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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.0076877843038582255:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.004220693910151683:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, \frac{-1}{3}, \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.0076877843038582255:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.004220693910151683:\\
\;\;\;\;\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, \frac{-1}{3}, \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 r886001 = 2.0;
        double r886002 = 1.0;
        double r886003 = -2.0;
        double r886004 = x;
        double r886005 = r886003 * r886004;
        double r886006 = exp(r886005);
        double r886007 = r886002 + r886006;
        double r886008 = r886001 / r886007;
        double r886009 = r886008 - r886002;
        return r886009;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r886010 = x;
        double r886011 = -0.0076877843038582255;
        bool r886012 = r886010 <= r886011;
        double r886013 = 2.0;
        double r886014 = -2.0;
        double r886015 = r886014 * r886010;
        double r886016 = exp(r886015);
        double r886017 = 1.0;
        double r886018 = r886016 + r886017;
        double r886019 = r886013 / r886018;
        double r886020 = r886019 - r886017;
        double r886021 = 0.004220693910151683;
        bool r886022 = r886010 <= r886021;
        double r886023 = r886010 * r886010;
        double r886024 = r886023 * r886010;
        double r886025 = -0.3333333333333333;
        double r886026 = 5.0;
        double r886027 = pow(r886010, r886026);
        double r886028 = 0.13333333333333333;
        double r886029 = fma(r886027, r886028, r886010);
        double r886030 = fma(r886024, r886025, r886029);
        double r886031 = r886022 ? r886030 : r886020;
        double r886032 = r886012 ? r886020 : r886031;
        return r886032;
}

Derivation

Split input into 2 regimes
if x < -0.0076877843038582255 or 0.004220693910151683 < 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
  \[\leadsto \color{blue}{\frac{2}{1 + e^{x \cdot -2}} - 1}\]
if -0.0076877843038582255 < x < 0.004220693910151683
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
  \[\leadsto \color{blue}{\frac{2}{1 + e^{x \cdot -2}} - 1}\]
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
  \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, \frac{-1}{3}, \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.0076877843038582255:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.004220693910151683:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, \frac{-1}{3}, \mathsf{fma}\left({x}^{5}, \frac{2}{15}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

unused variable y

Error

Derivation

`if x < -0.0076877843038582255 or 0.004220693910151683 < x`

`if -0.0076877843038582255 < x < 0.004220693910151683`

Reproduce