Original	50.9
Comparison	50.4
Herbie	10.4

Derivation

Split input into 3 regimes.
if i < -0.058764479831025576
1. Initial program 27.7
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied flip3-- 27.7
  \[\leadsto 100 \cdot \frac{\color{blue}{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^{3} - {1}^{3}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}}{\frac{i}{n}}\]
4. Applied simplify 27.7
  \[\leadsto 100 \cdot \frac{\frac{\color{blue}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^3 - 1}}{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 + \left({1}^2 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}{\frac{i}{n}}\]
5. Applied simplify 27.7
  \[\leadsto 100 \cdot \frac{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^3 - 1}{\color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + 1\right) + {\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2}}}{\frac{i}{n}}\]
if -0.058764479831025576 < i < 4.370354623930509e-12
1. Initial program 61.7
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Applied taylor 14.5
  \[\leadsto 100 \cdot \frac{\frac{1}{6} \cdot {i}^{3} + \left(i + \frac{1}{2} \cdot {i}^2\right)}{\frac{i}{n}}\]
3. Taylor expanded around 0 14.5
  
  \[\leadsto 100 \cdot \frac{\color{blue}{\frac{1}{6} \cdot {i}^{3} + \left(i + \frac{1}{2} \cdot {i}^2\right)}}{\frac{i}{n}}\]
4. Applied taylor 0.0
  \[\leadsto 100 \cdot n + \left(\frac{50}{3} \cdot \left(n \cdot {i}^2\right) + 50 \cdot \left(n \cdot i\right)\right)\]
5. Taylor expanded around 0 0.0
  
  \[\leadsto \color{blue}{100 \cdot n + \left(\frac{50}{3} \cdot \left(n \cdot {i}^2\right) + 50 \cdot \left(n \cdot i\right)\right)}\]
6. Applied simplify 0.0
  \[\leadsto \color{blue}{n \cdot \left(\left(100 + 50 \cdot i\right) + \frac{50}{3} \cdot \left(i \cdot i\right)\right)}\]
7. Using strategy rm
8. Applied add-exp-log 0.0
  \[\leadsto n \cdot \left(\left(100 + 50 \cdot i\right) + \color{blue}{e^{\log \left(\frac{50}{3} \cdot \left(i \cdot i\right)\right)}}\right)\]
9. Applied simplify 0.0
  \[\leadsto n \cdot \left(\left(100 + 50 \cdot i\right) + e^{\color{blue}{\log \left(\frac{50}{3} \cdot {i}^2\right)}}\right)\]
if 4.370354623930509e-12 < i
1. Initial program 32.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied div-sub 32.8
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \frac{1}{\frac{i}{n}}\right)}\]
4. Applied simplify 35.7
  \[\leadsto 100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \color{blue}{\frac{n}{i}}\right)\]
Recombined 3 regimes into one program.
Removed slow pow expressions

Error

Target

Derivation

`if i < -0.058764479831025576`

`if -0.058764479831025576 < i < 4.370354623930509e-12`

`if 4.370354623930509e-12 < i`

Runtime