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

↓

\[\begin{array}{l} \mathbf{if}\;i \le -1.0226829360061689:\\ \;\;\;\;\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100\\ \mathbf{elif}\;i \le 0.7031677524180419:\\ \;\;\;\;\left(n \cdot \left(i + i \cdot \left(i \cdot \left(i \cdot \frac{1}{6} + \frac{1}{2}\right)\right)\right)\right) \cdot \left(\frac{1}{i} \cdot 100\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

double f(double i, double n) {
        double r50319678 = 100.0;
        double r50319679 = 1.0;
        double r50319680 = i;
        double r50319681 = n;
        double r50319682 = r50319680 / r50319681;
        double r50319683 = r50319679 + r50319682;
        double r50319684 = pow(r50319683, r50319681);
        double r50319685 = r50319684 - r50319679;
        double r50319686 = r50319685 / r50319682;
        double r50319687 = r50319678 * r50319686;
        return r50319687;
}

↓

double f(double i, double n) {
        double r50319688 = i;
        double r50319689 = -1.0226829360061689;
        bool r50319690 = r50319688 <= r50319689;
        double r50319691 = n;
        double r50319692 = r50319691 / r50319688;
        double r50319693 = 1.0;
        double r50319694 = r50319693 / r50319692;
        double r50319695 = pow(r50319694, r50319691);
        double r50319696 = r50319695 - r50319693;
        double r50319697 = r50319692 * r50319696;
        double r50319698 = 100.0;
        double r50319699 = r50319697 * r50319698;
        double r50319700 = 0.7031677524180419;
        bool r50319701 = r50319688 <= r50319700;
        double r50319702 = 0.16666666666666666;
        double r50319703 = r50319688 * r50319702;
        double r50319704 = 0.5;
        double r50319705 = r50319703 + r50319704;
        double r50319706 = r50319688 * r50319705;
        double r50319707 = r50319688 * r50319706;
        double r50319708 = r50319688 + r50319707;
        double r50319709 = r50319691 * r50319708;
        double r50319710 = r50319693 / r50319688;
        double r50319711 = r50319710 * r50319698;
        double r50319712 = r50319709 * r50319711;
        double r50319713 = 0.0;
        double r50319714 = r50319701 ? r50319712 : r50319713;
        double r50319715 = r50319690 ? r50319699 : r50319714;
        return r50319715;
}

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

↓

\begin{array}{l}
\mathbf{if}\;i \le -1.0226829360061689:\\
\;\;\;\;\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100\\

\mathbf{elif}\;i \le 0.7031677524180419:\\
\;\;\;\;\left(n \cdot \left(i + i \cdot \left(i \cdot \left(i \cdot \frac{1}{6} + \frac{1}{2}\right)\right)\right)\right) \cdot \left(\frac{1}{i} \cdot 100\right)\\

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

\end{array}

Original	42.6
Target	41.9
Herbie	18.4

Derivation

Split input into 3 regimes
if i < -1.0226829360061689
1. Initial program 29.5
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
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. Simplified19.6
  \[\leadsto \color{blue}{\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100}\]
if -1.0226829360061689 < i < 0.7031677524180419
1. Initial program 49.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 32.3
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(\frac{1}{2} \cdot {i}^{2} + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{i}{n}}\]
3. Simplified32.3
  \[\leadsto 100 \cdot \frac{\color{blue}{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}}{\frac{i}{n}}\]
4. Using strategy rm
5. Applied div-inv32.4
  \[\leadsto 100 \cdot \frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{\color{blue}{i \cdot \frac{1}{n}}}\]
6. Applied *-un-lft-identity32.4
  \[\leadsto 100 \cdot \frac{\color{blue}{1 \cdot \left(i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)\right)}}{i \cdot \frac{1}{n}}\]
7. Applied times-frac15.2
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{1}{i} \cdot \frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{\frac{1}{n}}\right)}\]
8. Applied associate-*r*15.6
  \[\leadsto \color{blue}{\left(100 \cdot \frac{1}{i}\right) \cdot \frac{i + \left(i \cdot i\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)}{\frac{1}{n}}}\]
9. Simplified15.6
  \[\leadsto \left(100 \cdot \frac{1}{i}\right) \cdot \color{blue}{\left(n \cdot \left(i + i \cdot \left(\left(i \cdot \frac{1}{6} + \frac{1}{2}\right) \cdot i\right)\right)\right)}\]
if 0.7031677524180419 < i
1. Initial program 31.2
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 29.5
  \[\leadsto \color{blue}{0}\]
Recombined 3 regimes into one program.
Final simplification18.4
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le -1.0226829360061689:\\ \;\;\;\;\left(\frac{n}{i} \cdot \left({\left(\frac{1}{\frac{n}{i}}\right)}^{n} - 1\right)\right) \cdot 100\\ \mathbf{elif}\;i \le 0.7031677524180419:\\ \;\;\;\;\left(n \cdot \left(i + i \cdot \left(i \cdot \left(i \cdot \frac{1}{6} + \frac{1}{2}\right)\right)\right)\right) \cdot \left(\frac{1}{i} \cdot 100\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Error

Target

Derivation

`if i < -1.0226829360061689`

`if -1.0226829360061689 < i < 0.7031677524180419`

`if 0.7031677524180419 < i`

Reproduce