Initial program 0.4
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
Initial simplification0.2
\[\leadsto \left(\left(a + d\right) + \left(c + b\right)\right) + e\]
- Using strategy
rm Applied add-log-exp0.2
\[\leadsto \left(\left(a + d\right) + \color{blue}{\log \left(e^{c + b}\right)}\right) + e\]
Applied add-log-exp0.2
\[\leadsto \left(\color{blue}{\log \left(e^{a + d}\right)} + \log \left(e^{c + b}\right)\right) + e\]
Applied sum-log0.2
\[\leadsto \color{blue}{\log \left(e^{a + d} \cdot e^{c + b}\right)} + e\]
Simplified0.2
\[\leadsto \log \color{blue}{\left(e^{\left(d + b\right) + \left(a + c\right)}\right)} + e\]
- Using strategy
rm Applied flip3-+0.3
\[\leadsto \log \left(e^{\left(d + b\right) + \color{blue}{\frac{{a}^{3} + {c}^{3}}{a \cdot a + \left(c \cdot c - a \cdot c\right)}}}\right) + e\]
Applied flip-+0.3
\[\leadsto \log \left(e^{\color{blue}{\frac{d \cdot d - b \cdot b}{d - b}} + \frac{{a}^{3} + {c}^{3}}{a \cdot a + \left(c \cdot c - a \cdot c\right)}}\right) + e\]
Applied frac-add0.3
\[\leadsto \log \left(e^{\color{blue}{\frac{\left(d \cdot d - b \cdot b\right) \cdot \left(a \cdot a + \left(c \cdot c - a \cdot c\right)\right) + \left(d - b\right) \cdot \left({a}^{3} + {c}^{3}\right)}{\left(d - b\right) \cdot \left(a \cdot a + \left(c \cdot c - a \cdot c\right)\right)}}}\right) + e\]
Simplified0.4
\[\leadsto \log \left(e^{\frac{\color{blue}{(\left((a \cdot \left(a \cdot a\right) + \left({c}^{3}\right))_*\right) \cdot \left(d - b\right) + \left((\left(c - a\right) \cdot c + \left(a \cdot a\right))_* \cdot \left(\left(d - b\right) \cdot \left(d + b\right)\right)\right))_*}}{\left(d - b\right) \cdot \left(a \cdot a + \left(c \cdot c - a \cdot c\right)\right)}}\right) + e\]
Simplified0.3
\[\leadsto \log \left(e^{\frac{(\left((a \cdot \left(a \cdot a\right) + \left({c}^{3}\right))_*\right) \cdot \left(d - b\right) + \left((\left(c - a\right) \cdot c + \left(a \cdot a\right))_* \cdot \left(\left(d - b\right) \cdot \left(d + b\right)\right)\right))_*}{\color{blue}{\left(d - b\right) \cdot (c \cdot \left(c - a\right) + \left(a \cdot a\right))_*}}}\right) + e\]
Final simplification0.3
\[\leadsto e + \log \left(e^{\frac{(\left((a \cdot \left(a \cdot a\right) + \left({c}^{3}\right))_*\right) \cdot \left(d - b\right) + \left(\left(\left(b + d\right) \cdot \left(d - b\right)\right) \cdot (\left(c - a\right) \cdot c + \left(a \cdot a\right))_*\right))_*}{(c \cdot \left(c - a\right) + \left(a \cdot a\right))_* \cdot \left(d - b\right)}}\right)\]
