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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.006299562239894887:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.00702088019611751:\\ \;\;\;\;x + \left(\frac{-1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right) + \frac{2}{15} \cdot {x}^{5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.006299562239894887:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.00702088019611751:\\
\;\;\;\;x + \left(\frac{-1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right) + \frac{2}{15} \cdot {x}^{5}\right)\\

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

\end{array}

double f(double x, double __attribute__((unused)) y) {
        double r1251665 = 2.0;
        double r1251666 = 1.0;
        double r1251667 = -2.0;
        double r1251668 = x;
        double r1251669 = r1251667 * r1251668;
        double r1251670 = exp(r1251669);
        double r1251671 = r1251666 + r1251670;
        double r1251672 = r1251665 / r1251671;
        double r1251673 = r1251672 - r1251666;
        return r1251673;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r1251674 = x;
        double r1251675 = -0.006299562239894887;
        bool r1251676 = r1251674 <= r1251675;
        double r1251677 = 2.0;
        double r1251678 = -2.0;
        double r1251679 = r1251678 * r1251674;
        double r1251680 = exp(r1251679);
        double r1251681 = 1.0;
        double r1251682 = r1251680 + r1251681;
        double r1251683 = r1251677 / r1251682;
        double r1251684 = r1251683 - r1251681;
        double r1251685 = 0.00702088019611751;
        bool r1251686 = r1251674 <= r1251685;
        double r1251687 = -0.3333333333333333;
        double r1251688 = r1251674 * r1251674;
        double r1251689 = r1251674 * r1251688;
        double r1251690 = r1251687 * r1251689;
        double r1251691 = 0.13333333333333333;
        double r1251692 = 5.0;
        double r1251693 = pow(r1251674, r1251692);
        double r1251694 = r1251691 * r1251693;
        double r1251695 = r1251690 + r1251694;
        double r1251696 = r1251674 + r1251695;
        double r1251697 = r1251686 ? r1251696 : r1251684;
        double r1251698 = r1251676 ? r1251684 : r1251697;
        return r1251698;
}

Derivation

Split input into 2 regimes
if x < -0.006299562239894887 or 0.00702088019611751 < 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 -0.006299562239894887 < x < 0.00702088019611751
1. Initial program 59.1
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
2. Taylor expanded around -inf 59.1
  \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{-2 \cdot x} + 1} - 1}\]
3. Simplified59.1
  \[\leadsto \color{blue}{\frac{2}{1 + e^{x \cdot -2}} - 1}\]
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
  \[\leadsto \color{blue}{x + \left({x}^{5} \cdot \frac{2}{15} + \frac{-1}{3} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.006299562239894887:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.00702088019611751:\\ \;\;\;\;x + \left(\frac{-1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right) + \frac{2}{15} \cdot {x}^{5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

unused variable y

Error

Try it out

Derivation

`if x < -0.006299562239894887 or 0.00702088019611751 < x`

`if -0.006299562239894887 < x < 0.00702088019611751`

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