R/frankExpr.R

In copula: Multivariate Dependence with Copulas

### MM: Should "prove" (empirically, but systematically) that
###  copFrank() is "uniformly at least as good" as this

E <- exp(1)# will be used when the *.expr[d]  below are eval()ed

## MM: Really should improve some of these -- they are numerically unstable for non-small |alpha|

## This file is not to be edited. It is generated by ../inst/docs/mathnb/exprPrep.R
`frankCopula.cdf.expr` <-
expression(-(log(E^(-(alpha * u1)))/alpha), -(log(1 + ((-1 + 
    E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))))/(-1 + E^(-alpha)))/alpha), 
    -(log(1 + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * 
        u2))) * (-1 + E^(-(alpha * u3))))/(-1 + E^(-alpha))^2)/alpha), 
    -(log(1 + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * 
        u2))) * (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * 
        u4))))/(-1 + E^(-alpha))^3)/alpha), -(log(1 + ((-1 + 
        E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + 
        E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * (-1 + 
        E^(-(alpha * u5))))/(-1 + E^(-alpha))^4)/alpha), -(log(1 + 
        ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
            (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * 
            (-1 + E^(-(alpha * u5))) * (-1 + E^(-(alpha * u6))))/(-1 + 
            E^(-alpha))^5)/alpha))
`frankCopula.cdf.algr` <-
expression({
    .value <- -(log(E^-(alpha * u1))/alpha)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .value <- -(log(1 + (.expr1 + E^-(alpha * u1)) * (.expr1 + 
        E^-(alpha * u2))/(.expr1 + E^-alpha))/alpha)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .value <- -(log(1 + (.expr1 + E^-(alpha * u1)) * (.expr1 + 
        E^-(alpha * u2)) * (.expr1 + E^-(alpha * u3))/(.expr1 + 
        E^-alpha)^2)/alpha)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .value <- -(log(1 + (.expr1 + E^-(alpha * u1)) * (.expr1 + 
        E^-(alpha * u2)) * (.expr1 + E^-(alpha * u3)) * (.expr1 + 
        E^-(alpha * u4))/(.expr1 + E^-alpha)^3)/alpha)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .value <- -(log(1 + (.expr1 + E^-(alpha * u1)) * (.expr1 + 
        E^-(alpha * u2)) * (.expr1 + E^-(alpha * u3)) * (.expr1 + 
        E^-(alpha * u4)) * (.expr1 + E^-(alpha * u5))/(.expr1 + 
        E^-alpha)^4)/alpha)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .value <- -(log(1 + (.expr1 + E^-(alpha * u1)) * (.expr1 + 
        E^-(alpha * u2)) * (.expr1 + E^-(alpha * u3)) * (.expr1 + 
        E^-(alpha * u4)) * (.expr1 + E^-(alpha * u5)) * (.expr1 + 
        E^-(alpha * u6))/(.expr1 + E^-alpha)^5)/alpha)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`frankCopula.cdfDerWrtArg.expr` <-
expression(E^(-(alpha * u1)) * (log(E) * alpha)/E^(-(alpha * 
    u1))/alpha, E^(-(alpha * u1)) * (log(E) * alpha) * (-1 + 
    E^(-(alpha * u2)))/(-1 + E^(-alpha))/(1 + ((-1 + E^(-(alpha * 
    u1))) * (-1 + E^(-(alpha * u2))))/(-1 + E^(-alpha)))/alpha, 
    E^(-(alpha * u1)) * (log(E) * alpha) * (-1 + E^(-(alpha * 
        u2))) * (-1 + E^(-(alpha * u3)))/(-1 + E^(-alpha))^2/(1 + 
        ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
            (-1 + E^(-(alpha * u3))))/(-1 + E^(-alpha))^2)/alpha, 
    E^(-(alpha * u1)) * (log(E) * alpha) * (-1 + E^(-(alpha * 
        u2))) * (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * 
        u4)))/(-1 + E^(-alpha))^3/(1 + ((-1 + E^(-(alpha * u1))) * 
        (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * 
        (-1 + E^(-(alpha * u4))))/(-1 + E^(-alpha))^3)/alpha, 
    E^(-(alpha * u1)) * (log(E) * alpha) * (-1 + E^(-(alpha * 
        u2))) * (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * 
        u4))) * (-1 + E^(-(alpha * u5)))/(-1 + E^(-alpha))^4/(1 + 
        ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
            (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * 
            (-1 + E^(-(alpha * u5))))/(-1 + E^(-alpha))^4)/alpha, 
    E^(-(alpha * u1)) * (log(E) * alpha) * (-1 + E^(-(alpha * 
        u2))) * (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * 
        u4))) * (-1 + E^(-(alpha * u5))) * (-1 + E^(-(alpha * 
        u6)))/(-1 + E^(-alpha))^5/(1 + ((-1 + E^(-(alpha * u1))) * 
        (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * 
        (-1 + E^(-(alpha * u4))) * (-1 + E^(-(alpha * u5))) * 
        (-1 + E^(-(alpha * u6))))/(-1 + E^(-alpha))^5)/alpha)
`frankCopula.cdfDerWrtArg.algr` <-
expression({
    .expr3 <- E^-(alpha * u1)
    .value <- .expr3 * (log(E) * alpha)/.expr3/alpha
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- E^-(alpha * u1)
    .expr7 <- -1
    .expr11 <- .expr7 + E^-(alpha * u2)
    .expr15 <- .expr7 + E^-alpha
    .value <- .expr3 * (log(E) * alpha) * .expr11/.expr15/(1 + 
        (.expr7 + .expr3) * .expr11/.expr15)/alpha
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- E^-(alpha * u1)
    .expr7 <- -1
    .expr11 <- .expr7 + E^-(alpha * u2)
    .expr16 <- .expr7 + E^-(alpha * u3)
    .expr21 <- (.expr7 + E^-alpha)^2
    .value <- .expr3 * (log(E) * alpha) * .expr11 * .expr16/.expr21/(1 + 
        (.expr7 + .expr3) * .expr11 * .expr16/.expr21)/alpha
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- E^-(alpha * u1)
    .expr7 <- -1
    .expr11 <- .expr7 + E^-(alpha * u2)
    .expr16 <- .expr7 + E^-(alpha * u3)
    .expr21 <- .expr7 + E^-(alpha * u4)
    .expr26 <- (.expr7 + E^-alpha)^3
    .value <- .expr3 * (log(E) * alpha) * .expr11 * .expr16 * 
        .expr21/.expr26/(1 + (.expr7 + .expr3) * .expr11 * .expr16 * 
        .expr21/.expr26)/alpha
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- E^-(alpha * u1)
    .expr7 <- -1
    .expr11 <- .expr7 + E^-(alpha * u2)
    .expr16 <- .expr7 + E^-(alpha * u3)
    .expr21 <- .expr7 + E^-(alpha * u4)
    .expr26 <- .expr7 + E^-(alpha * u5)
    .expr31 <- (.expr7 + E^-alpha)^4
    .value <- .expr3 * (log(E) * alpha) * .expr11 * .expr16 * 
        .expr21 * .expr26/.expr31/(1 + (.expr7 + .expr3) * .expr11 * 
        .expr16 * .expr21 * .expr26/.expr31)/alpha
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- E^-(alpha * u1)
    .expr7 <- -1
    .expr11 <- .expr7 + E^-(alpha * u2)
    .expr16 <- .expr7 + E^-(alpha * u3)
    .expr21 <- .expr7 + E^-(alpha * u4)
    .expr26 <- .expr7 + E^-(alpha * u5)
    .expr31 <- .expr7 + E^-(alpha * u6)
    .expr36 <- (.expr7 + E^-alpha)^5
    .value <- .expr3 * (log(E) * alpha) * .expr11 * .expr16 * 
        .expr21 * .expr26 * .expr31/.expr36/(1 + (.expr7 + .expr3) * 
        .expr11 * .expr16 * .expr21 * .expr26 * .expr31/.expr36)/alpha
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`frankCopula.cdfDerWrtPar.expr` <-
expression(E^(-(alpha * u1)) * (log(E) * u1)/E^(-(alpha * u1))/alpha + 
    log(E^(-(alpha * u1)))/alpha^2, (((-1 + E^(-(alpha * u1))) * 
    (E^(-(alpha * u2)) * (log(E) * u2)) + E^(-(alpha * u1)) * 
    (log(E) * u1) * (-1 + E^(-(alpha * u2))))/(-1 + E^(-alpha)) - 
    ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2)))) * (E^(-alpha) * 
        log(E))/(-1 + E^(-alpha))^2)/(1 + ((-1 + E^(-(alpha * 
    u1))) * (-1 + E^(-(alpha * u2))))/(-1 + E^(-alpha)))/alpha + 
    log(1 + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))))/(-1 + 
        E^(-alpha)))/alpha^2, (((-1 + E^(-(alpha * u1))) * (-1 + 
    E^(-(alpha * u2))) * (E^(-(alpha * u3)) * (log(E) * u3)) + 
    ((-1 + E^(-(alpha * u1))) * (E^(-(alpha * u2)) * (log(E) * 
        u2)) + E^(-(alpha * u1)) * (log(E) * u1) * (-1 + E^(-(alpha * 
        u2)))) * (-1 + E^(-(alpha * u3))))/(-1 + E^(-alpha))^2 - 
    ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + 
        E^(-(alpha * u3)))) * (2 * (E^(-alpha) * log(E) * (-1 + 
        E^(-alpha))))/((-1 + E^(-alpha))^2)^2)/(1 + ((-1 + E^(-(alpha * 
    u1))) * (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))))/(-1 + 
    E^(-alpha))^2)/alpha + log(1 + ((-1 + E^(-(alpha * u1))) * 
    (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))))/(-1 + 
    E^(-alpha))^2)/alpha^2, (((-1 + E^(-(alpha * u1))) * (-1 + 
    E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * (E^(-(alpha * 
    u4)) * (log(E) * u4)) + ((-1 + E^(-(alpha * u1))) * (-1 + 
    E^(-(alpha * u2))) * (E^(-(alpha * u3)) * (log(E) * u3)) + 
    ((-1 + E^(-(alpha * u1))) * (E^(-(alpha * u2)) * (log(E) * 
        u2)) + E^(-(alpha * u1)) * (log(E) * u1) * (-1 + E^(-(alpha * 
        u2)))) * (-1 + E^(-(alpha * u3)))) * (-1 + E^(-(alpha * 
    u4))))/(-1 + E^(-alpha))^3 - ((-1 + E^(-(alpha * u1))) * 
    (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * (-1 + 
    E^(-(alpha * u4)))) * (3 * (E^(-alpha) * log(E) * (-1 + E^(-alpha))^2))/((-1 + 
    E^(-alpha))^3)^2)/(1 + ((-1 + E^(-(alpha * u1))) * (-1 + 
    E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * (-1 + E^(-(alpha * 
    u4))))/(-1 + E^(-alpha))^3)/alpha + log(1 + ((-1 + E^(-(alpha * 
    u1))) * (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * 
    (-1 + E^(-(alpha * u4))))/(-1 + E^(-alpha))^3)/alpha^2, (((-1 + 
    E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * 
    u3))) * (-1 + E^(-(alpha * u4))) * (E^(-(alpha * u5)) * (log(E) * 
    u5)) + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
    (-1 + E^(-(alpha * u3))) * (E^(-(alpha * u4)) * (log(E) * 
    u4)) + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
    (E^(-(alpha * u3)) * (log(E) * u3)) + ((-1 + E^(-(alpha * 
    u1))) * (E^(-(alpha * u2)) * (log(E) * u2)) + E^(-(alpha * 
    u1)) * (log(E) * u1) * (-1 + E^(-(alpha * u2)))) * (-1 + 
    E^(-(alpha * u3)))) * (-1 + E^(-(alpha * u4)))) * (-1 + E^(-(alpha * 
    u5))))/(-1 + E^(-alpha))^4 - ((-1 + E^(-(alpha * u1))) * 
    (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * (-1 + 
    E^(-(alpha * u4))) * (-1 + E^(-(alpha * u5)))) * (4 * (E^(-alpha) * 
    log(E) * (-1 + E^(-alpha))^3))/((-1 + E^(-alpha))^4)^2)/(1 + 
    ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + 
        E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * (-1 + 
        E^(-(alpha * u5))))/(-1 + E^(-alpha))^4)/alpha + log(1 + 
    ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + 
        E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * (-1 + 
        E^(-(alpha * u5))))/(-1 + E^(-alpha))^4)/alpha^2, (((-1 + 
    E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * 
    u3))) * (-1 + E^(-(alpha * u4))) * (-1 + E^(-(alpha * u5))) * 
    (E^(-(alpha * u6)) * (log(E) * u6)) + ((-1 + E^(-(alpha * 
    u1))) * (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * 
    (-1 + E^(-(alpha * u4))) * (E^(-(alpha * u5)) * (log(E) * 
    u5)) + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
    (-1 + E^(-(alpha * u3))) * (E^(-(alpha * u4)) * (log(E) * 
    u4)) + ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * 
    (E^(-(alpha * u3)) * (log(E) * u3)) + ((-1 + E^(-(alpha * 
    u1))) * (E^(-(alpha * u2)) * (log(E) * u2)) + E^(-(alpha * 
    u1)) * (log(E) * u1) * (-1 + E^(-(alpha * u2)))) * (-1 + 
    E^(-(alpha * u3)))) * (-1 + E^(-(alpha * u4)))) * (-1 + E^(-(alpha * 
    u5)))) * (-1 + E^(-(alpha * u6))))/(-1 + E^(-alpha))^5 - 
    ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + 
        E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * (-1 + 
        E^(-(alpha * u5))) * (-1 + E^(-(alpha * u6)))) * (5 * 
        (E^(-alpha) * log(E) * (-1 + E^(-alpha))^4))/((-1 + E^(-alpha))^5)^2)/(1 + 
    ((-1 + E^(-(alpha * u1))) * (-1 + E^(-(alpha * u2))) * (-1 + 
        E^(-(alpha * u3))) * (-1 + E^(-(alpha * u4))) * (-1 + 
        E^(-(alpha * u5))) * (-1 + E^(-(alpha * u6))))/(-1 + 
        E^(-alpha))^5)/alpha + log(1 + ((-1 + E^(-(alpha * u1))) * 
    (-1 + E^(-(alpha * u2))) * (-1 + E^(-(alpha * u3))) * (-1 + 
    E^(-(alpha * u4))) * (-1 + E^(-(alpha * u5))) * (-1 + E^(-(alpha * 
    u6))))/(-1 + E^(-alpha))^5)/alpha^2)
`frankCopula.cdfDerWrtPar.algr` <-
expression({
    .expr3 <- E^-(alpha * u1)
    .value <- .expr3 * (log(E) * u1)/.expr3/alpha + log(.expr3)/alpha^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .expr4 <- E^-(alpha * u1)
    .expr5 <- .expr1 + .expr4
    .expr8 <- E^-(alpha * u2)
    .expr9 <- log(E)
    .expr15 <- .expr1 + .expr8
    .expr19 <- E^-alpha
    .expr20 <- .expr1 + .expr19
    .expr22 <- .expr5 * .expr15
    .expr29 <- 1 + .expr22/.expr20
    .value <- ((.expr5 * (.expr8 * (.expr9 * u2)) + .expr4 * 
        (.expr9 * u1) * .expr15)/.expr20 - .expr22 * (.expr19 * 
        .expr9)/.expr20^2)/.expr29/alpha + log(.expr29)/alpha^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .expr4 <- E^-(alpha * u1)
    .expr5 <- .expr1 + .expr4
    .expr8 <- E^-(alpha * u2)
    .expr9 <- .expr1 + .expr8
    .expr10 <- .expr5 * .expr9
    .expr13 <- E^-(alpha * u3)
    .expr14 <- log(E)
    .expr25 <- .expr1 + .expr13
    .expr29 <- E^-alpha
    .expr30 <- .expr1 + .expr29
    .expr31 <- .expr30^2
    .expr33 <- .expr10 * .expr25
    .expr42 <- 1 + .expr33/.expr31
    .value <- ((.expr10 * (.expr13 * (.expr14 * u3)) + (.expr5 * 
        (.expr8 * (.expr14 * u2)) + .expr4 * (.expr14 * u1) * 
        .expr9) * .expr25)/.expr31 - .expr33 * (2 * (.expr29 * 
        .expr14 * .expr30))/.expr31^2)/.expr42/alpha + log(.expr42)/alpha^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .expr4 <- E^-(alpha * u1)
    .expr5 <- .expr1 + .expr4
    .expr8 <- E^-(alpha * u2)
    .expr9 <- .expr1 + .expr8
    .expr10 <- .expr5 * .expr9
    .expr13 <- E^-(alpha * u3)
    .expr14 <- .expr1 + .expr13
    .expr15 <- .expr10 * .expr14
    .expr18 <- E^-(alpha * u4)
    .expr19 <- log(E)
    .expr35 <- .expr1 + .expr18
    .expr39 <- E^-alpha
    .expr40 <- .expr1 + .expr39
    .expr41 <- .expr40^3
    .expr43 <- .expr15 * .expr35
    .expr53 <- 1 + .expr43/.expr41
    .value <- ((.expr15 * (.expr18 * (.expr19 * u4)) + (.expr10 * 
        (.expr13 * (.expr19 * u3)) + (.expr5 * (.expr8 * (.expr19 * 
        u2)) + .expr4 * (.expr19 * u1) * .expr9) * .expr14) * 
        .expr35)/.expr41 - .expr43 * (3 * (.expr39 * .expr19 * 
        .expr40^2))/.expr41^2)/.expr53/alpha + log(.expr53)/alpha^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .expr4 <- E^-(alpha * u1)
    .expr5 <- .expr1 + .expr4
    .expr8 <- E^-(alpha * u2)
    .expr9 <- .expr1 + .expr8
    .expr10 <- .expr5 * .expr9
    .expr13 <- E^-(alpha * u3)
    .expr14 <- .expr1 + .expr13
    .expr15 <- .expr10 * .expr14
    .expr18 <- E^-(alpha * u4)
    .expr19 <- .expr1 + .expr18
    .expr20 <- .expr15 * .expr19
    .expr23 <- E^-(alpha * u5)
    .expr24 <- log(E)
    .expr45 <- .expr1 + .expr23
    .expr49 <- E^-alpha
    .expr50 <- .expr1 + .expr49
    .expr51 <- .expr50^4
    .expr53 <- .expr20 * .expr45
    .expr63 <- 1 + .expr53/.expr51
    .value <- ((.expr20 * (.expr23 * (.expr24 * u5)) + (.expr15 * 
        (.expr18 * (.expr24 * u4)) + (.expr10 * (.expr13 * (.expr24 * 
        u3)) + (.expr5 * (.expr8 * (.expr24 * u2)) + .expr4 * 
        (.expr24 * u1) * .expr9) * .expr14) * .expr19) * .expr45)/.expr51 - 
        .expr53 * (4 * (.expr49 * .expr24 * .expr50^3))/.expr51^2)/.expr63/alpha + 
        log(.expr63)/alpha^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .expr4 <- E^-(alpha * u1)
    .expr5 <- .expr1 + .expr4
    .expr8 <- E^-(alpha * u2)
    .expr9 <- .expr1 + .expr8
    .expr10 <- .expr5 * .expr9
    .expr13 <- E^-(alpha * u3)
    .expr14 <- .expr1 + .expr13
    .expr15 <- .expr10 * .expr14
    .expr18 <- E^-(alpha * u4)
    .expr19 <- .expr1 + .expr18
    .expr20 <- .expr15 * .expr19
    .expr23 <- E^-(alpha * u5)
    .expr24 <- .expr1 + .expr23
    .expr25 <- .expr20 * .expr24
    .expr28 <- E^-(alpha * u6)
    .expr29 <- log(E)
    .expr55 <- .expr1 + .expr28
    .expr59 <- E^-alpha
    .expr60 <- .expr1 + .expr59
    .expr61 <- .expr60^5
    .expr63 <- .expr25 * .expr55
    .expr73 <- 1 + .expr63/.expr61
    .value <- ((.expr25 * (.expr28 * (.expr29 * u6)) + (.expr20 * 
        (.expr23 * (.expr29 * u5)) + (.expr15 * (.expr18 * (.expr29 * 
        u4)) + (.expr10 * (.expr13 * (.expr29 * u3)) + (.expr5 * 
        (.expr8 * (.expr29 * u2)) + .expr4 * (.expr29 * u1) * 
        .expr9) * .expr14) * .expr19) * .expr24) * .expr55)/.expr61 - 
        .expr63 * (5 * (.expr59 * .expr29 * .expr60^4))/.expr61^2)/.expr73/alpha + 
        log(.expr73)/alpha^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`frankCopula.pdf.expr` <-
expression(1, (alpha * E^(alpha * (1 + u1 + u2)) * (-1 + E^alpha))/(E^alpha - 
    E^(alpha + alpha * u1) + E^(alpha * (u1 + u2)) - E^(alpha + 
    alpha * u2))^2, (alpha^2 * E^(alpha * (-2 + u1 + u2 + u3)) * 
    (-1 + E^alpha)^2 * (-1 + E^(alpha * u1) + E^(alpha * u2) - 
    E^(alpha * (u1 + u2)) + E^(alpha * u3) - E^(alpha * (u1 + 
    u3)) - E^(alpha * (u2 + u3)) + E^(alpha * (-2 + u1 + u2 + 
    u3)) - 2 * E^(alpha * (-1 + u1 + u2 + u3)) + 2 * E^(alpha * 
    (u1 + u2 + u3))))/(1 - E^(alpha * u1) - E^(alpha * u2) + 
    E^(alpha * (u1 + u2)) - E^(alpha * u3) + E^(alpha * (u1 + 
    u3)) + E^(alpha * (u2 + u3)) + E^(alpha * (-2 + u1 + u2 + 
    u3)) - 2 * E^(alpha * (-1 + u1 + u2 + u3)))^3, (alpha^3 * 
    E^(alpha * (1 + u1 + u2 + u3 + u4)) * (-1 + E^(-alpha))^4 * 
    (-1 + E^alpha) * (1 - 2 * E^alpha + E^(2 * alpha) + (E^(2 * 
    alpha * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^8)/((-1 + 
    E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
    u3))^2 * (-1 + E^(alpha * u4))^2) - (4 * E^(alpha * (-3 + 
    u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
    u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
    E^(alpha * u4))) + (4 * E^(alpha * (-2 + u1 + u2 + u3 + u4)) * 
    (-1 + E^alpha)^4)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
    u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)))))/((-1 + 
    E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
    u3))^2 * (-1 + E^(alpha * u4))^2 * (1 - E^alpha + (E^(alpha * 
    (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
    u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
    E^(alpha * u4))))^4), -((alpha^4 * E^(alpha * (1 + u1 + u2 + 
    u3 + u4 + u5)) * (-1 + E^(-alpha))^5 * (-1 + E^alpha) * (-1 + 
    3 * E^alpha - 3 * E^(2 * alpha) + E^(3 * alpha) + (11 * E^(3 * 
    alpha) * (-1 + E^(-alpha))^10)/((-1 + E^(-(alpha * u1)))^2 * 
    (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * 
    (-1 + E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * u5)))^2) + 
    (E^(3 * alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^15)/((-1 + 
        E^(alpha * u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * 
        u3))^3 * (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3) - 
    (11 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
        E^alpha)^10)/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
        (-1 + E^(alpha * u5))^2) + (11 * E^(alpha * (-4 + u1 + 
    u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * 
    u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
    E^(alpha * u4)) * (-1 + E^(alpha * u5))) - (22 * E^(alpha * 
    (-3 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
    E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
    u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))) + (11 * 
    E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
    E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
    u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)))))/((-1 + 
    E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
    u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
    (1 - E^alpha + (E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
        (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
        u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
        (-1 + E^(alpha * u5))))^5)), (alpha^5 * E^(alpha * (1 + 
    u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^(-alpha))^6 * (-1 + 
    E^alpha) * (1 - 4 * E^alpha + 6 * E^(2 * alpha) - 4 * E^(3 * 
    alpha) + E^(4 * alpha) + (26 * E^(4 * alpha) * (-1 + E^(-alpha))^18)/((-1 + 
    E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * (-1 + 
    E^(-(alpha * u3)))^3 * (-1 + E^(-(alpha * u4)))^3 * (-1 + 
    E^(-(alpha * u5)))^3 * (-1 + E^(-(alpha * u6)))^3) - (132 * 
    E^(3 * alpha) * (-1 + E^(-alpha))^12)/((-1 + E^(-(alpha * 
    u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * 
    u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * 
    u5)))^2 * (-1 + E^(-(alpha * u6)))^2) + (E^(4 * alpha * (-5 + 
    u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^24)/((-1 + 
    E^(alpha * u1))^4 * (-1 + E^(alpha * u2))^4 * (-1 + E^(alpha * 
    u3))^4 * (-1 + E^(alpha * u4))^4 * (-1 + E^(alpha * u5))^4 * 
    (-1 + E^(alpha * u6))^4) - (26 * E^(3 * alpha * (-5 + u1 + 
    u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^18)/((-1 + E^(alpha * 
    u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * 
    (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + 
    E^(alpha * u6))^3) + (66 * E^(2 * alpha * (-5 + u1 + u2 + 
    u3 + u4 + u5 + u6)) * (-1 + E^alpha)^12)/((-1 + E^(alpha * 
    u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
    (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + 
    E^(alpha * u6))^2) + (66 * E^(2 * alpha * (-4 + u1 + u2 + 
    u3 + u4 + u5 + u6)) * (-1 + E^alpha)^12)/((-1 + E^(alpha * 
    u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
    (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + 
    E^(alpha * u6))^2) - (26 * E^(alpha * (-5 + u1 + u2 + u3 + 
    u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * 
    (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
    u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) + (78 * 
    E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
    E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
    u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + 
    E^(alpha * u6))) - (78 * E^(alpha * (-3 + u1 + u2 + u3 + 
    u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * 
    (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
    u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) + (26 * 
    E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
    E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
    u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + 
    E^(alpha * u6)))))/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
    u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
    (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2 * (1 - 
    E^alpha + (E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
    (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
    u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + 
    E^(alpha * u5)) * (-1 + E^(alpha * u6))))^6))
`frankCopula.pdf.algr` <-
expression({
    .value <- 1
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr7 <- E^alpha
    .value <- alpha * E^(alpha * (1 + u1 + u2)) * (-1 + .expr7)/(.expr7 - 
        E^(alpha + alpha * u1) + E^(alpha * (u1 + u2)) - E^(alpha + 
        alpha * u2))^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr7 <- E^(alpha * (-2 + u1 + u2 + u3))
    .expr9 <- -1
    .expr15 <- E^(alpha * u1)
    .expr18 <- E^(alpha * u2)
    .expr20 <- u1 + u2
    .expr22 <- E^(alpha * .expr20)
    .expr25 <- E^(alpha * u3)
    .expr29 <- E^(alpha * (u1 + u3))
    .expr33 <- E^(alpha * (u2 + u3))
    .expr41 <- 2 * E^(alpha * (.expr9 + u1 + u2 + u3))
    .value <- alpha^2 * .expr7 * (.expr9 + E^alpha)^2 * (.expr9 + 
        .expr15 + .expr18 - .expr22 + .expr25 - .expr29 - .expr33 + 
        .expr7 - .expr41 + 2 * E^(alpha * (.expr20 + u3)))/(1 - 
        .expr15 - .expr18 + .expr22 - .expr25 + .expr29 + .expr33 + 
        .expr7 - .expr41)^3
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr9 <- -1
    .expr15 <- E^alpha
    .expr16 <- .expr9 + .expr15
    .expr20 <- 2 * alpha
    .expr27 <- -3 + u1 + u2 + u3 + u4
    .expr34 <- .expr9 + E^(alpha * u1)
    .expr38 <- .expr9 + E^(alpha * u2)
    .expr43 <- .expr9 + E^(alpha * u3)
    .expr48 <- .expr9 + E^(alpha * u4)
    .expr50 <- .expr34^2 * .expr38^2 * .expr43^2 * .expr48^2
    .expr54 <- E^(alpha * .expr27)
    .expr56 <- .expr16^4
    .expr60 <- .expr34 * .expr38 * .expr43 * .expr48
    .value <- alpha^3 * E^(alpha * (1 + u1 + u2 + u3 + u4)) * 
        (.expr9 + E^-alpha)^4 * .expr16 * (1 - 2 * .expr15 + 
        E^.expr20 + E^(.expr20 * .expr27) * .expr16^8/.expr50 - 
        4 * .expr54 * .expr56/.expr60 + 4 * E^(alpha * (-2 + 
        u1 + u2 + u3 + u4)) * .expr56/.expr60)/(.expr50 * (1 - 
        .expr15 + .expr54 * .expr56/.expr60)^4)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr10 <- -1
    .expr13 <- .expr10 + E^-alpha
    .expr16 <- E^alpha
    .expr17 <- .expr10 + .expr16
    .expr21 <- 2 * alpha
    .expr25 <- 3 * alpha
    .expr26 <- E^.expr25
    .expr31 <- alpha * u1
    .expr36 <- alpha * u2
    .expr42 <- alpha * u3
    .expr48 <- alpha * u4
    .expr54 <- alpha * u5
    .expr67 <- -4 + u1 + u2 + u3 + u4 + u5
    .expr73 <- .expr10 + E^.expr31
    .expr76 <- .expr10 + E^.expr36
    .expr80 <- .expr10 + E^.expr42
    .expr84 <- .expr10 + E^.expr48
    .expr88 <- .expr10 + E^.expr54
    .expr106 <- .expr73^2 * .expr76^2 * .expr80^2 * .expr84^2 * 
        .expr88^2
    .expr110 <- E^(alpha * .expr67)
    .expr112 <- .expr17^5
    .expr117 <- .expr73 * .expr76 * .expr80 * .expr84 * .expr88
    .value <- -(alpha^4 * E^(alpha * (1 + u1 + u2 + u3 + u4 + 
        u5)) * .expr13^5 * .expr17 * (.expr10 + 3 * .expr16 - 
        3 * E^.expr21 + .expr26 + 11 * .expr26 * .expr13^10/((.expr10 + 
        E^-.expr31)^2 * (.expr10 + E^-.expr36)^2 * (.expr10 + 
        E^-.expr42)^2 * (.expr10 + E^-.expr48)^2 * (.expr10 + 
        E^-.expr54)^2) + E^(.expr25 * .expr67) * .expr17^15/(.expr73^3 * 
        .expr76^3 * .expr80^3 * .expr84^3 * .expr88^3) - 11 * 
        E^(.expr21 * .expr67) * .expr17^10/.expr106 + 11 * .expr110 * 
        .expr112/.expr117 - 22 * E^(alpha * (-3 + u1 + u2 + u3 + 
        u4 + u5)) * .expr112/.expr117 + 11 * E^(alpha * (-2 + 
        u1 + u2 + u3 + u4 + u5)) * .expr112/.expr117)/(.expr106 * 
        (1 - .expr16 + .expr110 * .expr112/.expr117)^5))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr11 <- -1
    .expr14 <- .expr11 + E^-alpha
    .expr17 <- E^alpha
    .expr18 <- .expr11 + .expr17
    .expr22 <- 2 * alpha
    .expr26 <- 3 * alpha
    .expr27 <- E^.expr26
    .expr30 <- 4 * alpha
    .expr31 <- E^.expr30
    .expr36 <- alpha * u1
    .expr39 <- .expr11 + E^-.expr36
    .expr41 <- alpha * u2
    .expr44 <- .expr11 + E^-.expr41
    .expr47 <- alpha * u3
    .expr50 <- .expr11 + E^-.expr47
    .expr53 <- alpha * u4
    .expr56 <- .expr11 + E^-.expr53
    .expr59 <- alpha * u5
    .expr62 <- .expr11 + E^-.expr59
    .expr65 <- alpha * u6
    .expr68 <- .expr11 + E^-.expr65
    .expr95 <- -5 + u1 + u2 + u3 + u4 + u5 + u6
    .expr101 <- .expr11 + E^.expr36
    .expr104 <- .expr11 + E^.expr41
    .expr108 <- .expr11 + E^.expr47
    .expr112 <- .expr11 + E^.expr53
    .expr116 <- .expr11 + E^.expr59
    .expr120 <- .expr11 + E^.expr65
    .expr146 <- .expr18^12
    .expr158 <- .expr101^2 * .expr104^2 * .expr108^2 * .expr112^2 * 
        .expr116^2 * .expr120^2
    .expr167 <- -4 + u1 + u2 + u3 + u4 + u5 + u6
    .expr175 <- E^(alpha * .expr95)
    .expr177 <- .expr18^6
    .expr183 <- .expr101 * .expr104 * .expr108 * .expr112 * .expr116 * 
        .expr120
    .value <- alpha^5 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5 + 
        u6)) * .expr14^6 * .expr18 * (1 - 4 * .expr17 + 6 * E^.expr22 - 
        4 * .expr27 + .expr31 + 26 * .expr31 * .expr14^18/(.expr39^3 * 
        .expr44^3 * .expr50^3 * .expr56^3 * .expr62^3 * .expr68^3) - 
        132 * .expr27 * .expr14^12/(.expr39^2 * .expr44^2 * .expr50^2 * 
            .expr56^2 * .expr62^2 * .expr68^2) + E^(.expr30 * 
        .expr95) * .expr18^24/(.expr101^4 * .expr104^4 * .expr108^4 * 
        .expr112^4 * .expr116^4 * .expr120^4) - 26 * E^(.expr26 * 
        .expr95) * .expr18^18/(.expr101^3 * .expr104^3 * .expr108^3 * 
        .expr112^3 * .expr116^3 * .expr120^3) + 66 * E^(.expr22 * 
        .expr95) * .expr146/.expr158 + 66 * E^(.expr22 * .expr167) * 
        .expr146/.expr158 - 26 * .expr175 * .expr177/.expr183 + 
        78 * E^(alpha * .expr167) * .expr177/.expr183 - 78 * 
        E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5 + u6)) * .expr177/.expr183 + 
        26 * E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            .expr177/.expr183)/(.expr158 * (1 - .expr17 + .expr175 * 
        .expr177/.expr183)^6)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`frankCopula.pdfDerWrtArg.expr` <-
expression(0, alpha * (E^(alpha * (1 + u1 + u2)) * (log(E) * 
    alpha)) * (-1 + E^alpha)/(E^alpha - E^(alpha + alpha * u1) + 
    E^(alpha * (u1 + u2)) - E^(alpha + alpha * u2))^2 - (alpha * 
    E^(alpha * (1 + u1 + u2)) * (-1 + E^alpha)) * (2 * ((E^(alpha * 
    (u1 + u2)) * (log(E) * alpha) - E^(alpha + alpha * u1) * 
    (log(E) * alpha)) * (E^alpha - E^(alpha + alpha * u1) + E^(alpha * 
    (u1 + u2)) - E^(alpha + alpha * u2))))/((E^alpha - E^(alpha + 
    alpha * u1) + E^(alpha * (u1 + u2)) - E^(alpha + alpha * 
    u2))^2)^2, (alpha^2 * (E^(alpha * (-2 + u1 + u2 + u3)) * 
    (log(E) * alpha)) * (-1 + E^alpha)^2 * (-1 + E^(alpha * u1) + 
    E^(alpha * u2) - E^(alpha * (u1 + u2)) + E^(alpha * u3) - 
    E^(alpha * (u1 + u3)) - E^(alpha * (u2 + u3)) + E^(alpha * 
    (-2 + u1 + u2 + u3)) - 2 * E^(alpha * (-1 + u1 + u2 + u3)) + 
    2 * E^(alpha * (u1 + u2 + u3))) + alpha^2 * E^(alpha * (-2 + 
    u1 + u2 + u3)) * (-1 + E^alpha)^2 * (E^(alpha * u1) * (log(E) * 
    alpha) - E^(alpha * (u1 + u2)) * (log(E) * alpha) - E^(alpha * 
    (u1 + u3)) * (log(E) * alpha) + E^(alpha * (-2 + u1 + u2 + 
    u3)) * (log(E) * alpha) - 2 * (E^(alpha * (-1 + u1 + u2 + 
    u3)) * (log(E) * alpha)) + 2 * (E^(alpha * (u1 + u2 + u3)) * 
    (log(E) * alpha))))/(1 - E^(alpha * u1) - E^(alpha * u2) + 
    E^(alpha * (u1 + u2)) - E^(alpha * u3) + E^(alpha * (u1 + 
    u3)) + E^(alpha * (u2 + u3)) + E^(alpha * (-2 + u1 + u2 + 
    u3)) - 2 * E^(alpha * (-1 + u1 + u2 + u3)))^3 - (alpha^2 * 
    E^(alpha * (-2 + u1 + u2 + u3)) * (-1 + E^alpha)^2 * (-1 + 
    E^(alpha * u1) + E^(alpha * u2) - E^(alpha * (u1 + u2)) + 
    E^(alpha * u3) - E^(alpha * (u1 + u3)) - E^(alpha * (u2 + 
    u3)) + E^(alpha * (-2 + u1 + u2 + u3)) - 2 * E^(alpha * (-1 + 
    u1 + u2 + u3)) + 2 * E^(alpha * (u1 + u2 + u3)))) * (3 * 
    ((E^(alpha * (u1 + u2)) * (log(E) * alpha) - E^(alpha * u1) * 
        (log(E) * alpha) + E^(alpha * (u1 + u3)) * (log(E) * 
        alpha) + E^(alpha * (-2 + u1 + u2 + u3)) * (log(E) * 
        alpha) - 2 * (E^(alpha * (-1 + u1 + u2 + u3)) * (log(E) * 
        alpha))) * (1 - E^(alpha * u1) - E^(alpha * u2) + E^(alpha * 
        (u1 + u2)) - E^(alpha * u3) + E^(alpha * (u1 + u3)) + 
        E^(alpha * (u2 + u3)) + E^(alpha * (-2 + u1 + u2 + u3)) - 
        2 * E^(alpha * (-1 + u1 + u2 + u3)))^2))/((1 - E^(alpha * 
    u1) - E^(alpha * u2) + E^(alpha * (u1 + u2)) - E^(alpha * 
    u3) + E^(alpha * (u1 + u3)) + E^(alpha * (u2 + u3)) + E^(alpha * 
    (-2 + u1 + u2 + u3)) - 2 * E^(alpha * (-1 + u1 + u2 + u3)))^3)^2, 
    (alpha^3 * (E^(alpha * (1 + u1 + u2 + u3 + u4)) * (log(E) * 
        alpha)) * (-1 + E^(-alpha))^4 * (-1 + E^alpha) * (1 - 
        2 * E^alpha + E^(2 * alpha) + (E^(2 * alpha * (-3 + u1 + 
        u2 + u3 + u4)) * (-1 + E^alpha)^8)/((-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (-1 + E^(alpha * u4))^2) - (4 * E^(alpha * (-3 + u1 + 
        u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4))) + (4 * E^(alpha * (-2 + u1 + u2 + 
        u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)))) + alpha^3 * E^(alpha * (1 + u1 + u2 + 
        u3 + u4)) * (-1 + E^(-alpha))^4 * (-1 + E^alpha) * (E^(2 * 
        alpha * (-3 + u1 + u2 + u3 + u4)) * (log(E) * (2 * alpha)) * 
        (-1 + E^alpha)^8/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2) - 
        (E^(2 * alpha * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^8) * 
            (2 * (E^(alpha * u1) * (log(E) * alpha) * (-1 + E^(alpha * 
                u1))) * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
                u3))^2 * (-1 + E^(alpha * u4))^2)/((-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2)^2 - (4 * (E^(alpha * 
        (-3 + u1 + u2 + u3 + u4)) * (log(E) * alpha)) * (-1 + 
        E^alpha)^4/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
        u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4))) - 
        (4 * E^(alpha * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4) * 
            (E^(alpha * u1) * (log(E) * alpha) * (-1 + E^(alpha * 
                u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                u4)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)))^2) + 
        (4 * (E^(alpha * (-2 + u1 + u2 + u3 + u4)) * (log(E) * 
            alpha)) * (-1 + E^alpha)^4/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4))) - (4 * E^(alpha * (-2 + u1 + u2 + 
            u3 + u4)) * (-1 + E^alpha)^4) * (E^(alpha * u1) * 
            (log(E) * alpha) * (-1 + E^(alpha * u2)) * (-1 + 
            E^(alpha * u3)) * (-1 + E^(alpha * u4)))/((-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)))^2)))/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (1 - E^alpha + (E^(alpha * (-3 + 
        u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4))))^4) - (alpha^3 * E^(alpha * (1 + 
        u1 + u2 + u3 + u4)) * (-1 + E^(-alpha))^4 * (-1 + E^alpha) * 
        (1 - 2 * E^alpha + E^(2 * alpha) + (E^(2 * alpha * (-3 + 
            u1 + u2 + u3 + u4)) * (-1 + E^alpha)^8)/((-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2) - (4 * E^(alpha * 
            (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4))) + (4 * E^(alpha * (-2 + 
            u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4))))) * (2 * (E^(alpha * u1) * 
        (log(E) * alpha) * (-1 + E^(alpha * u1))) * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
        (1 - E^alpha + (E^(alpha * (-3 + u1 + u2 + u3 + u4)) * 
            (-1 + E^alpha)^4)/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4))))^4 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
        (4 * ((E^(alpha * (-3 + u1 + u2 + u3 + u4)) * (log(E) * 
            alpha) * (-1 + E^alpha)^4/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4))) - (E^(alpha * (-3 + u1 + u2 + u3 + 
            u4)) * (-1 + E^alpha)^4) * (E^(alpha * u1) * (log(E) * 
            alpha) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)))/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4)))^2) * (1 - E^alpha + (E^(alpha * 
            (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4))))^3)))/((-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (-1 + E^(alpha * u4))^2 * (1 - E^alpha + (E^(alpha * 
        (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4))))^4)^2, -((alpha^4 * (E^(alpha * 
        (1 + u1 + u2 + u3 + u4 + u5)) * (log(E) * alpha)) * (-1 + 
        E^(-alpha))^5 * (-1 + E^alpha) * (-1 + 3 * E^alpha - 
        3 * E^(2 * alpha) + E^(3 * alpha) + (11 * E^(3 * alpha) * 
        (-1 + E^(-alpha))^10)/((-1 + E^(-(alpha * u1)))^2 * (-1 + 
        E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (-1 + 
        E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * u5)))^2) + 
        (E^(3 * alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
            E^alpha)^15)/((-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
            u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + E^(alpha * 
            u4))^3 * (-1 + E^(alpha * u5))^3) - (11 * E^(2 * 
        alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^10)/((-1 + 
        E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
        u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2) + 
        (11 * E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
            E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5))) - (22 * E^(alpha * (-3 + u1 + 
        u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))) + (11 * 
        E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)))) + 
        alpha^4 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5)) * 
            (-1 + E^(-alpha))^5 * (-1 + E^alpha) * ((11 * E^(3 * 
            alpha) * (-1 + E^(-alpha))^10) * (2 * (E^(-(alpha * 
            u1)) * (log(E) * alpha) * (-1 + E^(-(alpha * u1)))) * 
            (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * 
            (-1 + E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * u5)))^2)/((-1 + 
            E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
            (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * 
            (-1 + E^(-(alpha * u5)))^2)^2 + (E^(3 * alpha * (-4 + 
            u1 + u2 + u3 + u4 + u5)) * (log(E) * (3 * alpha)) * 
            (-1 + E^alpha)^15/((-1 + E^(alpha * u1))^3 * (-1 + 
            E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + 
            E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3) - (E^(3 * 
            alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^15) * 
            (3 * (E^(alpha * u1) * (log(E) * alpha) * (-1 + E^(alpha * 
                u1))^2) * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * 
                u3))^3 * (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * 
                u5))^3)/((-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
            u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + E^(alpha * 
            u4))^3 * (-1 + E^(alpha * u5))^3)^2) - (11 * (E^(2 * 
            alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (log(E) * 
            (2 * alpha))) * (-1 + E^alpha)^10/((-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
            u5))^2) - (11 * E^(2 * alpha * (-4 + u1 + u2 + u3 + 
            u4 + u5)) * (-1 + E^alpha)^10) * (2 * (E^(alpha * 
            u1) * (log(E) * alpha) * (-1 + E^(alpha * u1))) * 
            (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
            (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2)/((-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + 
            E^(alpha * u5))^2)^2) + (11 * (E^(alpha * (-4 + u1 + 
            u2 + u3 + u4 + u5)) * (log(E) * alpha)) * (-1 + E^alpha)^5/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))) - 
            (11 * E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
                (-1 + E^alpha)^5) * (E^(alpha * u1) * (log(E) * 
                alpha) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
                u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                u4)) * (-1 + E^(alpha * u5)))^2) - (22 * (E^(alpha * 
            (-3 + u1 + u2 + u3 + u4 + u5)) * (log(E) * alpha)) * 
            (-1 + E^alpha)^5/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5))) - (22 * E^(alpha * (-3 + u1 + 
            u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5) * (E^(alpha * 
            u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * 
            (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + 
            E^(alpha * u5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5)))^2) + (11 * (E^(alpha * (-2 + 
            u1 + u2 + u3 + u4 + u5)) * (log(E) * alpha)) * (-1 + 
            E^alpha)^5/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5))) - (11 * E^(alpha * (-2 + u1 + 
            u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5) * (E^(alpha * 
            u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * 
            (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + 
            E^(alpha * u5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5)))^2)))/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (1 - E^alpha + 
        (E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))))^5) - 
        (alpha^4 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5)) * 
            (-1 + E^(-alpha))^5 * (-1 + E^alpha) * (-1 + 3 * 
            E^alpha - 3 * E^(2 * alpha) + E^(3 * alpha) + (11 * 
            E^(3 * alpha) * (-1 + E^(-alpha))^10)/((-1 + E^(-(alpha * 
            u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * 
            u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * 
            u5)))^2) + (E^(3 * alpha * (-4 + u1 + u2 + u3 + u4 + 
            u5)) * (-1 + E^alpha)^15)/((-1 + E^(alpha * u1))^3 * 
            (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * 
            (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3) - 
            (11 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
                (-1 + E^alpha)^10)/((-1 + E^(alpha * u1))^2 * 
                (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
                (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2) + 
            (11 * E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
                (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (-1 + E^(alpha * u5))) - (22 * 
            E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
            E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5))) + (11 * E^(alpha * (-2 + u1 + 
            u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))))) * 
            (2 * (E^(alpha * u1) * (log(E) * alpha) * (-1 + E^(alpha * 
                u1))) * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
                u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
                u5))^2 * (1 - E^alpha + (E^(alpha * (-4 + u1 + 
                u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
                E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + 
                E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + 
                E^(alpha * u5))))^5 + (-1 + E^(alpha * u1))^2 * 
                (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
                (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
                (5 * ((E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
                  (log(E) * alpha) * (-1 + E^alpha)^5/((-1 + 
                  E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + 
                  E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + 
                  E^(alpha * u5))) - (E^(alpha * (-4 + u1 + u2 + 
                  u3 + u4 + u5)) * (-1 + E^alpha)^5) * (E^(alpha * 
                  u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * 
                  (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
                  (-1 + E^(alpha * u5)))/((-1 + E^(alpha * u1)) * 
                  (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
                  (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)))^2) * 
                  (1 - E^alpha + (E^(alpha * (-4 + u1 + u2 + 
                    u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
                    E^(alpha * u1)) * (-1 + E^(alpha * u2)) * 
                    (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                    u4)) * (-1 + E^(alpha * u5))))^4)))/((-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + 
            E^(alpha * u5))^2 * (1 - E^alpha + (E^(alpha * (-4 + 
            u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))))^5)^2), 
    (alpha^5 * (E^(alpha * (1 + u1 + u2 + u3 + u4 + u5 + u6)) * 
        (log(E) * alpha)) * (-1 + E^(-alpha))^6 * (-1 + E^alpha) * 
        (1 - 4 * E^alpha + 6 * E^(2 * alpha) - 4 * E^(3 * alpha) + 
            E^(4 * alpha) + (26 * E^(4 * alpha) * (-1 + E^(-alpha))^18)/((-1 + 
            E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * 
            (-1 + E^(-(alpha * u3)))^3 * (-1 + E^(-(alpha * u4)))^3 * 
            (-1 + E^(-(alpha * u5)))^3 * (-1 + E^(-(alpha * u6)))^3) - 
            (132 * E^(3 * alpha) * (-1 + E^(-alpha))^12)/((-1 + 
                E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
                (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * 
                u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * (-1 + 
                E^(-(alpha * u6)))^2) + (E^(4 * alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^24)/((-1 + 
            E^(alpha * u1))^4 * (-1 + E^(alpha * u2))^4 * (-1 + 
            E^(alpha * u3))^4 * (-1 + E^(alpha * u4))^4 * (-1 + 
            E^(alpha * u5))^4 * (-1 + E^(alpha * u6))^4) - (26 * 
            E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^18)/((-1 + E^(alpha * u1))^3 * (-1 + 
            E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + 
            E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + 
            E^(alpha * u6))^3) + (66 * E^(2 * alpha * (-5 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^12)/((-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + 
            E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2) + (66 * 
            E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^12)/((-1 + E^(alpha * u1))^2 * (-1 + 
            E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
            E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + 
            E^(alpha * u6))^2) - (26 * E^(alpha * (-5 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) + (78 * E^(alpha * (-4 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) - (78 * E^(alpha * (-3 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) + (26 * E^(alpha * (-2 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6)))) + alpha^5 * E^(alpha * (1 + 
        u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^(-alpha))^6 * 
        (-1 + E^alpha) * ((26 * E^(4 * alpha) * (-1 + E^(-alpha))^18) * 
        (3 * (E^(-(alpha * u1)) * (log(E) * alpha) * (-1 + E^(-(alpha * 
            u1)))^2) * (-1 + E^(-(alpha * u2)))^3 * (-1 + E^(-(alpha * 
            u3)))^3 * (-1 + E^(-(alpha * u4)))^3 * (-1 + E^(-(alpha * 
            u5)))^3 * (-1 + E^(-(alpha * u6)))^3)/((-1 + E^(-(alpha * 
        u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * (-1 + E^(-(alpha * 
        u3)))^3 * (-1 + E^(-(alpha * u4)))^3 * (-1 + E^(-(alpha * 
        u5)))^3 * (-1 + E^(-(alpha * u6)))^3)^2 - (132 * E^(3 * 
        alpha) * (-1 + E^(-alpha))^12) * (2 * (E^(-(alpha * u1)) * 
        (log(E) * alpha) * (-1 + E^(-(alpha * u1)))) * (-1 + 
        E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (-1 + 
        E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * (-1 + 
        E^(-(alpha * u6)))^2)/((-1 + E^(-(alpha * u1)))^2 * (-1 + 
        E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (-1 + 
        E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * (-1 + 
        E^(-(alpha * u6)))^2)^2 + (E^(4 * alpha * (-5 + u1 + 
        u2 + u3 + u4 + u5 + u6)) * (log(E) * (4 * alpha)) * (-1 + 
        E^alpha)^24/((-1 + E^(alpha * u1))^4 * (-1 + E^(alpha * 
        u2))^4 * (-1 + E^(alpha * u3))^4 * (-1 + E^(alpha * u4))^4 * 
        (-1 + E^(alpha * u5))^4 * (-1 + E^(alpha * u6))^4) - 
        (E^(4 * alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^24) * (4 * (E^(alpha * u1) * (log(E) * 
            alpha) * (-1 + E^(alpha * u1))^3) * (-1 + E^(alpha * 
            u2))^4 * (-1 + E^(alpha * u3))^4 * (-1 + E^(alpha * 
            u4))^4 * (-1 + E^(alpha * u5))^4 * (-1 + E^(alpha * 
            u6))^4)/((-1 + E^(alpha * u1))^4 * (-1 + E^(alpha * 
            u2))^4 * (-1 + E^(alpha * u3))^4 * (-1 + E^(alpha * 
            u4))^4 * (-1 + E^(alpha * u5))^4 * (-1 + E^(alpha * 
            u6))^4)^2) - (26 * (E^(3 * alpha * (-5 + u1 + u2 + 
        u3 + u4 + u5 + u6)) * (log(E) * (3 * alpha))) * (-1 + 
        E^alpha)^18/((-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
        u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + E^(alpha * u4))^3 * 
        (-1 + E^(alpha * u5))^3 * (-1 + E^(alpha * u6))^3) - 
        (26 * E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^18) * (3 * (E^(alpha * u1) * (log(E) * 
            alpha) * (-1 + E^(alpha * u1))^2) * (-1 + E^(alpha * 
            u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + E^(alpha * 
            u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + E^(alpha * 
            u6))^3)/((-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
            u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + E^(alpha * 
            u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + E^(alpha * 
            u6))^3)^2) + (66 * (E^(2 * alpha * (-5 + u1 + u2 + 
        u3 + u4 + u5 + u6)) * (log(E) * (2 * alpha))) * (-1 + 
        E^alpha)^12/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
        (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2) - 
        (66 * E^(2 * alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^12) * (2 * (E^(alpha * u1) * (log(E) * 
            alpha) * (-1 + E^(alpha * u1))) * (-1 + E^(alpha * 
            u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
            u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
            u6))^2)/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
            u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
            u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
            u6))^2)^2) + (66 * (E^(2 * alpha * (-4 + u1 + u2 + 
        u3 + u4 + u5 + u6)) * (log(E) * (2 * alpha))) * (-1 + 
        E^alpha)^12/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
        (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2) - 
        (66 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^12) * (2 * (E^(alpha * u1) * (log(E) * 
            alpha) * (-1 + E^(alpha * u1))) * (-1 + E^(alpha * 
            u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
            u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
            u6))^2)/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
            u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
            u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
            u6))^2)^2) - (26 * (E^(alpha * (-5 + u1 + u2 + u3 + 
        u4 + u5 + u6)) * (log(E) * alpha)) * (-1 + E^alpha)^6/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
        (-1 + E^(alpha * u6))) - (26 * E^(alpha * (-5 + u1 + 
        u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * (E^(alpha * 
        u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * (-1 + 
        E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
        u5)) * (-1 + E^(alpha * u6)))/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
        u6)))^2) + (78 * (E^(alpha * (-4 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (log(E) * alpha)) * (-1 + E^alpha)^6/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
        (-1 + E^(alpha * u6))) - (78 * E^(alpha * (-4 + u1 + 
        u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * (E^(alpha * 
        u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * (-1 + 
        E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
        u5)) * (-1 + E^(alpha * u6)))/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
        u6)))^2) - (78 * (E^(alpha * (-3 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (log(E) * alpha)) * (-1 + E^alpha)^6/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
        (-1 + E^(alpha * u6))) - (78 * E^(alpha * (-3 + u1 + 
        u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * (E^(alpha * 
        u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * (-1 + 
        E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
        u5)) * (-1 + E^(alpha * u6)))/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
        u6)))^2) + (26 * (E^(alpha * (-2 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (log(E) * alpha)) * (-1 + E^alpha)^6/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
        (-1 + E^(alpha * u6))) - (26 * E^(alpha * (-2 + u1 + 
        u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * (E^(alpha * 
        u1) * (log(E) * alpha) * (-1 + E^(alpha * u2)) * (-1 + 
        E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
        u5)) * (-1 + E^(alpha * u6)))/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
        u6)))^2)))/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
        (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2 * (1 - 
        E^alpha + (E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + 
        u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
        E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
        u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))))^6) - 
        (alpha^5 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^(-alpha))^6 * (-1 + E^alpha) * (1 - 4 * E^alpha + 
            6 * E^(2 * alpha) - 4 * E^(3 * alpha) + E^(4 * alpha) + 
            (26 * E^(4 * alpha) * (-1 + E^(-alpha))^18)/((-1 + 
                E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * 
                (-1 + E^(-(alpha * u3)))^3 * (-1 + E^(-(alpha * 
                u4)))^3 * (-1 + E^(-(alpha * u5)))^3 * (-1 + 
                E^(-(alpha * u6)))^3) - (132 * E^(3 * alpha) * 
            (-1 + E^(-alpha))^12)/((-1 + E^(-(alpha * u1)))^2 * 
            (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * 
            (-1 + E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * 
            (-1 + E^(-(alpha * u6)))^2) + (E^(4 * alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^24)/((-1 + 
            E^(alpha * u1))^4 * (-1 + E^(alpha * u2))^4 * (-1 + 
            E^(alpha * u3))^4 * (-1 + E^(alpha * u4))^4 * (-1 + 
            E^(alpha * u5))^4 * (-1 + E^(alpha * u6))^4) - (26 * 
            E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^18)/((-1 + E^(alpha * u1))^3 * (-1 + 
            E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + 
            E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + 
            E^(alpha * u6))^3) + (66 * E^(2 * alpha * (-5 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^12)/((-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + 
            E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2) + (66 * 
            E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^12)/((-1 + E^(alpha * u1))^2 * (-1 + 
            E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
            E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + 
            E^(alpha * u6))^2) - (26 * E^(alpha * (-5 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) + (78 * E^(alpha * (-4 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) - (78 * E^(alpha * (-3 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) + (26 * E^(alpha * (-2 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))))) * (2 * (E^(alpha * u1) * 
            (log(E) * alpha) * (-1 + E^(alpha * u1))) * (-1 + 
            E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
            E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + 
            E^(alpha * u6))^2 * (1 - E^alpha + (E^(alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))))^6 + (-1 + E^(alpha * u1))^2 * 
            (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
            (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
            (-1 + E^(alpha * u6))^2 * (6 * ((E^(alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (log(E) * alpha) * 
            (-1 + E^alpha)^6/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) - 
            (E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (-1 + E^alpha)^6) * (E^(alpha * u1) * (log(E) * 
                alpha) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (-1 + E^(alpha * u6)))/((-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (-1 + E^(alpha * u6)))^2) * (1 - E^alpha + 
            (E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + 
                E^(alpha * u6))))^5)))/((-1 + E^(alpha * u1))^2 * 
            (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
            (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
            (-1 + E^(alpha * u6))^2 * (1 - E^alpha + (E^(alpha * 
            (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))))^6)^2)
`frankCopula.pdfDerWrtArg.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr4 <- E^(alpha * (1 + u1 + u2))
    .expr6 <- log(E) * alpha
    .expr10 <- E^alpha
    .expr11 <- -1 + .expr10
    .expr15 <- E^(alpha + alpha * u1)
    .expr19 <- E^(alpha * (u1 + u2))
    .expr24 <- .expr10 - .expr15 + .expr19 - E^(alpha + alpha * 
        u2)
    .expr25 <- .expr24^2
    .value <- alpha * (.expr4 * .expr6) * .expr11/.expr25 - alpha * 
        .expr4 * .expr11 * (2 * ((.expr19 * .expr6 - .expr15 * 
        .expr6) * .expr24))/.expr25^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- alpha^2
    .expr7 <- E^(alpha * (-2 + u1 + u2 + u3))
    .expr9 <- log(E) * alpha
    .expr10 <- .expr7 * .expr9
    .expr12 <- -1
    .expr15 <- (.expr12 + E^alpha)^2
    .expr18 <- E^(alpha * u1)
    .expr21 <- E^(alpha * u2)
    .expr23 <- u1 + u2
    .expr25 <- E^(alpha * .expr23)
    .expr28 <- E^(alpha * u3)
    .expr32 <- E^(alpha * (u1 + u3))
    .expr36 <- E^(alpha * (u2 + u3))
    .expr43 <- E^(alpha * (.expr12 + u1 + u2 + u3))
    .expr44 <- 2 * .expr43
    .expr48 <- E^(alpha * (.expr23 + u3))
    .expr50 <- .expr12 + .expr18 + .expr21 - .expr25 + .expr28 - 
        .expr32 - .expr36 + .expr7 - .expr44 + 2 * .expr48
    .expr53 <- .expr1 * .expr7 * .expr15
    .expr54 <- .expr18 * .expr9
    .expr55 <- .expr25 * .expr9
    .expr57 <- .expr32 * .expr9
    .expr61 <- 2 * (.expr43 * .expr9)
    .expr75 <- 1 - .expr18 - .expr21 + .expr25 - .expr28 + .expr32 + 
        .expr36 + .expr7 - .expr44
    .expr76 <- .expr75^3
    .value <- (.expr1 * .expr10 * .expr15 * .expr50 + .expr53 * 
        (.expr54 - .expr55 - .expr57 + .expr10 - .expr61 + 2 * 
            (.expr48 * .expr9)))/.expr76 - .expr53 * .expr50 * 
        (3 * ((.expr55 - .expr54 + .expr57 + .expr10 - .expr61) * 
            .expr75^2))/.expr76^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- alpha^3
    .expr7 <- E^(alpha * (1 + u1 + u2 + u3 + u4))
    .expr8 <- log(E)
    .expr9 <- .expr8 * alpha
    .expr12 <- -1
    .expr16 <- (.expr12 + E^-alpha)^4
    .expr18 <- E^alpha
    .expr19 <- .expr12 + .expr18
    .expr23 <- 2 * alpha
    .expr30 <- -3 + u1 + u2 + u3 + u4
    .expr32 <- E^(.expr23 * .expr30)
    .expr33 <- .expr19^8
    .expr34 <- .expr32 * .expr33
    .expr36 <- E^(alpha * u1)
    .expr37 <- .expr12 + .expr36
    .expr41 <- .expr12 + E^(alpha * u2)
    .expr42 <- .expr41^2
    .expr46 <- .expr12 + E^(alpha * u3)
    .expr47 <- .expr46^2
    .expr51 <- .expr12 + E^(alpha * u4)
    .expr52 <- .expr51^2
    .expr53 <- .expr37^2 * .expr42 * .expr47 * .expr52
    .expr57 <- E^(alpha * .expr30)
    .expr59 <- .expr19^4
    .expr60 <- 4 * .expr57 * .expr59
    .expr63 <- .expr37 * .expr41 * .expr46 * .expr51
    .expr72 <- E^(alpha * (-2 + u1 + u2 + u3 + u4))
    .expr74 <- 4 * .expr72 * .expr59
    .expr76 <- 1 - 2 * .expr18 + E^.expr23 + .expr34/.expr53 - 
        .expr60/.expr63 + .expr74/.expr63
    .expr80 <- .expr1 * .expr7 * .expr16 * .expr19
    .expr85 <- .expr36 * .expr9
    .expr90 <- 2 * (.expr85 * .expr37) * .expr42 * .expr47 * 
        .expr52
    .expr95 <- .expr57 * .expr9
    .expr101 <- .expr85 * .expr41 * .expr46 * .expr51
    .expr103 <- .expr63^2
    .expr118 <- .expr57 * .expr59
    .expr120 <- 1 - .expr18 + .expr118/.expr63
    .expr121 <- .expr120^4
    .expr122 <- .expr53 * .expr121
    .value <- (.expr1 * (.expr7 * .expr9) * .expr16 * .expr19 * 
        .expr76 + .expr80 * (.expr32 * (.expr8 * .expr23) * .expr33/.expr53 - 
        .expr34 * .expr90/.expr53^2 - (4 * .expr95 * .expr59/.expr63 - 
        .expr60 * .expr101/.expr103) + (4 * (.expr72 * .expr9) * 
        .expr59/.expr63 - .expr74 * .expr101/.expr103)))/.expr122 - 
        .expr80 * .expr76 * (.expr90 * .expr121 + .expr53 * (4 * 
            ((.expr95 * .expr59/.expr63 - .expr118 * .expr101/.expr103) * 
                .expr120^3)))/.expr122^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- alpha^4
    .expr8 <- E^(alpha * (1 + u1 + u2 + u3 + u4 + u5))
    .expr9 <- log(E)
    .expr10 <- .expr9 * alpha
    .expr13 <- -1
    .expr16 <- .expr13 + E^-alpha
    .expr17 <- .expr16^5
    .expr19 <- E^alpha
    .expr20 <- .expr13 + .expr19
    .expr24 <- 2 * alpha
    .expr28 <- 3 * alpha
    .expr29 <- E^.expr28
    .expr33 <- 11 * .expr29 * .expr16^10
    .expr34 <- alpha * u1
    .expr36 <- E^-.expr34
    .expr37 <- .expr13 + .expr36
    .expr39 <- alpha * u2
    .expr43 <- (.expr13 + E^-.expr39)^2
    .expr45 <- alpha * u3
    .expr49 <- (.expr13 + E^-.expr45)^2
    .expr51 <- alpha * u4
    .expr55 <- (.expr13 + E^-.expr51)^2
    .expr57 <- alpha * u5
    .expr61 <- (.expr13 + E^-.expr57)^2
    .expr62 <- .expr37^2 * .expr43 * .expr49 * .expr55 * .expr61
    .expr70 <- -4 + u1 + u2 + u3 + u4 + u5
    .expr72 <- E^(.expr28 * .expr70)
    .expr73 <- .expr20^15
    .expr74 <- .expr72 * .expr73
    .expr75 <- E^.expr34
    .expr76 <- .expr13 + .expr75
    .expr79 <- .expr13 + E^.expr39
    .expr80 <- .expr79^3
    .expr83 <- .expr13 + E^.expr45
    .expr84 <- .expr83^3
    .expr87 <- .expr13 + E^.expr51
    .expr88 <- .expr87^3
    .expr91 <- .expr13 + E^.expr57
    .expr92 <- .expr91^3
    .expr93 <- .expr76^3 * .expr80 * .expr84 * .expr88 * .expr92
    .expr97 <- E^(.expr24 * .expr70)
    .expr99 <- .expr20^10
    .expr100 <- 11 * .expr97 * .expr99
    .expr101 <- .expr76^2
    .expr102 <- .expr79^2
    .expr104 <- .expr83^2
    .expr106 <- .expr87^2
    .expr108 <- .expr91^2
    .expr109 <- .expr101 * .expr102 * .expr104 * .expr106 * .expr108
    .expr113 <- E^(alpha * .expr70)
    .expr115 <- .expr20^5
    .expr116 <- 11 * .expr113 * .expr115
    .expr120 <- .expr76 * .expr79 * .expr83 * .expr87 * .expr91
    .expr130 <- E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5))
    .expr132 <- 22 * .expr130 * .expr115
    .expr142 <- E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5))
    .expr144 <- 11 * .expr142 * .expr115
    .expr146 <- .expr13 + 3 * .expr19 - 3 * E^.expr24 + .expr29 + 
        .expr33/.expr62 + .expr74/.expr93 - .expr100/.expr109 + 
        .expr116/.expr120 - .expr132/.expr120 + .expr144/.expr120
    .expr150 <- .expr1 * .expr8 * .expr17 * .expr20
    .expr165 <- .expr75 * .expr10
    .expr187 <- 2 * (.expr165 * .expr76) * .expr102 * .expr104 * 
        .expr106 * .expr108
    .expr193 <- .expr113 * .expr10
    .expr200 <- .expr165 * .expr79 * .expr83 * .expr87 * .expr91
    .expr202 <- .expr120^2
    .expr225 <- .expr113 * .expr115
    .expr227 <- 1 - .expr19 + .expr225/.expr120
    .expr228 <- .expr227^5
    .expr229 <- .expr109 * .expr228
    .value <- -((.expr1 * (.expr8 * .expr10) * .expr17 * .expr20 * 
        .expr146 + .expr150 * (.expr33 * (2 * (.expr36 * .expr10 * 
        .expr37) * .expr43 * .expr49 * .expr55 * .expr61)/.expr62^2 + 
        (.expr72 * (.expr9 * .expr28) * .expr73/.expr93 - .expr74 * 
            (3 * (.expr165 * .expr101) * .expr80 * .expr84 * 
                .expr88 * .expr92)/.expr93^2) - (11 * (.expr97 * 
        (.expr9 * .expr24)) * .expr99/.expr109 - .expr100 * .expr187/.expr109^2) + 
        (11 * .expr193 * .expr115/.expr120 - .expr116 * .expr200/.expr202) - 
        (22 * (.expr130 * .expr10) * .expr115/.expr120 - .expr132 * 
            .expr200/.expr202) + (11 * (.expr142 * .expr10) * 
        .expr115/.expr120 - .expr144 * .expr200/.expr202)))/.expr229 - 
        .expr150 * .expr146 * (.expr187 * .expr228 + .expr109 * 
            (5 * ((.expr193 * .expr115/.expr120 - .expr225 * 
                .expr200/.expr202) * .expr227^4)))/.expr229^2)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- alpha^5
    .expr9 <- E^(alpha * (1 + u1 + u2 + u3 + u4 + u5 + u6))
    .expr10 <- log(E)
    .expr11 <- .expr10 * alpha
    .expr14 <- -1
    .expr17 <- .expr14 + E^-alpha
    .expr18 <- .expr17^6
    .expr20 <- E^alpha
    .expr21 <- .expr14 + .expr20
    .expr25 <- 2 * alpha
    .expr29 <- 3 * alpha
    .expr30 <- E^.expr29
    .expr33 <- 4 * alpha
    .expr34 <- E^.expr33
    .expr38 <- 26 * .expr34 * .expr17^18
    .expr39 <- alpha * u1
    .expr41 <- E^-.expr39
    .expr42 <- .expr14 + .expr41
    .expr44 <- alpha * u2
    .expr47 <- .expr14 + E^-.expr44
    .expr48 <- .expr47^3
    .expr50 <- alpha * u3
    .expr53 <- .expr14 + E^-.expr50
    .expr54 <- .expr53^3
    .expr56 <- alpha * u4
    .expr59 <- .expr14 + E^-.expr56
    .expr60 <- .expr59^3
    .expr62 <- alpha * u5
    .expr65 <- .expr14 + E^-.expr62
    .expr66 <- .expr65^3
    .expr68 <- alpha * u6
    .expr71 <- .expr14 + E^-.expr68
    .expr72 <- .expr71^3
    .expr73 <- .expr42^3 * .expr48 * .expr54 * .expr60 * .expr66 * 
        .expr72
    .expr78 <- 132 * .expr30 * .expr17^12
    .expr79 <- .expr42^2
    .expr80 <- .expr47^2
    .expr82 <- .expr53^2
    .expr84 <- .expr59^2
    .expr86 <- .expr65^2
    .expr88 <- .expr71^2
    .expr89 <- .expr79 * .expr80 * .expr82 * .expr84 * .expr86 * 
        .expr88
    .expr98 <- -5 + u1 + u2 + u3 + u4 + u5 + u6
    .expr100 <- E^(.expr33 * .expr98)
    .expr101 <- .expr21^24
    .expr102 <- .expr100 * .expr101
    .expr103 <- E^.expr39
    .expr104 <- .expr14 + .expr103
    .expr107 <- .expr14 + E^.expr44
    .expr108 <- .expr107^4
    .expr111 <- .expr14 + E^.expr50
    .expr112 <- .expr111^4
    .expr115 <- .expr14 + E^.expr56
    .expr116 <- .expr115^4
    .expr119 <- .expr14 + E^.expr62
    .expr120 <- .expr119^4
    .expr123 <- .expr14 + E^.expr68
    .expr124 <- .expr123^4
    .expr125 <- .expr104^4 * .expr108 * .expr112 * .expr116 * 
        .expr120 * .expr124
    .expr129 <- E^(.expr29 * .expr98)
    .expr131 <- .expr21^18
    .expr132 <- 26 * .expr129 * .expr131
    .expr133 <- .expr104^3
    .expr134 <- .expr107^3
    .expr136 <- .expr111^3
    .expr138 <- .expr115^3
    .expr140 <- .expr119^3
    .expr142 <- .expr123^3
    .expr143 <- .expr133 * .expr134 * .expr136 * .expr138 * .expr140 * 
        .expr142
    .expr147 <- E^(.expr25 * .expr98)
    .expr149 <- .expr21^12
    .expr150 <- 66 * .expr147 * .expr149
    .expr151 <- .expr104^2
    .expr152 <- .expr107^2
    .expr154 <- .expr111^2
    .expr156 <- .expr115^2
    .expr158 <- .expr119^2
    .expr160 <- .expr123^2
    .expr161 <- .expr151 * .expr152 * .expr154 * .expr156 * .expr158 * 
        .expr160
    .expr170 <- -4 + u1 + u2 + u3 + u4 + u5 + u6
    .expr172 <- E^(.expr25 * .expr170)
    .expr174 <- 66 * .expr172 * .expr149
    .expr178 <- E^(alpha * .expr98)
    .expr180 <- .expr21^6
    .expr181 <- 26 * .expr178 * .expr180
    .expr186 <- .expr104 * .expr107 * .expr111 * .expr115 * .expr119 * 
        .expr123
    .expr190 <- E^(alpha * .expr170)
    .expr192 <- 78 * .expr190 * .expr180
    .expr203 <- E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5 + u6))
    .expr205 <- 78 * .expr203 * .expr180
    .expr216 <- E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5 + u6))
    .expr218 <- 26 * .expr216 * .expr180
    .expr220 <- 1 - 4 * .expr20 + 6 * E^.expr25 - 4 * .expr30 + 
        .expr34 + .expr38/.expr73 - .expr78/.expr89 + .expr102/.expr125 - 
        .expr132/.expr143 + .expr150/.expr161 + .expr174/.expr161 - 
        .expr181/.expr186 + .expr192/.expr186 - .expr205/.expr186 + 
        .expr218/.expr186
    .expr224 <- .expr1 * .expr9 * .expr18 * .expr21
    .expr225 <- .expr41 * .expr11
    .expr251 <- .expr103 * .expr11
    .expr281 <- .expr10 * .expr25
    .expr292 <- 2 * (.expr251 * .expr104) * .expr152 * .expr154 * 
        .expr156 * .expr158 * .expr160
    .expr294 <- .expr161^2
    .expr306 <- .expr178 * .expr11
    .expr314 <- .expr251 * .expr107 * .expr111 * .expr115 * .expr119 * 
        .expr123
    .expr316 <- .expr186^2
    .expr347 <- .expr178 * .expr180
    .expr349 <- 1 - .expr20 + .expr347/.expr186
    .expr350 <- .expr349^6
    .expr351 <- .expr161 * .expr350
    .value <- (.expr1 * (.expr9 * .expr11) * .expr18 * .expr21 * 
        .expr220 + .expr224 * (.expr38 * (3 * (.expr225 * .expr79) * 
        .expr48 * .expr54 * .expr60 * .expr66 * .expr72)/.expr73^2 - 
        .expr78 * (2 * (.expr225 * .expr42) * .expr80 * .expr82 * 
            .expr84 * .expr86 * .expr88)/.expr89^2 + (.expr100 * 
        (.expr10 * .expr33) * .expr101/.expr125 - .expr102 * 
        (4 * (.expr251 * .expr133) * .expr108 * .expr112 * .expr116 * 
            .expr120 * .expr124)/.expr125^2) - (26 * (.expr129 * 
        (.expr10 * .expr29)) * .expr131/.expr143 - .expr132 * 
        (3 * (.expr251 * .expr151) * .expr134 * .expr136 * .expr138 * 
            .expr140 * .expr142)/.expr143^2) + (66 * (.expr147 * 
        .expr281) * .expr149/.expr161 - .expr150 * .expr292/.expr294) + 
        (66 * (.expr172 * .expr281) * .expr149/.expr161 - .expr174 * 
            .expr292/.expr294) - (26 * .expr306 * .expr180/.expr186 - 
        .expr181 * .expr314/.expr316) + (78 * (.expr190 * .expr11) * 
        .expr180/.expr186 - .expr192 * .expr314/.expr316) - (78 * 
        (.expr203 * .expr11) * .expr180/.expr186 - .expr205 * 
        .expr314/.expr316) + (26 * (.expr216 * .expr11) * .expr180/.expr186 - 
        .expr218 * .expr314/.expr316)))/.expr351 - .expr224 * 
        .expr220 * (.expr292 * .expr350 + .expr161 * (6 * ((.expr306 * 
        .expr180/.expr186 - .expr347 * .expr314/.expr316) * .expr349^5)))/.expr351^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`frankCopula.pdfDerWrtPar.expr` <-
expression(0, ((E^(alpha * (1 + u1 + u2)) + alpha * (E^(alpha * 
    (1 + u1 + u2)) * (log(E) * (1 + u1 + u2)))) * (-1 + E^alpha) + 
    alpha * E^(alpha * (1 + u1 + u2)) * (E^alpha * log(E)))/(E^alpha - 
    E^(alpha + alpha * u1) + E^(alpha * (u1 + u2)) - E^(alpha + 
    alpha * u2))^2 - (alpha * E^(alpha * (1 + u1 + u2)) * (-1 + 
    E^alpha)) * (2 * ((E^alpha * log(E) - E^(alpha + alpha * 
    u1) * (log(E) * (1 + u1)) + E^(alpha * (u1 + u2)) * (log(E) * 
    (u1 + u2)) - E^(alpha + alpha * u2) * (log(E) * (1 + u2))) * 
    (E^alpha - E^(alpha + alpha * u1) + E^(alpha * (u1 + u2)) - 
        E^(alpha + alpha * u2))))/((E^alpha - E^(alpha + alpha * 
    u1) + E^(alpha * (u1 + u2)) - E^(alpha + alpha * u2))^2)^2, 
    (((2 * alpha * E^(alpha * (-2 + u1 + u2 + u3)) + alpha^2 * 
        (E^(alpha * (-2 + u1 + u2 + u3)) * (log(E) * (-2 + u1 + 
            u2 + u3)))) * (-1 + E^alpha)^2 + alpha^2 * E^(alpha * 
        (-2 + u1 + u2 + u3)) * (2 * (E^alpha * log(E) * (-1 + 
        E^alpha)))) * (-1 + E^(alpha * u1) + E^(alpha * u2) - 
        E^(alpha * (u1 + u2)) + E^(alpha * u3) - E^(alpha * (u1 + 
        u3)) - E^(alpha * (u2 + u3)) + E^(alpha * (-2 + u1 + 
        u2 + u3)) - 2 * E^(alpha * (-1 + u1 + u2 + u3)) + 2 * 
        E^(alpha * (u1 + u2 + u3))) + alpha^2 * E^(alpha * (-2 + 
        u1 + u2 + u3)) * (-1 + E^alpha)^2 * (E^(alpha * u1) * 
        (log(E) * u1) + E^(alpha * u2) * (log(E) * u2) - E^(alpha * 
        (u1 + u2)) * (log(E) * (u1 + u2)) + E^(alpha * u3) * 
        (log(E) * u3) - E^(alpha * (u1 + u3)) * (log(E) * (u1 + 
        u3)) - E^(alpha * (u2 + u3)) * (log(E) * (u2 + u3)) + 
        E^(alpha * (-2 + u1 + u2 + u3)) * (log(E) * (-2 + u1 + 
            u2 + u3)) - 2 * (E^(alpha * (-1 + u1 + u2 + u3)) * 
        (log(E) * (-1 + u1 + u2 + u3))) + 2 * (E^(alpha * (u1 + 
        u2 + u3)) * (log(E) * (u1 + u2 + u3)))))/(1 - E^(alpha * 
        u1) - E^(alpha * u2) + E^(alpha * (u1 + u2)) - E^(alpha * 
        u3) + E^(alpha * (u1 + u3)) + E^(alpha * (u2 + u3)) + 
        E^(alpha * (-2 + u1 + u2 + u3)) - 2 * E^(alpha * (-1 + 
        u1 + u2 + u3)))^3 - (alpha^2 * E^(alpha * (-2 + u1 + 
        u2 + u3)) * (-1 + E^alpha)^2 * (-1 + E^(alpha * u1) + 
        E^(alpha * u2) - E^(alpha * (u1 + u2)) + E^(alpha * u3) - 
        E^(alpha * (u1 + u3)) - E^(alpha * (u2 + u3)) + E^(alpha * 
        (-2 + u1 + u2 + u3)) - 2 * E^(alpha * (-1 + u1 + u2 + 
        u3)) + 2 * E^(alpha * (u1 + u2 + u3)))) * (3 * ((E^(alpha * 
        (u1 + u2)) * (log(E) * (u1 + u2)) - (E^(alpha * u1) * 
        (log(E) * u1) + E^(alpha * u2) * (log(E) * u2)) - E^(alpha * 
        u3) * (log(E) * u3) + E^(alpha * (u1 + u3)) * (log(E) * 
        (u1 + u3)) + E^(alpha * (u2 + u3)) * (log(E) * (u2 + 
        u3)) + E^(alpha * (-2 + u1 + u2 + u3)) * (log(E) * (-2 + 
        u1 + u2 + u3)) - 2 * (E^(alpha * (-1 + u1 + u2 + u3)) * 
        (log(E) * (-1 + u1 + u2 + u3)))) * (1 - E^(alpha * u1) - 
        E^(alpha * u2) + E^(alpha * (u1 + u2)) - E^(alpha * u3) + 
        E^(alpha * (u1 + u3)) + E^(alpha * (u2 + u3)) + E^(alpha * 
        (-2 + u1 + u2 + u3)) - 2 * E^(alpha * (-1 + u1 + u2 + 
        u3)))^2))/((1 - E^(alpha * u1) - E^(alpha * u2) + E^(alpha * 
        (u1 + u2)) - E^(alpha * u3) + E^(alpha * (u1 + u3)) + 
        E^(alpha * (u2 + u3)) + E^(alpha * (-2 + u1 + u2 + u3)) - 
        2 * E^(alpha * (-1 + u1 + u2 + u3)))^3)^2, ((((3 * alpha^2 * 
        E^(alpha * (1 + u1 + u2 + u3 + u4)) + alpha^3 * (E^(alpha * 
        (1 + u1 + u2 + u3 + u4)) * (log(E) * (1 + u1 + u2 + u3 + 
        u4)))) * (-1 + E^(-alpha))^4 - alpha^3 * E^(alpha * (1 + 
        u1 + u2 + u3 + u4)) * (4 * (E^(-alpha) * log(E) * (-1 + 
        E^(-alpha))^3))) * (-1 + E^alpha) + alpha^3 * E^(alpha * 
        (1 + u1 + u2 + u3 + u4)) * (-1 + E^(-alpha))^4 * (E^alpha * 
        log(E))) * (1 - 2 * E^alpha + E^(2 * alpha) + (E^(2 * 
        alpha * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^8)/((-1 + 
        E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
        u3))^2 * (-1 + E^(alpha * u4))^2) - (4 * E^(alpha * (-3 + 
        u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4))) + (4 * E^(alpha * (-2 + u1 + u2 + 
        u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)))) + alpha^3 * E^(alpha * (1 + u1 + u2 + 
        u3 + u4)) * (-1 + E^(-alpha))^4 * (-1 + E^alpha) * (E^(2 * 
        alpha) * (log(E) * 2) - 2 * (E^alpha * log(E)) + ((E^(2 * 
        alpha * (-3 + u1 + u2 + u3 + u4)) * (log(E) * (2 * (-3 + 
        u1 + u2 + u3 + u4))) * (-1 + E^alpha)^8 + E^(2 * alpha * 
        (-3 + u1 + u2 + u3 + u4)) * (8 * (E^alpha * log(E) * 
        (-1 + E^alpha)^7)))/((-1 + E^(alpha * u1))^2 * (-1 + 
        E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
        u4))^2) - (E^(2 * alpha * (-3 + u1 + u2 + u3 + u4)) * 
        (-1 + E^alpha)^8) * (((2 * (E^(alpha * u1) * (log(E) * 
        u1) * (-1 + E^(alpha * u1))) * (-1 + E^(alpha * u2))^2 + 
        (-1 + E^(alpha * u1))^2 * (2 * (E^(alpha * u2) * (log(E) * 
            u2) * (-1 + E^(alpha * u2))))) * (-1 + E^(alpha * 
        u3))^2 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * 
        (2 * (E^(alpha * u3) * (log(E) * u3) * (-1 + E^(alpha * 
            u3))))) * (-1 + E^(alpha * u4))^2 + (-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (2 * (E^(alpha * u4) * (log(E) * u4) * (-1 + E^(alpha * 
            u4)))))/((-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
        u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2)^2) - 
        ((4 * (E^(alpha * (-3 + u1 + u2 + u3 + u4)) * (log(E) * 
            (-3 + u1 + u2 + u3 + u4))) * (-1 + E^alpha)^4 + 4 * 
            E^(alpha * (-3 + u1 + u2 + u3 + u4)) * (4 * (E^alpha * 
            log(E) * (-1 + E^alpha)^3)))/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4))) - (4 * E^(alpha * (-3 + u1 + u2 + 
            u3 + u4)) * (-1 + E^alpha)^4) * (((E^(alpha * u1) * 
            (log(E) * u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
            u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
            E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (E^(alpha * u3) * (log(E) * u3))) * (-1 + 
            E^(alpha * u4)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (E^(alpha * u4) * 
            (log(E) * u4)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)))^2) + 
        ((4 * (E^(alpha * (-2 + u1 + u2 + u3 + u4)) * (log(E) * 
            (-2 + u1 + u2 + u3 + u4))) * (-1 + E^alpha)^4 + 4 * 
            E^(alpha * (-2 + u1 + u2 + u3 + u4)) * (4 * (E^alpha * 
            log(E) * (-1 + E^alpha)^3)))/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4))) - (4 * E^(alpha * (-2 + u1 + u2 + 
            u3 + u4)) * (-1 + E^alpha)^4) * (((E^(alpha * u1) * 
            (log(E) * u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
            u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
            E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (E^(alpha * u3) * (log(E) * u3))) * (-1 + 
            E^(alpha * u4)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (E^(alpha * u4) * 
            (log(E) * u4)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)))^2)))/((-1 + 
        E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
        u3))^2 * (-1 + E^(alpha * u4))^2 * (1 - E^alpha + (E^(alpha * 
        (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4))))^4) - (alpha^3 * E^(alpha * 
        (1 + u1 + u2 + u3 + u4)) * (-1 + E^(-alpha))^4 * (-1 + 
        E^alpha) * (1 - 2 * E^alpha + E^(2 * alpha) + (E^(2 * 
        alpha * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^8)/((-1 + 
        E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
        u3))^2 * (-1 + E^(alpha * u4))^2) - (4 * E^(alpha * (-3 + 
        u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4))) + (4 * E^(alpha * (-2 + u1 + u2 + 
        u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4))))) * ((((2 * (E^(alpha * u1) * (log(E) * 
        u1) * (-1 + E^(alpha * u1))) * (-1 + E^(alpha * u2))^2 + 
        (-1 + E^(alpha * u1))^2 * (2 * (E^(alpha * u2) * (log(E) * 
            u2) * (-1 + E^(alpha * u2))))) * (-1 + E^(alpha * 
        u3))^2 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * 
        (2 * (E^(alpha * u3) * (log(E) * u3) * (-1 + E^(alpha * 
            u3))))) * (-1 + E^(alpha * u4))^2 + (-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (2 * (E^(alpha * u4) * (log(E) * u4) * (-1 + E^(alpha * 
            u4))))) * (1 - E^alpha + (E^(alpha * (-3 + u1 + u2 + 
        u3 + u4)) * (-1 + E^alpha)^4)/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4))))^4 + (-1 + E^(alpha * u1))^2 * (-1 + 
        E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
        u4))^2 * (4 * (((E^(alpha * (-3 + u1 + u2 + u3 + u4)) * 
        (log(E) * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4 + 
        E^(alpha * (-3 + u1 + u2 + u3 + u4)) * (4 * (E^alpha * 
            log(E) * (-1 + E^alpha)^3)))/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4))) - (E^(alpha * (-3 + u1 + u2 + u3 + u4)) * 
        (-1 + E^alpha)^4) * (((E^(alpha * u1) * (log(E) * u1) * 
        (-1 + E^(alpha * u2)) + (-1 + E^(alpha * u1)) * (E^(alpha * 
        u2) * (log(E) * u2))) * (-1 + E^(alpha * u3)) + (-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (E^(alpha * 
        u3) * (log(E) * u3))) * (-1 + E^(alpha * u4)) + (-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (E^(alpha * u4) * (log(E) * u4)))/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4)))^2 - E^alpha * log(E)) * (1 - E^alpha + 
        (E^(alpha * (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4))))^3)))/((-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (-1 + E^(alpha * u4))^2 * (1 - E^alpha + (E^(alpha * 
        (-3 + u1 + u2 + u3 + u4)) * (-1 + E^alpha)^4)/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4))))^4)^2, -(((((4 * alpha^3 * 
        E^(alpha * (1 + u1 + u2 + u3 + u4 + u5)) + alpha^4 * 
        (E^(alpha * (1 + u1 + u2 + u3 + u4 + u5)) * (log(E) * 
            (1 + u1 + u2 + u3 + u4 + u5)))) * (-1 + E^(-alpha))^5 - 
        alpha^4 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5)) * 
            (5 * (E^(-alpha) * log(E) * (-1 + E^(-alpha))^4))) * 
        (-1 + E^alpha) + alpha^4 * E^(alpha * (1 + u1 + u2 + 
        u3 + u4 + u5)) * (-1 + E^(-alpha))^5 * (E^alpha * log(E))) * 
        (-1 + 3 * E^alpha - 3 * E^(2 * alpha) + E^(3 * alpha) + 
            (11 * E^(3 * alpha) * (-1 + E^(-alpha))^10)/((-1 + 
                E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
                (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * 
                u4)))^2 * (-1 + E^(-(alpha * u5)))^2) + (E^(3 * 
            alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^15)/((-1 + 
            E^(alpha * u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + 
            E^(alpha * u3))^3 * (-1 + E^(alpha * u4))^3 * (-1 + 
            E^(alpha * u5))^3) - (11 * E^(2 * alpha * (-4 + u1 + 
            u2 + u3 + u4 + u5)) * (-1 + E^alpha)^10)/((-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
            u5))^2) + (11 * E^(alpha * (-4 + u1 + u2 + u3 + u4 + 
            u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4)) * (-1 + E^(alpha * u5))) - (22 * 
            E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
            E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5))) + (11 * E^(alpha * (-2 + u1 + 
            u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)))) + 
        alpha^4 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5)) * 
            (-1 + E^(-alpha))^5 * (-1 + E^alpha) * (3 * (E^alpha * 
            log(E)) - 3 * (E^(2 * alpha) * (log(E) * 2)) + E^(3 * 
            alpha) * (log(E) * 3) + ((11 * (E^(3 * alpha) * (log(E) * 
            3)) * (-1 + E^(-alpha))^10 - 11 * E^(3 * alpha) * 
            (10 * (E^(-alpha) * log(E) * (-1 + E^(-alpha))^9)))/((-1 + 
            E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
            (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * 
            (-1 + E^(-(alpha * u5)))^2) + (11 * E^(3 * alpha) * 
            (-1 + E^(-alpha))^10) * ((-1 + E^(-(alpha * u1)))^2 * 
            (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * 
            (-1 + E^(-(alpha * u4)))^2 * (2 * (E^(-(alpha * u5)) * 
            (log(E) * u5) * (-1 + E^(-(alpha * u5))))) + ((-1 + 
            E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
            (-1 + E^(-(alpha * u3)))^2 * (2 * (E^(-(alpha * u4)) * 
            (log(E) * u4) * (-1 + E^(-(alpha * u4))))) + ((-1 + 
            E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
            (2 * (E^(-(alpha * u3)) * (log(E) * u3) * (-1 + E^(-(alpha * 
                u3))))) + ((-1 + E^(-(alpha * u1)))^2 * (2 * 
            (E^(-(alpha * u2)) * (log(E) * u2) * (-1 + E^(-(alpha * 
                u2))))) + 2 * (E^(-(alpha * u1)) * (log(E) * 
            u1) * (-1 + E^(-(alpha * u1)))) * (-1 + E^(-(alpha * 
            u2)))^2) * (-1 + E^(-(alpha * u3)))^2) * (-1 + E^(-(alpha * 
            u4)))^2) * (-1 + E^(-(alpha * u5)))^2)/((-1 + E^(-(alpha * 
            u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * (-1 + E^(-(alpha * 
            u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * (-1 + E^(-(alpha * 
            u5)))^2)^2) + ((E^(3 * alpha * (-4 + u1 + u2 + u3 + 
            u4 + u5)) * (log(E) * (3 * (-4 + u1 + u2 + u3 + u4 + 
            u5))) * (-1 + E^alpha)^15 + E^(3 * alpha * (-4 + 
            u1 + u2 + u3 + u4 + u5)) * (15 * (E^alpha * log(E) * 
            (-1 + E^alpha)^14)))/((-1 + E^(alpha * u1))^3 * (-1 + 
            E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + 
            E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3) - (E^(3 * 
            alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^15) * 
            ((((3 * (E^(alpha * u1) * (log(E) * u1) * (-1 + E^(alpha * 
                u1))^2) * (-1 + E^(alpha * u2))^3 + (-1 + E^(alpha * 
                u1))^3 * (3 * (E^(alpha * u2) * (log(E) * u2) * 
                (-1 + E^(alpha * u2))^2))) * (-1 + E^(alpha * 
                u3))^3 + (-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
                u2))^3 * (3 * (E^(alpha * u3) * (log(E) * u3) * 
                (-1 + E^(alpha * u3))^2))) * (-1 + E^(alpha * 
                u4))^3 + (-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
                u2))^3 * (-1 + E^(alpha * u3))^3 * (3 * (E^(alpha * 
                u4) * (log(E) * u4) * (-1 + E^(alpha * u4))^2))) * 
                (-1 + E^(alpha * u5))^3 + (-1 + E^(alpha * u1))^3 * 
                (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * 
                (-1 + E^(alpha * u4))^3 * (3 * (E^(alpha * u5) * 
                (log(E) * u5) * (-1 + E^(alpha * u5))^2)))/((-1 + 
            E^(alpha * u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + 
            E^(alpha * u3))^3 * (-1 + E^(alpha * u4))^3 * (-1 + 
            E^(alpha * u5))^3)^2) - ((11 * (E^(2 * alpha * (-4 + 
            u1 + u2 + u3 + u4 + u5)) * (log(E) * (2 * (-4 + u1 + 
            u2 + u3 + u4 + u5)))) * (-1 + E^alpha)^10 + 11 * 
            E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (10 * 
            (E^alpha * log(E) * (-1 + E^alpha)^9)))/((-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
            u5))^2) - (11 * E^(2 * alpha * (-4 + u1 + u2 + u3 + 
            u4 + u5)) * (-1 + E^alpha)^10) * ((((2 * (E^(alpha * 
            u1) * (log(E) * u1) * (-1 + E^(alpha * u1))) * (-1 + 
            E^(alpha * u2))^2 + (-1 + E^(alpha * u1))^2 * (2 * 
            (E^(alpha * u2) * (log(E) * u2) * (-1 + E^(alpha * 
                u2))))) * (-1 + E^(alpha * u3))^2 + (-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (2 * (E^(alpha * 
            u3) * (log(E) * u3) * (-1 + E^(alpha * u3))))) * 
            (-1 + E^(alpha * u4))^2 + (-1 + E^(alpha * u1))^2 * 
            (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
            (2 * (E^(alpha * u4) * (log(E) * u4) * (-1 + E^(alpha * 
                u4))))) * (-1 + E^(alpha * u5))^2 + (-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2 * (2 * (E^(alpha * 
            u5) * (log(E) * u5) * (-1 + E^(alpha * u5)))))/((-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + 
            E^(alpha * u5))^2)^2) + ((11 * (E^(alpha * (-4 + 
            u1 + u2 + u3 + u4 + u5)) * (log(E) * (-4 + u1 + u2 + 
            u3 + u4 + u5))) * (-1 + E^alpha)^5 + 11 * E^(alpha * 
            (-4 + u1 + u2 + u3 + u4 + u5)) * (5 * (E^alpha * 
            log(E) * (-1 + E^alpha)^4)))/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4)) * (-1 + E^(alpha * u5))) - (11 * 
            E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
            E^alpha)^5) * ((((E^(alpha * u1) * (log(E) * u1) * 
            (-1 + E^(alpha * u2)) + (-1 + E^(alpha * u1)) * (E^(alpha * 
            u2) * (log(E) * u2))) * (-1 + E^(alpha * u3)) + (-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (E^(alpha * 
            u3) * (log(E) * u3))) * (-1 + E^(alpha * u4)) + (-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (E^(alpha * u4) * (log(E) * u4))) * (-1 + 
            E^(alpha * u5)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (E^(alpha * u5) * (log(E) * u5)))/((-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)))^2) - 
            ((22 * (E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5)) * 
                (log(E) * (-3 + u1 + u2 + u3 + u4 + u5))) * (-1 + 
                E^alpha)^5 + 22 * E^(alpha * (-3 + u1 + u2 + 
                u3 + u4 + u5)) * (5 * (E^alpha * log(E) * (-1 + 
                E^alpha)^4)))/((-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (-1 + E^(alpha * u5))) - (22 * 
                E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
                E^alpha)^5) * ((((E^(alpha * u1) * (log(E) * 
                u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
                u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
                E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (E^(alpha * u3) * (log(E) * 
                u3))) * (-1 + E^(alpha * u4)) + (-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (E^(alpha * u4) * (log(E) * u4))) * (-1 + 
                E^(alpha * u5)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (E^(alpha * u5) * (log(E) * 
                u5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
                u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                u4)) * (-1 + E^(alpha * u5)))^2) + ((11 * (E^(alpha * 
            (-2 + u1 + u2 + u3 + u4 + u5)) * (log(E) * (-2 + 
            u1 + u2 + u3 + u4 + u5))) * (-1 + E^alpha)^5 + 11 * 
            E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5)) * (5 * 
            (E^alpha * log(E) * (-1 + E^alpha)^4)))/((-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))) - 
            (11 * E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5)) * 
                (-1 + E^alpha)^5) * ((((E^(alpha * u1) * (log(E) * 
                u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
                u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
                E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (E^(alpha * u3) * (log(E) * 
                u3))) * (-1 + E^(alpha * u4)) + (-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (E^(alpha * u4) * (log(E) * u4))) * (-1 + 
                E^(alpha * u5)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (E^(alpha * u5) * (log(E) * 
                u5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
                u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                u4)) * (-1 + E^(alpha * u5)))^2)))/((-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (1 - 
        E^alpha + (E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
        (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
        u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
        (-1 + E^(alpha * u5))))^5) - (alpha^4 * E^(alpha * (1 + 
        u1 + u2 + u3 + u4 + u5)) * (-1 + E^(-alpha))^5 * (-1 + 
        E^alpha) * (-1 + 3 * E^alpha - 3 * E^(2 * alpha) + E^(3 * 
        alpha) + (11 * E^(3 * alpha) * (-1 + E^(-alpha))^10)/((-1 + 
        E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * (-1 + 
        E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * (-1 + 
        E^(-(alpha * u5)))^2) + (E^(3 * alpha * (-4 + u1 + u2 + 
        u3 + u4 + u5)) * (-1 + E^alpha)^15)/((-1 + E^(alpha * 
        u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * 
        (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3) - 
        (11 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * 
            (-1 + E^alpha)^10)/((-1 + E^(alpha * u1))^2 * (-1 + 
            E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
            E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2) + (11 * 
        E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))) - 
        (22 * E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
            E^alpha)^5)/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5))) + (11 * E^(alpha * (-2 + u1 + 
        u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))))) * (((((2 * 
        (E^(alpha * u1) * (log(E) * u1) * (-1 + E^(alpha * u1))) * 
        (-1 + E^(alpha * u2))^2 + (-1 + E^(alpha * u1))^2 * (2 * 
        (E^(alpha * u2) * (log(E) * u2) * (-1 + E^(alpha * u2))))) * 
        (-1 + E^(alpha * u3))^2 + (-1 + E^(alpha * u1))^2 * (-1 + 
        E^(alpha * u2))^2 * (2 * (E^(alpha * u3) * (log(E) * 
        u3) * (-1 + E^(alpha * u3))))) * (-1 + E^(alpha * u4))^2 + 
        (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (2 * (E^(alpha * u4) * (log(E) * 
            u4) * (-1 + E^(alpha * u4))))) * (-1 + E^(alpha * 
        u5))^2 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * 
        (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (2 * 
        (E^(alpha * u5) * (log(E) * u5) * (-1 + E^(alpha * u5))))) * 
        (1 - E^alpha + (E^(alpha * (-4 + u1 + u2 + u3 + u4 + 
            u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4)) * (-1 + E^(alpha * u5))))^5 + (-1 + 
        E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
        u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
        (5 * (((E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (log(E) * 
            (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + E^alpha)^5 + 
            E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (5 * 
                (E^alpha * log(E) * (-1 + E^alpha)^4)))/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))) - 
            (E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5)) * (-1 + 
                E^alpha)^5) * ((((E^(alpha * u1) * (log(E) * 
                u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
                u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
                E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (E^(alpha * u3) * (log(E) * 
                u3))) * (-1 + E^(alpha * u4)) + (-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (E^(alpha * u4) * (log(E) * u4))) * (-1 + 
                E^(alpha * u5)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (E^(alpha * u5) * (log(E) * 
                u5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
                u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                u4)) * (-1 + E^(alpha * u5)))^2 - E^alpha * log(E)) * 
            (1 - E^alpha + (E^(alpha * (-4 + u1 + u2 + u3 + u4 + 
                u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * 
                (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
                (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5))))^4)))/((-1 + 
        E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
        u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
        (1 - E^alpha + (E^(alpha * (-4 + u1 + u2 + u3 + u4 + 
            u5)) * (-1 + E^alpha)^5)/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4)) * (-1 + E^(alpha * u5))))^5)^2), 
    ((((5 * alpha^4 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5 + 
        u6)) + alpha^5 * (E^(alpha * (1 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (log(E) * (1 + u1 + u2 + u3 + u4 + u5 + u6)))) * 
        (-1 + E^(-alpha))^6 - alpha^5 * E^(alpha * (1 + u1 + 
        u2 + u3 + u4 + u5 + u6)) * (6 * (E^(-alpha) * log(E) * 
        (-1 + E^(-alpha))^5))) * (-1 + E^alpha) + alpha^5 * E^(alpha * 
        (1 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^(-alpha))^6 * 
        (E^alpha * log(E))) * (1 - 4 * E^alpha + 6 * E^(2 * alpha) - 
        4 * E^(3 * alpha) + E^(4 * alpha) + (26 * E^(4 * alpha) * 
        (-1 + E^(-alpha))^18)/((-1 + E^(-(alpha * u1)))^3 * (-1 + 
        E^(-(alpha * u2)))^3 * (-1 + E^(-(alpha * u3)))^3 * (-1 + 
        E^(-(alpha * u4)))^3 * (-1 + E^(-(alpha * u5)))^3 * (-1 + 
        E^(-(alpha * u6)))^3) - (132 * E^(3 * alpha) * (-1 + 
        E^(-alpha))^12)/((-1 + E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * 
        u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * 
        u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * (-1 + E^(-(alpha * 
        u6)))^2) + (E^(4 * alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^24)/((-1 + E^(alpha * u1))^4 * 
        (-1 + E^(alpha * u2))^4 * (-1 + E^(alpha * u3))^4 * (-1 + 
        E^(alpha * u4))^4 * (-1 + E^(alpha * u5))^4 * (-1 + E^(alpha * 
        u6))^4) - (26 * E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^18)/((-1 + E^(alpha * u1))^3 * 
        (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + 
        E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + E^(alpha * 
        u6))^3) + (66 * E^(2 * alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^12)/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
        u6))^2) + (66 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^12)/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
        u6))^2) - (26 * E^(alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
        u6))) + (78 * E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5 + 
        u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
        E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
        u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) - 
        (78 * E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) + 
        (26 * E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6)))) + 
        alpha^5 * E^(alpha * (1 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^(-alpha))^6 * (-1 + E^alpha) * (6 * (E^(2 * 
            alpha) * (log(E) * 2)) - 4 * (E^alpha * log(E)) - 
            4 * (E^(3 * alpha) * (log(E) * 3)) + E^(4 * alpha) * 
            (log(E) * 4) + ((26 * (E^(4 * alpha) * (log(E) * 
            4)) * (-1 + E^(-alpha))^18 - 26 * E^(4 * alpha) * 
            (18 * (E^(-alpha) * log(E) * (-1 + E^(-alpha))^17)))/((-1 + 
            E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * 
            (-1 + E^(-(alpha * u3)))^3 * (-1 + E^(-(alpha * u4)))^3 * 
            (-1 + E^(-(alpha * u5)))^3 * (-1 + E^(-(alpha * u6)))^3) + 
            (26 * E^(4 * alpha) * (-1 + E^(-alpha))^18) * ((-1 + 
                E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * 
                (-1 + E^(-(alpha * u3)))^3 * (-1 + E^(-(alpha * 
                u4)))^3 * (-1 + E^(-(alpha * u5)))^3 * (3 * (E^(-(alpha * 
                u6)) * (log(E) * u6) * (-1 + E^(-(alpha * u6)))^2)) + 
                ((-1 + E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * 
                  u2)))^3 * (-1 + E^(-(alpha * u3)))^3 * (-1 + 
                  E^(-(alpha * u4)))^3 * (3 * (E^(-(alpha * u5)) * 
                  (log(E) * u5) * (-1 + E^(-(alpha * u5)))^2)) + 
                  ((-1 + E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * 
                    u2)))^3 * (-1 + E^(-(alpha * u3)))^3 * (3 * 
                    (E^(-(alpha * u4)) * (log(E) * u4) * (-1 + 
                      E^(-(alpha * u4)))^2)) + ((-1 + E^(-(alpha * 
                    u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * (3 * 
                    (E^(-(alpha * u3)) * (log(E) * u3) * (-1 + 
                      E^(-(alpha * u3)))^2)) + ((-1 + E^(-(alpha * 
                    u1)))^3 * (3 * (E^(-(alpha * u2)) * (log(E) * 
                    u2) * (-1 + E^(-(alpha * u2)))^2)) + 3 * 
                    (E^(-(alpha * u1)) * (log(E) * u1) * (-1 + 
                      E^(-(alpha * u1)))^2) * (-1 + E^(-(alpha * 
                    u2)))^3) * (-1 + E^(-(alpha * u3)))^3) * 
                    (-1 + E^(-(alpha * u4)))^3) * (-1 + E^(-(alpha * 
                    u5)))^3) * (-1 + E^(-(alpha * u6)))^3)/((-1 + 
                E^(-(alpha * u1)))^3 * (-1 + E^(-(alpha * u2)))^3 * 
                (-1 + E^(-(alpha * u3)))^3 * (-1 + E^(-(alpha * 
                u4)))^3 * (-1 + E^(-(alpha * u5)))^3 * (-1 + 
                E^(-(alpha * u6)))^3)^2) - ((132 * (E^(3 * alpha) * 
            (log(E) * 3)) * (-1 + E^(-alpha))^12 - 132 * E^(3 * 
            alpha) * (12 * (E^(-alpha) * log(E) * (-1 + E^(-alpha))^11)))/((-1 + 
            E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
            (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * 
            (-1 + E^(-(alpha * u5)))^2 * (-1 + E^(-(alpha * u6)))^2) + 
            (132 * E^(3 * alpha) * (-1 + E^(-alpha))^12) * ((-1 + 
                E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * 
                (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * 
                u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * (2 * (E^(-(alpha * 
                u6)) * (log(E) * u6) * (-1 + E^(-(alpha * u6))))) + 
                ((-1 + E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * 
                  u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (-1 + 
                  E^(-(alpha * u4)))^2 * (2 * (E^(-(alpha * u5)) * 
                  (log(E) * u5) * (-1 + E^(-(alpha * u5))))) + 
                  ((-1 + E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * 
                    u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (2 * 
                    (E^(-(alpha * u4)) * (log(E) * u4) * (-1 + 
                      E^(-(alpha * u4))))) + ((-1 + E^(-(alpha * 
                    u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * (2 * 
                    (E^(-(alpha * u3)) * (log(E) * u3) * (-1 + 
                      E^(-(alpha * u3))))) + ((-1 + E^(-(alpha * 
                    u1)))^2 * (2 * (E^(-(alpha * u2)) * (log(E) * 
                    u2) * (-1 + E^(-(alpha * u2))))) + 2 * (E^(-(alpha * 
                    u1)) * (log(E) * u1) * (-1 + E^(-(alpha * 
                    u1)))) * (-1 + E^(-(alpha * u2)))^2) * (-1 + 
                    E^(-(alpha * u3)))^2) * (-1 + E^(-(alpha * 
                    u4)))^2) * (-1 + E^(-(alpha * u5)))^2) * 
                  (-1 + E^(-(alpha * u6)))^2)/((-1 + E^(-(alpha * 
                u1)))^2 * (-1 + E^(-(alpha * u2)))^2 * (-1 + 
                E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * u4)))^2 * 
                (-1 + E^(-(alpha * u5)))^2 * (-1 + E^(-(alpha * 
                u6)))^2)^2) + ((E^(4 * alpha * (-5 + u1 + u2 + 
            u3 + u4 + u5 + u6)) * (log(E) * (4 * (-5 + u1 + u2 + 
            u3 + u4 + u5 + u6))) * (-1 + E^alpha)^24 + E^(4 * 
            alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * (24 * 
            (E^alpha * log(E) * (-1 + E^alpha)^23)))/((-1 + E^(alpha * 
            u1))^4 * (-1 + E^(alpha * u2))^4 * (-1 + E^(alpha * 
            u3))^4 * (-1 + E^(alpha * u4))^4 * (-1 + E^(alpha * 
            u5))^4 * (-1 + E^(alpha * u6))^4) - (E^(4 * alpha * 
            (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^24) * 
            (((((4 * (E^(alpha * u1) * (log(E) * u1) * (-1 + 
                E^(alpha * u1))^3) * (-1 + E^(alpha * u2))^4 + 
                (-1 + E^(alpha * u1))^4 * (4 * (E^(alpha * u2) * 
                  (log(E) * u2) * (-1 + E^(alpha * u2))^3))) * 
                (-1 + E^(alpha * u3))^4 + (-1 + E^(alpha * u1))^4 * 
                (-1 + E^(alpha * u2))^4 * (4 * (E^(alpha * u3) * 
                (log(E) * u3) * (-1 + E^(alpha * u3))^3))) * 
                (-1 + E^(alpha * u4))^4 + (-1 + E^(alpha * u1))^4 * 
                (-1 + E^(alpha * u2))^4 * (-1 + E^(alpha * u3))^4 * 
                (4 * (E^(alpha * u4) * (log(E) * u4) * (-1 + 
                  E^(alpha * u4))^3))) * (-1 + E^(alpha * u5))^4 + 
                (-1 + E^(alpha * u1))^4 * (-1 + E^(alpha * u2))^4 * 
                  (-1 + E^(alpha * u3))^4 * (-1 + E^(alpha * 
                  u4))^4 * (4 * (E^(alpha * u5) * (log(E) * u5) * 
                  (-1 + E^(alpha * u5))^3))) * (-1 + E^(alpha * 
                u6))^4 + (-1 + E^(alpha * u1))^4 * (-1 + E^(alpha * 
                u2))^4 * (-1 + E^(alpha * u3))^4 * (-1 + E^(alpha * 
                u4))^4 * (-1 + E^(alpha * u5))^4 * (4 * (E^(alpha * 
                u6) * (log(E) * u6) * (-1 + E^(alpha * u6))^3)))/((-1 + 
            E^(alpha * u1))^4 * (-1 + E^(alpha * u2))^4 * (-1 + 
            E^(alpha * u3))^4 * (-1 + E^(alpha * u4))^4 * (-1 + 
            E^(alpha * u5))^4 * (-1 + E^(alpha * u6))^4)^2) - 
            ((26 * (E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + 
                u5 + u6)) * (log(E) * (3 * (-5 + u1 + u2 + u3 + 
                u4 + u5 + u6)))) * (-1 + E^alpha)^18 + 26 * E^(3 * 
                alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (18 * (E^alpha * log(E) * (-1 + E^alpha)^17)))/((-1 + 
                E^(alpha * u1))^3 * (-1 + E^(alpha * u2))^3 * 
                (-1 + E^(alpha * u3))^3 * (-1 + E^(alpha * u4))^3 * 
                (-1 + E^(alpha * u5))^3 * (-1 + E^(alpha * u6))^3) - 
                (26 * E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + 
                  u5 + u6)) * (-1 + E^alpha)^18) * (((((3 * (E^(alpha * 
                  u1) * (log(E) * u1) * (-1 + E^(alpha * u1))^2) * 
                  (-1 + E^(alpha * u2))^3 + (-1 + E^(alpha * 
                  u1))^3 * (3 * (E^(alpha * u2) * (log(E) * u2) * 
                  (-1 + E^(alpha * u2))^2))) * (-1 + E^(alpha * 
                  u3))^3 + (-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
                  u2))^3 * (3 * (E^(alpha * u3) * (log(E) * u3) * 
                  (-1 + E^(alpha * u3))^2))) * (-1 + E^(alpha * 
                  u4))^3 + (-1 + E^(alpha * u1))^3 * (-1 + E^(alpha * 
                  u2))^3 * (-1 + E^(alpha * u3))^3 * (3 * (E^(alpha * 
                  u4) * (log(E) * u4) * (-1 + E^(alpha * u4))^2))) * 
                  (-1 + E^(alpha * u5))^3 + (-1 + E^(alpha * 
                  u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * 
                  u3))^3 * (-1 + E^(alpha * u4))^3 * (3 * (E^(alpha * 
                  u5) * (log(E) * u5) * (-1 + E^(alpha * u5))^2))) * 
                  (-1 + E^(alpha * u6))^3 + (-1 + E^(alpha * 
                  u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * 
                  u3))^3 * (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * 
                  u5))^3 * (3 * (E^(alpha * u6) * (log(E) * u6) * 
                  (-1 + E^(alpha * u6))^2)))/((-1 + E^(alpha * 
                  u1))^3 * (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * 
                  u3))^3 * (-1 + E^(alpha * u4))^3 * (-1 + E^(alpha * 
                  u5))^3 * (-1 + E^(alpha * u6))^3)^2) + ((66 * 
            (E^(2 * alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (log(E) * (2 * (-5 + u1 + u2 + u3 + u4 + u5 + 
                  u6)))) * (-1 + E^alpha)^12 + 66 * E^(2 * alpha * 
            (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * (12 * (E^alpha * 
            log(E) * (-1 + E^alpha)^11)))/((-1 + E^(alpha * u1))^2 * 
            (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
            (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
            (-1 + E^(alpha * u6))^2) - (66 * E^(2 * alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^12) * 
            (((((2 * (E^(alpha * u1) * (log(E) * u1) * (-1 + 
                E^(alpha * u1))) * (-1 + E^(alpha * u2))^2 + 
                (-1 + E^(alpha * u1))^2 * (2 * (E^(alpha * u2) * 
                  (log(E) * u2) * (-1 + E^(alpha * u2))))) * 
                (-1 + E^(alpha * u3))^2 + (-1 + E^(alpha * u1))^2 * 
                (-1 + E^(alpha * u2))^2 * (2 * (E^(alpha * u3) * 
                (log(E) * u3) * (-1 + E^(alpha * u3))))) * (-1 + 
                E^(alpha * u4))^2 + (-1 + E^(alpha * u1))^2 * 
                (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
                (2 * (E^(alpha * u4) * (log(E) * u4) * (-1 + 
                  E^(alpha * u4))))) * (-1 + E^(alpha * u5))^2 + 
                (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * 
                  (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
                  u4))^2 * (2 * (E^(alpha * u5) * (log(E) * u5) * 
                  (-1 + E^(alpha * u5))))) * (-1 + E^(alpha * 
                u6))^2 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
                u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * 
                u4))^2 * (-1 + E^(alpha * u5))^2 * (2 * (E^(alpha * 
                u6) * (log(E) * u6) * (-1 + E^(alpha * u6)))))/((-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + 
            E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2)^2) + 
            ((66 * (E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + 
                u5 + u6)) * (log(E) * (2 * (-4 + u1 + u2 + u3 + 
                u4 + u5 + u6)))) * (-1 + E^alpha)^12 + 66 * E^(2 * 
                alpha * (-4 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (12 * (E^alpha * log(E) * (-1 + E^alpha)^11)))/((-1 + 
                E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * 
                (-1 + E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * 
                (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * u6))^2) - 
                (66 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + 
                  u5 + u6)) * (-1 + E^alpha)^12) * (((((2 * (E^(alpha * 
                  u1) * (log(E) * u1) * (-1 + E^(alpha * u1))) * 
                  (-1 + E^(alpha * u2))^2 + (-1 + E^(alpha * 
                  u1))^2 * (2 * (E^(alpha * u2) * (log(E) * u2) * 
                  (-1 + E^(alpha * u2))))) * (-1 + E^(alpha * 
                  u3))^2 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
                  u2))^2 * (2 * (E^(alpha * u3) * (log(E) * u3) * 
                  (-1 + E^(alpha * u3))))) * (-1 + E^(alpha * 
                  u4))^2 + (-1 + E^(alpha * u1))^2 * (-1 + E^(alpha * 
                  u2))^2 * (-1 + E^(alpha * u3))^2 * (2 * (E^(alpha * 
                  u4) * (log(E) * u4) * (-1 + E^(alpha * u4))))) * 
                  (-1 + E^(alpha * u5))^2 + (-1 + E^(alpha * 
                  u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
                  u3))^2 * (-1 + E^(alpha * u4))^2 * (2 * (E^(alpha * 
                  u5) * (log(E) * u5) * (-1 + E^(alpha * u5))))) * 
                  (-1 + E^(alpha * u6))^2 + (-1 + E^(alpha * 
                  u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
                  u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
                  u5))^2 * (2 * (E^(alpha * u6) * (log(E) * u6) * 
                  (-1 + E^(alpha * u6)))))/((-1 + E^(alpha * 
                  u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
                  u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
                  u5))^2 * (-1 + E^(alpha * u6))^2)^2) - ((26 * 
            (E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (log(E) * (-5 + u1 + u2 + u3 + u4 + u5 + u6))) * 
            (-1 + E^alpha)^6 + 26 * E^(alpha * (-5 + u1 + u2 + 
            u3 + u4 + u5 + u6)) * (6 * (E^alpha * log(E) * (-1 + 
            E^alpha)^5)))/((-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * u4)) * 
            (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) - 
            (26 * E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (-1 + E^alpha)^6) * (((((E^(alpha * u1) * (log(E) * 
                u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
                u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
                E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (E^(alpha * u3) * (log(E) * 
                u3))) * (-1 + E^(alpha * u4)) + (-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (E^(alpha * u4) * (log(E) * u4))) * (-1 + 
                E^(alpha * u5)) + (-1 + E^(alpha * u1)) * (-1 + 
                E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
                E^(alpha * u4)) * (E^(alpha * u5) * (log(E) * 
                u5))) * (-1 + E^(alpha * u6)) + (-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (E^(alpha * u6) * (log(E) * u6)))/((-1 + 
                E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + 
                E^(alpha * u3)) * (-1 + E^(alpha * u4)) * (-1 + 
                E^(alpha * u5)) * (-1 + E^(alpha * u6)))^2) + 
            ((78 * (E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5 + 
                u6)) * (log(E) * (-4 + u1 + u2 + u3 + u4 + u5 + 
                u6))) * (-1 + E^alpha)^6 + 78 * E^(alpha * (-4 + 
                u1 + u2 + u3 + u4 + u5 + u6)) * (6 * (E^alpha * 
                log(E) * (-1 + E^alpha)^5)))/((-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (-1 + E^(alpha * u6))) - (78 * E^(alpha * 
                (-4 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * 
                (((((E^(alpha * u1) * (log(E) * u1) * (-1 + E^(alpha * 
                  u2)) + (-1 + E^(alpha * u1)) * (E^(alpha * 
                  u2) * (log(E) * u2))) * (-1 + E^(alpha * u3)) + 
                  (-1 + E^(alpha * u1)) * (-1 + E^(alpha * u2)) * 
                    (E^(alpha * u3) * (log(E) * u3))) * (-1 + 
                  E^(alpha * u4)) + (-1 + E^(alpha * u1)) * (-1 + 
                  E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (E^(alpha * 
                  u4) * (log(E) * u4))) * (-1 + E^(alpha * u5)) + 
                  (-1 + E^(alpha * u1)) * (-1 + E^(alpha * u2)) * 
                    (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                    u4)) * (E^(alpha * u5) * (log(E) * u5))) * 
                  (-1 + E^(alpha * u6)) + (-1 + E^(alpha * u1)) * 
                  (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
                  (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
                  (E^(alpha * u6) * (log(E) * u6)))/((-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (-1 + E^(alpha * u6)))^2) - ((78 * (E^(alpha * 
            (-3 + u1 + u2 + u3 + u4 + u5 + u6)) * (log(E) * (-3 + 
            u1 + u2 + u3 + u4 + u5 + u6))) * (-1 + E^alpha)^6 + 
            78 * E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5 + u6)) * 
                (6 * (E^alpha * log(E) * (-1 + E^alpha)^5)))/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))) - (78 * E^(alpha * (-3 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * (((((E^(alpha * 
            u1) * (log(E) * u1) * (-1 + E^(alpha * u2)) + (-1 + 
            E^(alpha * u1)) * (E^(alpha * u2) * (log(E) * u2))) * 
            (-1 + E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (E^(alpha * u3) * (log(E) * u3))) * 
            (-1 + E^(alpha * u4)) + (-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (E^(alpha * 
            u4) * (log(E) * u4))) * (-1 + E^(alpha * u5)) + (-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (E^(alpha * u5) * 
            (log(E) * u5))) * (-1 + E^(alpha * u6)) + (-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (E^(alpha * 
            u6) * (log(E) * u6)))/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6)))^2) + 
            ((26 * (E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5 + 
                u6)) * (log(E) * (-2 + u1 + u2 + u3 + u4 + u5 + 
                u6))) * (-1 + E^alpha)^6 + 26 * E^(alpha * (-2 + 
                u1 + u2 + u3 + u4 + u5 + u6)) * (6 * (E^alpha * 
                log(E) * (-1 + E^alpha)^5)))/((-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (-1 + E^(alpha * u6))) - (26 * E^(alpha * 
                (-2 + u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6) * 
                (((((E^(alpha * u1) * (log(E) * u1) * (-1 + E^(alpha * 
                  u2)) + (-1 + E^(alpha * u1)) * (E^(alpha * 
                  u2) * (log(E) * u2))) * (-1 + E^(alpha * u3)) + 
                  (-1 + E^(alpha * u1)) * (-1 + E^(alpha * u2)) * 
                    (E^(alpha * u3) * (log(E) * u3))) * (-1 + 
                  E^(alpha * u4)) + (-1 + E^(alpha * u1)) * (-1 + 
                  E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (E^(alpha * 
                  u4) * (log(E) * u4))) * (-1 + E^(alpha * u5)) + 
                  (-1 + E^(alpha * u1)) * (-1 + E^(alpha * u2)) * 
                    (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
                    u4)) * (E^(alpha * u5) * (log(E) * u5))) * 
                  (-1 + E^(alpha * u6)) + (-1 + E^(alpha * u1)) * 
                  (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
                  (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
                  (E^(alpha * u6) * (log(E) * u6)))/((-1 + E^(alpha * 
                u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
                u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * 
                u5)) * (-1 + E^(alpha * u6)))^2)))/((-1 + E^(alpha * 
        u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
        (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + 
        E^(alpha * u6))^2 * (1 - E^alpha + (E^(alpha * (-5 + 
        u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
        E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
        u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
        (-1 + E^(alpha * u6))))^6) - (alpha^5 * E^(alpha * (1 + 
        u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^(-alpha))^6 * 
        (-1 + E^alpha) * (1 - 4 * E^alpha + 6 * E^(2 * alpha) - 
        4 * E^(3 * alpha) + E^(4 * alpha) + (26 * E^(4 * alpha) * 
        (-1 + E^(-alpha))^18)/((-1 + E^(-(alpha * u1)))^3 * (-1 + 
        E^(-(alpha * u2)))^3 * (-1 + E^(-(alpha * u3)))^3 * (-1 + 
        E^(-(alpha * u4)))^3 * (-1 + E^(-(alpha * u5)))^3 * (-1 + 
        E^(-(alpha * u6)))^3) - (132 * E^(3 * alpha) * (-1 + 
        E^(-alpha))^12)/((-1 + E^(-(alpha * u1)))^2 * (-1 + E^(-(alpha * 
        u2)))^2 * (-1 + E^(-(alpha * u3)))^2 * (-1 + E^(-(alpha * 
        u4)))^2 * (-1 + E^(-(alpha * u5)))^2 * (-1 + E^(-(alpha * 
        u6)))^2) + (E^(4 * alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^24)/((-1 + E^(alpha * u1))^4 * 
        (-1 + E^(alpha * u2))^4 * (-1 + E^(alpha * u3))^4 * (-1 + 
        E^(alpha * u4))^4 * (-1 + E^(alpha * u5))^4 * (-1 + E^(alpha * 
        u6))^4) - (26 * E^(3 * alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^18)/((-1 + E^(alpha * u1))^3 * 
        (-1 + E^(alpha * u2))^3 * (-1 + E^(alpha * u3))^3 * (-1 + 
        E^(alpha * u4))^3 * (-1 + E^(alpha * u5))^3 * (-1 + E^(alpha * 
        u6))^3) + (66 * E^(2 * alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^12)/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
        u6))^2) + (66 * E^(2 * alpha * (-4 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^12)/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
        u6))^2) - (26 * E^(alpha * (-5 + u1 + u2 + u3 + u4 + 
        u5 + u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * 
        (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
        E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
        u6))) + (78 * E^(alpha * (-4 + u1 + u2 + u3 + u4 + u5 + 
        u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
        E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
        u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) - 
        (78 * E^(alpha * (-3 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))) + 
        (26 * E^(alpha * (-2 + u1 + u2 + u3 + u4 + u5 + u6)) * 
            (-1 + E^alpha)^6)/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6))))) * 
        ((((((2 * (E^(alpha * u1) * (log(E) * u1) * (-1 + E^(alpha * 
            u1))) * (-1 + E^(alpha * u2))^2 + (-1 + E^(alpha * 
            u1))^2 * (2 * (E^(alpha * u2) * (log(E) * u2) * (-1 + 
            E^(alpha * u2))))) * (-1 + E^(alpha * u3))^2 + (-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (2 * 
            (E^(alpha * u3) * (log(E) * u3) * (-1 + E^(alpha * 
                u3))))) * (-1 + E^(alpha * u4))^2 + (-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (2 * (E^(alpha * u4) * (log(E) * u4) * (-1 + 
            E^(alpha * u4))))) * (-1 + E^(alpha * u5))^2 + (-1 + 
            E^(alpha * u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + 
            E^(alpha * u3))^2 * (-1 + E^(alpha * u4))^2 * (2 * 
            (E^(alpha * u5) * (log(E) * u5) * (-1 + E^(alpha * 
                u5))))) * (-1 + E^(alpha * u6))^2 + (-1 + E^(alpha * 
            u1))^2 * (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * 
            u3))^2 * (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * 
            u5))^2 * (2 * (E^(alpha * u6) * (log(E) * u6) * (-1 + 
            E^(alpha * u6))))) * (1 - E^alpha + (E^(alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))))^6 + (-1 + E^(alpha * u1))^2 * 
            (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * 
            (-1 + E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * 
            (-1 + E^(alpha * u6))^2 * (6 * (((E^(alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (log(E) * (-5 + u1 + 
            u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6 + E^(alpha * 
            (-5 + u1 + u2 + u3 + u4 + u5 + u6)) * (6 * (E^alpha * 
            log(E) * (-1 + E^alpha)^5)))/((-1 + E^(alpha * u1)) * 
            (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + 
            E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * 
            u6))) - (E^(alpha * (-5 + u1 + u2 + u3 + u4 + u5 + 
            u6)) * (-1 + E^alpha)^6) * (((((E^(alpha * u1) * 
            (log(E) * u1) * (-1 + E^(alpha * u2)) + (-1 + E^(alpha * 
            u1)) * (E^(alpha * u2) * (log(E) * u2))) * (-1 + 
            E^(alpha * u3)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (E^(alpha * u3) * (log(E) * u3))) * (-1 + 
            E^(alpha * u4)) + (-1 + E^(alpha * u1)) * (-1 + E^(alpha * 
            u2)) * (-1 + E^(alpha * u3)) * (E^(alpha * u4) * 
            (log(E) * u4))) * (-1 + E^(alpha * u5)) + (-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (E^(alpha * u5) * (log(E) * 
            u5))) * (-1 + E^(alpha * u6)) + (-1 + E^(alpha * 
            u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
            (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (E^(alpha * 
            u6) * (log(E) * u6)))/((-1 + E^(alpha * u1)) * (-1 + 
            E^(alpha * u2)) * (-1 + E^(alpha * u3)) * (-1 + E^(alpha * 
            u4)) * (-1 + E^(alpha * u5)) * (-1 + E^(alpha * u6)))^2 - 
            E^alpha * log(E)) * (1 - E^alpha + (E^(alpha * (-5 + 
            u1 + u2 + u3 + u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + 
            E^(alpha * u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * 
            u3)) * (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * 
            (-1 + E^(alpha * u6))))^5)))/((-1 + E^(alpha * u1))^2 * 
        (-1 + E^(alpha * u2))^2 * (-1 + E^(alpha * u3))^2 * (-1 + 
        E^(alpha * u4))^2 * (-1 + E^(alpha * u5))^2 * (-1 + E^(alpha * 
        u6))^2 * (1 - E^alpha + (E^(alpha * (-5 + u1 + u2 + u3 + 
        u4 + u5 + u6)) * (-1 + E^alpha)^6)/((-1 + E^(alpha * 
        u1)) * (-1 + E^(alpha * u2)) * (-1 + E^(alpha * u3)) * 
        (-1 + E^(alpha * u4)) * (-1 + E^(alpha * u5)) * (-1 + 
        E^(alpha * u6))))^6)^2)
`frankCopula.pdfDerWrtPar.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- 1 + u1
    .expr2 <- .expr1 + u2
    .expr4 <- E^(alpha * .expr2)
    .expr5 <- log(E)
    .expr11 <- E^alpha
    .expr12 <- -1 + .expr11
    .expr14 <- alpha * .expr4
    .expr15 <- .expr11 * .expr5
    .expr20 <- E^(alpha + alpha * u1)
    .expr22 <- u1 + u2
    .expr24 <- E^(alpha * .expr22)
    .expr28 <- E^(alpha + alpha * u2)
    .expr29 <- .expr11 - .expr20 + .expr24 - .expr28
    .expr30 <- .expr29^2
    .value <- ((.expr4 + alpha * (.expr4 * (.expr5 * .expr2))) * 
        .expr12 + .expr14 * .expr15)/.expr30 - .expr14 * .expr12 * 
        (2 * ((.expr15 - .expr20 * (.expr5 * .expr1) + .expr24 * 
            (.expr5 * .expr22) - .expr28 * (.expr5 * (1 + u2))) * 
            .expr29))/.expr30^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr5 <- -2 + u1 + u2 + u3
    .expr7 <- E^(alpha * .expr5)
    .expr9 <- alpha^2
    .expr10 <- log(E)
    .expr12 <- .expr7 * (.expr10 * .expr5)
    .expr15 <- -1
    .expr16 <- E^alpha
    .expr17 <- .expr15 + .expr16
    .expr18 <- .expr17^2
    .expr20 <- .expr9 * .expr7
    .expr27 <- E^(alpha * u1)
    .expr30 <- E^(alpha * u2)
    .expr32 <- u1 + u2
    .expr34 <- E^(alpha * .expr32)
    .expr37 <- E^(alpha * u3)
    .expr39 <- u1 + u3
    .expr41 <- E^(alpha * .expr39)
    .expr43 <- u2 + u3
    .expr45 <- E^(alpha * .expr43)
    .expr50 <- .expr15 + u1 + u2 + u3
    .expr52 <- E^(alpha * .expr50)
    .expr53 <- 2 * .expr52
    .expr55 <- .expr32 + u3
    .expr57 <- E^(alpha * .expr55)
    .expr59 <- .expr15 + .expr27 + .expr30 - .expr34 + .expr37 - 
        .expr41 - .expr45 + .expr7 - .expr53 + 2 * .expr57
    .expr61 <- .expr20 * .expr18
    .expr66 <- .expr27 * (.expr10 * u1) + .expr30 * (.expr10 * 
        u2)
    .expr68 <- .expr34 * (.expr10 * .expr32)
    .expr71 <- .expr37 * (.expr10 * u3)
    .expr74 <- .expr41 * (.expr10 * .expr39)
    .expr77 <- .expr45 * (.expr10 * .expr43)
    .expr82 <- 2 * (.expr52 * (.expr10 * .expr50))
    .expr97 <- 1 - .expr27 - .expr30 + .expr34 - .expr37 + .expr41 + 
        .expr45 + .expr7 - .expr53
    .expr98 <- .expr97^3
    .value <- (((2 * alpha * .expr7 + .expr9 * .expr12) * .expr18 + 
        .expr20 * (2 * (.expr16 * .expr10 * .expr17))) * .expr59 + 
        .expr61 * (.expr66 - .expr68 + .expr71 - .expr74 - .expr77 + 
            .expr12 - .expr82 + 2 * (.expr57 * (.expr10 * .expr55))))/.expr98 - 
        .expr61 * .expr59 * (3 * ((.expr68 - .expr66 - .expr71 + 
            .expr74 + .expr77 + .expr12 - .expr82) * .expr97^2))/.expr98^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr6 <- 1 + u1 + u2 + u3 + u4
    .expr8 <- E^(alpha * .expr6)
    .expr10 <- alpha^3
    .expr11 <- log(E)
    .expr16 <- -1
    .expr18 <- E^-alpha
    .expr19 <- .expr16 + .expr18
    .expr20 <- .expr19^4
    .expr22 <- .expr10 * .expr8
    .expr29 <- E^alpha
    .expr30 <- .expr16 + .expr29
    .expr32 <- .expr22 * .expr20
    .expr33 <- .expr29 * .expr11
    .expr38 <- 2 * alpha
    .expr39 <- E^.expr38
    .expr45 <- -3 + u1 + u2 + u3 + u4
    .expr47 <- E^(.expr38 * .expr45)
    .expr48 <- .expr30^8
    .expr49 <- .expr47 * .expr48
    .expr51 <- E^(alpha * u1)
    .expr52 <- .expr16 + .expr51
    .expr53 <- .expr52^2
    .expr55 <- E^(alpha * u2)
    .expr56 <- .expr16 + .expr55
    .expr57 <- .expr56^2
    .expr58 <- .expr53 * .expr57
    .expr60 <- E^(alpha * u3)
    .expr61 <- .expr16 + .expr60
    .expr62 <- .expr61^2
    .expr63 <- .expr58 * .expr62
    .expr65 <- E^(alpha * u4)
    .expr66 <- .expr16 + .expr65
    .expr67 <- .expr66^2
    .expr68 <- .expr63 * .expr67
    .expr72 <- E^(alpha * .expr45)
    .expr73 <- 4 * .expr72
    .expr74 <- .expr30^4
    .expr75 <- .expr73 * .expr74
    .expr76 <- .expr52 * .expr56
    .expr77 <- .expr76 * .expr61
    .expr78 <- .expr77 * .expr66
    .expr85 <- -2 + u1 + u2 + u3 + u4
    .expr87 <- E^(alpha * .expr85)
    .expr88 <- 4 * .expr87
    .expr89 <- .expr88 * .expr74
    .expr91 <- 1 - 2 * .expr29 + .expr39 + .expr49/.expr68 - 
        .expr75/.expr78 + .expr89/.expr78
    .expr93 <- .expr32 * .expr30
    .expr109 <- .expr51 * (.expr11 * u1)
    .expr114 <- .expr55 * (.expr11 * u2)
    .expr121 <- .expr60 * (.expr11 * u3)
    .expr128 <- .expr65 * (.expr11 * u4)
    .expr132 <- ((2 * (.expr109 * .expr52) * .expr57 + .expr53 * 
        (2 * (.expr114 * .expr56))) * .expr62 + .expr58 * (2 * 
        (.expr121 * .expr61))) * .expr67 + .expr63 * (2 * (.expr128 * 
        .expr66))
    .expr139 <- .expr72 * (.expr11 * .expr45)
    .expr144 <- 4 * (.expr33 * .expr30^3)
    .expr156 <- ((.expr109 * .expr56 + .expr52 * .expr114) * 
        .expr61 + .expr76 * .expr121) * .expr66 + .expr77 * .expr128
    .expr158 <- .expr78^2
    .expr176 <- .expr72 * .expr74
    .expr178 <- 1 - .expr29 + .expr176/.expr78
    .expr179 <- .expr178^4
    .expr180 <- .expr68 * .expr179
    .value <- ((((3 * alpha^2 * .expr8 + .expr10 * (.expr8 * 
        (.expr11 * .expr6))) * .expr20 - .expr22 * (4 * (.expr18 * 
        .expr11 * .expr19^3))) * .expr30 + .expr32 * .expr33) * 
        .expr91 + .expr93 * (.expr39 * (.expr11 * 2) - 2 * .expr33 + 
        ((.expr47 * (.expr11 * (2 * .expr45)) * .expr48 + .expr47 * 
            (8 * (.expr33 * .expr30^7)))/.expr68 - .expr49 * 
            .expr132/.expr68^2) - ((4 * .expr139 * .expr74 + 
        .expr73 * .expr144)/.expr78 - .expr75 * .expr156/.expr158) + 
        ((4 * (.expr87 * (.expr11 * .expr85)) * .expr74 + .expr88 * 
            .expr144)/.expr78 - .expr89 * .expr156/.expr158)))/.expr180 - 
        .expr93 * .expr91 * (.expr132 * .expr179 + .expr68 * 
            (4 * (((.expr139 * .expr74 + .expr72 * .expr144)/.expr78 - 
                .expr176 * .expr156/.expr158 - .expr33) * .expr178^3)))/.expr180^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr7 <- 1 + u1 + u2 + u3 + u4 + u5
    .expr9 <- E^(alpha * .expr7)
    .expr11 <- alpha^4
    .expr12 <- log(E)
    .expr17 <- -1
    .expr19 <- E^-alpha
    .expr20 <- .expr17 + .expr19
    .expr21 <- .expr20^5
    .expr23 <- .expr11 * .expr9
    .expr24 <- .expr19 * .expr12
    .expr30 <- E^alpha
    .expr31 <- .expr17 + .expr30
    .expr33 <- .expr23 * .expr21
    .expr34 <- .expr30 * .expr12
    .expr39 <- 2 * alpha
    .expr40 <- E^.expr39
    .expr43 <- 3 * alpha
    .expr44 <- E^.expr43
    .expr46 <- 11 * .expr44
    .expr47 <- .expr20^10
    .expr48 <- .expr46 * .expr47
    .expr49 <- alpha * u1
    .expr51 <- E^-.expr49
    .expr52 <- .expr17 + .expr51
    .expr53 <- .expr52^2
    .expr54 <- alpha * u2
    .expr56 <- E^-.expr54
    .expr57 <- .expr17 + .expr56
    .expr58 <- .expr57^2
    .expr59 <- .expr53 * .expr58
    .expr60 <- alpha * u3
    .expr62 <- E^-.expr60
    .expr63 <- .expr17 + .expr62
    .expr64 <- .expr63^2
    .expr65 <- .expr59 * .expr64
    .expr66 <- alpha * u4
    .expr68 <- E^-.expr66
    .expr69 <- .expr17 + .expr68
    .expr70 <- .expr69^2
    .expr71 <- .expr65 * .expr70
    .expr72 <- alpha * u5
    .expr74 <- E^-.expr72
    .expr75 <- .expr17 + .expr74
    .expr76 <- .expr75^2
    .expr77 <- .expr71 * .expr76
    .expr85 <- -4 + u1 + u2 + u3 + u4 + u5
    .expr87 <- E^(.expr43 * .expr85)
    .expr88 <- .expr31^15
    .expr89 <- .expr87 * .expr88
    .expr90 <- E^.expr49
    .expr91 <- .expr17 + .expr90
    .expr92 <- .expr91^3
    .expr93 <- E^.expr54
    .expr94 <- .expr17 + .expr93
    .expr95 <- .expr94^3
    .expr96 <- .expr92 * .expr95
    .expr97 <- E^.expr60
    .expr98 <- .expr17 + .expr97
    .expr99 <- .expr98^3
    .expr100 <- .expr96 * .expr99
    .expr101 <- E^.expr66
    .expr102 <- .expr17 + .expr101
    .expr103 <- .expr102^3
    .expr104 <- .expr100 * .expr103
    .expr105 <- E^.expr72
    .expr106 <- .expr17 + .expr105
    .expr107 <- .expr106^3
    .expr108 <- .expr104 * .expr107
    .expr112 <- E^(.expr39 * .expr85)
    .expr113 <- 11 * .expr112
    .expr114 <- .expr31^10
    .expr115 <- .expr113 * .expr114
    .expr116 <- .expr91^2
    .expr117 <- .expr94^2
    .expr118 <- .expr116 * .expr117
    .expr119 <- .expr98^2
    .expr120 <- .expr118 * .expr119
    .expr121 <- .expr102^2
    .expr122 <- .expr120 * .expr121
    .expr123 <- .expr106^2
    .expr124 <- .expr122 * .expr123
    .expr128 <- E^(alpha * .expr85)
    .expr129 <- 11 * .expr128
    .expr130 <- .expr31^5
    .expr131 <- .expr129 * .expr130
    .expr132 <- .expr91 * .expr94
    .expr133 <- .expr132 * .expr98
    .expr134 <- .expr133 * .expr102
    .expr135 <- .expr134 * .expr106
    .expr143 <- -3 + u1 + u2 + u3 + u4 + u5
    .expr145 <- E^(alpha * .expr143)
    .expr146 <- 22 * .expr145
    .expr147 <- .expr146 * .expr130
    .expr155 <- -2 + u1 + u2 + u3 + u4 + u5
    .expr157 <- E^(alpha * .expr155)
    .expr158 <- 11 * .expr157
    .expr159 <- .expr158 * .expr130
    .expr161 <- .expr17 + 3 * .expr30 - 3 * .expr40 + .expr44 + 
        .expr48/.expr77 + .expr89/.expr108 - .expr115/.expr124 + 
        .expr131/.expr135 - .expr147/.expr135 + .expr159/.expr135
    .expr163 <- .expr33 * .expr31
    .expr170 <- .expr44 * (.expr12 * 3)
    .expr180 <- .expr12 * u5
    .expr185 <- .expr12 * u4
    .expr190 <- .expr12 * u3
    .expr195 <- .expr12 * u2
    .expr200 <- .expr12 * u1
    .expr227 <- .expr90 * .expr200
    .expr231 <- .expr93 * .expr195
    .expr237 <- .expr97 * .expr190
    .expr243 <- .expr101 * .expr185
    .expr249 <- .expr105 * .expr180
    .expr291 <- (((2 * (.expr227 * .expr91) * .expr117 + .expr116 * 
        (2 * (.expr231 * .expr94))) * .expr119 + .expr118 * (2 * 
        (.expr237 * .expr98))) * .expr121 + .expr120 * (2 * (.expr243 * 
        .expr102))) * .expr123 + .expr122 * (2 * (.expr249 * 
        .expr106))
    .expr298 <- .expr128 * (.expr12 * .expr85)
    .expr303 <- 5 * (.expr34 * .expr31^4)
    .expr318 <- (((.expr227 * .expr94 + .expr91 * .expr231) * 
        .expr98 + .expr132 * .expr237) * .expr102 + .expr133 * 
        .expr243) * .expr106 + .expr134 * .expr249
    .expr320 <- .expr135^2
    .expr349 <- .expr128 * .expr130
    .expr351 <- 1 - .expr30 + .expr349/.expr135
    .expr352 <- .expr351^5
    .expr353 <- .expr124 * .expr352
    .value <- -(((((4 * alpha^3 * .expr9 + .expr11 * (.expr9 * 
        (.expr12 * .expr7))) * .expr21 - .expr23 * (5 * (.expr24 * 
        .expr20^4))) * .expr31 + .expr33 * .expr34) * .expr161 + 
        .expr163 * (3 * .expr34 - 3 * (.expr40 * (.expr12 * 2)) + 
            .expr170 + ((11 * .expr170 * .expr47 - .expr46 * 
            (10 * (.expr24 * .expr20^9)))/.expr77 + .expr48 * 
            (.expr71 * (2 * (.expr74 * .expr180 * .expr75)) + 
                (.expr65 * (2 * (.expr68 * .expr185 * .expr69)) + 
                  (.expr59 * (2 * (.expr62 * .expr190 * .expr63)) + 
                    (.expr53 * (2 * (.expr56 * .expr195 * .expr57)) + 
                      2 * (.expr51 * .expr200 * .expr52) * .expr58) * 
                      .expr64) * .expr70) * .expr76)/.expr77^2) + 
            ((.expr87 * (.expr12 * (3 * .expr85)) * .expr88 + 
                .expr87 * (15 * (.expr34 * .expr31^14)))/.expr108 - 
                .expr89 * ((((3 * (.expr227 * .expr116) * .expr95 + 
                  .expr92 * (3 * (.expr231 * .expr117))) * .expr99 + 
                  .expr96 * (3 * (.expr237 * .expr119))) * .expr103 + 
                  .expr100 * (3 * (.expr243 * .expr121))) * .expr107 + 
                  .expr104 * (3 * (.expr249 * .expr123)))/.expr108^2) - 
            ((11 * (.expr112 * (.expr12 * (2 * .expr85))) * .expr114 + 
                .expr113 * (10 * (.expr34 * .expr31^9)))/.expr124 - 
                .expr115 * .expr291/.expr124^2) + ((11 * .expr298 * 
            .expr130 + .expr129 * .expr303)/.expr135 - .expr131 * 
            .expr318/.expr320) - ((22 * (.expr145 * (.expr12 * 
            .expr143)) * .expr130 + .expr146 * .expr303)/.expr135 - 
            .expr147 * .expr318/.expr320) + ((11 * (.expr157 * 
            (.expr12 * .expr155)) * .expr130 + .expr158 * .expr303)/.expr135 - 
            .expr159 * .expr318/.expr320)))/.expr353 - .expr163 * 
        .expr161 * (.expr291 * .expr352 + .expr124 * (5 * (((.expr298 * 
        .expr130 + .expr128 * .expr303)/.expr135 - .expr349 * 
        .expr318/.expr320 - .expr34) * .expr351^4)))/.expr353^2)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr8 <- 1 + u1 + u2 + u3 + u4 + u5 + u6
    .expr10 <- E^(alpha * .expr8)
    .expr12 <- alpha^5
    .expr13 <- log(E)
    .expr18 <- -1
    .expr20 <- E^-alpha
    .expr21 <- .expr18 + .expr20
    .expr22 <- .expr21^6
    .expr24 <- .expr12 * .expr10
    .expr25 <- .expr20 * .expr13
    .expr31 <- E^alpha
    .expr32 <- .expr18 + .expr31
    .expr34 <- .expr24 * .expr22
    .expr35 <- .expr31 * .expr13
    .expr40 <- 2 * alpha
    .expr41 <- E^.expr40
    .expr44 <- 3 * alpha
    .expr45 <- E^.expr44
    .expr48 <- 4 * alpha
    .expr49 <- E^.expr48
    .expr51 <- 26 * .expr49
    .expr52 <- .expr21^18
    .expr53 <- .expr51 * .expr52
    .expr54 <- alpha * u1
    .expr56 <- E^-.expr54
    .expr57 <- .expr18 + .expr56
    .expr58 <- .expr57^3
    .expr59 <- alpha * u2
    .expr61 <- E^-.expr59
    .expr62 <- .expr18 + .expr61
    .expr63 <- .expr62^3
    .expr64 <- .expr58 * .expr63
    .expr65 <- alpha * u3
    .expr67 <- E^-.expr65
    .expr68 <- .expr18 + .expr67
    .expr69 <- .expr68^3
    .expr70 <- .expr64 * .expr69
    .expr71 <- alpha * u4
    .expr73 <- E^-.expr71
    .expr74 <- .expr18 + .expr73
    .expr75 <- .expr74^3
    .expr76 <- .expr70 * .expr75
    .expr77 <- alpha * u5
    .expr79 <- E^-.expr77
    .expr80 <- .expr18 + .expr79
    .expr81 <- .expr80^3
    .expr82 <- .expr76 * .expr81
    .expr83 <- alpha * u6
    .expr85 <- E^-.expr83
    .expr86 <- .expr18 + .expr85
    .expr87 <- .expr86^3
    .expr88 <- .expr82 * .expr87
    .expr91 <- 132 * .expr45
    .expr92 <- .expr21^12
    .expr93 <- .expr91 * .expr92
    .expr94 <- .expr57^2
    .expr95 <- .expr62^2
    .expr96 <- .expr94 * .expr95
    .expr97 <- .expr68^2
    .expr98 <- .expr96 * .expr97
    .expr99 <- .expr74^2
    .expr100 <- .expr98 * .expr99
    .expr101 <- .expr80^2
    .expr102 <- .expr100 * .expr101
    .expr103 <- .expr86^2
    .expr104 <- .expr102 * .expr103
    .expr113 <- -5 + u1 + u2 + u3 + u4 + u5 + u6
    .expr115 <- E^(.expr48 * .expr113)
    .expr116 <- .expr32^24
    .expr117 <- .expr115 * .expr116
    .expr118 <- E^.expr54
    .expr119 <- .expr18 + .expr118
    .expr120 <- .expr119^4
    .expr121 <- E^.expr59
    .expr122 <- .expr18 + .expr121
    .expr123 <- .expr122^4
    .expr124 <- .expr120 * .expr123
    .expr125 <- E^.expr65
    .expr126 <- .expr18 + .expr125
    .expr127 <- .expr126^4
    .expr128 <- .expr124 * .expr127
    .expr129 <- E^.expr71
    .expr130 <- .expr18 + .expr129
    .expr131 <- .expr130^4
    .expr132 <- .expr128 * .expr131
    .expr133 <- E^.expr77
    .expr134 <- .expr18 + .expr133
    .expr135 <- .expr134^4
    .expr136 <- .expr132 * .expr135
    .expr137 <- E^.expr83
    .expr138 <- .expr18 + .expr137
    .expr139 <- .expr138^4
    .expr140 <- .expr136 * .expr139
    .expr144 <- E^(.expr44 * .expr113)
    .expr145 <- 26 * .expr144
    .expr146 <- .expr32^18
    .expr147 <- .expr145 * .expr146
    .expr148 <- .expr119^3
    .expr149 <- .expr122^3
    .expr150 <- .expr148 * .expr149
    .expr151 <- .expr126^3
    .expr152 <- .expr150 * .expr151
    .expr153 <- .expr130^3
    .expr154 <- .expr152 * .expr153
    .expr155 <- .expr134^3
    .expr156 <- .expr154 * .expr155
    .expr157 <- .expr138^3
    .expr158 <- .expr156 * .expr157
    .expr162 <- E^(.expr40 * .expr113)
    .expr163 <- 66 * .expr162
    .expr164 <- .expr32^12
    .expr165 <- .expr163 * .expr164
    .expr166 <- .expr119^2
    .expr167 <- .expr122^2
    .expr168 <- .expr166 * .expr167
    .expr169 <- .expr126^2
    .expr170 <- .expr168 * .expr169
    .expr171 <- .expr130^2
    .expr172 <- .expr170 * .expr171
    .expr173 <- .expr134^2
    .expr174 <- .expr172 * .expr173
    .expr175 <- .expr138^2
    .expr176 <- .expr174 * .expr175
    .expr185 <- -4 + u1 + u2 + u3 + u4 + u5 + u6
    .expr187 <- E^(.expr40 * .expr185)
    .expr188 <- 66 * .expr187
    .expr189 <- .expr188 * .expr164
    .expr193 <- E^(alpha * .expr113)
    .expr194 <- 26 * .expr193
    .expr195 <- .expr32^6
    .expr196 <- .expr194 * .expr195
    .expr197 <- .expr119 * .expr122
    .expr198 <- .expr197 * .expr126
    .expr199 <- .expr198 * .expr130
    .expr200 <- .expr199 * .expr134
    .expr201 <- .expr200 * .expr138
    .expr205 <- E^(alpha * .expr185)
    .expr206 <- 78 * .expr205
    .expr207 <- .expr206 * .expr195
    .expr216 <- -3 + u1 + u2 + u3 + u4 + u5 + u6
    .expr218 <- E^(alpha * .expr216)
    .expr219 <- 78 * .expr218
    .expr220 <- .expr219 * .expr195
    .expr229 <- -2 + u1 + u2 + u3 + u4 + u5 + u6
    .expr231 <- E^(alpha * .expr229)
    .expr232 <- 26 * .expr231
    .expr233 <- .expr232 * .expr195
    .expr235 <- 1 - 4 * .expr31 + 6 * .expr41 - 4 * .expr45 + 
        .expr49 + .expr53/.expr88 - .expr93/.expr104 + .expr117/.expr140 - 
        .expr147/.expr158 + .expr165/.expr176 + .expr189/.expr176 - 
        .expr196/.expr201 + .expr207/.expr201 - .expr220/.expr201 + 
        .expr233/.expr201
    .expr237 <- .expr34 * .expr32
    .expr244 <- .expr45 * (.expr13 * 3)
    .expr248 <- .expr49 * (.expr13 * 4)
    .expr258 <- .expr13 * u6
    .expr259 <- .expr85 * .expr258
    .expr263 <- .expr13 * u5
    .expr264 <- .expr79 * .expr263
    .expr268 <- .expr13 * u4
    .expr269 <- .expr73 * .expr268
    .expr273 <- .expr13 * u3
    .expr274 <- .expr67 * .expr273
    .expr278 <- .expr13 * u2
    .expr279 <- .expr61 * .expr278
    .expr283 <- .expr13 * u1
    .expr284 <- .expr56 * .expr283
    .expr352 <- .expr118 * .expr283
    .expr356 <- .expr121 * .expr278
    .expr362 <- .expr125 * .expr273
    .expr368 <- .expr129 * .expr268
    .expr374 <- .expr133 * .expr263
    .expr380 <- .expr137 * .expr258
    .expr440 <- 12 * (.expr35 * .expr32^11)
    .expr470 <- ((((2 * (.expr352 * .expr119) * .expr167 + .expr166 * 
        (2 * (.expr356 * .expr122))) * .expr169 + .expr168 * 
        (2 * (.expr362 * .expr126))) * .expr171 + .expr170 * 
        (2 * (.expr368 * .expr130))) * .expr173 + .expr172 * 
        (2 * (.expr374 * .expr134))) * .expr175 + .expr174 * 
        (2 * (.expr380 * .expr138))
    .expr472 <- .expr176^2
    .expr489 <- .expr193 * (.expr13 * .expr113)
    .expr494 <- 6 * (.expr35 * .expr32^5)
    .expr512 <- ((((.expr352 * .expr122 + .expr119 * .expr356) * 
        .expr126 + .expr197 * .expr362) * .expr130 + .expr198 * 
        .expr368) * .expr134 + .expr199 * .expr374) * .expr138 + 
        .expr200 * .expr380
    .expr514 <- .expr201^2
    .expr554 <- .expr193 * .expr195
    .expr556 <- 1 - .expr31 + .expr554/.expr201
    .expr557 <- .expr556^6
    .expr558 <- .expr176 * .expr557
    .value <- ((((5 * alpha^4 * .expr10 + .expr12 * (.expr10 * 
        (.expr13 * .expr8))) * .expr22 - .expr24 * (6 * (.expr25 * 
        .expr21^5))) * .expr32 + .expr34 * .expr35) * .expr235 + 
        .expr237 * (6 * (.expr41 * (.expr13 * 2)) - 4 * .expr35 - 
            4 * .expr244 + .expr248 + ((26 * .expr248 * .expr52 - 
            .expr51 * (18 * (.expr25 * .expr21^17)))/.expr88 + 
            .expr53 * (.expr82 * (3 * (.expr259 * .expr103)) + 
                (.expr76 * (3 * (.expr264 * .expr101)) + (.expr70 * 
                  (3 * (.expr269 * .expr99)) + (.expr64 * (3 * 
                  (.expr274 * .expr97)) + (.expr58 * (3 * (.expr279 * 
                  .expr95)) + 3 * (.expr284 * .expr94) * .expr63) * 
                  .expr69) * .expr75) * .expr81) * .expr87)/.expr88^2) - 
            ((132 * .expr244 * .expr92 - .expr91 * (12 * (.expr25 * 
                .expr21^11)))/.expr104 + .expr93 * (.expr102 * 
                (2 * (.expr259 * .expr86)) + (.expr100 * (2 * 
                (.expr264 * .expr80)) + (.expr98 * (2 * (.expr269 * 
                .expr74)) + (.expr96 * (2 * (.expr274 * .expr68)) + 
                (.expr94 * (2 * (.expr279 * .expr62)) + 2 * (.expr284 * 
                  .expr57) * .expr95) * .expr97) * .expr99) * 
                .expr101) * .expr103)/.expr104^2) + ((.expr115 * 
            (.expr13 * (4 * .expr113)) * .expr116 + .expr115 * 
            (24 * (.expr35 * .expr32^23)))/.expr140 - .expr117 * 
            (((((4 * (.expr352 * .expr148) * .expr123 + .expr120 * 
                (4 * (.expr356 * .expr149))) * .expr127 + .expr124 * 
                (4 * (.expr362 * .expr151))) * .expr131 + .expr128 * 
                (4 * (.expr368 * .expr153))) * .expr135 + .expr132 * 
                (4 * (.expr374 * .expr155))) * .expr139 + .expr136 * 
                (4 * (.expr380 * .expr157)))/.expr140^2) - ((26 * 
            (.expr144 * (.expr13 * (3 * .expr113))) * .expr146 + 
            .expr145 * (18 * (.expr35 * .expr32^17)))/.expr158 - 
            .expr147 * (((((3 * (.expr352 * .expr166) * .expr149 + 
                .expr148 * (3 * (.expr356 * .expr167))) * .expr151 + 
                .expr150 * (3 * (.expr362 * .expr169))) * .expr153 + 
                .expr152 * (3 * (.expr368 * .expr171))) * .expr155 + 
                .expr154 * (3 * (.expr374 * .expr173))) * .expr157 + 
                .expr156 * (3 * (.expr380 * .expr175)))/.expr158^2) + 
            ((66 * (.expr162 * (.expr13 * (2 * .expr113))) * 
                .expr164 + .expr163 * .expr440)/.expr176 - .expr165 * 
                .expr470/.expr472) + ((66 * (.expr187 * (.expr13 * 
            (2 * .expr185))) * .expr164 + .expr188 * .expr440)/.expr176 - 
            .expr189 * .expr470/.expr472) - ((26 * .expr489 * 
            .expr195 + .expr194 * .expr494)/.expr201 - .expr196 * 
            .expr512/.expr514) + ((78 * (.expr205 * (.expr13 * 
            .expr185)) * .expr195 + .expr206 * .expr494)/.expr201 - 
            .expr207 * .expr512/.expr514) - ((78 * (.expr218 * 
            (.expr13 * .expr216)) * .expr195 + .expr219 * .expr494)/.expr201 - 
            .expr220 * .expr512/.expr514) + ((26 * (.expr231 * 
            (.expr13 * .expr229)) * .expr195 + .expr232 * .expr494)/.expr201 - 
            .expr233 * .expr512/.expr514)))/.expr558 - .expr237 * 
        .expr235 * (.expr470 * .expr557 + .expr176 * (6 * (((.expr489 * 
        .expr195 + .expr193 * .expr494)/.expr201 - .expr554 * 
        .expr512/.expr514 - .expr35) * .expr556^5)))/.expr558^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`frankCopula.genfunDer.expr` <-
expression(alpha/(1 - E^(alpha * u)), (alpha^2 * E^(alpha * u))/(-1 + 
    E^(alpha * u))^2)
`frankCopula.genfunDer.algr` <-
expression({
    .value <- alpha/(1 - E^(alpha * u))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- E^(alpha * u)
    .value <- alpha^2 * .expr3/(-1 + .expr3)^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})