\(e^{\log \left({\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2\right) - \log \left(\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)\right)} - 1\)
- Started with
\[\left(\left(N + 1\right) \cdot \log \left(N + 1\right) - N \cdot \log N\right) - 1\]
63.0
- Using strategy
rm 63.0
- Applied add-cube-cbrt to get
\[\left(\left(N + 1\right) \cdot \color{red}{\log \left(N + 1\right)} - N \cdot \log N\right) - 1 \leadsto \left(\left(N + 1\right) \cdot \color{blue}{{\left(\sqrt[3]{\log \left(N + 1\right)}\right)}^3} - N \cdot \log N\right) - 1\]
61.9
- Applied add-cube-cbrt to get
\[\left(\color{red}{\left(N + 1\right)} \cdot {\left(\sqrt[3]{\log \left(N + 1\right)}\right)}^3 - N \cdot \log N\right) - 1 \leadsto \left(\color{blue}{{\left(\sqrt[3]{N + 1}\right)}^3} \cdot {\left(\sqrt[3]{\log \left(N + 1\right)}\right)}^3 - N \cdot \log N\right) - 1\]
61.7
- Applied cube-unprod to get
\[\left(\color{red}{{\left(\sqrt[3]{N + 1}\right)}^3 \cdot {\left(\sqrt[3]{\log \left(N + 1\right)}\right)}^3} - N \cdot \log N\right) - 1 \leadsto \left(\color{blue}{{\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3} - N \cdot \log N\right) - 1\]
61.7
- Using strategy
rm 61.7
- Applied flip-- to get
\[\color{red}{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3 - N \cdot \log N\right)} - 1 \leadsto \color{blue}{\frac{{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2}{{\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3 + N \cdot \log N}} - 1\]
61.5
- Applied simplify to get
\[\frac{{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2}{\color{red}{{\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3 + N \cdot \log N}} - 1 \leadsto \frac{{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2}{\color{blue}{\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)}} - 1\]
61.5
- Using strategy
rm 61.5
- Applied add-exp-log to get
\[\frac{{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2}{\color{red}{\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)}} - 1 \leadsto \frac{{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2}{\color{blue}{e^{\log \left(\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)\right)}}} - 1\]
61.5
- Applied add-exp-log to get
\[\frac{\color{red}{{\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2}}{e^{\log \left(\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)\right)}} - 1 \leadsto \frac{\color{blue}{e^{\log \left({\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2\right)}}}{e^{\log \left(\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)\right)}} - 1\]
61.3
- Applied div-exp to get
\[\color{red}{\frac{e^{\log \left({\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2\right)}}{e^{\log \left(\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)\right)}}} - 1 \leadsto \color{blue}{e^{\log \left({\left({\left(\sqrt[3]{N + 1} \cdot \sqrt[3]{\log \left(N + 1\right)}\right)}^3\right)}^2 - {\left(N \cdot \log N\right)}^2\right) - \log \left(\log N \cdot N + \log \left(N + 1\right) \cdot \left(N + 1\right)\right)}} - 1\]
61.3
- Removed slow pow expressions
