Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 6

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))

C

double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * (y - 1.0d0)) - (y * 0.5d0)) + 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Python

def code(x, y):
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673

Julia

function code(x, y)
	return Float64(Float64(Float64(x * Float64(y - 1.0)) - Float64(y * 0.5)) + 0.918938533204673)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))

C

double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * (y - 1.0d0)) - (y * 0.5d0)) + 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Python

def code(x, y):
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673

Julia

function code(x, y)
	return Float64(Float64(Float64(x * Float64(y - 1.0)) - Float64(y * 0.5)) + 0.918938533204673)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(y \cdot \left(x + -0.5\right) + 0.918938533204673\right) - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (+ (* y (+ x -0.5)) 0.918938533204673) x))

C

double code(double x, double y) {
	return ((y * (x + -0.5)) + 0.918938533204673) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((y * (x + (-0.5d0))) + 0.918938533204673d0) - x
end function

Java

public static double code(double x, double y) {
	return ((y * (x + -0.5)) + 0.918938533204673) - x;
}

Python

def code(x, y):
	return ((y * (x + -0.5)) + 0.918938533204673) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(y * Float64(x + -0.5)) + 0.918938533204673) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((y * (x + -0.5)) + 0.918938533204673) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(y * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision] - x), $MachinePrecision]

Derivation

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

Alternative 2: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.66 \lor \neg \left(y \leq 9.8 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.66) (not (<= y 9.8e-8)))
   (+ (* y x) (- 0.918938533204673 (* y 0.5)))
   (- (+ 0.918938533204673 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.66) || !(y <= 9.8e-8)) {
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	} else {
		tmp = (0.918938533204673 + (y * x)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.66d0)) .or. (.not. (y <= 9.8d-8))) then
        tmp = (y * x) + (0.918938533204673d0 - (y * 0.5d0))
    else
        tmp = (0.918938533204673d0 + (y * x)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.66) || !(y <= 9.8e-8)) {
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	} else {
		tmp = (0.918938533204673 + (y * x)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.66) or not (y <= 9.8e-8):
		tmp = (y * x) + (0.918938533204673 - (y * 0.5))
	else:
		tmp = (0.918938533204673 + (y * x)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.66) || !(y <= 9.8e-8))
		tmp = Float64(Float64(y * x) + Float64(0.918938533204673 - Float64(y * 0.5)));
	else
		tmp = Float64(Float64(0.918938533204673 + Float64(y * x)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.66) || ~((y <= 9.8e-8)))
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	else
		tmp = (0.918938533204673 + (y * x)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.66], N[Not[LessEqual[y, 9.8e-8]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] + N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.918938533204673 + N[(y * x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

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

Alternative 3: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900000 \lor \neg \left(y \leq 1200000\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -900000.0) (not (<= y 1200000.0)))
   (* y (- x 0.5))
   (- (+ 0.918938533204673 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -900000.0) || !(y <= 1200000.0)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = (0.918938533204673 + (y * x)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-900000.0d0)) .or. (.not. (y <= 1200000.0d0))) then
        tmp = y * (x - 0.5d0)
    else
        tmp = (0.918938533204673d0 + (y * x)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -900000.0) || !(y <= 1200000.0)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = (0.918938533204673 + (y * x)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -900000.0) or not (y <= 1200000.0):
		tmp = y * (x - 0.5)
	else:
		tmp = (0.918938533204673 + (y * x)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -900000.0) || !(y <= 1200000.0))
		tmp = Float64(y * Float64(x - 0.5));
	else
		tmp = Float64(Float64(0.918938533204673 + Float64(y * x)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -900000.0) || ~((y <= 1200000.0)))
		tmp = y * (x - 0.5);
	else
		tmp = (0.918938533204673 + (y * x)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -900000.0], N[Not[LessEqual[y, 1200000.0]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.918938533204673 + N[(y * x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

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

Alternative 4: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1.5\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4) (not (<= y 1.5)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4) || !(y <= 1.5)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.4d0)) .or. (.not. (y <= 1.5d0))) then
        tmp = y * (x - 0.5d0)
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.4) || !(y <= 1.5)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4) or not (y <= 1.5):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4) || !(y <= 1.5))
		tmp = Float64(y * Float64(x - 0.5));
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4) || ~((y <= 1.5)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4], N[Not[LessEqual[y, 1.5]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

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

Alternative 5: 50.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ 0.918938533204673 - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 0.918938533204673 x))

C

double code(double x, double y) {
	return 0.918938533204673 - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.918938533204673d0 - x
end function

Java

public static double code(double x, double y) {
	return 0.918938533204673 - x;
}

Python

def code(x, y):
	return 0.918938533204673 - x

Julia

function code(x, y)
	return Float64(0.918938533204673 - x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.918938533204673 - x;
end

Wolfram

code[x_, y_] := N[(0.918938533204673 - x), $MachinePrecision]

Derivation

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

Alternative 6: 26.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.918938533204673)

C

double code(double x, double y) {
	return 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return 0.918938533204673;
}

Python

def code(x, y):
	return 0.918938533204673

Julia

function code(x, y)
	return 0.918938533204673
end

MATLAB

function tmp = code(x, y)
	tmp = 0.918938533204673;
end

Wolfram

code[x_, y_] := 0.918938533204673

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))