From 9b989e242ffb427900c6c1e49ccb3f4d9844f4b2 Mon Sep 17 00:00:00 2001 From: jthorn Date: Sat, 12 Oct 2002 18:46:40 +0000 Subject: * expand NaN checks in gridfns to "is finite" checks (also catchs +/-infinity) * move final stage of calculation of LHS function H(h) out of Maple-generated code (in src/gr.cg/) into hand-written code in src/gr/horizon_function.c (comput_H()) so we can check that HD > 0 before taking its sqrt. [HD <= 0 probably means the inerpolated g_ij isn't positive definite] * also systematize CCTK_VWarn() printing for various error conditions in horizon_function.c git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@829 f88db872-0e4f-0410-b76b-b9085cfa78c5 --- src/gr.cg/horizon_Jacobian.c | 1217 +++++++++++++++++++++--------------------- src/gr.cg/horizon_function.c | 338 ++++++------ 2 files changed, 776 insertions(+), 779 deletions(-) (limited to 'src/gr.cg') diff --git a/src/gr.cg/horizon_Jacobian.c b/src/gr.cg/horizon_Jacobian.c index 3d540e1..eff036b 100644 --- a/src/gr.cg/horizon_Jacobian.c +++ b/src/gr.cg/horizon_Jacobian.c @@ -1,55 +1,55 @@ /* * inputs = {r, partial_d_ln_sqrt_g, partial_d_g_uu, X_ud, X_udd, g_uu, K_uu, h, HA, HB, HC, HD} * outputs = {partial_H_wrt_partial_d_h, partial_H_wrt_partial_dd_h} - * cost = 457*assignments+10*divisions+7*functions+1708*multiplications+729*additions + * cost = 457*assignments+10*divisions+7*functions+1685*multiplications+729*additions */ fp t1, t2, t4, t5, t7, t8, t10, t11, t12, t14; -fp t16, t18, t19, t20, t21, t24, t26, t28, t30, t31; -fp t32, t33, t34, t36, t38, t41, t43, t44, t46, t47; -fp t50, t51, t53, t54, t57, t58, t61, t63, t67, t69; -fp t73, t74, t77, t78, t79, t81, t82, t83, t84, t87; -fp t89, t91, t93, t96, t98, t102, t103, t104, t105, t107; -fp t108, t109, t112, t113, t116, t117, t118, t122, t123, t124; -fp t130, t134, t136, t138, t141, t143, t147, t148, t149, t151; -fp t154, t155, t156, t159, t160, t161, t164, t168, t172, t174; -fp t178, t179, t182, t183, t184, t187, t188, t189, t192, t193; -fp t194, t197, t198, t201, t203, t207, t208, t209, t212, t217; -fp t218, t221, t223, t224, t226, t227, t228, t232, t236, t240; -fp t241, t245, t246, t247, t250, t251, t253, t255, t256, t259; -fp t260, t264, t268, t269, t272, t274, t275, t277, t280, t281; -fp t287, t288, t292, t293, t297, t300, t304, t305, t306, t310; -fp t311, t314, t317, t324, t327, t329, t330, t338, t340, t343; -fp t344, t345, t349, t350, t359, t363, t365, t369, t373, t376; -fp t383, t386, t393, t397, t398, t401, t404, t405, t407, t411; -fp t415, t419, t423, t429, t430, t433, t435, t438, t441, t442; -fp t445, t448, t449, t454, t457, t460, t465, t470, t472, t473; -fp t476, t479, t488, t489, t491, t501, t502, t504, t506, t507; -fp t508, t510, t514, t519, t520, t522, t523, t530, t531, t535; -fp t539, t540, t543, t551, t552, t553, t559, t562, t570, t572; -fp t573, t575, t578, t582, t584, t589, t602, t612, t615, t616; -fp t617, t621, t624, t639, t640, t642, t647, t654, t665, t687; -fp t688, t692, t695, t697, t699, t707, t710, t714, t717, t722; -fp t724, t726, t745, t752, t754, t764, t773, t784, t789, t791; -fp t796, t800, t801, t803, t804, t806, t807, t809, t811, t813; -fp t815, t817, t819, t821, t823, t826, t828, t831, t833, t836; -fp t839, t841, t844, t847, t851, t864, t873, t876, t879, t882; -fp t884, t889, t893, t901, t908, t914, t918, t921, t922, t925; -fp t935, t943, t947, t953, t955, t958, t968, t972, t981, t985; -fp t988, t989, t992, t1002, t1008, t1017, t1020, t1028, t1047, t1050; -fp t1062, t1065, t1067, t1070, t1078, t1081, t1082, t1084, t1086, t1088; -fp t1095, t1098, t1100, t1106, t1136, t1137, t1138, t1148, t1165, t1170; -fp t1197, t1205, t1221, t1225, t1227, t1234, t1240, t1253, t1255, t1257; -fp t1260, t1266, t1269, t1271, t1295, t1302, t1308, t1311, t1322, t1326; -fp t1331, t1337, t1345, t1352, t1354, t1360, t1362, t1373, t1375, t1386; -fp t1394, t1410, t1419, t1432, t1466, t1469, t1472, t1473, t1474, t1477; -fp t1478, t1485, t1486, t1487, t1490, t1491, t1495, t1498, t1501, t1502; -fp t1511, t1517, t1520, t1523, t1526, t1529, t1532, t1534, t1539, t1557; -fp t1560, t1573, t1576, t1582, t1585, t1597, t1598, t1603, t1606, t1607; -fp t1609, t1616, t1619, t1621, t1633, t1634, t1639, t1651, t1654, t1659; -fp t1660, t1663, t1669, t1680, t1692, t1726, t1737, t1741, t1744, t1747; -fp t1756, t1762, t1763, t1766, t1769, t1772, t1778, t1793, t1795, t1800; -fp t1818, t1842; - t1 = g_uu_12; +fp t16, t18, t19, t20, t21, t23, t24, t25, t26, t29; +fp t30, t33, t35, t36, t37, t38, t40, t42, t44, t46; +fp t48, t49, t51, t52, t55, t56, t58, t59, t62, t63; +fp t66, t68, t72, t74, t78, t82, t83, t86, t87, t88; +fp t91, t92, t93, t94, t95, t97, t98, t101, t104, t107; +fp t108, t109, t112, t113, t115, t119, t121, t125, t127, t131; +fp t132, t135, t136, t137, t138, t142, t143, t146, t147, t150; +fp t151, t152, t154, t157, t160, t162, t164, t166, t169, t171; +fp t175, t182, t186, t188, t194, t196, t199, t206, t207, t210; +fp t213, t215, t216, t219, t220, t221, t224, t226, t229, t235; +fp t236, t239, t240, t242, t243, t244, t247, t248, t255, t259; +fp t261, t265, t266, t270, t271, t273, t274, t275, t277, t280; +fp t281, t282, t283, t286, t289, t290, t292, t295, t296, t299; +fp t303, t309, t313, t319, t320, t323, t327, t333, t335, t337; +fp t339, t342, t344, t345, t348, t351, t354, t359, t360, t361; +fp t363, t366, t370, t371, t374, t375, t378, t381, t384, t385; +fp t387, t390, t396, t398, t399, t403, t404, t406, t416, t417; +fp t419, t423, t426, t429, t432, t440, t443, t445, t453, t454; +fp t458, t460, t462, t464, t465, t467, t468, t470, t473, t479; +fp t484, t485, t487, t488, t491, t494, t495, t497, t499, t503; +fp t510, t514, t518, t521, t522, t537, t538, t540, t557, t560; +fp t561, t566, t570, t573, t579, t581, t582, t589, t596, t606; +fp t611, t619, t620, t622, t626, t630, t631, t636, t645, t647; +fp t649, t650, t654, t659, t660, t662, t663, t672, t675, t676; +fp t685, t686, t688, t697, t715, t719, t722, t725, t730, t747; +fp t750, t751, t752, t758, t764, t777, t779, t786, t791, t793; +fp t798, t802, t803, t805, t806, t808, t809, t811, t813, t815; +fp t817, t819, t821, t823, t825, t828, t830, t833, t835, t838; +fp t841, t843, t846, t849, t853, t866, t875, t877, t880, t883; +fp t884, t886, t889, t895, t897, t900, t902, t905, t907, t909; +fp t911, t912, t914, t924, t930, t936, t946, t948, t950, t954; +fp t956, t957, t960, t963, t966, t971, t974, t978, t980, t985; +fp t987, t988, t993, t994, t999, t1005, t1017, t1022, t1028, t1038; +fp t1043, t1044, t1048, t1051, t1057, t1066, t1068, t1073, t1081, t1088; +fp t1092, t1094, t1104, t1107, t1116, t1120, t1122, t1129, t1153, t1163; +fp t1165, t1187, t1209, t1226, t1252, t1258, t1288, t1292, t1302, t1307; +fp t1310, t1315, t1327, t1344, t1359, t1361, t1368, t1373, t1377, t1383; +fp t1394, t1409, t1418, t1431, t1461, t1464, t1465, t1466, t1472, t1474; +fp t1477, t1478, t1479, t1483, t1492, t1493, t1494, t1497, t1500, t1505; +fp t1507, t1513, t1518, t1526, t1528, t1536, t1540, t1542, t1546, t1548; +fp t1550, t1552, t1556, t1559, t1562, t1582, t1583, t1586, t1590, t1594; +fp t1595, t1598, t1607, t1612, t1615, t1618, t1623, t1626, t1644, t1656; +fp t1657, t1677, t1679, t1686, t1695, t1714, t1730, t1742, t1745, t1746; +fp t1749, t1768, t1774, t1776, t1784, t1791, t1794, t1797, t1800, t1803; +fp t1806, t1818; + t1 = g_uu_23; t2 = 1/r; t4 = X_ud_12; t5 = PARTIAL_RHO(h); @@ -57,570 +57,569 @@ fp t1818, t1842; t8 = PARTIAL_SIGMA(h); t10 = yy*t2-t4*t5-t7*t8; t11 = t1*t10; - t12 = g_uu_11; - t14 = X_ud_11; - t16 = X_ud_21; - t18 = xx*t2-t14*t5-t16*t8; + t12 = partial_d_g_uu_313; + t14 = X_ud_13; + t16 = X_ud_23; + t18 = zz*t2-t14*t5-t16*t8; t19 = t12*t18; - t20 = X_udd_111; + t20 = X_ud_11; t21 = t19*t20; - t24 = g_uu_13; - t26 = X_ud_13; - t28 = X_ud_23; - t30 = zz*t2-t26*t5-t28*t8; - t31 = t24*t30; - t32 = t12*t14; - t33 = yy*yy; - t34 = zz*zz; - t36 = r*r; - t38 = 1/t36/r; - t41 = X_udd_211; - t43 = t14*t14; - t44 = PARTIAL_RHO_RHO(h); - t46 = t16*t14; - t47 = PARTIAL_RHO_SIGMA(h); - t50 = t16*t16; - t51 = PARTIAL_SIGMA_SIGMA(h); - t53 = (t33+t34)*t38-t20*t5-t41*t8-t43*t44-2.0*t46*t47-t50*t51; - t54 = t32*t53; - t57 = g_uu_23; - t58 = t57*t10; - t61 = X_udd_113; - t63 = X_udd_213; - t67 = t16*t26; - t69 = t14*t28; - t73 = -xx*zz*t38-t61*t5-t63*t8-t14*t26*t44-t67*t47-t69*t47-t16*t28*t51; - t74 = t32*t73; - t77 = t1*t1; - t78 = t10*t10; - t79 = t77*t78; - t81 = t57*t30; - t82 = g_uu_22; - t83 = t82*t4; - t84 = xx*xx; - t87 = X_udd_122; - t89 = X_udd_222; - t91 = t4*t4; - t93 = t7*t4; - t96 = t7*t7; - t98 = (t84+t34)*t38-t87*t5-t89*t8-t91*t44-2.0*t93*t47-t96*t51; - t102 = t1*t18; - t103 = partial_d_g_uu_223; - t104 = t103*t26; - t105 = t104*t10; - t107 = t82*t10; - t108 = X_udd_112; - t109 = t19*t108; - t112 = t57*t26; - t113 = t107*t98; - t116 = g_uu_33; - t117 = t116*t30; - t118 = X_udd_133; - t122 = t1*t4; - t123 = t24*t18; - t124 = t123*t73; - t130 = t57*t4; - t134 = X_udd_233; - t136 = t26*t26; - t138 = t28*t26; - t141 = t28*t28; - t143 = (t84+t33)*t38-t118*t5-t134*t8-t136*t44-2.0*t138*t47-t141*t51; - t147 = partial_d_g_uu_112; - t148 = t147*t4; - t149 = t148*t18; - t151 = t19*t53; - t154 = 2.0*t11*t21+2.0*t31*t54+2.0*t58*t74+t79*t20+2.0*t81*t83*t98+t102* -t105+2.0*t107*t109+2.0*t112*t113+2.0*t117*t58*t118+2.0*t122*t124+2.0*t81*t107* -t87+2.0*t117*t130*t143+t31*t149+2.0*t122*t151; - t155 = X_udd_123; - t156 = t102*t155; - t159 = partial_d_g_uu_213; - t160 = t159*t30; - t161 = t160*t14; - t164 = t1*t14; - t168 = X_udd_223; - t172 = t7*t26; - t174 = t4*t28; - t178 = -yy*zz*t38-t155*t5-t168*t8-t4*t26*t44-t172*t47-t174*t47-t7*t28*t51 + t23 = g_uu_13; + t24 = t18*t18; + t25 = t23*t24; + t26 = partial_d_g_uu_113; + t29 = t1*t14; + t30 = g_uu_12; + t33 = X_ud_21; + t35 = xx*t2-t20*t5-t33*t8; + t36 = t30*t35; + t37 = xx*xx; + t38 = zz*zz; + t40 = r*r; + t42 = 1/t40/r; + t44 = X_udd_122; + t46 = X_udd_222; + t48 = t4*t4; + t49 = PARTIAL_RHO_RHO(h); + t51 = t7*t4; + t52 = PARTIAL_RHO_SIGMA(h); + t55 = t7*t7; + t56 = PARTIAL_SIGMA_SIGMA(h); + t58 = (t37+t38)*t42-t44*t5-t46*t8-t48*t49-2.0*t51*t52-t55*t56; + t59 = t36*t58; + t62 = t23*t18; + t63 = t1*t4; + t66 = X_udd_113; + t68 = X_udd_213; + t72 = t33*t14; + t74 = t20*t16; + t78 = -xx*zz*t42-t66*t5-t68*t8-t20*t14*t49-t72*t52-t74*t52-t33*t16*t56; + t82 = partial_d_g_uu_333; + t83 = t82*t24; + t86 = t1*t18; + t87 = t30*t20; + t88 = t87*t58; + t91 = g_uu_11; + t92 = t91*t35; + t93 = partial_d_g_uu_122; + t94 = t93*t10; + t95 = t94*t4; + t97 = t35*t35; + t98 = t23*t97; + t101 = t23*t35; + t104 = t23*t20; + t107 = t91*t20; + t108 = partial_d_g_uu_133; + t109 = t108*t24; + t112 = t1*t1; + t113 = t112*t24; + t115 = t30*t30; + t119 = X_udd_112; + t121 = X_udd_212; + t125 = t33*t4; + t127 = t20*t7; + t131 = -xx*yy*t42-t119*t5-t121*t8-t20*t4*t49-t125*t52-t127*t52-t33*t7*t56 ; - t179 = t164*t178; - t182 = partial_d_g_uu_113; - t183 = t182*t30; - t184 = t183*t14; - t187 = partial_d_g_uu_133; - t188 = t187*t30; - t189 = t188*t26; - t192 = partial_d_g_uu_313; - t193 = t192*t30; - t194 = t193*t14; - t197 = partial_d_g_uu_222; - t198 = t197*t78; - t201 = partial_d_g_uu_312; - t203 = t201*t18*t4; - t207 = partial_d_g_uu_233; - t208 = t30*t30; - t209 = t207*t208; - t212 = t187*t208; - t217 = t116*t26; - t218 = t107*t178; - t221 = 2.0*t58*t156+2.0*t102*t161+2.0*t58*t179+2.0*t19*t184+t19*t189+t11* -t184+2.0*t123*t194+RATIONAL(1.0,2.0)*t112*t198+2.0*t58*t203+t11*t189+RATIONAL( -1.0,2.0)*t83*t209+RATIONAL(1.0,2.0)*t32*t212+RATIONAL(1.0,2.0)*t122*t212+2.0* -t217*t218; - t223 = t201*t10; - t224 = t223*t18; - t226 = partial_d_g_uu_212; - t227 = t226*t10; - t228 = t227*t14; - t232 = t77*t10; - t236 = t77*t18; - t240 = t24*t24; - t241 = t240*t18; - t245 = t24*t26; - t246 = partial_d_g_uu_122; - t247 = t246*t78; - t250 = t192*t26; - t251 = t250*t18; - t253 = t82*t78; - t255 = t1*t78; - t256 = partial_d_g_uu_123; - t259 = t57*t57; - t260 = t259*t10; - t264 = t57*t208; - t268 = t147*t10; - t269 = t268*t14; - t272 = t223*t14; - t274 = t217*t224+2.0*t102*t228+t117*t203+2.0*t232*t53*t4+2.0*t236*t98*t14 -+2.0*t241*t143*t14+RATIONAL(1.0,2.0)*t245*t247+t58*t251+t253*t104+t255*t256*t26 -+2.0*t260*t143*t4+2.0*t264*t24*t108+2.0*t19*t269+t117*t272; - t275 = partial_d_g_uu_323; - t277 = t275*t10*t26; - t280 = t182*t26; - t281 = t280*t18; - t287 = t12*t12; - t288 = t287*t18; - t292 = t82*t178; - t293 = t292*t4; - t297 = t10*t178; - t300 = t259*t30; - t304 = partial_d_g_uu_111; - t305 = t304*t18; - t306 = t305*t14; - t310 = t226*t4; - t311 = t310*t18; - t314 = t159*t18*t26; - t317 = t240*t30; - t324 = 2.0*t117*t277+t11*t281+RATIONAL(3.0,2.0)*t255*t246*t4+t81*t228+2.0 -*t288*t53*t14+4.0*t58*t293+2.0*t259*t26*t297+2.0*t300*t10*t155+t11*t306+2.0* -t117*t293+t81*t311+2.0*t81*t314+2.0*t317*t18*t61+2.0*t11*t123*t61; - t327 = t259*t78; - t329 = partial_d_g_uu_322; - t330 = t329*t78; - t338 = t183*t18; - t340 = t123*t155; - t343 = t18*t18; - t344 = t24*t343; - t345 = partial_d_g_uu_311; - t349 = partial_d_g_uu_333; - t350 = t349*t208; - t359 = X_udd_212; - t363 = t16*t4; - t365 = t14*t7; - t369 = -xx*yy*t38-t108*t5-t359*t8-t14*t4*t44-t363*t47-t365*t47-t16*t7*t51 + t132 = t35*t131; + t135 = t10*t10; + t136 = t1*t135; + t137 = g_uu_22; + t138 = X_udd_123; + t142 = t11*t21+t25*t26*t20+2.0*t29*t59+2.0*t62*t63*t78+RATIONAL(1.0,2.0)* +t63*t83+2.0*t86*t88+t92*t95+t98*t12*t14+2.0*t101*t21+RATIONAL(1.0,2.0)*t104*t83 ++RATIONAL(1.0,2.0)*t107*t109+t113*t44+2.0*t115*t4*t132+2.0*t136*t137*t138; + t143 = t30*t4; + t146 = t137*t135; + t147 = t30*t119; + t150 = g_uu_33; + t151 = t150*t18; + t152 = partial_d_g_uu_323; + t154 = t152*t10*t14; + t157 = yy*yy; + t160 = X_udd_133; + t162 = X_udd_233; + t164 = t14*t14; + t166 = t16*t14; + t169 = t16*t16; + t171 = (t37+t157)*t42-t160*t5-t162*t8-t164*t49-2.0*t166*t52-t169*t56; + t175 = t115*t10; + t182 = t23*t131; + t186 = partial_d_g_uu_223; + t188 = t186*t10*t14; + t194 = t23*t23; + t196 = t35*t78; + t199 = t194*t18; + t206 = t150*t14; + t207 = t101*t171; + t210 = t101*t160; + t213 = RATIONAL(1.0,2.0)*t143*t109+2.0*t146*t147+2.0*t151*t154+2.0*t151* +t63*t171+2.0*t175*t20*t131+RATIONAL(3.0,2.0)*t25*t108*t14+4.0*t86*t182*t14+2.0* +t86*t188+2.0*t175*t35*t119+2.0*t194*t14*t196+2.0*t199*t20*t78+2.0*t199*t35*t66+ +2.0*t206*t207+2.0*t151*t210; + t215 = t26*t35; + t216 = t215*t14; + t219 = t91*t97; + t220 = partial_d_g_uu_111; + t221 = t220*t20; + t224 = partial_d_g_uu_123; + t226 = t224*t10*t14; + t229 = t104*t171; + t235 = t137*t10; + t236 = t107*t131; + t239 = partial_d_g_uu_312; + t240 = t239*t4; + t242 = partial_d_g_uu_213; + t243 = t242*t35; + t244 = t243*t14; + t247 = t150*t150; + t248 = t247*t24; + t255 = X_udd_223; + t259 = t7*t14; + t261 = t4*t16; + t265 = -yy*zz*t42-t138*t5-t255*t8-t4*t14*t49-t259*t52-t261*t52-t7*t16*t56 ; - t373 = t123*t178; - t376 = t1*t343; - t383 = t18*t73; - t386 = t327*t118+RATIONAL(1.0,2.0)*t217*t330+2.0*t317*t14*t73+2.0*t117* -t251+t122*t338+2.0*t107*t340+RATIONAL(3.0,2.0)*t344*t345*t14+RATIONAL(1.0,2.0)* -t130*t350+2.0*t117*t107*t155+2.0*t232*t14*t369+2.0*t83*t373+2.0*t376*t12*t108+ -2.0*t31*t281+2.0*t240*t26*t383; - t393 = t24*t14; - t397 = t116*t208; - t398 = t24*t61; - t401 = t19*t61; - t404 = t349*t30; - t405 = t404*t26; - t407 = t24*t369; - t411 = t123*t143; - t415 = t24*t73; - t419 = t107*t369; - t423 = t18*t369; - t429 = t256*t10; - t430 = t429*t26; - t433 = 2.0*t232*t18*t108+RATIONAL(3.0,2.0)*t264*t207*t26+2.0*t11*t393*t73 -+2.0*t397*t398+2.0*t117*t401+t123*t405+4.0*t81*t407*t26+2.0*t130*t411+t58*t194+ -4.0*t117*t415*t26+2.0*t245*t419+2.0*t77*t4*t423+2.0*t300*t4*t178+2.0*t31*t430; - t435 = t393*t143; - t438 = t11*t369; - t441 = t1*t369; - t442 = t441*t4; - t445 = t393*t178; - t448 = t207*t30; - t449 = t448*t26; - t454 = t123*t118; - t457 = t19*t73; - t460 = t11*t73; - t465 = t32*t369; - t470 = t227*t18; - t472 = 2.0*t58*t435+2.0*t112*t438+4.0*t107*t442+2.0*t107*t445+t107*t449+ -t376*t310+4.0*t123*t74+2.0*t58*t454+2.0*t217*t457+2.0*t217*t460+2.0*t130*t457+ -2.0*t81*t465+2.0*t58*t401+t112*t470; - t473 = t11*t53; - t476 = t164*t98; - t479 = t77*t343; - t488 = t345*t18; - t489 = t488*t14; - t491 = t19*t369; - t501 = t103*t30; - t502 = t501*t4; - t504 = t501*t10; - t506 = partial_d_g_uu_211; - t507 = t506*t18; - t508 = t507*t14; - t510 = 2.0*t245*t473+2.0*t107*t476+t479*t87+2.0*t117*t74+2.0*t117*t435+ -2.0*t117*t11*t61+t117*t489+2.0*t112*t491+2.0*t217*t411+2.0*t31*t83*t369+2.0*t11 -*t54+t102*t502+t164*t504+t107*t508; - t514 = t24*t208; - t519 = t275*t30; - t520 = t519*t10; - t522 = t256*t30; - t523 = t522*t4; - t530 = t82*t82; - t531 = t530*t10; - t535 = t519*t4; - t539 = t1*t73; - t540 = t539*t4; - t543 = t57*t78; - t551 = t514*t182*t14+2.0*t107*t465+t393*t520+t19*t523+2.0*t83*t491+t58* -t489+2.0*t117*t454+2.0*t531*t98*t4+t123*t535+2.0*t123*t272+4.0*t58*t540+2.0* -t543*t1*t61+2.0*t81*t11*t108+t123*t277; - t552 = t329*t10; - t553 = t552*t4; - t559 = t1*t108; - t562 = t275*t4; - t570 = t287*t343; - t572 = t197*t10; - t573 = t572*t4; - t575 = t522*t10; - t578 = t12*t343; - t582 = t123*t553+2.0*t107*t311+2.0*t81*t445+2.0*t253*t559+t397*t562+ -RATIONAL(1.0,2.0)*t393*t350+t264*t103*t4+t514*t256*t4+t570*t20+t102*t573+t32* -t575+t344*t250+t578*t280+t543*t201*t14; - t584 = t226*t14; - t589 = t193*t18; - t602 = t192*t14; - t612 = t57*t155; - t615 = t253*t584+2.0*t317*t53*t26+t130*t589+t19*t430+t376*t159*t26+ -RATIONAL(1.0,2.0)*t393*t330+t255*t147*t14+RATIONAL(1.0,2.0)*t32*t247+t264*t159* -t14+t397*t602+RATIONAL(1.0,2.0)*t164*t209+RATIONAL(3.0,2.0)*t376*t506*t14+2.0* -t344*t1*t155+2.0*t397*t612; - t616 = t116*t116; - t617 = t616*t30; - t621 = t506*t343; - t624 = t345*t343; - t639 = t246*t10; - t640 = t639*t4; - t642 = t197*t4; - t647 = t304*t343; - t654 = 2.0*t617*t143*t26+RATIONAL(1.0,2.0)*t112*t621+RATIONAL(1.0,2.0)* -t217*t624+2.0*t31*t122*t53+RATIONAL(3.0,2.0)*t514*t187*t26+t543*t275*t26+2.0* -t344*t12*t61+t117*t553+t31*t640+RATIONAL(3.0,2.0)*t253*t642+RATIONAL(1.0,2.0)* -t130*t624+RATIONAL(1.0,2.0)*t245*t647+t344*t201*t4+RATIONAL(1.0,2.0)*t122*t647; - t665 = t349*t26; - t687 = RATIONAL(1.0,2.0)*t83*t621+RATIONAL(3.0,2.0)*t543*t329*t4+2.0*t31* -t11*t20+RATIONAL(3.0,2.0)*t397*t665+t81*t573+2.0*t107*t502+2.0*t543*t82*t155+ -2.0*t11*t523+2.0*t31*t21+2.0*t31*t164*t369+t31*t269+2.0*t11*t149+t578*t148+ -RATIONAL(1.0,2.0)*t164*t198; - t688 = t58*t73; - t692 = t102*t98; - t695 = t530*t78; - t697 = t240*t343; - t699 = t102*t369; - t707 = t102*t87; - t710 = t57*t178; - t714 = t102*t178; - t717 = t268*t18; - t722 = 2.0*t245*t688+t81*t508+2.0*t83*t692+t695*t87+t697*t118+2.0*t245* -t699+2.0*t81*t109+2.0*t31*t102*t108+2.0*t107*t707+4.0*t117*t710*t26+2.0*t130* -t714+t245*t717+t31*t306+2.0*t117*t540; - t724 = t616*t208; - t726 = t58*t143; - t745 = t259*t208; - t752 = t240*t208; - t754 = t724*t118+2.0*t217*t726+2.0*t300*t98*t26+2.0*t31*t130*t73+t58*t405 -+4.0*t102*t465+2.0*t81*t442+t19*t640+2.0*t81*t707+2.0*t58*t535+t745*t87+2.0*t31 -*t58*t61+2.0*t81*t105+t752*t20; - t764 = t304*t14; - t773 = t160*t18; - t784 = 2.0*t112*t692+2.0*t245*t151+2.0*t117*t156+2.0*t117*t179+t107*t161+ -RATIONAL(3.0,2.0)*t578*t764+4.0*t123*t179+2.0*t217*t714+2.0*t81*t340+t83*t773+ -t102*t449+2.0*t31*t107*t108+2.0*t112*t373+t107*t314+2.0*t81*t476; - t789 = pow(HD,1.0*RATIONAL(1.0,2.0)); - t791 = 1/t789/HD; - t796 = -t764-t584-t602-t148-t642-t562-t280-t104-t665-t12*t20-2.0*t559-2.0 -*t398; - t800 = partial_d_ln_sqrt_g_1; - t801 = t12*t800; - t803 = partial_d_ln_sqrt_g_2; - t804 = t1*t803; - t806 = partial_d_ln_sqrt_g_3; - t807 = t24*t806; - t809 = t1*t800; - t811 = t82*t803; - t813 = t57*t806; - t815 = t24*t800; - t817 = t57*t803; - t819 = t116*t806; - t821 = -t82*t87-2.0*t612-t116*t118-t801*t14-t804*t14-t807*t14-t809*t4- -t811*t4-t813*t4-t815*t26-t817*t26-t819*t26; - t823 = 1/t789; - t826 = K_uu_11*t18; - t828 = K_uu_12; - t831 = t828*t10; - t833 = K_uu_13; - t836 = t833*t30; - t839 = K_uu_22*t10; - t841 = K_uu_23; - t844 = t841*t30; - t847 = K_uu_33*t30; - t851 = 1/HD; - t864 = HD*HD; - t873 = RATIONAL(3.0,2.0)*HA/t789/t864+RATIONAL(1.0,2.0)*HB*t791+HC/t864; - partial_H_wrt_partial_d_h_1 = (t154+t221+t274+t324+t386+t433+t472+t510+ -t551+t582+t615+t654+t687+t722+t754+t784)*t791+(t796+t821)*t823+(-2.0*t826*t14 --2.0*t828*t4*t18-2.0*t831*t14-2.0*t833*t26*t18-2.0*t836*t14-2.0*t839*t4-2.0* -t841*t26*t10-2.0*t844*t4-2.0*t847*t26)*t851-(-2.0*t19*t14-2.0*t122*t18-2.0*t11* -t14-2.0*t245*t18-2.0*t31*t14-2.0*t107*t4-2.0*t112*t10-2.0*t81*t4-2.0*t117*t26)* -t873; - t876 = t103*t10*t28; - t879 = t519*t7; - t882 = t188*t28; - t884 = t429*t28; - t889 = t12*t369*t16; - t893 = t24*t28; - t901 = t57*t7; - t908 = t116*t28; - t914 = 2.0*t81*t876+2.0*t58*t879+t19*t882+2.0*t31*t884+t11*t882+4.0*t102* -t889+t724*t134+2.0*t893*t688+2.0*t317*t53*t28+RATIONAL(1.0,2.0)*t893*t247+2.0* -t31*t901*t73+RATIONAL(3.0,2.0)*t264*t207*t28+2.0*t908*t714+RATIONAL(3.0,2.0)* -t255*t246*t7; - t918 = t304*t16; - t921 = t24*t16; - t922 = t921*t178; - t925 = t57*t28; - t935 = t349*t28; - t943 = t275*t7; - t947 = t1*t16; - t953 = 2.0*t288*t53*t16+RATIONAL(3.0,2.0)*t578*t918+2.0*t81*t922+2.0*t925 -*t113+RATIONAL(1.0,2.0)*t908*t330+2.0*t925*t373+4.0*t81*t407*t28+RATIONAL(3.0, -2.0)*t397*t935+RATIONAL(3.0,2.0)*t543*t329*t7+t514*t256*t7+t397*t943+RATIONAL( -1.0,2.0)*t921*t350+RATIONAL(1.0,2.0)*t947*t209+2.0*t31*t58*t63; - t955 = t102*t168; - t958 = t947*t178; - t968 = t82*t7; - t972 = t123*t168; - t981 = t103*t28; - t985 = t19*t41; - t988 = t12*t16; - t989 = t988*t53; - t992 = 2.0*t117*t955+2.0*t117*t958+2.0*t893*t151+2.0*t81*t107*t89+2.0* -t908*t411+2.0*t81*t968*t98+2.0*t81*t972+t255*t256*t28+RATIONAL(1.0,2.0)*t925* -t198+2.0*t925*t692+t253*t981+2.0*t893*t419+2.0*t31*t985+2.0*t31*t989; - t1002 = t102*t89; - t1008 = t947*t98; - t1017 = t197*t7; - t1020 = t292*t7; - t1028 = 2.0*t11*t123*t63+2.0*t543*t82*t168+2.0*t31*t107*t359+2.0*t81* -t1002+2.0*t31*t968*t369+2.0*t81*t1008+2.0*t260*t143*t7+4.0*t117*t415*t28+ -RATIONAL(3.0,2.0)*t253*t1017+4.0*t58*t1020+2.0*t908*t218+t570*t41+t327*t134+ -t695*t89; - t1047 = t123*t134; - t1050 = t921*t143; - t1062 = t697*t134+t79*t41+RATIONAL(3.0,2.0)*t344*t345*t16+2.0*t107*t972+ -2.0*t107*t922+2.0*t117*t1020+2.0*t968*t373+RATIONAL(3.0,2.0)*t376*t506*t16+2.0* -t58*t1047+2.0*t58*t1050+2.0*t117*t107*t168+t893*t717+2.0*t968*t692+2.0*t531*t98 -*t7; - t1065 = t268*t16; - t1067 = t19*t63; - t1070 = t988*t73; - t1078 = t1*t359; - t1081 = t147*t7; - t1082 = t1081*t18; - t1084 = t552*t7; - t1086 = t639*t7; - t1088 = t19*t359; - t1095 = t501*t7; - t1098 = 2.0*t901*t411+t31*t1065+2.0*t117*t1067+2.0*t117*t1070+2.0*t543*t1 -*t63+2.0*t908*t457+2.0*t253*t1078+t31*t1082+t117*t1084+t31*t1086+2.0*t81*t1088+ -2.0*t81*t889+2.0*t925*t491+2.0*t107*t1095; - t1100 = t522*t7; - t1106 = t572*t7; - t1136 = 2.0*t11*t1100+2.0*t77*t7*t423+t81*t1106+2.0*t31*t102*t359+2.0* -t232*t16*t369+2.0*t31*t947*t369+2.0*t107*t1008+2.0*t893*t699+2.0*t107*t1002+2.0 -*t901*t714+2.0*t240*t28*t383+2.0*t117*t58*t134+2.0*t117*t901*t143+2.0*t908*t726 + t266 = t1*t265; + t270 = partial_d_g_uu_212; + t271 = t270*t20; + t273 = partial_d_g_uu_322; + t274 = t273*t10; + t275 = t274*t4; + t277 = t1*t24; + t280 = 2.0*t62*t216+RATIONAL(3.0,2.0)*t219*t221+2.0*t62*t226+2.0*t151* +t229+2.0*t62*t11*t66+2.0*t235*t236+t98*t240+2.0*t86*t244+t248*t160+t136*t239* +t20+4.0*t151*t266*t14+t146*t271+t101*t275+t277*t186*t4; + t281 = t137*t4; + t282 = partial_d_g_uu_211; + t283 = t282*t97; + t286 = t36*t138; + t289 = t30*t10; + t290 = partial_d_g_uu_112; + t292 = t290*t35*t4; + t295 = partial_d_g_uu_311; + t296 = t295*t97; + t299 = t23*t78; + t303 = t92*t119; + t309 = t247*t18; + t313 = t87*t265; + t319 = t150*t24; + t320 = t82*t14; + t323 = t30*t135; + t327 = t112*t18; + t333 = X_udd_111; + t335 = X_udd_211; + t337 = t20*t20; + t339 = t33*t20; + t342 = t33*t33; + t344 = (t157+t38)*t42-t333*t5-t335*t8-t337*t49-2.0*t339*t52-t342*t56; + t345 = t107*t344; + t348 = RATIONAL(1.0,2.0)*t281*t283+2.0*t11*t286+2.0*t289*t292+RATIONAL( +1.0,2.0)*t63*t296+4.0*t151*t299*t14+2.0*t235*t303+RATIONAL(3.0,2.0)*t136*t273* +t4+2.0*t309*t171*t14+2.0*t11*t313+2.0*t98*t30*t138+RATIONAL(3.0,2.0)*t319*t320+ +RATIONAL(3.0,2.0)*t323*t93*t4+2.0*t327*t58*t14+2.0*t289*t345; + t351 = t273*t135; + t354 = t92*t333; + t359 = partial_d_g_uu_222; + t360 = t359*t10; + t361 = t360*t4; + t363 = t359*t4; + t366 = partial_d_g_uu_233; + t370 = t23*t14; + t371 = t11*t78; + t374 = t152*t18; + t375 = t374*t4; + t378 = t92*t344; + t381 = t92*t78; + t384 = t242*t18; + t385 = t384*t35; + t387 = t36*t265; + t390 = t30*t97; + t396 = RATIONAL(1.0,2.0)*t206*t351+2.0*t289*t354+RATIONAL(1.0,2.0)*t104* +t351+t36*t361+RATIONAL(3.0,2.0)*t146*t363+RATIONAL(3.0,2.0)*t277*t366*t14+2.0* +t370*t371+2.0*t11*t375+2.0*t143*t378+2.0*t63*t381+t281*t385+2.0*t63*t387+ +RATIONAL(3.0,2.0)*t390*t282*t20+t323*t290*t20; + t398 = t186*t18; + t399 = t398*t4; + t403 = t270*t10; + t404 = t403*t35; + t406 = t107*t78; + t416 = t290*t10; + t417 = t416*t20; + t419 = t186*t14; + t423 = t1*t138; + t426 = t23*t66; + t429 = t220*t97; + t432 = t62*t292+2.0*t235*t399+t235*t244+t29*t404+2.0*t11*t406+2.0*t390* +t91*t119+t289*t216+2.0*t289*t104*t78+t62*t417+t146*t419+t136*t152*t14+2.0*t319* +t423+2.0*t319*t426+RATIONAL(1.0,2.0)*t143*t429; + t440 = t36*t131; + t443 = t416*t35; + t445 = t36*t44; + t453 = t270*t4; + t454 = t453*t35; + t458 = t194*t97; + t460 = t115*t135; + t462 = t115*t97; + t464 = t91*t91; + t465 = t464*t97; + t467 = 2.0*t277*t23*t119+RATIONAL(3.0,2.0)*t98*t295*t20+2.0*t370*t440+ +t370*t443+2.0*t86*t445+2.0*t281*t59+RATIONAL(1.0,2.0)*t206*t296+t92*t226+t86* +t454+2.0*t235*t445+t458*t160+t460*t333+t462*t44+t465*t333; + t468 = t384*t20; + t470 = t92*t66; + t473 = t101*t78; + t479 = t403*t20; + t484 = t282*t35; + t485 = t484*t20; + t487 = t220*t35; + t488 = t487*t20; + t491 = t12*t35*t14; + t494 = t239*t10; + t495 = t494*t35; + t497 = t494*t20; + t499 = t101*t265; + t503 = t235*t468+2.0*t11*t470+2.0*t143*t473+2.0*t289*t101*t66+t86*t479+ +2.0*t235*t88+t86*t361+t235*t485+t289*t488+2.0*t151*t491+t206*t495+t151*t497+2.0 +*t281*t499+t62*t488; + t510 = t101*t138; + t514 = t112*t10; + t518 = t104*t265; + t521 = t295*t35; + t522 = t521*t20; + t537 = t62*t95+4.0*t36*t236+2.0*t235*t510+t86*t485+2.0*t514*t171*t4+2.0* +t235*t518+t11*t522+2.0*t86*t303+2.0*t63*t207+2.0*t36*t479+2.0*t11*t210+2.0*t11* +t229+2.0*t92*t417+t151*t522; + t538 = t240*t35; + t540 = t289*t131; + t557 = t289*t78; + t560 = t137*t265; + t561 = t560*t4; + t566 = t464*t35; + t570 = t93*t135; + t573 = t359*t135; + t579 = t151*t538+2.0*t29*t540+4.0*t101*t406+2.0*t136*t30*t66+2.0*t98*t91* +t66+2.0*t62*t36*t119+2.0*t62*t87*t131+2.0*t206*t557+4.0*t11*t561+t323*t224*t14+ +2.0*t566*t344*t20+RATIONAL(1.0,2.0)*t370*t570+RATIONAL(1.0,2.0)*t29*t573+2.0* +t175*t344*t4; + t581 = t30*t78; + t582 = t581*t4; + t589 = t143*t131; + t596 = t374*t10; + t606 = t115*t35; + t611 = t10*t265; + t619 = 4.0*t11*t582+2.0*t86*t289*t119+t151*t275+2.0*t86*t589+4.0*t101* +t313+4.0*t235*t589+t104*t596+2.0*t62*t289*t333+2.0*t151*t289*t66+2.0*t151*t582+ +2.0*t606*t58*t20+2.0*t112*t14*t611+2.0*t327*t4*t265+2.0*t101*t497; + t620 = t26*t14; + t622 = t92*t131; + t626 = t289*t344; + t630 = t224*t18; + t631 = t630*t4; + t636 = t194*t35; + t645 = t630*t10; + t647 = t194*t24; + t649 = t26*t18; + t650 = t649*t20; + t654 = t219*t620+2.0*t29*t622+t101*t375+2.0*t370*t626+t101*t154+t92*t631+ +2.0*t327*t10*t138+2.0*t636*t171*t20+2.0*t62*t143*t344+2.0*t235*t454+t107*t645+ +t647*t333+t289*t650+2.0*t86*t236; + t659 = t108*t18; + t660 = t659*t14; + t662 = t366*t18; + t663 = t662*t14; + t672 = t398*t10; + t675 = t82*t18; + t676 = t675*t14; + t685 = 2.0*t289*t631+t92*t660+t235*t663+2.0*t281*t622+2.0*t11*t538+t36* +t188+RATIONAL(1.0,2.0)*t370*t429+t87*t672+t36*t399+t101*t676+t289*t660+t11*t676 ++2.0*t62*t354+2.0*t62*t281*t131; + t686 = t290*t4; + t688 = t19*t35; + t697 = t235*t58; + t715 = t219*t686+t63*t688+t36*t663+2.0*t370*t378+RATIONAL(1.0,2.0)*t29* +t283+2.0*t206*t381+2.0*t29*t697+2.0*t62*t345+2.0*t86*t281*t58+2.0*t36*t468+2.0* +t86*t235*t44+t390*t453+2.0*t151*t313+2.0*t151*t561; + t719 = t366*t24; + t722 = t235*t131; + t725 = t12*t20; + t730 = t235*t265; + t747 = t152*t4; + t750 = 2.0*t151*t470+RATIONAL(1.0,2.0)*t281*t719+2.0*t370*t722+t319*t725+ +2.0*t62*t235*t119+2.0*t206*t730+2.0*t206*t387+2.0*t151*t11*t160+2.0*t92*t650+ +t390*t242*t14+2.0*t199*t344*t14+2.0*t151*t286+t319*t747+t11*t491; + t751 = t137*t137; + t752 = t751*t10; + t758 = t649*t35; + t764 = t11*t171; + t777 = t112*t135; + t779 = t751*t135; + t786 = 2.0*t752*t58*t4+RATIONAL(1.0,2.0)*t87*t719+t143*t758+2.0*t86*t518+ +t277*t242*t20+2.0*t206*t764+2.0*t151*t406+t25*t224*t4+2.0*t29*t499+2.0*t86*t510 ++RATIONAL(1.0,2.0)*t107*t570+t777*t160+t779*t44+2.0*t151*t235*t138+RATIONAL(1.0 +,2.0)*t87*t573; + t791 = pow(HD,1.0*RATIONAL(1.0,2.0)); + t793 = 1/t791/HD; + t798 = -t221-t271-t725-t686-t363-t747-t620-t419-t320-t91*t333-2.0*t147 +-2.0*t426; + t802 = partial_d_ln_sqrt_g_1; + t803 = t91*t802; + t805 = partial_d_ln_sqrt_g_2; + t806 = t30*t805; + t808 = partial_d_ln_sqrt_g_3; + t809 = t23*t808; + t811 = t30*t802; + t813 = t137*t805; + t815 = t1*t808; + t817 = t23*t802; + t819 = t1*t805; + t821 = t150*t808; + t823 = -t137*t44-2.0*t423-t150*t160-t803*t20-t806*t20-t809*t20-t811*t4- +t813*t4-t815*t4-t817*t14-t819*t14-t821*t14; + t825 = 1/t791; + t828 = K_uu_11*t35; + t830 = K_uu_12; + t833 = t830*t10; + t835 = K_uu_13; + t838 = t835*t18; + t841 = K_uu_22*t10; + t843 = K_uu_23; + t846 = t843*t18; + t849 = K_uu_33*t18; + t853 = 1/HD; + t866 = HD*HD; + t875 = RATIONAL(3.0,2.0)*HA/t791/t866+RATIONAL(1.0,2.0)*HB*t793+HC/t866; + partial_H_wrt_partial_d_h_1 = (t142+t213+t280+t348+t396+t432+t467+t503+ +t537+t579+t619+t654+t685+t715+t750+t786)*t793+(t798+t823)*t825+(-2.0*t828*t20 +-2.0*t830*t4*t35-2.0*t833*t20-2.0*t835*t14*t35-2.0*t838*t20-2.0*t841*t4-2.0* +t843*t14*t10-2.0*t846*t4-2.0*t849*t14)*t853-(-2.0*t92*t20-2.0*t143*t35-2.0*t289 +*t20-2.0*t370*t35-2.0*t62*t20-2.0*t235*t4-2.0*t29*t10-2.0*t86*t4-2.0*t151*t14)* +t875; + t877 = t215*t16; + t880 = t23*t16; + t883 = t290*t7; + t884 = t883*t35; + t886 = t220*t33; + t889 = t30*t33; + t895 = t662*t16; + t897 = t243*t16; + t900 = t675*t16; + t902 = t150*t16; + t905 = t270*t33; + t907 = t239*t7; + t909 = t659*t16; + t911 = t224*t16; + t912 = t911*t10; + t914 = 2.0*t62*t877+2.0*t880*t440+t62*t884+RATIONAL(3.0,2.0)*t219*t886+ +RATIONAL(1.0,2.0)*t889*t573+2.0*t327*t58*t16+t36*t895+2.0*t86*t897+t11*t900+2.0 +*t902*t207+t146*t905+t98*t907+t92*t909+t92*t912; + t924 = t82*t16; + t930 = t359*t7; + t936 = t23*t33; + t946 = t416*t33; + t948 = t26*t16; + t950 = 2.0*t289*t884+t101*t900+RATIONAL(3.0,2.0)*t25*t108*t16+RATIONAL( +3.0,2.0)*t277*t366*t16+RATIONAL(3.0,2.0)*t319*t924+RATIONAL(3.0,2.0)*t323*t93* +t7+RATIONAL(3.0,2.0)*t146*t930+RATIONAL(3.0,2.0)*t136*t273*t7+RATIONAL(1.0,2.0) +*t936*t351+2.0*t880*t378+2.0*t309*t171*t16+t390*t242*t16+t62*t946+t219*t948; + t954 = t630*t7; + t956 = t91*t33; + t957 = t956*t344; + t960 = t936*t265; + t963 = t36*t255; + t966 = t889*t265; + t971 = t92*t121; + t974 = t1*t16; + t978 = t487*t33; + t980 = t403*t33; + t985 = t1*t7; + t987 = t136*t239*t33+t92*t954+2.0*t62*t957+2.0*t86*t960+2.0*t151*t963+2.0 +*t151*t966+2.0*t92*t946+2.0*t235*t971+2.0*t974*t499+t974*t404+t62*t978+2.0*t36* +t980+2.0*t289*t957+t985*t688; + t988 = t30*t7; + t993 = t12*t16; + t994 = t993*t35; + t999 = t92*t335; + t1005 = t956*t131; + t1017 = t936*t171; + t1022 = 2.0*t988*t378+2.0*t11*t966+t11*t994+2.0*t985*t387+t880*t443+2.0* +t289*t999+2.0*t62*t889*t131+2.0*t235*t1005+2.0*t902*t387+2.0*t11*t963+2.0*t151* +t985*t171+2.0*t86*t971+2.0*t151*t1017+2.0*t86*t1005; + t1028 = t137*t7; + t1038 = t956*t78; + t1043 = t186*t16; + t1044 = t1043*t10; + t1048 = t36*t46; + t1051 = t889*t58; + t1057 = 2.0*t902*t381+t219*t883+2.0*t1028*t499+t86*t980+2.0*t151*t11*t162 ++2.0*t289*t101*t68+2.0*t151*t1038+2.0*t985*t381+t36*t1044+2.0*t1028*t622+2.0* +t235*t1048+2.0*t235*t1051+2.0*t62*t912+t889*t672; + t1066 = t398*t7; + t1068 = t92*t68; + t1073 = t101*t162; + t1081 = t581*t7; + t1088 = 2.0*t289*t954+t289*t909+2.0*t988*t473+2.0*t327*t10*t255+t36*t1066 ++2.0*t11*t1068+2.0*t11*t1038+2.0*t11*t1073+2.0*t11*t1017+2.0*t985*t207+t235* +t895+4.0*t11*t1081+2.0*t151*t1068+2.0*t974*t540; + t1092 = t494*t33; + t1094 = t560*t7; + t1104 = t988*t131; + t1107 = t101*t255; + t1116 = t384*t33; + t1120 = t649*t33; + t1122 = 2.0*t1028*t59+t151*t1092+4.0*t11*t1094+2.0*t235*t960+2.0*t289* +t936*t78+2.0*t151*t1073+2.0*t86*t1104+2.0*t235*t1107+2.0*t86*t289*t121+4.0*t151 +*t299*t16+t235*t1116+t235*t897+t1028*t385+t289*t1120; + t1129 = t484*t33; + t1153 = 2.0*t151*t994+RATIONAL(1.0,2.0)*t956*t109+2.0*t880*t626+t86*t1129 ++t235*t1129+2.0*t902*t557+2.0*t752*t58*t7+RATIONAL(1.0,2.0)*t936*t83+RATIONAL( +1.0,2.0)*t889*t719+2.0*t62*t289*t335+2.0*t62*t988*t344+t289*t978+2.0*t62*t999+ +2.0*t62*t11*t68; + t1163 = t521*t33; + t1165 = t907*t35; + t1187 = 2.0*t136*t30*t68+4.0*t151*t266*t16+t11*t1163+t151*t1165+RATIONAL( +1.0,2.0)*t974*t573+RATIONAL(1.0,2.0)*t880*t570+t151*t1163+2.0*t86*t1051+2.0* +t606*t58*t33+2.0*t974*t59+t956*t645+2.0*t902*t730+2.0*t390*t91*t121+2.0*t86* +t1048; + t1209 = t30*t121; + t1226 = 2.0*t62*t985*t78+2.0*t194*t16*t196+2.0*t199*t33*t78+2.0*t199*t35* +t68+2.0*t112*t16*t611+2.0*t327*t7*t265+2.0*t98*t30*t255+2.0*t146*t1209+RATIONAL +(1.0,2.0)*t902*t351+RATIONAL(1.0,2.0)*t988*t109+RATIONAL(1.0,2.0)*t1028*t719+ +2.0*t974*t697+2.0*t98*t91*t68+2.0*t151*t289*t68; + t1252 = t152*t7; + t1258 = 2.0*t62*t235*t121+2.0*t566*t344*t33+2.0*t880*t722+t777*t162+t146* +t1043+2.0*t636*t171*t33+2.0*t86*t235*t46+2.0*t86*t1028*t58+t779*t46+RATIONAL( +1.0,2.0)*t985*t83+RATIONAL(1.0,2.0)*t956*t570+t319*t1252+t277*t186*t7+t25*t224* +t7; + t1288 = t152*t16; + t1292 = 2.0*t136*t137*t255+t323*t911+2.0*t151*t1081+2.0*t151*t235*t255+ +4.0*t86*t182*t16+2.0*t880*t371+t458*t162+RATIONAL(1.0,2.0)*t880*t429+2.0*t62* +t1028*t131+2.0*t115*t7*t132+2.0*t175*t33*t131+2.0*t175*t35*t121+t136*t1288+ +RATIONAL(1.0,2.0)*t974*t283; + t1302 = t12*t33; + t1307 = t23*t68; + t1310 = t1*t255; + t1315 = t374*t7; + t1327 = RATIONAL(1.0,2.0)*t902*t296+t390*t270*t7+2.0*t199*t344*t16+t319* +t1302+2.0*t277*t23*t121+2.0*t319*t1307+2.0*t319*t1310+RATIONAL(1.0,2.0)*t988* +t429+2.0*t11*t1315+2.0*t902*t764+RATIONAL(1.0,2.0)*t1028*t283+RATIONAL(1.0,2.0) +*t985*t296+t98*t993+t25*t26*t33; + t1344 = t19*t33; + t1359 = t274*t7; + t1361 = t277*t242*t33+t323*t290*t33+2.0*t514*t171*t7+2.0*t175*t344*t7+ +RATIONAL(3.0,2.0)*t98*t295*t33+RATIONAL(3.0,2.0)*t390*t282*t33+t11*t1344+2.0* +t974*t622+2.0*t62*t36*t121+2.0*t86*t1107+2.0*t151*t1094+2.0*t235*t1066+4.0*t101 +*t1038+t151*t1359; + t1368 = t1288*t10; + t1373 = t360*t7; + t1377 = t94*t7; + t1383 = t936*t596+t289*t877+t460*t335+t462*t46+t465*t335+t101*t1368+t101* +t1315+2.0*t101*t1344+t86*t1373+4.0*t36*t1005+t62*t1377+t902*t495+t988*t758+4.0* +t101*t966; + t1394 = t270*t35*t7; + t1409 = 4.0*t235*t1104+t92*t1377+2.0*t151*t1368+2.0*t86*t1044+2.0*t101* +t1092+2.0*t235*t1394+2.0*t11*t1165+2.0*t92*t1120+2.0*t36*t1116+t36*t1373+t101* +t1359+t248*t162+t113*t46+t647*t335+t86*t1394; + t1418 = -t886-t905-t1302-t883-t930-t1252-t948-t1043-t924-t91*t335-2.0* +t1209-2.0*t1307; + t1431 = -t137*t46-2.0*t1310-t150*t162-t803*t33-t806*t33-t809*t33-t811*t7- +t813*t7-t815*t7-t817*t16-t819*t16-t821*t16; + partial_H_wrt_partial_d_h_2 = (t914+t950+t987+t1022+t1057+t1088+t1122+ +t1153+t1187+t1226+t1258+t1292+t1327+t1361+t1383+t1409)*t793+(t1418+t1431)*t825+ +(-2.0*t828*t33-2.0*t830*t7*t35-2.0*t833*t33-2.0*t835*t16*t35-2.0*t838*t33-2.0* +t841*t7-2.0*t843*t16*t10-2.0*t846*t7-2.0*t849*t16)*t853-(-2.0*t92*t33-2.0*t988* +t35-2.0*t289*t33-2.0*t880*t35-2.0*t62*t33-2.0*t235*t7-2.0*t974*t10-2.0*t86*t7 +-2.0*t151*t16)*t875; + t1461 = t36*t48; + t1464 = t11*t91; + t1465 = t35*t20; + t1466 = t1465*t14; + t1472 = t11*t30; + t1474 = t35*t4*t14; + t1477 = t151*t30; + t1478 = t10*t20; + t1479 = t1478*t14; + t1483 = t101*t164; + t1492 = 2.0*t235*t1461+2.0*t1464*t1466+2.0*t62*t289*t337+2.0*t1472*t1474+ +2.0*t1477*t1479+t779*t48+2.0*t11*t1483+t462*t48+t460*t337+2.0*t277*t104*t4+t458 +*t164; + t1493 = t86*t30; + t1494 = t1478*t4; + t1497 = t235*t23; + t1500 = t63*t14; + t1505 = t151*t137; + t1507 = t10*t4*t14; + t1513 = t104*t14; + t1518 = 2.0*t1493*t1494+2.0*t1497*t1474+2.0*t319*t1500+t465*t337+t647* +t337+2.0*t1505*t1507+t248*t164+t113*t48+t777*t164+2.0*t319*t1513+2.0*t199*t1466 ; - t1137 = t275*t28; - t1138 = t1137*t10; - t1148 = t1*t7; - t1165 = t441*t7; - t1170 = t123*t1138+2.0*t11*t921*t73+t921*t520+2.0*t58*t958+2.0*t58*t955+ -2.0*t1148*t124+2.0*t317*t18*t63+2.0*t317*t16*t73+t123*t879+2.0*t300*t7*t178+2.0 -*t1148*t151+2.0*t117*t1047+4.0*t107*t1165+2.0*t117*t1050; - t1197 = t192*t16; - t1205 = 2.0*t259*t28*t297+2.0*t300*t10*t168+2.0*t968*t491+2.0*t11*t985+ -2.0*t11*t989+2.0*t901*t457+2.0*t264*t24*t359+2.0*t107*t1088+2.0*t107*t889+t264* -t159*t16+t397*t1197+RATIONAL(1.0,2.0)*t988*t247+RATIONAL(1.0,2.0)*t947*t198+ -RATIONAL(1.0,2.0)*t921*t330; - t1221 = t226*t16; - t1225 = t182*t28; - t1227 = t159*t28; - t1234 = RATIONAL(1.0,2.0)*t901*t350+RATIONAL(1.0,2.0)*t968*t209+2.0*t344* -t12*t63+2.0*t344*t1*t168+t543*t1137+t264*t103*t7+t255*t147*t16+t253*t1221+t543* -t201*t16+t578*t1225+t376*t1227+t344*t192*t28+t514*t182*t16+t102*t1095; - t1240 = t24*t63; - t1253 = t488*t16; - t1255 = t507*t16; - t1257 = t448*t28; - t1260 = t539*t7; - t1266 = t102*t876+t947*t504+2.0*t58*t1067+2.0*t397*t1240+2.0*t58*t1070+ -RATIONAL(3.0,2.0)*t514*t187*t28+RATIONAL(1.0,2.0)*t988*t212+2.0*t236*t98*t16+ -t58*t1253+t107*t1255+t102*t1257+t19*t1100+4.0*t58*t1260+2.0*t232*t53*t7; - t1269 = t226*t7; - t1271 = t201*t7; - t1295 = t19*t884+t578*t1081+t376*t1269+t344*t1271+RATIONAL(1.0,2.0)*t1148 -*t647+RATIONAL(1.0,2.0)*t968*t621+RATIONAL(1.0,2.0)*t901*t624+RATIONAL(1.0,2.0) -*t893*t647+RATIONAL(1.0,2.0)*t925*t621+RATIONAL(1.0,2.0)*t908*t624+2.0*t617* -t143*t28+2.0*t241*t143*t16+t988*t575+2.0*t376*t12*t359; - t1302 = t305*t16; - t1308 = t182*t18*t28; - t1311 = t193*t16; - t1322 = t223*t16; - t1326 = t227*t16; - t1331 = t117*t1253+t81*t1255+RATIONAL(1.0,2.0)*t1148*t212+t31*t1302+2.0* -t300*t98*t28+2.0*t31*t1308+2.0*t123*t1311+4.0*t117*t710*t28+2.0*t11*t1082+2.0* -t117*t11*t63+2.0*t123*t1322+t11*t1302+2.0*t102*t1326+2.0*t117*t1260; - t1337 = t192*t18*t28; - t1345 = t1269*t18; - t1352 = t1271*t18; - t1354 = t160*t16; - t1360 = 2.0*t19*t1065+2.0*t908*t460+2.0*t117*t1337+t19*t1086+2.0*t31* -t1148*t53+t81*t1326+t81*t1345+t925*t470+t117*t1322+2.0*t232*t18*t359+t117*t1352 -+2.0*t102*t1354+t908*t224+2.0*t893*t473; - t1362 = t183*t16; - t1373 = t1227*t18; - t1375 = t57*t168; - t1386 = 2.0*t19*t1362+2.0*t107*t1345+2.0*t58*t1352+2.0*t925*t438+t901* -t589+t58*t1337+t107*t1373+2.0*t397*t1375+t107*t1354+t968*t773+t479*t89+t745*t89 -+t752*t41+2.0*t31*t11*t41; - t1394 = t404*t28; - t1410 = t123*t1084+t102*t1106+2.0*t81*t1373+4.0*t123*t1070+t107*t1257+t58 -*t1394+2.0*t81*t11*t359+t123*t1394+2.0*t117*t1138+2.0*t81*t1165+t11*t1308+t11* -t1362+t1148*t338+t58*t1311+4.0*t123*t958; - t1419 = -t918-t1221-t1197-t1081-t1017-t943-t1225-t981-t935-t12*t41-2.0* -t1078-2.0*t1240; - t1432 = -t82*t89-2.0*t1375-t116*t134-t801*t16-t804*t16-t807*t16-t809*t7- -t811*t7-t813*t7-t815*t28-t817*t28-t819*t28; - partial_H_wrt_partial_d_h_2 = (t914+t953+t992+t1028+t1062+t1098+t1136+ -t1170+t1205+t1234+t1266+t1295+t1331+t1360+t1386+t1410)*t791+(t1419+t1432)*t823+ -(-2.0*t826*t16-2.0*t828*t7*t18-2.0*t831*t16-2.0*t833*t28*t18-2.0*t836*t16-2.0* -t839*t7-2.0*t841*t28*t10-2.0*t844*t7-2.0*t847*t28)*t851-(-2.0*t19*t16-2.0*t1148 -*t18-2.0*t11*t16-2.0*t893*t18-2.0*t31*t16-2.0*t107*t7-2.0*t925*t10-2.0*t81*t7 --2.0*t117*t28)*t873; - t1466 = t10*t4*t26; - t1469 = t164*t4; - t1472 = t107*t12; - t1473 = t18*t14; - t1474 = t1473*t4; - t1477 = t117*t12; - t1478 = t1473*t26; - t1485 = t117*t1; - t1486 = t10*t14; - t1487 = t1486*t26; - t1490 = t81*t1; - t1491 = t1486*t4; - t1495 = t18*t4*t26; - t1498 = t81*t24; - t1501 = 2.0*t543*t164*t26+2.0*t300*t1466+2.0*t253*t1469+2.0*t1472*t1474+ -2.0*t1477*t1478+t327*t136+2.0*t344*t122*t26+2.0*t1485*t1487+2.0*t1490*t1491+2.0 -*t1485*t1495+2.0*t1498*t1495; - t1502 = t102*t91; - t1511 = t123*t136; - t1517 = t19*t43; - t1520 = t31*t82; - t1523 = t81*t12; - t1526 = t31*t1; - t1529 = t117*t82; - t1532 = 2.0*t81*t1502+2.0*t31*t11*t43+t479*t91+2.0*t1498*t1487+2.0*t117* -t1511+2.0*t81*t107*t91+2.0*t31*t1517+2.0*t1520*t1491+2.0*t1523*t1474+2.0*t1526* -t1474+2.0*t1529*t1466; - t1534 = t58*t12; - t1539 = t11*t24; - t1557 = t58*t1; - t1560 = 2.0*t1534*t1478+t79*t43+t697*t136+2.0*t1539*t1478+2.0*t232*t1474+ -2.0*t11*t1517+2.0*t107*t1502+2.0*t117*t58*t136+2.0*t543*t83*t26+2.0*t264*t393* -t4+2.0*t1557*t1495; - t1573 = t393*t26; - t1576 = t130*t26; - t1582 = t107*t24; - t1585 = 2.0*t317*t1478+t695*t91+2.0*t344*t32*t26+2.0*t376*t32*t4+2.0*t58* -t1511+t570*t43+2.0*t397*t1573+2.0*t397*t1576+t752*t43+t724*t136+t745*t91+2.0* -t1582*t1495; - partial_H_wrt_partial_dd_h_11 = (t1501+t1532+t1560+t1585)*t791+(-t12*t43 --2.0*t1469-2.0*t1573-t82*t91-2.0*t1576-t116*t136)*t823; - t1597 = -t363-t365; - t1598 = t1*t1597; - t1603 = -t67-t69; - t1606 = -t172-t174; - t1607 = t57*t1606; - t1609 = t19*t1597; - t1616 = t102*t1606; - t1619 = -t253*t1598+t745*t93-t264*t24*t1597-t543*t1*t1603-t397*t1607-t81* -t1609-t317*t18*t1603+t570*t46-t300*t10*t1606-t117*t1616+t479*t93; - t1621 = t123*t1606; - t1633 = t18*t16; - t1634 = t1633*t14; - t1639 = t24*t1603; - t1651 = t18*t28*t26; - t1654 = -2.0*t107*t1621-2.0*t376*t12*t1597-2.0*t344*t1*t1606+2.0*t724* -t138+4.0*t31*t12*t1634+2.0*t752*t46-2.0*t397*t1639+2.0*t79*t46+2.0*t697*t138+ -4.0*t11*t12*t1634+4.0*t58*t24*t1651; - t1659 = t18*t7; - t1660 = t1659*t4; - t1663 = t19*t1603; - t1669 = t10*t16; - t1680 = t10*t7; - t1692 = -2.0*t232*t18*t1597+4.0*t1490*t1660-2.0*t58*t1663+4.0*t107*t1* -t1660+4.0*t1526*t1669*t14-2.0*t117*t11*t1603-2.0*t344*t12*t1603+4.0*t81*t82* -t1680*t4-2.0*t31*t58*t1603+2.0*t327*t138-2.0*t81*t11*t1597; - t1726 = -2.0*t117*t107*t1606+2.0*t695*t93-2.0*t58*t1616-2.0*t31*t107* -t1597-2.0*t31*t102*t1597-2.0*t543*t82*t1606+4.0*t117*t57*t10*t28*t26-2.0*t107* -t1609-2.0*t11*t123*t1603-2.0*t117*t1663-2.0*t81*t1621+4.0*t117*t24*t1651; - partial_H_wrt_partial_dd_h_12 = (2.0*t1619+t1654+t1692+t1726)*t791+(-2.0* -t988*t14+2.0*t1598+2.0*t1639-2.0*t968*t4+2.0*t1607-2.0*t908*t26)*t823; - t1737 = t123*t141; - t1741 = t1659*t28; - t1744 = t1633*t7; - t1747 = t1680*t28; - t1756 = t19*t50; - t1762 = t79*t50+2.0*t117*t1737+t724*t141+2.0*t1498*t1741+2.0*t1472*t1744+ -2.0*t300*t1747+2.0*t232*t1744+2.0*t543*t947*t28+t697*t141+2.0*t11*t1756+2.0*t81 -*t107*t96; - t1763 = t947*t7; - t1766 = t102*t96; - t1769 = t1633*t28; - t1772 = t921*t28; - t1778 = t901*t28; - t1793 = 2.0*t253*t1763+2.0*t107*t1766+2.0*t1534*t1769+2.0*t397*t1772+2.0* -t264*t921*t7+2.0*t397*t1778+t695*t96+2.0*t317*t1769+2.0*t344*t988*t28+2.0*t376* -t988*t7+2.0*t344*t1148*t28; - t1795 = t1669*t7; - t1800 = t1669*t28; - t1818 = 2.0*t1520*t1795+2.0*t1526*t1744+2.0*t1485*t1800+2.0*t1490*t1795+ -2.0*t1498*t1800+2.0*t1529*t1747+2.0*t117*t58*t141+2.0*t1485*t1741+t479*t96+2.0* -t58*t1737+t745*t96; - t1842 = 2.0*t1523*t1744+2.0*t31*t11*t50+2.0*t1477*t1769+2.0*t543*t968*t28 -+2.0*t1539*t1769+2.0*t31*t1756+2.0*t1582*t1741+2.0*t1557*t1741+t752*t50+t570* -t50+2.0*t81*t1766+t327*t141; - partial_H_wrt_partial_dd_h_22 = (t1762+t1793+t1818+t1842)*t791+(-t12*t50 --2.0*t1763-2.0*t1772-t82*t96-2.0*t1778-t116*t141)*t823; + t1526 = t289*t23; + t1528 = t62*t137; + t1536 = t62*t1; + t1540 = t136*t87*t14+t86*t235*t48+t136*t281*t14+t1526*t1466+t1528*t1494+ +t151*t11*t164+t86*t1461+t327*t1507+t98*t107*t14+t1536*t1479+t390*t107*t4; + t1542 = t87*t4; + t1546 = t1465*t4; + t1548 = t92*t337; + t1550 = t62*t30; + t1552 = t86*t91; + t1556 = t151*t91; + t1559 = t235*t91; + t1562 = t146*t1542+t98*t143*t14+t175*t1546+t62*t1548+t1550*t1546+t1552* +t1546+t151*t1483+t289*t1548+t1556*t1466+t1536*t1474+t1559*t1546+t1477*t1474; + partial_H_wrt_partial_dd_h_11 = (t1492+t1518+2.0*t1540+2.0*t1562)*t793+(- +t91*t337-2.0*t1542-2.0*t1513-t137*t48-2.0*t1500-t150*t164)*t825; + t1582 = -t72-t74; + t1583 = t92*t1582; + t1586 = -t125-t127; + t1590 = t92*t1586; + t1594 = t35*t33; + t1595 = t1594*t20; + t1598 = -t259-t261; + t1607 = t30*t1586; + t1612 = 2.0*t777*t166+4.0*t151*t1*t10*t16*t14-2.0*t151*t1583-2.0*t175*t35 +*t1586-2.0*t86*t1590+4.0*t62*t91*t1595-2.0*t98*t30*t1598-2.0*t390*t91*t1586-2.0 +*t235*t1590-2.0*t146*t1607+2.0*t113*t51; + t1615 = t35*t16*t14; + t1618 = t36*t1598; + t1623 = t23*t1582; + t1626 = t101*t1598; + t1644 = 4.0*t151*t23*t1615-2.0*t151*t1618+2.0*t460*t339-2.0*t319*t1623 +-2.0*t86*t1626+2.0*t462*t51+2.0*t458*t166-2.0*t98*t91*t1582+4.0*t289*t91*t1595 +-2.0*t11*t1583-2.0*t199*t35*t1582; + t1656 = t35*t7; + t1657 = t1656*t4; + t1677 = -2.0*t11*t1618+2.0*t647*t339-2.0*t136*t137*t1598-2.0*t235*t1626+ +4.0*t235*t30*t1657+4.0*t11*t23*t1615-2.0*t136*t30*t1582-2.0*t62*t235*t1586-2.0* +t277*t23*t1586-2.0*t151*t289*t1582+2.0*t465*t339; + t1679 = t10*t7; + t1686 = t10*t33; + t1695 = t1*t1598; + t1714 = 4.0*t86*t137*t1679*t4-2.0*t86*t289*t1586+4.0*t1550*t1686*t20+2.0* +t248*t166-2.0*t151*t235*t1598-2.0*t319*t1695-2.0*t327*t10*t1598-2.0*t289*t101* +t1582-2.0*t62*t11*t1582+4.0*t1493*t1657+2.0*t779*t51-2.0*t62*t36*t1586; + partial_H_wrt_partial_dd_h_12 = (t1612+t1644+t1677+t1714)*t793+(-2.0*t956 +*t20+2.0*t1607+2.0*t1623-2.0*t1028*t4+2.0*t1695-2.0*t902*t14)*t825; + t1730 = t1686*t7; + t1742 = t1656*t16; + t1745 = t458*t169+t248*t169+t465*t342+t113*t55+t462*t55+t460*t342+2.0* +t1528*t1730+2.0*t62*t289*t342+2.0*t136*t1028*t16+2.0*t136*t889*t16+2.0*t1497* +t1742; + t1746 = t889*t7; + t1749 = t1594*t16; + t1768 = t101*t169; + t1774 = 2.0*t146*t1746+2.0*t1526*t1749+2.0*t390*t956*t7+2.0*t199*t1749+ +2.0*t1493*t1730+t647*t342+2.0*t98*t988*t16+2.0*t98*t956*t16+2.0*t1464*t1749+2.0 +*t11*t1768+2.0*t277*t936*t7; + t1776 = t36*t55; + t1784 = t1594*t7; + t1791 = t1686*t16; + t1794 = t1679*t16; + t1797 = t985*t16; + t1800 = t92*t342; + t1803 = 2.0*t86*t1776+2.0*t151*t11*t169+2.0*t1556*t1749+2.0*t175*t1784+ +2.0*t235*t1776+t779*t55+t777*t169+2.0*t1477*t1791+2.0*t327*t1794+2.0*t319*t1797 ++2.0*t62*t1800; + t1806 = t936*t16; + t1818 = t86*t235*t55+t319*t1806+t1505*t1794+t1550*t1784+t1536*t1791+t151* +t1768+t1559*t1784+t289*t1800+t1472*t1742+t1477*t1742+t1552*t1784+t1536*t1742; + partial_H_wrt_partial_dd_h_22 = (t1745+t1774+t1803+2.0*t1818)*t793+(-t91* +t342-2.0*t1746-2.0*t1806-t137*t55-2.0*t1797-t150*t169)*t825; diff --git a/src/gr.cg/horizon_function.c b/src/gr.cg/horizon_function.c index c31778c..7e6e717 100644 --- a/src/gr.cg/horizon_function.c +++ b/src/gr.cg/horizon_function.c @@ -1,23 +1,22 @@ /* - * inputs = {r, partial_d_ln_sqrt_g, partial_d_g_uu, X_ud, X_udd, g_uu, K_uu, h, HA, HB, HC, HD, K} - * outputs = {H, HA, HB, HC, HD} - * cost = 136*assignments+7*divisions+7*functions+402*multiplications+176*additions + * inputs = {r, partial_d_ln_sqrt_g, partial_d_g_uu, X_ud, X_udd, g_uu, K_uu, h} + * outputs = {HA, HB, HC, HD} + * cost = 134*assignments+3*divisions+5*functions+401*multiplications+173*additions */ fp t1, t2, t4, t5, t7, t8, t10, t11, t12, t14; -fp t16, t18, t19, t21, t23, t25, t28, t29, t30, t32; -fp t33, t35, t37, t43, t44, t47, t50, t51, t53, t55; -fp t56, t57, t58, t61, t62, t63, t64, t65, t67, t69; -fp t72, t73, t76, t78, t85, t90, t92, t94, t95, t96; -fp t99, t100, t101, t102, t105, t106, t107, t111, t114, t115; -fp t117, t118, t133, t134, t137, t138, t141, t142, t145, t146; -fp t149, t150, t158, t163, t165, t169, t170, t173, t174, t179; -fp t194, t198, t199, t204, t220, t227, t234, t237, t239, t242; -fp t247, t250, t254, t261, t262, t265, t267, t270, t273, t276; -fp t279, t292, t295, t296, t299, t306, t307, t312, t315, t318; -fp t320, t323, t333, t342, t343, t346, t349, t350, t361, t362; -fp t368, t378, t394, t413, t431, t440, t444, t447, t450, t465; -fp t490; - t1 = g_uu_13; +fp t16, t18, t19, t20, t23, t24, t25, t26, t29, t30; +fp t31, t33, t35, t37, t38, t40, t41, t42, t43, t45; +fp t46, t47, t48, t50, t51, t52, t53, t55, t58, t59; +fp t61, t64, t67, t68, t70, t72, t73, t75, t77, t83; +fp t84, t87, t90, t91, t93, t95, t112, t130, t134, t137; +fp t139, t143, t147, t150, t152, t159, t164, t166, t168, t176; +fp t181, t183, t199, t203, t206, t209, t213, t216, t217, t219; +fp t228, t229, t232, t235, t236, t237, t240, t243, t247, t251; +fp t254, t259, t260, t262, t263, t269, t272, t273, t276, t279; +fp t282, t283, t290, t293, t296, t299, t302, t305, t312, t315; +fp t318, t324, t325, t329, t330, t338, t358, t381, t392, t395; +fp t396, t397, t408, t411, t431, t440, t444, t447, t450, t465; + t1 = g_uu_33; t2 = 1/r; t4 = X_ud_13; t5 = PARTIAL_RHO(h); @@ -25,160 +24,159 @@ fp t490; t8 = PARTIAL_SIGMA(h); t10 = zz*t2-t4*t5-t7*t8; t11 = t1*t10; - t12 = partial_d_g_uu_112; - t14 = X_ud_12; - t16 = X_ud_22; - t18 = yy*t2-t14*t5-t16*t8; - t19 = t12*t18; - t21 = X_ud_11; - t23 = X_ud_21; - t25 = xx*t2-t21*t5-t23*t8; - t28 = g_uu_23; - t29 = t28*t28; - t30 = t10*t10; - t32 = xx*xx; - t33 = zz*zz; - t35 = r*r; - t37 = 1/t35/r; - t43 = t14*t14; - t44 = PARTIAL_RHO_RHO(h); - t47 = PARTIAL_RHO_SIGMA(h); - t50 = t16*t16; - t51 = PARTIAL_SIGMA_SIGMA(h); - t53 = (t32+t33)*t37-X_udd_122*t5-X_udd_222*t8-t43*t44-2.0*t16*t14*t47-t50 -*t51; - t55 = g_uu_33; - t56 = t55*t10; - t57 = partial_d_g_uu_312; - t58 = t57*t18; - t61 = g_uu_22; - t62 = t18*t18; - t63 = t61*t62; - t64 = partial_d_g_uu_212; - t65 = t64*t25; - t67 = t30*t10; - t69 = partial_d_g_uu_233; - t72 = t28*t10; - t73 = t64*t18; - t76 = t55*t55; - t78 = yy*yy; - t85 = t4*t4; - t90 = t7*t7; - t92 = (t32+t78)*t37-X_udd_133*t5-X_udd_233*t8-t85*t44-2.0*t7*t4*t47-t90* -t51; - t94 = t61*t18; - t95 = partial_d_g_uu_213; - t96 = t95*t10; - t99 = g_uu_12; - t100 = t99*t18; - t101 = partial_d_g_uu_113; - t102 = t101*t10; - t105 = t28*t18; - t106 = partial_d_g_uu_313; - t107 = t106*t10; - t111 = partial_d_g_uu_133; - t114 = t25*t25; - t115 = t1*t114; - t117 = -t11*t19*t25-t29*t30*t53-t56*t58*t25-t63*t65+RATIONAL(-1.0,2.0)* -t28*t67*t69-t72*t73*t25-t76*t30*t92-t94*t96*t25-t100*t102*t25-t105*t107*t25+ -RATIONAL(-1.0,2.0)*t1*t67*t111-t115*t107; - t118 = t55*t30; - t133 = -yy*zz*t37-X_udd_123*t5-X_udd_223*t8-t14*t4*t44-t16*t4*t47-t14*t7* -t47-t16*t7*t51; - t134 = t28*t133; - t137 = partial_d_g_uu_111; - t138 = t137*t114; - t141 = partial_d_g_uu_311; - t142 = t141*t114; - t145 = partial_d_g_uu_211; - t146 = t145*t114; - t149 = g_uu_11; - t150 = t149*t149; - t158 = t21*t21; - t163 = t23*t23; - t165 = (t78+t33)*t37-X_udd_111*t5-X_udd_211*t8-t158*t44-2.0*t23*t21*t47- -t163*t51; - t169 = t99*t25; - t170 = t69*t30; - t173 = t149*t25; - t174 = t111*t30; - t179 = t99*t114; - t194 = -xx*yy*t37-X_udd_112*t5-X_udd_212*t8-t21*t14*t44-t23*t14*t47-t21* -t16*t47-t23*t16*t51; - t198 = partial_d_g_uu_333; - t199 = t198*t30; - t204 = -2.0*t118*t134+RATIONAL(-1.0,2.0)*t11*t138+RATIONAL(-1.0,2.0)*t105 -*t142+RATIONAL(-1.0,2.0)*t94*t146-t150*t114*t165+RATIONAL(-1.0,2.0)*t100*t138+ -RATIONAL(-1.0,2.0)*t169*t170+RATIONAL(-1.0,2.0)*t173*t174+RATIONAL(-1.0,2.0)* -t100*t174-2.0*t179*t149*t194+RATIONAL(-1.0,2.0)*t105*t199+RATIONAL(-1.0,2.0)* -t94*t170; - t220 = -xx*zz*t37-X_udd_113*t5-X_udd_213*t8-t21*t4*t44-t23*t4*t47-t21*t7* -t47-t23*t7*t51; - t227 = t99*t194; - t234 = t99*t99; - t237 = t149*t114; - t239 = t28*t30; - t242 = t1*t1; - t247 = t61*t61; - t250 = t28*t62; - t254 = -2.0*t115*t149*t220-2.0*t115*t99*t133-2.0*t63*t227+RATIONAL(-1.0, -2.0)*t72*t146+RATIONAL(-1.0,2.0)*t56*t142-t234*t114*t53-t237*t19-t239*t95*t25- -t242*t114*t92-t234*t62*t165-t247*t62*t53-2.0*t250*t99*t220; - t261 = partial_d_g_uu_222; - t262 = t261*t62; - t265 = t106*t25; - t267 = t1*t30; - t270 = t169*t53; - t273 = t173*t220; - t276 = t173*t165; - t279 = t114*t25; - t292 = -2.0*t234*t18*t25*t194-t179*t96-t237*t102+RATIONAL(-1.0,2.0)*t169* -t262-t118*t265-t267*t101*t25-2.0*t94*t270-2.0*t105*t273-2.0*t100*t276+RATIONAL( --1.0,2.0)*t149*t279*t137+RATIONAL(-1.0,2.0)*t99*t279*t145+RATIONAL(-1.0,2.0)* -t55*t67*t198+RATIONAL(-1.0,2.0)*t1*t279*t141; - t295 = partial_d_g_uu_122; - t296 = t295*t62; - t299 = t173*t194; - t306 = t1*t25; - t307 = t306*t133; - t312 = t169*t133; - t315 = t306*t92; - t318 = t62*t18; - t320 = partial_d_g_uu_322; - t323 = t320*t62; - t333 = RATIONAL(-1.0,2.0)*t173*t296-2.0*t94*t299-2.0*t242*t10*t25*t220 --2.0*t72*t307-t250*t57*t25-2.0*t56*t312-2.0*t56*t315+RATIONAL(-1.0,2.0)*t28* -t318*t320+RATIONAL(-1.0,2.0)*t306*t323+RATIONAL(-1.0,2.0)*t99*t318*t295-2.0*t72 -*t270+RATIONAL(-1.0,2.0)*t56*t323; - t342 = partial_d_g_uu_223; - t343 = t342*t10; - t346 = t99*t62; - t349 = partial_d_g_uu_323; - t350 = t349*t10; - t361 = partial_d_g_uu_123; - t362 = t361*t10; - t368 = -t179*t73+RATIONAL(-1.0,2.0)*t61*t318*t261-2.0*t56*t273-2.0*t72* -t299-t169*t343*t18-t346*t12*t25-t306*t350*t18-2.0*t11*t276-2.0*t94*t307-2.0* -t105*t315+RATIONAL(-1.0,2.0)*t11*t296-t346*t362-2.0*t29*t10*t18*t133; - t378 = t349*t18; - t394 = RATIONAL(-1.0,2.0)*t72*t262-t63*t343-t250*t350-t239*t342*t18-t267* -t361*t18-t118*t378+RATIONAL(-1.0,2.0)*t306*t199-t173*t362*t18-2.0*t105*t312-2.0 -*t100*t306*t220-2.0*t250*t61*t133-t29*t62*t92; - t413 = t1*t220; - t431 = -2.0*t56*t94*t133-2.0*t56*t105*t92-t115*t58-2.0*t11*t169*t194-t242 -*t30*t165-2.0*t11*t100*t165-2.0*t239*t1*t194-2.0*t118*t413-2.0*t11*t105*t220 --2.0*t72*t94*t53-2.0*t11*t94*t194-2.0*t56*t100*t220-2.0*t72*t100*t194; - HA = t117+t204+t254+t292+t333+t368+t394+t431; - t440 = t137*t25+t65+t265+t19+t261*t18+t378+t102+t343+t198*t10+t149*t165+ -2.0*t227+2.0*t413; + t12 = partial_d_g_uu_311; + t14 = X_ud_11; + t16 = X_ud_21; + t18 = xx*t2-t14*t5-t16*t8; + t19 = t18*t18; + t20 = t12*t19; + t23 = g_uu_23; + t24 = t23*t10; + t25 = partial_d_g_uu_211; + t26 = t25*t19; + t29 = g_uu_13; + t30 = t29*t19; + t31 = partial_d_g_uu_312; + t33 = X_ud_12; + t35 = X_ud_22; + t37 = yy*t2-t33*t5-t35*t8; + t38 = t31*t37; + t40 = g_uu_12; + t41 = t40*t19; + t42 = partial_d_g_uu_212; + t43 = t42*t37; + t45 = g_uu_11; + t46 = t45*t19; + t47 = partial_d_g_uu_112; + t48 = t47*t37; + t50 = g_uu_22; + t51 = t37*t37; + t52 = t50*t51; + t53 = t42*t18; + t55 = t40*t51; + t58 = partial_d_g_uu_113; + t59 = t58*t10; + t61 = t23*t51; + t64 = t29*t10; + t67 = partial_d_g_uu_213; + t68 = t67*t10; + t70 = t45*t45; + t72 = yy*yy; + t73 = zz*zz; + t75 = r*r; + t77 = 1/t75/r; + t83 = t14*t14; + t84 = PARTIAL_RHO_RHO(h); + t87 = PARTIAL_RHO_SIGMA(h); + t90 = t16*t16; + t91 = PARTIAL_SIGMA_SIGMA(h); + t93 = (t72+t73)*t77-X_udd_111*t5-X_udd_211*t8-t83*t84-2.0*t16*t14*t87-t90 +*t91; + t95 = RATIONAL(-1.0,2.0)*t11*t20+RATIONAL(-1.0,2.0)*t24*t26-t30*t38-t41* +t43-t46*t48-t52*t53-t55*t47*t18-t46*t59-t61*t31*t18-t64*t48*t18-t41*t68-t70*t19 +*t93; + t112 = -xx*yy*t77-X_udd_112*t5-X_udd_212*t8-t14*t33*t84-t16*t33*t87-t14* +t35*t87-t16*t35*t91; + t130 = -xx*zz*t77-X_udd_113*t5-X_udd_213*t8-t14*t4*t84-t16*t4*t87-t14*t7* +t87-t16*t7*t91; + t134 = t40*t37; + t137 = t51*t37; + t139 = partial_d_g_uu_322; + t143 = partial_d_g_uu_122; + t147 = partial_d_g_uu_222; + t150 = t40*t40; + t152 = xx*xx; + t159 = t33*t33; + t164 = t35*t35; + t166 = (t152+t73)*t77-X_udd_122*t5-X_udd_222*t8-t159*t84-2.0*t35*t33*t87- +t164*t91; + t168 = t29*t29; + t176 = t4*t4; + t181 = t7*t7; + t183 = (t152+t72)*t77-X_udd_133*t5-X_udd_233*t8-t176*t84-2.0*t7*t4*t87- +t181*t91; + t199 = -yy*zz*t77-X_udd_123*t5-X_udd_223*t8-t33*t4*t84-t35*t4*t87-t33*t7* +t87-t35*t7*t91; + t203 = t40*t112; + t206 = t50*t37; + t209 = -t24*t43*t18-2.0*t41*t45*t112-2.0*t30*t45*t130-t134*t59*t18+ +RATIONAL(-1.0,2.0)*t23*t137*t139+RATIONAL(-1.0,2.0)*t40*t137*t143+RATIONAL(-1.0 +,2.0)*t50*t137*t147-t150*t19*t166-t168*t19*t183-2.0*t30*t40*t199-2.0*t52*t203- +t206*t68*t18; + t213 = t50*t50; + t216 = t10*t10; + t217 = t216*t10; + t219 = partial_d_g_uu_333; + t228 = partial_d_g_uu_123; + t229 = t228*t10; + t232 = partial_d_g_uu_233; + t235 = t23*t37; + t236 = partial_d_g_uu_313; + t237 = t236*t10; + t240 = t23*t23; + t243 = t29*t18; + t247 = t243*t183; + t251 = partial_d_g_uu_133; + t254 = -t150*t51*t93-t213*t51*t166+RATIONAL(-1.0,2.0)*t1*t217*t219-2.0* +t61*t40*t130-2.0*t61*t50*t199-t55*t229+RATIONAL(-1.0,2.0)*t23*t217*t232-t235* +t237*t18-t240*t51*t183-2.0*t134*t243*t130-2.0*t235*t247+RATIONAL(-1.0,2.0)*t29* +t217*t251; + t259 = partial_d_g_uu_323; + t260 = t259*t10; + t262 = partial_d_g_uu_223; + t263 = t262*t10; + t269 = t243*t199; + t272 = t40*t18; + t273 = t272*t166; + t276 = t272*t199; + t279 = t219*t216; + t282 = t45*t18; + t283 = t251*t216; + t290 = t232*t216; + t293 = t23*t216; + t296 = -2.0*t150*t37*t18*t112-t61*t260-t52*t263-2.0*t168*t10*t18*t130-2.0 +*t206*t269-2.0*t206*t273-2.0*t235*t276+RATIONAL(-1.0,2.0)*t243*t279+RATIONAL( +-1.0,2.0)*t282*t283+RATIONAL(-1.0,2.0)*t235*t279+RATIONAL(-1.0,2.0)*t134*t283+ +RATIONAL(-1.0,2.0)*t206*t290-t293*t262*t37; + t299 = t29*t216; + t302 = t147*t51; + t305 = t139*t51; + t312 = t282*t93; + t315 = t282*t130; + t318 = t282*t112; + t324 = t1*t216; + t325 = t236*t18; + t329 = -t299*t228*t37+RATIONAL(-1.0,2.0)*t272*t302+RATIONAL(-1.0,2.0)*t11 +*t305+RATIONAL(-1.0,2.0)*t24*t302+RATIONAL(-1.0,2.0)*t272*t290-2.0*t134*t312 +-2.0*t235*t315-2.0*t206*t318-t30*t237-2.0*t24*t269-t324*t325-2.0*t11*t247; + t330 = t259*t37; + t338 = t143*t51; + t358 = -t324*t330-2.0*t11*t315-t272*t263*t37-2.0*t11*t276+RATIONAL(-1.0, +2.0)*t282*t338-t243*t260*t37-2.0*t64*t312-t282*t229*t37-t299*t58*t18-2.0*t24* +t273-2.0*t24*t318+RATIONAL(-1.0,2.0)*t64*t338-2.0*t64*t235*t130; + t381 = t29*t130; + t392 = t23*t199; + t395 = -2.0*t240*t10*t37*t199-2.0*t11*t235*t183-2.0*t11*t134*t130-2.0*t64 +*t134*t93-2.0*t24*t206*t166-t11*t38*t18-2.0*t293*t29*t112-2.0*t324*t381-2.0*t11 +*t206*t199-2.0*t64*t206*t112-t168*t216*t93-2.0*t324*t392; + t396 = partial_d_g_uu_111; + t397 = t396*t19; + t408 = t1*t1; + t411 = t19*t18; + t431 = RATIONAL(-1.0,2.0)*t134*t397+RATIONAL(-1.0,2.0)*t206*t26+RATIONAL( +-1.0,2.0)*t235*t20+RATIONAL(-1.0,2.0)*t64*t397-t240*t216*t166-t408*t216*t183+ +RATIONAL(-1.0,2.0)*t45*t411*t396+RATIONAL(-1.0,2.0)*t40*t411*t25+RATIONAL(-1.0, +2.0)*t29*t411*t12-2.0*t24*t134*t112+RATIONAL(-1.0,2.0)*t243*t305-t293*t67*t18 +-2.0*t64*t272*t112; + HA = t95+t209+t254+t296+t329+t358+t395+t431; + t440 = t396*t18+t53+t325+t48+t147*t37+t330+t59+t263+t219*t10+t45*t93+2.0* +t203+2.0*t381; t444 = partial_d_ln_sqrt_g_1; t447 = partial_d_ln_sqrt_g_2; t450 = partial_d_ln_sqrt_g_3; - t465 = t61*t53+2.0*t134+t55*t92+t149*t444*t25+t99*t447*t25+t1*t450*t25+ -t99*t444*t18+t61*t447*t18+t28*t450*t18+t1*t444*t10+t28*t447*t10+t55*t450*t10; + t465 = t50*t166+2.0*t392+t1*t183+t45*t444*t18+t40*t447*t18+t29*t450*t18+ +t40*t444*t37+t50*t447*t37+t23*t450*t37+t29*t444*t10+t23*t447*t10+t1*t450*t10; HB = t440+t465; - HC = K_uu_11*t114+2.0*K_uu_12*t18*t25+2.0*K_uu_13*t10*t25+K_uu_22*t62+2.0 -*K_uu_23*t10*t18+K_uu_33*t30; - HD = t237+2.0*t100*t25+2.0*t11*t25+t63+2.0*t72*t18+t118; - t490 = pow(HD,1.0*RATIONAL(1.0,2.0)); - H = HA/t490/HD+HB/t490+HC/HD-K; + HC = K_uu_11*t19+2.0*K_uu_12*t37*t18+2.0*K_uu_13*t10*t18+K_uu_22*t51+2.0* +K_uu_23*t10*t37+K_uu_33*t216; + HD = t46+2.0*t134*t18+2.0*t64*t18+t52+2.0*t24*t37+t324; -- cgit v1.2.3