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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -0.020377340814253832:\\ \;\;\;\;\frac{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot 100}{\frac{i}{n}}\\ \mathbf{if}\;i \le 2.4695557279739083 \cdot 10^{+28}:\\ \;\;\;\;\frac{\left(100 \cdot n\right) \cdot \left(1 + \frac{1}{2} \cdot i\right)}{1}\\ \mathbf{if}\;i \le 1.1918327281230139 \cdot 10^{+212}:\\ \;\;\;\;\left(n \cdot \frac{100}{i}\right) \cdot \left({\left(e^{n}\right)}^{\left(\log i - \log n\right)} - 1\right)\\ \mathbf{if}\;i \le 9.983371006406189 \cdot 10^{+256}:\\ \;\;\;\;\frac{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot 100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(n \cdot \frac{100}{i}\right) \cdot \left({\left(e^{n}\right)}^{\left(\log i - \log n\right)} - 1\right)\\ \end{array}\]

Original	47.2
Target	46.7
Herbie	16.7

Derivation

Split input into 3 regimes
if i < -0.020377340814253832 or 1.1918327281230139e+212 < i < 9.983371006406189e+256
1. Initial program 28.1
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied associate-*r/28.0
  \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}}\]
if -0.020377340814253832 < i < 2.4695557279739083e+28
1. Initial program 56.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 56.6
  \[\leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^{2} + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
3. Applied simplify26.3
  \[\leadsto \color{blue}{\frac{i + i \cdot \left(i \cdot \frac{1}{2}\right)}{\frac{\frac{i}{n}}{100}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity26.3
  \[\leadsto \frac{i + i \cdot \left(i \cdot \frac{1}{2}\right)}{\color{blue}{1 \cdot \frac{\frac{i}{n}}{100}}}\]
6. Applied *-un-lft-identity26.3
  \[\leadsto \frac{\color{blue}{1 \cdot \left(i + i \cdot \left(i \cdot \frac{1}{2}\right)\right)}}{1 \cdot \frac{\frac{i}{n}}{100}}\]
7. Applied times-frac26.3
  \[\leadsto \color{blue}{\frac{1}{1} \cdot \frac{i + i \cdot \left(i \cdot \frac{1}{2}\right)}{\frac{\frac{i}{n}}{100}}}\]
8. Applied simplify26.3
  \[\leadsto \color{blue}{1} \cdot \frac{i + i \cdot \left(i \cdot \frac{1}{2}\right)}{\frac{\frac{i}{n}}{100}}\]
9. Applied simplify10.6
  \[\leadsto 1 \cdot \color{blue}{\frac{\left(n \cdot 100\right) \cdot \left(1 + \frac{1}{2} \cdot i\right)}{1}}\]
if 2.4695557279739083e+28 < i < 1.1918327281230139e+212 or 9.983371006406189e+256 < i
1. Initial program 32.3
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around inf 27.8
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{n \cdot \left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right)} - 1}}{\frac{i}{n}}\]
3. Applied simplify28.1
  \[\leadsto \color{blue}{\left(\frac{100}{i} \cdot n\right) \cdot \left({\left(e^{n}\right)}^{\left(\left(\log i + 0\right) - \log n\right)} - 1\right)}\]
Recombined 3 regimes into one program.
Applied simplify16.7
\[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;i \le -0.020377340814253832:\\ \;\;\;\;\frac{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot 100}{\frac{i}{n}}\\ \mathbf{if}\;i \le 2.4695557279739083 \cdot 10^{+28}:\\ \;\;\;\;\frac{\left(100 \cdot n\right) \cdot \left(1 + \frac{1}{2} \cdot i\right)}{1}\\ \mathbf{if}\;i \le 1.1918327281230139 \cdot 10^{+212}:\\ \;\;\;\;\left(n \cdot \frac{100}{i}\right) \cdot \left({\left(e^{n}\right)}^{\left(\log i - \log n\right)} - 1\right)\\ \mathbf{if}\;i \le 9.983371006406189 \cdot 10^{+256}:\\ \;\;\;\;\frac{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot 100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(n \cdot \frac{100}{i}\right) \cdot \left({\left(e^{n}\right)}^{\left(\log i - \log n\right)} - 1\right)\\ \end{array}}\]

Error

Target

Derivation

`if i < -0.020377340814253832 or 1.1918327281230139e+212 < i < 9.983371006406189e+256`

`if -0.020377340814253832 < i < 2.4695557279739083e+28`

`if 2.4695557279739083e+28 < i < 1.1918327281230139e+212 or 9.983371006406189e+256 < i`

Runtime