\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

↓

\[\begin{array}{l} \mathbf{if}\;i \le 251.56079759840287:\\ \;\;\;\;\frac{i}{4} \cdot \frac{i}{4 \cdot \left(i \cdot i\right) - 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{16} + \frac{0.015625 + \frac{\frac{0.00390625}{i}}{i}}{i \cdot i}\\ \end{array}\]

double f(double i) {
        double r3969445 = i;
        double r3969446 = r3969445 * r3969445;
        double r3969447 = r3969446 * r3969446;
        double r3969448 = 2.0;
        double r3969449 = r3969448 * r3969445;
        double r3969450 = r3969449 * r3969449;
        double r3969451 = r3969447 / r3969450;
        double r3969452 = 1.0;
        double r3969453 = r3969450 - r3969452;
        double r3969454 = r3969451 / r3969453;
        return r3969454;
}

↓

double f(double i) {
        double r3969455 = i;
        double r3969456 = 251.56079759840287;
        bool r3969457 = r3969455 <= r3969456;
        double r3969458 = 4.0;
        double r3969459 = r3969455 / r3969458;
        double r3969460 = r3969455 * r3969455;
        double r3969461 = r3969458 * r3969460;
        double r3969462 = 1.0;
        double r3969463 = r3969461 - r3969462;
        double r3969464 = r3969455 / r3969463;
        double r3969465 = r3969459 * r3969464;
        double r3969466 = 0.0625;
        double r3969467 = 0.015625;
        double r3969468 = 0.00390625;
        double r3969469 = r3969468 / r3969455;
        double r3969470 = r3969469 / r3969455;
        double r3969471 = r3969467 + r3969470;
        double r3969472 = r3969471 / r3969460;
        double r3969473 = r3969466 + r3969472;
        double r3969474 = r3969457 ? r3969465 : r3969473;
        return r3969474;
}

\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}

↓

\begin{array}{l}
\mathbf{if}\;i \le 251.56079759840287:\\
\;\;\;\;\frac{i}{4} \cdot \frac{i}{4 \cdot \left(i \cdot i\right) - 1.0}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{16} + \frac{0.015625 + \frac{\frac{0.00390625}{i}}{i}}{i \cdot i}\\

\end{array}

Derivation

Split input into 2 regimes
if i < 251.56079759840287
1. Initial program 44.9
  \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
2. Simplified0.0
  \[\leadsto \color{blue}{\frac{i \cdot i}{\left(4 \cdot \left(i \cdot i\right) - 1.0\right) \cdot 4}}\]
3. Using strategy rm
4. Applied times-frac0.0
  \[\leadsto \color{blue}{\frac{i}{4 \cdot \left(i \cdot i\right) - 1.0} \cdot \frac{i}{4}}\]
if 251.56079759840287 < i
1. Initial program 46.1
  \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
2. Simplified31.2
  \[\leadsto \color{blue}{\frac{i \cdot i}{\left(4 \cdot \left(i \cdot i\right) - 1.0\right) \cdot 4}}\]
3. Using strategy rm
4. Applied times-frac31.3
  \[\leadsto \color{blue}{\frac{i}{4 \cdot \left(i \cdot i\right) - 1.0} \cdot \frac{i}{4}}\]
5. Taylor expanded around -inf 0.0
  \[\leadsto \color{blue}{0.015625 \cdot \frac{1}{{i}^{2}} + \left(\frac{1}{16} + 0.00390625 \cdot \frac{1}{{i}^{4}}\right)}\]
6. Simplified0
  \[\leadsto \color{blue}{\frac{0.015625 + \frac{\frac{0.00390625}{i}}{i}}{i \cdot i} + \frac{1}{16}}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le 251.56079759840287:\\ \;\;\;\;\frac{i}{4} \cdot \frac{i}{4 \cdot \left(i \cdot i\right) - 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{16} + \frac{0.015625 + \frac{\frac{0.00390625}{i}}{i}}{i \cdot i}\\ \end{array}\]

Error

Derivation

`if i < 251.56079759840287`

`if 251.56079759840287 < i`

Reproduce