Average Error: 29.2 → 0.0
Time: 12.0s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.007634363267689736:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007348611436970888:\\ \;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} + x\right) + \left(x \cdot \left(x \cdot x\right)\right) \cdot \frac{-1}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.007634363267689736:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.007348611436970888:\\
\;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} + x\right) + \left(x \cdot \left(x \cdot x\right)\right) \cdot \frac{-1}{3}\\

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

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r586506 = 2.0;
        double r586507 = 1.0;
        double r586508 = -2.0;
        double r586509 = x;
        double r586510 = r586508 * r586509;
        double r586511 = exp(r586510);
        double r586512 = r586507 + r586511;
        double r586513 = r586506 / r586512;
        double r586514 = r586513 - r586507;
        return r586514;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r586515 = x;
        double r586516 = -0.007634363267689736;
        bool r586517 = r586515 <= r586516;
        double r586518 = 2.0;
        double r586519 = -2.0;
        double r586520 = r586519 * r586515;
        double r586521 = exp(r586520);
        double r586522 = 1.0;
        double r586523 = r586521 + r586522;
        double r586524 = r586518 / r586523;
        double r586525 = r586524 - r586522;
        double r586526 = 0.007348611436970888;
        bool r586527 = r586515 <= r586526;
        double r586528 = 0.13333333333333333;
        double r586529 = 5.0;
        double r586530 = pow(r586515, r586529);
        double r586531 = r586528 * r586530;
        double r586532 = r586531 + r586515;
        double r586533 = r586515 * r586515;
        double r586534 = r586515 * r586533;
        double r586535 = -0.3333333333333333;
        double r586536 = r586534 * r586535;
        double r586537 = r586532 + r586536;
        double r586538 = r586527 ? r586537 : r586525;
        double r586539 = r586517 ? r586525 : r586538;
        return r586539;
}

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 < -0.007634363267689736 or 0.007348611436970888 < 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 -0.007634363267689736 < x < 0.007348611436970888

    1. Initial program 59.0

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

    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

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007634363267689736:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007348611436970888:\\ \;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} + x\right) + \left(x \cdot \left(x \cdot x\right)\right) \cdot \frac{-1}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019155 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))