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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -0.007173240275337271:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.00717296389704887:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot x\right), \frac{-1}{3}, \left(\mathsf{fma}\left(\left({x}^{5}\right), \frac{2}{15}, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{2}{e^{-2 \cdot x} + 1} - 1} \cdot \sqrt{\frac{2}{e^{-2 \cdot x} + 1} - 1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -0.007173240275337271:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.00717296389704887:\\
\;\;\;\;\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot x\right), \frac{-1}{3}, \left(\mathsf{fma}\left(\left({x}^{5}\right), \frac{2}{15}, x\right)\right)\right)\\

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

\end{array}

double f(double x, double __attribute__((unused)) y) {
        double r2436387 = 2.0;
        double r2436388 = 1.0;
        double r2436389 = -2.0;
        double r2436390 = x;
        double r2436391 = r2436389 * r2436390;
        double r2436392 = exp(r2436391);
        double r2436393 = r2436388 + r2436392;
        double r2436394 = r2436387 / r2436393;
        double r2436395 = r2436394 - r2436388;
        return r2436395;
}

↓

double f(double x, double __attribute__((unused)) y) {
        double r2436396 = x;
        double r2436397 = -0.007173240275337271;
        bool r2436398 = r2436396 <= r2436397;
        double r2436399 = 2.0;
        double r2436400 = -2.0;
        double r2436401 = r2436400 * r2436396;
        double r2436402 = exp(r2436401);
        double r2436403 = 1.0;
        double r2436404 = r2436402 + r2436403;
        double r2436405 = r2436399 / r2436404;
        double r2436406 = r2436405 - r2436403;
        double r2436407 = 0.00717296389704887;
        bool r2436408 = r2436396 <= r2436407;
        double r2436409 = r2436396 * r2436396;
        double r2436410 = r2436409 * r2436396;
        double r2436411 = -0.3333333333333333;
        double r2436412 = 5.0;
        double r2436413 = pow(r2436396, r2436412);
        double r2436414 = 0.13333333333333333;
        double r2436415 = fma(r2436413, r2436414, r2436396);
        double r2436416 = fma(r2436410, r2436411, r2436415);
        double r2436417 = sqrt(r2436406);
        double r2436418 = r2436417 * r2436417;
        double r2436419 = r2436408 ? r2436416 : r2436418;
        double r2436420 = r2436398 ? r2436406 : r2436419;
        return r2436420;
}

Derivation

Split input into 3 regimes
if x < -0.007173240275337271
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 -0.007173240275337271 < x < 0.00717296389704887
1. Initial program 58.9
  \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
2. Taylor expanded around -inf 58.9
  \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{-2 \cdot x} + 1} - 1}\]
3. Simplified58.9
  \[\leadsto \color{blue}{\frac{2}{1 + e^{-2 \cdot x}} - 1}\]
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
  \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot x\right), \frac{-1}{3}, \left(\mathsf{fma}\left(\left({x}^{5}\right), \frac{2}{15}, x\right)\right)\right)}\]
if 0.00717296389704887 < 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
  \[\leadsto \color{blue}{\frac{2}{1 + e^{-2 \cdot x}} - 1}\]
4. Using strategy rm
5. Applied add-sqr-sqrt0.0
  \[\leadsto \color{blue}{\sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1} \cdot \sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1}}\]
Recombined 3 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007173240275337271:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.00717296389704887:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot x\right), \frac{-1}{3}, \left(\mathsf{fma}\left(\left({x}^{5}\right), \frac{2}{15}, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{2}{e^{-2 \cdot x} + 1} - 1} \cdot \sqrt{\frac{2}{e^{-2 \cdot x} + 1} - 1}\\ \end{array}\]

unused variable y

Error

Derivation

`if x < -0.007173240275337271`

`if -0.007173240275337271 < x < 0.00717296389704887`

`if 0.00717296389704887 < x`

Reproduce