# How to translate the result from generalized linear regression with $\log$ link function to an equation

I have a following generalized linear model with $\log$ as a link function.

Call:
glm(formula = time ~ I(1/nprocs) + ndoms + nDOF + nDOF:ndoms +
I(nDOF^2):ndoms + I(1/nprocs):nDOF + I(1/nprocs):nDOF,
data = dataFact)

Deviance Residuals:
Min        1Q    Median        3Q       Max
-0.10398  -0.02385  -0.01383   0.01055   0.09257

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)      -4.082e+00  9.860e-02 -41.401  < 2e-16 ***
I(1/nprocs)       8.230e-01  8.693e-02   9.468  < 2e-16 ***
ndoms             4.169e-04  1.210e-04   3.447 0.000682 ***
nDOF              1.693e-04  7.458e-06  22.706  < 2e-16 ***
ndoms:nDOF        2.288e-07  1.692e-08  13.524  < 2e-16 ***
ndoms:I(nDOF^2)  -1.120e-11  6.918e-13 -16.185  < 2e-16 ***
I(1/nprocs):nDOF -4.167e-05  6.739e-06  -6.183 3.08e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.0009785681)

Null deviance: 12.39092  on 223  degrees of freedom
Residual deviance:  0.21235  on 217  degrees of freedom
AIC: -907.61


But I'm not sure, what's the resulting mathematical formula now. Is it correct to just exponentiate the whole expression like this?

$$\operatorname{time} = \\ \small\exp \left[ c_1 \!+\! \frac{c_2}{\scriptsize\operatorname{nprocs}}\! +\! c_3 {\scriptsize(\operatorname{ndoms})}\! +\! c_4 {\scriptsize(\operatorname{nDOF})}\! +\! c_5 {\scriptsize(\operatorname{nDOF})}{\scriptsize(\operatorname{ndoms})}\! +\! c_6 {\scriptsize(\operatorname{nDOF})}^2 {\scriptsize(\operatorname{ndoms})}\! +\! c_7 \small\frac{\scriptsize\operatorname{nDOF}}{\scriptsize\operatorname{nprocs}}\right]$$