Octave 3.8, jcobi/3

Percentage Accurate: 94.1% → 98.9%

Time: 16.0s

Alternatives: 15

Speedup: 3.2×

Specification

\[\alpha > -1 \land \beta > -1\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\alpha + \beta\right) + 2 \cdot 1\\ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{t_0}}{t_0}}{t_0 + 1} \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ (+ alpha beta) (* 2.0 1.0))))
   (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) t_0) t_0) (+ t_0 1.0))))

C

double code(double alpha, double beta) {
	double t_0 = (alpha + beta) + (2.0 * 1.0);
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0);
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    t_0 = (alpha + beta) + (2.0d0 * 1.0d0)
    code = (((((alpha + beta) + (beta * alpha)) + 1.0d0) / t_0) / t_0) / (t_0 + 1.0d0)
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = (alpha + beta) + (2.0 * 1.0);
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0);
}

Python

def code(alpha, beta):
	t_0 = (alpha + beta) + (2.0 * 1.0)
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0)

Julia

function code(alpha, beta)
	t_0 = Float64(Float64(alpha + beta) + Float64(2.0 * 1.0))
	return Float64(Float64(Float64(Float64(Float64(Float64(alpha + beta) + Float64(beta * alpha)) + 1.0) / t_0) / t_0) / Float64(t_0 + 1.0))
end

MATLAB

function tmp = code(alpha, beta)
	t_0 = (alpha + beta) + (2.0 * 1.0);
	tmp = (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0);
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(N[(N[(alpha + beta), $MachinePrecision] + N[(beta * alpha), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]]

Initial Program: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\alpha + \beta\right) + 2 \cdot 1\\ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{t_0}}{t_0}}{t_0 + 1} \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ (+ alpha beta) (* 2.0 1.0))))
   (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) t_0) t_0) (+ t_0 1.0))))

C

double code(double alpha, double beta) {
	double t_0 = (alpha + beta) + (2.0 * 1.0);
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0);
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    t_0 = (alpha + beta) + (2.0d0 * 1.0d0)
    code = (((((alpha + beta) + (beta * alpha)) + 1.0d0) / t_0) / t_0) / (t_0 + 1.0d0)
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = (alpha + beta) + (2.0 * 1.0);
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0);
}

Python

def code(alpha, beta):
	t_0 = (alpha + beta) + (2.0 * 1.0)
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0)

Julia

function code(alpha, beta)
	t_0 = Float64(Float64(alpha + beta) + Float64(2.0 * 1.0))
	return Float64(Float64(Float64(Float64(Float64(Float64(alpha + beta) + Float64(beta * alpha)) + 1.0) / t_0) / t_0) / Float64(t_0 + 1.0))
end

MATLAB

function tmp = code(alpha, beta)
	t_0 = (alpha + beta) + (2.0 * 1.0);
	tmp = (((((alpha + beta) + (beta * alpha)) + 1.0) / t_0) / t_0) / (t_0 + 1.0);
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(N[(N[(alpha + beta), $MachinePrecision] + N[(beta * alpha), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 98.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 1.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{1 + \left(\beta + \alpha\right)}{t_0}}{t_0 \cdot \left(3 + \left(\beta + \alpha\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \alpha}{t_0} \cdot \frac{1 - \frac{\alpha}{\beta}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (if (<= beta 1.8e+51)
     (/ (/ (+ 1.0 (+ beta alpha)) t_0) (* t_0 (+ 3.0 (+ beta alpha))))
     (*
      (/ (+ 1.0 alpha) t_0)
      (/ (- 1.0 (/ alpha beta)) (+ alpha (+ beta 3.0)))))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 1.8e+51) {
		tmp = ((1.0 + (beta + alpha)) / t_0) / (t_0 * (3.0 + (beta + alpha)));
	} else {
		tmp = ((1.0 + alpha) / t_0) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    real(8) :: tmp
    t_0 = alpha + (beta + 2.0d0)
    if (beta <= 1.8d+51) then
        tmp = ((1.0d0 + (beta + alpha)) / t_0) / (t_0 * (3.0d0 + (beta + alpha)))
    else
        tmp = ((1.0d0 + alpha) / t_0) * ((1.0d0 - (alpha / beta)) / (alpha + (beta + 3.0d0)))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 1.8e+51) {
		tmp = ((1.0 + (beta + alpha)) / t_0) / (t_0 * (3.0 + (beta + alpha)));
	} else {
		tmp = ((1.0 + alpha) / t_0) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	tmp = 0
	if beta <= 1.8e+51:
		tmp = ((1.0 + (beta + alpha)) / t_0) / (t_0 * (3.0 + (beta + alpha)))
	else:
		tmp = ((1.0 + alpha) / t_0) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	tmp = 0.0
	if (beta <= 1.8e+51)
		tmp = Float64(Float64(Float64(1.0 + Float64(beta + alpha)) / t_0) / Float64(t_0 * Float64(3.0 + Float64(beta + alpha))));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / t_0) * Float64(Float64(1.0 - Float64(alpha / beta)) / Float64(alpha + Float64(beta + 3.0))));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = 0.0;
	if (beta <= 1.8e+51)
		tmp = ((1.0 + (beta + alpha)) / t_0) / (t_0 * (3.0 + (beta + alpha)));
	else
		tmp = ((1.0 + alpha) / t_0) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 1.8e+51], N[(N[(N[(1.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(t$95$0 * N[(3.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(N[(1.0 - N[(alpha / beta), $MachinePrecision]), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 2: 99.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \frac{\frac{1 + \beta}{t_0}}{\alpha + \left(\beta + 3\right)} \cdot \frac{1 + \alpha}{t_0} \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (* (/ (/ (+ 1.0 beta) t_0) (+ alpha (+ beta 3.0))) (/ (+ 1.0 alpha) t_0))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	return (((1.0 + beta) / t_0) / (alpha + (beta + 3.0))) * ((1.0 + alpha) / t_0);
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    t_0 = alpha + (beta + 2.0d0)
    code = (((1.0d0 + beta) / t_0) / (alpha + (beta + 3.0d0))) * ((1.0d0 + alpha) / t_0)
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	return (((1.0 + beta) / t_0) / (alpha + (beta + 3.0))) * ((1.0 + alpha) / t_0);
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	return (((1.0 + beta) / t_0) / (alpha + (beta + 3.0))) * ((1.0 + alpha) / t_0)

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	return Float64(Float64(Float64(Float64(1.0 + beta) / t_0) / Float64(alpha + Float64(beta + 3.0))) * Float64(Float64(1.0 + alpha) / t_0))
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = (((1.0 + beta) / t_0) / (alpha + (beta + 3.0))) * ((1.0 + alpha) / t_0);
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(1.0 + beta), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 98.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{1}{\beta + 2}}{\beta + 2} \cdot \frac{1 + \beta}{\beta + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)} \cdot \frac{1 - \frac{\alpha}{\beta}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 2.3e-31)
   (* (/ (/ 1.0 (+ beta 2.0)) (+ beta 2.0)) (/ (+ 1.0 beta) (+ beta 3.0)))
   (*
    (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0)))
    (/ (- 1.0 (/ alpha beta)) (+ alpha (+ beta 3.0))))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 2.3e-31) {
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 2.3d-31) then
        tmp = ((1.0d0 / (beta + 2.0d0)) / (beta + 2.0d0)) * ((1.0d0 + beta) / (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) * ((1.0d0 - (alpha / beta)) / (alpha + (beta + 3.0d0)))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 2.3e-31) {
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if alpha <= 2.3e-31:
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 2.3e-31)
		tmp = Float64(Float64(Float64(1.0 / Float64(beta + 2.0)) / Float64(beta + 2.0)) * Float64(Float64(1.0 + beta) / Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) * Float64(Float64(1.0 - Float64(alpha / beta)) / Float64(alpha + Float64(beta + 3.0))));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 2.3e-31)
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) * ((1.0 - (alpha / beta)) / (alpha + (beta + 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[alpha, 2.3e-31], N[(N[(N[(1.0 / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - N[(alpha / beta), $MachinePrecision]), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 98.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 1.28 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{1 + \beta}{\beta + 2}}{t_0 \cdot \left(3 + \left(\beta + \alpha\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{t_0}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (if (<= beta 1.28e+42)
     (/ (/ (+ 1.0 beta) (+ beta 2.0)) (* t_0 (+ 3.0 (+ beta alpha))))
     (/ (/ (+ 1.0 alpha) t_0) (+ alpha (+ beta 3.0))))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 1.28e+42) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / (t_0 * (3.0 + (beta + alpha)));
	} else {
		tmp = ((1.0 + alpha) / t_0) / (alpha + (beta + 3.0));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    real(8) :: tmp
    t_0 = alpha + (beta + 2.0d0)
    if (beta <= 1.28d+42) then
        tmp = ((1.0d0 + beta) / (beta + 2.0d0)) / (t_0 * (3.0d0 + (beta + alpha)))
    else
        tmp = ((1.0d0 + alpha) / t_0) / (alpha + (beta + 3.0d0))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 1.28e+42) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / (t_0 * (3.0 + (beta + alpha)));
	} else {
		tmp = ((1.0 + alpha) / t_0) / (alpha + (beta + 3.0));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	tmp = 0
	if beta <= 1.28e+42:
		tmp = ((1.0 + beta) / (beta + 2.0)) / (t_0 * (3.0 + (beta + alpha)))
	else:
		tmp = ((1.0 + alpha) / t_0) / (alpha + (beta + 3.0))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	tmp = 0.0
	if (beta <= 1.28e+42)
		tmp = Float64(Float64(Float64(1.0 + beta) / Float64(beta + 2.0)) / Float64(t_0 * Float64(3.0 + Float64(beta + alpha))));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / t_0) / Float64(alpha + Float64(beta + 3.0)));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = 0.0;
	if (beta <= 1.28e+42)
		tmp = ((1.0 + beta) / (beta + 2.0)) / (t_0 * (3.0 + (beta + alpha)));
	else
		tmp = ((1.0 + alpha) / t_0) / (alpha + (beta + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 1.28e+42], N[(N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * N[(3.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 97.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 6.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{1}{\beta + 2}}{\beta + 2} \cdot \frac{1 + \beta}{\beta + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \frac{\beta}{1 + \alpha}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 6.8e-7)
   (* (/ (/ 1.0 (+ beta 2.0)) (+ beta 2.0)) (/ (+ 1.0 beta) (+ beta 3.0)))
   (/ 1.0 (* (+ alpha (+ beta 2.0)) (/ beta (+ 1.0 alpha))))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 6.8e-7) {
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	} else {
		tmp = 1.0 / ((alpha + (beta + 2.0)) * (beta / (1.0 + alpha)));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 6.8d-7) then
        tmp = ((1.0d0 / (beta + 2.0d0)) / (beta + 2.0d0)) * ((1.0d0 + beta) / (beta + 3.0d0))
    else
        tmp = 1.0d0 / ((alpha + (beta + 2.0d0)) * (beta / (1.0d0 + alpha)))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 6.8e-7) {
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	} else {
		tmp = 1.0 / ((alpha + (beta + 2.0)) * (beta / (1.0 + alpha)));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if alpha <= 6.8e-7:
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0))
	else:
		tmp = 1.0 / ((alpha + (beta + 2.0)) * (beta / (1.0 + alpha)))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 6.8e-7)
		tmp = Float64(Float64(Float64(1.0 / Float64(beta + 2.0)) / Float64(beta + 2.0)) * Float64(Float64(1.0 + beta) / Float64(beta + 3.0)));
	else
		tmp = Float64(1.0 / Float64(Float64(alpha + Float64(beta + 2.0)) * Float64(beta / Float64(1.0 + alpha))));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 6.8e-7)
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	else
		tmp = 1.0 / ((alpha + (beta + 2.0)) * (beta / (1.0 + alpha)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[alpha, 6.8e-7], N[(N[(N[(1.0 / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] * N[(beta / N[(1.0 + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 97.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{1}{\beta + 2}}{\beta + 2} \cdot \frac{1 + \beta}{\beta + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(\alpha + \left(\beta + 3\right)\right) \cdot \frac{\alpha + \left(\beta + 2\right)}{1 + \alpha}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 2e-6)
   (* (/ (/ 1.0 (+ beta 2.0)) (+ beta 2.0)) (/ (+ 1.0 beta) (+ beta 3.0)))
   (/
    1.0
    (* (+ alpha (+ beta 3.0)) (/ (+ alpha (+ beta 2.0)) (+ 1.0 alpha))))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 2e-6) {
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	} else {
		tmp = 1.0 / ((alpha + (beta + 3.0)) * ((alpha + (beta + 2.0)) / (1.0 + alpha)));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 2d-6) then
        tmp = ((1.0d0 / (beta + 2.0d0)) / (beta + 2.0d0)) * ((1.0d0 + beta) / (beta + 3.0d0))
    else
        tmp = 1.0d0 / ((alpha + (beta + 3.0d0)) * ((alpha + (beta + 2.0d0)) / (1.0d0 + alpha)))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 2e-6) {
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	} else {
		tmp = 1.0 / ((alpha + (beta + 3.0)) * ((alpha + (beta + 2.0)) / (1.0 + alpha)));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if alpha <= 2e-6:
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0))
	else:
		tmp = 1.0 / ((alpha + (beta + 3.0)) * ((alpha + (beta + 2.0)) / (1.0 + alpha)))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 2e-6)
		tmp = Float64(Float64(Float64(1.0 / Float64(beta + 2.0)) / Float64(beta + 2.0)) * Float64(Float64(1.0 + beta) / Float64(beta + 3.0)));
	else
		tmp = Float64(1.0 / Float64(Float64(alpha + Float64(beta + 3.0)) * Float64(Float64(alpha + Float64(beta + 2.0)) / Float64(1.0 + alpha))));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 2e-6)
		tmp = ((1.0 / (beta + 2.0)) / (beta + 2.0)) * ((1.0 + beta) / (beta + 3.0));
	else
		tmp = 1.0 / ((alpha + (beta + 3.0)) * ((alpha + (beta + 2.0)) / (1.0 + alpha)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[alpha, 2e-6], N[(N[(N[(1.0 / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision] * N[(N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 97.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 2.3:\\ \;\;\;\;\frac{\frac{1 + \beta}{\beta + 2}}{6 + \beta \cdot 5}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 2.3)
   (/ (/ (+ 1.0 beta) (+ beta 2.0)) (+ 6.0 (* beta 5.0)))
   (/ (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0))) (+ alpha (+ beta 3.0)))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.3) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 2.3d0) then
        tmp = ((1.0d0 + beta) / (beta + 2.0d0)) / (6.0d0 + (beta * 5.0d0))
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) / (alpha + (beta + 3.0d0))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.3) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 2.3:
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0))
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 2.3)
		tmp = Float64(Float64(Float64(1.0 + beta) / Float64(beta + 2.0)) / Float64(6.0 + Float64(beta * 5.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) / Float64(alpha + Float64(beta + 3.0)));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 2.3)
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0));
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[beta, 2.3], N[(N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(6.0 + N[(beta * 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 97.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 3:\\ \;\;\;\;\frac{\frac{\frac{1 + \alpha}{\alpha + 2}}{\alpha + 2}}{\alpha + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 3.0)
   (/ (/ (/ (+ 1.0 alpha) (+ alpha 2.0)) (+ alpha 2.0)) (+ alpha 3.0))
   (/ (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0))) (+ alpha (+ beta 3.0)))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 3.0) {
		tmp = (((1.0 + alpha) / (alpha + 2.0)) / (alpha + 2.0)) / (alpha + 3.0);
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0));
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 3.0d0) then
        tmp = (((1.0d0 + alpha) / (alpha + 2.0d0)) / (alpha + 2.0d0)) / (alpha + 3.0d0)
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) / (alpha + (beta + 3.0d0))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 3.0) {
		tmp = (((1.0 + alpha) / (alpha + 2.0)) / (alpha + 2.0)) / (alpha + 3.0);
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 3.0:
		tmp = (((1.0 + alpha) / (alpha + 2.0)) / (alpha + 2.0)) / (alpha + 3.0)
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 3.0)
		tmp = Float64(Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + 2.0)) / Float64(alpha + 2.0)) / Float64(alpha + 3.0));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) / Float64(alpha + Float64(beta + 3.0)));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 3.0)
		tmp = (((1.0 + alpha) / (alpha + 2.0)) / (alpha + 2.0)) / (alpha + 3.0);
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (alpha + (beta + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[beta, 3.0], N[(N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 97.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 5.2:\\ \;\;\;\;\frac{\frac{1 + \beta}{\beta + 2}}{6 + \beta \cdot 5}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{2 + \left(\beta + \alpha\right)}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 5.2)
   (/ (/ (+ 1.0 beta) (+ beta 2.0)) (+ 6.0 (* beta 5.0)))
   (/ (/ (+ 1.0 alpha) (+ 2.0 (+ beta alpha))) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 5.2) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0));
	} else {
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta;
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 5.2d0) then
        tmp = ((1.0d0 + beta) / (beta + 2.0d0)) / (6.0d0 + (beta * 5.0d0))
    else
        tmp = ((1.0d0 + alpha) / (2.0d0 + (beta + alpha))) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 5.2) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0));
	} else {
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 5.2:
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0))
	else:
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 5.2)
		tmp = Float64(Float64(Float64(1.0 + beta) / Float64(beta + 2.0)) / Float64(6.0 + Float64(beta * 5.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + Float64(beta + alpha))) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 5.2)
		tmp = ((1.0 + beta) / (beta + 2.0)) / (6.0 + (beta * 5.0));
	else
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[beta, 5.2], N[(N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(6.0 + N[(beta * 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 10: 96.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 6:\\ \;\;\;\;\frac{0.5}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{2 + \left(\beta + \alpha\right)}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 6.0)
   (/ 0.5 (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) (+ 2.0 (+ beta alpha))) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 6.0) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta;
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 6.0d0) then
        tmp = 0.5d0 / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / (2.0d0 + (beta + alpha))) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 6.0) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 6.0:
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 6.0)
		tmp = Float64(0.5 / Float64(Float64(beta + 2.0) * Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + Float64(beta + alpha))) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 6.0)
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / (2.0 + (beta + alpha))) / beta;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[beta, 6.0], N[(0.5 / N[(N[(beta + 2.0), $MachinePrecision] * N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 11: 96.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 9.5:\\ \;\;\;\;\frac{0.5}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 9.5)
   (/ 0.5 (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) beta) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 9.5) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / beta;
	}
	return tmp;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 9.5d0) then
        tmp = 0.5d0 / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / beta) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 9.5) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 9.5:
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / beta) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 9.5)
		tmp = Float64(0.5 / Float64(Float64(beta + 2.0) * Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / beta) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 9.5)
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / beta) / beta;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := If[LessEqual[beta, 9.5], N[(0.5 / N[(N[(beta + 2.0), $MachinePrecision] * N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / beta), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 12: 50.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \frac{1}{\beta \cdot \left(\beta + 3\right)} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 (/ 1.0 (* beta (+ beta 3.0))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return 1.0 / (beta * (beta + 3.0));
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = 1.0d0 / (beta * (beta + 3.0d0))
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return 1.0 / (beta * (beta + 3.0));
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return 1.0 / (beta * (beta + 3.0))

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return Float64(1.0 / Float64(beta * Float64(beta + 3.0)))
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = 1.0 / (beta * (beta + 3.0));
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := N[(1.0 / N[(beta * N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 56.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \frac{\frac{1 + \alpha}{\beta}}{\beta} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 (/ (/ (+ 1.0 alpha) beta) beta))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return ((1.0 + alpha) / beta) / beta;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = ((1.0d0 + alpha) / beta) / beta
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return ((1.0 + alpha) / beta) / beta;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return ((1.0 + alpha) / beta) / beta

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return Float64(Float64(Float64(1.0 + alpha) / beta) / beta)
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = ((1.0 + alpha) / beta) / beta;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := N[(N[(N[(1.0 + alpha), $MachinePrecision] / beta), $MachinePrecision] / beta), $MachinePrecision]

Derivation

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

Alternative 14: 6.1% accurate, 8.8× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \frac{--0.3333333333333333}{\beta} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 (/ (- -0.3333333333333333) beta))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return -(-0.3333333333333333) / beta;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = -(-0.3333333333333333d0) / beta
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return -(-0.3333333333333333) / beta;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return -(-0.3333333333333333) / beta

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return Float64(Float64(-(-0.3333333333333333)) / beta)
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = -(-0.3333333333333333) / beta;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := N[((--0.3333333333333333) / beta), $MachinePrecision]

Derivation

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

Alternative 15: 3.7% accurate, 11.7× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \frac{-1}{\beta} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 (/ -1.0 beta))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return -1.0 / beta;
}

Fortran

NOTE: alpha and beta should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = (-1.0d0) / beta
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return -1.0 / beta;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return -1.0 / beta

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return Float64(-1.0 / beta)
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = -1.0 / beta;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := N[(-1.0 / beta), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))