if i < -2.6993148136786055e-05

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   29.0
2. Using strategy rm
   29.0
3. Applied flip3-- to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^{3} - {1}^{3}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}}{\frac{i}{n}}\]
   29.0
4. Applied simplify to get
   \[100 \cdot \frac{\frac{\color{red}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^{3} - {1}^{3}}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\frac{\color{blue}{{\left({\left(\frac{i}{n} + 1\right)}^{n}\right)}^3 - 1}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}}\]
   29.0
5. Applied taylor to get
   \[100 \cdot \frac{\frac{{\left({\left(\frac{i}{n} + 1\right)}^{n}\right)}^3 - 1}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\frac{{\left({\left(\frac{i}{n} + 1\right)}^{n}\right)}^3 - 1}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}}\]
   29.0
6. Taylor expanded around 0 to get
   \[100 \cdot \frac{\frac{\color{red}{{\left({\left(\frac{i}{n} + 1\right)}^{n}\right)}^3 - 1}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\frac{\color{blue}{{\left({\left(\frac{i}{n} + 1\right)}^{n}\right)}^3 - 1}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}}\]
   29.0
7. Applied simplify to get
   \[100 \cdot \frac{\frac{{\left({\left(\frac{i}{n} + 1\right)}^{n}\right)}^3 - 1}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}} \leadsto \frac{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^3 - 1}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left(1 + {\left(1 + \frac{i}{n}\right)}^{n}\right)} \cdot \frac{100}{\frac{i}{n}}\]
   29.0

---

8. Applied final simplification

if -2.6993148136786055e-05 < i < 46118455070.99842

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   61.7
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
   58.9
3. Taylor expanded around 0 to get
   \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
   58.9
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
   14.3
5. Applied taylor to get
   \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \left(100 \cdot n\right)\]
   0.0
6. Taylor expanded around 0 to get
   \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \color{red}{\left(100 \cdot n\right)} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \color{blue}{\left(100 \cdot n\right)}\]
   0.0

if 46118455070.99842 < i

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   51.1
2. Using strategy rm
   51.1
3. Applied add-cbrt-cube to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{red}{\frac{i}{n}}} \leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{\sqrt[3]{{\left(\frac{i}{n}\right)}^3}}}\]
   51.9
4. Applied add-cbrt-cube to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\sqrt[3]{{\left(\frac{i}{n}\right)}^3}} \leadsto 100 \cdot \frac{\color{blue}{\sqrt[3]{{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}^3}}}{\sqrt[3]{{\left(\frac{i}{n}\right)}^3}}\]
   51.9
5. Applied cbrt-undiv to get
   \[100 \cdot \color{red}{\frac{\sqrt[3]{{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}^3}}{\sqrt[3]{{\left(\frac{i}{n}\right)}^3}}} \leadsto 100 \cdot \color{blue}{\sqrt[3]{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}^3}{{\left(\frac{i}{n}\right)}^3}}}\]
   51.9
6. Applied simplify to get
   \[100 \cdot \sqrt[3]{\color{red}{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}^3}{{\left(\frac{i}{n}\right)}^3}}} \leadsto 100 \cdot \sqrt[3]{\color{blue}{{\left(\frac{{\left(\frac{i}{n} + 1\right)}^{n} - 1}{\frac{i}{n}}\right)}^3}}\]
   51.9
7. Applied taylor to get
   \[100 \cdot \sqrt[3]{{\left(\frac{{\left(\frac{i}{n} + 1\right)}^{n} - 1}{\frac{i}{n}}\right)}^3} \leadsto 100 \cdot \left(\left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + \left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{1}{6} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(\frac{{n}^{4} \cdot \log i}{{i}^2} + \left(\frac{{n}^2 \cdot \log i}{i} + \left(\frac{{n}^{3}}{{i}^2} + \frac{1}{2} \cdot \frac{{\left(\log n\right)}^2 \cdot \left({n}^{4} \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(\frac{1}{2} \cdot \frac{{n}^{4}}{{i}^{3}} + \left(\frac{\log n \cdot {n}^{4}}{{i}^2} + \left(\frac{1}{6} \cdot \frac{{\left(\log n\right)}^{3} \cdot {n}^{4}}{i} + \left(\frac{{n}^2 \cdot \log n}{i} + \left(\frac{1}{2} \cdot \frac{\log n \cdot \left({n}^{4} \cdot {\left(\log i\right)}^2\right)}{i} + \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right)\]
   5.4
8. Taylor expanded around 0 to get
   \[100 \cdot \color{red}{\left(\left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + \left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{1}{6} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(\frac{{n}^{4} \cdot \log i}{{i}^2} + \left(\frac{{n}^2 \cdot \log i}{i} + \left(\frac{{n}^{3}}{{i}^2} + \frac{1}{2} \cdot \frac{{\left(\log n\right)}^2 \cdot \left({n}^{4} \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(\frac{1}{2} \cdot \frac{{n}^{4}}{{i}^{3}} + \left(\frac{\log n \cdot {n}^{4}}{{i}^2} + \left(\frac{1}{6} \cdot \frac{{\left(\log n\right)}^{3} \cdot {n}^{4}}{i} + \left(\frac{{n}^2 \cdot \log n}{i} + \left(\frac{1}{2} \cdot \frac{\log n \cdot \left({n}^{4} \cdot {\left(\log i\right)}^2\right)}{i} + \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right)} \leadsto 100 \cdot \color{blue}{\left(\left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + \left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{1}{6} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(\frac{{n}^{4} \cdot \log i}{{i}^2} + \left(\frac{{n}^2 \cdot \log i}{i} + \left(\frac{{n}^{3}}{{i}^2} + \frac{1}{2} \cdot \frac{{\left(\log n\right)}^2 \cdot \left({n}^{4} \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(\frac{1}{2} \cdot \frac{{n}^{4}}{{i}^{3}} + \left(\frac{\log n \cdot {n}^{4}}{{i}^2} + \left(\frac{1}{6} \cdot \frac{{\left(\log n\right)}^{3} \cdot {n}^{4}}{i} + \left(\frac{{n}^2 \cdot \log n}{i} + \left(\frac{1}{2} \cdot \frac{\log n \cdot \left({n}^{4} \cdot {\left(\log i\right)}^2\right)}{i} + \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right)}\]
   5.4
9. Applied simplify to get
   \[100 \cdot \left(\left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + \left(\frac{1}{2} \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{1}{6} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(\frac{{n}^{4} \cdot \log i}{{i}^2} + \left(\frac{{n}^2 \cdot \log i}{i} + \left(\frac{{n}^{3}}{{i}^2} + \frac{1}{2} \cdot \frac{{\left(\log n\right)}^2 \cdot \left({n}^{4} \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(\frac{1}{2} \cdot \frac{{n}^{4}}{{i}^{3}} + \left(\frac{\log n \cdot {n}^{4}}{{i}^2} + \left(\frac{1}{6} \cdot \frac{{\left(\log n\right)}^{3} \cdot {n}^{4}}{i} + \left(\frac{{n}^2 \cdot \log n}{i} + \left(\frac{1}{2} \cdot \frac{\log n \cdot \left({n}^{4} \cdot {\left(\log i\right)}^2\right)}{i} + \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) \leadsto \left(\left(\frac{1}{2} \cdot \left(\frac{{n}^3}{i} \cdot {\left(\log i\right)}^2 + \frac{{n}^3}{i} \cdot {\left(\log n\right)}^2\right) + \left(\frac{{n}^{4}}{i} \cdot {\left(\log i\right)}^3\right) \cdot \frac{1}{6}\right) + \left(\left(\left(\left(\frac{\left(\frac{1}{2} \cdot \log n\right) \cdot \left(\log n \cdot {n}^{4}\right)}{\frac{i}{\log i}} + \frac{{n}^3}{i \cdot i}\right) + \left(\frac{n \cdot n}{i} \cdot \log i + \frac{{n}^{4}}{\frac{i \cdot i}{\log i}}\right)\right) - \frac{{n}^{4}}{i} \cdot \frac{\frac{1}{2}}{i \cdot i}\right) - \left(\left(\left(\log n \cdot \frac{n \cdot n}{i} + \frac{\log n \cdot {n}^3}{\frac{i}{\log i}}\right) + \frac{\left(\frac{1}{2} \cdot \log n\right) \cdot \left(\log i \cdot \left({n}^{4} \cdot \log i\right)\right)}{i}\right) + \left(\frac{\frac{1}{6} \cdot {\left(\log n\right)}^3}{\frac{i}{{n}^{4}}} + \frac{{n}^{4}}{i} \cdot \frac{\log n}{i}\right)\right)\right)\right) \cdot 100\]
   5.6

---

10. Applied final simplification
11. Applied simplify to get
    \[\color{red}{\left(\left(\frac{1}{2} \cdot \left(\frac{{n}^3}{i} \cdot {\left(\log i\right)}^2 + \frac{{n}^3}{i} \cdot {\left(\log n\right)}^2\right) + \left(\frac{{n}^{4}}{i} \cdot {\left(\log i\right)}^3\right) \cdot \frac{1}{6}\right) + \left(\left(\left(\left(\frac{\left(\frac{1}{2} \cdot \log n\right) \cdot \left(\log n \cdot {n}^{4}\right)}{\frac{i}{\log i}} + \frac{{n}^3}{i \cdot i}\right) + \left(\frac{n \cdot n}{i} \cdot \log i + \frac{{n}^{4}}{\frac{i \cdot i}{\log i}}\right)\right) - \frac{{n}^{4}}{i} \cdot \frac{\frac{1}{2}}{i \cdot i}\right) - \left(\left(\left(\log n \cdot \frac{n \cdot n}{i} + \frac{\log n \cdot {n}^3}{\frac{i}{\log i}}\right) + \frac{\left(\frac{1}{2} \cdot \log n\right) \cdot \left(\log i \cdot \left({n}^{4} \cdot \log i\right)\right)}{i}\right) + \left(\frac{\frac{1}{6} \cdot {\left(\log n\right)}^3}{\frac{i}{{n}^{4}}} + \frac{{n}^{4}}{i} \cdot \frac{\log n}{i}\right)\right)\right)\right) \cdot 100} \leadsto \color{blue}{100 \cdot \left(\left(\left(\frac{{n}^{4}}{i} \cdot \left({\left(\log i\right)}^3 \cdot \frac{1}{6}\right) + \left(\frac{1}{2} \cdot \frac{n \cdot n}{\frac{i}{n}}\right) \cdot \left(\log n \cdot \log n + \log i \cdot \log i\right)\right) + \left(\left(\frac{n}{\frac{i}{n}} \cdot \left(\frac{n}{i} + \log i\right) + \frac{\log i \cdot \left(\frac{1}{2} \cdot \log n\right)}{\frac{i}{{n}^{4} \cdot \log n}}\right) + \frac{{n}^{4}}{i} \cdot \left(\frac{\log i}{i} - \frac{\frac{1}{2}}{i \cdot i}\right)\right)\right) - \left(\left(\left(\frac{\frac{1}{6}}{i} \cdot {n}^{4}\right) \cdot {\left(\log n\right)}^3 + \frac{{n}^{4}}{i} \cdot \frac{\log n}{i}\right) + \left(\left(\frac{\log n \cdot {n}^3}{\frac{i}{\log i}} + \log n \cdot \frac{n}{\frac{i}{n}}\right) + \frac{\frac{1}{2} \cdot \left(\left(\log n \cdot \log i\right) \cdot \left({n}^{4} \cdot \log i\right)\right)}{i}\right)\right)\right)}\]
    5.6