R/tawnExpr.R

In copula: Multivariate Dependence with Copulas

## This file is not to be edited. It is generated by ../inst/docs/mathnb/exprPrep.R
`tawnCopula.cdf.expr` <-
expression(0, u1 * u2 * exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)))
`tawnCopula.cdf.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- u1 * u2
    .value <- .expr1 * exp(-alpha * log(u1) * log(u2)/log(.expr1))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`tawnCopula.cdfDerWrtArg.expr` <-
expression(0, u2 * exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) - 
    u1 * u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * 
        (alpha * (1/u1) * log(u2)/log(u1 * u2) + -alpha * log(u1) * 
            log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2)))
`tawnCopula.cdfDerWrtArg.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr4 <- log(u2)
    .expr5 <- -alpha * log(u1) * .expr4
    .expr6 <- u1 * u2
    .expr7 <- log(.expr6)
    .expr9 <- exp(.expr5/.expr7)
    .value <- u2 * .expr9 - .expr6 * (.expr9 * (alpha * (1/u1) * 
        .expr4/.expr7 + .expr5 * (u2/.expr6)/.expr7^2))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`tawnCopula.cdfDerWrtPar.expr` <-
expression(0, -(u1 * u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (log(u1) * log(u2)/log(u1 * u2)))))
`tawnCopula.cdfDerWrtPar.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- u1 * u2
    .expr3 <- log(u1)
    .expr5 <- log(u2)
    .expr7 <- log(.expr1)
    .value <- -(.expr1 * (exp(-alpha * .expr3 * .expr5/.expr7) * 
        (.expr3 * .expr5/.expr7)))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`tawnCopula.pdf.expr` <-
expression(0, exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) + 
    u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * (-alpha * 
        log(u1) * (1/u2)/log(u1 * u2) - -alpha * log(u1) * log(u2) * 
        (u1/(u1 * u2))/log(u1 * u2)^2)) - (u1 * (exp(-alpha * 
    log(u1) * log(u2)/log(u1 * u2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
    u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
    u2)^2)) + u1 * u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (-alpha * log(u1) * (1/u2)/log(u1 * u2) - -alpha * 
    log(u1) * log(u2) * (u1/(u1 * u2))/log(u1 * u2)^2) * (alpha * 
    (1/u1) * log(u2)/log(u1 * u2) + -alpha * log(u1) * log(u2) * 
    (u2/(u1 * u2))/log(u1 * u2)^2) + exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (alpha * (1/u1) * (1/u2)/log(u1 * u2) - alpha * (1/u1) * 
    log(u2) * (u1/(u1 * u2))/log(u1 * u2)^2 + ((-alpha * log(u1) * 
    (1/u2) * (u2/(u1 * u2)) + -alpha * log(u1) * log(u2) * (1/(u1 * 
    u2) - u2 * u1/(u1 * u2)^2))/log(u1 * u2)^2 - -alpha * log(u1) * 
    log(u2) * (u2/(u1 * u2)) * (2 * (u1/(u1 * u2) * log(u1 * 
    u2)))/(log(u1 * u2)^2)^2)))))
`tawnCopula.pdf.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- -alpha * log(u1)
    .expr4 <- log(u2)
    .expr5 <- .expr3 * .expr4
    .expr6 <- u1 * u2
    .expr7 <- log(.expr6)
    .expr9 <- exp(.expr5/.expr7)
    .expr10 <- 1/u2
    .expr11 <- .expr3 * .expr10
    .expr13 <- u1/.expr6
    .expr15 <- .expr7^2
    .expr18 <- .expr9 * (.expr11/.expr7 - .expr5 * .expr13/.expr15)
    .expr22 <- alpha * (1/u1)
    .expr23 <- .expr22 * .expr4
    .expr25 <- u2/.expr6
    .expr26 <- .expr5 * .expr25
    .expr28 <- .expr23/.expr7 + .expr26/.expr15
    .value <- .expr9 + u2 * .expr18 - (u1 * (.expr9 * .expr28) + 
        .expr6 * (.expr18 * .expr28 + .expr9 * (.expr22 * .expr10/.expr7 - 
            .expr23 * .expr13/.expr15 + ((.expr11 * .expr25 + 
            .expr5 * (1/.expr6 - u2 * u1/.expr6^2))/.expr15 - 
            .expr26 * (2 * (.expr13 * .expr7))/.expr15^2))))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`tawnCopula.pdfDerWrtArg.expr` <-
expression(0, -(u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (alpha * (1/u1) * (1/u2)/log(u1 * u2) + -alpha * log(u1) * 
    (1/u2) * (u2/(u1 * u2))/log(u1 * u2)^2 + ((-alpha * log(u1) * 
    log(u2) * (1/(u1 * u2) - u1 * u2/(u1 * u2)^2) - alpha * (1/u1) * 
    log(u2) * (u1/(u1 * u2)))/log(u1 * u2)^2 - -alpha * log(u1) * 
    log(u2) * (u1/(u1 * u2)) * (2 * (u2/(u1 * u2) * log(u1 * 
    u2)))/(log(u1 * u2)^2)^2)) + exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (alpha * (1/u1) * log(u2)/log(u1 * u2) + -alpha * 
    log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2) * (-alpha * 
    log(u1) * (1/u2)/log(u1 * u2) - -alpha * log(u1) * log(u2) * 
    (u1/(u1 * u2))/log(u1 * u2)^2)) + exp(-alpha * log(u1) * 
    log(u2)/log(u1 * u2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
    u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
    u2)^2) + ((exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * 
    (alpha * (1/u1) * log(u2)/log(u1 * u2) + -alpha * log(u1) * 
        log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2)) - u1 * (exp(-alpha * 
    log(u1) * log(u2)/log(u1 * u2)) * ((-alpha * log(u1) * log(u2) * 
    (u2 * u2/(u1 * u2)^2) + alpha * (1/u1) * log(u2) * (u2/(u1 * 
    u2)))/log(u1 * u2)^2 + -alpha * log(u1) * log(u2) * (u2/(u1 * 
    u2)) * (2 * (u2/(u1 * u2) * log(u1 * u2)))/(log(u1 * u2)^2)^2 + 
    (alpha * (1/u1^2) * log(u2)/log(u1 * u2) + alpha * (1/u1) * 
        log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2)) + exp(-alpha * 
    log(u1) * log(u2)/log(u1 * u2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
    u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
    u2)^2) * (alpha * (1/u1) * log(u2)/log(u1 * u2) + -alpha * 
    log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2)) + (u2 * 
    (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * (-alpha * 
        log(u1) * (1/u2)/log(u1 * u2) - -alpha * log(u1) * log(u2) * 
        (u1/(u1 * u2))/log(u1 * u2)^2) * (alpha * (1/u1) * log(u2)/log(u1 * 
        u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
        u2)^2) + exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * 
        (alpha * (1/u1) * (1/u2)/log(u1 * u2) - alpha * (1/u1) * 
            log(u2) * (u1/(u1 * u2))/log(u1 * u2)^2 + ((-alpha * 
            log(u1) * (1/u2) * (u2/(u1 * u2)) + -alpha * log(u1) * 
            log(u2) * (1/(u1 * u2) - u2 * u1/(u1 * u2)^2))/log(u1 * 
            u2)^2 - -alpha * log(u1) * log(u2) * (u2/(u1 * u2)) * 
            (2 * (u1/(u1 * u2) * log(u1 * u2)))/(log(u1 * u2)^2)^2))) - 
    u1 * u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * 
        ((-alpha * log(u1) * log(u2) * (u2/(u1 * u2)^2 + (u2/(u1 * 
            u2)^2 - u2 * u1 * (2 * (u2 * (u1 * u2)))/((u1 * u2)^2)^2)) + 
            alpha * (1/u1) * log(u2) * (1/(u1 * u2) - u2 * u1/(u1 * 
                u2)^2) + (-alpha * log(u1) * (1/u2) * (u2 * u2/(u1 * 
            u2)^2) + alpha * (1/u1) * (1/u2) * (u2/(u1 * u2))))/log(u1 * 
            u2)^2 + (-alpha * log(u1) * (1/u2) * (u2/(u1 * u2)) + 
            -alpha * log(u1) * log(u2) * (1/(u1 * u2) - u2 * 
                u1/(u1 * u2)^2)) * (2 * (u2/(u1 * u2) * log(u1 * 
            u2)))/(log(u1 * u2)^2)^2 + ((-alpha * log(u1) * log(u2) * 
            (u2/(u1 * u2)) * (2 * ((1/(u1 * u2) - u1 * u2/(u1 * 
            u2)^2) * log(u1 * u2) + u1/(u1 * u2) * (u2/(u1 * 
            u2)))) - (-alpha * log(u1) * log(u2) * (u2 * u2/(u1 * 
            u2)^2) + alpha * (1/u1) * log(u2) * (u2/(u1 * u2))) * 
            (2 * (u1/(u1 * u2) * log(u1 * u2))))/(log(u1 * u2)^2)^2 - 
            -alpha * log(u1) * log(u2) * (u2/(u1 * u2)) * (2 * 
                (u1/(u1 * u2) * log(u1 * u2))) * (2 * (2 * (u2/(u1 * 
                u2) * log(u1 * u2)) * (log(u1 * u2)^2)))/((log(u1 * 
                u2)^2)^2)^2) + (alpha * (1/u1^2) * (1/u2)/log(u1 * 
            u2) + alpha * (1/u1) * (1/u2) * (u2/(u1 * u2))/log(u1 * 
            u2)^2 + ((alpha * (1/u1) * log(u2) * (1/(u1 * u2) - 
            u1 * u2/(u1 * u2)^2) - alpha * (1/u1^2) * log(u2) * 
            (u1/(u1 * u2)))/log(u1 * u2)^2 - alpha * (1/u1) * 
            log(u2) * (u1/(u1 * u2)) * (2 * (u2/(u1 * u2) * log(u1 * 
            u2)))/(log(u1 * u2)^2)^2))) + exp(-alpha * log(u1) * 
        log(u2)/log(u1 * u2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
        u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
        u2)^2) * (alpha * (1/u1) * (1/u2)/log(u1 * u2) - alpha * 
        (1/u1) * log(u2) * (u1/(u1 * u2))/log(u1 * u2)^2 + ((-alpha * 
        log(u1) * (1/u2) * (u2/(u1 * u2)) + -alpha * log(u1) * 
        log(u2) * (1/(u1 * u2) - u2 * u1/(u1 * u2)^2))/log(u1 * 
        u2)^2 - -alpha * log(u1) * log(u2) * (u2/(u1 * u2)) * 
        (2 * (u1/(u1 * u2) * log(u1 * u2)))/(log(u1 * u2)^2)^2)) + 
        (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * (-alpha * 
            log(u1) * (1/u2)/log(u1 * u2) - -alpha * log(u1) * 
            log(u2) * (u1/(u1 * u2))/log(u1 * u2)^2) * ((-alpha * 
            log(u1) * log(u2) * (u2 * u2/(u1 * u2)^2) + alpha * 
            (1/u1) * log(u2) * (u2/(u1 * u2)))/log(u1 * u2)^2 + 
            -alpha * log(u1) * log(u2) * (u2/(u1 * u2)) * (2 * 
                (u2/(u1 * u2) * log(u1 * u2)))/(log(u1 * u2)^2)^2 + 
            (alpha * (1/u1^2) * log(u2)/log(u1 * u2) + alpha * 
                (1/u1) * log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2)) + 
            (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * (alpha * 
                (1/u1) * (1/u2)/log(u1 * u2) + -alpha * log(u1) * 
                (1/u2) * (u2/(u1 * u2))/log(u1 * u2)^2 + ((-alpha * 
                log(u1) * log(u2) * (1/(u1 * u2) - u1 * u2/(u1 * 
                u2)^2) - alpha * (1/u1) * log(u2) * (u1/(u1 * 
                u2)))/log(u1 * u2)^2 - -alpha * log(u1) * log(u2) * 
                (u1/(u1 * u2)) * (2 * (u2/(u1 * u2) * log(u1 * 
                u2)))/(log(u1 * u2)^2)^2)) + exp(-alpha * log(u1) * 
                log(u2)/log(u1 * u2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
                u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * 
                u2))/log(u1 * u2)^2) * (-alpha * log(u1) * (1/u2)/log(u1 * 
                u2) - -alpha * log(u1) * log(u2) * (u1/(u1 * 
                u2))/log(u1 * u2)^2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
                u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * 
                u2))/log(u1 * u2)^2)))))))
`tawnCopula.pdfDerWrtArg.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr3 <- -alpha * log(u1)
    .expr4 <- log(u2)
    .expr5 <- .expr3 * .expr4
    .expr6 <- u1 * u2
    .expr7 <- log(.expr6)
    .expr9 <- exp(.expr5/.expr7)
    .expr11 <- alpha * (1/u1)
    .expr12 <- 1/u2
    .expr13 <- .expr11 * .expr12
    .expr14 <- .expr13/.expr7
    .expr15 <- .expr3 * .expr12
    .expr16 <- u2/.expr6
    .expr17 <- .expr15 * .expr16
    .expr18 <- .expr7^2
    .expr21 <- 1/.expr6
    .expr22 <- .expr6^2
    .expr24 <- .expr21 - .expr6/.expr22
    .expr26 <- .expr11 * .expr4
    .expr27 <- u1/.expr6
    .expr28 <- .expr26 * .expr27
    .expr31 <- .expr5 * .expr27
    .expr33 <- 2 * (.expr16 * .expr7)
    .expr35 <- .expr18^2
    .expr41 <- .expr5 * .expr16
    .expr43 <- .expr26/.expr7 + .expr41/.expr18
    .expr44 <- .expr9 * .expr43
    .expr47 <- .expr15/.expr7 - .expr31/.expr18
    .expr49 <- .expr9 * (.expr14 + .expr17/.expr18 + ((.expr5 * 
        .expr24 - .expr28)/.expr18 - .expr31 * .expr33/.expr35)) + 
        .expr44 * .expr47
    .expr53 <- u2 * u2/.expr22
    .expr55 <- .expr26 * .expr16
    .expr56 <- .expr5 * .expr53 + .expr55
    .expr63 <- alpha * (1/u1^2)
    .expr64 <- .expr63 * .expr4
    .expr68 <- .expr56/.expr18 + .expr41 * .expr33/.expr35 + 
        (.expr64/.expr7 + .expr55/.expr18)
    .expr74 <- .expr9 * .expr47
    .expr78 <- u2 * u1
    .expr80 <- .expr21 - .expr78/.expr22
    .expr82 <- .expr17 + .expr5 * .expr80
    .expr85 <- 2 * (.expr27 * .expr7)
    .expr86 <- .expr41 * .expr85
    .expr89 <- .expr14 - .expr28/.expr18 + (.expr82/.expr18 - 
        .expr86/.expr35)
    .expr93 <- u2/.expr22
    .expr105 <- .expr13 * .expr16
    .value <- -(u2 * .expr49 + .expr44 + (.expr44 - u1 * (.expr9 * 
        .expr68 + .expr44 * .expr43) + (u2 * (.expr74 * .expr43 + 
        .expr9 * .expr89) - .expr6 * (.expr9 * ((.expr5 * (.expr93 + 
        (.expr93 - .expr78 * (2 * (u2 * .expr6))/.expr22^2)) + 
        .expr26 * .expr80 + (.expr15 * .expr53 + .expr105))/.expr18 + 
        .expr82 * .expr33/.expr35 + ((.expr41 * (2 * (.expr24 * 
        .expr7 + .expr27 * .expr16)) - .expr56 * .expr85)/.expr35 - 
        .expr86 * (2 * (.expr33 * .expr18))/.expr35^2) + (.expr63 * 
        .expr12/.expr7 + .expr105/.expr18 + ((.expr26 * .expr24 - 
        .expr64 * .expr27)/.expr18 - .expr28 * .expr33/.expr35))) + 
        .expr44 * .expr89 + (.expr74 * .expr68 + .expr49 * .expr43)))))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`tawnCopula.pdfDerWrtPar.expr` <-
expression(0, -(u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (log(u1) * (1/u2)/log(u1 * u2) - log(u1) * log(u2) * 
    (u1/(u1 * u2))/log(u1 * u2)^2) + exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (log(u1) * log(u2)/log(u1 * u2)) * (-alpha * log(u1) * 
    (1/u2)/log(u1 * u2) - -alpha * log(u1) * log(u2) * (u1/(u1 * 
    u2))/log(u1 * u2)^2)) + exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (log(u1) * log(u2)/log(u1 * u2)) + (u1 * (exp(-alpha * 
    log(u1) * log(u2)/log(u1 * u2)) * ((1/u1) * log(u2)/log(u1 * 
    u2) - log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * u2)^2) - 
    exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * (log(u1) * 
        log(u2)/log(u1 * u2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
        u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
        u2)^2)) + u1 * u2 * (exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (-alpha * log(u1) * (1/u2)/log(u1 * u2) - -alpha * 
    log(u1) * log(u2) * (u1/(u1 * u2))/log(u1 * u2)^2) * ((1/u1) * 
    log(u2)/log(u1 * u2) - log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
    u2)^2) - (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * 
    (log(u1) * (1/u2)/log(u1 * u2) - log(u1) * log(u2) * (u1/(u1 * 
        u2))/log(u1 * u2)^2) + exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (log(u1) * log(u2)/log(u1 * u2)) * (-alpha * log(u1) * 
    (1/u2)/log(u1 * u2) - -alpha * log(u1) * log(u2) * (u1/(u1 * 
    u2))/log(u1 * u2)^2)) * (alpha * (1/u1) * log(u2)/log(u1 * 
    u2) + -alpha * log(u1) * log(u2) * (u2/(u1 * u2))/log(u1 * 
    u2)^2) + (exp(-alpha * log(u1) * log(u2)/log(u1 * u2)) * 
    ((1/u1) * (1/u2)/log(u1 * u2) - (1/u1) * log(u2) * (u1/(u1 * 
        u2))/log(u1 * u2)^2 - ((log(u1) * log(u2) * (1/(u1 * 
        u2) - u2 * u1/(u1 * u2)^2) + log(u1) * (1/u2) * (u2/(u1 * 
        u2)))/log(u1 * u2)^2 - log(u1) * log(u2) * (u2/(u1 * 
        u2)) * (2 * (u1/(u1 * u2) * log(u1 * u2)))/(log(u1 * 
        u2)^2)^2)) - exp(-alpha * log(u1) * log(u2)/log(u1 * 
    u2)) * (log(u1) * log(u2)/log(u1 * u2)) * (alpha * (1/u1) * 
    (1/u2)/log(u1 * u2) - alpha * (1/u1) * log(u2) * (u1/(u1 * 
    u2))/log(u1 * u2)^2 + ((-alpha * log(u1) * (1/u2) * (u2/(u1 * 
    u2)) + -alpha * log(u1) * log(u2) * (1/(u1 * u2) - u2 * u1/(u1 * 
    u2)^2))/log(u1 * u2)^2 - -alpha * log(u1) * log(u2) * (u2/(u1 * 
    u2)) * (2 * (u1/(u1 * u2) * log(u1 * u2)))/(log(u1 * u2)^2)^2)))))))
`tawnCopula.pdfDerWrtPar.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr2 <- log(u1)
    .expr3 <- -alpha * .expr2
    .expr4 <- log(u2)
    .expr5 <- .expr3 * .expr4
    .expr6 <- u1 * u2
    .expr7 <- log(.expr6)
    .expr9 <- exp(.expr5/.expr7)
    .expr10 <- 1/u2
    .expr11 <- .expr2 * .expr10
    .expr13 <- .expr2 * .expr4
    .expr14 <- u1/.expr6
    .expr16 <- .expr7^2
    .expr21 <- .expr9 * (.expr13/.expr7)
    .expr22 <- .expr3 * .expr10
    .expr26 <- .expr22/.expr7 - .expr5 * .expr14/.expr16
    .expr28 <- .expr9 * (.expr11/.expr7 - .expr13 * .expr14/.expr16) + 
        .expr21 * .expr26
    .expr31 <- 1/u1
    .expr32 <- .expr31 * .expr4
    .expr34 <- u2/.expr6
    .expr35 <- .expr13 * .expr34
    .expr37 <- .expr32/.expr7 - .expr35/.expr16
    .expr39 <- alpha * .expr31
    .expr40 <- .expr39 * .expr4
    .expr42 <- .expr5 * .expr34
    .expr44 <- .expr40/.expr7 + .expr42/.expr16
    .expr61 <- 1/.expr6 - u2 * u1/.expr6^2
    .expr67 <- 2 * (.expr14 * .expr7)
    .expr69 <- .expr16^2
    .value <- -(u2 * .expr28 + .expr21 + (u1 * (.expr9 * .expr37 - 
        .expr21 * .expr44) + .expr6 * (.expr9 * .expr26 * .expr37 - 
        .expr28 * .expr44 + (.expr9 * (.expr31 * .expr10/.expr7 - 
        .expr32 * .expr14/.expr16 - ((.expr13 * .expr61 + .expr11 * 
        .expr34)/.expr16 - .expr35 * .expr67/.expr69)) - .expr21 * 
        (.expr39 * .expr10/.expr7 - .expr40 * .expr14/.expr16 + 
            ((.expr22 * .expr34 + .expr5 * .expr61)/.expr16 - 
                .expr42 * .expr67/.expr69))))))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})