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

↓

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

double f(double i) {
        double r7004786 = i;
        double r7004787 = r7004786 * r7004786;
        double r7004788 = r7004787 * r7004787;
        double r7004789 = 2.0;
        double r7004790 = r7004789 * r7004786;
        double r7004791 = r7004790 * r7004790;
        double r7004792 = r7004788 / r7004791;
        double r7004793 = 1.0;
        double r7004794 = r7004791 - r7004793;
        double r7004795 = r7004792 / r7004794;
        return r7004795;
}

↓

double f(double i) {
        double r7004796 = i;
        double r7004797 = 251.56079759840287;
        bool r7004798 = r7004796 <= r7004797;
        double r7004799 = 4.0;
        double r7004800 = r7004796 / r7004799;
        double r7004801 = r7004796 * r7004796;
        double r7004802 = r7004799 * r7004801;
        double r7004803 = 1.0;
        double r7004804 = r7004802 - r7004803;
        double r7004805 = r7004796 / r7004804;
        double r7004806 = r7004800 * r7004805;
        double r7004807 = 0.0625;
        double r7004808 = 0.00390625;
        double r7004809 = r7004808 / r7004801;
        double r7004810 = 0.015625;
        double r7004811 = r7004809 + r7004810;
        double r7004812 = r7004811 / r7004801;
        double r7004813 = r7004807 + r7004812;
        double r7004814 = r7004798 ? r7004806 : r7004813;
        return r7004814;
}

\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{\frac{0.00390625}{i \cdot i} + 0.015625}{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 div-inv31.3
  \[\leadsto \color{blue}{\left(i \cdot i\right) \cdot \frac{1}{\left(4 \cdot \left(i \cdot i\right) - 1.0\right) \cdot 4}}\]
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
  \[\leadsto \color{blue}{\frac{1}{16} + \frac{\frac{0.00390625}{i \cdot i} + 0.015625}{i \cdot i}}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;i \le 251.56079759840287:\\ \;\;\;\;\frac{i}{4} \cdot \frac{i}{4 \cdot \left(i \cdot i\right) - 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{16} + \frac{\frac{0.00390625}{i \cdot i} + 0.015625}{i \cdot i}\\ \end{array}\]

Error

Derivation

`if i < 251.56079759840287`

`if 251.56079759840287 < i`

Reproduce