Initial program 0.4
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
- Using strategy
rm Applied add-log-exp0.4
\[\leadsto \left(\left(\left(e + d\right) + c\right) + b\right) + \color{blue}{\log \left(e^{a}\right)}\]
Applied add-log-exp0.4
\[\leadsto \left(\left(\left(e + d\right) + c\right) + \color{blue}{\log \left(e^{b}\right)}\right) + \log \left(e^{a}\right)\]
Applied add-log-exp0.4
\[\leadsto \left(\left(\left(e + d\right) + \color{blue}{\log \left(e^{c}\right)}\right) + \log \left(e^{b}\right)\right) + \log \left(e^{a}\right)\]
Applied add-log-exp0.4
\[\leadsto \left(\left(\color{blue}{\log \left(e^{e + d}\right)} + \log \left(e^{c}\right)\right) + \log \left(e^{b}\right)\right) + \log \left(e^{a}\right)\]
Applied sum-log0.4
\[\leadsto \left(\color{blue}{\log \left(e^{e + d} \cdot e^{c}\right)} + \log \left(e^{b}\right)\right) + \log \left(e^{a}\right)\]
Applied sum-log0.3
\[\leadsto \color{blue}{\log \left(\left(e^{e + d} \cdot e^{c}\right) \cdot e^{b}\right)} + \log \left(e^{a}\right)\]
Applied sum-log0.2
\[\leadsto \color{blue}{\log \left(\left(\left(e^{e + d} \cdot e^{c}\right) \cdot e^{b}\right) \cdot e^{a}\right)}\]
Simplified0.3
\[\leadsto \log \color{blue}{\left(e^{\left(d + e\right) + \left(\left(c + a\right) + b\right)}\right)}\]
- Using strategy
rm Applied add-log-exp0.3
\[\leadsto \log \left(e^{\left(d + e\right) + \color{blue}{\log \left(e^{\left(c + a\right) + b}\right)}}\right)\]
Applied add-log-exp0.3
\[\leadsto \log \left(e^{\color{blue}{\log \left(e^{d + e}\right)} + \log \left(e^{\left(c + a\right) + b}\right)}\right)\]
Applied sum-log0.3
\[\leadsto \log \left(e^{\color{blue}{\log \left(e^{d + e} \cdot e^{\left(c + a\right) + b}\right)}}\right)\]
Simplified0.2
\[\leadsto \log \left(e^{\log \color{blue}{\left(e^{e + \left(d + \left(b + \left(a + c\right)\right)\right)}\right)}}\right)\]
- Using strategy
rm Applied add-log-exp0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \left(d + \left(b + \left(a + \color{blue}{\log \left(e^{c}\right)}\right)\right)\right)}\right)}\right)\]
Applied add-log-exp0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \left(d + \left(b + \left(\color{blue}{\log \left(e^{a}\right)} + \log \left(e^{c}\right)\right)\right)\right)}\right)}\right)\]
Applied sum-log0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \left(d + \left(b + \color{blue}{\log \left(e^{a} \cdot e^{c}\right)}\right)\right)}\right)}\right)\]
Applied add-log-exp0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \left(d + \left(\color{blue}{\log \left(e^{b}\right)} + \log \left(e^{a} \cdot e^{c}\right)\right)\right)}\right)}\right)\]
Applied sum-log0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \left(d + \color{blue}{\log \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)}\right)}\right)}\right)\]
Applied add-log-exp0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \left(\color{blue}{\log \left(e^{d}\right)} + \log \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)}\right)}\right)\]
Applied sum-log0.2
\[\leadsto \log \left(e^{\log \left(e^{e + \color{blue}{\log \left(e^{d} \cdot \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)}}\right)}\right)\]
Applied add-log-exp0.2
\[\leadsto \log \left(e^{\log \left(e^{\color{blue}{\log \left(e^{e}\right)} + \log \left(e^{d} \cdot \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)}\right)}\right)\]
Applied sum-log0.0
\[\leadsto \log \left(e^{\log \left(e^{\color{blue}{\log \left(e^{e} \cdot \left(e^{d} \cdot \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)\right)}}\right)}\right)\]
Applied rem-exp-log0.0
\[\leadsto \log \left(e^{\log \color{blue}{\left(e^{e} \cdot \left(e^{d} \cdot \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)\right)}}\right)\]
Final simplification0.0
\[\leadsto \log \left(e^{\log \left(e^{e} \cdot \left(e^{d} \cdot \left(e^{b} \cdot \left(e^{c} \cdot e^{a}\right)\right)\right)\right)}\right)\]
