Octave 3.8, jcobi/3

Percentage Accurate: 94.6% → 99.8%

Time: 29.6s

Alternatives: 20

Speedup: 1.4×

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: 94.6% 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, 1.4× speedup

Math

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

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (/ (/ (* (+ 1.0 beta) (/ (+ 1.0 alpha) t_0)) t_0) (+ beta (+ alpha 3.0)))))

C

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

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

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = (((1.0 + beta) * ((1.0 + alpha) / t_0)) / t_0) / (beta + (alpha + 3.0));
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(1.0 + beta), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 97.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 2.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{1 + \alpha}{t_0 \cdot \left(\alpha + \left(\beta + 3\right)\right)} \cdot \frac{1 + \beta}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(1 + \beta\right) \cdot \frac{1 + \alpha}{t_0}}{t_0}}{\beta}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (if (<= beta 2.7e+139)
     (* (/ (+ 1.0 alpha) (* t_0 (+ alpha (+ beta 3.0)))) (/ (+ 1.0 beta) t_0))
     (/ (/ (* (+ 1.0 beta) (/ (+ 1.0 alpha) t_0)) t_0) beta))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 2.7e+139) {
		tmp = ((1.0 + alpha) / (t_0 * (alpha + (beta + 3.0)))) * ((1.0 + beta) / t_0);
	} else {
		tmp = (((1.0 + beta) * ((1.0 + alpha) / t_0)) / t_0) / beta;
	}
	return tmp;
}

Fortran

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 <= 2.7d+139) then
        tmp = ((1.0d0 + alpha) / (t_0 * (alpha + (beta + 3.0d0)))) * ((1.0d0 + beta) / t_0)
    else
        tmp = (((1.0d0 + beta) * ((1.0d0 + alpha) / t_0)) / t_0) / beta
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 2.7e+139) {
		tmp = ((1.0 + alpha) / (t_0 * (alpha + (beta + 3.0)))) * ((1.0 + beta) / t_0);
	} else {
		tmp = (((1.0 + beta) * ((1.0 + alpha) / t_0)) / t_0) / beta;
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	tmp = 0
	if beta <= 2.7e+139:
		tmp = ((1.0 + alpha) / (t_0 * (alpha + (beta + 3.0)))) * ((1.0 + beta) / t_0)
	else:
		tmp = (((1.0 + beta) * ((1.0 + alpha) / t_0)) / t_0) / beta
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	tmp = 0.0
	if (beta <= 2.7e+139)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(t_0 * Float64(alpha + Float64(beta + 3.0)))) * Float64(Float64(1.0 + beta) / t_0));
	else
		tmp = Float64(Float64(Float64(Float64(1.0 + beta) * Float64(Float64(1.0 + alpha) / t_0)) / t_0) / beta);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = 0.0;
	if (beta <= 2.7e+139)
		tmp = ((1.0 + alpha) / (t_0 * (alpha + (beta + 3.0)))) * ((1.0 + beta) / t_0);
	else
		tmp = (((1.0 + beta) * ((1.0 + alpha) / t_0)) / t_0) / beta;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 2.7e+139], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(t$95$0 * N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + beta), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(1.0 + beta), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / beta), $MachinePrecision]]]

Derivation

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

Alternative 3: 72.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 5.2 \cdot 10^{+74}:\\ \;\;\;\;\frac{\left(1 + \beta\right) \cdot \left(1 + \alpha\right)}{t_0 \cdot \left(\left(\beta + 2\right) \cdot \left(\beta + 3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{t_0}}{\beta + \left(\alpha + 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (if (<= beta 5.2e+74)
     (/ (* (+ 1.0 beta) (+ 1.0 alpha)) (* t_0 (* (+ beta 2.0) (+ beta 3.0))))
     (/ (/ (+ 1.0 alpha) t_0) (+ beta (+ alpha 3.0))))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 5.2e+74) {
		tmp = ((1.0 + beta) * (1.0 + alpha)) / (t_0 * ((beta + 2.0) * (beta + 3.0)));
	} else {
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Fortran

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 <= 5.2d+74) then
        tmp = ((1.0d0 + beta) * (1.0d0 + alpha)) / (t_0 * ((beta + 2.0d0) * (beta + 3.0d0)))
    else
        tmp = ((1.0d0 + alpha) / t_0) / (beta + (alpha + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 5.2e+74) {
		tmp = ((1.0 + beta) * (1.0 + alpha)) / (t_0 * ((beta + 2.0) * (beta + 3.0)));
	} else {
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	tmp = 0
	if beta <= 5.2e+74:
		tmp = ((1.0 + beta) * (1.0 + alpha)) / (t_0 * ((beta + 2.0) * (beta + 3.0)))
	else:
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0))
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	tmp = 0.0
	if (beta <= 5.2e+74)
		tmp = Float64(Float64(Float64(1.0 + beta) * Float64(1.0 + alpha)) / Float64(t_0 * Float64(Float64(beta + 2.0) * Float64(beta + 3.0))));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / t_0) / Float64(beta + Float64(alpha + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = 0.0;
	if (beta <= 5.2e+74)
		tmp = ((1.0 + beta) * (1.0 + alpha)) / (t_0 * ((beta + 2.0) * (beta + 3.0)));
	else
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 5.2e+74], N[(N[(N[(1.0 + beta), $MachinePrecision] * N[(1.0 + alpha), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * N[(N[(beta + 2.0), $MachinePrecision] * N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 72.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 7.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{1 + \beta}{t_0} \cdot \frac{1}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{t_0}}{\beta + \left(\alpha + 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (if (<= beta 7.4e+15)
     (* (/ (+ 1.0 beta) t_0) (/ 1.0 (* (+ beta 2.0) (+ beta 3.0))))
     (/ (/ (+ 1.0 alpha) t_0) (+ beta (+ alpha 3.0))))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 7.4e+15) {
		tmp = ((1.0 + beta) / t_0) * (1.0 / ((beta + 2.0) * (beta + 3.0)));
	} else {
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Fortran

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 <= 7.4d+15) then
        tmp = ((1.0d0 + beta) / t_0) * (1.0d0 / ((beta + 2.0d0) * (beta + 3.0d0)))
    else
        tmp = ((1.0d0 + alpha) / t_0) / (beta + (alpha + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 7.4e+15) {
		tmp = ((1.0 + beta) / t_0) * (1.0 / ((beta + 2.0) * (beta + 3.0)));
	} else {
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	tmp = 0
	if beta <= 7.4e+15:
		tmp = ((1.0 + beta) / t_0) * (1.0 / ((beta + 2.0) * (beta + 3.0)))
	else:
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0))
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	tmp = 0.0
	if (beta <= 7.4e+15)
		tmp = Float64(Float64(Float64(1.0 + beta) / t_0) * Float64(1.0 / Float64(Float64(beta + 2.0) * Float64(beta + 3.0))));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / t_0) / Float64(beta + Float64(alpha + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = 0.0;
	if (beta <= 7.4e+15)
		tmp = ((1.0 + beta) / t_0) * (1.0 / ((beta + 2.0) * (beta + 3.0)));
	else
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 7.4e+15], N[(N[(N[(1.0 + beta), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(1.0 / N[(N[(beta + 2.0), $MachinePrecision] * N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 72.3% accurate, 1.5× speedup

Math

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

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ 2.0 (+ beta alpha))))
   (/ (* (/ (+ 1.0 beta) t_0) (/ (+ 1.0 alpha) t_0)) (+ beta 3.0))))

C

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

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    t_0 = 2.0d0 + (beta + alpha)
    code = (((1.0d0 + beta) / t_0) * ((1.0d0 + alpha) / t_0)) / (beta + 3.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(alpha, beta)
	t_0 = 2.0 + (beta + alpha);
	tmp = (((1.0 + beta) / t_0) * ((1.0 + alpha) / t_0)) / (beta + 3.0);
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(1.0 + beta), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 72.3% accurate, 1.5× speedup

Math

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

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (/ (/ (* (+ 1.0 beta) (/ (+ 1.0 alpha) t_0)) t_0) (+ beta 3.0))))

C

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

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

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = (((1.0 + beta) * ((1.0 + alpha) / t_0)) / t_0) / (beta + 3.0);
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(1.0 + beta), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 72.3% accurate, 1.5× speedup

Math

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

FPCore

(FPCore (alpha beta)
 :precision binary64
 (/
  (/
   (/ (+ 1.0 alpha) (/ (+ beta (+ alpha 2.0)) (+ 1.0 beta)))
   (+ alpha (+ beta 2.0)))
  (+ beta 3.0)))

C

double code(double alpha, double beta) {
	return (((1.0 + alpha) / ((beta + (alpha + 2.0)) / (1.0 + beta))) / (alpha + (beta + 2.0))) / (beta + 3.0);
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = (((1.0d0 + alpha) / ((beta + (alpha + 2.0d0)) / (1.0d0 + beta))) / (alpha + (beta + 2.0d0))) / (beta + 3.0d0)
end function

Java

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

Python

def code(alpha, beta):
	return (((1.0 + alpha) / ((beta + (alpha + 2.0)) / (1.0 + beta))) / (alpha + (beta + 2.0))) / (beta + 3.0)

Julia

function code(alpha, beta)
	return Float64(Float64(Float64(Float64(1.0 + alpha) / Float64(Float64(beta + Float64(alpha + 2.0)) / Float64(1.0 + beta))) / Float64(alpha + Float64(beta + 2.0))) / Float64(beta + 3.0))
end

MATLAB

function tmp = code(alpha, beta)
	tmp = (((1.0 + alpha) / ((beta + (alpha + 2.0)) / (1.0 + beta))) / (alpha + (beta + 2.0))) / (beta + 3.0);
end

Wolfram

code[alpha_, beta_] := N[(N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + beta), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 8: 72.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{\frac{1 + \beta}{\beta + 2}}{t_0}}{\beta + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{t_0}}{\beta + \left(\alpha + 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))))
   (if (<= beta 2e+18)
     (/ (/ (/ (+ 1.0 beta) (+ beta 2.0)) t_0) (+ beta 3.0))
     (/ (/ (+ 1.0 alpha) t_0) (+ beta (+ alpha 3.0))))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 2e+18) {
		tmp = (((1.0 + beta) / (beta + 2.0)) / t_0) / (beta + 3.0);
	} else {
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Fortran

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 <= 2d+18) then
        tmp = (((1.0d0 + beta) / (beta + 2.0d0)) / t_0) / (beta + 3.0d0)
    else
        tmp = ((1.0d0 + alpha) / t_0) / (beta + (alpha + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double tmp;
	if (beta <= 2e+18) {
		tmp = (((1.0 + beta) / (beta + 2.0)) / t_0) / (beta + 3.0);
	} else {
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	tmp = 0
	if beta <= 2e+18:
		tmp = (((1.0 + beta) / (beta + 2.0)) / t_0) / (beta + 3.0)
	else:
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0))
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	tmp = 0.0
	if (beta <= 2e+18)
		tmp = Float64(Float64(Float64(Float64(1.0 + beta) / Float64(beta + 2.0)) / t_0) / Float64(beta + 3.0));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / t_0) / Float64(beta + Float64(alpha + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	tmp = 0.0;
	if (beta <= 2e+18)
		tmp = (((1.0 + beta) / (beta + 2.0)) / t_0) / (beta + 3.0);
	else
		tmp = ((1.0 + alpha) / t_0) / (beta + (alpha + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 2e+18], N[(N[(N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 71.5% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (alpha beta)
 :precision binary64
 (/
  (/ (* (+ 1.0 beta) (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0)))) (+ beta 2.0))
  (+ beta 3.0)))

C

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

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = (((1.0d0 + beta) * ((1.0d0 + alpha) / (alpha + (beta + 2.0d0)))) / (beta + 2.0d0)) / (beta + 3.0d0)
end function

Java

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

Python

def code(alpha, beta):
	return (((1.0 + beta) * ((1.0 + alpha) / (alpha + (beta + 2.0)))) / (beta + 2.0)) / (beta + 3.0)

Julia

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

MATLAB

function tmp = code(alpha, beta)
	tmp = (((1.0 + beta) * ((1.0 + alpha) / (alpha + (beta + 2.0)))) / (beta + 2.0)) / (beta + 3.0);
end

Wolfram

code[alpha_, beta_] := N[(N[(N[(N[(1.0 + beta), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 92.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 2.8:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + 2}}{\left(\alpha + 3\right) \cdot \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)}}{\beta + 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 2.8)
   (/ (/ (+ 1.0 alpha) (+ alpha 2.0)) (* (+ alpha 3.0) (+ alpha 2.0)))
   (/ (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0))) (+ beta 3.0))))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.8) {
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 2.8d0) then
        tmp = ((1.0d0 + alpha) / (alpha + 2.0d0)) / ((alpha + 3.0d0) * (alpha + 2.0d0))
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) / (beta + 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 2.8) {
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0);
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 2.8:
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0))
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0)
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 2.8)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + 2.0)) / Float64(Float64(alpha + 3.0) * Float64(alpha + 2.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) / Float64(beta + 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 2.8)
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0));
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 2.8], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(alpha + 3.0), $MachinePrecision] * N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 92.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 4.2:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + 2}}{\left(\alpha + 3\right) \cdot \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)}}{\beta + \left(\alpha + 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 4.2)
   (/ (/ (+ 1.0 alpha) (+ alpha 2.0)) (* (+ alpha 3.0) (+ alpha 2.0)))
   (/ (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0))) (+ beta (+ alpha 3.0)))))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 4.2) {
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 4.2d0) then
        tmp = ((1.0d0 + alpha) / (alpha + 2.0d0)) / ((alpha + 3.0d0) * (alpha + 2.0d0))
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) / (beta + (alpha + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 4.2) {
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 4.2:
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0))
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0))
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 4.2)
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + 2.0)) / Float64(Float64(alpha + 3.0) * Float64(alpha + 2.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) / Float64(beta + Float64(alpha + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 4.2)
		tmp = ((1.0 + alpha) / (alpha + 2.0)) / ((alpha + 3.0) * (alpha + 2.0));
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 4.2], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(alpha + 3.0), $MachinePrecision] * N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + alpha), $MachinePrecision] / N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 71.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 7.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{1 + \beta}{\beta + 2}}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)}}{\beta + \left(\alpha + 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 7.8e+15)
   (/ (/ (+ 1.0 beta) (+ beta 2.0)) (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0))) (+ beta (+ alpha 3.0)))))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 7.8e+15) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 7.8d+15) then
        tmp = ((1.0d0 + beta) / (beta + 2.0d0)) / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) / (beta + (alpha + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 7.8e+15) {
		tmp = ((1.0 + beta) / (beta + 2.0)) / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 7.8e+15:
		tmp = ((1.0 + beta) / (beta + 2.0)) / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0))
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 7.8e+15)
		tmp = Float64(Float64(Float64(1.0 + beta) / Float64(beta + 2.0)) / Float64(Float64(beta + 2.0) * Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) / Float64(beta + Float64(alpha + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 7.8e+15)
		tmp = ((1.0 + beta) / (beta + 2.0)) / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + (alpha + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 7.8e+15], N[(N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(beta + 2.0), $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[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 70.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 1.7:\\ \;\;\;\;\frac{0.5}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 2\right)}}{\beta + 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 1.7)
   (/ 0.5 (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) (+ alpha (+ beta 2.0))) (+ beta 3.0))))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 1.7) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 1.7d0) then
        tmp = 0.5d0 / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / (alpha + (beta + 2.0d0))) / (beta + 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 1.7) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0);
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 1.7:
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0)
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 1.7)
		tmp = Float64(0.5 / Float64(Float64(beta + 2.0) * Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / Float64(alpha + Float64(beta + 2.0))) / Float64(beta + 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 1.7)
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / (alpha + (beta + 2.0))) / (beta + 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 1.7], N[(0.5 / N[(N[(beta + 2.0), $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[(beta + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 70.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 4.5:\\ \;\;\;\;\frac{0.5}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\beta + \left(\alpha + 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 4.5)
   (/ 0.5 (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) beta) (+ beta (+ alpha 3.0)))))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 4.5) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 4.5d0) then
        tmp = 0.5d0 / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / beta) / (beta + (alpha + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 4.5) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / (beta + (alpha + 3.0));
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 4.5:
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / beta) / (beta + (alpha + 3.0))
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 4.5)
		tmp = Float64(0.5 / Float64(Float64(beta + 2.0) * Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / beta) / Float64(beta + Float64(alpha + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 4.5)
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / beta) / (beta + (alpha + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 4.5], 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] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 15: 70.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 9:\\ \;\;\;\;\frac{0.5}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\beta}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 9.0)
   (/ 0.5 (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) beta) beta)))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 9.0) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / beta;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 9.0d0) then
        tmp = 0.5d0 / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / beta) / beta
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 9.0) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / beta;
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 9.0:
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / beta) / beta
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 9.0)
		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

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 9.0)
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / beta) / beta;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 9.0], 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 16: 70.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\beta \leq 4.8:\\ \;\;\;\;\frac{0.5}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\beta + 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= beta 4.8)
   (/ 0.5 (* (+ beta 2.0) (+ beta 3.0)))
   (/ (/ (+ 1.0 alpha) beta) (+ beta 3.0))))

C

double code(double alpha, double beta) {
	double tmp;
	if (beta <= 4.8) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / (beta + 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (beta <= 4.8d0) then
        tmp = 0.5d0 / ((beta + 2.0d0) * (beta + 3.0d0))
    else
        tmp = ((1.0d0 + alpha) / beta) / (beta + 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (beta <= 4.8) {
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	} else {
		tmp = ((1.0 + alpha) / beta) / (beta + 3.0);
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if beta <= 4.8:
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0))
	else:
		tmp = ((1.0 + alpha) / beta) / (beta + 3.0)
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (beta <= 4.8)
		tmp = Float64(0.5 / Float64(Float64(beta + 2.0) * Float64(beta + 3.0)));
	else
		tmp = Float64(Float64(Float64(1.0 + alpha) / beta) / Float64(beta + 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 4.8)
		tmp = 0.5 / ((beta + 2.0) * (beta + 3.0));
	else
		tmp = ((1.0 + alpha) / beta) / (beta + 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 4.8], 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] / N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 26.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\beta \cdot \left(\beta + 3\right)} \end{array} \]

FPCore

(FPCore (alpha beta) :precision binary64 (/ 1.0 (* beta (+ beta 3.0))))

C

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

Fortran

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

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

Python

def code(alpha, beta):
	return 1.0 / (beta * (beta + 3.0))

Julia

function code(alpha, beta)
	return Float64(1.0 / Float64(beta * Float64(beta + 3.0)))
end

MATLAB

function tmp = code(alpha, beta)
	tmp = 1.0 / (beta * (beta + 3.0));
end

Wolfram

code[alpha_, beta_] := N[(1.0 / N[(beta * N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 18: 28.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1 + \alpha}{\beta}}{\beta} \end{array} \]

FPCore

(FPCore (alpha beta) :precision binary64 (/ (/ (+ 1.0 alpha) beta) beta))

C

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

Fortran

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

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

Python

def code(alpha, beta):
	return ((1.0 + alpha) / beta) / beta

Julia

function code(alpha, beta)
	return Float64(Float64(Float64(1.0 + alpha) / beta) / beta)
end

MATLAB

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

Wolfram

code[alpha_, beta_] := N[(N[(N[(1.0 + alpha), $MachinePrecision] / beta), $MachinePrecision] / beta), $MachinePrecision]

Derivation

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

Alternative 19: 4.2% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\alpha} \end{array} \]

FPCore

(FPCore (alpha beta) :precision binary64 (/ 1.0 alpha))

C

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

Fortran

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

Java

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

Python

def code(alpha, beta):
	return 1.0 / alpha

Julia

function code(alpha, beta)
	return Float64(1.0 / alpha)
end

MATLAB

function tmp = code(alpha, beta)
	tmp = 1.0 / alpha;
end

Wolfram

code[alpha_, beta_] := N[(1.0 / alpha), $MachinePrecision]

Derivation

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

Alternative 20: 4.2% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\beta} \end{array} \]

FPCore

(FPCore (alpha beta) :precision binary64 (/ 1.0 beta))

C

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

Fortran

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

Java

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

Python

def code(alpha, beta):
	return 1.0 / beta

Julia

function code(alpha, beta)
	return Float64(1.0 / beta)
end

MATLAB

function tmp = code(alpha, beta)
	tmp = 1.0 / beta;
end

Wolfram

code[alpha_, beta_] := N[(1.0 / beta), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024006 
(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)))