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

↓

\[\begin{array}{l} \mathbf{if}\;n \le -6.15239565177811 \cdot 10^{+40}:\\ \;\;\;\;100 \cdot \frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{\frac{i}{n}}\\ \mathbf{elif}\;n \le -240361969150.9007:\\ \;\;\;\;100 \cdot \left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right)\\ \mathbf{elif}\;n \le -1.9906372068903042:\\ \;\;\;\;100 \cdot \frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{\frac{i}{n}}\\ \mathbf{elif}\;n \le 1.566547185340197 \cdot 10^{-126}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \le 1.302728670222634 \cdot 10^{+231}:\\ \;\;\;\;100 \cdot \frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right)\\ \end{array}\]

Original	42.4
Target	42.0
Herbie	30.2

Derivation

Split input into 3 regimes
if n < -6.15239565177811e+40 or -240361969150.9007 < n < -1.9906372068903042 or 1.566547185340197e-126 < n < 1.302728670222634e+231
1. Initial program 52.5
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 36.1
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(\frac{1}{2} \cdot {i}^{2} + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{i}{n}}\]
3. Simplified36.0
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{\frac{i}{n}}\]
if -6.15239565177811e+40 < n < -240361969150.9007 or 1.302728670222634e+231 < n
1. Initial program 50.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around inf 61.9
  \[\leadsto \color{blue}{100 \cdot \frac{\left(e^{\left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right) \cdot n} - 1\right) \cdot n}{i}}\]
3. Simplified39.2
  \[\leadsto \color{blue}{\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100}\]
if -1.9906372068903042 < n < 1.566547185340197e-126
1. Initial program 24.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 18.8
  \[\leadsto \color{blue}{0}\]
Recombined 3 regimes into one program.
Final simplification30.2
\[\leadsto \begin{array}{l} \mathbf{if}\;n \le -6.15239565177811 \cdot 10^{+40}:\\ \;\;\;\;100 \cdot \frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{\frac{i}{n}}\\ \mathbf{elif}\;n \le -240361969150.9007:\\ \;\;\;\;100 \cdot \left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right)\\ \mathbf{elif}\;n \le -1.9906372068903042:\\ \;\;\;\;100 \cdot \frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{\frac{i}{n}}\\ \mathbf{elif}\;n \le 1.566547185340197 \cdot 10^{-126}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \le 1.302728670222634 \cdot 10^{+231}:\\ \;\;\;\;100 \cdot \frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right)\\ \end{array}\]

Error

Target

Derivation

`if n < -6.15239565177811e+40 or -240361969150.9007 < n < -1.9906372068903042 or 1.566547185340197e-126 < n < 1.302728670222634e+231`

`if -6.15239565177811e+40 < n < -240361969150.9007 or 1.302728670222634e+231 < n`

`if -1.9906372068903042 < n < 1.566547185340197e-126`

Reproduce