 0.426 0.505 0.000 0.139 1.072
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 145 0 58 33 124 154 0 119 44
normalized size 1 0.00 0.40 0.23 0.86 1.06 0.00 0.82 0.30
time (sec) N/A 0.007 0.182 0.103 0.433 0.516 0.000 0.121 1.068
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 26 10 18 15 20 15
normalized size 1 1.00 1.00 2.17 0.83 1.50 1.25 1.67 1.25
time (sec) N/A 0.014 0.025 0.012 0.317 0.993 0.231 0.139 1.123
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F C C A B F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 147 0 59 42 125 204 0 121 45
normalized size 1 0.00 0.40 0.29 0.85 1.39 0.00 0.82 0.31
time (sec) N/A 0.024 0.171 0.113 0.451 0.607 0.000 0.135 1.091
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 20 0 40 44 19 21 0 16 24
normalized size 1 0.00 2.00 2.20 0.95 1.05 0.00 0.80 1.20
time (sec) N/A 0.024 0.162 0.106 0.433 0.920 0.000 0.115 1.045
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A A A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 47 0 86 42 40 58 0 39 39
normalized size 1 0.00 1.83 0.89 0.85 1.23 0.00 0.83 0.83
time (sec) N/A 0.068 0.116 0.076 0.336 0.505 0.000 0.138 1.122
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 173 0 174 53 144 231 0 139 67
normalized size 1 0.00 1.01 0.31 0.83 1.34 0.00 0.80 0.39
time (sec) N/A 0.048 0.708 0.080 0.432 0.968 0.000 0.152 1.123
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 40 0 41 57 35 50 0 35 41
normalized size 1 0.00 1.02 1.42 0.88 1.25 0.00 0.88 1.02
time (sec) N/A 0.030 0.407 0.092 0.428 0.414 0.000 0.121 1.050
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A B F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 165 0 146 47 138 228 0 133 61
normalized size 1 0.00 0.88 0.28 0.84 1.38 0.00 0.81 0.37
time (sec) N/A 0.010 0.584 0.095 0.436 0.642 0.000 0.146 1.091
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 24 35 21 28 12 19 28
normalized size 1 1.00 1.71 2.50 1.50 2.00 0.86 1.36 2.00
time (sec) N/A 0.024 0.038 0.015 0.333 0.465 0.365 0.137 1.065
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A B F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 190 0 181 64 146 274 0 143 68
normalized size 1 0.00 0.95 0.34 0.77 1.44 0.00 0.75 0.36
time (sec) N/A 0.045 0.800 0.090 0.437 0.693 0.000 0.128 1.103
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C A A F A B
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 59 0 40 66 37 51 0 39 47
normalized size 1 0.00 0.68 1.12 0.63 0.86 0.00 0.66 0.80
time (sec) N/A 0.053 0.398 0.093 0.435 0.622 0.000 0.122 1.063
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 60 0 47 0 0 0 0 0 -1
normalized size 1 0.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.102 0.099 0.000 0.618 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 79 0 79 0 0 0 0 0 -1
normalized size 1 0.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.069 0.183 0.085 0.000 0.886 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 176 0 111 0 0 0 0 0 -1
normalized size 1 0.00 0.63 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.074 0.246 0.095 0.000 0.498 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 79 0 259 0 0 0 0 0 -1
normalized size 1 0.00 3.28 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.023 2.235 0.295 0.000 0.884 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 99 0 126 0 0 0 0 0 -1
normalized size 1 0.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.114 3.193 0.091 0.000 0.491 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 51 0 76 0 0 0 0 0 -1
normalized size 1 0.00 1.49 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 3.142 0.117 0.000 0.554 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 106 0 121 0 0 0 0 0 -1
normalized size 1 0.00 1.14 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.053 3.103 0.119 0.000 0.596 0.000 0.000 0.000
Problem 167 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 158 0 177 0 0 0 0 0 -1
normalized size 1 0.00 1.12 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 4.280 0.122 0.000 1.535 0.000 0.000 0.000
Problem 168 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 190 0 177 0 0 0 0 0 -1
normalized size 1 0.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 3.407 0.113 0.000 2.807 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0 -1
normalized size 1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.016 1.740 0.140 0.000 0.705 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0 -1
normalized size 1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.011 1.979 0.141 0.000 0.566 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0 -1
normalized size 1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.018 2.081 0.141 0.000 0.507 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 59 0 127 0 0 0 0 0 -1
normalized size 1 0.00 2.15 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.042 7.906 1.182 0.000 0.432 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 63 0 136 0 0 0 0 0 -1
normalized size 1 0.00 2.16 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.030 7.711 1.168 0.000 0.624 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 55 0 122 0 0 0 0 0 -1
normalized size 1 0.00 2.22 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.024 7.808 1.074 0.000 0.475 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 53 0 126 0 0 0 0 0 -1
normalized size 1 0.00 2.38 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.011 8.726 0.961 0.000 0.980 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 24 56 24 76 36 74 34
normalized size 1 1.00 0.96 2.24 0.96 3.04 1.44 2.96 1.36
time (sec) N/A 0.020 0.052 0.013 0.300 0.522 3.083 0.289 1.061
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 59 0 126 0 0 0 0 0 -1
normalized size 1 0.00 2.14 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.029 3.309 1.034 0.000 0.511 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 56 0 120 0 0 0 0 0 -1
normalized size 1 0.00 2.14 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.029 3.294 1.053 0.000 0.827 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F(-1) F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 133 0 159 0 0 0 0 0 -1
normalized size 1 0.00 1.20 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.086 8.266 1.087 0.000 0.639 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 137 0 169 0 0 0 0 0 -1
normalized size 1 0.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.060 8.172 1.068 0.000 0.786 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 131 0 155 0 0 0 0 0 -1
normalized size 1 0.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.043 8.337 1.041 0.000 0.495 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 127 0 163 0 0 0 0 0 -1
normalized size 1 0.00 1.28 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.014 9.096 0.986 0.000 1.010 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 51 80 36 72 70 37 34
normalized size 1 1.00 1.82 2.86 1.29 2.57 2.50 1.32 1.21
time (sec) N/A 0.029 0.085 0.014 0.411 0.552 6.719 0.294 1.063
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 135 0 162 0 0 0 0 0 -1
normalized size 1 0.00 1.20 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 3.538 1.132 0.000 0.580 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 136 0 159 0 0 0 0 0 -1
normalized size 1 0.00 1.17 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 3.587 1.086 0.000 0.476 0.000 0.000 0.000
Problem 186 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 43 43 43 67 304 566 75 127 94
normalized size 1 1.00 1.00 1.56 7.07 13.16 1.74 2.95 2.19
time (sec) N/A 0.041 0.146 0.016 0.507 0.643 3.709 0.359 1.067
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 62 86 494 194 71 67 162
normalized size 1 1.00 1.38 1.91 10.98 4.31 1.58 1.49 3.60
time (sec) N/A 0.039 0.111 0.015 0.525 0.771 8.470 0.341 1.094
Problem 188 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 66 66 55 88 829 1568 97 161 227
normalized size 1 1.00 0.83 1.33 12.56 23.76 1.47 2.44 3.44
time (sec) N/A 0.057 0.222 0.015 0.706 0.630 19.600 0.396 1.058
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 88 0 160 0 0 0 0 0 -1
normalized size 1 0.00 1.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.046 14.327 1.519 0.000 0.659 0.000 0.000 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 169 0 516 0 0 0 0 0 -1
normalized size 1 0.00 3.05 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 16.804 1.481 0.000 0.559 0.000 0.000 0.000
Problem 191 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 307 0 606 0 0 0 0 0 -1
normalized size 1 0.00 1.97 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.071 17.365 1.545 0.000 0.465 0.000 0.000 0.000
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 115 0 387 0 0 0 0 0 -1
normalized size 1 0.00 3.37 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.014 4.129 0.266 0.000 0.418 0.000 0.000 0.000
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F(-1) F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 135 0 174 0 0 0 0 0 -1
normalized size 1 0.00 1.29 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.099 5.603 0.209 0.000 0.551 0.000 0.000 0.000
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 64 93 0 625 0 0 65
normalized size 1 1.00 0.88 1.27 0.00 8.56 0.00 0.00 0.89
time (sec) N/A 0.053 0.290 0.160 0.000 0.589 0.000 0.000 2.247
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 57 92 0 334 0 0 51
normalized size 1 1.00 0.81 1.31 0.00 4.77 0.00 0.00 0.73
time (sec) N/A 0.052 0.139 0.135 0.000 0.938 0.000 0.000 1.804
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 48 72 0 303 66 0 39
normalized size 1 1.00 1.00 1.50 0.00 6.31 1.38 0.00 0.81
time (sec) N/A 0.041 0.080 0.122 0.000 0.471 2.581 0.000 1.452
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 44 0 305 66 0 36
normalized size 1 1.00 1.00 0.94 0.00 6.49 1.40 0.00 0.77
time (sec) N/A 0.040 0.120 0.127 0.000 0.676 4.195 0.000 1.546
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 44 93 0 625 0 0 65
normalized size 1 1.00 0.62 1.31 0.00 8.80 0.00 0.00 0.92
time (sec) N/A 0.052 0.165 0.117 0.000 0.478 0.000 0.000 1.718
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F(-1) F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 46 92 0 1110 0 0 64
normalized size 1 1.00 0.64 1.28 0.00 15.42 0.00 0.00 0.89
time (sec) N/A 0.050 0.219 0.125 0.000 0.922 0.000 0.000 2.476
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 136 149 0 8891 0 0 -1
normalized size 1 1.00 1.01 1.10 0.00 65.86 0.00 0.00 -0.01
time (sec) N/A 0.358 1.380 0.275 0.000 2.893 0.000 0.000 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 105 90 0 6663 0 0 -1
normalized size 1 1.00 1.00 0.86 0.00 63.46 0.00 0.00 -0.01
time (sec) N/A 0.225 0.078 0.173 0.000 2.805 0.000 0.000 0.000
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 58 52 0 1748 0 0 -1
normalized size 1 1.00 1.00 0.90 0.00 30.14 0.00 0.00 -0.02
time (sec) N/A 0.120 0.033 0.194 0.000 1.887 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(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 109 0 0 6705 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 63.25 0.00 0.00 -0.01
time (sec) N/A 0.249 0.351 0.508 0.000 2.208 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(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 142 0 0 9168 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 50.10 0.00 0.00 -0.01
time (sec) N/A 0.337 0.654 0.479 0.000 2.834 0.000 0.000 0.000
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 131 559 0 7896 0 0 -1
normalized size 1 1.00 0.99 4.23 0.00 59.82 0.00 0.00 -0.01
time (sec) N/A 0.231 0.354 0.179 0.000 3.797 0.000 0.000 0.000
Problem 206 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 107 107 76 124 94 604 0 68 155
normalized size 1 1.00 0.71 1.16 0.88 5.64 0.00 0.64 1.45
time (sec) N/A 0.069 0.150 0.296 0.439 0.757 0.000 0.354 0.101
Problem 207 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 77 77 60 103 69 339 0 52 93
normalized size 1 1.00 0.78 1.34 0.90 4.40 0.00 0.68 1.21
time (sec) N/A 0.050 0.119 0.219 0.426 0.506 0.000 0.649 0.080
Problem 208 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 51 51 40 57 47 147 0 41 58
normalized size 1 1.00 0.78 1.12 0.92 2.88 0.00 0.80 1.14
time (sec) N/A 0.035 0.097 0.089 0.514 0.930 0.000 0.124 1.067
Problem 209 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 25 25 22 34 23 38 0 23 34
normalized size 1 1.00 0.88 1.36 0.92 1.52 0.00 0.92 1.36
time (sec) N/A 0.015 0.016 0.098 0.413 0.614 0.000 0.133 0.055
Problem 210 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 25 25 22 27 38 49 0 32 38
normalized size 1 1.00 0.88 1.08 1.52 1.96 0.00 1.28 1.52
time (sec) N/A 0.017 0.020 0.089 0.379 0.469 0.000 0.116 0.083
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 53 53 179 48 62 198 0 56 62
normalized size 1 1.00 3.38 0.91 1.17 3.74 0.00 1.06 1.17
time (sec) N/A 0.038 1.913 0.050 0.343 0.473 0.000 0.121 0.072
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 81 81 286 89 88 459 0 72 97
normalized size 1 1.00 3.53 1.10 1.09 5.67 0.00 0.89 1.20
time (sec) N/A 0.052 2.371 0.268 0.306 0.632 0.000 0.130 1.110
Problem 213 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 113 113 115 107 110 796 0 83 160
normalized size 1 1.00 1.02 0.95 0.97 7.04 0.00 0.73 1.42
time (sec) N/A 0.072 10.116 0.270 0.323 0.520 0.000 0.138 0.100
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 48 35 89 168 0 89 86
normalized size 1 1.00 0.42 0.31 0.79 1.49 0.00 0.79 0.76
time (sec) N/A 0.087 0.048 0.206 0.414 1.136 0.000 0.132 0.246
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 95 24 78 113 0 78 81
normalized size 1 1.00 1.00 0.25 0.82 1.19 0.00 0.82 0.85
time (sec) N/A 0.062 0.035 0.181 0.461 0.584 0.000 0.111 1.256
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 36 22 31 0 23 26
normalized size 1 1.00 1.00 2.25 1.38 1.94 0.00 1.44 1.62
time (sec) N/A 0.014 0.013 0.201 0.426 0.510 0.000 0.134 0.167
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 35 35 113 48 34 230 0 35 38
normalized size 1 1.00 3.23 1.37 0.97 6.57 0.00 1.00 1.09
time (sec) N/A 0.029 1.619 0.221 0.430 0.532 0.000 0.116 1.179
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 97 59 81 160 0 81 86
normalized size 1 1.00 0.86 0.52 0.72 1.42 0.00 0.72 0.76
time (sec) N/A 0.212 0.084 0.326 0.426 0.524 0.000 0.115 0.323
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 24 47 69 107 0 69 70
normalized size 1 1.00 0.25 0.48 0.71 1.10 0.00 0.71 0.72
time (sec) N/A 0.186 0.013 0.231 0.454 0.489 0.000 0.113 0.264
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 22 138 75 113 0 76 81
normalized size 1 1.00 0.26 1.62 0.88 1.33 0.00 0.89 0.95
time (sec) N/A 0.122 0.017 0.221 0.415 0.700 0.000 0.134 0.259
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 108 108 113 150 87 628 0 88 93
normalized size 1 1.00 1.05 1.39 0.81 5.81 0.00 0.81 0.86
time (sec) N/A 0.147 1.901 0.260 0.484 0.561 0.000 0.134 1.378
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 382 382 51 36 0 1373 0 263 474
normalized size 1 1.00 0.13 0.09 0.00 3.59 0.00 0.69 1.24
time (sec) N/A 0.405 0.051 0.247 0.000 0.575 0.000 0.137 3.985
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 366 366 24 24 0 1089 0 251 457
normalized size 1 1.00 0.07 0.07 0.00 2.98 0.00 0.69 1.25
time (sec) N/A 0.244 0.013 0.199 0.000 0.650 0.000 0.152 3.819
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 22 56 97 134 0 98 104
normalized size 1 1.00 0.19 0.48 0.84 1.16 0.00 0.84 0.90
time (sec) N/A 0.078 0.018 0.242 0.530 1.072 0.000 0.123 1.333
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 134 134 113 68 109 213 0 110 122
normalized size 1 1.00 0.84 0.51 0.81 1.59 0.00 0.82 0.91
time (sec) N/A 0.101 1.879 0.273 0.500 0.527 0.000 0.137 1.395
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 81 87 0 440 0 328 163
normalized size 1 1.00 0.76 0.81 0.00 4.11 0.00 3.07 1.52
time (sec) N/A 0.126 0.086 0.293 0.000 0.497 0.000 0.125 2.448
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-2) B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 107 476 0 1163 0 456 280
normalized size 1 1.00 0.70 3.13 0.00 7.65 0.00 3.00 1.84
time (sec) N/A 0.176 0.167 0.365 0.000 0.607 0.000 0.146 23.355
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 167 167 205 0 0 0 0 0 -1
normalized size 1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.188 4.451 0.342 0.000 0.750 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 117 117 169 0 0 0 0 0 -1
normalized size 1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.127 3.483 0.305 0.000 0.560 0.000 0.000 0.000
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 141 0 0 0 0 0 -1
normalized size 1 1.00 2.10 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 1.958 0.269 0.000 0.805 0.000 0.000 0.000
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 134 0 0 0 0 0 -1
normalized size 1 1.00 2.06 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.071 2.539 0.272 0.000 0.532 0.000 0.000 0.000
Problem 232 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 113 113 145 0 0 0 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.126 3.354 0.297 0.000 0.504 0.000 0.000 0.000
Problem 233 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 161 161 185 0 0 0 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.176 3.609 0.377 0.000 0.555 0.000 0.000 0.000
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 311 311 133 324 145 1226 0 184 -1
normalized size 1 1.00 0.43 1.04 0.47 3.94 0.00 0.59 -0.00
time (sec) N/A 0.902 0.232 0.832 0.635 0.541 0.000 0.206 0.000
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 104 301 90 458 0 129 -1
normalized size 1 1.00 0.54 1.56 0.47 2.37 0.00 0.67 -0.01
time (sec) N/A 0.280 0.173 0.704 0.418 0.579 0.000 0.180 0.000
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 51 218 35 53 0 60 -1
normalized size 1 1.00 0.61 2.63 0.42 0.64 0.00 0.72 -0.01
time (sec) N/A 0.150 0.057 0.743 0.418 0.619 0.000 0.149 0.000
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 51 213 56 70 0 88 -1
normalized size 1 1.00 0.61 2.57 0.67 0.84 0.00 1.06 -0.01
time (sec) N/A 0.199 0.133 1.022 0.755 0.493 0.000 0.207 0.000
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 197 197 334 298 112 613 0 161 -1
normalized size 1 1.00 1.70 1.51 0.57 3.11 0.00 0.82 -0.01
time (sec) N/A 0.865 7.724 0.977 0.413 0.581 0.000 0.263 0.000
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 319 319 164 320 167 1617 0 215 -1
normalized size 1 1.00 0.51 1.00 0.52 5.07 0.00 0.67 -0.00
time (sec) N/A 1.770 10.691 0.990 0.490 0.933 0.000 0.361 0.000
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 124 118 0 296 0 0 -1
normalized size 1 1.00 0.79 0.75 0.00 1.89 0.00 0.00 -0.01
time (sec) N/A 0.395 0.230 0.099 0.000 0.708 0.000 0.000 0.000
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 88 102 0 155 0 0 -1
normalized size 1 1.00 0.77 0.89 0.00 1.35 0.00 0.00 -0.01
time (sec) N/A 0.266 0.153 0.094 0.000 0.545 0.000 0.000 0.000
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 59 58 0 149 0 0 -1
normalized size 1 1.00 0.77 0.75 0.00 1.94 0.00 0.00 -0.01
time (sec) N/A 0.146 0.139 0.097 0.000 0.979 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 A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 67 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 3.493 0.599 0.000 0.620 0.000 0.000 0.000
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 124 118 0 298 0 0 -1
normalized size 1 1.00 0.79 0.75 0.00 1.90 0.00 0.00 -0.01
time (sec) N/A 0.373 0.272 0.089 0.000 0.594 0.000 0.000 0.000
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 88 102 0 155 0 0 -1
normalized size 1 1.00 0.77 0.89 0.00 1.35 0.00 0.00 -0.01
time (sec) N/A 0.250 0.168 0.095 0.000 1.441 0.000 0.000 0.000
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 62 58 0 151 0 0 -1
normalized size 1 1.00 0.81 0.75 0.00 1.96 0.00 0.00 -0.01
time (sec) N/A 0.139 0.113 0.103 0.000 0.521 0.000 0.000 0.000
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 67 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 5.689 0.501 0.000 0.504 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 [224] had the largest ratio of [1.500]

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 2 1.00 8 0.250
2 A 3 2 1.00 8 0.250
3 A 3 2 1.00 8 0.250
4 A 2 2 1.00 8 0.250
5 A 2 2 1.00 8 0.250
6 A 1 1 1.00 6 0.167
7 A 1 1 1.00 6 0.167
8 A 2 2 1.00 8 0.250
9 A 2 2 1.00 8 0.250
10 A 3 2 1.00 8 0.250
11 A 3 2 1.00 8 0.250
12 A 4 2 1.00 8 0.250
13 A 7 6 1.00 12 0.500
14 A 6 6 1.00 12 0.500
15 A 6 6 1.00 12 0.500
16 A 5 5 1.00 12 0.417
17 A 5 5 1.00 12 0.417
18 A 6 6 1.00 12 0.500
19 A 6 6 1.00 12 0.500
20 A 7 6 1.00 12 0.500
21 A 9 9 1.00 8 1.125
22 A 2 2 1.00 8 0.250
23 A 2 2 1.00 10 0.200
24 A 3 3 1.00 10 0.300
25 A 2 2 1.00 10 0.200
26 A 2 2 1.00 10 0.200
27 A 4 3 1.00 14 0.214
28 A 3 3 1.00 14 0.214
29 A 2 2 1.00 14 0.143
30 A 2 2 1.00 14 0.143
31 A 3 3 1.00 14 0.214
32 A 4 3 1.00 14 0.214
33 A 7 7 1.00 8 0.875
34 A 8 7 1.00 10 0.700
35 A 7 7 1.00 10 0.700
36 A 7 7 1.00 10 0.700
37 A 5 3 1.00 10 0.300
38 A 3 3 1.00 10 0.300
39 A 3 3 1.00 10 0.300
40 A 3 3 1.00 12 0.250
41 A 5 3 1.00 12 0.250
42 A 4 3 1.00 12 0.250
43 A 3 3 1.00 12 0.250
44 A 2 2 1.00 12 0.167
45 A 2 2 1.00 12 0.167
46 A 3 2 1.00 12 0.167
47 A 4 2 1.00 12 0.167
48 A 5 2 1.00 12 0.167
49 A 6 2 1.00 12 0.167
50 A 5 3 1.00 8 0.375
51 A 4 3 1.00 8 0.375
52 A 3 3 1.00 8 0.375
53 A 2 2 1.00 8 0.250
54 A 3 3 1.00 8 0.375
55 A 4 3 1.00 8 0.375
56 A 5 3 1.00 8 0.375
57 A 5 4 1.00 12 0.333
58 A 4 4 1.00 12 0.333
59 A 3 3 1.00 12 0.250
60 A 2 2 1.00 12 0.167
61 A 2 2 1.00 12 0.167
62 A 3 3 1.00 12 0.250
63 A 4 4 1.00 12 0.333
64 A 5 4 1.00 12 0.333
65 A 2 2 1.00 12 0.167
66 A 2 2 1.00 12 0.167
67 A 5 4 1.00 14 0.286
68 A 5 4 1.00 14 0.286
69 A 5 4 1.00 11 0.364
70 A 9 7 1.00 11 0.636
71 A 5 4 1.00 11 0.364
72 A 8 6 1.00 9 0.667
73 A 8 7 1.00 9 0.778
74 A 3 2 1.00 11 0.182
75 A 8 7 1.00 11 0.636
76 A 4 3 1.00 11 0.273
77 A 9 8 1.00 11 0.727
78 A 4 3 1.00 11 0.273
79 A 10 8 1.00 11 0.727
80 A 5 3 1.00 13 0.231
81 A 10 9 1.00 13 0.692
82 A 4 3 1.00 13 0.231
83 A 6 6 1.00 11 0.546
84 A 6 5 1.00 11 0.454
85 A 3 2 1.00 13 0.154
86 A 15 11 1.00 13 0.846
87 A 3 2 1.00 13 0.154
88 A 29 13 1.00 13 1.000
89 A 3 2 1.00 13 0.154
90 A 6 5 1.00 11 0.454
91 A 4 3 1.00 11 0.273
92 A 3 2 1.00 11 0.182
93 A 4 3 1.00 11 0.273
94 A 2 2 1.00 9 0.222
95 A 1 1 1.00 9 0.111
96 A 2 2 1.00 11 0.182
97 A 2 2 1.00 11 0.182
98 A 2 1 1.00 11 0.091
99 A 3 3 1.00 11 0.273
100 A 3 2 1.00 11 0.182
101 A 4 3 1.00 11 0.273
102 A 3 2 1.00 13 0.154
103 A 3 2 1.00 13 0.154
104 A 3 2 1.00 13 0.154
105 A 2 2 1.00 13 0.154
106 A 2 2 1.00 8 0.250
107 A 4 3 1.00 13 0.231
108 A 5 4 1.00 13 0.308
109 A 14 6 1.19 13 0.462
110 A 9 6 1.07 13 0.462
111 A 5 5 1.00 13 0.385
112 A 2 2 1.00 11 0.182
113 A 5 5 1.00 11 0.454
114 A 9 6 1.00 13 0.462
115 A 5 4 1.00 11 0.364
116 A 4 4 1.00 11 0.364
117 A 3 3 1.00 11 0.273
118 A 3 2 1.00 11 0.182
119 A 2 2 1.00 9 0.222
120 A 2 2 1.00 6 0.333
121 A 4 4 1.00 9 0.444
122 A 4 4 1.00 11 0.364
123 A 5 4 1.00 11 0.364
124 A 6 4 1.00 11 0.364
125 A 4 4 1.00 11 0.364
126 A 3 3 1.00 11 0.273
127 A 3 3 1.00 11 0.273
128 A 4 4 1.00 11 0.364
129 A 4 4 1.00 13 0.308
130 A 3 3 1.00 13 0.231
131 A 4 4 1.00 13 0.308
132 A 4 4 1.00 13 0.308
133 A 7 7 1.00 13 0.538
134 A 6 6 1.00 13 0.462
135 A 5 5 1.00 13 0.385
136 A 4 4 1.00 13 0.308
137 A 2 2 1.00 11 0.182
138 A 2 2 1.00 8 0.250
139 A 3 3 1.00 11 0.273
140 A 4 4 1.00 13 0.308
141 A 5 5 1.00 13 0.385
142 A 6 6 1.00 13 0.462
143 A 3 3 1.00 14 0.214
144 A 9 6 1.00 24 0.250
145 A 11 7 1.00 26 0.269
146 F 0 0 N/A 0 N/A
147 F 0 0 N/A 0 N/A
148 F 0 0 N/A 0 N/A
149 F 0 0 N/A 0 N/A
150 A 2 1 1.00 11 0.091
151 F 0 0 N/A 0 N/A
152 F 0 0 N/A 0 N/A
153 F 0 0 N/A 0 N/A
154 F 0 0 N/A 0 N/A
155 F 0 0 N/A 0 N/A
156 F 0 0 N/A 0 N/A
157 A 3 2 1.00 13 0.154
158 F 0 0 N/A 0 N/A
159 F 0 0 N/A 0 N/A
160 F 0 0 N/A 0 N/A
161 F 0 0 N/A 0 N/A
162 F 0 0 N/A 0 N/A
163 F 0 0 N/A 0 N/A
164 F 0 0 N/A 0 N/A
165 F 0 0 N/A 0 N/A
166 F 0 0 N/A 0 N/A
167 F 0 0 N/A 0 N/A
168 F 0 0 N/A 0 N/A
169 F 0 0 N/A 0 N/A
170 F 0 0 N/A 0 N/A
171 F 0 0 N/A 0 N/A
172 F 0 0 N/A 0 N/A
173 F 0 0 N/A 0 N/A
174 F 0 0 N/A 0 N/A
175 F 0 0 N/A 0 N/A
176 A 2 1 1.00 17 0.059
177 F 0 0 N/A 0 N/A
178 F 0 0 N/A 0 N/A
179 F 0 0 N/A 0 N/A
180 F 0 0 N/A 0 N/A
181 F 0 0 N/A 0 N/A
182 F 0 0 N/A 0 N/A
183 A 3 2 1.00 19 0.105
184 F 0 0 N/A 0 N/A
185 F 0 0 N/A 0 N/A
186 A 3 2 1.00 17 0.118
187 A 4 2 1.00 17 0.118
188 A 4 2 1.00 17 0.118
189 F 0 0 N/A 0 N/A
190 F 0 0 N/A 0 N/A
191 F 0 0 N/A 0 N/A
192 F 0 0 N/A 0 N/A
193 F 0 0 N/A 0 N/A
194 A 7 6 1.00 19 0.316
195 A 7 6 1.00 19 0.316
196 A 6 5 1.00 19 0.263
197 A 6 5 1.00 19 0.263
198 A 7 6 1.00 19 0.316
199 A 7 6 1.00 19 0.316
200 A 8 7 1.00 23 0.304
201 A 7 6 1.00 23 0.261
202 A 4 4 1.00 21 0.190
203 A 8 5 1.00 21 0.238
204 A 11 6 1.00 23 0.261
205 A 8 7 1.00 21 0.333
206 A 7 6 1.00 16 0.375
207 A 7 6 1.00 16 0.375
208 A 5 4 1.00 16 0.250
209 A 3 3 1.00 14 0.214
210 A 3 3 1.00 14 0.214
211 A 5 4 1.00 16 0.250
212 A 7 6 1.00 16 0.375
213 A 7 6 1.00 16 0.375
214 A 13 9 1.00 10 0.900
215 A 11 8 1.00 8 1.000
216 A 5 5 1.00 8 0.625
217 A 7 6 1.00 10 0.600
218 A 14 9 1.00 10 0.900
219 A 12 8 1.00 8 1.000
220 A 12 8 1.00 8 1.000
221 A 14 9 1.00 10 0.900
222 A 23 9 1.00 10 0.900
223 A 21 8 1.00 8 1.000
224 A 15 12 1.00 8 1.500
225 A 17 13 1.00 10 1.300
226 A 5 5 1.00 14 0.357
227 A 7 6 1.00 14 0.429
228 A 6 3 1.00 18 0.167
229 A 5 3 1.00 18 0.167
230 A 4 3 1.00 16 0.188
231 A 4 3 1.00 16 0.188
232 A 5 3 1.00 18 0.167
233 A 6 3 1.00 18 0.167
234 A 9 7 1.00 25 0.280
235 A 8 7 1.00 25 0.280
236 A 4 4 1.00 25 0.160
237 A 4 4 1.00 25 0.160
238 A 8 7 1.00 25 0.280
239 A 9 7 1.00 25 0.280
240 A 19 5 1.00 9 0.556
241 A 13 5 1.00 9 0.556
242 A 9 4 1.00 7 0.571
243 A 0 0 0.00 0 0.000
244 A 19 5 1.00 9 0.556
245 A 13 5 1.00 9 0.556
246 A 9 4 1.00 7 0.571
247 A 0 0 0.00 0 0.000

[next] [prev] [prev-tail] [front] [up]