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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -5.044652344559801 \cdot 10^{-130}:\\ \;\;\;\;100 \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.1890433884445756 \cdot 10^{-164}:\\ \;\;\;\;100 \cdot \frac{1}{(\left(\frac{i}{n}\right) \cdot \left(\frac{\frac{1}{2}}{n} - \frac{1}{2}\right) + \left(\frac{1}{n}\right))_*}\\ \mathbf{elif}\;i \le 2.389310129035718 \cdot 10^{+141}:\\ \;\;\;\;100 \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.9402021625128326 \cdot 10^{+232}:\\ \;\;\;\;(\left({\left(1 + \frac{i}{n}\right)}^{n}\right) \cdot \left(\frac{100}{i} \cdot n\right) + \left(\frac{-100}{\frac{i}{n}}\right))_*\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{1}{(\left(\frac{i}{n}\right) \cdot \left(\frac{\frac{1}{2}}{n} - \frac{1}{2}\right) + \left(\frac{1}{n}\right))_*}\\ \end{array}\]

Original	47.1
Target	47.0
Herbie	6.7

Derivation

Split input into 3 regimes
if i < -5.044652344559801e-130 or 1.1890433884445756e-164 < i < 2.389310129035718e+141
1. Initial program 41.6
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied add-exp-log42.6
  \[\leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
4. Applied pow-exp42.6
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
5. Applied expm1-def34.5
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
6. Simplified5.8
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
if -5.044652344559801e-130 < i < 1.1890433884445756e-164 or 1.9402021625128326e+232 < i
1. Initial program 56.5
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied add-exp-log59.4
  \[\leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
4. Applied pow-exp59.4
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
5. Applied expm1-def56.6
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
6. Simplified27.0
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
7. Using strategy rm
8. Applied clear-num27.2
  \[\leadsto 100 \cdot \color{blue}{\frac{1}{\frac{\frac{i}{n}}{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}}}\]
9. Taylor expanded around 0 13.9
  \[\leadsto 100 \cdot \frac{1}{\color{blue}{\left(\frac{1}{2} \cdot \frac{i}{{n}^{2}} + \frac{1}{n}\right) - \frac{1}{2} \cdot \frac{i}{n}}}\]
10. Simplified4.8
  \[\leadsto 100 \cdot \frac{1}{\color{blue}{(\left(\frac{i}{n}\right) \cdot \left(\frac{\frac{1}{2}}{n} - \frac{1}{2}\right) + \left(\frac{1}{n}\right))_*}}\]
if 2.389310129035718e+141 < i < 1.9402021625128326e+232
1. Initial program 30.5
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Initial simplification32.3
  \[\leadsto (\left({\left(1 + \frac{i}{n}\right)}^{n}\right) \cdot \left(n \cdot \frac{100}{i}\right) + \left(\frac{-100}{\frac{i}{n}}\right))_*\]
Recombined 3 regimes into one program.
Final simplification6.7
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -5.044652344559801 \cdot 10^{-130}:\\ \;\;\;\;100 \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.1890433884445756 \cdot 10^{-164}:\\ \;\;\;\;100 \cdot \frac{1}{(\left(\frac{i}{n}\right) \cdot \left(\frac{\frac{1}{2}}{n} - \frac{1}{2}\right) + \left(\frac{1}{n}\right))_*}\\ \mathbf{elif}\;i \le 2.389310129035718 \cdot 10^{+141}:\\ \;\;\;\;100 \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.9402021625128326 \cdot 10^{+232}:\\ \;\;\;\;(\left({\left(1 + \frac{i}{n}\right)}^{n}\right) \cdot \left(\frac{100}{i} \cdot n\right) + \left(\frac{-100}{\frac{i}{n}}\right))_*\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{1}{(\left(\frac{i}{n}\right) \cdot \left(\frac{\frac{1}{2}}{n} - \frac{1}{2}\right) + \left(\frac{1}{n}\right))_*}\\ \end{array}\]

Error

Target

Derivation

`if i < -5.044652344559801e-130 or 1.1890433884445756e-164 < i < 2.389310129035718e+141`

`if -5.044652344559801e-130 < i < 1.1890433884445756e-164 or 1.9402021625128326e+232 < i`

`if 2.389310129035718e+141 < i < 1.9402021625128326e+232`

Runtime