Average Error: 29.1 → 0.0
Time: 11.3s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.006778948484773374:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.008141227619400067:\\ \;\;\;\;x + \left({x}^{5} \cdot \frac{2}{15} + \frac{-1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.006778948484773374:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.008141227619400067:\\
\;\;\;\;x + \left({x}^{5} \cdot \frac{2}{15} + \frac{-1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\\

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

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r2688717 = 2.0;
        double r2688718 = 1.0;
        double r2688719 = -2.0;
        double r2688720 = x;
        double r2688721 = r2688719 * r2688720;
        double r2688722 = exp(r2688721);
        double r2688723 = r2688718 + r2688722;
        double r2688724 = r2688717 / r2688723;
        double r2688725 = r2688724 - r2688718;
        return r2688725;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r2688726 = x;
        double r2688727 = -0.006778948484773374;
        bool r2688728 = r2688726 <= r2688727;
        double r2688729 = 2.0;
        double r2688730 = -2.0;
        double r2688731 = r2688730 * r2688726;
        double r2688732 = exp(r2688731);
        double r2688733 = 1.0;
        double r2688734 = r2688732 + r2688733;
        double r2688735 = r2688729 / r2688734;
        double r2688736 = r2688735 - r2688733;
        double r2688737 = 0.008141227619400067;
        bool r2688738 = r2688726 <= r2688737;
        double r2688739 = 5.0;
        double r2688740 = pow(r2688726, r2688739);
        double r2688741 = 0.13333333333333333;
        double r2688742 = r2688740 * r2688741;
        double r2688743 = -0.3333333333333333;
        double r2688744 = r2688726 * r2688726;
        double r2688745 = r2688726 * r2688744;
        double r2688746 = r2688743 * r2688745;
        double r2688747 = r2688742 + r2688746;
        double r2688748 = r2688726 + r2688747;
        double r2688749 = r2688738 ? r2688748 : r2688736;
        double r2688750 = r2688728 ? r2688736 : r2688749;
        return r2688750;
}

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 x < -0.006778948484773374 or 0.008141227619400067 < 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 -0.006778948484773374 < x < 0.008141227619400067

    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

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.006778948484773374:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.008141227619400067:\\ \;\;\;\;x + \left({x}^{5} \cdot \frac{2}{15} + \frac{-1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))