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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -0.00016446858584625898:\\ \;\;\;\;\frac{100 \cdot e^{i} - 100}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 9.023414928266507 \cdot 10^{-12}:\\ \;\;\;\;\left(n \cdot i\right) \cdot \left(i \cdot \frac{50}{3} + 50\right) + 100 \cdot n\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^{2} \cdot \log i\right)}{i} + \left(\frac{50}{3} \cdot \frac{{\left(\log i\right)}^{3} \cdot {n}^{4}}{i} + \left(100 \cdot \frac{{n}^{2} \cdot \log i}{i} + \left(\frac{{\left(\log n\right)}^{2} \cdot {n}^{3}}{i} \cdot 50 + 50 \cdot \frac{{\left(\log i\right)}^{2} \cdot {n}^{3}}{i}\right)\right)\right)\right) + \frac{100}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^{2} \cdot \log i\right)}{i}\right) - \left(\frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} \cdot \frac{50}{3} + \left(\frac{\left({\left(\log i\right)}^{2} \cdot \log n\right) \cdot {n}^{4}}{i} \cdot \frac{50}{3} + \left(\left(\frac{100}{3} \cdot \frac{\left({\left(\log i\right)}^{2} \cdot \log n\right) \cdot {n}^{4}}{i} + \left(\frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} \cdot 50 + 100 \cdot \frac{\log n \cdot {n}^{2}}{i}\right)\right) + \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} \cdot 50\right)\right)\right)\\ \end{array}\]

Original	42.4
Target	42.1
Herbie	16.4

Derivation

Split input into 3 regimes
if i < -0.00016446858584625898
1. Initial program 28.5
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification29.1
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
3. Taylor expanded around -inf 12.5
  \[\leadsto \color{blue}{\frac{\left(100 \cdot e^{i} - 100\right) \cdot n}{i}}\]
4. Using strategy rm
5. Applied associate-/l*11.7
  \[\leadsto \color{blue}{\frac{100 \cdot e^{i} - 100}{\frac{i}{n}}}\]
if -0.00016446858584625898 < i < 9.023414928266507e-12
1. Initial program 50.0
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification50.0
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
3. Taylor expanded around -inf 49.9
  \[\leadsto \color{blue}{\frac{\left(100 \cdot e^{i} - 100\right) \cdot n}{i}}\]
4. Taylor expanded around 0 16.6
  \[\leadsto \color{blue}{\frac{50}{3} \cdot \left({i}^{2} \cdot n\right) + \left(100 \cdot n + 50 \cdot \left(i \cdot n\right)\right)}\]
5. Simplified16.6
  \[\leadsto \color{blue}{\left(i \cdot n\right) \cdot \left(50 + \frac{50}{3} \cdot i\right) + 100 \cdot n}\]
if 9.023414928266507e-12 < i
1. Initial program 31.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification31.8
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
3. Taylor expanded around 0 22.9
  \[\leadsto \color{blue}{\left(\frac{100}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^{2} \cdot \log i\right)}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot \left(\log i \cdot {\left(\log n\right)}^{2}\right)}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log i\right)}^{3}}{i} + \left(100 \cdot \frac{{n}^{2} \cdot \log i}{i} + \left(50 \cdot \frac{{n}^{3} \cdot {\left(\log i\right)}^{2}}{i} + 50 \cdot \frac{{n}^{3} \cdot {\left(\log n\right)}^{2}}{i}\right)\right)\right)\right)\right) - \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} + \left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot \left(\log n \cdot {\left(\log i\right)}^{2}\right)}{i} + \left(50 \cdot \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} + \left(\frac{100}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log i\right)}^{2} \cdot \log n\right)}{i} + \left(100 \cdot \frac{{n}^{2} \cdot \log n}{i} + 50 \cdot \frac{{n}^{3} \cdot \left(\log i \cdot \log n\right)}{i}\right)\right)\right)\right)\right)}\]
Recombined 3 regimes into one program.
Final simplification16.4
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -0.00016446858584625898:\\ \;\;\;\;\frac{100 \cdot e^{i} - 100}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 9.023414928266507 \cdot 10^{-12}:\\ \;\;\;\;\left(n \cdot i\right) \cdot \left(i \cdot \frac{50}{3} + 50\right) + 100 \cdot n\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{50}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^{2} \cdot \log i\right)}{i} + \left(\frac{50}{3} \cdot \frac{{\left(\log i\right)}^{3} \cdot {n}^{4}}{i} + \left(100 \cdot \frac{{n}^{2} \cdot \log i}{i} + \left(\frac{{\left(\log n\right)}^{2} \cdot {n}^{3}}{i} \cdot 50 + 50 \cdot \frac{{\left(\log i\right)}^{2} \cdot {n}^{3}}{i}\right)\right)\right)\right) + \frac{100}{3} \cdot \frac{{n}^{4} \cdot \left({\left(\log n\right)}^{2} \cdot \log i\right)}{i}\right) - \left(\frac{{n}^{4} \cdot {\left(\log n\right)}^{3}}{i} \cdot \frac{50}{3} + \left(\frac{\left({\left(\log i\right)}^{2} \cdot \log n\right) \cdot {n}^{4}}{i} \cdot \frac{50}{3} + \left(\left(\frac{100}{3} \cdot \frac{\left({\left(\log i\right)}^{2} \cdot \log n\right) \cdot {n}^{4}}{i} + \left(\frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} \cdot 50 + 100 \cdot \frac{\log n \cdot {n}^{2}}{i}\right)\right) + \frac{{n}^{3} \cdot \left(\log n \cdot \log i\right)}{i} \cdot 50\right)\right)\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if i < -0.00016446858584625898`

`if -0.00016446858584625898 < i < 9.023414928266507e-12`

`if 9.023414928266507e-12 < i`

Runtime

In
Out