Average Error: 30.2 → 0.1
Time: 17.0s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;-2 \cdot x \le -4.521691874239059:\\ \;\;\;\;\frac{\frac{2}{\sqrt{e^{-2 \cdot x} + 1}}}{\sqrt{e^{-2 \cdot x} + 1}} - 1\\ \mathbf{elif}\;-2 \cdot x \le 9.96322552535665 \cdot 10^{-05}:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot x\right) \cdot \frac{-1}{3} + \left({x}^{5} \cdot \frac{2}{15} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{\sqrt{e^{-2 \cdot x} + 1}}}{\sqrt{e^{-2 \cdot x} + 1}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;-2 \cdot x \le -4.521691874239059:\\
\;\;\;\;\frac{\frac{2}{\sqrt{e^{-2 \cdot x} + 1}}}{\sqrt{e^{-2 \cdot x} + 1}} - 1\\

\mathbf{elif}\;-2 \cdot x \le 9.96322552535665 \cdot 10^{-05}:\\
\;\;\;\;\left(\left(x \cdot x\right) \cdot x\right) \cdot \frac{-1}{3} + \left({x}^{5} \cdot \frac{2}{15} + x\right)\\

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

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r2261969 = 2.0;
        double r2261970 = 1.0;
        double r2261971 = -2.0;
        double r2261972 = x;
        double r2261973 = r2261971 * r2261972;
        double r2261974 = exp(r2261973);
        double r2261975 = r2261970 + r2261974;
        double r2261976 = r2261969 / r2261975;
        double r2261977 = r2261976 - r2261970;
        return r2261977;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r2261978 = -2.0;
        double r2261979 = x;
        double r2261980 = r2261978 * r2261979;
        double r2261981 = -4.521691874239059;
        bool r2261982 = r2261980 <= r2261981;
        double r2261983 = 2.0;
        double r2261984 = exp(r2261980);
        double r2261985 = 1.0;
        double r2261986 = r2261984 + r2261985;
        double r2261987 = sqrt(r2261986);
        double r2261988 = r2261983 / r2261987;
        double r2261989 = r2261988 / r2261987;
        double r2261990 = r2261989 - r2261985;
        double r2261991 = 9.96322552535665e-05;
        bool r2261992 = r2261980 <= r2261991;
        double r2261993 = r2261979 * r2261979;
        double r2261994 = r2261993 * r2261979;
        double r2261995 = -0.3333333333333333;
        double r2261996 = r2261994 * r2261995;
        double r2261997 = 5.0;
        double r2261998 = pow(r2261979, r2261997);
        double r2261999 = 0.13333333333333333;
        double r2262000 = r2261998 * r2261999;
        double r2262001 = r2262000 + r2261979;
        double r2262002 = r2261996 + r2262001;
        double r2262003 = r2261992 ? r2262002 : r2261990;
        double r2262004 = r2261982 ? r2261990 : r2262003;
        return r2262004;
}

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) < -4.521691874239059 or 9.96322552535665e-05 < (* -2 x)

    1. Initial program 0.0

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt0.0

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

    4. Applied associate-/r*0.0

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

    if -4.521691874239059 < (* -2 x) < 9.96322552535665e-05

    1. Initial program 58.8

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

    2. Taylor expanded around 0 0.1

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

    3. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \le -4.521691874239059:\\ \;\;\;\;\frac{\frac{2}{\sqrt{e^{-2 \cdot x} + 1}}}{\sqrt{e^{-2 \cdot x} + 1}} - 1\\ \mathbf{elif}\;-2 \cdot x \le 9.96322552535665 \cdot 10^{-05}:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot x\right) \cdot \frac{-1}{3} + \left({x}^{5} \cdot \frac{2}{15} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{\sqrt{e^{-2 \cdot x} + 1}}}{\sqrt{e^{-2 \cdot x} + 1}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))