Original	42.5
Target	42.5
Herbie	17.9

Derivation

Split input into 4 regimes
if n < -5675.168278704127
1. Initial program 44.1
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied add-exp-log44.1
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def44.1
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)} - 1)^*}}{\frac{i}{n}}\]
5. Simplified25.9
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1)^*}{\frac{i}{n}}\]
6. Using strategy rm
7. Applied associate-*r/25.9
  \[\leadsto \color{blue}{\frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
8. Using strategy rm
9. Applied *-un-lft-identity25.9
  \[\leadsto \frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\color{blue}{1 \cdot \frac{i}{n}}}\]
10. Applied times-frac25.9
  \[\leadsto \color{blue}{\frac{100}{1} \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
11. Simplified25.9
  \[\leadsto \color{blue}{100} \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\]
12. Taylor expanded around 0 25.7
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{i}} - 1)^*}{\frac{i}{n}}\]
if -5675.168278704127 < n < -1.5501848268953156e-256
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 add-exp-log17.9
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def17.9
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)} - 1)^*}}{\frac{i}{n}}\]
5. Simplified24.0
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1)^*}{\frac{i}{n}}\]
6. Using strategy rm
7. Applied associate-*r/23.9
  \[\leadsto \color{blue}{\frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
8. Using strategy rm
9. Applied add-cbrt-cube11.9
  \[\leadsto \frac{100 \cdot (e^{\color{blue}{\sqrt[3]{\left(\log_* (1 + \frac{i}{n}) \cdot \log_* (1 + \frac{i}{n})\right) \cdot \log_* (1 + \frac{i}{n})}} \cdot n} - 1)^*}{\frac{i}{n}}\]
if -1.5501848268953156e-256 < n < 2.0212085251283908e-196
1. Initial program 30.2
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied add-exp-log30.2
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def30.2
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)} - 1)^*}}{\frac{i}{n}}\]
5. Simplified18.6
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1)^*}{\frac{i}{n}}\]
6. Using strategy rm
7. Applied associate-*r/18.5
  \[\leadsto \color{blue}{\frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
8. Using strategy rm
9. Applied *-un-lft-identity18.5
  \[\leadsto \frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\color{blue}{1 \cdot \frac{i}{n}}}\]
10. Applied times-frac18.6
  \[\leadsto \color{blue}{\frac{100}{1} \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
11. Simplified18.6
  \[\leadsto \color{blue}{100} \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\]
12. Taylor expanded around 0 12.6
  \[\leadsto \color{blue}{0}\]
if 2.0212085251283908e-196 < n
1. Initial program 57.3
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied add-exp-log57.3
  \[\leadsto 100 \cdot \frac{\color{blue}{e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)}} - 1}{\frac{i}{n}}\]
4. Applied expm1-def57.3
  \[\leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left({\left(1 + \frac{i}{n}\right)}^{n}\right)} - 1)^*}}{\frac{i}{n}}\]
5. Simplified15.9
  \[\leadsto 100 \cdot \frac{(e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1)^*}{\frac{i}{n}}\]
6. Using strategy rm
7. Applied associate-*r/15.9
  \[\leadsto \color{blue}{\frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
8. Using strategy rm
9. Applied *-un-lft-identity15.9
  \[\leadsto \frac{100 \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\color{blue}{1 \cdot \frac{i}{n}}}\]
10. Applied times-frac15.9
  \[\leadsto \color{blue}{\frac{100}{1} \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}}\]
11. Simplified15.9
  \[\leadsto \color{blue}{100} \cdot \frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}}\]
Recombined 4 regimes into one program.
Final simplification17.9
\[\leadsto \begin{array}{l} \mathbf{if}\;n \le -5675.168278704127:\\ \;\;\;\;100 \cdot \frac{(e^{i} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;n \le -1.5501848268953156 \cdot 10^{-256}:\\ \;\;\;\;\frac{100 \cdot (e^{n \cdot \sqrt[3]{\log_* (1 + \frac{i}{n}) \cdot \left(\log_* (1 + \frac{i}{n}) \cdot \log_* (1 + \frac{i}{n})\right)}} - 1)^*}{\frac{i}{n}}\\ \mathbf{elif}\;n \le 2.0212085251283908 \cdot 10^{-196}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{(e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*}{\frac{i}{n}} \cdot 100\\ \end{array}\]

Error

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Target

Derivation

`if n < -5675.168278704127`

`if -5675.168278704127 < n < -1.5501848268953156e-256`

`if -1.5501848268953156e-256 < n < 2.0212085251283908e-196`

`if 2.0212085251283908e-196 < n`

Runtime

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