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

↓

\[\begin{array}{l} \mathbf{if}\;n \le -3.0141441825975826 \cdot 10^{+60}:\\ \;\;\;\;\left(e^{\log \left(\frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{i}\right)} \cdot 100\right) \cdot n\\ \mathbf{elif}\;n \le -2.8191387785351184 \cdot 10^{+38}:\\ \;\;\;\;{\left(\frac{i}{n} + 1\right)}^{n} \cdot \frac{100 \cdot n}{i} - \frac{100 \cdot n}{i}\\ \mathbf{elif}\;n \le -0.49358309211804946 \lor \neg \left(n \le 1.0786542170041112 \cdot 10^{-192}\right):\\ \;\;\;\;\left(e^{\log \left(\frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{i}\right)} \cdot 100\right) \cdot n\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Original	42.1
Target	41.8
Herbie	21.0

Derivation

Split input into 3 regimes
if n < -3.0141441825975826e+60 or -2.8191387785351184e+38 < n < -0.49358309211804946 or 1.0786542170041112e-192 < n
1. Initial program 52.3
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 37.6
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(\frac{1}{2} \cdot {i}^{2} + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{i}{n}}\]
3. Simplified37.5
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{\frac{i}{n}}\]
4. Using strategy rm
5. Applied associate-/r/22.6
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{i} \cdot n\right)}\]
6. Applied associate-*r*22.6
  \[\leadsto \color{blue}{\left(100 \cdot \frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{i}\right) \cdot n}\]
7. Using strategy rm
8. Applied add-exp-log22.6
  \[\leadsto \left(100 \cdot \color{blue}{e^{\log \left(\frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{i}\right)}}\right) \cdot n\]
if -3.0141441825975826e+60 < n < -2.8191387785351184e+38
1. Initial program 33.0
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification33.0
  \[\leadsto \frac{n \cdot 100}{i} \cdot {\left(1 + \frac{i}{n}\right)}^{n} - \frac{n \cdot 100}{i}\]
if -0.49358309211804946 < n < 1.0786542170041112e-192
1. Initial program 21.1
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 16.5
  \[\leadsto \color{blue}{0}\]
Recombined 3 regimes into one program.
Final simplification21.0
\[\leadsto \begin{array}{l} \mathbf{if}\;n \le -3.0141441825975826 \cdot 10^{+60}:\\ \;\;\;\;\left(e^{\log \left(\frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{i}\right)} \cdot 100\right) \cdot n\\ \mathbf{elif}\;n \le -2.8191387785351184 \cdot 10^{+38}:\\ \;\;\;\;{\left(\frac{i}{n} + 1\right)}^{n} \cdot \frac{100 \cdot n}{i} - \frac{100 \cdot n}{i}\\ \mathbf{elif}\;n \le -0.49358309211804946 \lor \neg \left(n \le 1.0786542170041112 \cdot 10^{-192}\right):\\ \;\;\;\;\left(e^{\log \left(\frac{\left(\frac{1}{6} \cdot i + \frac{1}{2}\right) \cdot \left(i \cdot i\right) + i}{i}\right)} \cdot 100\right) \cdot n\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Error

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Target

Derivation

`if n < -3.0141441825975826e+60 or -2.8191387785351184e+38 < n < -0.49358309211804946 or 1.0786542170041112e-192 < n`

`if -3.0141441825975826e+60 < n < -2.8191387785351184e+38`

`if -0.49358309211804946 < n < 1.0786542170041112e-192`

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