\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.007072373127510205:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.006564839170329155:\\ \;\;\;\;\mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right) - \left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

\frac{2}{1 + e^{-2 \cdot x}} - 1

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.007072373127510205:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.006564839170329155:\\
\;\;\;\;\mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right) - \left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{3}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\end{array}

double f(double x, double __attribute__((unused)) y) {
        double r1437813 = 2.0;
        double r1437814 = 1.0;
        double r1437815 = -2.0;
        double r1437816 = x;
        double r1437817 = r1437815 * r1437816;
        double r1437818 = exp(r1437817);
        double r1437819 = r1437814 + r1437818;
        double r1437820 = r1437813 / r1437819;
        double r1437821 = r1437820 - r1437814;
        return r1437821;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r1437822 = x;
        double r1437823 = -0.007072373127510205;
        bool r1437824 = r1437822 <= r1437823;
        double r1437825 = 2.0;
        double r1437826 = -2.0;
        double r1437827 = r1437826 * r1437822;
        double r1437828 = exp(r1437827);
        double r1437829 = 1.0;
        double r1437830 = r1437828 + r1437829;
        double r1437831 = r1437825 / r1437830;
        double r1437832 = r1437831 - r1437829;
        double r1437833 = 0.006564839170329155;
        bool r1437834 = r1437822 <= r1437833;
        double r1437835 = 5.0;
        double r1437836 = pow(r1437822, r1437835);
        double r1437837 = 0.13333333333333333;
        double r1437838 = fma(r1437836, r1437837, r1437822);
        double r1437839 = r1437822 * r1437822;
        double r1437840 = 0.3333333333333333;
        double r1437841 = r1437822 * r1437840;
        double r1437842 = r1437839 * r1437841;
        double r1437843 = r1437838 - r1437842;
        double r1437844 = r1437834 ? r1437843 : r1437832;
        double r1437845 = r1437824 ? r1437832 : r1437844;
        return r1437845;
}

Derivation

Split input into 2 regimes
if x < -0.007072373127510205 or 0.006564839170329155 < x
1. Initial program 0.0
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
2. Taylor expanded around -inf 0.0
  \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{-2 \cdot x} + 1} - 1}\]
3. Simplified0.0
  \[\leadsto \color{blue}{\frac{2}{1 + e^{-2 \cdot x}} - 1}\]
if -0.007072373127510205 < x < 0.006564839170329155
1. Initial program 58.9
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
2. Taylor expanded around -inf 58.9
  \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{-2 \cdot x} + 1} - 1}\]
3. Simplified58.9
  \[\leadsto \color{blue}{\frac{2}{1 + e^{-2 \cdot x}} - 1}\]
4. Taylor expanded around 0 0.0
  \[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]
5. Simplified0.0
  \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right) - \left(x \cdot x\right) \cdot \left(\frac{1}{3} \cdot x\right)}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007072373127510205:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.006564839170329155:\\ \;\;\;\;\mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right) - \left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

unused variable y

Error

Derivation

`if x < -0.007072373127510205 or 0.006564839170329155 < x`

`if -0.007072373127510205 < x < 0.006564839170329155`

Reproduce