diff options
Diffstat (limited to 'src/gr.cg/expansion.c')
| -rw-r--r-- | src/gr.cg/expansion.c | 349 |
1 files changed, 175 insertions, 174 deletions
diff --git a/src/gr.cg/expansion.c b/src/gr.cg/expansion.c index 65f3677..e9e0161 100644 --- a/src/gr.cg/expansion.c +++ b/src/gr.cg/expansion.c @@ -1,182 +1,183 @@ /* - * inputs = {r, partial_d_ln_sqrt_g, partial_d_g_uu, X_ud, X_udd, g_uu, K_uu, h} + * inputs = {partial_d_ln_sqrt_g, partial_d_g_uu, r, X_ud, X_udd, g_uu, K_uu, h} * outputs = {Theta_A, Theta_B, Theta_C, Theta_D} - * cost = 134*assignments+401*multiplications+3*divisions+5*functions+173*additions + * cost = 134*assignments+3*divisions+5*functions+401*multiplications+173*additions */ -fp t1, t2, t3, t5, t6, t8, t9, t11, t12, t14; -fp t15, t17, t19, t25, t26, t27, t29, t31, t34, t35; -fp t37, t39, t40, t42, t44, t46, t47, t49, t56, t61; -fp t63, t65, t66, t67, t82, t93, t98, t100, t102, t106; -fp t107, t110, t111, t112, t116, t119, t120, t121, t123, t124; -fp t127, t128, t129, t130, t131, t133, t134, t135, t137, t138; -fp t139, t141, t142, t143, t148, t149, t150, t153, t154, t155; -fp t158, t159, t160, t163, t164, t167, t168, t171, t172, t177; -fp t181, t182, t185, t186, t189, t191, t197, t198, t200, t205; -fp t220, t224, t232, t239, t266, t273, t276, t280, t283, t289; -fp t292, t302, t303, t306, t307, t310, t311, t314, t317, t326; -fp t330, t334, t337, t340, t343, t353, t355, t356, t360, t362; -fp t366, t382, t387, t394, t431, t440, t444, t447, t450, t465; +fp t1, t2, t4, t5, t7, t8, t10, t11, t12, t14; +fp t16, t18, t19, t21, t23, t29, t31, t33, t35, t40; +fp t42, t46, t47, t48, t49, t56, t61, t63, t67, t83; +fp t87, t102, t106, t107, t108, t109, t113, t116, t123, t128; +fp t130, t134, t135, t138, t139, t140, t141, t144, t145, t148; +fp t149, t155, t156, t159, t160, t161, t162, t163, t166, t167; +fp t168, t171, t172, t173, t176, t177, t180, t181, t182, t185; +fp t186, t197, t198, t205, t207, t210, t213, t221, t226, t228; +fp t230, t241, t242, t248, t255, t258, t259, t260, t263, t270; +fp t271, t274, t277, t278, t281, t282, t285, t291, t293, t294; +fp t295, t297, t298, t301, t304, t309, t318, t323, t324, t330; +fp t333, t340, t341, t344, t363, t369, t376, t378, t380, t384; +fp t393, t396, t398, t411, t431, t440, t444, t447, t450, t465; t1 = g_uu_13; - t2 = t1*t1; - t3 = 1/r; - t5 = X_ud_13; - t6 = PARTIAL_RHO(h); - t8 = X_ud_23; - t9 = PARTIAL_SIGMA(h); - t11 = zz*t3-t5*t6-t8*t9; - t12 = t11*t11; - t14 = yy*yy; - t15 = zz*zz; - t17 = r*r; - t19 = 1/t17/r; - t25 = X_ud_11; - t26 = t25*t25; - t27 = PARTIAL_RHO_RHO(h); - t29 = X_ud_21; - t31 = PARTIAL_RHO_SIGMA(h); - t34 = t29*t29; - t35 = PARTIAL_SIGMA_SIGMA(h); - t37 = (t14+t15)*t19-X_udd_111*t6-X_udd_211*t9-t26*t27-2.0*t29*t25*t31-t34 -*t35; - t39 = g_uu_23; - t40 = t39*t39; - t42 = X_ud_12; - t44 = X_ud_22; - t46 = yy*t3-t42*t6-t44*t9; - t47 = t46*t46; - t49 = xx*xx; - t56 = t5*t5; - t61 = t8*t8; - t63 = (t49+t14)*t19-X_udd_133*t6-X_udd_233*t9-t56*t27-2.0*t8*t5*t31-t61* -t35; - t65 = t1*t11; - t66 = g_uu_22; - t67 = t66*t46; - t82 = -xx*yy*t19-X_udd_112*t6-X_udd_212*t9-t25*t42*t27-t29*t42*t31-t25* -t44*t31-t29*t44*t35; - t93 = t42*t42; - t98 = t44*t44; - t100 = (t49+t15)*t19-X_udd_122*t6-X_udd_222*t9-t93*t27-2.0*t44*t42*t31- -t98*t35; - t102 = t39*t11; - t106 = t1*t12; - t107 = partial_d_g_uu_123; - t110 = g_uu_12; - t111 = t110*t47; - t112 = partial_d_g_uu_112; - t116 = xx*t3-t25*t6-t29*t9; - t119 = t66*t47; - t120 = partial_d_g_uu_212; - t121 = t120*t116; - t123 = t39*t47; - t124 = partial_d_g_uu_312; - t127 = g_uu_11; - t128 = t116*t116; - t129 = t127*t128; - t130 = partial_d_g_uu_113; - t131 = t130*t11; - t133 = t1*t128; - t134 = partial_d_g_uu_313; - t135 = t134*t11; - t137 = g_uu_33; - t138 = t137*t12; - t139 = t134*t116; - t141 = -t2*t12*t37-t40*t47*t63-2.0*t65*t67*t82-t40*t12*t100-2.0*t102*t67* -t100-t106*t107*t46-t111*t112*t116-t119*t121-t123*t124*t116-t129*t131-t133*t135- -t138*t139; - t142 = t39*t12; - t143 = partial_d_g_uu_213; - t148 = t1*t116; - t149 = partial_d_g_uu_322; - t150 = t149*t47; - t153 = t110*t116; - t154 = partial_d_g_uu_222; - t155 = t154*t47; - t158 = t127*t116; - t159 = partial_d_g_uu_122; - t160 = t159*t47; - t163 = partial_d_g_uu_333; - t164 = t163*t12; - t167 = partial_d_g_uu_133; - t168 = t167*t12; - t171 = partial_d_g_uu_233; - t172 = t171*t12; - t177 = t110*t46; - t181 = partial_d_g_uu_323; - t182 = t181*t11; - t185 = t137*t11; - t186 = t124*t46; - t189 = -t142*t143*t116-t106*t130*t116+RATIONAL(-1.0,2.0)*t148*t150+ -RATIONAL(-1.0,2.0)*t153*t155+RATIONAL(-1.0,2.0)*t158*t160+RATIONAL(-1.0,2.0)* -t148*t164+RATIONAL(-1.0,2.0)*t158*t168+RATIONAL(-1.0,2.0)*t153*t172+RATIONAL( --1.0,2.0)*t65*t160-2.0*t65*t177*t37-t148*t182*t46-t185*t186*t116; - t191 = t127*t127; - t197 = t110*t128; - t198 = t143*t11; - t200 = t137*t137; - t205 = t39*t46; - t220 = -xx*zz*t19-X_udd_113*t6-X_udd_213*t9-t25*t5*t27-t29*t5*t31-t25*t8* -t31-t29*t8*t35; - t224 = t12*t11; - t232 = t1*t220; - t239 = -t191*t128*t37-2.0*t142*t1*t82-t197*t198-t200*t12*t63-t177*t131* -t116-2.0*t65*t205*t220+RATIONAL(-1.0,2.0)*t39*t224*t171-t67*t198*t116-t205*t135 -*t116-2.0*t138*t232+RATIONAL(-1.0,2.0)*t205*t164+RATIONAL(-1.0,2.0)*t177*t168; - t266 = -yy*zz*t19-X_udd_123*t6-X_udd_223*t9-t42*t5*t27-t44*t5*t31-t42*t8* -t31-t44*t8*t35; - t273 = t110*t110; - t276 = t47*t46; - t280 = t39*t266; - t283 = t158*t37; - t289 = t148*t266; - t292 = RATIONAL(-1.0,2.0)*t67*t172+RATIONAL(-1.0,2.0)*t185*t150+RATIONAL( --1.0,2.0)*t102*t155-2.0*t197*t127*t82-2.0*t133*t127*t220-2.0*t133*t110*t266+ -RATIONAL(-1.0,2.0)*t1*t224*t167-t273*t128*t100+RATIONAL(-1.0,2.0)*t39*t276*t149 --2.0*t138*t280-2.0*t65*t283+RATIONAL(-1.0,2.0)*t110*t276*t159-2.0*t67*t289; - t302 = partial_d_g_uu_311; - t303 = t302*t128; - t306 = partial_d_g_uu_211; - t307 = t306*t128; - t310 = partial_d_g_uu_111; - t311 = t310*t128; - t314 = t148*t63; - t317 = t153*t266; - t326 = t107*t11; - t330 = RATIONAL(-1.0,2.0)*t66*t276*t154-2.0*t273*t46*t116*t82+RATIONAL( --1.0,2.0)*t205*t303+RATIONAL(-1.0,2.0)*t67*t307+RATIONAL(-1.0,2.0)*t177*t311 --2.0*t205*t314-2.0*t205*t317+RATIONAL(-1.0,2.0)*t185*t303+RATIONAL(-1.0,2.0)* -t102*t307+RATIONAL(-1.0,2.0)*t65*t311-t111*t326-t158*t326*t46; - t334 = t158*t82; - t337 = t110*t82; - t340 = t158*t220; - t343 = t153*t100; - t353 = t112*t46; - t355 = partial_d_g_uu_223; - t356 = t355*t11; - t360 = t120*t46; - t362 = -2.0*t177*t148*t220-2.0*t67*t334-2.0*t119*t337-2.0*t205*t340-2.0* -t67*t343+RATIONAL(-1.0,2.0)*t137*t224*t163-t2*t128*t63-t273*t47*t37-t129*t353- -t119*t356-t123*t182-t133*t186-t197*t360; - t366 = t181*t46; - t382 = t66*t66; - t387 = t128*t116; - t394 = -t142*t355*t46-t138*t366-2.0*t177*t283-2.0*t123*t110*t220-2.0*t123 -*t66*t266-t153*t356*t46-t65*t353*t116-t102*t360*t116-t382*t47*t100-2.0*t185* -t317+RATIONAL(-1.0,2.0)*t127*t387*t310+RATIONAL(-1.0,2.0)*t110*t387*t306; - t431 = RATIONAL(-1.0,2.0)*t1*t387*t302-2.0*t2*t11*t116*t220-2.0*t185*t314 --2.0*t102*t289-2.0*t65*t153*t82-2.0*t185*t205*t63-2.0*t40*t11*t46*t266-2.0*t102 -*t343-2.0*t102*t334-2.0*t185*t340-2.0*t102*t177*t82-2.0*t185*t67*t266-2.0*t185* -t177*t220; - Theta_A = t141+t189+t239+t292+t330+t362+t394+t431; - t440 = t310*t116+t121+t139+t353+t154*t46+t366+t131+t356+t163*t11+t127*t37 -+2.0*t337+2.0*t232; + 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_23; + t14 = X_ud_12; + t16 = X_ud_22; + t18 = yy*t2-t14*t5-t16*t8; + t19 = t12*t18; + t21 = r*r; + t23 = 1/t21/r; + t29 = X_ud_11; + t31 = PARTIAL_RHO_RHO(h); + t33 = X_ud_21; + t35 = PARTIAL_RHO_SIGMA(h); + t40 = PARTIAL_SIGMA_SIGMA(h); + t42 = -xx*zz*t23-X_udd_113*t5-X_udd_213*t8-t29*t4*t31-t33*t4*t35-t29*t7* +t35-t33*t7*t40; + t46 = g_uu_12; + t47 = t46*t18; + t48 = yy*yy; + t49 = zz*zz; + t56 = t29*t29; + t61 = t33*t33; + t63 = (t48+t49)*t23-X_udd_111*t5-X_udd_211*t8-t56*t31-2.0*t33*t29*t35-t61 +*t40; + t67 = t12*t12; + t83 = -yy*zz*t23-X_udd_123*t5-X_udd_223*t8-t14*t4*t31-t16*t4*t35-t14*t7* +t35-t16*t7*t40; + t87 = t12*t10; + t102 = -xx*yy*t23-X_udd_112*t5-X_udd_212*t8-t29*t14*t31-t33*t14*t35-t29* +t16*t35-t33*t16*t40; + t106 = g_uu_33; + t107 = t106*t10; + t108 = partial_d_g_uu_312; + t109 = t108*t18; + t113 = xx*t2-t29*t5-t33*t8; + t116 = xx*xx; + t123 = t4*t4; + t128 = t7*t7; + t130 = (t116+t48)*t23-X_udd_133*t5-X_udd_233*t8-t123*t31-2.0*t7*t4*t35- +t128*t40; + t134 = partial_d_g_uu_212; + t135 = t134*t18; + t138 = g_uu_22; + t139 = t138*t18; + t140 = partial_d_g_uu_213; + t141 = t140*t10; + t144 = partial_d_g_uu_113; + t145 = t144*t10; + t148 = partial_d_g_uu_313; + t149 = t148*t10; + t155 = t10*t10; + t156 = t12*t155; + t159 = -2.0*t11*t19*t42-2.0*t11*t47*t63-2.0*t67*t10*t18*t83-2.0*t87*t47* +t102-t107*t109*t113-2.0*t107*t19*t130-t87*t135*t113-t139*t141*t113-t47*t145* +t113-t19*t149*t113-2.0*t107*t139*t83-t156*t140*t113; + t160 = g_uu_11; + t161 = t160*t113; + t162 = partial_d_g_uu_133; + t163 = t162*t155; + t166 = t46*t113; + t167 = partial_d_g_uu_233; + t168 = t167*t155; + t171 = partial_d_g_uu_222; + t172 = t18*t18; + t173 = t171*t172; + t176 = partial_d_g_uu_122; + t177 = t176*t172; + t180 = t1*t113; + t181 = partial_d_g_uu_333; + t182 = t181*t155; + t185 = partial_d_g_uu_322; + t186 = t185*t172; + t197 = t113*t113; + t198 = t46*t197; + t205 = RATIONAL(-1.0,2.0)*t161*t163+RATIONAL(-1.0,2.0)*t166*t168+RATIONAL +(-1.0,2.0)*t166*t173+RATIONAL(-1.0,2.0)*t161*t177+RATIONAL(-1.0,2.0)*t180*t182+ +RATIONAL(-1.0,2.0)*t180*t186+RATIONAL(-1.0,2.0)*t47*t163+RATIONAL(-1.0,2.0)* +t139*t168+RATIONAL(-1.0,2.0)*t19*t182+RATIONAL(-1.0,2.0)*t11*t177-2.0*t198*t160 +*t102-2.0*t11*t139*t102; + t207 = t160*t160; + t210 = t106*t106; + t213 = t46*t46; + t221 = t14*t14; + t226 = t16*t16; + t228 = (t116+t49)*t23-X_udd_122*t5-X_udd_222*t8-t221*t31-2.0*t16*t14*t35- +t226*t40; + t230 = t1*t197; + t241 = partial_d_g_uu_112; + t242 = t241*t18; + t248 = t172*t18; + t255 = t180*t130; + t258 = -t207*t197*t63-t210*t155*t130-t213*t197*t228-2.0*t230*t160*t42-2.0 +*t230*t46*t83+RATIONAL(-1.0,2.0)*t107*t186+RATIONAL(-1.0,2.0)*t87*t173-t11*t242 +*t113-2.0*t47*t180*t42+RATIONAL(-1.0,2.0)*t12*t248*t185-2.0*t87*t139*t228-2.0* +t19*t255; + t259 = t106*t155; + t260 = t12*t83; + t263 = t180*t83; + t270 = partial_d_g_uu_123; + t271 = t270*t10; + t274 = t166*t228; + t277 = partial_d_g_uu_211; + t278 = t277*t197; + t281 = partial_d_g_uu_111; + t282 = t281*t197; + t285 = t161*t102; + t291 = t46*t172; + t293 = t138*t172; + t294 = partial_d_g_uu_223; + t295 = t294*t10; + t297 = partial_d_g_uu_311; + t298 = t297*t197; + t301 = t161*t42; + t304 = -2.0*t259*t260-2.0*t139*t263-2.0*t213*t18*t113*t102-t161*t271*t18 +-2.0*t139*t274+RATIONAL(-1.0,2.0)*t139*t278+RATIONAL(-1.0,2.0)*t47*t282-2.0* +t139*t285+RATIONAL(-1.0,2.0)*t138*t248*t171-t291*t271-t293*t295+RATIONAL(-1.0, +2.0)*t107*t298-2.0*t19*t301; + t309 = t1*t1; + t318 = t166*t83; + t323 = partial_d_g_uu_323; + t324 = t323*t10; + t330 = t161*t63; + t333 = t155*t10; + t340 = RATIONAL(-1.0,2.0)*t87*t278-t309*t197*t130-t213*t172*t63+RATIONAL( +-1.0,2.0)*t11*t282+RATIONAL(-1.0,2.0)*t19*t298-2.0*t19*t318-t166*t295*t18-t180* +t324*t18+RATIONAL(-1.0,2.0)*t46*t248*t176-2.0*t47*t330+RATIONAL(-1.0,2.0)*t12* +t333*t167+RATIONAL(-1.0,2.0)*t1*t333*t162; + t341 = t46*t102; + t344 = t12*t172; + t363 = t138*t138; + t369 = t1*t42; + t376 = -2.0*t293*t341-2.0*t344*t46*t42-2.0*t344*t138*t83+RATIONAL(-1.0, +2.0)*t106*t333*t181-t344*t324-t67*t172*t130-t309*t155*t63-t67*t155*t228-t156* +t294*t18-t363*t172*t228-2.0*t156*t1*t102-2.0*t259*t369-2.0*t309*t10*t113*t42; + t378 = t323*t18; + t380 = t160*t197; + t384 = t134*t113; + t393 = t1*t155; + t396 = t148*t113; + t398 = -t259*t378-t380*t242-t198*t135-t230*t109-t293*t384-t291*t241*t113- +t344*t108*t113-t198*t141-t380*t145-t230*t149-t393*t144*t113-t259*t396; + t411 = t197*t113; + t431 = -t393*t270*t18-2.0*t107*t47*t42-2.0*t11*t166*t102-2.0*t87*t274-2.0 +*t107*t255+RATIONAL(-1.0,2.0)*t160*t411*t281+RATIONAL(-1.0,2.0)*t46*t411*t277+ +RATIONAL(-1.0,2.0)*t1*t411*t297-2.0*t87*t263-2.0*t87*t285-2.0*t11*t330-2.0*t107 +*t318-2.0*t107*t301; + Theta_A = t159+t205+t258+t304+t340+t376+t398+t431; + t440 = t281*t113+t384+t396+t242+t171*t18+t378+t145+t295+t181*t10+t160*t63 ++2.0*t341+2.0*t369; t444 = partial_d_ln_sqrt_g_1; t447 = partial_d_ln_sqrt_g_2; t450 = partial_d_ln_sqrt_g_3; - t465 = t66*t100+2.0*t280+t137*t63+t127*t444*t116+t110*t447*t116+t1*t450* -t116+t110*t444*t46+t66*t447*t46+t39*t450*t46+t1*t444*t11+t39*t447*t11+t137*t450 -*t11; + t465 = t138*t228+2.0*t260+t106*t130+t160*t444*t113+t46*t447*t113+t1*t450* +t113+t46*t444*t18+t138*t447*t18+t12*t450*t18+t1*t444*t10+t12*t447*t10+t106*t450 +*t10; Theta_B = t440+t465; - Theta_C = K_uu_11*t128+2.0*K_uu_12*t46*t116+2.0*K_uu_13*t11*t116+K_uu_22* -t47+2.0*K_uu_23*t11*t46+K_uu_33*t12; - Theta_D = t129+2.0*t177*t116+2.0*t65*t116+t119+2.0*t102*t46+t138; + Theta_C = K_uu_11*t197+2.0*K_uu_12*t18*t113+2.0*K_uu_13*t10*t113+K_uu_22* +t172+2.0*K_uu_23*t10*t18+K_uu_33*t155; + Theta_D = t380+2.0*t47*t113+2.0*t11*t113+t293+2.0*t87*t18+t259; |