if i < -2.1890592f-23

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   17.2
2. Using strategy rm
   17.2
3. Applied add-exp-log to get
   \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
   17.2
4. Applied pow-exp to get
   \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
   17.2
5. Applied expm1-def to get
   \[100 \cdot \frac{\color{red}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
   14.1
6. Using strategy rm
   14.1
7. Applied expm1-log1p-u to get
   \[100 \cdot \frac{(e^{\color{red}{\log \left(1 + \frac{i}{n}\right)} \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{(e^{\color{blue}{(e^{\log_* (1 + \log \left(1 + \frac{i}{n}\right))} - 1)^*} \cdot n} - 1)^*}{\frac{i}{n}}\]
   14.1
8. Applied simplify to get
   \[100 \cdot \frac{(e^{(e^{\color{red}{\log_* (1 + \log \left(1 + \frac{i}{n}\right))}} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{(e^{(e^{\color{blue}{\log_* (1 + \log_* (1 + \frac{i}{n}))}} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}}\]
   1.4

if -2.1890592f-23 < i < 2.9389908f-22

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
   \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
   29.6
4. Applied pow-exp to get
   \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
   29.6
5. Applied expm1-def to get
   \[100 \cdot \frac{\color{red}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
   28.3
6. Using strategy rm
   28.3
7. Applied div-inv to get
   \[100 \cdot \color{red}{\frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{\frac{i}{n}}} \leadsto 100 \cdot \color{blue}{\left((e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^* \cdot \frac{1}{\frac{i}{n}}\right)}\]
   28.4
8. Applied simplify to get
   \[100 \cdot \left((e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^* \cdot \color{red}{\frac{1}{\frac{i}{n}}}\right) \leadsto 100 \cdot \left((e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^* \cdot \color{blue}{\frac{n}{i}}\right)\]
   28.4
9. Applied taylor to get
   \[100 \cdot \left((e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^* \cdot \frac{n}{i}\right) \leadsto 100 \cdot \left((e^{i} - 1)^* \cdot \frac{n}{i}\right)\]
   10.8
10. Taylor expanded around 0 to get
    \[100 \cdot \left((e^{\color{red}{i}} - 1)^* \cdot \frac{n}{i}\right) \leadsto 100 \cdot \left((e^{\color{blue}{i}} - 1)^* \cdot \frac{n}{i}\right)\]
    10.8
11. Applied simplify to get
    \[100 \cdot \left((e^{i} - 1)^* \cdot \frac{n}{i}\right) \leadsto \frac{\left(100 \cdot n\right) \cdot (e^{i} - 1)^*}{i}\]
    0

---

12. Applied final simplification

if 2.9389908f-22 < i < 5.2930678f+26

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   24.5
2. Using strategy rm
   24.5
3. Applied add-exp-log to get
   \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
   24.5
4. Applied pow-exp to get
   \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
   24.5
5. Applied expm1-def to get
   \[100 \cdot \frac{\color{red}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
   18.5
6. Using strategy rm
   18.5
7. Applied div-inv to get
   \[100 \cdot \frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{\color{red}{\frac{i}{n}}} \leadsto 100 \cdot \frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{\color{blue}{i \cdot \frac{1}{n}}}\]
   18.5
8. Applied associate-/r* to get
   \[100 \cdot \color{red}{\frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{i \cdot \frac{1}{n}}} \leadsto 100 \cdot \color{blue}{\frac{\frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{i}}{\frac{1}{n}}}\]
   18.6
9. Applied simplify to get
   \[100 \cdot \frac{\color{red}{\frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{i}}}{\frac{1}{n}} \leadsto 100 \cdot \frac{\color{blue}{\frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{i}}}{\frac{1}{n}}\]
   5.3

if 5.2930678f+26 < i

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   30.8
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\frac{\log n - \log i}{n}} - 1}{\frac{i}{n}}\]
   13.5
3. Taylor expanded around inf to get
   \[100 \cdot \frac{\color{red}{e^{\frac{\log n - \log i}{n}} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\frac{\log n - \log i}{n}} - 1}}{\frac{i}{n}}\]
   13.5
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{e^{\frac{\log n - \log i}{n}} - 1}{\frac{i}{n}}} \leadsto \color{blue}{\frac{(e^{\frac{\log n - \log i}{n}} - 1)^*}{\frac{\frac{i}{100}}{n}}}\]
   1.7