Average Error: 29.0 → 0.1
Time: 3.6s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;-2 \cdot x \le -0.00295305623757643977:\\ \;\;\;\;\frac{\left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) \cdot \left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) - \left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right)}{\left(\frac{2}{1 + e^{-2 \cdot x}} + 1\right) \cdot \left(\left(\frac{1}{{\left(e^{-2 \cdot x} + 1\right)}^{2}} \cdot \left(\frac{2}{1 - e^{-2 \cdot x}} \cdot \frac{2}{1 - e^{-2 \cdot x}}\right)\right) \cdot \left(\left(1 - e^{-2 \cdot x}\right) \cdot \left(1 - e^{-2 \cdot x}\right)\right) + 1 \cdot 1\right)}\\ \mathbf{elif}\;-2 \cdot x \le 2.87307640774032159 \cdot 10^{-8}:\\ \;\;\;\;1 \cdot x - \left(4.996 \cdot 10^{-16} \cdot {x}^{4} + 0.33333333333333348 \cdot {x}^{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;-2 \cdot x \le -0.00295305623757643977:\\
\;\;\;\;\frac{\left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) \cdot \left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) - \left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right)}{\left(\frac{2}{1 + e^{-2 \cdot x}} + 1\right) \cdot \left(\left(\frac{1}{{\left(e^{-2 \cdot x} + 1\right)}^{2}} \cdot \left(\frac{2}{1 - e^{-2 \cdot x}} \cdot \frac{2}{1 - e^{-2 \cdot x}}\right)\right) \cdot \left(\left(1 - e^{-2 \cdot x}\right) \cdot \left(1 - e^{-2 \cdot x}\right)\right) + 1 \cdot 1\right)}\\

\mathbf{elif}\;-2 \cdot x \le 2.87307640774032159 \cdot 10^{-8}:\\
\;\;\;\;1 \cdot x - \left(4.996 \cdot 10^{-16} \cdot {x}^{4} + 0.33333333333333348 \cdot {x}^{3}\right)\\

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

\end{array}
double code(double x, double y) {
	return ((2.0 / (1.0 + exp((-2.0 * x)))) - 1.0);
}
↓
double code(double x, double y) {
	double VAR;
	if (((-2.0 * x) <= -0.0029530562375764398)) {
		VAR = (((((2.0 / (1.0 + exp((-2.0 * x)))) * (2.0 / (1.0 + exp((-2.0 * x))))) * ((2.0 / (1.0 + exp((-2.0 * x)))) * (2.0 / (1.0 + exp((-2.0 * x)))))) - ((1.0 * 1.0) * (1.0 * 1.0))) / (((2.0 / (1.0 + exp((-2.0 * x)))) + 1.0) * ((((1.0 / pow((exp((-2.0 * x)) + 1.0), 2.0)) * ((2.0 / (1.0 - exp((-2.0 * x)))) * (2.0 / (1.0 - exp((-2.0 * x)))))) * ((1.0 - exp((-2.0 * x))) * (1.0 - exp((-2.0 * x))))) + (1.0 * 1.0))));
	} else {
		double VAR_1;
		if (((-2.0 * x) <= 2.8730764077403216e-08)) {
			VAR_1 = ((1.0 * x) - ((4.996003610813204e-16 * pow(x, 4.0)) + (0.3333333333333335 * pow(x, 3.0))));
		} else {
			VAR_1 = ((2.0 / (1.0 + exp((-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) < -0.0029530562375764398

    1. Initial program 0.0

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

    3. Applied flip--0.0

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

    5. Applied flip--0.0

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

    6. Applied associate-/l/0.0

      \[\leadsto \color{blue}{\frac{\left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) \cdot \left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) - \left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right)}{\left(\frac{2}{1 + e^{-2 \cdot x}} + 1\right) \cdot \left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}} + 1 \cdot 1\right)}}\]
    7. Using strategy rm

    8. Applied flip-+0.0

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

    9. Applied associate-/r/0.0

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

    10. Applied flip-+0.0

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

    11. Applied associate-/r/0.0

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

    12. Applied swap-sqr0.0

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

    13. Simplified0.0

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

    if -0.0029530562375764398 < (* -2.0 x) < 2.8730764077403216e-08

    1. Initial program 59.4

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

    3. Applied flip--59.4

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

    4. Taylor expanded around 0 0.0

      \[\leadsto \color{blue}{1 \cdot x - \left(4.996 \cdot 10^{-16} \cdot {x}^{4} + 0.33333333333333348 \cdot {x}^{3}\right)}\]

    if 2.8730764077403216e-08 < (* -2.0 x)

    1. Initial program 0.4

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \le -0.00295305623757643977:\\ \;\;\;\;\frac{\left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) \cdot \left(\frac{2}{1 + e^{-2 \cdot x}} \cdot \frac{2}{1 + e^{-2 \cdot x}}\right) - \left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right)}{\left(\frac{2}{1 + e^{-2 \cdot x}} + 1\right) \cdot \left(\left(\frac{1}{{\left(e^{-2 \cdot x} + 1\right)}^{2}} \cdot \left(\frac{2}{1 - e^{-2 \cdot x}} \cdot \frac{2}{1 - e^{-2 \cdot x}}\right)\right) \cdot \left(\left(1 - e^{-2 \cdot x}\right) \cdot \left(1 - e^{-2 \cdot x}\right)\right) + 1 \cdot 1\right)}\\ \mathbf{elif}\;-2 \cdot x \le 2.87307640774032159 \cdot 10^{-8}:\\ \;\;\;\;1 \cdot x - \left(4.996 \cdot 10^{-16} \cdot {x}^{4} + 0.33333333333333348 \cdot {x}^{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))