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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.007956784398241263:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.0076963482510729354:\\ \;\;\;\;\mathsf{fma}\left({x}^{5}, \frac{2}{15}, \mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.007956784398241263:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.0076963482510729354:\\
\;\;\;\;\mathsf{fma}\left({x}^{5}, \frac{2}{15}, \mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), x\right)\right)\\

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

\end{array}

double f(double x, double __attribute__((unused)) y) {
        double r1873198 = 2.0;
        double r1873199 = 1.0;
        double r1873200 = -2.0;
        double r1873201 = x;
        double r1873202 = r1873200 * r1873201;
        double r1873203 = exp(r1873202);
        double r1873204 = r1873199 + r1873203;
        double r1873205 = r1873198 / r1873204;
        double r1873206 = r1873205 - r1873199;
        return r1873206;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r1873207 = x;
        double r1873208 = -0.007956784398241263;
        bool r1873209 = r1873207 <= r1873208;
        double r1873210 = 2.0;
        double r1873211 = -2.0;
        double r1873212 = r1873211 * r1873207;
        double r1873213 = exp(r1873212);
        double r1873214 = 1.0;
        double r1873215 = r1873213 + r1873214;
        double r1873216 = r1873210 / r1873215;
        double r1873217 = r1873216 - r1873214;
        double r1873218 = 0.0076963482510729354;
        bool r1873219 = r1873207 <= r1873218;
        double r1873220 = 5.0;
        double r1873221 = pow(r1873207, r1873220);
        double r1873222 = 0.13333333333333333;
        double r1873223 = -0.3333333333333333;
        double r1873224 = r1873207 * r1873207;
        double r1873225 = r1873207 * r1873224;
        double r1873226 = fma(r1873223, r1873225, r1873207);
        double r1873227 = fma(r1873221, r1873222, r1873226);
        double r1873228 = r1873219 ? r1873227 : r1873217;
        double r1873229 = r1873209 ? r1873217 : r1873228;
        return r1873229;
}

Derivation

Split input into 2 regimes
if x < -0.007956784398241263 or 0.0076963482510729354 < 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 -0.007956784398241263 < x < 0.0076963482510729354
1. Initial program 58.9
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
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
  \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{5}, \frac{2}{15}, \mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), x\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007956784398241263:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.0076963482510729354:\\ \;\;\;\;\mathsf{fma}\left({x}^{5}, \frac{2}{15}, \mathsf{fma}\left(\frac{-1}{3}, x \cdot \left(x \cdot x\right), x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

unused variable y

Error

Derivation

`if x < -0.007956784398241263 or 0.0076963482510729354 < x`

`if -0.007956784398241263 < x < 0.0076963482510729354`

Reproduce