## Chapter 2detailed summary tables of results

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 List of integrals sorted by grade for each CAS

#### 2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 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, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376 }

#### 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, 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, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 213, 214, 215, 216, 217, 218, 219, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 237, 238, 239, 240, 241, 242, 243, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 371, 372, 373, 374, 375, 376 }

B grade: { 80, 81, 100, 102, 103, 104, 113, 121, 152, 195, 211, 212, 221, 245, 246, 297, 328, 355, 370 }

C grade: { 220, 235, 236, 244, 316, 334 }

#### 2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 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, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 322, 324, 325, 326, 327, 328, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 371, 372, 373, 374, 375, 376 }

B grade: { 63, 74, 89, 92, 93, 95, 117, 226, 227, 256, 270, 296, 308, 314, 329, 341, 370 }

C grade: { 323, 363 }

#### 2.1.4 Maxima

A grade: { 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, 30, 31, 32, 33, 36, 37, 38, 39, 40, 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, 96, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 242, 243, 247, 249, 251, 252, 254, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 272, 273, 274, 275, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 293, 294, 295, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 331, 332, 333, 334, 335, 336, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376

B grade: { 29, 34, 35, 41, 95, 97, 103, 104, 112, 113, 220, 221, 225, 235, 241, 244, 245, 246, 248, 253, 255, 271, 276, 291, 298, 313, 328, 329, 355, 363 }

F grade: { 1, 133, 250, 330, 337 }

#### 2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 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, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 106, 107, 109, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 242, 243, 245, 247, 252, 253, 254, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 293, 294, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, 335, 336, 338, 339, 340, 342, 343, 345, 346, 347, 348, 349, 350, 352, 353, 354, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 371, 372, 373, 374, 375, 376 }

B grade: { 7, 8, 13, 14, 29, 41, 67, 79, 86, 97, 98, 99, 100, 101, 102, 103, 104, 105, 108, 113, 115, 130, 139, 143, 145, 195, 220, 221, 225, 235, 241, 244, 246, 248, 249, 250, 251, 255, 270, 291, 295, 298, 311, 312, 313, 314, 328, 334, 337, 341, 344, 351, 355, 370 }

#### 2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 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, 68, 69, 70, 71, 72, 73, 77, 78, 79, 81, 83, 85, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 103, 105, 107, 109, 110, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 143, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 225, 227, 228, 229, 231, 232, 233, 234, 236, 237, 239, 240, 242, 243, 245, 246, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 267, 268, 269, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 284, 285, 286, 287, 289, 290, 292, 293, 294, 299, 300, 302, 303, 304, 305, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 321, 323, 326, 327, 329, 331, 332, 333, 335, 336, 338, 339, 342, 343, 345, 346, 347, 348, 349, 350, 352, 354, 355, 356, 357, 358, 361, 362, 363, 364, 366, 367, 368, 369, 371, 373, 374, 375, 376 }

B grade: { 7, 8, 42, 67, 75, 76, 80, 82, 84, 86, 87, 100, 102, 104, 106, 108, 111, 113, 127, 139, 142, 181, 195, 226, 230, 235, 241, 266, 270, 283, 291, 296, 297, 298, 306, 320, 330, 334, 341, 344, 370, 372 }

F grade: { 29, 41, 74, 123, 144, 145, 146, 147, 149, 220, 238, 244, 247, 248, 249, 250, 288, 295, 301, 322, 325, 328, 337, 340, 351, 353, 359, 360, 365 }

#### 2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 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, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 131, 132, 134, 135, 136, 137, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 256, 257, 258, 259, 260, 261, 262, 264, 265, 266, 267, 268, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 294, 295, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 330, 331, 332, 333, 334, 335, 336, 338, 339, 340, 341, 342, 343, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 369, 370, 371, 372, 373, 374, 375, 376 }

B grade: { 11, 12, 14, 29, 41, 79, 97, 98, 103, 104, 113, 115, 124, 130, 133, 138, 145, 195, 205, 225, 241, 244, 255, 263, 270, 291, 293, 298, 328, 329, 344, 368 }

F grade: { 269, 337 }

### 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 grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 11 11 11 12 0 20 12 15 normalized size 1 1. 1. 1.09 0. 1.82 1.09 1.36 time (sec) N/A 0.002 0.001 0.003 0. 1.896 0.053 1.071
 Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 3 3 3 3 3 7 2 3 normalized size 1 1. 1. 1. 1. 2.33 0.67 1. time (sec) N/A 0.001 0. 0. 0.917 1.798 0.039 1.059
 Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 2 2 2 3 3 11 2 4 normalized size 1 1. 1. 1.5 1.5 5.5 1. 2. time (sec) N/A 0. 0. 0. 0.922 1.782 0.05 1.051
 Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 9 11 16 8 11 normalized size 1 1. 1. 1.12 1.38 2. 1. 1.38 time (sec) N/A 0.002 0.001 0. 0.922 1.9 0.083 1.041
 Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 4 4 4 5 5 12 3 5 normalized size 1 1. 1. 1.25 1.25 3. 0.75 1.25 time (sec) N/A 0.002 0.001 0. 0.926 2.005 0.053 1.066
 Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 2 2 2 3 3 11 2 3 normalized size 1 1. 1. 1.5 1.5 5.5 1. 1.5 time (sec) N/A 0.002 0.001 0.001 0.928 1.986 0.053 1.058
 Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 2 2 2 3 3 20 5 3 normalized size 1 1. 1. 1.5 1.5 10. 2.5 1.5 time (sec) N/A 0.006 0.002 0.003 0.927 1.91 0.059 1.063
 Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 4 4 4 5 8 22 7 8 normalized size 1 1. 1. 1.25 2. 5.5 1.75 2. time (sec) N/A 0.005 0.002 0.003 0.938 1.847 0.059 1.082
 Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 2 2 2 3 5 14 3 5 normalized size 1 1. 1. 1.5 2.5 7. 1.5 2.5 time (sec) N/A 0.007 0.001 0.006 0.928 1.855 0.061 1.064
 Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 4 4 4 5 8 15 5 8 normalized size 1 1. 1. 1.25 2. 3.75 1.25 2. time (sec) N/A 0.008 0.002 0.005 0.919 1.866 0.063 1.06
 Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 2 2 2 3 3 12 2 15 normalized size 1 1. 1. 1.5 1.5 6. 1. 7.5 time (sec) N/A 0.003 0.001 0. 0.919 1.904 0.11 1.059
 Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 2 2 2 3 3 12 2 15 normalized size 1 1. 1. 1.5 1.5 6. 1. 7.5 time (sec) N/A 0.002 0.001 0.002 0.921 1.891 0.11 1.056
 Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 5 5 5 6 4 38 5 8 normalized size 1 1. 1. 1.2 0.8 7.6 1. 1.6 time (sec) N/A 0.002 0.002 0. 0.929 2.006 0.058 1.06
 Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 3 3 3 4 4 41 3 15 normalized size 1 1. 1. 1.33 1.33 13.67 1. 5. time (sec) N/A 0.002 0.002 0. 0.927 2.031 0.058 1.056
 Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 9 11 27 7 11 normalized size 1 1. 1. 1.12 1.38 3.38 0.88 1.38 time (sec) N/A 0.009 0.002 0. 0.933 1.91 0.167 1.049
 Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 9 11 19 5 11 normalized size 1 1. 1. 1.12 1.38 2.38 0.62 1.38 time (sec) N/A 0.001 0.001 0.001 0.922 1.828 0.076 1.059
 Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 12 12 15 28 10 15 normalized size 1 1. 0.63 0.63 0.79 1.47 0.53 0.79 time (sec) N/A 0.02 0.005 0.002 0.935 1.889 0.078 1.049
 Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 14 14 15 46 15 15 normalized size 1 1. 0.74 0.74 0.79 2.42 0.79 0.79 time (sec) N/A 0.007 0.005 0. 0.928 1.924 0.283 1.047
 Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 15 14 18 43 12 18 normalized size 1 1. 1. 0.93 1.2 2.87 0.8 1.2 time (sec) N/A 0.004 0.002 0.001 0.937 2.02 0.184 1.042
 Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 15 12 15 31 10 15 normalized size 1 1. 0.75 0.6 0.75 1.55 0.5 0.75 time (sec) N/A 0.008 0.004 0. 0.936 1.831 0.075 1.055
 Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 7 7 7 8 9 26 7 9 normalized size 1 1. 1. 1.14 1.29 3.71 1. 1.29 time (sec) N/A 0.009 0.002 0. 0.938 1.901 0.164 1.041
 Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 15 19 45 14 19 normalized size 1 1. 1. 0.83 1.06 2.5 0.78 1.06 time (sec) N/A 0.01 0.011 0.008 0.949 1.947 0.167 1.05
 Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 18 35 12 18 normalized size 1 1. 1. 0.82 1.06 2.06 0.71 1.06 time (sec) N/A 0.003 0.001 0. 0.935 1.873 0.08 1.051
 Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 29 29 25 24 28 59 27 28 normalized size 1 1. 0.86 0.83 0.97 2.03 0.93 0.97 time (sec) N/A 0.025 0.027 0.008 0.941 2.028 0.304 1.04
 Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 29 29 25 24 28 59 24 28 normalized size 1 1. 0.86 0.83 0.97 2.03 0.83 0.97 time (sec) N/A 0.023 0.024 0.006 0.948 1.94 0.292 1.043
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 15 16 16 42 15 20 normalized size 1 1. 1. 1.07 1.07 2.8 1. 1.33 time (sec) N/A 0.003 0.001 0. 0.936 1.751 0.087 1.046
 Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 16 15 19 41 12 19 normalized size 1 1. 1. 0.94 1.19 2.56 0.75 1.19 time (sec) N/A 0.004 0.002 0. 1.402 2.025 0.117 1.065
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 23 23 18 18 19 61 24 19 normalized size 1 1. 0.78 0.78 0.83 2.65 1.04 0.83 time (sec) N/A 0.013 0.003 0.001 0.938 1.956 0.313 1.051
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 9 100 55 0 139 normalized size 1 1. 1. 1.12 12.5 6.88 0. 17.38 time (sec) N/A 0.018 0.005 0.004 1.426 2.087 0. 1.102
 Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 18 35 12 18 normalized size 1 1. 1. 0.82 1.06 2.06 0.71 1.06 time (sec) N/A 0.007 0.001 0.001 0.936 1.834 0.083 1.059
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 27 27 17 17 22 39 15 22 normalized size 1 1. 0.63 0.63 0.81 1.44 0.56 0.81 time (sec) N/A 0.031 0.006 0.002 0.934 1.831 0.08 1.05
 Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 27 27 22 22 26 65 26 26 normalized size 1 1. 0.81 0.81 0.96 2.41 0.96 0.96 time (sec) N/A 0.011 0.032 0.004 0.926 1.925 0.293 1.059
 Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 27 27 20 22 23 62 20 23 normalized size 1 1. 0.74 0.81 0.85 2.3 0.74 0.85 time (sec) N/A 0.011 0.027 0.007 0.937 1.879 0.458 1.052
 Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 9 9 9 10 46 28 7 23 normalized size 1 1. 1. 1.11 5.11 3.11 0.78 2.56 time (sec) N/A 0.012 0.003 0.001 0.948 1.781 0.171 1.049
 Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 19 19 77 45 20 41 normalized size 1 1. 1. 1. 4.05 2.37 1.05 2.16 time (sec) N/A 0.016 0.013 0.009 0.95 1.771 0.212 1.053
 Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 11 10 12 23 7 12 normalized size 1 1. 0.69 0.62 0.75 1.44 0.44 0.75 time (sec) N/A 0.009 0.004 0.001 0.925 1.991 0.073 1.048
 Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 21 21 15 14 18 43 66 18 normalized size 1 1. 0.71 0.67 0.86 2.05 3.14 0.86 time (sec) N/A 0.008 0.003 0.003 0.934 2.175 2.037 1.049
 Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 15 19 42 14 19 normalized size 1 1. 1. 0.83 1.06 2.33 0.78 1.06 time (sec) N/A 0.012 0.009 0.005 0.936 2.375 0.162 1.041
 Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 26 26 16 15 19 34 12 19 normalized size 1 1. 0.62 0.58 0.73 1.31 0.46 0.73 time (sec) N/A 0.018 0.006 0.001 0.938 2.061 0.079 1.054
 Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 17 22 41 12 22 normalized size 1 1. 1. 0.94 1.22 2.28 0.67 1.22 time (sec) N/A 0.004 0.002 0.001 1.406 2.39 0.118 1.048
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 9 9 9 10 140 61 0 70 normalized size 1 1. 1. 1.11 15.56 6.78 0. 7.78 time (sec) N/A 0.016 0.015 0.003 0.945 2.618 0. 1.095
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 18 76 26 18 normalized size 1 1. 1. 0.82 1.06 4.47 1.53 1.06 time (sec) N/A 0.009 0.007 0.074 0.934 2.692 0.513 1.059
 Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 9 18 43 22 18 normalized size 1 1. 1. 0.53 1.06 2.53 1.29 1.06 time (sec) N/A 0.008 0.006 0.01 0.933 2.415 0.558 1.101
 Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 11 11 11 12 15 39 10 15 normalized size 1 1. 1. 1.09 1.36 3.55 0.91 1.36 time (sec) N/A 0.01 0.002 0.004 0.926 2.28 0.876 1.058
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 14 12 15 31 10 15 normalized size 1 1. 0.64 0.55 0.68 1.41 0.45 0.68 time (sec) N/A 0.019 0.002 0.002 0.941 2.326 0.078 1.06
 Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 9 9 16 20 7 11 normalized size 1 1. 0.6 0.6 1.07 1.33 0.47 0.73 time (sec) N/A 0.008 0.009 0. 0.944 2.242 0.074 1.055
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 14 15 19 39 14 19 normalized size 1 1. 0.74 0.79 1. 2.05 0.74 1. time (sec) N/A 0.009 0.003 0.004 1.425 2.24 0.091 1.049
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 14 53 15 18 normalized size 1 1. 1. 0.82 0.82 3.12 0.88 1.06 time (sec) N/A 0.003 0.003 0. 0.937 2.374 0.376 1.052
 Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 24 24 16 17 15 36 20 15 normalized size 1 1. 0.67 0.71 0.62 1.5 0.83 0.62 time (sec) N/A 0.008 0.006 0. 0.946 2.218 0.178 1.067
 Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 12 10 12 30 8 12 normalized size 1 1. 0.86 0.71 0.86 2.14 0.57 0.86 time (sec) N/A 0.001 0.001 0. 0.937 2.215 0.079 1.05
 Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 16 54 15 18 normalized size 1 1. 1. 0.82 0.94 3.18 0.88 1.06 time (sec) N/A 0.003 0.002 0.001 0.938 2.36 0.375 1.048
 Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 22 17 22 57 20 22 normalized size 1 1. 1. 0.77 1. 2.59 0.91 1. time (sec) N/A 0.011 0.012 0. 0.935 2.258 0.294 1.049
 Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 17 22 45 15 22 normalized size 1 1. 1. 0.85 1.1 2.25 0.75 1.1 time (sec) N/A 0.016 0.009 0.004 0.939 2.307 1.852 1.065
 Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 28 28 19 17 22 42 15 22 normalized size 1 1. 0.68 0.61 0.79 1.5 0.54 0.79 time (sec) N/A 0.034 0.002 0.001 0.943 2.288 0.085 1.066
 Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 21 21 21 16 20 45 15 20 normalized size 1 1. 1. 0.76 0.95 2.14 0.71 0.95 time (sec) N/A 0.009 0.003 0. 1.42 2.278 0.334 1.056
 Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 17 22 47 15 24 normalized size 1 1. 1. 0.94 1.22 2.61 0.83 1.33 time (sec) N/A 0.013 0.015 0.005 0.935 2.561 0.217 1.052
 Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 21 21 15 14 18 43 66 18 normalized size 1 1. 0.71 0.67 0.86 2.05 3.14 0.86 time (sec) N/A 0.006 0.002 0.002 0.94 2.51 2.123 1.061
 Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 14 15 14 43 14 14 normalized size 1 1. 0.78 0.83 0.78 2.39 0.78 0.78 time (sec) N/A 0.006 0.006 0.007 0.936 2.583 0.061 1.073
 Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 14 11 14 36 10 14 normalized size 1 1. 1. 0.79 1. 2.57 0.71 1. time (sec) N/A 0.006 0.002 0.005 0.94 2.218 0.058 1.05
 Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 24 24 22 18 22 59 24 22 normalized size 1 1. 0.92 0.75 0.92 2.46 1. 0.92 time (sec) N/A 0.013 0.002 0.001 0.953 2.089 0.059 1.058
 Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 13 13 15 11 15 31 8 15 normalized size 1 1. 1.15 0.85 1.15 2.38 0.62 1.15 time (sec) N/A 0.005 0.002 0. 0.928 1.971 0.064 1.077
 Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 31 18 18 39 12 18 normalized size 1 1. 1.82 1.06 1.06 2.29 0.71 1.06 time (sec) N/A 0.023 0.01 0.006 0.957 2.219 0.062 1.06
 Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 31 30 18 73 12 18 normalized size 1 1. 1.82 1.76 1.06 4.29 0.71 1.06 time (sec) N/A 0.022 0.009 0.004 0.928 2.132 0.063 1.046
 Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 36 36 30 29 24 81 31 30 normalized size 1 1. 0.83 0.81 0.67 2.25 0.86 0.83 time (sec) N/A 0.045 0.007 0.006 0.937 2.018 0.061 1.065
 Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 24 24 14 19 14 58 14 14 normalized size 1 1. 0.58 0.79 0.58 2.42 0.58 0.58 time (sec) N/A 0.025 0.004 0. 0.925 2.039 0.066 1.051
 Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 18 19 19 58 37 19 normalized size 1 1. 0.82 0.86 0.86 2.64 1.68 0.86 time (sec) N/A 0.009 0.008 0.023 0.936 1.976 0.177 1.056
 Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 15 19 105 37 19 normalized size 1 1. 1. 0.75 0.95 5.25 1.85 0.95 time (sec) N/A 0.014 0.011 0.029 0.933 1.983 0.545 1.06
 Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 25 25 25 28 26 63 19 26 normalized size 1 1. 1. 1.12 1.04 2.52 0.76 1.04 time (sec) N/A 0.03 0.01 0.007 0.928 2.003 0.068 1.051
 Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 34 34 30 24 32 84 36 30 normalized size 1 1. 0.88 0.71 0.94 2.47 1.06 0.88 time (sec) N/A 0.017 0.002 0. 0.924 1.998 0.061 1.053
 Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 34 34 30 24 32 82 36 30 normalized size 1 1. 0.88 0.71 0.94 2.41 1.06 0.88 time (sec) N/A 0.017 0.002 0.029 0.927 2.051 0.057 1.047
 Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 46 46 30 36 24 92 41 30 normalized size 1 1. 0.65 0.78 0.52 2. 0.89 0.65 time (sec) N/A 0.036 0.014 0.011 0.939 1.995 0.062 1.052
 Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 21 21 23 17 23 53 17 23 normalized size 1 1. 1.1 0.81 1.1 2.52 0.81 1.1 time (sec) N/A 0.007 0.002 0.004 0.929 1.977 0.063 1.045
 Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 46 46 22 36 22 103 31 22 normalized size 1 1. 0.48 0.78 0.48 2.24 0.67 0.48 time (sec) N/A 0.052 0.007 0.005 0.929 2.105 0.067 1.048
 Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 21 21 34 39 18 58 0 18 normalized size 1 1. 1.62 1.86 0.86 2.76 0. 0.86 time (sec) N/A 0.022 0.063 0.033 0.93 2.062 0. 1.053
 Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 21 21 18 14 18 49 167 18 normalized size 1 1. 0.86 0.67 0.86 2.33 7.95 0.86 time (sec) N/A 0.022 0.011 0.02 0.933 2.066 42.137 1.05
 Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 18 14 16 50 39 16 normalized size 1 1. 0.95 0.74 0.84 2.63 2.05 0.84 time (sec) N/A 0.02 0.027 0.009 0.927 1.879 0.321 1.048
 Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 19 15 20 42 22 20 normalized size 1 1. 1. 0.79 1.05 2.21 1.16 1.05 time (sec) N/A 0.014 0.015 0.006 0.931 2.066 0.572 1.056
 Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 14 13 22 39 10 19 normalized size 1 1. 1. 0.93 1.57 2.79 0.71 1.36 time (sec) N/A 0.013 0.005 0.011 0.93 2.115 0.08 1.071
 Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 20 29 27 116 20 49 normalized size 1 1. 0.91 1.32 1.23 5.27 0.91 2.23 time (sec) N/A 0.029 0.023 0.013 0.931 2.069 0.095 1.07
 Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 5 5 36 6 7 23 19 7 normalized size 1 1. 7.2 1.2 1.4 4.6 3.8 1.4 time (sec) N/A 0.013 0.007 0.021 0.935 2.076 0.318 1.054
 Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 11 11 25 11 20 61 8 14 normalized size 1 1. 2.27 1. 1.82 5.55 0.73 1.27 time (sec) N/A 0.008 0.012 0. 0.932 1.942 0.381 1.056
 Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 6 6 6 7 8 18 7 8 normalized size 1 1. 1. 1.17 1.33 3. 1.17 1.33 time (sec) N/A 0.004 0.002 0.002 1.407 1.977 0.062 1.064
 Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 18 13 16 36 19 16 normalized size 1 1. 1.29 0.93 1.14 2.57 1.36 1.14 time (sec) N/A 0.008 0.004 0.001 1.41 1.91 0.066 1.055
 Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 11 11 17 13 12 51 19 12 normalized size 1 1. 1.55 1.18 1.09 4.64 1.73 1.09 time (sec) N/A 0.007 0.002 0.027 0.924 1.965 0.061 1.079
 Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 27 19 20 70 31 20 normalized size 1 1. 1.42 1. 1.05 3.68 1.63 1.05 time (sec) N/A 0.009 0.003 0.027 0.926 1.948 0.062 1.056
 Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 11 8 66 29 8 normalized size 1 1. 1. 1.38 1. 8.25 3.62 1. time (sec) N/A 0.02 0.002 0.011 0.924 1.977 0.063 1.056
 Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 27 22 18 69 29 18 normalized size 1 1. 1.59 1.29 1.06 4.06 1.71 1.06 time (sec) N/A 0.022 0.019 0.012 0.924 1.975 0.065 1.07
 Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 7 8 19 7 8 normalized size 1 1. 1. 0.88 1. 2.38 0.88 1. time (sec) N/A 0.012 0.005 0.006 0.927 1.972 0.065 1.054
 Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 42 19 45 15 19 normalized size 1 1. 1. 2.47 1.12 2.65 0.88 1.12 time (sec) N/A 0.023 0.023 0.011 0.925 2.237 0.097 1.051
 Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 20 23 46 77 20 30 normalized size 1 1. 0.91 1.05 2.09 3.5 0.91 1.36 time (sec) N/A 0.01 0.003 0.002 0.925 2.259 0.104 1.059
 Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 30 19 24 57 31 24 normalized size 1 1. 1.36 0.86 1.09 2.59 1.41 1.09 time (sec) N/A 0.013 0.004 0.002 1.411 2.036 0.067 1.058
 Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 19 48 27 63 20 27 normalized size 1 1. 1. 2.53 1.42 3.32 1.05 1.42 time (sec) N/A 0.016 0.01 0.008 0.938 2.028 0.104 1.059
 Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 25 25 25 58 27 66 20 27 normalized size 1 1. 1. 2.32 1.08 2.64 0.8 1.08 time (sec) N/A 0.029 0.012 0.012 0.926 2.058 0.115 1.065
 Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 7 14 19 7 8 normalized size 1 1. 1. 0.88 1.75 2.38 0.88 1. time (sec) N/A 0.013 0.004 0.007 0.925 2.003 0.068 1.058
 Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B B A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 32 49 45 15 19 normalized size 1 1. 1. 1.88 2.88 2.65 0.88 1.12 time (sec) N/A 0.028 0.013 0.013 0.928 1.945 0.127 1.049
 Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 7 14 19 7 8 normalized size 1 1. 1. 0.88 1.75 2.38 0.88 1. time (sec) N/A 0.012 0.004 0.01 0.925 2.04 0.067 1.054
 Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 16 24 36 109 27 39 normalized size 1 1. 1. 1.5 2.25 6.81 1.69 2.44 time (sec) N/A 0.015 0.006 0.008 0.929 2.172 0.109 1.059
 Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 12 14 53 8 24 normalized size 1 1. 1. 1.5 1.75 6.62 1. 3. time (sec) N/A 0.005 0.002 0.003 1.409 2.098 0.059 1.068
 Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 14 17 19 90 14 30 normalized size 1 1. 1. 1.21 1.36 6.43 1. 2.14 time (sec) N/A 0.007 0.003 0.002 0.93 1.972 0.088 1.061
 Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 37 22 19 112 41 19 normalized size 1 1. 2.18 1.29 1.12 6.59 2.41 1.12 time (sec) N/A 0.026 0.027 0.013 0.934 1.958 0.067 1.077
 Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 22 19 86 14 24 normalized size 1 1. 1. 1.29 1.12 5.06 0.82 1.41 time (sec) N/A 0.026 0.007 0.013 0.94 2.018 0.103 1.053
 Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 5 5 17 9 11 77 15 8 normalized size 1 1. 3.4 1.8 2.2 15.4 3. 1.6 time (sec) N/A 0.002 0.003 0.002 0.931 2.151 0.093 1.073
 Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A B B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 47 18 36 150 27 73 normalized size 1 1. 2.94 1.12 2.25 9.38 1.69 4.56 time (sec) N/A 0.007 0.005 0.031 0.932 2.044 0.112 1.065
 Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 19 12 23 88 19 26 normalized size 1 1. 2.38 1.5 2.88 11. 2.38 3.25 time (sec) N/A 0.011 0.004 0.007 0.924 2.153 0.093 1.055
 Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 13 13 17 12 19 73 20 19 normalized size 1 1. 1.31 0.92 1.46 5.62 1.54 1.46 time (sec) N/A 0.007 0.002 0.026 0.93 1.962 0.057 1.058
 Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 18 81 26 18 normalized size 1 1. 1. 0.82 1.06 4.76 1.53 1.06 time (sec) N/A 0.008 0.007 0.046 0.933 2.082 0.503 1.046
 Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 14 18 35 22 18 normalized size 1 1. 1. 0.82 1.06 2.06 1.29 1.06 time (sec) N/A 0.008 0.005 0.029 0.93 1.934 0.512 1.072
 Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 15 12 15 78 26 15 normalized size 1 1. 1. 0.8 1. 5.2 1.73 1. time (sec) N/A 0.008 0.006 0.049 0.925 2.13 0.493 1.054
 Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 9 18 43 24 18 normalized size 1 1. 1. 0.53 1.06 2.53 1.41 1.06 time (sec) N/A 0.008 0.006 0.01 0.939 2.103 0.533 1.052
 Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 7 8 20 7 8 normalized size 1 1. 1. 0.88 1. 2.5 0.88 1. time (sec) N/A 0.013 0.001 0.001 0.928 1.951 0.056 1.053
 Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 30 30 30 23 30 81 112 30 normalized size 1 1. 1. 0.77 1. 2.7 3.73 1. time (sec) N/A 0.031 0.008 0. 0.931 1.97 14.487 1.067
 Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 5 5 8 6 15 20 7 12 normalized size 1 1. 1.6 1.2 3. 4. 1.4 2.4 time (sec) N/A 0.022 0.002 0.016 0.93 2.124 0.414 1.063
 Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B A B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 61 20 93 149 32 39 normalized size 1 1. 4.07 1.33 6.2 9.93 2.13 2.6 time (sec) N/A 0.053 0.009 0.049 1.438 2.096 1.051 1.101
 Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 14 13 22 39 10 24 normalized size 1 1. 1. 0.93 1.57 2.79 0.71 1.71 time (sec) N/A 0.015 0.005 0.011 0.927 2.167 0.077 1.081
 Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 20 29 27 116 20 49 normalized size 1 1. 0.91 1.32 1.23 5.27 0.91 2.23 time (sec) N/A 0.052 0.012 0.013 0.926 2.074 0.095 1.06
 Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 8 8 8 7 8 19 7 8 normalized size 1 1. 1. 0.88 1. 2.38 0.88 1. time (sec) N/A 0.015 0.003 0. 0.935 1.996 0.062 1.049
 Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A A A A veriﬁed N/A Yes Yes TBD TBD TBD