Average Error: 29.0 → 0.0
Time: 30.2s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.007463572132942926:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.00654275487662059:\\ \;\;\;\;x + \left(\frac{2}{15} \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot x\right) - x \cdot \left(\left(x \cdot x\right) \cdot \frac{1}{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.007463572132942926:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;x \le 0.00654275487662059:\\
\;\;\;\;x + \left(\frac{2}{15} \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot x\right) - x \cdot \left(\left(x \cdot x\right) \cdot \frac{1}{3}\right)\right)\\

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

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r2020132 = 2.0;
        double r2020133 = 1.0;
        double r2020134 = -2.0;
        double r2020135 = x;
        double r2020136 = r2020134 * r2020135;
        double r2020137 = exp(r2020136);
        double r2020138 = r2020133 + r2020137;
        double r2020139 = r2020132 / r2020138;
        double r2020140 = r2020139 - r2020133;
        return r2020140;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r2020141 = x;
        double r2020142 = -0.007463572132942926;
        bool r2020143 = r2020141 <= r2020142;
        double r2020144 = 2.0;
        double r2020145 = 1.0;
        double r2020146 = -2.0;
        double r2020147 = r2020146 * r2020141;
        double r2020148 = exp(r2020147);
        double r2020149 = r2020145 + r2020148;
        double r2020150 = r2020144 / r2020149;
        double r2020151 = r2020150 - r2020145;
        double r2020152 = 0.00654275487662059;
        bool r2020153 = r2020141 <= r2020152;
        double r2020154 = 0.13333333333333333;
        double r2020155 = r2020141 * r2020141;
        double r2020156 = r2020155 * r2020155;
        double r2020157 = r2020156 * r2020141;
        double r2020158 = r2020154 * r2020157;
        double r2020159 = 0.3333333333333333;
        double r2020160 = r2020155 * r2020159;
        double r2020161 = r2020141 * r2020160;
        double r2020162 = r2020158 - r2020161;
        double r2020163 = r2020141 + r2020162;
        double r2020164 = r2020153 ? r2020163 : r2020151;
        double r2020165 = r2020143 ? r2020151 : r2020164;
        return r2020165;
}

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 < -0.007463572132942926 or 0.00654275487662059 < 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 -0.007463572132942926 < x < 0.00654275487662059

    1. Initial program 59.0

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

    2. Taylor expanded around -inf 59.0

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

    3. Taylor expanded around 0 0.0

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

    4. Simplified0.0

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

    5. Taylor expanded around -inf 0.0

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

    6. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007463572132942926:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.00654275487662059:\\ \;\;\;\;x + \left(\frac{2}{15} \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot x\right) - x \cdot \left(\left(x \cdot x\right) \cdot \frac{1}{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))