if i < -16.941984f0

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   10.0
2. Using strategy rm
   10.0
3. Applied add-log-exp to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n} - 1}\right)}}{\frac{i}{n}}\]
   10.0

if -16.941984f0 < i < 6.774447f-05

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   29.6
2. Using strategy rm
   29.6
3. Applied add-exp-log to get
   \[100 \cdot \color{red}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \leadsto 100 \cdot \color{blue}{e^{\log \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\right)}}\]
   29.8
4. Applied taylor to get
   \[100 \cdot e^{\log \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\right)} \leadsto 100 \cdot e^{\frac{1}{24} \cdot {i}^2 + \left(\log n + \frac{1}{2} \cdot i\right)}\]
   17.6
5. Taylor expanded around 0 to get
   \[100 \cdot e^{\color{red}{\frac{1}{24} \cdot {i}^2 + \left(\log n + \frac{1}{2} \cdot i\right)}} \leadsto 100 \cdot e^{\color{blue}{\frac{1}{24} \cdot {i}^2 + \left(\log n + \frac{1}{2} \cdot i\right)}}\]
   17.6
6. Applied simplify to get
   \[100 \cdot e^{\frac{1}{24} \cdot {i}^2 + \left(\log n + \frac{1}{2} \cdot i\right)} \leadsto \left({\left(e^{\frac{1}{24}}\right)}^{\left(i \cdot i\right)} \cdot 100\right) \cdot \left(n \cdot e^{\frac{1}{2} \cdot i}\right)\]
   0.1

---

7. Applied final simplification

if 6.774447f-05 < i

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   22.7
2. Using strategy rm
   22.7
3. Applied add-cube-cbrt to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{{\left(\sqrt[3]{{\left(1 + \frac{i}{n}\right)}^{n}}\right)}^3} - 1}{\frac{i}{n}}\]
   22.9
4. Applied taylor to get
   \[100 \cdot \frac{{\left(\sqrt[3]{{\left(1 + \frac{i}{n}\right)}^{n}}\right)}^3 - 1}{\frac{i}{n}} \leadsto \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^{4} \cdot \log i}{{i}^2} + \left(100 \cdot \frac{{n}^2 \cdot \log i}{i} + \left(100 \cdot \frac{{n}^{3}}{{i}^2} + \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + 50 \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(50 \cdot \frac{{n}^{4}}{{i}^{3}} + \left(100 \cdot \frac{{n}^{4} \cdot \log n}{{i}^2} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^2 \cdot \log n}{i} + \left(100 \cdot \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} + 50 \cdot \frac{{n}^{4} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)}{i}\right)\right)\right)\right)\right)\]
   2.5
5. Taylor expanded around 0 to get
   \[\color{red}{\left(50 \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^{4} \cdot \log i}{{i}^2} + \left(100 \cdot \frac{{n}^2 \cdot \log i}{i} + \left(100 \cdot \frac{{n}^{3}}{{i}^2} + \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + 50 \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(50 \cdot \frac{{n}^{4}}{{i}^{3}} + \left(100 \cdot \frac{{n}^{4} \cdot \log n}{{i}^2} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^2 \cdot \log n}{i} + \left(100 \cdot \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} + 50 \cdot \frac{{n}^{4} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)}{i}\right)\right)\right)\right)\right)} \leadsto \color{blue}{\left(50 \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^{4} \cdot \log i}{{i}^2} + \left(100 \cdot \frac{{n}^2 \cdot \log i}{i} + \left(100 \cdot \frac{{n}^{3}}{{i}^2} + \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + 50 \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(50 \cdot \frac{{n}^{4}}{{i}^{3}} + \left(100 \cdot \frac{{n}^{4} \cdot \log n}{{i}^2} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^2 \cdot \log n}{i} + \left(100 \cdot \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} + 50 \cdot \frac{{n}^{4} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)}{i}\right)\right)\right)\right)\right)}\]
   2.5
6. Applied simplify to get
   \[\left(50 \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^2}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^{4} \cdot \log i}{{i}^2} + \left(100 \cdot \frac{{n}^2 \cdot \log i}{i} + \left(100 \cdot \frac{{n}^{3}}{{i}^2} + \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^2}{i} + 50 \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)}{i}\right)\right)\right)\right)\right)\right) - \left(50 \cdot \frac{{n}^{4}}{{i}^{3}} + \left(100 \cdot \frac{{n}^{4} \cdot \log n}{{i}^2} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^2 \cdot \log n}{i} + \left(100 \cdot \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} + 50 \cdot \frac{{n}^{4} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)}{i}\right)\right)\right)\right)\right) \leadsto \left(\left(\left(\frac{\frac{50}{3} \cdot {n}^{4}}{\frac{i}{{\left(\log i\right)}^3}} + 50 \cdot \left(\frac{{n}^3}{i} \cdot \left(\log n \cdot \log n\right)\right)\right) + \frac{\log i \cdot 100}{\frac{i \cdot i}{{n}^{4}}}\right) + \left(\left(\frac{50 \cdot {\left(\log i\right)}^2}{\frac{i}{{n}^3}} + \frac{\left(50 \cdot {n}^{4}\right) \cdot \left(\log n \cdot \log n\right)}{\frac{i}{\log i}}\right) + \left(\frac{100}{i} \cdot \frac{{n}^3}{i} + \frac{100 \cdot \left(n \cdot n\right)}{\frac{i}{\log i}}\right)\right)\right) - \left(\left(\left(\frac{100 \cdot \log n}{\frac{i \cdot i}{{n}^{4}}} + \frac{{n}^{4}}{\frac{{i}^3}{50}}\right) + \frac{\frac{50}{3} \cdot {n}^{4}}{\frac{i}{{\left(\log n\right)}^3}}\right) + \left(100 \cdot \left(\frac{n \cdot n}{i} \cdot \log n + \frac{\log n \cdot {n}^3}{\frac{i}{\log i}}\right) + \frac{\left(50 \cdot {n}^{4}\right) \cdot \log n}{\frac{i}{{\left(\log i\right)}^2}}\right)\right)\]
   3.3

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\left(\left(\left(\frac{\frac{50}{3} \cdot {n}^{4}}{\frac{i}{{\left(\log i\right)}^3}} + 50 \cdot \left(\frac{{n}^3}{i} \cdot \left(\log n \cdot \log n\right)\right)\right) + \frac{\log i \cdot 100}{\frac{i \cdot i}{{n}^{4}}}\right) + \left(\left(\frac{50 \cdot {\left(\log i\right)}^2}{\frac{i}{{n}^3}} + \frac{\left(50 \cdot {n}^{4}\right) \cdot \left(\log n \cdot \log n\right)}{\frac{i}{\log i}}\right) + \left(\frac{100}{i} \cdot \frac{{n}^3}{i} + \frac{100 \cdot \left(n \cdot n\right)}{\frac{i}{\log i}}\right)\right)\right) - \left(\left(\left(\frac{100 \cdot \log n}{\frac{i \cdot i}{{n}^{4}}} + \frac{{n}^{4}}{\frac{{i}^3}{50}}\right) + \frac{\frac{50}{3} \cdot {n}^{4}}{\frac{i}{{\left(\log n\right)}^3}}\right) + \left(100 \cdot \left(\frac{n \cdot n}{i} \cdot \log n + \frac{\log n \cdot {n}^3}{\frac{i}{\log i}}\right) + \frac{\left(50 \cdot {n}^{4}\right) \cdot \log n}{\frac{i}{{\left(\log i\right)}^2}}\right)\right)} \leadsto \color{blue}{\left(\left(\frac{100}{i} \cdot \frac{{n}^3}{i} + \frac{100 \cdot \log i}{\frac{\frac{i}{n}}{n}}\right) - \left(\left(\frac{{n}^{4} \cdot 50}{\frac{i}{\log n}} \cdot {\left(\log i\right)}^2 + \left(\frac{50}{\frac{{i}^3}{{n}^{4}}} + \frac{\log n}{\frac{i}{100}} \cdot \frac{{n}^{4}}{i}\right)\right) + \left(\left(\log n \cdot \left(\frac{n}{i} \cdot \left(n \cdot 100\right)\right) + \frac{\log n}{\frac{i}{100}} \cdot \left({n}^3 \cdot \log i\right)\right) + \frac{{n}^{4}}{\frac{i}{\frac{50}{3}}} \cdot {\left(\log n\right)}^3\right)\right)\right) + \left(\left(\frac{50 \cdot {\left(\log i\right)}^2}{\frac{i}{{n}^3}} + \frac{\left({n}^{4} \cdot 50\right) \cdot {\left(\log n\right)}^2}{\frac{i}{\log i}}\right) + \left(\left(\frac{\log i}{\frac{i}{100}} \cdot \frac{{n}^{4}}{i} + \frac{{n}^{4}}{\frac{i}{\frac{50}{3}}} \cdot {\left(\log i\right)}^3\right) + 50 \cdot \left(\frac{{n}^3}{i} \cdot {\left(\log n\right)}^2\right)\right)\right)}\]
   4.0