Average Error: 42.5 → 19.8
Time: 25.9s
Precision: 64
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -0.004925238971644983407283113763241999549791:\\ \;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 5.658601216877151786166504652674880498349 \cdot 10^{-101}:\\ \;\;\;\;\frac{100 \cdot \left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}{i} \cdot n\\ \mathbf{elif}\;i \le 6.016226308891130762023549201754330631598 \cdot 10^{-81}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.375765293115240280599712497820055847687 \cdot 10^{-33}:\\ \;\;\;\;\frac{100 \cdot \left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}{i} \cdot n\\ \mathbf{elif}\;i \le 1.839157578225845005008058914892445589939 \cdot 10^{175}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 6.730961542171691275593369492599343975653 \cdot 10^{212}:\\ \;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.379305565720718542631518091583665992206 \cdot 10^{276}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 7.987224426181112598166338351215203562955 \cdot 10^{300}:\\ \;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \end{array}\]
100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}
↓
\begin{array}{l}
\mathbf{if}\;i \le -0.004925238971644983407283113763241999549791:\\
\;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\

\mathbf{elif}\;i \le 5.658601216877151786166504652674880498349 \cdot 10^{-101}:\\
\;\;\;\;\frac{100 \cdot \left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}{i} \cdot n\\

\mathbf{elif}\;i \le 6.016226308891130762023549201754330631598 \cdot 10^{-81}:\\
\;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\

\mathbf{elif}\;i \le 1.375765293115240280599712497820055847687 \cdot 10^{-33}:\\
\;\;\;\;\frac{100 \cdot \left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}{i} \cdot n\\

\mathbf{elif}\;i \le 1.839157578225845005008058914892445589939 \cdot 10^{175}:\\
\;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\

\mathbf{elif}\;i \le 6.730961542171691275593369492599343975653 \cdot 10^{212}:\\
\;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\

\mathbf{elif}\;i \le 1.379305565720718542631518091583665992206 \cdot 10^{276}:\\
\;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\

\mathbf{elif}\;i \le 7.987224426181112598166338351215203562955 \cdot 10^{300}:\\
\;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\

\mathbf{else}:\\
\;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\

\end{array}
double f(double i, double n) {
        double r128970 = 100.0;
        double r128971 = 1.0;
        double r128972 = i;
        double r128973 = n;
        double r128974 = r128972 / r128973;
        double r128975 = r128971 + r128974;
        double r128976 = pow(r128975, r128973);
        double r128977 = r128976 - r128971;
        double r128978 = r128977 / r128974;
        double r128979 = r128970 * r128978;
        return r128979;
}
↓
double f(double i, double n) {
        double r128980 = i;
        double r128981 = -0.004925238971644983;
        bool r128982 = r128980 <= r128981;
        double r128983 = 100.0;
        double r128984 = n;
        double r128985 = r128980 / r128984;
        double r128986 = pow(r128985, r128984);
        double r128987 = 1.0;
        double r128988 = r128986 - r128987;
        double r128989 = r128983 * r128988;
        double r128990 = r128989 / r128985;
        double r128991 = 5.658601216877152e-101;
        bool r128992 = r128980 <= r128991;
        double r128993 = r128987 * r128980;
        double r128994 = 0.5;
        double r128995 = 2.0;
        double r128996 = pow(r128980, r128995);
        double r128997 = r128994 * r128996;
        double r128998 = log(r128987);
        double r128999 = r128998 * r128984;
        double r129000 = r128997 + r128999;
        double r129001 = r128993 + r129000;
        double r129002 = r128996 * r128998;
        double r129003 = r128994 * r129002;
        double r129004 = r129001 - r129003;
        double r129005 = r128983 * r129004;
        double r129006 = r129005 / r128980;
        double r129007 = r129006 * r128984;
        double r129008 = 6.016226308891131e-81;
        bool r129009 = r128980 <= r129008;
        double r129010 = 0.5;
        double r129011 = log(r128980);
        double r129012 = pow(r129011, r128995);
        double r129013 = pow(r128984, r128995);
        double r129014 = r129012 * r129013;
        double r129015 = log(r128984);
        double r129016 = pow(r129015, r128995);
        double r129017 = r129013 * r129016;
        double r129018 = r129014 + r129017;
        double r129019 = r129010 * r129018;
        double r129020 = 0.16666666666666666;
        double r129021 = 3.0;
        double r129022 = pow(r129011, r129021);
        double r129023 = pow(r128984, r129021);
        double r129024 = r129022 * r129023;
        double r129025 = r129020 * r129024;
        double r129026 = r129011 * r128984;
        double r129027 = r129025 + r129026;
        double r129028 = r129019 + r129027;
        double r129029 = r129023 * r129016;
        double r129030 = r129011 * r129029;
        double r129031 = r129010 * r129030;
        double r129032 = r129028 + r129031;
        double r129033 = r129011 * r129013;
        double r129034 = r129033 + r128984;
        double r129035 = r129015 * r129034;
        double r129036 = r129032 - r129035;
        double r129037 = r129023 * r129015;
        double r129038 = r129012 * r129037;
        double r129039 = r129010 * r129038;
        double r129040 = pow(r129015, r129021);
        double r129041 = r129023 * r129040;
        double r129042 = r129020 * r129041;
        double r129043 = r129039 + r129042;
        double r129044 = r129036 - r129043;
        double r129045 = r128983 * r129044;
        double r129046 = r129045 / r128985;
        double r129047 = 1.3757652931152403e-33;
        bool r129048 = r128980 <= r129047;
        double r129049 = 1.839157578225845e+175;
        bool r129050 = r128980 <= r129049;
        double r129051 = 6.730961542171691e+212;
        bool r129052 = r128980 <= r129051;
        double r129053 = 1.3793055657207185e+276;
        bool r129054 = r128980 <= r129053;
        double r129055 = 7.987224426181113e+300;
        bool r129056 = r128980 <= r129055;
        double r129057 = r129056 ? r128990 : r129046;
        double r129058 = r129054 ? r129046 : r129057;
        double r129059 = r129052 ? r128990 : r129058;
        double r129060 = r129050 ? r129046 : r129059;
        double r129061 = r129048 ? r129007 : r129060;
        double r129062 = r129009 ? r129046 : r129061;
        double r129063 = r128992 ? r129007 : r129062;
        double r129064 = r128982 ? r128990 : r129063;
        return r129064;
}

Error

Bits error versus i

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original42.5
Target42.3
Herbie19.8
\[100 \cdot \frac{e^{n \cdot \begin{array}{l} \mathbf{if}\;1 + \frac{i}{n} = 1:\\ \;\;\;\;\frac{i}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{i}{n} \cdot \log \left(1 + \frac{i}{n}\right)}{\left(\frac{i}{n} + 1\right) - 1}\\ \end{array}} - 1}{\frac{i}{n}}\]

Derivation

  1. Split input into 3 regimes

  2. if i < -0.004925238971644983 or 1.839157578225845e+175 < i < 6.730961542171691e+212 or 1.3793055657207185e+276 < i < 7.987224426181113e+300

    1. Initial program 28.8

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
    2. Using strategy rm

    3. Applied associate-*r/28.8

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

    4. Taylor expanded around inf 59.0

      \[\leadsto \frac{100 \cdot \left(\color{blue}{e^{\left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right) \cdot n}} - 1\right)}{\frac{i}{n}}\]

    5. Simplified20.4

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

    if -0.004925238971644983 < i < 5.658601216877152e-101 or 6.016226308891131e-81 < i < 1.3757652931152403e-33

    1. Initial program 49.9

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
    2. Using strategy rm

    3. Applied associate-*r/49.9

      \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}}\]
    4. Using strategy rm

    5. Applied associate-/r/49.5

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

    6. Taylor expanded around 0 17.4

      \[\leadsto \frac{100 \cdot \color{blue}{\left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}}{i} \cdot n\]

    if 5.658601216877152e-101 < i < 6.016226308891131e-81 or 1.3757652931152403e-33 < i < 1.839157578225845e+175 or 6.730961542171691e+212 < i < 1.3793055657207185e+276 or 7.987224426181113e+300 < i

    1. Initial program 37.6

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
    2. Using strategy rm

    3. Applied associate-*r/37.5

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

    4. Taylor expanded around inf 38.6

      \[\leadsto \frac{100 \cdot \left(\color{blue}{e^{\left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right) \cdot n}} - 1\right)}{\frac{i}{n}}\]

    5. Simplified38.3

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

    6. Taylor expanded around 0 28.4

      \[\leadsto \frac{100 \cdot \color{blue}{\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2}\right) + \left(\frac{1}{2} \cdot \left({n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \left(\log i \cdot n + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right)\right)\right)\right) - \left(n \cdot \log n + \left(\log i \cdot \left({n}^{2} \cdot \log n\right) + \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)\right)\right)}}{\frac{i}{n}}\]

    7. Simplified28.4

      \[\leadsto \frac{100 \cdot \color{blue}{\left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}}{\frac{i}{n}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification19.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -0.004925238971644983407283113763241999549791:\\ \;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 5.658601216877151786166504652674880498349 \cdot 10^{-101}:\\ \;\;\;\;\frac{100 \cdot \left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}{i} \cdot n\\ \mathbf{elif}\;i \le 6.016226308891130762023549201754330631598 \cdot 10^{-81}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.375765293115240280599712497820055847687 \cdot 10^{-33}:\\ \;\;\;\;\frac{100 \cdot \left(\left(1 \cdot i + \left(0.5 \cdot {i}^{2} + \log 1 \cdot n\right)\right) - 0.5 \cdot \left({i}^{2} \cdot \log 1\right)\right)}{i} \cdot n\\ \mathbf{elif}\;i \le 1.839157578225845005008058914892445589939 \cdot 10^{175}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 6.730961542171691275593369492599343975653 \cdot 10^{212}:\\ \;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 1.379305565720718542631518091583665992206 \cdot 10^{276}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 7.987224426181112598166338351215203562955 \cdot 10^{300}:\\ \;\;\;\;\frac{100 \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{100 \cdot \left(\left(\left(\left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot {n}^{2} + {n}^{2} \cdot {\left(\log n\right)}^{2}\right) + \left(\frac{1}{6} \cdot \left({\left(\log i\right)}^{3} \cdot {n}^{3}\right) + \log i \cdot n\right)\right) + \frac{1}{2} \cdot \left(\log i \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{2}\right)\right)\right) - \log n \cdot \left(\log i \cdot {n}^{2} + n\right)\right) - \left(\frac{1}{2} \cdot \left({\left(\log i\right)}^{2} \cdot \left({n}^{3} \cdot \log n\right)\right) + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)}{\frac{i}{n}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019297 
(FPCore (i n)
  :name "Compound Interest"
  :precision binary64

  :herbie-target
  (* 100 (/ (- (exp (* n (if (== (+ 1 (/ i n)) 1) (/ i n) (/ (* (/ i n) (log (+ 1 (/ i n)))) (- (+ (/ i n) 1) 1))))) 1) (/ i n)))

  (* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))))