- Split input into 2 regimes
if i < 1.6613234683176963e+118
Initial program 49.0
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
- Using strategy
rm Applied add-exp-log49.4
\[\leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
Applied pow-exp49.4
\[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
Applied expm1-def43.1
\[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
Simplified12.2
\[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
- Using strategy
rm Applied expm1-log1p-u12.3
\[\leadsto 100 \cdot \frac{(e^{n \cdot \color{blue}{(e^{\log_* (1 + \log_* (1 + \frac{i}{n}))} - 1)^*}} - 1)^*}{\frac{i}{n}}\]
if 1.6613234683176963e+118 < i
Initial program 31.2
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
- Using strategy
rm Applied add-exp-log56.1
\[\leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
Applied pow-exp56.1
\[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
Applied expm1-def52.3
\[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
Simplified52.3
\[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
Taylor expanded around 0 29.7
\[\leadsto \color{blue}{0}\]
- Recombined 2 regimes into one program.
Final simplification13.9
\[\leadsto \begin{array}{l}
\mathbf{if}\;i \le 1.6613234683176963 \cdot 10^{+118}:\\
\;\;\;\;100 \cdot \frac{(e^{n \cdot (e^{\log_* (1 + \log_* (1 + \frac{i}{n}))} - 1)^*} - 1)^*}{\frac{i}{n}}\\
\mathbf{else}:\\
\;\;\;\;0\\
\end{array}\]
