Average Error: 29.3 → 0.1
Time: 56.9s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;-2 \cdot x \le -2.9497819558082474:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;-2 \cdot x \le 0.01489453933322274:\\ \;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} - \left(\frac{1}{3} \cdot x\right) \cdot \left(x \cdot x\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;-2 \cdot x \le -2.9497819558082474:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;-2 \cdot x \le 0.01489453933322274:\\
\;\;\;\;\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 r1957915 = 2.0;
        double r1957916 = 1.0;
        double r1957917 = -2.0;
        double r1957918 = x;
        double r1957919 = r1957917 * r1957918;
        double r1957920 = exp(r1957919);
        double r1957921 = r1957916 + r1957920;
        double r1957922 = r1957915 / r1957921;
        double r1957923 = r1957922 - r1957916;
        return r1957923;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r1957924 = -2.0;
        double r1957925 = x;
        double r1957926 = r1957924 * r1957925;
        double r1957927 = -2.9497819558082474;
        bool r1957928 = r1957926 <= r1957927;
        double r1957929 = 2.0;
        double r1957930 = 1.0;
        double r1957931 = exp(r1957926);
        double r1957932 = r1957930 + r1957931;
        double r1957933 = r1957929 / r1957932;
        double r1957934 = r1957933 - r1957930;
        double r1957935 = 0.01489453933322274;
        bool r1957936 = r1957926 <= r1957935;
        double r1957937 = 0.13333333333333333;
        double r1957938 = 5.0;
        double r1957939 = pow(r1957925, r1957938);
        double r1957940 = r1957937 * r1957939;
        double r1957941 = 0.3333333333333333;
        double r1957942 = r1957941 * r1957925;
        double r1957943 = r1957925 * r1957925;
        double r1957944 = r1957942 * r1957943;
        double r1957945 = r1957940 - r1957944;
        double r1957946 = r1957945 + r1957925;
        double r1957947 = r1957936 ? r1957946 : r1957934;
        double r1957948 = r1957928 ? r1957934 : r1957947;
        return r1957948;
}

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) < -2.9497819558082474 or 0.01489453933322274 < (* -2 x)

    1. Initial program 0.0

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

    2. Taylor expanded around -inf 0.0

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

    if -2.9497819558082474 < (* -2 x) < 0.01489453933322274

    1. Initial program 59.0

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

    2. Taylor expanded around -inf 59.0

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

    3. Taylor expanded around 0 0.1

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \le -2.9497819558082474:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;-2 \cdot x \le 0.01489453933322274:\\ \;\;\;\;\left(\frac{2}{15} \cdot {x}^{5} - \left(\frac{1}{3} \cdot x\right) \cdot \left(x \cdot x\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019142 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))