diff options
Diffstat (limited to 'src/gr.cg/expansion_Jacobian.c')
-rw-r--r-- | src/gr.cg/expansion_Jacobian.c | 1253 |
1 files changed, 628 insertions, 625 deletions
diff --git a/src/gr.cg/expansion_Jacobian.c b/src/gr.cg/expansion_Jacobian.c index b5d2427..1017901 100644 --- a/src/gr.cg/expansion_Jacobian.c +++ b/src/gr.cg/expansion_Jacobian.c @@ -1,628 +1,631 @@ /* - * inputs = {r, partial_d_ln_sqrt_g, partial_d_g_uu, X_ud, X_udd, g_uu, K_uu, Theta_A, Theta_B, Theta_C, Theta_D, h} - * outputs = {partial_Theta_wrt_partial_d_h, partial_Theta_wrt_partial_dd_h} - * cost = 458*assignments+1692*multiplications+10*divisions+7*functions+729*additions + * inputs = {partial_d_ln_sqrt_g, partial_d_g_uu, r, X_ud, X_udd, g_uu, K_uu, Theta_A, Theta_B, Theta_C, Theta_D, h} + * outputs = {partial_Theta_X_wrt_partial_d_h, partial_Theta_Y_wrt_partial_d_h, partial_Theta_X_wrt_partial_dd_h, partial_Theta_Y_wrt_partial_dd_h} + * cost = 466*assignments+10*divisions+7*functions+1722*multiplications+728*additions */ -fp t1, t2, t3, t4, t5, t7, t8, t10, t11, t13; -fp t14, t16, t18, t20, t22, t24, t26, t28, t29, t31; -fp t32, t35, t37, t38, t41, t42, t43, t46, t48, t52; -fp t54, t55, t59, t60, t63, t67, t68, t69, t70, t71; -fp t74, t76, t78, t80, t83, t85, t86, t92, t93, t94; -fp t98, t99, t102, t103, t104, t107, t108, t112, t113, t114; -fp t115, t116, t118, t119, t120, t122, t123, t126, t127, t128; -fp t133, t136, t140, t141, t142, t143, t153, t156, t158, t160; -fp t162, t165, t167, t168, t171, t172, t173, t174, t179, t183; -fp t185, t189, t190, t193, t194, t195, t197, t198, t202, t205; -fp t208, t209, t212, t216, t217, t218, t220, t222, t223, t224; -fp t226, t227, t232, t235, t236, t237, t238, t240, t247, t248; -fp t249, t254, t259, t263, t266, t267, t275, t278, t281, t284; -fp t287, t288, t291, t296, t297, t298, t300, t307, t309, t311; -fp t314, t316, t317, t322, t325, t326, t329, t334, t335, t336; -fp t340, t346, t350, t351, t352, t354, t357, t358, t359, t361; -fp t364, t365, t366, t368, t370, t373, t374, t376, t381, t385; -fp t386, t392, t398, t401, t404, t405, t407, t408, t411, t414; -fp t416, t417, t419, t421, t422, t424, t428, t431, t432, t434; -fp t437, t440, t442, t449, t454, t458, t461, t467, t470, t471; -fp t474, t475, t481, t485, t489, t494, t498, t503, t504, t505; -fp t507, t514, t518, t534, t536, t542, t545, t548, t551, t552; -fp t559, t561, t562, t565, t569, t571, t572, t573, t575, t576; -fp t588, t589, t590, t593, t594, t599, t601, t605, t608, t609; -fp t612, t613, t627, t632, t633, t640, t644, t652, t656, t664; -fp t669, t672, t677, t678, t680, t694, t704, t707, t712, t716; -fp t723, t738, t741, t746, t748, t750, t774, t776, t780, t785; -fp t787, t792, t796, t797, t799, t800, t802, t803, t805, t807; -fp t809, t811, t813, t815, t817, t819, t822, t824, t827, t829; -fp t832, t835, t837, t840, t843, t847, t860, t869, t871, t876; -fp t882, t886, t890, t891, t897, t899, t900, t902, t904, t905; -fp t907, t913, t920, t929, t930, t933, t938, t944, t947, t949; -fp t962, t970, t971, t976, t979, t983, t996, t997, t1000, t1001; -fp t1004, t1010, t1012, t1015, t1033, t1036, t1039, t1047, t1048, t1050; -fp t1062, t1065, t1070, t1074, t1075, t1078, t1080, t1082, t1087, t1093; -fp t1095, t1097, t1103, t1107, t1112, t1114, t1138, t1139, t1141, t1145; -fp t1150, t1163, t1166, t1169, t1174, t1186, t1189, t1192, t1200, t1214; -fp t1234, t1266, t1281, t1289, t1300, t1301, t1308, t1335, t1342, t1345; -fp t1364, t1370, t1405, t1414, t1427, t1457, t1460, t1463, t1465, t1469; -fp t1475, t1476, t1477, t1483, t1486, t1487, t1491, t1492, t1493, t1497; -fp t1505, t1508, t1510, t1513, t1516, t1517, t1520, t1526, t1536, t1547; -fp t1552, t1555, t1558, t1561, t1572, t1580, t1594, t1600, t1606, t1610; -fp t1622, t1629, t1639, t1641, t1643, t1645, t1648, t1655, t1659, t1660; -fp t1666, t1667, t1684, t1697, t1704, t1718, t1721, t1739, t1748, t1751; -fp t1757, t1760, t1761, t1768, t1771, t1783, t1785, t1788, t1791, t1803; -fp t1809, t1812, t1825; +fp t1, t2, t4, t5, t7, t8, t10, t11, t12, t14; +fp t16, t18, t19, t20, t24, t25, t26, t28, t30, t32; +fp t34, t36, t38, t40, t41, t42, t44, t47, t49, t50; +fp t53, t54, t55, t56, t59, t60, t61, t68, t69, t70; +fp t71, t75, t76, t79, t80, t81, t87, t91, t93, t97; +fp t98, t101, t102, t108, t109, t112, t113, t114, t115, t117; +fp t118, t119, t120, t123, t124, t126, t127, t128, t131, t133; +fp t136, t137, t139, t140, t144, t146, t148, t151, t153, t154; +fp t157, t160, t161, t162, t165, t166, t167, t169, t170, t171; +fp t173, t177, t178, t179, t181, t184, t186, t190, t192, t196; +fp t197, t198, t201, t203, t206, t207, t208, t209, t212, t213; +fp t216, t218, t221, t222, t223, t226, t227, t228, t230, t232; +fp t235, t237, t239, t241, t244, t246, t247, t251, t252, t254; +fp t255, t257, t258, t262, t263, t265, t269, t271, t272, t273; +fp t275, t278, t279, t284, t287, t288, t291, t294, t295, t298; +fp t301, t307, t311, t312, t314, t317, t318, t322, t328, t330; +fp t333, t337, t339, t341, t345, t357, t360, t363, t364, t365; +fp t370, t372, t374, t377, t379, t380, t383, t384, t385, t387; +fp t390, t397, t400, t405, t408, t410, t411, t412, t414, t419; +fp t427, t430, t433, t436, t439, t443, t446, t447, t448, t451; +fp t452, t454, t457, t458, t459, t462, t465, t471, t474, t478; +fp t479, t481, t485, t489, t493, t499, t503, t508, t511, t513; +fp t514, t521, t528, t534, t537, t539, t544, t550, t553, t556; +fp t560, t564, t565, t574, t580, t582, t587, t595, t611, t616; +fp t625, t627, t628, t629, t631, t632, t637, t639, t648, t652; +fp t663, t676, t680, t681, t682, t698, t703, t709, t715, t718; +fp t731, t735, t740, t742, t745, t747, t751, t759, t785, t790; +fp t792, t797, t801, t802, t804, t805, t807, t808, t810, t812; +fp t814, t816, t818, t820, t822, t824, t836, t837, t844, t846; +fp t847, t849, t850, t852, t854, t856, t858, t860, t862, t866; +fp t868, t873, t877, t879, t881, t884, t886, t890, t894, t895; +fp t898, t902, t905, t910, t912, t914, t921, t926, t931, t934; +fp t938, t940, t944, t946, t947, t950, t951, t956, t960, t964; +fp t967, t970, t973, t976, t980, t983, t986, t991, t994, t999; +fp t1005, t1009, t1012, t1015, t1016, t1024, t1030, t1034, t1037, t1044; +fp t1057, t1066, t1076, t1089, t1101, t1112, t1123, t1130, t1143, t1162; +fp t1172, t1185, t1206, t1230, t1236, t1272, t1283, t1313, t1326, t1332; +fp t1341, t1346, t1351, t1380, t1389, t1402, t1415, t1418, t1420, t1423; +fp t1425, t1428, t1431, t1433, t1436, t1439, t1443, t1446, t1465, t1466; +fp t1467, t1470, t1476, t1477, t1478, t1481, t1484, t1485, t1490, t1497; +fp t1500, t1501, t1504, t1506, t1511, t1514, t1518, t1524, t1532, t1537; +fp t1540, t1543, t1556, t1560, t1567, t1568, t1582, t1585, t1588, t1600; +fp t1601, t1606, t1610, t1613, t1631, t1635, t1641, t1646, t1652, t1662; +fp t1668, t1673, t1674, t1688, t1694, t1695, t1704, t1705, t1711, t1739; +fp t1749, t1752, t1755, t1766, t1769, t1772, t1777, t1782, t1791, t1794; +fp t1803, t1809, t1819, t1830, t1834, t1855; t1 = g_uu_13; - t2 = X_ud_13; - t3 = t1*t2; - t4 = g_uu_12; - t5 = 1/r; - t7 = X_ud_11; - t8 = PARTIAL_RHO(h); - t10 = X_ud_21; - t11 = PARTIAL_SIGMA(h); - t13 = xx*t5-t7*t8-t10*t11; - t14 = t4*t13; - t16 = r*r; - t18 = 1/t16/r; - t20 = X_udd_112; - t22 = X_udd_212; - t24 = X_ud_12; - t26 = PARTIAL_RHO_RHO(h); - t28 = t10*t24; - t29 = PARTIAL_RHO_SIGMA(h); - t31 = X_ud_22; - t32 = t7*t31; - t35 = PARTIAL_SIGMA_SIGMA(h); - t37 = -xx*yy*t18-t20*t8-t22*t11-t7*t24*t26-t28*t29-t32*t29-t10*t31*t35; - t38 = t14*t37; - t41 = g_uu_22; - t42 = t41*t24; - t43 = t1*t13; - t46 = X_udd_123; - t48 = X_udd_223; - t52 = t31*t2; - t54 = X_ud_23; - t55 = t24*t54; - t59 = -yy*zz*t18-t46*t8-t48*t11-t24*t2*t26-t52*t29-t55*t29-t31*t54*t35; - t60 = t43*t59; - t63 = g_uu_23; - t67 = yy*t5-t24*t8-t31*t11; - t68 = t63*t67; - t69 = t1*t7; - t70 = xx*xx; - t71 = yy*yy; - t74 = X_udd_133; - t76 = X_udd_233; - t78 = t2*t2; - t80 = t54*t2; - t83 = t54*t54; - t85 = (t70+t71)*t18-t74*t8-t76*t11-t78*t26-2.0*t80*t29-t83*t35; - t86 = t69*t85; - t92 = zz*t5-t2*t8-t54*t11; - t93 = t63*t92; - t94 = t4*t67; - t98 = t41*t67; - t99 = t69*t59; - t102 = g_uu_33; - t103 = t102*t92; - t104 = t43*t74; - t107 = t1*t92; - t108 = t4*t7; - t112 = g_uu_11; - t113 = t112*t13; - t114 = partial_d_g_uu_123; - t115 = t114*t2; - t116 = t115*t67; - t118 = partial_d_g_uu_211; - t119 = t118*t13; - t120 = t119*t7; - t122 = t63*t2; - t123 = t94*t37; - t126 = partial_d_g_uu_122; - t127 = t126*t67; - t128 = t127*t24; - t133 = t98*t37; - t136 = X_udd_113; - t140 = 2.0*t3*t38+2.0*t42*t60+2.0*t68*t86+2.0*t93*t94*t20+2.0*t98*t99+2.0 -*t103*t104+2.0*t107*t108*t37+t113*t116+t93*t120+2.0*t122*t123+t113*t128+2.0* -t107*t14*t20+2.0*t3*t133+2.0*t107*t68*t136; - t141 = partial_d_g_uu_311; - t142 = t141*t13; - t143 = t142*t7; - t153 = zz*zz; - t156 = X_udd_122; - t158 = X_udd_222; - t160 = t24*t24; - t162 = t31*t24; - t165 = t31*t31; - t167 = (t70+t153)*t18-t156*t8-t158*t11-t160*t26-2.0*t162*t29-t165*t35; - t168 = t108*t167; - t171 = t13*t13; - t172 = t112*t171; - t173 = partial_d_g_uu_112; - t174 = t173*t24; - t179 = X_udd_213; - t183 = t10*t2; - t185 = t7*t54; - t189 = -xx*zz*t18-t136*t8-t179*t11-t7*t2*t26-t183*t29-t185*t29-t10*t54* -t35; - t190 = t68*t189; - t193 = t112*t7; - t194 = t114*t92; - t195 = t194*t67; - t197 = t4*t4; - t198 = t197*t67; - t202 = t108*t59; - t205 = t193*t37; - t208 = t102*t2; - t209 = t14*t59; - t212 = t63*t24; - t216 = t63*t63; - t217 = t92*t92; - t218 = t216*t217; - t220 = t103*t143+2.0*t94*t43*t136+2.0*t107*t98*t20+2.0*t68*t104+2.0*t93* -t168+t172*t174+2.0*t3*t190+t193*t195+2.0*t198*t7*t37+2.0*t103*t202+2.0*t93*t205 -+2.0*t208*t209+2.0*t107*t212*t189+t218*t156; - t222 = t1*t1; - t223 = t222*t217; - t224 = X_udd_111; - t226 = t102*t102; - t227 = t226*t217; - t232 = t113*t189; - t235 = t67*t67; - t236 = t41*t235; - t237 = partial_d_g_uu_223; - t238 = t237*t2; - t240 = t194*t24; - t247 = partial_d_g_uu_333; - t248 = t247*t92; - t249 = t248*t2; - t254 = t113*t136; - t259 = t1*t171; - t263 = t193*t189; - t266 = t223*t224+t227*t74+2.0*t107*t42*t37+2.0*t208*t232+t236*t238+t113* -t240+2.0*t93*t98*t156+2.0*t68*t202+t43*t249+2.0*t93*t42*t167+2.0*t103*t254+2.0* -t212*t209+2.0*t259*t4*t46+2.0*t103*t263; - t267 = t98*t167; - t275 = t14*t46; - t278 = t43*t46; - t281 = t113*t224; - t284 = t113*t37; - t287 = t102*t217; - t288 = t63*t46; - t291 = t113*t20; - t296 = partial_d_g_uu_312; - t297 = t296*t67; - t298 = t297*t13; - t300 = t222*t92; - t307 = X_udd_211; - t309 = t7*t7; - t311 = t10*t7; - t314 = t10*t10; - t316 = (t71+t153)*t18-t224*t8-t307*t11-t309*t26-2.0*t311*t29-t314*t35; - t317 = t113*t316; - t322 = 2.0*t122*t267+2.0*t94*t69*t189+4.0*t43*t263+2.0*t103*t275+2.0*t98* -t278+2.0*t107*t281+2.0*t122*t284+2.0*t287*t288+2.0*t93*t291+2.0*t68*t275+t208* -t298+2.0*t300*t7*t189+2.0*t3*t317+2.0*t103*t86; - t325 = t4*t24; - t326 = t325*t189; - t329 = t43*t85; - t334 = partial_d_g_uu_313; - t335 = t334*t92; - t336 = t335*t13; - t340 = t335*t7; - t346 = t63*t59; - t350 = partial_d_g_uu_111; - t351 = t350*t13; - t352 = t351*t7; - t354 = t193*t316; - t357 = partial_d_g_uu_113; - t358 = t357*t2; - t359 = t358*t13; - t361 = t94*t189; - t364 = partial_d_g_uu_323; - t365 = t364*t2; - t366 = t365*t67; - t368 = 2.0*t103*t326+2.0*t208*t329+2.0*t212*t329+t212*t336+4.0*t68*t326+ -t68*t340+2.0*t93*t278+4.0*t43*t202+4.0*t103*t346*t2+t94*t352+2.0*t107*t354+t94* -t359+2.0*t208*t361+t43*t366; - t370 = t41*t59*t24; - t373 = t357*t92; - t374 = t373*t13; - t376 = t1*t189; - t381 = t63*t235; - t385 = partial_d_g_uu_133; - t386 = t385*t217; - t392 = t4*t20; - t398 = t350*t171; - t401 = t118*t171; - t404 = t334*t2; - t405 = t404*t13; - t407 = t4*t37; - t408 = t407*t24; - t411 = t43*t189; - t414 = 4.0*t68*t370+t325*t374+4.0*t103*t376*t2+t98*t120+2.0*t381*t41*t46+ -RATIONAL(1.0,2.0)*t193*t386+2.0*t381*t4*t136+2.0*t236*t392+2.0*t259*t112*t136+ -RATIONAL(1.0,2.0)*t3*t398+RATIONAL(1.0,2.0)*t122*t401+t68*t405+4.0*t98*t408+2.0 -*t325*t411; - t416 = t364*t92; - t417 = t416*t67; - t419 = t297*t7; - t421 = t296*t24; - t422 = t421*t13; - t424 = t1*t37; - t428 = t94*t316; - t431 = t41*t41; - t432 = t431*t235; - t434 = t126*t235; - t437 = t247*t217; - t440 = t416*t24; - t442 = t373*t7; - t449 = t431*t67; - t454 = t69*t417+t103*t419+t103*t422+4.0*t93*t424*t2+2.0*t3*t428+t432*t156 -+RATIONAL(1.0,2.0)*t193*t434+RATIONAL(1.0,2.0)*t69*t437+t43*t440+t94*t442+2.0* -t300*t13*t136+t381*t296*t7+2.0*t449*t167*t24+t259*t421; - t458 = t350*t7; - t461 = t4*t235; - t467 = t13*t189; - t470 = t237*t92; - t471 = t470*t24; - t474 = t385*t92; - t475 = t474*t2; - t481 = t13*t37; - t485 = t67*t59; - t489 = t238*t67; - t494 = RATIONAL(3.0,2.0)*t259*t141*t7+RATIONAL(3.0,2.0)*t172*t458+t461* -t115+2.0*t198*t13*t20+2.0*t222*t2*t467+2.0*t98*t471+t113*t475+2.0*t107*t94*t224 -+2.0*t197*t24*t481+2.0*t216*t2*t485+t68*t249+t14*t489+t107*t128+2.0*t93*t99; - t498 = t470*t67; - t503 = partial_d_g_uu_233; - t504 = t503*t92; - t505 = t504*t2; - t507 = t4*t171; - t514 = t216*t92; - t518 = t334*t7; - t534 = t108*t498+2.0*t103*t94*t136+t14*t505+RATIONAL(3.0,2.0)*t507*t118* -t7+2.0*t107*t325*t316+2.0*t514*t24*t59+t287*t518+t259*t404+RATIONAL(3.0,2.0)* -t461*t126*t24+2.0*t514*t67*t46+RATIONAL(1.0,2.0)*t3*t434+2.0*t68*t440+t172*t358 -+2.0*t68*t422; - t536 = partial_d_g_uu_213; - t542 = t98*t59; - t545 = t68*t85; - t548 = t216*t235; - t551 = t536*t13; - t552 = t551*t2; - t559 = t174*t13; - t561 = t536*t92; - t562 = t561*t7; - t565 = t226*t92; - t569 = t94*t475+t507*t536*t2+2.0*t43*t340+t14*t471+2.0*t208*t542+2.0*t208 -*t545+t548*t74+t98*t505+2.0*t93*t552+2.0*t94*t240+2.0*t113*t442+t107*t559+2.0* -t14*t562+2.0*t565*t85*t2; - t571 = partial_d_g_uu_322; - t572 = t571*t67; - t573 = t572*t24; - t575 = t173*t67; - t576 = t575*t13; - t588 = partial_d_g_uu_212; - t589 = t588*t24; - t590 = t589*t13; - t593 = t588*t67; - t594 = t593*t13; - t599 = t575*t7; - t601 = t63*t217; - t605 = t141*t171; - t608 = t43*t573+t3*t576+2.0*t103*t405+2.0*t43*t419+t103*t573+2.0*t107* -t359+2.0*t514*t167*t2+t93*t590+t381*t365+t122*t594+2.0*t103*t98*t46+t107*t599+ -2.0*t601*t1*t20+RATIONAL(1.0,2.0)*t208*t605; - t609 = t593*t7; - t612 = partial_d_g_uu_222; - t613 = t612*t24; - t627 = t588*t7; - t632 = t612*t67; - t633 = t632*t24; - t640 = t216*t67; - t644 = 2.0*t14*t609+RATIONAL(3.0,2.0)*t236*t613+t93*t609+2.0*t113*t599+ -RATIONAL(1.0,2.0)*t42*t401+2.0*t107*t116+RATIONAL(1.0,2.0)*t325*t398+2.0*t103* -t366+t236*t627+2.0*t103*t212*t85+t14*t633+2.0*t93*t489+RATIONAL(3.0,2.0)*t381* -t571*t24+2.0*t640*t85*t24; - t652 = t364*t24; - t656 = t1*t217; - t664 = t247*t2; - t669 = t1*t136; - t672 = t503*t217; - t677 = t112*t112; - t678 = t677*t171; - t680 = 4.0*t14*t205+2.0*t103*t68*t74+t287*t652+t461*t173*t7+t656*t114*t24 -+t601*t237*t24+t507*t589+t601*t536*t7+RATIONAL(3.0,2.0)*t287*t664+RATIONAL(1.0, -2.0)*t212*t437+2.0*t287*t669+RATIONAL(1.0,2.0)*t108*t672+RATIONAL(1.0,2.0)*t42* -t672+t678*t224; - t694 = t677*t13; - t704 = t571*t235; - t707 = t612*t235; - t712 = t222*t13; - t716 = 2.0*t98*t590+2.0*t300*t316*t2+2.0*t94*t559+t98*t562+2.0*t122*t60+ -t93*t633+2.0*t103*t370+2.0*t694*t316*t7+RATIONAL(3.0,2.0)*t656*t385*t2+RATIONAL -(3.0,2.0)*t601*t503*t2+RATIONAL(1.0,2.0)*t208*t704+RATIONAL(1.0,2.0)*t122*t707+ -RATIONAL(1.0,2.0)*t69*t704+2.0*t712*t85*t7; - t723 = t197*t13; - t738 = t14*t167; - t741 = t14*t156; - t746 = t561*t13; - t748 = t197*t235; - t750 = 2.0*t198*t316*t24+t656*t357*t7+2.0*t723*t167*t7+t68*t143+2.0*t507* -t112*t20+2.0*t94*t354+t98*t552+RATIONAL(1.0,2.0)*t108*t707+RATIONAL(1.0,2.0)* -t212*t605+2.0*t122*t738+2.0*t98*t741+2.0*t93*t408+t42*t746+t748*t224; - t774 = t197*t171; - t776 = t222*t171; - t780 = 2.0*t94*t281+2.0*t42*t284+2.0*t98*t168+t107*t352+2.0*t212*t232+2.0 -*t93*t741+RATIONAL(1.0,2.0)*t325*t386+2.0*t42*t738+2.0*t98*t205+2.0*t98*t291+ -2.0*t325*t317+2.0*t68*t254+t774*t156+t776*t74+2.0*t68*t263; - t785 = pow(Theta_D,1.0*RATIONAL(1.0,2.0)); - t787 = 1/t785/Theta_D; - t792 = -t458-t627-t518-t174-t613-t652-t358-t238-t664-t112*t224-2.0*t392 --2.0*t669; - t796 = partial_d_ln_sqrt_g_1; - t797 = t112*t796; - t799 = partial_d_ln_sqrt_g_2; - t800 = t4*t799; - t802 = partial_d_ln_sqrt_g_3; - t803 = t1*t802; - t805 = t4*t796; - t807 = t41*t799; - t809 = t63*t802; - t811 = t1*t796; - t813 = t63*t799; - t815 = t102*t802; - t817 = -t41*t156-2.0*t288-t102*t74-t797*t7-t800*t7-t803*t7-t805*t24-t807* -t24-t809*t24-t811*t2-t813*t2-t815*t2; - t819 = 1/t785; - t822 = K_uu_11*t13; - t824 = K_uu_12; - t827 = t824*t67; - t829 = K_uu_13; - t832 = t829*t92; - t835 = K_uu_22*t67; - t837 = K_uu_23; - t840 = t837*t92; - t843 = K_uu_33*t92; - t847 = 1/Theta_D; - t860 = Theta_D*Theta_D; - t869 = RATIONAL(3.0,2.0)*Theta_A/t785/t860+RATIONAL(1.0,2.0)*Theta_B*t787 -+Theta_C/t860; - partial_Theta_wrt_partial_d_h_1 = (t140+t220+t266+t322+t368+t414+t454+ -t494+t534+t569+t608+t644+t680+t716+t750+t780)*t787+(t792+t817)*t819+(-2.0*t822* -t7-2.0*t824*t24*t13-2.0*t827*t7-2.0*t829*t2*t13-2.0*t832*t7-2.0*t835*t24-2.0* -t837*t2*t67-2.0*t840*t24-2.0*t843*t2)*t847-(-2.0*t113*t7-2.0*t325*t13-2.0*t94* -t7-2.0*t3*t13-2.0*t107*t7-2.0*t98*t24-2.0*t122*t67-2.0*t93*t24-2.0*t103*t2)* -t869; - t871 = t113*t22; - t876 = t63*t54; - t882 = t551*t54; - t886 = t561*t10; - t890 = t112*t10; - t891 = t890*t316; - t897 = t334*t10; - t899 = 2.0*t93*t871+t381*t296*t10+t876*t594+2.0*t93*t94*t22+t432*t158+2.0 -*t93*t882+t218*t158+2.0*t14*t886+t748*t307+2.0*t94*t891+t890*t195+t548*t76+t223 -*t307+t287*t897; - t900 = t194*t31; - t902 = t334*t54; - t904 = t114*t54; - t905 = t904*t67; - t907 = t63*t31; - t913 = t102*t54; - t920 = t14*t48; - t929 = t4*t10; - t930 = t929*t59; - t933 = t335*t10; - t938 = t113*t900+t259*t902+t113*t905+2.0*t907*t209+2.0*t300*t13*t179+2.0* -t913*t545+t507*t536*t54+t601*t536*t10+2.0*t68*t920+2.0*t712*t85*t10+2.0*t449* -t167*t31+2.0*t68*t930+t68*t933+2.0*t197*t31*t481; - t944 = t1*t54; - t947 = t588*t31; - t949 = t113*t307; - t962 = t364*t54; - t970 = t4*t31; - t971 = t970*t189; - t976 = t913*t298+2.0*t103*t907*t85+2.0*t944*t317+t507*t947+2.0*t107*t949+ -RATIONAL(3.0,2.0)*t507*t118*t10+2.0*t259*t4*t48+t259*t296*t31+2.0*t107*t891+ -t381*t962+2.0*t198*t13*t22+2.0*t103*t68*t76+2.0*t103*t971+2.0*t876*t60; - t979 = t416*t31; - t983 = t351*t10; - t996 = t1*t10; - t997 = t996*t85; - t1000 = t41*t31; - t1001 = t1000*t59; - t1004 = t996*t59; - t1010 = t142*t10; - t1012 = 2.0*t907*t329+t43*t979+2.0*t913*t361+t107*t983+2.0*t944*t38+4.0* -t93*t424*t54+2.0*t107*t929*t37+2.0*t103*t94*t179+2.0*t68*t997+2.0*t103*t1001+ -2.0*t98*t1004+t970*t374+2.0*t913*t542+t103*t1010; - t1015 = t119*t10; - t1033 = t43*t48; - t1036 = t297*t10; - t1039 = t373*t10; - t1047 = t357*t54; - t1048 = t1047*t13; - t1050 = t93*t1015+2.0*t107*t1000*t37+2.0*t259*t112*t179+2.0*t970*t411+2.0 -*t944*t133+2.0*t93*t1004+2.0*t103*t98*t48+t774*t158+2.0*t98*t1033+2.0*t43*t1036 -+2.0*t113*t1039+2.0*t1000*t60+2.0*t94*t43*t179+t94*t1048; - t1062 = t43*t76; - t1065 = t113*t179; - t1070 = t470*t31; - t1074 = t237*t54; - t1075 = t1074*t67; - t1078 = t504*t54; - t1080 = t474*t54; - t1082 = 2.0*t107*t98*t22+2.0*t94*t996*t189+t98*t1015+2.0*t970*t317+2.0* -t876*t123+2.0*t68*t1062+2.0*t68*t1065+2.0*t944*t428+t14*t1070+2.0*t94*t949+t14* -t1075+t94*t1039+t14*t1078+t113*t1080; - t1087 = t112*t189*t10; - t1093 = t248*t54; - t1095 = t127*t31; - t1097 = t572*t31; - t1103 = t296*t13*t31; - t1107 = t407*t31; - t1112 = t632*t31; - t1114 = 4.0*t43*t930+4.0*t43*t1087+t227*t76+4.0*t68*t971+t68*t1093+t107* -t1095+t103*t1097+4.0*t68*t1001+t98*t1078+2.0*t68*t1103+t678*t307+4.0*t98*t1107+ -RATIONAL(1.0,2.0)*t1000*t672+t93*t1112; - t1138 = t173*t31; - t1139 = t1138*t13; - t1141 = t4*t22; - t1145 = 2.0*t381*t41*t48+2.0*t216*t54*t485+t103*t1103+RATIONAL(1.0,2.0)* -t996*t704+t103*t1036+t601*t237*t31+t172*t1047+RATIONAL(3.0,2.0)*t601*t503*t54+ -2.0*t514*t31*t59+2.0*t514*t67*t48+t776*t76+t107*t1139+2.0*t236*t1141+t996*t417; - t1150 = t593*t10; - t1163 = t947*t13; - t1166 = t962*t67; - t1169 = t575*t10; - t1174 = t944*t576+t93*t1150+2.0*t723*t167*t10+RATIONAL(1.0,2.0)*t890*t386 -+RATIONAL(1.0,2.0)*t929*t672+RATIONAL(1.0,2.0)*t944*t434+RATIONAL(1.0,2.0)*t907 -*t437+t93*t1163+t98*t882+t43*t1166+t1000*t746+t107*t1169+t43*t1097+2.0*t107* -t1048; - t1186 = t112*t37*t10; - t1189 = t929*t167; - t1192 = t14*t158; - t1200 = t43*t1093+t907*t336+2.0*t98*t1070+t113*t1095+2.0*t113*t1169+t68* -t1010+t98*t886+t94*t1080+4.0*t14*t1186+2.0*t93*t1189+2.0*t93*t1192+2.0*t913* -t232+2.0*t876*t738+t14*t1112; - t1214 = t902*t13; - t1234 = 2.0*t107*t14*t22+2.0*t1000*t738+2.0*t876*t267+2.0*t107*t68*t179+ -2.0*t94*t900+t68*t1214+2.0*t103*t920+2.0*t944*t190+2.0*t68*t1087+2.0*t93*t98* -t158+2.0*t907*t232+2.0*t93*t1000*t167+2.0*t98*t1192+2.0*t98*t1189; - t1266 = 2.0*t103*t1065+t94*t983+2.0*t1000*t284+2.0*t198*t316*t31+2.0*t107 -*t907*t189+RATIONAL(1.0,2.0)*t890*t434+2.0*t103*t1166+2.0*t43*t933+2.0*t103* -t930+2.0*t94*t1139+2.0*t98*t1163+2.0*t98*t1186+RATIONAL(3.0,2.0)*t259*t141*t10+ -2.0*t222*t54*t467; - t1281 = t588*t10; - t1289 = t247*t54; - t1300 = 2.0*t300*t10*t189+RATIONAL(3.0,2.0)*t656*t385*t54+t461*t904+t172* -t1138+t236*t1074+2.0*t694*t316*t10+t236*t1281+RATIONAL(3.0,2.0)*t381*t571*t31+ -RATIONAL(3.0,2.0)*t461*t126*t31+RATIONAL(3.0,2.0)*t287*t1289+2.0*t103*t1087+2.0 -*t107*t905+2.0*t68*t979+2.0*t98*t871; - t1301 = t612*t31; - t1308 = t364*t31; - t1335 = RATIONAL(3.0,2.0)*t236*t1301+2.0*t93*t1075+2.0*t14*t1150+t287* -t1308+t656*t114*t31+t461*t173*t10+RATIONAL(1.0,2.0)*t1000*t401+t656*t357*t10+ -2.0*t300*t316*t54+2.0*t507*t112*t22+2.0*t640*t85*t31+2.0*t601*t1*t22+RATIONAL( -1.0,2.0)*t876*t707+2.0*t565*t85*t54; - t1342 = t63*t48; - t1345 = t1*t179; - t1364 = t350*t10; - t1370 = RATIONAL(1.0,2.0)*t913*t704+2.0*t514*t167*t54+2.0*t287*t1342+2.0* -t287*t1345+RATIONAL(1.0,2.0)*t970*t398+RATIONAL(1.0,2.0)*t996*t437+RATIONAL(1.0 -,2.0)*t907*t605+RATIONAL(1.0,2.0)*t944*t398+RATIONAL(1.0,2.0)*t876*t401+ -RATIONAL(1.0,2.0)*t913*t605+RATIONAL(1.0,2.0)*t929*t707+RATIONAL(1.0,2.0)*t970* -t386+RATIONAL(3.0,2.0)*t172*t1364+2.0*t198*t10*t37; - t1405 = 4.0*t103*t376*t54+2.0*t103*t1214+4.0*t103*t346*t54+2.0*t93*t1107+ -2.0*t107*t94*t307+2.0*t107*t970*t316+2.0*t913*t209+2.0*t381*t4*t179+t929*t498+ -2.0*t93*t1033+2.0*t103*t997+2.0*t103*t1062+2.0*t913*t329+2.0*t876*t284+2.0*t93* -t1186; - t1414 = -t1364-t1281-t897-t1138-t1301-t1308-t1047-t1074-t1289-t112*t307 --2.0*t1141-2.0*t1345; - t1427 = -t41*t158-2.0*t1342-t102*t76-t797*t10-t800*t10-t803*t10-t805*t31- -t807*t31-t809*t31-t811*t54-t813*t54-t815*t54; - partial_Theta_wrt_partial_d_h_2 = (t899+t938+t976+t1012+t1050+t1082+t1114 -+t1145+t1174+t1200+t1234+t1266+t1300+t1335+t1370+t1405)*t787+(t1414+t1427)*t819 -+(-2.0*t822*t10-2.0*t824*t31*t13-2.0*t827*t10-2.0*t829*t54*t13-2.0*t832*t10-2.0 -*t835*t31-2.0*t837*t54*t67-2.0*t840*t31-2.0*t843*t54)*t847-(-2.0*t113*t10-2.0* -t970*t13-2.0*t94*t10-2.0*t944*t13-2.0*t107*t10-2.0*t98*t31-2.0*t876*t67-2.0*t93 -*t31-2.0*t103*t54)*t869; - t1457 = t14*t160; - t1460 = t69*t2; - t1463 = t68*t4; - t1465 = t13*t24*t2; - t1469 = t43*t78; - t1475 = t103*t4; - t1476 = t67*t7; - t1477 = t1476*t2; - t1483 = t212*t2; - t1486 = t107*t41; - t1487 = t1476*t24; - t1491 = 2.0*t98*t1457+2.0*t287*t1460+2.0*t1463*t1465+t774*t160+2.0*t68* -t1469+2.0*t107*t94*t309+2.0*t1475*t1477+2.0*t381*t108*t2+2.0*t287*t1483+2.0* -t1486*t1487+t218*t160; - t1492 = t13*t7; - t1493 = t1492*t24; - t1497 = t113*t309; - t1505 = t98*t1; - t1508 = t103*t41; - t1510 = t67*t24*t2; - t1513 = t93*t4; - t1516 = t94*t1; - t1517 = t1492*t2; - t1520 = t107*t4; - t1526 = 2.0*t198*t1493+t223*t309+2.0*t107*t1497+2.0*t259*t193*t2+2.0*t93* -t1457+2.0*t1505*t1465+2.0*t1508*t1510+2.0*t1513*t1487+2.0*t1516*t1517+2.0*t1520 -*t1493+2.0*t103*t68*t78; - t1536 = t93*t112; - t1547 = t93*t1; - t1552 = t432*t160+2.0*t93*t98*t160+t548*t78+2.0*t514*t1510+t748*t309+2.0* -t1536*t1493+2.0*t300*t1517+2.0*t381*t42*t2+2.0*t507*t193*t24+2.0*t1547*t1465+ -2.0*t1475*t1465; - t1555 = t103*t112; - t1558 = t98*t112; - t1561 = t108*t24; - t1572 = t68*t112; - t1580 = 2.0*t1547*t1477+2.0*t1555*t1517+2.0*t1558*t1493+2.0*t236*t1561+ -2.0*t259*t325*t2+t776*t78+t678*t309+t227*t78+2.0*t94*t1497+2.0*t1572*t1517+2.0* -t103*t1469+2.0*t601*t69*t24; - partial_Theta_wrt_partial_dd_h_11 = (t1491+t1526+t1552+t1580)*t787+(-t112 -*t309-2.0*t1561-2.0*t1460-t41*t160-2.0*t1483-t102*t78)*t819; - t1594 = -t183-t185; - t1600 = t67*t10; - t1606 = -t28-t32; - t1610 = t1*t1594; - t1622 = 2.0*t218*t162-2.0*t107*t68*t1594+2.0*t432*t162+4.0*t1520*t1600*t7 -+2.0*t776*t80-2.0*t601*t1*t1606-2.0*t287*t1610+2.0*t223*t311+2.0*t748*t311-2.0* -t93*t94*t1606+2.0*t774*t162; - t1629 = -t52-t55; - t1639 = t113*t1606; - t1641 = t113*t1594; - t1643 = t14*t1629; - t1645 = -t381*t4*t1594-t300*t13*t1594-t107*t98*t1606-t259*t4*t1629-t103* -t94*t1594-t107*t14*t1606+t678*t311-t507*t112*t1606-t93*t1639-t103*t1641-t103* -t1643; - t1648 = t43*t1629; - t1655 = t13*t54*t2; - t1659 = t13*t10; - t1660 = t1659*t7; - t1666 = t13*t31; - t1667 = t1666*t24; - t1684 = -2.0*t93*t1648+2.0*t227*t80+4.0*t103*t1*t1655+4.0*t94*t112*t1660 --2.0*t198*t13*t1606+4.0*t1513*t1667-2.0*t514*t67*t1629-2.0*t94*t43*t1594+4.0* -t68*t1*t1655+4.0*t98*t4*t1667-2.0*t98*t1639; - t1697 = t4*t1606; - t1704 = t67*t31; - t1718 = t63*t1629; - t1721 = -2.0*t259*t112*t1594-2.0*t68*t1643-2.0*t68*t1641-2.0*t98*t1648+ -4.0*t107*t112*t1660-2.0*t236*t1697-2.0*t381*t41*t1629+4.0*t93*t41*t1704*t24-2.0 -*t103*t98*t1629+2.0*t548*t80+4.0*t103*t63*t67*t54*t2-2.0*t287*t1718; - partial_Theta_wrt_partial_dd_h_12 = (t1622+2.0*t1645+t1684+t1721)*t787+( --2.0*t890*t7+2.0*t1697+2.0*t1610-2.0*t1000*t24+2.0*t1718-2.0*t913*t2)*t819; - t1739 = t996*t54; - t1748 = t1704*t54; - t1751 = t1600*t54; - t1757 = t1600*t31; - t1760 = 2.0*t507*t890*t31+2.0*t93*t98*t165+t227*t83+t548*t83+2.0*t287* -t1739+2.0*t259*t970*t54+2.0*t601*t996*t31+2.0*t514*t1748+2.0*t1547*t1751+2.0* -t107*t94*t314+2.0*t1486*t1757; - t1761 = t907*t54; - t1768 = t1659*t31; - t1771 = t113*t314; - t1783 = 2.0*t287*t1761+t748*t314+t774*t165+t678*t314+t223*t314+2.0*t198* -t1768+2.0*t94*t1771+2.0*t1513*t1757+2.0*t1520*t1768+2.0*t1475*t1751+2.0*t103* -t68*t83; - t1785 = t1666*t54; - t1788 = t1659*t54; - t1791 = t43*t83; - t1803 = t14*t165; - t1809 = 2.0*t1547*t1785+2.0*t1516*t1788+2.0*t68*t1791+2.0*t1558*t1768+2.0 -*t259*t890*t54+2.0*t107*t1771+2.0*t1463*t1785+2.0*t98*t1803+t218*t165+t776*t83+ -t432*t165; - t1812 = t929*t31; - t1825 = t1572*t1788+t1505*t1785+t236*t1812+t103*t1791+t300*t1788+t381* -t1000*t54+t381*t929*t54+t93*t1803+t1555*t1788+t1536*t1768+t1475*t1785+t1508* -t1748; - partial_Theta_wrt_partial_dd_h_22 = (t1760+t1783+t1809+2.0*t1825)*t787+(- -t112*t314-2.0*t1812-2.0*t1739-t41*t165-2.0*t1761-t102*t83)*t819; + t2 = 1/r; + t4 = X_ud_13; + t5 = PARTIAL_RHO(h); + t7 = X_ud_23; + t8 = PARTIAL_SIGMA(h); + t10 = zz*t2-t4*t5-t7*t8; + t11 = t1*t10; + t12 = g_uu_12; + t14 = X_ud_12; + t16 = X_ud_22; + t18 = yy*t2-t14*t5-t16*t8; + t19 = t12*t18; + t20 = X_udd_111; + t24 = g_uu_23; + t25 = t24*t10; + t26 = t12*t14; + t28 = r*r; + t30 = 1/t28/r; + t32 = X_udd_112; + t34 = X_udd_212; + t36 = X_ud_11; + t38 = PARTIAL_RHO_RHO(h); + t40 = X_ud_21; + t41 = t40*t14; + t42 = PARTIAL_RHO_SIGMA(h); + t44 = t36*t16; + t47 = PARTIAL_SIGMA_SIGMA(h); + t49 = -xx*yy*t30-t32*t5-t34*t8-t36*t14*t38-t41*t42-t44*t42-t40*t16*t47; + t50 = t26*t49; + t53 = t1*t4; + t54 = partial_d_g_uu_122; + t55 = t18*t18; + t56 = t54*t55; + t59 = g_uu_33; + t60 = t59*t10; + t61 = X_udd_113; + t68 = xx*t2-t36*t5-t40*t8; + t69 = t68*t68; + t70 = t12*t69; + t71 = g_uu_11; + t75 = t24*t4; + t76 = t19*t49; + t79 = partial_d_g_uu_112; + t80 = t79*t68; + t81 = t80*t14; + t87 = X_udd_213; + t91 = t40*t4; + t93 = t36*t7; + t97 = -xx*zz*t30-t61*t5-t87*t8-t36*t4*t38-t91*t42-t93*t42-t40*t7*t47; + t98 = t26*t97; + t101 = g_uu_22; + t102 = t101*t18; + t108 = t59*t4; + t109 = t19*t97; + t112 = t71*t68; + t113 = partial_d_g_uu_133; + t114 = t113*t10; + t115 = t114*t4; + t117 = t12*t68; + t118 = partial_d_g_uu_213; + t119 = t118*t10; + t120 = t119*t36; + t123 = t79*t18; + t124 = t123*t36; + t126 = 2.0*t11*t19*t20+2.0*t25*t50+RATIONAL(1.0,2.0)*t53*t56+2.0*t60*t19* +t61+2.0*t70*t71*t32+2.0*t75*t76+2.0*t19*t81+2.0*t60*t98+4.0*t102*t50+2.0*t11* +t102*t32+2.0*t108*t109+t112*t115+2.0*t117*t120+t11*t124; + t127 = t101*t55; + t128 = t12*t32; + t131 = partial_d_g_uu_313; + t133 = t131*t68*t4; + t136 = t54*t18; + t137 = t136*t14; + t139 = yy*yy; + t140 = zz*zz; + t144 = X_udd_211; + t146 = t36*t36; + t148 = t40*t36; + t151 = t40*t40; + t153 = (t139+t140)*t30-t20*t5-t144*t8-t146*t38-2.0*t148*t42-t151*t47; + t154 = t19*t153; + t157 = t102*t49; + t160 = partial_d_g_uu_123; + t161 = t160*t10; + t162 = t161*t14; + t165 = partial_d_g_uu_312; + t166 = t165*t18; + t167 = t166*t36; + t169 = partial_d_g_uu_233; + t170 = t169*t10; + t171 = t170*t4; + t173 = t101*t14; + t177 = partial_d_g_uu_222; + t178 = t177*t18; + t179 = t178*t14; + t181 = t24*t18; + t184 = X_udd_123; + t186 = X_udd_223; + t190 = t16*t4; + t192 = t14*t7; + t196 = -yy*zz*t30-t184*t5-t186*t8-t14*t4*t38-t190*t42-t192*t42-t16*t7*t47 +; + t197 = t101*t196; + t198 = t197*t14; + t201 = t12*t12; + t203 = t68*t49; + t206 = t1*t36; + t207 = partial_d_g_uu_333; + t208 = t10*t10; + t209 = t207*t208; + t212 = partial_d_g_uu_322; + t213 = t212*t55; + t216 = 2.0*t127*t128+2.0*t60*t133+t112*t137+2.0*t53*t154+2.0*t53*t157+2.0 +*t19*t162+t60*t167+t117*t171+2.0*t11*t173*t49+t117*t179+4.0*t181*t198+2.0*t201* +t14*t203+RATIONAL(1.0,2.0)*t206*t209+RATIONAL(1.0,2.0)*t206*t213; + t218 = t113*t208; + t221 = t24*t24; + t222 = t221*t55; + t223 = X_udd_133; + t226 = t1*t68; + t227 = t212*t18; + t228 = t227*t14; + t230 = t166*t68; + t232 = xx*xx; + t235 = X_udd_122; + t237 = X_udd_222; + t239 = t14*t14; + t241 = t16*t14; + t244 = t16*t16; + t246 = (t232+t140)*t30-t235*t5-t237*t8-t239*t38-2.0*t241*t42-t244*t47; + t247 = t102*t246; + t251 = partial_d_g_uu_212; + t252 = t251*t14; + t254 = t1*t1; + t255 = t254*t208; + t257 = t207*t10; + t258 = t257*t4; + t262 = t251*t18; + t263 = t262*t68; + t265 = t262*t36; + t269 = RATIONAL(1.0,2.0)*t26*t218+t222*t223+t19*t115+t226*t228+t108*t230+ +2.0*t75*t247+t11*t81+t70*t252+t255*t20+t226*t258+2.0*t112*t124+t75*t263+t25* +t265+2.0*t60*t198; + t271 = t24*t14; + t272 = t131*t10; + t273 = t272*t68; + t275 = t226*t223; + t278 = t165*t14; + t279 = t278*t68; + t284 = t71*t36; + t287 = t12*t36; + t288 = t177*t55; + t291 = t169*t208; + t294 = t24*t208; + t295 = partial_d_g_uu_223; + t298 = t1*t208; + t301 = t12*t55; + t307 = t254*t10; + t311 = t71*t71; + t312 = t311*t69; + t314 = t181*t133+t271*t273+2.0*t60*t275+t60*t279+2.0*t25*t102*t235+ +RATIONAL(1.0,2.0)*t284*t56+RATIONAL(1.0,2.0)*t287*t288+RATIONAL(1.0,2.0)*t287* +t291+t294*t295*t14+t298*t160*t14+RATIONAL(3.0,2.0)*t301*t54*t14+2.0*t226*t167+ +2.0*t307*t68*t61+t312*t20; + t317 = t59*t208; + t318 = t1*t61; + t322 = t118*t68*t4; + t328 = t221*t208; + t330 = t102*t196; + t333 = t1*t97; + t337 = t272*t36; + t339 = t252*t68; + t341 = t221*t10; + t345 = t1*t69; + t357 = 2.0*t317*t318+2.0*t25*t322+2.0*t25*t19*t32+t328*t235+2.0*t108*t330 ++4.0*t60*t333*t4+t181*t337+t25*t339+2.0*t341*t18*t184+t345*t278+RATIONAL(1.0, +2.0)*t284*t218+t294*t118*t36+2.0*t60*t102*t184+2.0*t25*t173*t246; + t360 = t112*t97; + t363 = partial_d_g_uu_111; + t364 = t363*t68; + t365 = t364*t36; + t370 = X_udd_233; + t372 = t4*t4; + t374 = t7*t4; + t377 = t7*t7; + t379 = (t232+t139)*t30-t223*t5-t370*t8-t372*t38-2.0*t374*t42-t377*t47; + t380 = t181*t379; + t383 = partial_d_g_uu_311; + t384 = t383*t68; + t385 = t384*t36; + t387 = t226*t196; + t390 = t201*t68; + t397 = t206*t196; + t400 = t383*t69; + t405 = t112*t61; + t408 = t201*t69; + t410 = partial_d_g_uu_211; + t411 = t410*t68; + t412 = t411*t36; + t414 = 2.0*t117*t265+2.0*t271*t360+t11*t365+2.0*t108*t380+t181*t385+2.0* +t75*t387+2.0*t390*t246*t36+2.0*t11*t26*t153+2.0*t25*t397+RATIONAL(1.0,2.0)*t271 +*t400+t345*t131*t4+2.0*t181*t405+t408*t235+t25*t412; + t419 = t284*t97; + t427 = t226*t379; + t430 = t117*t184; + t433 = t181*t97; + t436 = t117*t246; + t439 = t24*t196; + t443 = t287*t196; + t446 = partial_d_g_uu_323; + t447 = t446*t18; + t448 = t447*t4; + t451 = t295*t10; + t452 = t451*t14; + t454 = t117*t235; + t457 = 2.0*t60*t181*t223+2.0*t181*t419+t60*t385+t102*t412+2.0*t60*t271* +t379+2.0*t271*t427+2.0*t181*t430+2.0*t53*t433+2.0*t173*t436+4.0*t60*t439*t4+2.0 +*t181*t443+2.0*t60*t448+t117*t452+2.0*t102*t454; + t458 = t295*t18; + t459 = t458*t4; + t462 = t287*t246; + t465 = t117*t196; + t471 = t177*t14; + t474 = t24*t55; + t478 = t446*t10; + t479 = t478*t14; + t481 = t1*t49; + t485 = t206*t379; + t489 = t160*t18*t4; + t493 = t112*t20; + t499 = 2.0*t25*t459+2.0*t102*t462+2.0*t271*t465+2.0*t11*t271*t97+RATIONAL +(3.0,2.0)*t127*t471+RATIONAL(3.0,2.0)*t474*t212*t14+t226*t479+4.0*t25*t481*t4+ +2.0*t181*t485+2.0*t11*t489+t117*t459+2.0*t19*t493+2.0*t108*t360+t19*t365; + t503 = t161*t18; + t508 = t284*t49; + t511 = t451*t18; + t513 = t59*t59; + t514 = t513*t10; + t521 = t478*t18; + t528 = t112*t153; + t534 = t207*t4; + t537 = t446*t14; + t539 = t284*t503+2.0*t307*t153*t4+2.0*t25*t508+t287*t511+2.0*t514*t379*t4 ++t226*t448+2.0*t181*t275+t206*t521+2.0*t11*t181*t61+2.0*t102*t397+2.0*t26*t528+ +RATIONAL(3.0,2.0)*t298*t113*t4+RATIONAL(3.0,2.0)*t317*t534+t317*t537; + t544 = t112*t32; + t550 = t24*t184; + t553 = t226*t184; + t556 = t254*t68; + t560 = t201*t18; + t564 = t101*t101; + t565 = t564*t18; + t574 = t112*t49; + t580 = 2.0*t294*t1*t32+t112*t162+2.0*t25*t544+t112*t489+2.0*t60*t419+2.0* +t317*t550+2.0*t102*t553+2.0*t556*t379*t36+2.0*t560*t153*t14+2.0*t565*t246*t14+ +2.0*t60*t405+2.0*t341*t246*t4+2.0*t75*t574+2.0*t19*t226*t61; + t582 = t284*t153; + t587 = t131*t36; + t595 = t68*t97; + t611 = t363*t69; + t616 = 2.0*t19*t582+2.0*t53*t528+t317*t587+2.0*t19*t206*t97+2.0*t60*t430+ +2.0*t254*t4*t595+2.0*t307*t36*t97+2.0*t108*t465+4.0*t181*t98+2.0*t181*t479+2.0* +t173*t574+2.0*t102*t452+RATIONAL(1.0,2.0)*t26*t611+2.0*t102*t544; + t625 = t564*t55; + t627 = partial_d_g_uu_113; + t628 = t627*t10; + t629 = t628*t36; + t631 = t627*t68; + t632 = t631*t4; + t637 = t201*t55; + t639 = t628*t68; + t648 = 2.0*t60*t485+2.0*t25*t454+2.0*t108*t427+2.0*t60*t443+t625*t235+t19 +*t629+2.0*t11*t632+2.0*t25*t462+t637*t20+t26*t639+2.0*t226*t337+t19*t632+t474* +t165*t36+2.0*t11*t493; + t652 = t119*t68; + t663 = t221*t18; + t676 = t251*t36; + t680 = t102*t322+t173*t652+2.0*t75*t436+2.0*t173*t387+2.0*t181*t279+t70* +t118*t4+t102*t120+2.0*t663*t379*t14+2.0*t112*t629+2.0*t102*t339+2.0*t11*t117* +t32+2.0*t11*t582+t127*t676+t301*t160*t4; + t681 = t71*t69; + t682 = t363*t36; + t698 = t226*t97; + t703 = t311*t68; + t709 = t410*t69; + t715 = t18*t196; + t718 = RATIONAL(3.0,2.0)*t681*t682+t298*t627*t36+RATIONAL(3.0,2.0)*t294* +t169*t4+2.0*t11*t287*t49+t181*t258+t102*t171+2.0*t474*t12*t61+2.0*t26*t698+ +RATIONAL(1.0,2.0)*t271*t209+2.0*t703*t153*t36+RATIONAL(1.0,2.0)*t53*t611+ +RATIONAL(1.0,2.0)*t173*t709+RATIONAL(1.0,2.0)*t75*t709+2.0*t221*t4*t715; + t731 = t295*t4; + t735 = t627*t4; + t740 = t79*t14; + t742 = t117*t49; + t745 = t513*t208; + t747 = t123*t68; + t751 = 2.0*t341*t14*t196+RATIONAL(1.0,2.0)*t173*t291+RATIONAL(3.0,2.0)* +t70*t410*t36+RATIONAL(3.0,2.0)*t345*t383*t36+t127*t731+t474*t446*t4+t681*t735+ +t301*t79*t36+t11*t137+t681*t740+2.0*t53*t742+t745*t223+t53*t747+2.0*t102*t508; + t759 = t254*t69; + t785 = RATIONAL(1.0,2.0)*t108*t400+2.0*t474*t101*t184+2.0*t25*t553+t759* +t223+t25*t179+4.0*t226*t443+t60*t228+4.0*t226*t419+2.0*t345*t12*t184+2.0*t560* +t36*t49+2.0*t560*t68*t32+RATIONAL(1.0,2.0)*t75*t288+RATIONAL(1.0,2.0)*t108*t213 ++2.0*t345*t71*t61+4.0*t117*t508; + t790 = pow(Theta_D,1.0*RATIONAL(1.0,2.0)); + t792 = 1/t790/Theta_D; + t797 = -t682-t676-t587-t740-t471-t537-t735-t731-t534-t71*t20-2.0*t128-2.0 +*t318; + t801 = partial_d_ln_sqrt_g_1; + t802 = t71*t801; + t804 = partial_d_ln_sqrt_g_2; + t805 = t12*t804; + t807 = partial_d_ln_sqrt_g_3; + t808 = t1*t807; + t810 = t12*t801; + t812 = t101*t804; + t814 = t24*t807; + t816 = t1*t801; + t818 = t24*t804; + t820 = t59*t807; + t822 = -t101*t235-2.0*t550-t59*t223-t802*t36-t805*t36-t808*t36-t810*t14- +t812*t14-t814*t14-t816*t4-t818*t4-t820*t4; + t824 = 1/t790; + t836 = -2.0*t112*t36-2.0*t26*t68-2.0*t19*t36-2.0*t53*t68-2.0*t11*t36-2.0* +t102*t14-2.0*t75*t18-2.0*t25*t14-2.0*t60*t4; + t837 = Theta_D*Theta_D; + t844 = RATIONAL(3.0,2.0)*Theta_A/t790/t837+RATIONAL(1.0,2.0)*Theta_B*t792 +; + partial_Theta_X_wrt_partial_d_h_1 = (t126+t216+t269+t314+t357+t414+t457+ +t499+t539+t580+t616+t648+t680+t718+t751+t785)*t792+(t797+t822)*t824-t836*t844; + t846 = t118*t7; + t847 = t846*t68; + t849 = t131*t7; + t850 = t849*t68; + t852 = t272*t40; + t854 = t251*t16; + t856 = t79*t16; + t858 = t119*t40; + t860 = t627*t7; + t862 = t1*t40; + t866 = t384*t40; + t868 = t59*t7; + t873 = t12*t40; + t877 = t628*t40; + t879 = t166*t40; + t881 = t102*t847+t181*t850+t181*t852+t70*t854+t681*t856+t102*t858+t681* +t860+2.0*t19*t862*t97+t60*t866+2.0*t868*t360+t474*t165*t40+2.0*t11*t873*t49+t19 +*t877+t60*t879; + t884 = t251*t40; + t886 = t862*t379; + t890 = t131*t40; + t894 = t71*t40; + t895 = t894*t97; + t898 = t12*t16; + t902 = t631*t7; + t905 = t226*t370; + t910 = t24*t7; + t912 = t854*t68; + t914 = 2.0*t226*t852+t127*t884+2.0*t60*t886+t70*t846+t317*t890+2.0*t868* +t427+2.0*t60*t895+t898*t639+RATIONAL(1.0,2.0)*t898*t218+2.0*t11*t902+2.0*t60* +t905+RATIONAL(1.0,2.0)*t862*t213+t910*t263+t25*t912; + t921 = t451*t16; + t926 = t161*t16; + t931 = t862*t196; + t934 = t478*t16; + t938 = t262*t40; + t940 = t873*t246; + t944 = t446*t16; + t946 = 4.0*t25*t481*t7+t294*t118*t40+2.0*t102*t921+2.0*t910*t387+2.0*t19* +t926+t862*t521+t894*t503+2.0*t25*t931+t226*t934+2.0*t181*t934+t25*t938+2.0*t25* +t940+t112*t926+t317*t944; + t947 = t226*t186; + t950 = t160*t7; + t951 = t950*t18; + t956 = t170*t7; + t960 = t112*t144; + t964 = t1*t7; + t967 = t894*t153; + t970 = t117*t237; + t973 = t112*t34; + t976 = t894*t49; + t980 = 2.0*t25*t947+t112*t951+2.0*t19*t226*t87+t102*t956+t759*t370+t625* +t237+2.0*t19*t960+t637*t144+2.0*t964*t742+2.0*t19*t967+2.0*t25*t970+2.0*t102* +t973+2.0*t102*t976+t312*t144; + t983 = t136*t16; + t986 = t257*t7; + t991 = t12*t196*t40; + t994 = t101*t16; + t999 = t112*t87; + t1005 = t80*t16; + t1009 = t24*t16; + t1012 = t123*t40; + t1015 = t11*t983+t408*t237+t181*t986+2.0*t102*t931+4.0*t226*t991+2.0*t994 +*t387+4.0*t226*t895+2.0*t181*t999+t964*t747+4.0*t117*t976+2.0*t19*t1005+t181* +t866+2.0*t1009*t465+2.0*t112*t1012; + t1016 = t411*t40; + t1024 = t227*t16; + t1030 = t458*t7; + t1034 = t117*t186; + t1037 = t364*t40; + t1044 = t102*t1016+2.0*t226*t879+RATIONAL(1.0,2.0)*t894*t218+RATIONAL(1.0 +,2.0)*t873*t291+t60*t1024+2.0*t181*t991+2.0*t1009*t360+2.0*t25*t1030+t255*t144+ +2.0*t181*t1034+t11*t1037+2.0*t181*t895+2.0*t112*t877+t11*t1005; + t1057 = t447*t7; + t1066 = t197*t16; + t1076 = 2.0*t181*t905+2.0*t898*t528+t11*t1012+2.0*t994*t574+2.0*t11*t181* +t87+t868*t230+2.0*t60*t1057+2.0*t60*t19*t87+4.0*t60*t333*t7+4.0*t181*t1066+2.0* +t994*t436+t25*t1016+2.0*t910*t436+2.0*t102*t970; + t1089 = t12*t97*t16; + t1101 = t898*t49; + t1112 = 2.0*t102*t940+t226*t1057+2.0*t117*t938+2.0*t181*t886+2.0*t1009* +t427+2.0*t910*t76+4.0*t181*t1089+2.0*t60*t1009*t379+2.0*t11*t19*t144+2.0*t25* +t19*t34+2.0*t25*t1101+4.0*t60*t439*t7+2.0*t910*t247+2.0*t60*t181*t370; + t1123 = t178*t16; + t1130 = t114*t7; + t1143 = 2.0*t868*t109+2.0*t25*t994*t246+4.0*t102*t1101+t25*t1123+2.0*t102 +*t947+2.0*t964*t154+t117*t956+t112*t1130+2.0*t60*t1089+2.0*t25*t102*t237+t345* +t849+2.0*t25*t847+t117*t1123+2.0*t60*t1066; + t1162 = t165*t68*t16; + t1172 = 2.0*t868*t380+t873*t511+RATIONAL(1.0,2.0)*t862*t209+2.0*t898*t698 ++2.0*t11*t994*t49+t745*t370+2.0*t60*t850+2.0*t868*t330+t19*t902+t226*t1024+2.0* +t181*t1162+2.0*t201*t16*t203+2.0*t102*t912+t298*t627*t40; + t1185 = t12*t34; + t1206 = t226*t986+2.0*t60*t102*t186+t112*t983+2.0*t560*t40*t49+2.0*t560* +t68*t34+2.0*t127*t1185+2.0*t514*t379*t7+2.0*t221*t7*t715+2.0*t11*t898*t153+ +RATIONAL(1.0,2.0)*t894*t56+2.0*t11*t102*t34+t117*t1030+2.0*t964*t157+t19*t1130; + t1230 = t24*t186; + t1236 = 2.0*t60*t991+t60*t1162+2.0*t868*t465+t328*t237+2.0*t117*t858+2.0* +t60*t999+t19*t1037+2.0*t60*t1034+t222*t370+2.0*t11*t1009*t97+2.0*t341*t16*t196+ +2.0*t341*t18*t186+2.0*t317*t1230+2.0*t556*t379*t40; + t1272 = 2.0*t390*t246*t40+2.0*t565*t246*t16+2.0*t703*t153*t40+RATIONAL( +1.0,2.0)*t994*t291+RATIONAL(1.0,2.0)*t1009*t209+RATIONAL(1.0,2.0)*t964*t56+2.0* +t70*t71*t34+2.0*t345*t71*t87+2.0*t345*t12*t186+RATIONAL(1.0,2.0)*t868*t213+ +RATIONAL(1.0,2.0)*t910*t288+t301*t79*t40+t994*t652+2.0*t964*t433; + t1283 = t1*t87; + t1313 = 2.0*t11*t117*t34+2.0*t11*t967+2.0*t964*t528+2.0*t474*t101*t186+ +2.0*t317*t1283+2.0*t254*t7*t595+2.0*t307*t40*t97+2.0*t307*t68*t87+2.0*t560*t153 +*t16+2.0*t307*t153*t7+2.0*t474*t12*t87+2.0*t341*t246*t7+RATIONAL(3.0,2.0)*t70* +t410*t40+RATIONAL(3.0,2.0)*t345*t383*t40; + t1326 = t177*t16; + t1332 = t207*t7; + t1341 = t295*t7; + t1346 = t363*t40; + t1351 = 2.0*t294*t1*t34+2.0*t663*t379*t16+t298*t160*t16+RATIONAL(3.0,2.0) +*t474*t212*t16+RATIONAL(3.0,2.0)*t127*t1326+RATIONAL(3.0,2.0)*t301*t54*t16+ +RATIONAL(3.0,2.0)*t317*t1332+RATIONAL(3.0,2.0)*t294*t169*t7+RATIONAL(3.0,2.0)* +t298*t113*t7+t127*t1341+t474*t446*t7+t301*t950+RATIONAL(3.0,2.0)*t681*t1346+ +t345*t165*t16; + t1380 = t294*t295*t16+RATIONAL(1.0,2.0)*t994*t709+RATIONAL(1.0,2.0)*t1009 +*t400+RATIONAL(1.0,2.0)*t964*t611+RATIONAL(1.0,2.0)*t898*t611+RATIONAL(1.0,2.0) +*t910*t709+RATIONAL(1.0,2.0)*t868*t400+RATIONAL(1.0,2.0)*t873*t288+t117*t921+ +2.0*t910*t574+2.0*t11*t951+2.0*t11*t960+2.0*t25*t973+2.0*t25*t976+t1009*t273; + t1389 = -t1346-t884-t890-t856-t1326-t944-t860-t1341-t1332-t71*t144-2.0* +t1185-2.0*t1283; + t1402 = -t101*t237-2.0*t1230-t59*t370-t802*t40-t805*t40-t808*t40-t810*t16 +-t812*t16-t814*t16-t816*t7-t818*t7-t820*t7; + t1415 = -2.0*t112*t40-2.0*t898*t68-2.0*t19*t40-2.0*t964*t68-2.0*t11*t40 +-2.0*t102*t16-2.0*t910*t18-2.0*t25*t16-2.0*t60*t7; + partial_Theta_X_wrt_partial_d_h_2 = (t881+t914+t946+t980+t1015+t1044+ +t1076+t1112+t1143+t1172+t1206+t1236+t1272+t1313+t1351+t1380)*t792+(t1389+t1402) +*t824-t1415*t844; + t1418 = K_uu_11*t68; + t1420 = K_uu_12; + t1423 = t1420*t18; + t1425 = K_uu_13; + t1428 = t1425*t10; + t1431 = K_uu_22*t18; + t1433 = K_uu_23; + t1436 = t1433*t10; + t1439 = K_uu_33*t10; + t1443 = 1/Theta_D; + t1446 = 1/t837; + partial_Theta_Y_wrt_partial_d_h_1 = (-2.0*t1418*t36-2.0*t1420*t14*t68-2.0 +*t1423*t36-2.0*t1425*t4*t68-2.0*t1428*t36-2.0*t1431*t14-2.0*t1433*t4*t18-2.0* +t1436*t14-2.0*t1439*t4)*t1443-t836*Theta_C*t1446; + partial_Theta_Y_wrt_partial_d_h_2 = (-2.0*t1418*t40-2.0*t1420*t16*t68-2.0 +*t1423*t40-2.0*t1425*t7*t68-2.0*t1428*t40-2.0*t1431*t16-2.0*t1433*t7*t18-2.0* +t1436*t16-2.0*t1439*t7)*t1443-t1415*Theta_C*t1446; + t1465 = t11*t24; + t1466 = t18*t36; + t1467 = t1466*t4; + t1470 = t112*t146; + t1476 = t60*t71; + t1477 = t68*t36; + t1478 = t1477*t4; + t1481 = t181*t71; + t1484 = t102*t71; + t1485 = t1477*t14; + t1490 = t117*t239; + t1497 = t25*t71; + t1500 = 2.0*t1465*t1467+2.0*t19*t1470+2.0*t294*t206*t14+2.0*t1476*t1478+ +2.0*t1481*t1478+2.0*t1484*t1485+2.0*t11*t1470+2.0*t102*t1490+2.0*t345*t284*t4+ +t408*t239+2.0*t1497*t1485; + t1501 = t287*t14; + t1504 = t102*t1; + t1506 = t68*t14*t4; + t1511 = t226*t372; + t1514 = t19*t1; + t1518 = t18*t14*t4; + t1524 = t181*t12; + t1532 = 2.0*t127*t1501+2.0*t1504*t1506+2.0*t560*t1485+2.0*t181*t1511+2.0* +t1514*t1478+2.0*t341*t1518+2.0*t70*t284*t14+2.0*t1524*t1506+2.0*t60*t1511+t328* +t239+2.0*t1465*t1506; + t1537 = t206*t4; + t1540 = t11*t12; + t1543 = t60*t12; + t1556 = t271*t4; + t1560 = 2.0*t345*t26*t4+2.0*t317*t1537+2.0*t1540*t1485+2.0*t1543*t1467+ +2.0*t307*t1478+t255*t146+t222*t372+2.0*t11*t19*t146+2.0*t25*t102*t239+2.0*t317* +t1556+t637*t146; + t1567 = t25*t12; + t1568 = t1466*t14; + t1582 = t11*t101; + t1585 = t60*t101; + t1588 = 2.0*t25*t1490+t759*t372+2.0*t474*t173*t4+2.0*t1567*t1568+t625* +t239+2.0*t1543*t1506+2.0*t474*t287*t4+t745*t372+t312*t146+2.0*t60*t181*t372+2.0 +*t1582*t1568+2.0*t1585*t1518; + partial_Theta_X_wrt_partial_dd_h_11 = (t1500+t1532+t1560+t1588)*t792+(- +t71*t146-2.0*t1501-2.0*t1537-t101*t239-2.0*t1556-t59*t372)*t824; + t1600 = -t91-t93; + t1601 = t1*t1600; + t1606 = -t190-t192; + t1610 = t117*t1606; + t1613 = -t41-t44; + t1631 = t18*t40; + t1635 = -2.0*t317*t1601+2.0*t408*t241-2.0*t345*t12*t1606-2.0*t181*t1610 +-2.0*t25*t19*t1613+2.0*t328*t241-2.0*t19*t226*t1600-2.0*t60*t19*t1600-2.0*t11* +t102*t1613-2.0*t345*t71*t1600+4.0*t1540*t1631*t36; + t1641 = t112*t1600; + t1646 = t112*t1613; + t1652 = t18*t16; + t1662 = t24*t1606; + t1668 = 2.0*t255*t148-2.0*t70*t71*t1613-2.0*t60*t1641+2.0*t625*t241-2.0* +t25*t1646+2.0*t312*t148+4.0*t25*t101*t1652*t14-2.0*t11*t181*t1600-2.0*t341*t18* +t1606-2.0*t317*t1662-2.0*t560*t68*t1613; + t1673 = t68*t40; + t1674 = t1673*t36; + t1688 = t68*t7*t4; + t1694 = t68*t16; + t1695 = t1694*t14; + t1704 = -2.0*t60*t1610+4.0*t11*t71*t1674+2.0*t759*t374-2.0*t294*t1*t1613+ +2.0*t637*t148+2.0*t222*t374+4.0*t60*t1*t1688-2.0*t474*t12*t1600+4.0*t1567*t1695 +-2.0*t474*t101*t1606-2.0*t11*t117*t1613; + t1705 = t226*t1606; + t1711 = t12*t1613; + t1739 = -2.0*t25*t1705-2.0*t307*t68*t1600-2.0*t127*t1711-2.0*t181*t1641+ +4.0*t181*t1*t1688-2.0*t102*t1705+4.0*t102*t12*t1695+4.0*t19*t71*t1674+2.0*t745* +t374+4.0*t60*t24*t18*t7*t4-2.0*t102*t1646-2.0*t60*t102*t1606; + partial_Theta_X_wrt_partial_dd_h_12 = (t1635+t1668+t1704+t1739)*t792+( +-2.0*t894*t36+2.0*t1711+2.0*t1601-2.0*t994*t14+2.0*t1662-2.0*t868*t4)*t824; + t1749 = t226*t377; + t1752 = t1673*t7; + t1755 = t1694*t7; + t1766 = t873*t16; + t1769 = t1673*t16; + t1772 = t1631*t7; + t1777 = 2.0*t181*t1749+2.0*t1481*t1752+2.0*t1524*t1755+2.0*t345*t898*t7+ +t408*t244+t745*t377+2.0*t345*t894*t7+2.0*t127*t1766+2.0*t560*t1769+2.0*t1543* +t1772+2.0*t1514*t1752; + t1782 = t117*t244; + t1791 = t1652*t7; + t1794 = t862*t7; + t1803 = 2.0*t474*t994*t7+t255*t151+2.0*t102*t1782+2.0*t25*t102*t244+2.0* +t70*t894*t16+2.0*t341*t1791+2.0*t317*t1794+t759*t377+2.0*t60*t1749+t222*t377+ +2.0*t307*t1752; + t1809 = t1009*t7; + t1819 = t112*t151; + t1830 = 2.0*t1540*t1769+2.0*t25*t1782+2.0*t317*t1809+2.0*t1543*t1755+t328 +*t244+2.0*t1465*t1755+2.0*t1476*t1752+2.0*t11*t1819+2.0*t60*t181*t377+2.0*t474* +t873*t7+2.0*t1497*t1769; + t1834 = t1631*t16; + t1855 = 2.0*t11*t19*t151+2.0*t1582*t1834+2.0*t1465*t1772+2.0*t1504*t1755+ +2.0*t294*t862*t16+2.0*t1567*t1834+t637*t151+t625*t244+t312*t151+2.0*t19*t1819+ +2.0*t1484*t1769+2.0*t1585*t1791; + partial_Theta_X_wrt_partial_dd_h_22 = (t1777+t1803+t1830+t1855)*t792+(- +t71*t151-2.0*t1766-2.0*t1794-t101*t244-2.0*t1809-t59*t377)*t824; + partial_Theta_Y_wrt_partial_dd_h_11 = RATIONAL(0.0,1.0); + partial_Theta_Y_wrt_partial_dd_h_12 = RATIONAL(0.0,1.0); + partial_Theta_Y_wrt_partial_dd_h_22 = RATIONAL(0.0,1.0); |