Average Error: 29.8 → 0.4
Time: 4.2s
Precision: binary64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;-2 \cdot x \le -1241651.01825957955 \lor \neg \left(-2 \cdot x \le 7.6631203134992746 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{\left(\sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1} \cdot \sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1}\right) \cdot \sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1}}{\frac{2}{1 + e^{-2 \cdot x}} + 1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;-2 \cdot x \le -1241651.01825957955 \lor \neg \left(-2 \cdot x \le 7.6631203134992746 \cdot 10^{-5}\right):\\
\;\;\;\;\frac{\left(\sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1} \cdot \sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1}\right) \cdot \sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1}}{\frac{2}{1 + e^{-2 \cdot x}} + 1}\\

\mathbf{else}:\\
\;\;\;\;1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)\\

\end{array}
double code(double x, double y) {
	return ((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) - 1.0));
}
↓
double code(double x, double y) {
	double VAR;
	if (((((double) (-2.0 * x)) <= -1241651.0182595795) || !(((double) (-2.0 * x)) <= 7.663120313499275e-05))) {
		VAR = ((double) (((double) (((double) (((double) cbrt(((double) (((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) * ((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))))) - ((double) (1.0 * 1.0)))))) * ((double) cbrt(((double) (((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) * ((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))))) - ((double) (1.0 * 1.0)))))))) * ((double) cbrt(((double) (((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) * ((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))))) - ((double) (1.0 * 1.0)))))))) / ((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) + 1.0))));
	} else {
		VAR = ((double) (((double) (1.0 * x)) - ((double) (((double) (5.551115123125783e-17 * ((double) pow(x, 4.0)))) + ((double) (0.33333333333333337 * ((double) pow(x, 3.0))))))));
	}
	return VAR;
}

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 (* -2.0 x) < -1241651.01825957955 or 7.6631203134992746e-5 < (* -2.0 x)

    1. Initial program 0.1

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

    3. Applied flip--0.1

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

    5. Applied add-cube-cbrt0.1

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

    if -1241651.01825957955 < (* -2.0 x) < 7.6631203134992746e-5

    1. Initial program 58.5

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

    2. Taylor expanded around 0 0.8

      \[\leadsto \color{blue}{1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \le -1241651.01825957955 \lor \neg \left(-2 \cdot x \le 7.6631203134992746 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{\left(\sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1} \cdot \sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1}\right) \cdot \sqrt[3]{\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} - 1 \cdot 1}}{\frac{2}{1 + e^{-2 \cdot x}} + 1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))