# Speed up and make successful a definite Integrate of 3 variables?

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 HI, I have a vector field in a form of mHi3ret[x,y,z}={f[x,y,z],g[x,y,z],h[x,y,z]}. I need to integrate the first component f[x,y,z] over a rectangular area. f[x,y,z] is has many tags in different forms of elementary function like: 1. (0. + 1. (-0.1 + 1. (0. + 1.25664*10^-6 (1.05042*10^6 (OutputSizeLimitSkeleton[1]) + 1.32*10^7 UnitStep[ QuantityMagnitude[ 0.000025 - (-0.1 + 1. (0. + 1. (0.1 + OutputSizeLimitSkeleton[ 1])))^2]] UnitStep[ QuantityMagnitude[ 0.000025 - 1. (0. + 1. (OutputSizeLimitSkeleton[1]))^2]] UnitStep[ QuantityMagnitude[ 0.000025 - 1. (0. + 1. (0.1 - 1. z))^2]]))) + 1. (OutputSizeLimitSkeleton[1]) + 1. (OutputSizeLimitSkeleton[1]) + 1. (0.120359 - 1. (0. - 0.304293 (OutputSizeLimitSkeleton[1]) + 1.22279*10^-6 (OutputSizeLimitSkeleton[1]))) + 1. (0. + 1. (0. + 1.24046 (((-0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2)/((-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 OutputSizeLimitSkeleton[1] - 0.341889 (0. + OutputSizeLimitSkeleton[ 1])))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^( 3/2) - (-0.005 - 1. (0. + 1. (0. + 1. y)))/ Sqrt[(-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2] - ((0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (OutputSizeLimitSkeleton[ 1]))^2)/((OutputSizeLimitSkeleton[6] - OutputSizeLimitSkeleton[1])^2 + OutputSizeLimitSkeleton[ 1]^2 + (OutputSizeLimitSkeleton[1])^2)^(3/2) + OutputSizeLimitSkeleton[210] + Log[0.005 - 1. (0. + 1. (0. + 1. y)) + Sqrt[(0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2]]) + 4.2963*10^-7 (1.05042*10^6 (((-0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))) (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))))/((-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^( 3/2) - ((0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))) (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))))/((0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^( 3/2) - ((-0.005 - 1. (0. + 1. (0. + 1. y))) (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))) (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))))/((-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^( 3/2) + ((0.005 - 1. (0. + 1. (0. + 1. y))) (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))) (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))))/((0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^( 3/2) - ((-0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))) (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))))/((-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^( 3/2) + ((0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))) (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))))/((0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2)^(3/2) + OutputSizeLimitSkeleton[152] + ArcTan[((0.005 - 1. (0. + 1. (0. + 1. y))) (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))))/((0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))) Sqrt[(0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.095 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2])] - ArcTan[((-0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))))/((0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))) Sqrt[(-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2])] + ArcTan[((0.005 - 1. (0. + 1. (0. + 1. y))) (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))))/((0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))) Sqrt[(0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (-0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2])] + ArcTan[((-0.005 - 1. (0. + 1. (0. + 1. y))) (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))))/((0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))) Sqrt[(-0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2])] - ArcTan[((0.005 - 1. (0. + 1. (0. + 1. y))) (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))))/((0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z))) Sqrt[(0.005 - 1. (0. + 1. (0. + 1. y)))^2 + (0.005 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z)))^2 + (0.105 - 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2])]) + 1.32*10^7 UnitStep[ QuantityMagnitude[ 0.000025 - 1. (0. + 1. (0. + 1. y))^2]] UnitStep[ QuantityMagnitude[ 0.000025 - 1. (0. + 0.93974 (0. + 1. x) - 0.341889 (0. + 1. z))^2]] UnitStep[ QuantityMagnitude[ 0.000025 - (-0.1 + 1. (0. + 0.341889 (0. + 1. x) + 0.93974 (0. + 1. z)))^2]])))) + OutputSizeLimitSkeleton[3] + 1. (OutputSizeLimitSkeleton[1]) So I try to do something like: mflx = Integrate[ mHi3ret[[1, 1]], {y, -cb/2, cb/2}, {z, R - c/2 - cmg - cb, }] /. x -> 0.0; // AbsoluteTiming where a = b = c = 0.01; R = 0.1; cb = 1.5*b; cc = 2*c; cd = a/20; cn = 10; cmg = c/10; all are some numerical values. Mathematica runs for hours, eats up good amount of real and virtual memory and ultimately OS X kills it. Here is an Activity Monitor stage after 3 hours of run.Any good hint to be able to have the Integrate finish its job? Thanks ahead, János
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