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 pow10.3
\[\leadsto \log \color{blue}{\left({\left(e^{\left(b + d\right) + \left(e + c\right)}\right)}^{1}\right)} + 1 \cdot a\]
Applied log-pow0.3
\[\leadsto \color{blue}{1 \cdot \log \left(e^{\left(b + d\right) + \left(e + c\right)}\right)} + 1 \cdot a\]
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
\[\leadsto 1 \cdot \color{blue}{\left(e + \left(c + \left(d + \left(b + a\right)\right)\right)\right)}\]
Final simplification0.2
\[\leadsto e + \left(\left(d + \left(a + b\right)\right) + c\right)\]
