Average Error: 29.8 → 0.2
Time: 45.8s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;-2 \cdot x \le -7725.496628004181:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;-2 \cdot x \le 0.0012862461380189684:\\ \;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} - \left(\frac{1}{3} \cdot x\right) \cdot \left(x \cdot x\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;-2 \cdot x \le -7725.496628004181:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;-2 \cdot x \le 0.0012862461380189684:\\
\;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} - \left(\frac{1}{3} \cdot x\right) \cdot \left(x \cdot x\right)\right) + x\\

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

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r2376267 = 2.0;
        double r2376268 = 1.0;
        double r2376269 = -2.0;
        double r2376270 = x;
        double r2376271 = r2376269 * r2376270;
        double r2376272 = exp(r2376271);
        double r2376273 = r2376268 + r2376272;
        double r2376274 = r2376267 / r2376273;
        double r2376275 = r2376274 - r2376268;
        return r2376275;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r2376276 = -2.0;
        double r2376277 = x;
        double r2376278 = r2376276 * r2376277;
        double r2376279 = -7725.496628004181;
        bool r2376280 = r2376278 <= r2376279;
        double r2376281 = 2.0;
        double r2376282 = 1.0;
        double r2376283 = exp(r2376278);
        double r2376284 = r2376282 + r2376283;
        double r2376285 = r2376281 / r2376284;
        double r2376286 = r2376285 - r2376282;
        double r2376287 = 0.0012862461380189684;
        bool r2376288 = r2376278 <= r2376287;
        double r2376289 = 0.13333333333333333;
        double r2376290 = 5.0;
        double r2376291 = pow(r2376277, r2376290);
        double r2376292 = r2376289 * r2376291;
        double r2376293 = 0.3333333333333333;
        double r2376294 = r2376293 * r2376277;
        double r2376295 = r2376277 * r2376277;
        double r2376296 = r2376294 * r2376295;
        double r2376297 = r2376292 - r2376296;
        double r2376298 = r2376297 + r2376277;
        double r2376299 = r2376288 ? r2376298 : r2376286;
        double r2376300 = r2376280 ? r2376286 : r2376299;
        return r2376300;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (* -2 x) < -7725.496628004181 or 0.0012862461380189684 < (* -2 x)

    1. Initial program 0.0

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

    2. Taylor expanded around inf 0.0

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

    if -7725.496628004181 < (* -2 x) < 0.0012862461380189684

    1. Initial program 58.9

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

    2. Taylor expanded around inf 58.9

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

    3. Taylor expanded around 0 0.4

      \[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]

    4. Simplified0.4

      \[\leadsto \color{blue}{\left({x}^{5} \cdot \frac{2}{15} - \left(x \cdot \frac{1}{3}\right) \cdot \left(x \cdot x\right)\right) + x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \le -7725.496628004181:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;-2 \cdot x \le 0.0012862461380189684:\\ \;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} - \left(\frac{1}{3} \cdot x\right) \cdot \left(x \cdot x\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))