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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.006917970556878751:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007657697468686109:\\ \;\;\;\;\mathsf{fma}\left(\left(\frac{-1}{3} \cdot x\right), \left(x \cdot x\right), \left(\mathsf{fma}\left(\frac{2}{15}, \left({x}^{5}\right), x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.006917970556878751:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.007657697468686109:\\
\;\;\;\;\mathsf{fma}\left(\left(\frac{-1}{3} \cdot x\right), \left(x \cdot x\right), \left(\mathsf{fma}\left(\frac{2}{15}, \left({x}^{5}\right), x\right)\right)\right)\\

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

\end{array}

double f(double x, double __attribute__((unused)) y) {
        double r11406811 = 2.0;
        double r11406812 = 1.0;
        double r11406813 = -2.0;
        double r11406814 = x;
        double r11406815 = r11406813 * r11406814;
        double r11406816 = exp(r11406815);
        double r11406817 = r11406812 + r11406816;
        double r11406818 = r11406811 / r11406817;
        double r11406819 = r11406818 - r11406812;
        return r11406819;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r11406820 = x;
        double r11406821 = -0.006917970556878751;
        bool r11406822 = r11406820 <= r11406821;
        double r11406823 = 2.0;
        double r11406824 = -2.0;
        double r11406825 = r11406824 * r11406820;
        double r11406826 = exp(r11406825);
        double r11406827 = 1.0;
        double r11406828 = r11406826 + r11406827;
        double r11406829 = r11406823 / r11406828;
        double r11406830 = r11406829 - r11406827;
        double r11406831 = 0.007657697468686109;
        bool r11406832 = r11406820 <= r11406831;
        double r11406833 = -0.3333333333333333;
        double r11406834 = r11406833 * r11406820;
        double r11406835 = r11406820 * r11406820;
        double r11406836 = 0.13333333333333333;
        double r11406837 = 5.0;
        double r11406838 = pow(r11406820, r11406837);
        double r11406839 = fma(r11406836, r11406838, r11406820);
        double r11406840 = fma(r11406834, r11406835, r11406839);
        double r11406841 = r11406832 ? r11406840 : r11406830;
        double r11406842 = r11406822 ? r11406830 : r11406841;
        return r11406842;
}

Derivation

Split input into 2 regimes
if x < -0.006917970556878751 or 0.007657697468686109 < 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 -0.006917970556878751 < x < 0.007657697468686109
1. Initial program 59.0
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
2. Taylor expanded around 0 0.0
  \[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]
3. Simplified0.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot \frac{-1}{3}\right), \left(x \cdot x\right), \left(\mathsf{fma}\left(\frac{2}{15}, \left({x}^{5}\right), x\right)\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.006917970556878751:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007657697468686109:\\ \;\;\;\;\mathsf{fma}\left(\left(\frac{-1}{3} \cdot x\right), \left(x \cdot x\right), \left(\mathsf{fma}\left(\frac{2}{15}, \left({x}^{5}\right), x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

unused variable y

Error

Derivation

`if x < -0.006917970556878751 or 0.007657697468686109 < x`

`if -0.006917970556878751 < x < 0.007657697468686109`

Reproduce