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292, 293, 294, 295, 314, 315, 316, 318, 319, 320, 321, 325, 339, 340, 344, 346], "graph": [1, 3, 4, 5, 340], "rule": 1, "evalu": [1, 3, 4, 5, 86, 115, 198, 213, 235, 245, 312, 314, 339, 344], "said": [1, 3], "start": [1, 2, 3, 5, 6, 14, 120, 177, 339, 341, 346], "discuss": 1, "more": [1, 4, 8, 56, 78, 131, 165, 166, 213, 217, 221, 256, 260, 263, 264, 266, 267, 268, 269, 336, 339, 340, 341, 344, 346], "detail": [1, 8, 213, 221, 256, 260, 264, 266, 267, 268, 269, 315, 317, 318, 320, 321, 341, 344], "thei": [1, 2, 3, 12, 71, 258, 286, 312, 321, 338, 339, 342, 344, 345, 346], "c": [1, 3, 118, 209, 215, 216, 217, 218, 219, 221, 222, 226, 229, 230, 343, 344, 346], "scalar": [1, 10, 12, 25, 36, 56, 59, 63, 65, 80, 81, 83, 104, 105, 106, 107, 108, 116, 117, 118, 120, 126, 127, 128, 129, 131, 133, 136, 138, 144, 154, 157, 158, 165, 184, 196, 200, 203, 295, 340, 342, 344], "sum": [1, 2, 10, 110, 118, 130, 175, 191, 213, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 341, 343], "element": [1, 9, 10, 15, 16, 17, 18, 19, 20, 23, 51, 64, 72, 73, 76, 80, 81, 83, 84, 85, 87, 89, 103, 104, 107, 108, 111, 112, 113, 114, 116, 117, 122, 123, 124, 125, 126, 127, 128, 129, 133, 136, 138, 139, 145, 147, 148, 159, 160, 163, 171, 172, 173, 174, 178, 179, 184, 187, 189, 190, 196, 200, 220, 221, 222, 231, 252, 256, 278, 280, 281, 296, 297, 299, 302, 303, 304, 339, 340], "wise": [1, 9, 10, 15, 16, 17, 18, 19, 20, 64, 72, 73, 80, 81, 83, 84, 85, 87, 103, 104, 107, 108, 116, 117, 122, 123, 124, 125, 126, 127, 128, 129, 133, 136, 138, 139, 159, 163, 171, 172, 173, 174, 178, 179, 184, 189, 190, 221, 222, 231, 252, 278, 280, 281, 296, 297, 299, 302, 303, 304, 339], "numpi": [1, 3, 4, 5, 10, 12, 14, 63, 80, 81, 83, 107, 108, 116, 117, 126, 131, 133, 136, 138, 184, 342, 344, 345], "style": [1, 10, 12, 80, 81, 83, 107, 108, 116, 117, 126, 131, 133, 136, 138, 184], "broadcast": [1, 10, 12, 63, 65, 80, 81, 83, 105, 107, 108, 116, 117, 126, 131, 133, 136, 138, 149, 150, 157, 158, 184, 188, 200, 251], "between": [1, 5, 65, 102, 263, 283, 286, 287, 290, 330, 342, 346], "input": [1, 2, 3, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 142, 143, 144, 145, 146, 147, 148, 156, 159, 160, 161, 162, 163, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 199, 200, 202, 215, 216, 217, 218, 219, 221, 222, 223, 225, 226, 227, 228, 229, 230, 251, 253, 254, 256, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 277, 282, 283, 285, 286, 287, 288, 290, 291, 293, 295, 306, 309, 339, 340, 341, 344, 345], "upcast": 1, "const": [1, 285], "factor": [1, 119, 264, 284, 329, 332], "streamordevic": 1, "stream": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 80, 81, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 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, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 197, 200, 201, 202, 346], "schedul": [1, 314, 328, 329, 330, 331, 332, 334, 346], "itself": [1, 323], "call": [1, 3, 4, 26, 104, 213, 223, 237, 248, 258, 312, 314, 323, 339, 340, 342], "other": [1, 3, 5, 118, 213, 238, 312, 321, 339, 341, 342, 344], "within": [1, 23], "simplest": [1, 213], "wai": [1, 3, 6, 213, 264, 339, 340, 341], "about": [1, 3, 4, 342, 346], "term": [1, 285, 315, 316, 317, 318, 319, 320, 326], "exist": [1, 3, 237, 248], "auto": [1, 6], "ax": [1, 11, 13, 21, 22, 57, 88, 91, 92, 94, 95, 97, 98, 100, 101, 102, 110, 118, 130, 132, 134, 135, 144, 146, 175, 180, 185, 186, 191, 192, 197, 340], "multipli": [1, 147, 148, 220, 260, 264], "earlier": 1, "goal": 1, "themselv": [1, 339], "contain": [1, 3, 23, 24, 49, 66, 78, 96, 97, 98, 118, 127, 128, 129, 147, 177, 200, 213, 236, 238, 239, 244, 263, 291, 309, 312, 339, 340], "act": [1, 290], "data": [1, 4, 5, 8, 14, 89, 99, 100, 105, 109, 120, 141, 157, 193, 201, 222, 265, 266, 267, 268, 269, 270, 271, 272, 339, 341, 343], "nor": [1, 106, 196], "rather": [1, 340, 346], "easi": [1, 213], "interfac": 1, "block": [1, 3, 263], "A": [1, 3, 5, 6, 7, 49, 59, 66, 106, 115, 118, 119, 121, 130, 131, 147, 149, 150, 151, 153, 154, 157, 158, 177, 181, 183, 196, 198, 199, 203, 204, 205, 206, 207, 213, 217, 221, 225, 226, 227, 236, 240, 241, 249, 250, 254, 258, 260, 263, 266, 267, 269, 276, 295, 296, 312, 314, 318, 320, 322, 323, 325, 330, 339, 340, 342, 343], "It": [1, 3, 6, 106, 170, 196, 213, 250, 253, 322, 334, 343, 345], "creat": [1, 3, 6, 89, 109, 183, 213, 312, 314, 330, 339, 341, 343], "output": [1, 3, 6, 11, 12, 13, 14, 23, 63, 66, 89, 96, 99, 100, 101, 105, 106, 109, 118, 120, 130, 132, 134, 135, 141, 142, 145, 146, 149, 150, 151, 153, 154, 157, 158, 167, 168, 175, 180, 185, 188, 193, 196, 197, 198, 199, 200, 201, 202, 215, 216, 217, 218, 219, 226, 228, 229, 230, 251, 253, 262, 263, 264, 266, 267, 268, 269, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 306, 309, 339, 340, 341, 342, 343, 344, 345, 346], "given": [1, 11, 13, 23, 63, 65, 67, 76, 78, 86, 88, 90, 91, 92, 93, 94, 95, 99, 100, 101, 105, 118, 130, 132, 134, 135, 140, 146, 154, 162, 170, 175, 177, 185, 193, 194, 195, 197, 207, 215, 216, 220, 229, 230, 236, 251, 283, 285, 291], "set": [1, 3, 4, 6, 66, 79, 82, 169, 170, 183, 224, 228, 235, 237, 244, 245, 248, 249, 253, 256, 262, 283, 295, 306, 312, 316, 323, 336, 340, 342], "further": [1, 6, 340], "class": [1, 3, 4, 7, 8, 25, 207, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 284, 312, 315, 316, 317, 318, 319, 320, 321, 326, 327, 334], "under": [1, 118], "These": [1, 66, 188, 284, 346], "word": 1, "bit": [1, 76, 147, 148, 209, 232, 253], "abstract": 1, "back": [1, 3, 343], "give": [1, 3, 4, 23, 339], "ourselv": 1, "concret": [1, 228, 342, 346], "imag": [1, 219, 221, 222, 264], "public": [1, 213], "explicit": [1, 323, 336, 343], "alpha_": 1, "beta_": 1, "must": [1, 6, 65, 105, 118, 149, 150, 154, 157, 158, 200, 264, 343], "know": [1, 3], "popul": 1, "To": [1, 2, 3, 4, 6, 213, 309, 339, 340, 344], "avoid": [1, 339], "unnecessari": [1, 3], "alloc": [1, 312], "respons": 1, "space": [1, 120, 293], "void": 1, "eval_cpu": 1, "std": [1, 271], "overrid": [1, 82], "eval_gpu": 1, "jacobian": [1, 115, 198, 344], "product": [1, 110, 115, 131, 143, 146, 191, 198, 251, 344], "primal": [1, 115, 198], "tangent": [1, 19, 20, 115, 189, 190, 307], "int": [1, 3, 4, 7, 11, 13, 14, 21, 22, 23, 24, 28, 29, 30, 31, 39, 40, 41, 42, 44, 47, 49, 52, 55, 56, 58, 63, 67, 68, 69, 70, 76, 77, 78, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 106, 109, 118, 120, 130, 132, 134, 135, 137, 141, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 160, 161, 162, 175, 176, 177, 180, 181, 185, 186, 187, 188, 191, 192, 193, 194, 195, 196, 197, 199, 201, 207, 213, 215, 216, 217, 218, 219, 223, 225, 226, 227, 228, 229, 230, 251, 253, 254, 256, 260, 263, 277, 283, 284, 288, 293, 295, 312, 328, 330, 331, 332], "argnum": [1, 106, 196, 340], "cotan": 1, "across": [1, 225], "pair": [1, 144, 239, 256], "repres": [1, 3, 291, 295, 343], "axi": [1, 3, 4, 11, 13, 21, 22, 23, 24, 28, 29, 30, 31, 39, 40, 41, 42, 44, 52, 55, 58, 67, 78, 88, 90, 93, 96, 97, 98, 99, 100, 101, 102, 118, 130, 132, 134, 135, 137, 144, 145, 146, 150, 160, 175, 176, 177, 180, 181, 185, 186, 187, 188, 192, 197, 199, 215, 216, 229, 230, 277, 281, 283, 284, 288, 293, 295, 303, 341], "correspond": [1, 11, 13, 56, 65, 76, 78, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 130, 132, 135, 146, 185, 191, 199, 205, 340], "dimens": [1, 3, 11, 13, 21, 22, 43, 49, 56, 60, 61, 62, 66, 69, 70, 78, 88, 97, 98, 100, 101, 102, 110, 118, 119, 130, 131, 132, 134, 135, 146, 147, 150, 156, 185, 188, 191, 192, 197, 217, 218, 219, 221, 222, 225, 226, 227, 251, 254, 256, 263, 264, 277, 284, 339, 340], "vmap": [1, 340, 342, 344], "print": [1, 2, 3, 4, 6, 204, 205, 206, 213, 336, 339, 340, 341, 342, 343, 344], "ostream": 1, "os": [1, 6], "equival": [1, 26, 46, 57, 81, 104, 187, 224, 250, 252, 253, 255, 257, 259, 261], "check": [1, 6, 59, 239, 340, 341], "bool": [1, 11, 12, 13, 21, 22, 28, 29, 30, 31, 39, 40, 41, 42, 44, 55, 56, 58, 59, 66, 70, 118, 121, 130, 132, 134, 135, 146, 148, 149, 154, 157, 158, 185, 197, 217, 218, 219, 225, 226, 227, 228, 232, 236, 237, 239, 245, 248, 251, 253, 256, 260, 263, 264, 282, 285, 316, 327], "is_equival": 1, "privat": 1, "fall": 1, "eval": [1, 2, 3, 4, 213, 312, 314, 339, 340, 342, 344], "deriv": [1, 340, 342], "base": [1, 118, 123, 125, 256, 263, 312, 314, 320, 334, 336, 339, 341], "abov": [1, 3, 6, 147, 194, 213, 264, 319, 340, 341, 342, 346], "demonstr": [1, 343], "treat": [1, 97, 98, 100, 101, 187, 264, 339], "paramet": [1, 2, 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 32, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 78, 80, 81, 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, 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, 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, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 232, 233, 236, 237, 239, 244, 245, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 277, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 306, 308, 309, 312, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 325, 326, 327, 328, 329, 330, 331, 332, 334, 339, 340, 342], "produc": [1, 66, 251, 309], "through": [1, 182, 263, 321, 339, 340, 343], "construct": [1, 4, 77, 105, 141, 201], "its": [1, 6, 131, 145, 156, 193, 203, 206, 213, 253, 318, 319, 320, 343, 346], "type": [1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 32, 49, 56, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 78, 80, 81, 83, 84, 85, 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, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 204, 213, 263, 265, 266, 267, 268, 269, 270, 271, 272, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 339, 341], "shape": [1, 3, 4, 46, 59, 63, 66, 68, 69, 70, 78, 90, 93, 96, 99, 100, 101, 105, 115, 131, 141, 142, 149, 150, 151, 153, 154, 157, 158, 161, 188, 198, 200, 201, 202, 213, 215, 216, 217, 218, 219, 221, 222, 226, 228, 229, 230, 239, 265, 266, 267, 268, 269, 270, 271, 272, 284, 295, 314, 339, 340, 341, 344, 346], "pass": [1, 3, 4, 46, 57, 143, 144, 196, 203, 204, 205, 213, 237, 248, 249, 250, 253, 258, 339, 342], "re": [1, 4, 6, 309], "now": [1, 3, 6, 253, 339, 343], "promot": 1, "dtype": [1, 3, 14, 25, 32, 56, 89, 102, 105, 109, 118, 119, 120, 141, 151, 153, 154, 157, 158, 193, 201, 209, 264, 265, 266, 267, 268, 269, 270, 271, 272, 282, 284, 291, 328, 329, 330, 331, 332, 339, 340, 341, 343, 344, 345], "promoted_dtyp": 1, "promote_typ": 1, "float32": [1, 14, 89, 109, 118, 119, 120, 141, 151, 153, 157, 158, 193, 201, 209, 264, 265, 266, 267, 268, 269, 270, 271, 272, 282, 284, 291, 328, 329, 330, 331, 332, 339, 340, 341, 342, 343, 344, 345], "non": [1, 6, 246, 296, 312], "point": [1, 2, 3, 6, 104, 148, 209], "out_dtyp": 1, "is_floating_point": 1, "cast": [1, 32, 99, 100, 101, 121, 232, 343], "up": [1, 3, 253, 339], "determin": [1, 78, 243, 345], "x_cast": 1, "astyp": [1, 3, 232, 343], "y_cast": 1, "broadcasted_input": 1, "broadcast_arrai": 1, "out_shap": 1, "0": [1, 2, 3, 4, 6, 7, 14, 47, 52, 58, 67, 68, 69, 70, 77, 78, 89, 102, 106, 118, 119, 144, 149, 153, 158, 160, 162, 177, 181, 193, 194, 195, 196, 197, 199, 204, 213, 215, 216, 217, 218, 219, 220, 221, 222, 224, 225, 226, 227, 229, 230, 252, 255, 256, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 271, 272, 273, 275, 276, 278, 279, 282, 284, 286, 287, 291, 294, 295, 297, 298, 299, 300, 305, 306, 309, 312, 315, 316, 318, 319, 320, 321, 323, 326, 327, 328, 329, 330, 331, 332, 336, 339, 340, 341, 342, 343, 344, 345], "unique_ptr": 1, "make_uniqu": 1, "to_stream": 1, "handl": [1, 213, 339], "resolv": 1, "No": [1, 3], "happen": [1, 3, 263, 314, 339, 342], "alon": [1, 343], "effect": [1, 221, 339, 342], "onli": [1, 3, 5, 6, 59, 68, 69, 70, 118, 147, 209, 213, 236, 237, 239, 245, 248, 249, 250, 312, 339, 340, 345, 346], "execut": [1, 6, 60, 61, 62, 343, 346], "depend": [1, 2, 56, 118, 341, 345, 346], 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