Average Error: 29.0 → 0.0
Time: 3.9s
Precision: binary64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;-2 \cdot x \le -0.034806015454620837:\\ \;\;\;\;\sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1} \cdot \sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1}\\ \mathbf{elif}\;-2 \cdot x \le 2.83489272234317225 \cdot 10^{-4}:\\ \;\;\;\;1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{\sqrt{1 + e^{-2 \cdot x}}}}{\sqrt{1 + e^{-2 \cdot x}}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;-2 \cdot x \le -0.034806015454620837:\\
\;\;\;\;\sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1} \cdot \sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1}\\

\mathbf{elif}\;-2 \cdot x \le 2.83489272234317225 \cdot 10^{-4}:\\
\;\;\;\;1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)\\

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

\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)) <= -0.03480601545462084)) {
		VAR = ((double) (((double) sqrt(((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) - 1.0)))) * ((double) sqrt(((double) (((double) (2.0 / ((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))) - 1.0))))));
	} else {
		double VAR_1;
		if ((((double) (-2.0 * x)) <= 0.0002834892722343172)) {
			VAR_1 = ((double) (((double) (1.0 * x)) - ((double) (((double) (5.551115123125783e-17 * ((double) pow(x, 4.0)))) + ((double) (0.33333333333333337 * ((double) pow(x, 3.0))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (2.0 / ((double) sqrt(((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))))) / ((double) sqrt(((double) (1.0 + ((double) exp(((double) (-2.0 * x)))))))))) - 1.0));
		}
		VAR = VAR_1;
	}
	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 3 regimes

  2. if (* -2.0 x) < -0.034806015454620837

    1. Initial program 0.0

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

    3. Applied add-sqr-sqrt0.0

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

    if -0.034806015454620837 < (* -2.0 x) < 2.83489272234317225e-4

    1. Initial program 59.2

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

    2. Taylor expanded around 0 0.0

      \[\leadsto \color{blue}{1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)}\]

    if 2.83489272234317225e-4 < (* -2.0 x)

    1. Initial program 0.1

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

    3. Applied add-sqr-sqrt0.1

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

    4. Applied associate-/r*0.1

      \[\leadsto \color{blue}{\frac{\frac{2}{\sqrt{1 + e^{-2 \cdot x}}}}{\sqrt{1 + e^{-2 \cdot x}}}} - 1\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \le -0.034806015454620837:\\ \;\;\;\;\sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1} \cdot \sqrt{\frac{2}{1 + e^{-2 \cdot x}} - 1}\\ \mathbf{elif}\;-2 \cdot x \le 2.83489272234317225 \cdot 10^{-4}:\\ \;\;\;\;1 \cdot x - \left(5.55112 \cdot 10^{-17} \cdot {x}^{4} + 0.33333333333333337 \cdot {x}^{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{\sqrt{1 + e^{-2 \cdot x}}}}{\sqrt{1 + e^{-2 \cdot x}}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))