Original	42.1
Target	41.8
Herbie	18.3

Derivation

Split input into 4 regimes
if n < -1.9959112682211866
1. Initial program 44.9
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied pow-to-exp53.1
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def53.1
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
5. Simplified24.5
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
6. Taylor expanded around inf 43.3
  \[\leadsto 100 \cdot \color{blue}{\frac{\left(e^{i} - 1\right) \cdot n}{i}}\]
7. Simplified24.4
  \[\leadsto 100 \cdot \color{blue}{\frac{(e^{i} - 1)^*}{\frac{i}{n}}}\]
if -1.9959112682211866 < n < -2.5875851879278052e-67
1. Initial program 17.9
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied associate-/r/18.2
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)}\]
4. Applied associate-*r*18.2
  \[\leadsto \color{blue}{\left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot n}\]
if -2.5875851879278052e-67 < n < -3.843767469236074e-200
1. Initial program 16.9
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied pow-to-exp16.9
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def2.8
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
5. Simplified25.9
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
6. Using strategy rm
7. Applied associate-*r/25.8
  \[\leadsto \color{blue}{\frac{100 \cdot (e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{i}{n}}}\]
8. Using strategy rm
9. Applied div-inv25.8
  \[\leadsto \frac{100 \cdot (e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\color{blue}{i \cdot \frac{1}{n}}}\]
10. Applied times-frac14.8
  \[\leadsto \color{blue}{\frac{100}{i} \cdot \frac{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{1}{n}}}\]
11. Simplified14.7
  \[\leadsto \frac{100}{i} \cdot \color{blue}{\left((e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^* \cdot n\right)}\]
if -3.843767469236074e-200 < n
1. Initial program 48.0
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied pow-to-exp48.1
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def41.2
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
5. Simplified15.3
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1)^*}{\frac{i}{n}}\]
Recombined 4 regimes into one program.
Final simplification18.3
\[\leadsto \begin{array}{l} \mathbf{if}\;n \le -1.9959112682211866:\\ \;\;\;\;100 \cdot \frac{(e^{i} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;n \le -2.5875851879278052 \cdot 10^{-67}:\\ \;\;\;\;n \cdot \left(\frac{{\left(\frac{i}{n} + 1\right)}^{n} - 1}{i} \cdot 100\right)\\ \mathbf{elif}\;n \le -3.843767469236074 \cdot 10^{-200}:\\ \;\;\;\;\left((e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^* \cdot n\right) \cdot \frac{100}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}} \cdot 100\\ \end{array}\]

Error

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Target

Derivation

`if n < -1.9959112682211866`

`if -1.9959112682211866 < n < -2.5875851879278052e-67`

`if -2.5875851879278052e-67 < n < -3.843767469236074e-200`

`if -3.843767469236074e-200 < n`

Runtime

In
Out