\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]

↓

\[\begin{array}{l} \mathbf{if}\;i \le -0.00020526279674285735:\\ \;\;\;\;\frac{100 \cdot e^{i} - 100}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 4.1504571246210365 \cdot 10^{-07}:\\ \;\;\;\;\frac{\left(i \cdot \left(\left(100 + 50 \cdot i\right) + i \cdot \left(\frac{50}{3} \cdot i\right)\right)\right) \cdot n}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{50}{3} \cdot \frac{\left({\left(\log n\right)}^{2} \cdot \log i\right) \cdot {n}^{4}}{i} + \left(\left(\left(\frac{{n}^{3} \cdot {\left(\log i\right)}^{2}}{i} \cdot 50 + \frac{{\left(\log n\right)}^{2} \cdot {n}^{3}}{i} \cdot 50\right) + 100 \cdot \frac{\log i \cdot {n}^{2}}{i}\right) + \frac{50}{3} \cdot \frac{{\left(\log i\right)}^{3} \cdot {n}^{4}}{i}\right)\right) + \frac{100}{3} \cdot \frac{\left({\left(\log n\right)}^{2} \cdot \log i\right) \cdot {n}^{4}}{i}\right) - \left(\frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} \cdot \frac{50}{3} + \left(\frac{\left(\log n \cdot {\left(\log i\right)}^{2}\right) \cdot {n}^{4}}{i} \cdot \frac{50}{3} + \left(50 \cdot \frac{\left(\log i \cdot \log n\right) \cdot {n}^{3}}{i} + \left(\left(\frac{\log n \cdot {n}^{2}}{i} \cdot 100 + 50 \cdot \frac{\left(\log i \cdot \log n\right) \cdot {n}^{3}}{i}\right) + \frac{100}{3} \cdot \frac{\left(\log n \cdot {\left(\log i\right)}^{2}\right) \cdot {n}^{4}}{i}\right)\right)\right)\right)\\ \end{array}\]

Original	42.2
Target	42.1
Herbie	15.9

Derivation

Split input into 3 regimes
if i < -0.00020526279674285735
1. Initial program 27.4
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification27.9
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
3. Taylor expanded around inf 12.7
  \[\leadsto \color{blue}{\frac{\left(100 \cdot e^{i} - 100\right) \cdot n}{i}}\]
4. Using strategy rm
5. Applied associate-/l*11.7
  \[\leadsto \color{blue}{\frac{100 \cdot e^{i} - 100}{\frac{i}{n}}}\]
if -0.00020526279674285735 < i < 4.1504571246210365e-07
1. Initial program 49.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification49.8
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
3. Taylor expanded around inf 49.7
  \[\leadsto \color{blue}{\frac{\left(100 \cdot e^{i} - 100\right) \cdot n}{i}}\]
4. Taylor expanded around 0 16.2
  \[\leadsto \frac{\color{blue}{\left(100 \cdot i + \left(50 \cdot {i}^{2} + \frac{50}{3} \cdot {i}^{3}\right)\right)} \cdot n}{i}\]
5. Simplified16.2
  \[\leadsto \frac{\color{blue}{\left(\left(\left(100 + 50 \cdot i\right) + \left(i \cdot \frac{50}{3}\right) \cdot i\right) \cdot i\right)} \cdot n}{i}\]
if 4.1504571246210365e-07 < i
1. Initial program 32.1
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification32.0
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
3. Taylor expanded around 0 21.5
  \[\leadsto \color{blue}{\left(\frac{100}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^{2} \cdot \log i\right)}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot \left(\log i \cdot {\left(\log n\right)}^{2}\right)}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^{2} \cdot \log i}{i} + \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^{2}}{i} + 50 \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^{2}}{i}\right)\right)\right)\right)\right) - \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot \left(\log n \cdot {\left(\log i\right)}^{2}\right)}{i} + \left(50 \cdot \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} + \left(\frac{100}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log i\right)}^{2} \cdot \log n\right)}{i} + \left(100 \cdot \frac{{n}^{2} \cdot \log n}{i} + 50 \cdot \frac{{n}^{3} \cdot \left(\log i \cdot \log n\right)}{i}\right)\right)\right)\right)\right)}\]
Recombined 3 regimes into one program.
Final simplification15.9
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -0.00020526279674285735:\\ \;\;\;\;\frac{100 \cdot e^{i} - 100}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 4.1504571246210365 \cdot 10^{-07}:\\ \;\;\;\;\frac{\left(i \cdot \left(\left(100 + 50 \cdot i\right) + i \cdot \left(\frac{50}{3} \cdot i\right)\right)\right) \cdot n}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{50}{3} \cdot \frac{\left({\left(\log n\right)}^{2} \cdot \log i\right) \cdot {n}^{4}}{i} + \left(\left(\left(\frac{{n}^{3} \cdot {\left(\log i\right)}^{2}}{i} \cdot 50 + \frac{{\left(\log n\right)}^{2} \cdot {n}^{3}}{i} \cdot 50\right) + 100 \cdot \frac{\log i \cdot {n}^{2}}{i}\right) + \frac{50}{3} \cdot \frac{{\left(\log i\right)}^{3} \cdot {n}^{4}}{i}\right)\right) + \frac{100}{3} \cdot \frac{\left({\left(\log n\right)}^{2} \cdot \log i\right) \cdot {n}^{4}}{i}\right) - \left(\frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} \cdot \frac{50}{3} + \left(\frac{\left(\log n \cdot {\left(\log i\right)}^{2}\right) \cdot {n}^{4}}{i} \cdot \frac{50}{3} + \left(50 \cdot \frac{\left(\log i \cdot \log n\right) \cdot {n}^{3}}{i} + \left(\left(\frac{\log n \cdot {n}^{2}}{i} \cdot 100 + 50 \cdot \frac{\left(\log i \cdot \log n\right) \cdot {n}^{3}}{i}\right) + \frac{100}{3} \cdot \frac{\left(\log n \cdot {\left(\log i\right)}^{2}\right) \cdot {n}^{4}}{i}\right)\right)\right)\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if i < -0.00020526279674285735`

`if -0.00020526279674285735 < i < 4.1504571246210365e-07`

`if 4.1504571246210365e-07 < i`

Runtime

In
Out