Original	47.2
Target	46.7
Herbie	15.1

Derivation

Split input into 4 regimes
if i < -747131245814696.0
1. Initial program 27.4
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around inf 62.9
  \[\leadsto \color{blue}{100 \cdot \frac{\left(e^{\left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right) \cdot n} - 1\right) \cdot n}{i}}\]
3. Simplified18.2
  \[\leadsto \color{blue}{\left(\frac{100}{i} \cdot n\right) \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}\]
if -747131245814696.0 < i < 22.870542718060396
1. Initial program 56.9
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 26.2
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(\frac{1}{2} \cdot {i}^{2} + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{i}{n}}\]
3. Simplified26.2
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{\frac{i}{n}}\]
4. Using strategy rm
5. Applied div-inv26.3
  \[\leadsto 100 \cdot \frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{\color{blue}{i \cdot \frac{1}{n}}}\]
6. Applied add-cube-cbrt26.9
  \[\leadsto 100 \cdot \frac{\color{blue}{\left(\sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)} \cdot \sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}\right) \cdot \sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}}{i \cdot \frac{1}{n}}\]
7. Applied times-frac11.7
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{\sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)} \cdot \sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{i} \cdot \frac{\sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{\frac{1}{n}}\right)}\]
8. Simplified11.6
  \[\leadsto 100 \cdot \left(\frac{\sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)} \cdot \sqrt[3]{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{i} \cdot \color{blue}{\left(n \cdot \sqrt[3]{i + \left(i \cdot \frac{1}{6} + \frac{1}{2}\right) \cdot \left(i \cdot i\right)}\right)}\right)\]
9. Taylor expanded around 0 38.3
  \[\leadsto 100 \cdot \left(\color{blue}{\left(\frac{1}{3} \cdot {\left({i}^{2}\right)}^{\frac{1}{3}} + \left({\left(\frac{1}{i}\right)}^{\frac{1}{3}} + \frac{1}{12} \cdot {\left({i}^{5}\right)}^{\frac{1}{3}}\right)\right)} \cdot \left(n \cdot \sqrt[3]{i + \left(i \cdot \frac{1}{6} + \frac{1}{2}\right) \cdot \left(i \cdot i\right)}\right)\right)\]
10. Simplified11.1
  \[\leadsto 100 \cdot \left(\color{blue}{\left(\sqrt[3]{i \cdot i} \cdot \frac{1}{3} + \left(\frac{1}{12} \cdot \sqrt[3]{{i}^{5}} + \sqrt[3]{\frac{1}{i}}\right)\right)} \cdot \left(n \cdot \sqrt[3]{i + \left(i \cdot \frac{1}{6} + \frac{1}{2}\right) \cdot \left(i \cdot i\right)}\right)\right)\]
11. Taylor expanded around 0 38.3
  \[\leadsto 100 \cdot \left(\left(\sqrt[3]{i \cdot i} \cdot \frac{1}{3} + \left(\frac{1}{12} \cdot \sqrt[3]{{i}^{5}} + \sqrt[3]{\frac{1}{i}}\right)\right) \cdot \left(n \cdot \color{blue}{\left({i}^{\frac{1}{3}} + \left(\frac{1}{6} \cdot {\left({i}^{4}\right)}^{\frac{1}{3}} + \frac{1}{36} \cdot {\left({i}^{7}\right)}^{\frac{1}{3}}\right)\right)}\right)\right)\]
12. Simplified11.1
  \[\leadsto 100 \cdot \left(\left(\sqrt[3]{i \cdot i} \cdot \frac{1}{3} + \left(\frac{1}{12} \cdot \sqrt[3]{{i}^{5}} + \sqrt[3]{\frac{1}{i}}\right)\right) \cdot \left(n \cdot \color{blue}{\left(\left(\frac{1}{6} \cdot \sqrt[3]{{i}^{4}} + \sqrt[3]{{i}^{7}} \cdot \frac{1}{36}\right) + \sqrt[3]{i}\right)}\right)\right)\]
if 22.870542718060396 < i < 3.4547076553386547e+252 or 4.97811435192654e+305 < i
1. Initial program 31.9
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 29.1
  \[\leadsto \color{blue}{0}\]
if 3.4547076553386547e+252 < i < 4.97811435192654e+305
1. Initial program 30.3
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied div-inv30.3
  \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{i \cdot \frac{1}{n}}}\]
4. Applied *-un-lft-identity30.3
  \[\leadsto 100 \cdot \frac{\color{blue}{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}{i \cdot \frac{1}{n}}\]
5. Applied times-frac30.3
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{1}{i} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\right)}\]
6. Simplified30.3
  \[\leadsto 100 \cdot \left(\frac{1}{i} \cdot \color{blue}{\left({\left(\frac{i}{n} + 1\right)}^{n} \cdot n - n\right)}\right)\]
Recombined 4 regimes into one program.
Final simplification15.1
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -747131245814696.0:\\ \;\;\;\;\left({\left(\frac{i}{n}\right)}^{n} - 1\right) \cdot \left(\frac{100}{i} \cdot n\right)\\ \mathbf{elif}\;i \le 22.870542718060396:\\ \;\;\;\;\left(\left(n \cdot \left(\sqrt[3]{i} + \left(\sqrt[3]{{i}^{4}} \cdot \frac{1}{6} + \frac{1}{36} \cdot \sqrt[3]{{i}^{7}}\right)\right)\right) \cdot \left(\left(\sqrt[3]{\frac{1}{i}} + \frac{1}{12} \cdot \sqrt[3]{{i}^{5}}\right) + \sqrt[3]{i \cdot i} \cdot \frac{1}{3}\right)\right) \cdot 100\\ \mathbf{elif}\;i \le 3.4547076553386547 \cdot 10^{+252} \lor \neg \left(i \le 4.97811435192654 \cdot 10^{+305}\right):\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(n \cdot {\left(1 + \frac{i}{n}\right)}^{n} - n\right) \cdot \frac{1}{i}\right) \cdot 100\\ \end{array}\]

Error

Try it out

Target

Derivation

`if i < -747131245814696.0`

`if -747131245814696.0 < i < 22.870542718060396`

`if 22.870542718060396 < i < 3.4547076553386547e+252 or 4.97811435192654e+305 < i`

`if 3.4547076553386547e+252 < i < 4.97811435192654e+305`

Runtime

In
Out