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
\[\leadsto \log \left(e^{\left(d + e\right) + \left(\left(c + a\right) + \color{blue}{\log \left(e^{b}\right)}\right)}\right)\]
Applied add-log-exp0.3
\[\leadsto \log \left(e^{\left(d + e\right) + \left(\left(c + \color{blue}{\log \left(e^{a}\right)}\right) + \log \left(e^{b}\right)\right)}\right)\]
Applied add-log-exp0.3
\[\leadsto \log \left(e^{\left(d + e\right) + \left(\left(\color{blue}{\log \left(e^{c}\right)} + \log \left(e^{a}\right)\right) + \log \left(e^{b}\right)\right)}\right)\]
Applied sum-log0.3
\[\leadsto \log \left(e^{\left(d + e\right) + \left(\color{blue}{\log \left(e^{c} \cdot e^{a}\right)} + \log \left(e^{b}\right)\right)}\right)\]
Applied sum-log0.3
\[\leadsto \log \left(e^{\left(d + e\right) + \color{blue}{\log \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)}}\right)\]
Applied add-log-exp0.3
\[\leadsto \log \left(e^{\color{blue}{\log \left(e^{d + e}\right)} + \log \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)}\right)\]
Applied sum-log0.2
\[\leadsto \log \left(e^{\color{blue}{\log \left(e^{d + e} \cdot \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)\right)}}\right)\]
Applied rem-exp-log0.2
\[\leadsto \log \color{blue}{\left(e^{d + e} \cdot \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)\right)}\]
- Using strategy
rm Applied add-log-exp0.2
\[\leadsto \log \left(e^{d + \color{blue}{\log \left(e^{e}\right)}} \cdot \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)\right)\]
Applied add-log-exp0.2
\[\leadsto \log \left(e^{\color{blue}{\log \left(e^{d}\right)} + \log \left(e^{e}\right)} \cdot \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)\right)\]
Applied sum-log0.2
\[\leadsto \log \left(e^{\color{blue}{\log \left(e^{d} \cdot e^{e}\right)}} \cdot \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)\right)\]
Applied rem-exp-log0.0
\[\leadsto \log \left(\color{blue}{\left(e^{d} \cdot e^{e}\right)} \cdot \left(\left(e^{c} \cdot e^{a}\right) \cdot e^{b}\right)\right)\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \log \left(\left(e^{d} \cdot e^{e}\right) \cdot \left(\left(\color{blue}{\left(\sqrt{e^{c}} \cdot \sqrt{e^{c}}\right)} \cdot e^{a}\right) \cdot e^{b}\right)\right)\]
Applied associate-*l*0.0
\[\leadsto \log \left(\left(e^{d} \cdot e^{e}\right) \cdot \left(\color{blue}{\left(\sqrt{e^{c}} \cdot \left(\sqrt{e^{c}} \cdot e^{a}\right)\right)} \cdot e^{b}\right)\right)\]
Final simplification0.0
\[\leadsto \log \left(\left(\left(\sqrt{e^{c}} \cdot \left(e^{a} \cdot \sqrt{e^{c}}\right)\right) \cdot e^{b}\right) \cdot \left(e^{e} \cdot e^{d}\right)\right)\]
