Logistic function from Lakshay Garg

Percentage Accurate: 55.0% → 99.5%

Time: 11.5s

Alternatives: 5

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: 55.0% 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: 99.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 - \mathsf{expm1}\left(-2 \cdot x\right)\\ t_1 := \frac{-2}{t_0}\\ \mathbf{if}\;-2 \cdot x \leq -10000:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 2 \cdot 10^{-6}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + t_1 \cdot \left(1 + t_1\right)} \cdot \left(-1 - \frac{8}{{t_0}^{3}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- -2.0 (expm1 (* -2.0 x)))) (t_1 (/ -2.0 t_0)))
   (if (<= (* -2.0 x) -10000.0)
     (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
     (if (<= (* -2.0 x) 2e-6)
       (+ x (* -0.3333333333333333 (pow x 3.0)))
       (*
        (/ 1.0 (+ 1.0 (* t_1 (+ 1.0 t_1))))
        (- -1.0 (/ 8.0 (pow t_0 3.0))))))))

C

double code(double x, double y) {
	double t_0 = -2.0 - expm1((-2.0 * x));
	double t_1 = -2.0 / t_0;
	double tmp;
	if ((-2.0 * x) <= -10000.0) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 2e-6) {
		tmp = x + (-0.3333333333333333 * pow(x, 3.0));
	} else {
		tmp = (1.0 / (1.0 + (t_1 * (1.0 + t_1)))) * (-1.0 - (8.0 / pow(t_0, 3.0)));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = -2.0 - Math.expm1((-2.0 * x));
	double t_1 = -2.0 / t_0;
	double tmp;
	if ((-2.0 * x) <= -10000.0) {
		tmp = (2.0 / (1.0 + Math.exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 2e-6) {
		tmp = x + (-0.3333333333333333 * Math.pow(x, 3.0));
	} else {
		tmp = (1.0 / (1.0 + (t_1 * (1.0 + t_1)))) * (-1.0 - (8.0 / Math.pow(t_0, 3.0)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -2.0 - math.expm1((-2.0 * x))
	t_1 = -2.0 / t_0
	tmp = 0
	if (-2.0 * x) <= -10000.0:
		tmp = (2.0 / (1.0 + math.exp((-2.0 * x)))) + -1.0
	elif (-2.0 * x) <= 2e-6:
		tmp = x + (-0.3333333333333333 * math.pow(x, 3.0))
	else:
		tmp = (1.0 / (1.0 + (t_1 * (1.0 + t_1)))) * (-1.0 - (8.0 / math.pow(t_0, 3.0)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-2.0 - expm1(Float64(-2.0 * x)))
	t_1 = Float64(-2.0 / t_0)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -10000.0)
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	elseif (Float64(-2.0 * x) <= 2e-6)
		tmp = Float64(x + Float64(-0.3333333333333333 * (x ^ 3.0)));
	else
		tmp = Float64(Float64(1.0 / Float64(1.0 + Float64(t_1 * Float64(1.0 + t_1)))) * Float64(-1.0 - Float64(8.0 / (t_0 ^ 3.0))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-2.0 - N[(Exp[N[(-2.0 * x), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-2.0 / t$95$0), $MachinePrecision]}, If[LessEqual[N[(-2.0 * x), $MachinePrecision], -10000.0], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-6], N[(x + N[(-0.3333333333333333 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(1.0 + N[(t$95$1 * N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(8.0 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 - \mathsf{expm1}\left(-2 \cdot x\right)\\ t_1 := \frac{-2}{t_0}\\ \mathbf{if}\;-2 \cdot x \leq -10000:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 2 \cdot 10^{-6}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 - \frac{8}{{t_0}^{3}}}{1 + t_1 \cdot \left(1 + t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- -2.0 (expm1 (* -2.0 x)))) (t_1 (/ -2.0 t_0)))
   (if (<= (* -2.0 x) -10000.0)
     (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
     (if (<= (* -2.0 x) 2e-6)
       (+ x (* -0.3333333333333333 (pow x 3.0)))
       (/ (- -1.0 (/ 8.0 (pow t_0 3.0))) (+ 1.0 (* t_1 (+ 1.0 t_1))))))))

C

double code(double x, double y) {
	double t_0 = -2.0 - expm1((-2.0 * x));
	double t_1 = -2.0 / t_0;
	double tmp;
	if ((-2.0 * x) <= -10000.0) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 2e-6) {
		tmp = x + (-0.3333333333333333 * pow(x, 3.0));
	} else {
		tmp = (-1.0 - (8.0 / pow(t_0, 3.0))) / (1.0 + (t_1 * (1.0 + t_1)));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = -2.0 - Math.expm1((-2.0 * x));
	double t_1 = -2.0 / t_0;
	double tmp;
	if ((-2.0 * x) <= -10000.0) {
		tmp = (2.0 / (1.0 + Math.exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 2e-6) {
		tmp = x + (-0.3333333333333333 * Math.pow(x, 3.0));
	} else {
		tmp = (-1.0 - (8.0 / Math.pow(t_0, 3.0))) / (1.0 + (t_1 * (1.0 + t_1)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -2.0 - math.expm1((-2.0 * x))
	t_1 = -2.0 / t_0
	tmp = 0
	if (-2.0 * x) <= -10000.0:
		tmp = (2.0 / (1.0 + math.exp((-2.0 * x)))) + -1.0
	elif (-2.0 * x) <= 2e-6:
		tmp = x + (-0.3333333333333333 * math.pow(x, 3.0))
	else:
		tmp = (-1.0 - (8.0 / math.pow(t_0, 3.0))) / (1.0 + (t_1 * (1.0 + t_1)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-2.0 - expm1(Float64(-2.0 * x)))
	t_1 = Float64(-2.0 / t_0)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -10000.0)
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	elseif (Float64(-2.0 * x) <= 2e-6)
		tmp = Float64(x + Float64(-0.3333333333333333 * (x ^ 3.0)));
	else
		tmp = Float64(Float64(-1.0 - Float64(8.0 / (t_0 ^ 3.0))) / Float64(1.0 + Float64(t_1 * Float64(1.0 + t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-2.0 - N[(Exp[N[(-2.0 * x), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-2.0 / t$95$0), $MachinePrecision]}, If[LessEqual[N[(-2.0 * x), $MachinePrecision], -10000.0], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-6], N[(x + N[(-0.3333333333333333 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 - N[(8.0 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$1 * N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -10000 \lor \neg \left(-2 \cdot x \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (* -2.0 x) -10000.0) (not (<= (* -2.0 x) 2e-6)))
   (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
   (+ x (* -0.3333333333333333 (pow x 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (((-2.0 * x) <= -10000.0) || !((-2.0 * x) <= 2e-6)) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else {
		tmp = x + (-0.3333333333333333 * pow(x, 3.0));
	}
	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) <= (-10000.0d0)) .or. (.not. (((-2.0d0) * x) <= 2d-6))) then
        tmp = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) + (-1.0d0)
    else
        tmp = x + ((-0.3333333333333333d0) * (x ** 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((-2.0 * x) <= -10000.0) || !((-2.0 * x) <= 2e-6)) {
		tmp = (2.0 / (1.0 + Math.exp((-2.0 * x)))) + -1.0;
	} else {
		tmp = x + (-0.3333333333333333 * Math.pow(x, 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((-2.0 * x) <= -10000.0) or not ((-2.0 * x) <= 2e-6):
		tmp = (2.0 / (1.0 + math.exp((-2.0 * x)))) + -1.0
	else:
		tmp = x + (-0.3333333333333333 * math.pow(x, 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(-2.0 * x) <= -10000.0) || !(Float64(-2.0 * x) <= 2e-6))
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	else
		tmp = Float64(x + Float64(-0.3333333333333333 * (x ^ 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((-2.0 * x) <= -10000.0) || ~(((-2.0 * x) <= 2e-6)))
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	else
		tmp = x + (-0.3333333333333333 * (x ^ 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(-2.0 * x), $MachinePrecision], -10000.0], N[Not[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-6]], $MachinePrecision]], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 27.5% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024006 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))