Initial program 0.4
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
- Using strategy
rm Applied add-log-exp0.4
\[\leadsto \left(\left(\left(e + d\right) + c\right) + \color{blue}{\log \left(e^{b}\right)}\right) + a\]
Applied add-log-exp0.4
\[\leadsto \left(\left(\left(e + d\right) + \color{blue}{\log \left(e^{c}\right)}\right) + \log \left(e^{b}\right)\right) + a\]
Applied add-log-exp0.4
\[\leadsto \left(\left(\color{blue}{\log \left(e^{e + d}\right)} + \log \left(e^{c}\right)\right) + \log \left(e^{b}\right)\right) + a\]
Applied sum-log0.4
\[\leadsto \left(\color{blue}{\log \left(e^{e + d} \cdot e^{c}\right)} + \log \left(e^{b}\right)\right) + a\]
Applied sum-log0.3
\[\leadsto \color{blue}{\log \left(\left(e^{e + d} \cdot e^{c}\right) \cdot e^{b}\right)} + a\]
Simplified0.3
\[\leadsto \log \color{blue}{\left(e^{\left(b + d\right) + \left(e + c\right)}\right)} + a\]
- Using strategy
rm Applied *-un-lft-identity0.3
\[\leadsto \log \left(e^{\left(b + d\right) + \left(e + c\right)}\right) + \color{blue}{1 \cdot a}\]
Applied *-un-lft-identity0.3
\[\leadsto \color{blue}{1 \cdot \log \left(e^{\left(b + d\right) + \left(e + c\right)}\right)} + 1 \cdot a\]
Applied distribute-lft-out0.3
\[\leadsto \color{blue}{1 \cdot \left(\log \left(e^{\left(b + d\right) + \left(e + c\right)}\right) + a\right)}\]
Simplified0.2
\[\leadsto 1 \cdot \color{blue}{\left(e + \left(c + \left(d + \left(b + a\right)\right)\right)\right)}\]
- Using strategy
rm Applied add-log-exp0.2
\[\leadsto 1 \cdot \left(e + \left(c + \left(d + \left(b + \color{blue}{\log \left(e^{a}\right)}\right)\right)\right)\right)\]
Applied add-log-exp0.2
\[\leadsto 1 \cdot \left(e + \left(c + \left(d + \left(\color{blue}{\log \left(e^{b}\right)} + \log \left(e^{a}\right)\right)\right)\right)\right)\]
Applied sum-log0.2
\[\leadsto 1 \cdot \left(e + \left(c + \left(d + \color{blue}{\log \left(e^{b} \cdot e^{a}\right)}\right)\right)\right)\]
Applied add-log-exp0.2
\[\leadsto 1 \cdot \left(e + \left(c + \left(\color{blue}{\log \left(e^{d}\right)} + \log \left(e^{b} \cdot e^{a}\right)\right)\right)\right)\]
Applied sum-log0.2
\[\leadsto 1 \cdot \left(e + \left(c + \color{blue}{\log \left(e^{d} \cdot \left(e^{b} \cdot e^{a}\right)\right)}\right)\right)\]
Applied add-log-exp0.2
\[\leadsto 1 \cdot \left(e + \left(\color{blue}{\log \left(e^{c}\right)} + \log \left(e^{d} \cdot \left(e^{b} \cdot e^{a}\right)\right)\right)\right)\]
Applied sum-log0.2
\[\leadsto 1 \cdot \left(e + \color{blue}{\log \left(e^{c} \cdot \left(e^{d} \cdot \left(e^{b} \cdot e^{a}\right)\right)\right)}\right)\]
Simplified0.2
\[\leadsto 1 \cdot \left(e + \log \color{blue}{\left(e^{\left(c + b\right) + \left(d + a\right)}\right)}\right)\]
Final simplification0.2
\[\leadsto e + \log \left(e^{\left(d + a\right) + \left(b + c\right)}\right)\]
