Logistic function from Lakshay Garg

Percentage Accurate: 54.7% → 99.6%

Time: 17.9s

Alternatives: 4

Speedup: 18.1×

Specification

Math

\[\begin{array}{l} \\ \frac{2}{1 + e^{-2 \cdot x}} - 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

C

double code(double x, double y) {
	return (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
end function

Java

public static double code(double x, double y) {
	return (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
}

Python

def code(x, y):
	return (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0

Julia

function code(x, y)
	return Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
end

Wolfram

code[x_, y_] := N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]

Initial Program: 54.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2}{1 + e^{-2 \cdot x}} - 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

C

double code(double x, double y) {
	return (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
end function

Java

public static double code(double x, double y) {
	return (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
}

Python

def code(x, y):
	return (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0

Julia

function code(x, y)
	return Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
end

Wolfram

code[x_, y_] := N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -0.04:\\ \;\;\;\;\sqrt[3]{{\left(-1 + \frac{2}{1 + e^{-2 \cdot x}}\right)}^{3}}\\ \mathbf{elif}\;-2 \cdot x \leq 10^{-6}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -0.04)
   (cbrt (pow (+ -1.0 (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3.0))
   (if (<= (* -2.0 x) 1e-6) (+ x (* -0.3333333333333333 (pow x 3.0))) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -0.04) {
		tmp = cbrt(pow((-1.0 + (2.0 / (1.0 + exp((-2.0 * x))))), 3.0));
	} else if ((-2.0 * x) <= 1e-6) {
		tmp = x + (-0.3333333333333333 * pow(x, 3.0));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -0.04) {
		tmp = Math.cbrt(Math.pow((-1.0 + (2.0 / (1.0 + Math.exp((-2.0 * x))))), 3.0));
	} else if ((-2.0 * x) <= 1e-6) {
		tmp = x + (-0.3333333333333333 * Math.pow(x, 3.0));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -0.04)
		tmp = cbrt((Float64(-1.0 + Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x))))) ^ 3.0));
	elseif (Float64(-2.0 * x) <= 1e-6)
		tmp = Float64(x + Float64(-0.3333333333333333 * (x ^ 3.0)));
	else
		tmp = -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -0.04], N[Power[N[Power[N[(-1.0 + N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 1e-6], N[(x + N[(-0.3333333333333333 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -0.0400000000000000008

   1. Initial program 99.9%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cbrt-cube 99.9%

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

      2. pow3 99.9%

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

      3. sub-neg 99.9%

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

      4. exp-prod 99.9%

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

      5. metadata-eval 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 99.9%

      \[\leadsto \sqrt[3]{{\left(\color{blue}{\frac{2}{1 + e^{-2 \cdot x}}} + -1\right)}^{3}} \]
   6. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{2}{\color{blue}{\left(0 - -1\right)} + e^{-2 \cdot x}} + -1\right)}^{3}} \]

      2. exp-prod 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{2}{\left(0 - -1\right) + \color{blue}{{\left(e^{-2}\right)}^{x}}} + -1\right)}^{3}} \]

      3. associate--r- 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{2}{\color{blue}{0 - \left(-1 - {\left(e^{-2}\right)}^{x}\right)}} + -1\right)}^{3}} \]

      4. neg-sub0 99.9%

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

      5. neg-sub0 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{2}{\color{blue}{0 - \left(-1 - {\left(e^{-2}\right)}^{x}\right)}} + -1\right)}^{3}} \]

      6. associate--r- 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{2}{\color{blue}{\left(0 - -1\right) + {\left(e^{-2}\right)}^{x}}} + -1\right)}^{3}} \]

      7. metadata-eval 99.9%

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

      8. exp-prod 99.9%

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

      9. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   if -0.0400000000000000008 < (*.f64 #s(literal -2 binary64) x) < 9.99999999999999955e-7

   1. Initial program 9.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.3333333333333333 \cdot {x}^{2}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto x \cdot \color{blue}{\left(-0.3333333333333333 \cdot {x}^{2} + 1\right)} \]

      2. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot {x}^{2}\right) \cdot x + 1 \cdot x} \]

      3. *-lft-identity 100.0%

         \[\leadsto \left(-0.3333333333333333 \cdot {x}^{2}\right) \cdot x + \color{blue}{x} \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left({x}^{2} \cdot x\right)} + x \]

      5. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, {x}^{2} \cdot x, x\right)} \]

      6. pow-plus 100.0%

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \color{blue}{{x}^{\left(2 + 1\right)}}, x\right) \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, {x}^{\color{blue}{3}}, x\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, {x}^{3}, x\right)} \]
   6. Step-by-step derivation

      1. fma-undefine 100.0%

         \[\leadsto \color{blue}{-0.3333333333333333 \cdot {x}^{3} + x} \]

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot {x}^{3} + x} \]

   if 9.99999999999999955e-7 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.9%

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

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -0.04:\\ \;\;\;\;\sqrt[3]{{\left(-1 + \frac{2}{1 + e^{-2 \cdot x}}\right)}^{3}}\\ \mathbf{elif}\;-2 \cdot x \leq 10^{-6}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -0.04:\\ \;\;\;\;-1 + \frac{2}{1 + e^{-2 \cdot x}}\\ \mathbf{elif}\;-2 \cdot x \leq 10^{-6}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -0.04)
   (+ -1.0 (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
   (if (<= (* -2.0 x) 1e-6) (+ x (* -0.3333333333333333 (pow x 3.0))) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -0.04) {
		tmp = -1.0 + (2.0 / (1.0 + exp((-2.0 * x))));
	} else if ((-2.0 * x) <= 1e-6) {
		tmp = x + (-0.3333333333333333 * pow(x, 3.0));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((-2.0d0) * x) <= (-0.04d0)) then
        tmp = (-1.0d0) + (2.0d0 / (1.0d0 + exp(((-2.0d0) * x))))
    else if (((-2.0d0) * x) <= 1d-6) then
        tmp = x + ((-0.3333333333333333d0) * (x ** 3.0d0))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -0.04) {
		tmp = -1.0 + (2.0 / (1.0 + Math.exp((-2.0 * x))));
	} else if ((-2.0 * x) <= 1e-6) {
		tmp = x + (-0.3333333333333333 * Math.pow(x, 3.0));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (-2.0 * x) <= -0.04:
		tmp = -1.0 + (2.0 / (1.0 + math.exp((-2.0 * x))))
	elif (-2.0 * x) <= 1e-6:
		tmp = x + (-0.3333333333333333 * math.pow(x, 3.0))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -0.04)
		tmp = Float64(-1.0 + Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))));
	elseif (Float64(-2.0 * x) <= 1e-6)
		tmp = Float64(x + Float64(-0.3333333333333333 * (x ^ 3.0)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((-2.0 * x) <= -0.04)
		tmp = -1.0 + (2.0 / (1.0 + exp((-2.0 * x))));
	elseif ((-2.0 * x) <= 1e-6)
		tmp = x + (-0.3333333333333333 * (x ^ 3.0));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -0.04], N[(-1.0 + N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 1e-6], N[(x + N[(-0.3333333333333333 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -0.0400000000000000008

   1. Initial program 99.9%

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

   if -0.0400000000000000008 < (*.f64 #s(literal -2 binary64) x) < 9.99999999999999955e-7

   1. Initial program 9.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.3333333333333333 \cdot {x}^{2}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto x \cdot \color{blue}{\left(-0.3333333333333333 \cdot {x}^{2} + 1\right)} \]

      2. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot {x}^{2}\right) \cdot x + 1 \cdot x} \]

      3. *-lft-identity 100.0%

         \[\leadsto \left(-0.3333333333333333 \cdot {x}^{2}\right) \cdot x + \color{blue}{x} \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left({x}^{2} \cdot x\right)} + x \]

      5. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, {x}^{2} \cdot x, x\right)} \]

      6. pow-plus 100.0%

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \color{blue}{{x}^{\left(2 + 1\right)}}, x\right) \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, {x}^{\color{blue}{3}}, x\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, {x}^{3}, x\right)} \]
   6. Step-by-step derivation

      1. fma-undefine 100.0%

         \[\leadsto \color{blue}{-0.3333333333333333 \cdot {x}^{3} + x} \]

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot {x}^{3} + x} \]

   if 9.99999999999999955e-7 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.9%

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

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -0.04:\\ \;\;\;\;-1 + \frac{2}{1 + e^{-2 \cdot x}}\\ \mathbf{elif}\;-2 \cdot x \leq 10^{-6}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.0) -1.0 x))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = -1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = -1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = -1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], -1.0, x]

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.9%

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

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1} \]

   if -1 < x

   1. Initial program 43.7%

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

   3. Taylor expanded in x around 0 64.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 27.4% accurate, 109.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 56.2%

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

3. Taylor expanded in x around 0 27.0%

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

4. Taylor expanded in x around inf 24.7%

   \[\leadsto \color{blue}{-1} \]

5. Final simplification 24.7%

   \[\leadsto -1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))