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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -8.017010211892022 \cdot 10^{-13}:\\ \;\;\;\;\frac{(100 \cdot \left(e^{\log_* (1 + \frac{i}{n}) \cdot n}\right) + -100)_*}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 3.850047993601629:\\ \;\;\;\;\frac{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_*}{i} \cdot \left(n \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

double f(double i, double n) {
        double r34722033 = 100.0;
        double r34722034 = 1.0;
        double r34722035 = i;
        double r34722036 = n;
        double r34722037 = r34722035 / r34722036;
        double r34722038 = r34722034 + r34722037;
        double r34722039 = pow(r34722038, r34722036);
        double r34722040 = r34722039 - r34722034;
        double r34722041 = r34722040 / r34722037;
        double r34722042 = r34722033 * r34722041;
        return r34722042;
}

↓

double f(double i, double n) {
        double r34722043 = i;
        double r34722044 = -8.017010211892022e-13;
        bool r34722045 = r34722043 <= r34722044;
        double r34722046 = 100.0;
        double r34722047 = n;
        double r34722048 = r34722043 / r34722047;
        double r34722049 = log1p(r34722048);
        double r34722050 = r34722049 * r34722047;
        double r34722051 = exp(r34722050);
        double r34722052 = -100.0;
        double r34722053 = fma(r34722046, r34722051, r34722052);
        double r34722054 = r34722053 / r34722048;
        double r34722055 = 3.850047993601629;
        bool r34722056 = r34722043 <= r34722055;
        double r34722057 = 16.666666666666668;
        double r34722058 = 50.0;
        double r34722059 = fma(r34722043, r34722057, r34722058);
        double r34722060 = fma(r34722043, r34722059, r34722046);
        double r34722061 = r34722060 / r34722043;
        double r34722062 = r34722047 * r34722043;
        double r34722063 = r34722061 * r34722062;
        double r34722064 = 0.0;
        double r34722065 = r34722056 ? r34722063 : r34722064;
        double r34722066 = r34722045 ? r34722054 : r34722065;
        return r34722066;
}

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

↓

\begin{array}{l}
\mathbf{if}\;i \le -8.017010211892022 \cdot 10^{-13}:\\
\;\;\;\;\frac{(100 \cdot \left(e^{\log_* (1 + \frac{i}{n}) \cdot n}\right) + -100)_*}{\frac{i}{n}}\\

\mathbf{elif}\;i \le 3.850047993601629:\\
\;\;\;\;\frac{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_*}{i} \cdot \left(n \cdot i\right)\\

\mathbf{else}:\\
\;\;\;\;0\\

\end{array}

Original	42.6
Target	41.9
Herbie	15.3

Derivation

Split input into 3 regimes
if i < -8.017010211892022e-13
1. Initial program 30.4
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Simplified30.4
  \[\leadsto \color{blue}{\frac{(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n}\right) + -100)_*}{\frac{i}{n}}}\]
3. Using strategy rm
4. Applied add-exp-log30.4
  \[\leadsto \frac{(100 \cdot \left({\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n}\right) + -100)_*}{\frac{i}{n}}\]
5. Applied pow-exp30.4
  \[\leadsto \frac{(100 \cdot \color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right) \cdot n}\right)} + -100)_*}{\frac{i}{n}}\]
6. Simplified7.3
  \[\leadsto \frac{(100 \cdot \left(e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}}\right) + -100)_*}{\frac{i}{n}}\]
if -8.017010211892022e-13 < i < 3.850047993601629
1. Initial program 49.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Simplified49.8
  \[\leadsto \color{blue}{\frac{(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n}\right) + -100)_*}{\frac{i}{n}}}\]
3. Taylor expanded around 0 32.5
  \[\leadsto \frac{\color{blue}{100 \cdot i + \left(50 \cdot {i}^{2} + \frac{50}{3} \cdot {i}^{3}\right)}}{\frac{i}{n}}\]
4. Simplified32.5
  \[\leadsto \frac{\color{blue}{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_* \cdot i}}{\frac{i}{n}}\]
5. Using strategy rm
6. Applied div-inv32.5
  \[\leadsto \frac{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_* \cdot i}{\color{blue}{i \cdot \frac{1}{n}}}\]
7. Applied times-frac15.4
  \[\leadsto \color{blue}{\frac{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_*}{i} \cdot \frac{i}{\frac{1}{n}}}\]
8. Simplified15.3
  \[\leadsto \frac{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_*}{i} \cdot \color{blue}{\left(i \cdot n\right)}\]
if 3.850047993601629 < i
1. Initial program 31.1
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Simplified31.1
  \[\leadsto \color{blue}{\frac{(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n}\right) + -100)_*}{\frac{i}{n}}}\]
3. Taylor expanded around 0 29.4
  \[\leadsto \color{blue}{0}\]
Recombined 3 regimes into one program.
Final simplification15.3
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -8.017010211892022 \cdot 10^{-13}:\\ \;\;\;\;\frac{(100 \cdot \left(e^{\log_* (1 + \frac{i}{n}) \cdot n}\right) + -100)_*}{\frac{i}{n}}\\ \mathbf{elif}\;i \le 3.850047993601629:\\ \;\;\;\;\frac{(i \cdot \left((i \cdot \frac{50}{3} + 50)_*\right) + 100)_*}{i} \cdot \left(n \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Error

Target

Derivation

`if i < -8.017010211892022e-13`

`if -8.017010211892022e-13 < i < 3.850047993601629`

`if 3.850047993601629 < i`

Reproduce