Logistic function from Lakshay Garg

Percentage Accurate: 54.7% → 99.5%

Time: 5.8s

Alternatives: 6

Speedup: 35.6×

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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -50000 \lor \neg \left(-2 \cdot x \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{else}:\\ \;\;\;\;x + \left(-0.3333333333333333 \cdot {x}^{3} + \left(-0.05396825396825397 \cdot {x}^{7} + 0.13333333333333333 \cdot {x}^{5}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (* -2.0 x) -50000.0) (not (<= (* -2.0 x) 2e-5)))
   (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
   (+
    x
    (+
     (* -0.3333333333333333 (pow x 3.0))
     (+
      (* -0.05396825396825397 (pow x 7.0))
      (* 0.13333333333333333 (pow x 5.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (((-2.0 * x) <= -50000.0) || !((-2.0 * x) <= 2e-5)) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else {
		tmp = x + ((-0.3333333333333333 * pow(x, 3.0)) + ((-0.05396825396825397 * pow(x, 7.0)) + (0.13333333333333333 * pow(x, 5.0))));
	}
	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) <= (-50000.0d0)) .or. (.not. (((-2.0d0) * x) <= 2d-5))) then
        tmp = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) + (-1.0d0)
    else
        tmp = x + (((-0.3333333333333333d0) * (x ** 3.0d0)) + (((-0.05396825396825397d0) * (x ** 7.0d0)) + (0.13333333333333333d0 * (x ** 5.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((-2.0 * x) <= -50000.0) || !((-2.0 * x) <= 2e-5)) {
		tmp = (2.0 / (1.0 + Math.exp((-2.0 * x)))) + -1.0;
	} else {
		tmp = x + ((-0.3333333333333333 * Math.pow(x, 3.0)) + ((-0.05396825396825397 * Math.pow(x, 7.0)) + (0.13333333333333333 * Math.pow(x, 5.0))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((-2.0 * x) <= -50000.0) or not ((-2.0 * x) <= 2e-5):
		tmp = (2.0 / (1.0 + math.exp((-2.0 * x)))) + -1.0
	else:
		tmp = x + ((-0.3333333333333333 * math.pow(x, 3.0)) + ((-0.05396825396825397 * math.pow(x, 7.0)) + (0.13333333333333333 * math.pow(x, 5.0))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(-2.0 * x) <= -50000.0) || !(Float64(-2.0 * x) <= 2e-5))
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	else
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 * (x ^ 3.0)) + Float64(Float64(-0.05396825396825397 * (x ^ 7.0)) + Float64(0.13333333333333333 * (x ^ 5.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((-2.0 * x) <= -50000.0) || ~(((-2.0 * x) <= 2e-5)))
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	else
		tmp = x + ((-0.3333333333333333 * (x ^ 3.0)) + ((-0.05396825396825397 * (x ^ 7.0)) + (0.13333333333333333 * (x ^ 5.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(-2.0 * x), $MachinePrecision], -50000.0], N[Not[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-5]], $MachinePrecision]], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(x + N[(N[(-0.3333333333333333 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-0.05396825396825397 * N[Power[x, 7.0], $MachinePrecision]), $MachinePrecision] + N[(0.13333333333333333 * N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 99.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -0.01 \lor \neg \left(-2 \cdot x \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot {x}^{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (* -2.0 x) -0.01) (not (<= (* -2.0 x) 2e-5)))
   (+ (/ 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) <= -0.01) || !((-2.0 * x) <= 2e-5)) {
		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) <= (-0.01d0)) .or. (.not. (((-2.0d0) * x) <= 2d-5))) 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) <= -0.01) || !((-2.0 * x) <= 2e-5)) {
		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) <= -0.01) or not ((-2.0 * x) <= 2e-5):
		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) <= -0.01) || !(Float64(-2.0 * x) <= 2e-5))
		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) <= -0.01) || ~(((-2.0 * x) <= 2e-5)))
		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], -0.01], N[Not[LessEqual[N[(-2.0 * x), $MachinePrecision], 2e-5]], $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 3: 55.0% accurate, 8.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{x + 2}\\ \mathbf{if}\;x \leq 0.68:\\ \;\;\;\;x \cdot \left(\left(x + 2\right) \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{\frac{0.5}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ x 2.0))))
   (if (<= x 0.68) (* x (* (+ x 2.0) t_0)) (/ t_0 (/ 0.5 x)))))

C

double code(double x, double y) {
	double t_0 = 1.0 / (x + 2.0);
	double tmp;
	if (x <= 0.68) {
		tmp = x * ((x + 2.0) * t_0);
	} else {
		tmp = t_0 / (0.5 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / (x + 2.0d0)
    if (x <= 0.68d0) then
        tmp = x * ((x + 2.0d0) * t_0)
    else
        tmp = t_0 / (0.5d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 / (x + 2.0);
	double tmp;
	if (x <= 0.68) {
		tmp = x * ((x + 2.0) * t_0);
	} else {
		tmp = t_0 / (0.5 / x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 / (x + 2.0)
	tmp = 0
	if x <= 0.68:
		tmp = x * ((x + 2.0) * t_0)
	else:
		tmp = t_0 / (0.5 / x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 / Float64(x + 2.0))
	tmp = 0.0
	if (x <= 0.68)
		tmp = Float64(x * Float64(Float64(x + 2.0) * t_0));
	else
		tmp = Float64(t_0 / Float64(0.5 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 / (x + 2.0);
	tmp = 0.0;
	if (x <= 0.68)
		tmp = x * ((x + 2.0) * t_0);
	else
		tmp = t_0 / (0.5 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[(x + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 0.68], N[(x * N[(N[(x + 2.0), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 / N[(0.5 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 55.0% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.68:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x + 2}}{\frac{0.5}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.68) x (/ (/ 1.0 (+ x 2.0)) (/ 0.5 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.68) {
		tmp = x;
	} else {
		tmp = (1.0 / (x + 2.0)) / (0.5 / 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 <= 0.68d0) then
        tmp = x
    else
        tmp = (1.0d0 / (x + 2.0d0)) / (0.5d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.68) {
		tmp = x;
	} else {
		tmp = (1.0 / (x + 2.0)) / (0.5 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.68:
		tmp = x
	else:
		tmp = (1.0 / (x + 2.0)) / (0.5 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.68)
		tmp = x;
	else
		tmp = Float64(Float64(1.0 / Float64(x + 2.0)) / Float64(0.5 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.68)
		tmp = x;
	else
		tmp = (1.0 / (x + 2.0)) / (0.5 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.68], x, N[(N[(1.0 / N[(x + 2.0), $MachinePrecision]), $MachinePrecision] / N[(0.5 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 55.0% accurate, 35.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 2.0) x 2.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.0) {
		tmp = x;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 2.0d0) then
        tmp = x
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.0) {
		tmp = x;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.0:
		tmp = x
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.0)
		tmp = x;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = x;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.0], x, 2.0]

Derivation

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

Alternative 6: 7.0% accurate, 109.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 2.0)

C

double code(double x, double y) {
	return 2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0
end function

Java

public static double code(double x, double y) {
	return 2.0;
}

Python

def code(x, y):
	return 2.0

Julia

function code(x, y)
	return 2.0
end

MATLAB

function tmp = code(x, y)
	tmp = 2.0;
end

Wolfram

code[x_, y_] := 2.0

Derivation

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

Reproduce

herbie shell --seed 2023350 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))