Octave 3.8, jcobi/3

Percentage Accurate: 94.2% → 99.8%

Time: 21.2s

Alternatives: 20

Speedup: 3.9×

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: 94.2% 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: 99.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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 = (beta + 2.0d0) + alpha
    code = (1.0d0 / t_0) / ((t_0 / (1.0d0 + beta)) * ((beta + (alpha + 3.0d0)) / (1.0d0 + alpha)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 99.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = (beta + 2.0) + alpha;
	return ((1.0 + alpha) / t_0) * (1.0 / (t_0 / ((1.0 + beta) / (alpha + (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
    real(8) :: t_0
    t_0 = (beta + 2.0d0) + alpha
    code = ((1.0d0 + alpha) / t_0) * (1.0d0 / (t_0 / ((1.0d0 + beta) / (alpha + (beta + 3.0d0)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 3: 96.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = (beta + 2.0) + alpha;
	return ((1.0 + alpha) / t_0) * ((1.0 + beta) / (t_0 * (alpha + (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
    real(8) :: t_0
    t_0 = (beta + 2.0d0) + alpha
    code = ((1.0d0 + alpha) / t_0) * ((1.0d0 + beta) / (t_0 * (alpha + (beta + 3.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 4: 96.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = (beta + 2.0) + alpha;
	return ((1.0 + alpha) * ((1.0 + beta) / (t_0 * (alpha + (beta + 3.0))))) / 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 = (beta + 2.0d0) + alpha
    code = ((1.0d0 + alpha) * ((1.0d0 + beta) / (t_0 * (alpha + (beta + 3.0d0))))) / t_0
end function

Java

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

Python

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

Julia

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

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	t_0 = (beta + 2.0) + alpha;
	tmp = ((1.0 + alpha) * ((1.0 + beta) / (t_0 * (alpha + (beta + 3.0))))) / 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[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]}, N[(N[(N[(1.0 + alpha), $MachinePrecision] * N[(N[(1.0 + beta), $MachinePrecision] / N[(t$95$0 * N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]]

Derivation

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

Alternative 5: 97.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double t_0 = (beta + 2.0) + alpha;
	return (1.0 + alpha) / (t_0 / ((1.0 + beta) / ((beta + (alpha + 3.0)) * 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 = (beta + 2.0d0) + alpha
    code = (1.0d0 + alpha) / (t_0 / ((1.0d0 + beta) / ((beta + (alpha + 3.0d0)) * t_0)))
end function

Java

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

Python

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

Julia

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

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	t_0 = (beta + 2.0) + alpha;
	tmp = (1.0 + alpha) / (t_0 / ((1.0 + beta) / ((beta + (alpha + 3.0)) * 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[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]}, N[(N[(1.0 + alpha), $MachinePrecision] / N[(t$95$0 / N[(N[(1.0 + beta), $MachinePrecision] / N[(N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 98.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / ((beta + 2.0) / ((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 + alpha) / ((beta + 2.0d0) + alpha)) * (1.0d0 / ((beta + 2.0d0) / ((1.0d0 + beta) / (beta + 3.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / ((beta + 2.0) / ((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[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(beta + 2.0), $MachinePrecision] / N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 7: 98.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 100000000:\\ \;\;\;\;\frac{1 + \beta}{\left(\beta + 3\right) \cdot \left(\left(\beta + 2\right) \cdot \left(\beta + \left(2 + \alpha\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \alpha}{\left(\beta + 2\right) + \alpha} \cdot \frac{1}{2 \cdot \alpha + \left(\beta + 4\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 100000000.0)
   (/ (+ 1.0 beta) (* (+ beta 3.0) (* (+ beta 2.0) (+ beta (+ 2.0 alpha)))))
   (*
    (/ (+ 1.0 alpha) (+ (+ beta 2.0) alpha))
    (/ 1.0 (+ (* 2.0 alpha) (+ beta 4.0))))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 100000000.0) {
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / ((2.0 * alpha) + (beta + 4.0)));
	}
	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 <= 100000000.0d0) then
        tmp = (1.0d0 + beta) / ((beta + 3.0d0) * ((beta + 2.0d0) * (beta + (2.0d0 + alpha))))
    else
        tmp = ((1.0d0 + alpha) / ((beta + 2.0d0) + alpha)) * (1.0d0 / ((2.0d0 * alpha) + (beta + 4.0d0)))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 100000000.0) {
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / ((2.0 * alpha) + (beta + 4.0)));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 100000000.0:
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))))
	else:
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / ((2.0 * alpha) + (beta + 4.0)))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 100000000.0)
		tmp = Float64(Float64(1.0 + beta) / Float64(Float64(beta + 3.0) * Float64(Float64(beta + 2.0) * Float64(beta + Float64(2.0 + alpha)))));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(Float64(beta + 2.0) + alpha)) * Float64(1.0 / Float64(Float64(2.0 * alpha) + Float64(beta + 4.0))));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 100000000.0)
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))));
	else
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / ((2.0 * alpha) + (beta + 4.0)));
	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, 100000000.0], N[(N[(1.0 + beta), $MachinePrecision] / N[(N[(beta + 3.0), $MachinePrecision] * N[(N[(beta + 2.0), $MachinePrecision] * N[(beta + N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(2.0 * alpha), $MachinePrecision] + N[(beta + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 97.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 0.9:\\ \;\;\;\;\frac{1 + \alpha}{2 + \alpha} \cdot \frac{1}{\left(2 + \alpha\right) \cdot \left(\alpha + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \alpha}{\left(\beta + 2\right) + \alpha} \cdot \frac{1}{\beta + 4}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 0.9)
   (* (/ (+ 1.0 alpha) (+ 2.0 alpha)) (/ 1.0 (* (+ 2.0 alpha) (+ alpha 3.0))))
   (* (/ (+ 1.0 alpha) (+ (+ beta 2.0) alpha)) (/ 1.0 (+ beta 4.0)))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 0.9) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (1.0 / ((2.0 + alpha) * (alpha + 3.0)));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0));
	}
	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 <= 0.9d0) then
        tmp = ((1.0d0 + alpha) / (2.0d0 + alpha)) * (1.0d0 / ((2.0d0 + alpha) * (alpha + 3.0d0)))
    else
        tmp = ((1.0d0 + alpha) / ((beta + 2.0d0) + alpha)) * (1.0d0 / (beta + 4.0d0))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 0.9) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (1.0 / ((2.0 + alpha) * (alpha + 3.0)));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 0.9:
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (1.0 / ((2.0 + alpha) * (alpha + 3.0)))
	else:
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 0.9)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + alpha)) * Float64(1.0 / Float64(Float64(2.0 + alpha) * Float64(alpha + 3.0))));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(Float64(beta + 2.0) + alpha)) * Float64(1.0 / Float64(beta + 4.0)));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 0.9)
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (1.0 / ((2.0 + alpha) * (alpha + 3.0)));
	else
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0));
	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, 0.9], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(2.0 + alpha), $MachinePrecision] * N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(beta + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 98.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 1.65 \cdot 10^{+16}:\\ \;\;\;\;\frac{1 + \beta}{\left(\beta + 3\right) \cdot \left(\left(\beta + 2\right) \cdot \left(\beta + \left(2 + \alpha\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{\left(\beta + 2\right) + \alpha}{1 + \alpha}}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 1.65e+16)
   (/ (+ 1.0 beta) (* (+ beta 3.0) (* (+ beta 2.0) (+ beta (+ 2.0 alpha)))))
   (/ (/ 1.0 (/ (+ (+ beta 2.0) alpha) (+ 1.0 alpha))) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 1.65e+16) {
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))));
	} else {
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + 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 <= 1.65d+16) then
        tmp = (1.0d0 + beta) / ((beta + 3.0d0) * ((beta + 2.0d0) * (beta + (2.0d0 + alpha))))
    else
        tmp = (1.0d0 / (((beta + 2.0d0) + alpha) / (1.0d0 + alpha))) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 1.65e+16) {
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))));
	} else {
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + alpha))) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 1.65e+16:
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))))
	else:
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + alpha))) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 1.65e+16)
		tmp = Float64(Float64(1.0 + beta) / Float64(Float64(beta + 3.0) * Float64(Float64(beta + 2.0) * Float64(beta + Float64(2.0 + alpha)))));
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(beta + 2.0) + alpha) / Float64(1.0 + alpha))) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 1.65e+16)
		tmp = (1.0 + beta) / ((beta + 3.0) * ((beta + 2.0) * (beta + (2.0 + alpha))));
	else
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + 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, 1.65e+16], N[(N[(1.0 + beta), $MachinePrecision] / N[(N[(beta + 3.0), $MachinePrecision] * N[(N[(beta + 2.0), $MachinePrecision] * N[(beta + N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision] / N[(1.0 + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 10: 97.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 0.48:\\ \;\;\;\;\frac{1 + \alpha}{2 + \alpha} \cdot \left(0.16666666666666666 + \alpha \cdot -0.1388888888888889\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \alpha}{\left(\beta + 2\right) + \alpha} \cdot \frac{1}{\beta + 4}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 0.48)
   (*
    (/ (+ 1.0 alpha) (+ 2.0 alpha))
    (+ 0.16666666666666666 (* alpha -0.1388888888888889)))
   (* (/ (+ 1.0 alpha) (+ (+ beta 2.0) alpha)) (/ 1.0 (+ beta 4.0)))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 0.48) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0));
	}
	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 <= 0.48d0) then
        tmp = ((1.0d0 + alpha) / (2.0d0 + alpha)) * (0.16666666666666666d0 + (alpha * (-0.1388888888888889d0)))
    else
        tmp = ((1.0d0 + alpha) / ((beta + 2.0d0) + alpha)) * (1.0d0 / (beta + 4.0d0))
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 0.48) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0));
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 0.48:
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889))
	else:
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0))
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 0.48)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + alpha)) * Float64(0.16666666666666666 + Float64(alpha * -0.1388888888888889)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(Float64(beta + 2.0) + alpha)) * Float64(1.0 / Float64(beta + 4.0)));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 0.48)
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	else
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) * (1.0 / (beta + 4.0));
	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, 0.48], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision] * N[(0.16666666666666666 + N[(alpha * -0.1388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(beta + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 97.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 2.2:\\ \;\;\;\;\frac{1 + \alpha}{2 + \alpha} \cdot \left(0.16666666666666666 + \alpha \cdot -0.1388888888888889\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\left(\beta + 2\right) + \alpha}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 2.2)
   (*
    (/ (+ 1.0 alpha) (+ 2.0 alpha))
    (+ 0.16666666666666666 (* alpha -0.1388888888888889)))
   (/ (/ (+ 1.0 alpha) (+ (+ beta 2.0) alpha)) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.2) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + 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 <= 2.2d0) then
        tmp = ((1.0d0 + alpha) / (2.0d0 + alpha)) * (0.16666666666666666d0 + (alpha * (-0.1388888888888889d0)))
    else
        tmp = ((1.0d0 + alpha) / ((beta + 2.0d0) + alpha)) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.2) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 2.2:
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889))
	else:
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 2.2)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + alpha)) * Float64(0.16666666666666666 + Float64(alpha * -0.1388888888888889)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(Float64(beta + 2.0) + alpha)) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 2.2)
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	else
		tmp = ((1.0 + alpha) / ((beta + 2.0) + 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, 2.2], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision] * N[(0.16666666666666666 + N[(alpha * -0.1388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 12: 97.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 1.95:\\ \;\;\;\;\frac{1 + \alpha}{2 + \alpha} \cdot \left(0.16666666666666666 + \alpha \cdot -0.1388888888888889\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 + \alpha\right) \cdot \frac{1}{\beta}}{\left(\beta + 2\right) + \alpha}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 1.95)
   (*
    (/ (+ 1.0 alpha) (+ 2.0 alpha))
    (+ 0.16666666666666666 (* alpha -0.1388888888888889)))
   (/ (* (+ 1.0 alpha) (/ 1.0 beta)) (+ (+ beta 2.0) alpha))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 1.95) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = ((1.0 + alpha) * (1.0 / beta)) / ((beta + 2.0) + 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 (beta <= 1.95d0) then
        tmp = ((1.0d0 + alpha) / (2.0d0 + alpha)) * (0.16666666666666666d0 + (alpha * (-0.1388888888888889d0)))
    else
        tmp = ((1.0d0 + alpha) * (1.0d0 / beta)) / ((beta + 2.0d0) + alpha)
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 1.95) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = ((1.0 + alpha) * (1.0 / beta)) / ((beta + 2.0) + alpha);
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 1.95:
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889))
	else:
		tmp = ((1.0 + alpha) * (1.0 / beta)) / ((beta + 2.0) + alpha)
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 1.95)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + alpha)) * Float64(0.16666666666666666 + Float64(alpha * -0.1388888888888889)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) * Float64(1.0 / beta)) / Float64(Float64(beta + 2.0) + alpha));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 1.95)
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	else
		tmp = ((1.0 + alpha) * (1.0 / beta)) / ((beta + 2.0) + 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[beta, 1.95], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision] * N[(0.16666666666666666 + N[(alpha * -0.1388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] * N[(1.0 / beta), $MachinePrecision]), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 97.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 2.5:\\ \;\;\;\;\frac{1 + \alpha}{2 + \alpha} \cdot \left(0.16666666666666666 + \alpha \cdot -0.1388888888888889\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{\left(\beta + 2\right) + \alpha}{1 + \alpha}}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 2.5)
   (*
    (/ (+ 1.0 alpha) (+ 2.0 alpha))
    (+ 0.16666666666666666 (* alpha -0.1388888888888889)))
   (/ (/ 1.0 (/ (+ (+ beta 2.0) alpha) (+ 1.0 alpha))) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.5) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + 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 <= 2.5d0) then
        tmp = ((1.0d0 + alpha) / (2.0d0 + alpha)) * (0.16666666666666666d0 + (alpha * (-0.1388888888888889d0)))
    else
        tmp = (1.0d0 / (((beta + 2.0d0) + alpha) / (1.0d0 + alpha))) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.5) {
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	} else {
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + alpha))) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 2.5:
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889))
	else:
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + alpha))) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 2.5)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(2.0 + alpha)) * Float64(0.16666666666666666 + Float64(alpha * -0.1388888888888889)));
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(beta + 2.0) + alpha) / Float64(1.0 + alpha))) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 2.5)
		tmp = ((1.0 + alpha) / (2.0 + alpha)) * (0.16666666666666666 + (alpha * -0.1388888888888889));
	else
		tmp = (1.0 / (((beta + 2.0) + alpha) / (1.0 + 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, 2.5], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision] * N[(0.16666666666666666 + N[(alpha * -0.1388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision] / N[(1.0 + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 14: 96.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 2.7:\\ \;\;\;\;\frac{0.16666666666666666}{2 + \alpha}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\left(\beta + 2\right) + \alpha}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 2.7)
   (/ 0.16666666666666666 (+ 2.0 alpha))
   (/ (/ (+ 1.0 alpha) (+ (+ beta 2.0) alpha)) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.7) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + 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 <= 2.7d0) then
        tmp = 0.16666666666666666d0 / (2.0d0 + alpha)
    else
        tmp = ((1.0d0 + alpha) / ((beta + 2.0d0) + alpha)) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.7) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 2.7:
		tmp = 0.16666666666666666 / (2.0 + alpha)
	else:
		tmp = ((1.0 + alpha) / ((beta + 2.0) + alpha)) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 2.7)
		tmp = Float64(0.16666666666666666 / Float64(2.0 + alpha));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(Float64(beta + 2.0) + alpha)) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 2.7)
		tmp = 0.16666666666666666 / (2.0 + alpha);
	else
		tmp = ((1.0 + alpha) / ((beta + 2.0) + 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, 2.7], N[(0.16666666666666666 / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + 2.0), $MachinePrecision] + alpha), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 15: 91.7% accurate, 3.9× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 2.6:\\ \;\;\;\;\frac{0.16666666666666666}{2 + \alpha}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta + 2}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 2.6)
   (/ 0.16666666666666666 (+ 2.0 alpha))
   (/ (/ 1.0 beta) (+ beta 2.0))))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.6) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = (1.0 / beta) / (beta + 2.0);
	}
	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 <= 2.6d0) then
        tmp = 0.16666666666666666d0 / (2.0d0 + alpha)
    else
        tmp = (1.0d0 / beta) / (beta + 2.0d0)
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.6) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = (1.0 / beta) / (beta + 2.0);
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 2.6:
		tmp = 0.16666666666666666 / (2.0 + alpha)
	else:
		tmp = (1.0 / beta) / (beta + 2.0)
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 2.6)
		tmp = Float64(0.16666666666666666 / Float64(2.0 + alpha));
	else
		tmp = Float64(Float64(1.0 / beta) / Float64(beta + 2.0));
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 2.6)
		tmp = 0.16666666666666666 / (2.0 + alpha);
	else
		tmp = (1.0 / beta) / (beta + 2.0);
	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, 2.6], N[(0.16666666666666666 / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / beta), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 16: 96.7% accurate, 3.9× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 3.7:\\ \;\;\;\;\frac{0.16666666666666666}{2 + \alpha}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 3.7)
   (/ 0.16666666666666666 (+ 2.0 alpha))
   (/ (/ (+ 1.0 alpha) beta) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 3.7) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} 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 <= 3.7d0) then
        tmp = 0.16666666666666666d0 / (2.0d0 + alpha)
    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 <= 3.7) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = ((1.0 + alpha) / beta) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 3.7:
		tmp = 0.16666666666666666 / (2.0 + alpha)
	else:
		tmp = ((1.0 + alpha) / beta) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 3.7)
		tmp = Float64(0.16666666666666666 / Float64(2.0 + alpha));
	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 <= 3.7)
		tmp = 0.16666666666666666 / (2.0 + alpha);
	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, 3.7], N[(0.16666666666666666 / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / beta), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 17: 91.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 3.7:\\ \;\;\;\;\frac{0.16666666666666666}{2 + \alpha}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 3.7)
   (/ 0.16666666666666666 (+ 2.0 alpha))
   (/ (/ 1.0 beta) beta)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	double tmp;
	if (beta <= 3.7) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = (1.0 / 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 <= 3.7d0) then
        tmp = 0.16666666666666666d0 / (2.0d0 + alpha)
    else
        tmp = (1.0d0 / beta) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 3.7) {
		tmp = 0.16666666666666666 / (2.0 + alpha);
	} else {
		tmp = (1.0 / beta) / beta;
	}
	return tmp;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	tmp = 0
	if beta <= 3.7:
		tmp = 0.16666666666666666 / (2.0 + alpha)
	else:
		tmp = (1.0 / beta) / beta
	return tmp

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	tmp = 0.0
	if (beta <= 3.7)
		tmp = Float64(0.16666666666666666 / Float64(2.0 + alpha));
	else
		tmp = Float64(Float64(1.0 / beta) / beta);
	end
	return tmp
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 3.7)
		tmp = 0.16666666666666666 / (2.0 + alpha);
	else
		tmp = (1.0 / 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, 3.7], N[(0.16666666666666666 / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / beta), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 18: 45.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \frac{0.16666666666666666}{2 + \alpha} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 (/ 0.16666666666666666 (+ 2.0 alpha)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return 0.16666666666666666 / (2.0 + alpha);
}

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 = 0.16666666666666666d0 / (2.0d0 + alpha)
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return 0.16666666666666666 / (2.0 + alpha);
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return 0.16666666666666666 / (2.0 + alpha)

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return Float64(0.16666666666666666 / Float64(2.0 + alpha))
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = 0.16666666666666666 / (2.0 + alpha);
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := N[(0.16666666666666666 / N[(2.0 + alpha), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 19: 47.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ \frac{0.16666666666666666}{\beta + 2} \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 (/ 0.16666666666666666 (+ beta 2.0)))

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return 0.16666666666666666 / (beta + 2.0);
}

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 = 0.16666666666666666d0 / (beta + 2.0d0)
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return 0.16666666666666666 / (beta + 2.0);
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return 0.16666666666666666 / (beta + 2.0)

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return Float64(0.16666666666666666 / Float64(beta + 2.0))
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = 0.16666666666666666 / (beta + 2.0);
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := N[(0.16666666666666666 / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 20: 45.3% accurate, 35.0× speedup

Math

\[\begin{array}{l} [alpha, beta] = \mathsf{sort}([alpha, beta])\\ \\ 0.08333333333333333 \end{array} \]

FPCore

NOTE: alpha and beta should be sorted in increasing order before calling this function.
(FPCore (alpha beta) :precision binary64 0.08333333333333333)

C

assert(alpha < beta);
double code(double alpha, double beta) {
	return 0.08333333333333333;
}

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 = 0.08333333333333333d0
end function

Java

assert alpha < beta;
public static double code(double alpha, double beta) {
	return 0.08333333333333333;
}

Python

[alpha, beta] = sort([alpha, beta])
def code(alpha, beta):
	return 0.08333333333333333

Julia

alpha, beta = sort([alpha, beta])
function code(alpha, beta)
	return 0.08333333333333333
end

MATLAB

alpha, beta = num2cell(sort([alpha, beta])){:}
function tmp = code(alpha, beta)
	tmp = 0.08333333333333333;
end

Wolfram

NOTE: alpha and beta should be sorted in increasing order before calling this function.
code[alpha_, beta_] := 0.08333333333333333

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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)))