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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.008471190016557226:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007486431308016665:\\ \;\;\;\;\mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.008471190016557226:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.007486431308016665:\\
\;\;\;\;\mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)\\

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

\end{array}

double f(double x, double __attribute__((unused)) y) {
        double r1285845 = 2.0;
        double r1285846 = 1.0;
        double r1285847 = -2.0;
        double r1285848 = x;
        double r1285849 = r1285847 * r1285848;
        double r1285850 = exp(r1285849);
        double r1285851 = r1285846 + r1285850;
        double r1285852 = r1285845 / r1285851;
        double r1285853 = r1285852 - r1285846;
        return r1285853;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r1285854 = x;
        double r1285855 = -0.008471190016557226;
        bool r1285856 = r1285854 <= r1285855;
        double r1285857 = 2.0;
        double r1285858 = -2.0;
        double r1285859 = r1285858 * r1285854;
        double r1285860 = exp(r1285859);
        double r1285861 = 1.0;
        double r1285862 = r1285860 + r1285861;
        double r1285863 = r1285857 / r1285862;
        double r1285864 = r1285863 - r1285861;
        double r1285865 = 0.007486431308016665;
        bool r1285866 = r1285854 <= r1285865;
        double r1285867 = -0.3333333333333333;
        double r1285868 = r1285854 * r1285854;
        double r1285869 = r1285854 * r1285868;
        double r1285870 = 5.0;
        double r1285871 = pow(r1285854, r1285870);
        double r1285872 = 0.13333333333333333;
        double r1285873 = fma(r1285871, r1285872, r1285854);
        double r1285874 = fma(r1285867, r1285869, r1285873);
        double r1285875 = r1285866 ? r1285874 : r1285864;
        double r1285876 = r1285856 ? r1285864 : r1285875;
        return r1285876;
}

Derivation

Split input into 2 regimes
if x < -0.008471190016557226 or 0.007486431308016665 < 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 -0.008471190016557226 < x < 0.007486431308016665
1. Initial program 59.0
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
2. Taylor expanded around inf 59.0
  \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{-2 \cdot x} + 1} - 1}\]
3. Simplified59.0
  \[\leadsto \color{blue}{\frac{2}{1 + e^{-2 \cdot x}} - 1}\]
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
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.008471190016557226:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007486431308016665:\\ \;\;\;\;\mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

unused variable y

Error

Derivation

`if x < -0.008471190016557226 or 0.007486431308016665 < x`

`if -0.008471190016557226 < x < 0.007486431308016665`

Reproduce