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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -30308.320454546014:\\ \;\;\;\;\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100\\ \mathbf{elif}\;i \le 1.5640068539209153:\\ \;\;\;\;n \cdot \left(i \cdot \left(i \cdot \frac{50}{3} + 50\right) + 100\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n} - 1}\right)}{\frac{i}{n}}\\ \end{array}\]

double f(double i, double n) {
        double r40090984 = 100.0;
        double r40090985 = 1.0;
        double r40090986 = i;
        double r40090987 = n;
        double r40090988 = r40090986 / r40090987;
        double r40090989 = r40090985 + r40090988;
        double r40090990 = pow(r40090989, r40090987);
        double r40090991 = r40090990 - r40090985;
        double r40090992 = r40090991 / r40090988;
        double r40090993 = r40090984 * r40090992;
        return r40090993;
}

↓

double f(double i, double n) {
        double r40090994 = i;
        double r40090995 = -30308.320454546014;
        bool r40090996 = r40090994 <= r40090995;
        double r40090997 = n;
        double r40090998 = r40090997 / r40090994;
        double r40090999 = 1.0;
        double r40091000 = r40090999 / r40090998;
        double r40091001 = pow(r40091000, r40090997);
        double r40091002 = r40091001 - r40090999;
        double r40091003 = r40090998 * r40091002;
        double r40091004 = 100.0;
        double r40091005 = r40091003 * r40091004;
        double r40091006 = 1.5640068539209153;
        bool r40091007 = r40090994 <= r40091006;
        double r40091008 = 16.666666666666668;
        double r40091009 = r40090994 * r40091008;
        double r40091010 = 50.0;
        double r40091011 = r40091009 + r40091010;
        double r40091012 = r40090994 * r40091011;
        double r40091013 = r40091012 + r40091004;
        double r40091014 = r40090997 * r40091013;
        double r40091015 = r40090994 / r40090997;
        double r40091016 = r40090999 + r40091015;
        double r40091017 = pow(r40091016, r40090997);
        double r40091018 = r40091017 - r40090999;
        double r40091019 = exp(r40091018);
        double r40091020 = log(r40091019);
        double r40091021 = r40091020 / r40091015;
        double r40091022 = r40091004 * r40091021;
        double r40091023 = r40091007 ? r40091014 : r40091022;
        double r40091024 = r40090996 ? r40091005 : r40091023;
        return r40091024;
}

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

↓

\begin{array}{l}
\mathbf{if}\;i \le -30308.320454546014:\\
\;\;\;\;\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100\\

\mathbf{elif}\;i \le 1.5640068539209153:\\
\;\;\;\;n \cdot \left(i \cdot \left(i \cdot \frac{50}{3} + 50\right) + 100\right)\\

\mathbf{else}:\\
\;\;\;\;100 \cdot \frac{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n} - 1}\right)}{\frac{i}{n}}\\

\end{array}

Original	42.6
Target	42.2
Herbie	19.3

Derivation

Split input into 3 regimes
if i < -30308.320454546014
1. Initial program 27.7
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
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. Simplified19.1
  \[\leadsto \color{blue}{\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100}\]
if -30308.320454546014 < i < 1.5640068539209153
1. Initial program 50.0
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 33.2
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(\frac{1}{2} \cdot {i}^{2} + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{i}{n}}\]
3. Simplified33.2
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{\frac{i}{n}}\]
4. Taylor expanded around 0 17.2
  \[\leadsto \color{blue}{\frac{50}{3} \cdot \left({i}^{2} \cdot n\right) + \left(100 \cdot n + 50 \cdot \left(i \cdot n\right)\right)}\]
5. Simplified17.2
  \[\leadsto \color{blue}{n \cdot \left(100 + i \cdot \left(\frac{50}{3} \cdot i + 50\right)\right)}\]
if 1.5640068539209153 < i
1. Initial program 30.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied add-log-exp30.8
  \[\leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - \color{blue}{\log \left(e^{1}\right)}}{\frac{i}{n}}\]
4. Applied add-log-exp31.0
  \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n}}\right)} - \log \left(e^{1}\right)}{\frac{i}{n}}\]
5. Applied diff-log31.0
  \[\leadsto 100 \cdot \frac{\color{blue}{\log \left(\frac{e^{{\left(1 + \frac{i}{n}\right)}^{n}}}{e^{1}}\right)}}{\frac{i}{n}}\]
6. Simplified31.0
  \[\leadsto 100 \cdot \frac{\log \color{blue}{\left(e^{{\left(\frac{i}{n} + 1\right)}^{n} - 1}\right)}}{\frac{i}{n}}\]
Recombined 3 regimes into one program.
Final simplification19.3
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -30308.320454546014:\\ \;\;\;\;\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100\\ \mathbf{elif}\;i \le 1.5640068539209153:\\ \;\;\;\;n \cdot \left(i \cdot \left(i \cdot \frac{50}{3} + 50\right) + 100\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n} - 1}\right)}{\frac{i}{n}}\\ \end{array}\]

Error

Target

Derivation

`if i < -30308.320454546014`

`if -30308.320454546014 < i < 1.5640068539209153`

`if 1.5640068539209153 < i`

Reproduce