Octave 3.8, jcobi/1

Percentage Accurate: 74.8% → 99.9%

Time: 12.5s

Alternatives: 13

Speedup: 1.2×

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ t_1 := \frac{\alpha}{t_0}\\ t_2 := t_1 - -1\\ t_3 := \frac{\beta}{\beta + \left(\alpha + 2\right)}\\ \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.999:\\ \;\;\;\;\frac{t_3 - \frac{\mathsf{fma}\left(-4, {\left(\frac{\beta + 2}{\alpha}\right)}^{3}, 3 \cdot {\left(\frac{-2 - \beta}{\alpha}\right)}^{2} - \frac{4 + \beta \cdot 2}{\alpha}\right)}{t_2}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 - \frac{-1 + \frac{t_1}{\frac{t_0}{\alpha}}}{t_2}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0)))
        (t_1 (/ alpha t_0))
        (t_2 (- t_1 -1.0))
        (t_3 (/ beta (+ beta (+ alpha 2.0)))))
   (if (<= (/ (- beta alpha) (+ (+ beta alpha) 2.0)) -0.999)
     (/
      (-
       t_3
       (/
        (fma
         -4.0
         (pow (/ (+ beta 2.0) alpha) 3.0)
         (-
          (* 3.0 (pow (/ (- -2.0 beta) alpha) 2.0))
          (/ (+ 4.0 (* beta 2.0)) alpha)))
        t_2))
      2.0)
     (/ (- t_3 (/ (+ -1.0 (/ t_1 (/ t_0 alpha))) t_2)) 2.0))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = alpha / t_0;
	double t_2 = t_1 - -1.0;
	double t_3 = beta / (beta + (alpha + 2.0));
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.999) {
		tmp = (t_3 - (fma(-4.0, pow(((beta + 2.0) / alpha), 3.0), ((3.0 * pow(((-2.0 - beta) / alpha), 2.0)) - ((4.0 + (beta * 2.0)) / alpha))) / t_2)) / 2.0;
	} else {
		tmp = (t_3 - ((-1.0 + (t_1 / (t_0 / alpha))) / t_2)) / 2.0;
	}
	return tmp;
}

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	t_1 = Float64(alpha / t_0)
	t_2 = Float64(t_1 - -1.0)
	t_3 = Float64(beta / Float64(beta + Float64(alpha + 2.0)))
	tmp = 0.0
	if (Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0)) <= -0.999)
		tmp = Float64(Float64(t_3 - Float64(fma(-4.0, (Float64(Float64(beta + 2.0) / alpha) ^ 3.0), Float64(Float64(3.0 * (Float64(Float64(-2.0 - beta) / alpha) ^ 2.0)) - Float64(Float64(4.0 + Float64(beta * 2.0)) / alpha))) / t_2)) / 2.0);
	else
		tmp = Float64(Float64(t_3 - Float64(Float64(-1.0 + Float64(t_1 / Float64(t_0 / alpha))) / t_2)) / 2.0);
	end
	return tmp
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(alpha / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - -1.0), $MachinePrecision]}, Block[{t$95$3 = N[(beta / N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], -0.999], N[(N[(t$95$3 - N[(N[(-4.0 * N[Power[N[(N[(beta + 2.0), $MachinePrecision] / alpha), $MachinePrecision], 3.0], $MachinePrecision] + N[(N[(3.0 * N[Power[N[(N[(-2.0 - beta), $MachinePrecision] / alpha), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(t$95$3 - N[(N[(-1.0 + N[(t$95$1 / N[(t$95$0 / alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ t_1 := \frac{\beta}{\beta + \left(\alpha + 2\right)}\\ t_2 := \frac{\alpha}{t_0}\\ t_3 := t_2 - -1\\ \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.999:\\ \;\;\;\;\frac{t_1 + \frac{\frac{4 + \beta \cdot 2}{\alpha} - 3 \cdot {\left(\frac{-2 - \beta}{\alpha}\right)}^{2}}{t_3}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 - \frac{-1 + \frac{t_2}{\frac{t_0}{\alpha}}}{t_3}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0)))
        (t_1 (/ beta (+ beta (+ alpha 2.0))))
        (t_2 (/ alpha t_0))
        (t_3 (- t_2 -1.0)))
   (if (<= (/ (- beta alpha) (+ (+ beta alpha) 2.0)) -0.999)
     (/
      (+
       t_1
       (/
        (-
         (/ (+ 4.0 (* beta 2.0)) alpha)
         (* 3.0 (pow (/ (- -2.0 beta) alpha) 2.0)))
        t_3))
      2.0)
     (/ (- t_1 (/ (+ -1.0 (/ t_2 (/ t_0 alpha))) t_3)) 2.0))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = beta / (beta + (alpha + 2.0));
	double t_2 = alpha / t_0;
	double t_3 = t_2 - -1.0;
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.999) {
		tmp = (t_1 + ((((4.0 + (beta * 2.0)) / alpha) - (3.0 * pow(((-2.0 - beta) / alpha), 2.0))) / t_3)) / 2.0;
	} else {
		tmp = (t_1 - ((-1.0 + (t_2 / (t_0 / alpha))) / t_3)) / 2.0;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = alpha + (beta + 2.0d0)
    t_1 = beta / (beta + (alpha + 2.0d0))
    t_2 = alpha / t_0
    t_3 = t_2 - (-1.0d0)
    if (((beta - alpha) / ((beta + alpha) + 2.0d0)) <= (-0.999d0)) then
        tmp = (t_1 + ((((4.0d0 + (beta * 2.0d0)) / alpha) - (3.0d0 * ((((-2.0d0) - beta) / alpha) ** 2.0d0))) / t_3)) / 2.0d0
    else
        tmp = (t_1 - (((-1.0d0) + (t_2 / (t_0 / alpha))) / t_3)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = beta / (beta + (alpha + 2.0));
	double t_2 = alpha / t_0;
	double t_3 = t_2 - -1.0;
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.999) {
		tmp = (t_1 + ((((4.0 + (beta * 2.0)) / alpha) - (3.0 * Math.pow(((-2.0 - beta) / alpha), 2.0))) / t_3)) / 2.0;
	} else {
		tmp = (t_1 - ((-1.0 + (t_2 / (t_0 / alpha))) / t_3)) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	t_1 = beta / (beta + (alpha + 2.0))
	t_2 = alpha / t_0
	t_3 = t_2 - -1.0
	tmp = 0
	if ((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.999:
		tmp = (t_1 + ((((4.0 + (beta * 2.0)) / alpha) - (3.0 * math.pow(((-2.0 - beta) / alpha), 2.0))) / t_3)) / 2.0
	else:
		tmp = (t_1 - ((-1.0 + (t_2 / (t_0 / alpha))) / t_3)) / 2.0
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	t_1 = Float64(beta / Float64(beta + Float64(alpha + 2.0)))
	t_2 = Float64(alpha / t_0)
	t_3 = Float64(t_2 - -1.0)
	tmp = 0.0
	if (Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0)) <= -0.999)
		tmp = Float64(Float64(t_1 + Float64(Float64(Float64(Float64(4.0 + Float64(beta * 2.0)) / alpha) - Float64(3.0 * (Float64(Float64(-2.0 - beta) / alpha) ^ 2.0))) / t_3)) / 2.0);
	else
		tmp = Float64(Float64(t_1 - Float64(Float64(-1.0 + Float64(t_2 / Float64(t_0 / alpha))) / t_3)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	t_1 = beta / (beta + (alpha + 2.0));
	t_2 = alpha / t_0;
	t_3 = t_2 - -1.0;
	tmp = 0.0;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.999)
		tmp = (t_1 + ((((4.0 + (beta * 2.0)) / alpha) - (3.0 * (((-2.0 - beta) / alpha) ^ 2.0))) / t_3)) / 2.0;
	else
		tmp = (t_1 - ((-1.0 + (t_2 / (t_0 / alpha))) / t_3)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(beta / N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(alpha / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - -1.0), $MachinePrecision]}, If[LessEqual[N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], -0.999], N[(N[(t$95$1 + N[(N[(N[(N[(4.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] - N[(3.0 * N[Power[N[(N[(-2.0 - beta), $MachinePrecision] / alpha), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(t$95$1 - N[(N[(-1.0 + N[(t$95$2 / N[(t$95$0 / alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ t_1 := \left(-2 - \beta\right) - \beta\\ t_2 := \frac{\alpha}{t_0}\\ \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.9999998:\\ \;\;\;\;\frac{\frac{\beta + 2}{{\alpha}^{2}} \cdot t_1 - \frac{t_1}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta}{\beta + \left(\alpha + 2\right)} - \frac{-1 + \frac{t_2}{\frac{t_0}{\alpha}}}{t_2 - -1}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0)))
        (t_1 (- (- -2.0 beta) beta))
        (t_2 (/ alpha t_0)))
   (if (<= (/ (- beta alpha) (+ (+ beta alpha) 2.0)) -0.9999998)
     (/ (- (* (/ (+ beta 2.0) (pow alpha 2.0)) t_1) (/ t_1 alpha)) 2.0)
     (/
      (-
       (/ beta (+ beta (+ alpha 2.0)))
       (/ (+ -1.0 (/ t_2 (/ t_0 alpha))) (- t_2 -1.0)))
      2.0))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = (-2.0 - beta) - beta;
	double t_2 = alpha / t_0;
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998) {
		tmp = ((((beta + 2.0) / pow(alpha, 2.0)) * t_1) - (t_1 / alpha)) / 2.0;
	} else {
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_2 / (t_0 / alpha))) / (t_2 - -1.0))) / 2.0;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = alpha + (beta + 2.0d0)
    t_1 = ((-2.0d0) - beta) - beta
    t_2 = alpha / t_0
    if (((beta - alpha) / ((beta + alpha) + 2.0d0)) <= (-0.9999998d0)) then
        tmp = ((((beta + 2.0d0) / (alpha ** 2.0d0)) * t_1) - (t_1 / alpha)) / 2.0d0
    else
        tmp = ((beta / (beta + (alpha + 2.0d0))) - (((-1.0d0) + (t_2 / (t_0 / alpha))) / (t_2 - (-1.0d0)))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = (-2.0 - beta) - beta;
	double t_2 = alpha / t_0;
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998) {
		tmp = ((((beta + 2.0) / Math.pow(alpha, 2.0)) * t_1) - (t_1 / alpha)) / 2.0;
	} else {
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_2 / (t_0 / alpha))) / (t_2 - -1.0))) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	t_1 = (-2.0 - beta) - beta
	t_2 = alpha / t_0
	tmp = 0
	if ((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998:
		tmp = ((((beta + 2.0) / math.pow(alpha, 2.0)) * t_1) - (t_1 / alpha)) / 2.0
	else:
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_2 / (t_0 / alpha))) / (t_2 - -1.0))) / 2.0
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	t_1 = Float64(Float64(-2.0 - beta) - beta)
	t_2 = Float64(alpha / t_0)
	tmp = 0.0
	if (Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0)) <= -0.9999998)
		tmp = Float64(Float64(Float64(Float64(Float64(beta + 2.0) / (alpha ^ 2.0)) * t_1) - Float64(t_1 / alpha)) / 2.0);
	else
		tmp = Float64(Float64(Float64(beta / Float64(beta + Float64(alpha + 2.0))) - Float64(Float64(-1.0 + Float64(t_2 / Float64(t_0 / alpha))) / Float64(t_2 - -1.0))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	t_1 = (-2.0 - beta) - beta;
	t_2 = alpha / t_0;
	tmp = 0.0;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998)
		tmp = ((((beta + 2.0) / (alpha ^ 2.0)) * t_1) - (t_1 / alpha)) / 2.0;
	else
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_2 / (t_0 / alpha))) / (t_2 - -1.0))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-2.0 - beta), $MachinePrecision] - beta), $MachinePrecision]}, Block[{t$95$2 = N[(alpha / t$95$0), $MachinePrecision]}, If[LessEqual[N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], -0.9999998], N[(N[(N[(N[(N[(beta + 2.0), $MachinePrecision] / N[Power[alpha, 2.0], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(t$95$1 / alpha), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(beta / N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 + N[(t$95$2 / N[(t$95$0 / alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]]]

Derivation

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

Alternative 4: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ t_1 := \frac{\alpha}{t_0}\\ \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.9999998:\\ \;\;\;\;\frac{\frac{2 + \beta \cdot 2}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta}{\beta + \left(\alpha + 2\right)} - \frac{-1 + \frac{t_1}{\frac{t_0}{\alpha}}}{t_1 - -1}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ alpha (+ beta 2.0))) (t_1 (/ alpha t_0)))
   (if (<= (/ (- beta alpha) (+ (+ beta alpha) 2.0)) -0.9999998)
     (/ (/ (+ 2.0 (* beta 2.0)) alpha) 2.0)
     (/
      (-
       (/ beta (+ beta (+ alpha 2.0)))
       (/ (+ -1.0 (/ t_1 (/ t_0 alpha))) (- t_1 -1.0)))
      2.0))))

C

double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = alpha / t_0;
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998) {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	} else {
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_1 / (t_0 / alpha))) / (t_1 - -1.0))) / 2.0;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = alpha + (beta + 2.0d0)
    t_1 = alpha / t_0
    if (((beta - alpha) / ((beta + alpha) + 2.0d0)) <= (-0.9999998d0)) then
        tmp = ((2.0d0 + (beta * 2.0d0)) / alpha) / 2.0d0
    else
        tmp = ((beta / (beta + (alpha + 2.0d0))) - (((-1.0d0) + (t_1 / (t_0 / alpha))) / (t_1 - (-1.0d0)))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = alpha + (beta + 2.0);
	double t_1 = alpha / t_0;
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998) {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	} else {
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_1 / (t_0 / alpha))) / (t_1 - -1.0))) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = alpha + (beta + 2.0)
	t_1 = alpha / t_0
	tmp = 0
	if ((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998:
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0
	else:
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_1 / (t_0 / alpha))) / (t_1 - -1.0))) / 2.0
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(alpha + Float64(beta + 2.0))
	t_1 = Float64(alpha / t_0)
	tmp = 0.0
	if (Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0)) <= -0.9999998)
		tmp = Float64(Float64(Float64(2.0 + Float64(beta * 2.0)) / alpha) / 2.0);
	else
		tmp = Float64(Float64(Float64(beta / Float64(beta + Float64(alpha + 2.0))) - Float64(Float64(-1.0 + Float64(t_1 / Float64(t_0 / alpha))) / Float64(t_1 - -1.0))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = alpha + (beta + 2.0);
	t_1 = alpha / t_0;
	tmp = 0.0;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998)
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	else
		tmp = ((beta / (beta + (alpha + 2.0))) - ((-1.0 + (t_1 / (t_0 / alpha))) / (t_1 - -1.0))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(alpha / t$95$0), $MachinePrecision]}, If[LessEqual[N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], -0.9999998], N[(N[(N[(2.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(beta / N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 + N[(t$95$1 / N[(t$95$0 / alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]]

Derivation

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

Alternative 5: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.9999998:\\ \;\;\;\;\frac{\frac{2 + \beta \cdot 2}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{1}{\frac{\alpha + \left(\beta + 2\right)}{\beta - \alpha}}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= (/ (- beta alpha) (+ (+ beta alpha) 2.0)) -0.9999998)
   (/ (/ (+ 2.0 (* beta 2.0)) alpha) 2.0)
   (/ (+ 1.0 (/ 1.0 (/ (+ alpha (+ beta 2.0)) (- beta alpha)))) 2.0)))

C

double code(double alpha, double beta) {
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998) {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	} else {
		tmp = (1.0 + (1.0 / ((alpha + (beta + 2.0)) / (beta - alpha)))) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (((beta - alpha) / ((beta + alpha) + 2.0d0)) <= (-0.9999998d0)) then
        tmp = ((2.0d0 + (beta * 2.0d0)) / alpha) / 2.0d0
    else
        tmp = (1.0d0 + (1.0d0 / ((alpha + (beta + 2.0d0)) / (beta - alpha)))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998) {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	} else {
		tmp = (1.0 + (1.0 / ((alpha + (beta + 2.0)) / (beta - alpha)))) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if ((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998:
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0
	else:
		tmp = (1.0 + (1.0 / ((alpha + (beta + 2.0)) / (beta - alpha)))) / 2.0
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0)) <= -0.9999998)
		tmp = Float64(Float64(Float64(2.0 + Float64(beta * 2.0)) / alpha) / 2.0);
	else
		tmp = Float64(Float64(1.0 + Float64(1.0 / Float64(Float64(alpha + Float64(beta + 2.0)) / Float64(beta - alpha)))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.9999998)
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	else
		tmp = (1.0 + (1.0 / ((alpha + (beta + 2.0)) / (beta - alpha)))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], -0.9999998], N[(N[(N[(2.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(1.0 + N[(1.0 / N[(N[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision] / N[(beta - alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

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

Alternative 6: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2}\\ \mathbf{if}\;t_0 \leq -0.9999998:\\ \;\;\;\;\frac{\frac{2 + \beta \cdot 2}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 + 1}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (/ (- beta alpha) (+ (+ beta alpha) 2.0))))
   (if (<= t_0 -0.9999998)
     (/ (/ (+ 2.0 (* beta 2.0)) alpha) 2.0)
     (/ (+ t_0 1.0) 2.0))))

C

double code(double alpha, double beta) {
	double t_0 = (beta - alpha) / ((beta + alpha) + 2.0);
	double tmp;
	if (t_0 <= -0.9999998) {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	} else {
		tmp = (t_0 + 1.0) / 2.0;
	}
	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 = (beta - alpha) / ((beta + alpha) + 2.0d0)
    if (t_0 <= (-0.9999998d0)) then
        tmp = ((2.0d0 + (beta * 2.0d0)) / alpha) / 2.0d0
    else
        tmp = (t_0 + 1.0d0) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double t_0 = (beta - alpha) / ((beta + alpha) + 2.0);
	double tmp;
	if (t_0 <= -0.9999998) {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	} else {
		tmp = (t_0 + 1.0) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	t_0 = (beta - alpha) / ((beta + alpha) + 2.0)
	tmp = 0
	if t_0 <= -0.9999998:
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0
	else:
		tmp = (t_0 + 1.0) / 2.0
	return tmp

Julia

function code(alpha, beta)
	t_0 = Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0))
	tmp = 0.0
	if (t_0 <= -0.9999998)
		tmp = Float64(Float64(Float64(2.0 + Float64(beta * 2.0)) / alpha) / 2.0);
	else
		tmp = Float64(Float64(t_0 + 1.0) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	t_0 = (beta - alpha) / ((beta + alpha) + 2.0);
	tmp = 0.0;
	if (t_0 <= -0.9999998)
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	else
		tmp = (t_0 + 1.0) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := Block[{t$95$0 = N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.9999998], N[(N[(N[(2.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(t$95$0 + 1.0), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

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

Alternative 7: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 31500000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;\alpha \leq 3.5 \cdot 10^{+219} \lor \neg \left(\alpha \leq 1.85 \cdot 10^{+252}\right):\\ \;\;\;\;\frac{\frac{2}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{\beta}{\alpha}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 31500000000000.0)
   1.0
   (if (or (<= alpha 3.5e+219) (not (<= alpha 1.85e+252)))
     (/ (/ 2.0 alpha) 2.0)
     (/ (* 2.0 (/ beta alpha)) 2.0))))

C

double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 31500000000000.0) {
		tmp = 1.0;
	} else if ((alpha <= 3.5e+219) || !(alpha <= 1.85e+252)) {
		tmp = (2.0 / alpha) / 2.0;
	} else {
		tmp = (2.0 * (beta / alpha)) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 31500000000000.0d0) then
        tmp = 1.0d0
    else if ((alpha <= 3.5d+219) .or. (.not. (alpha <= 1.85d+252))) then
        tmp = (2.0d0 / alpha) / 2.0d0
    else
        tmp = (2.0d0 * (beta / alpha)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 31500000000000.0) {
		tmp = 1.0;
	} else if ((alpha <= 3.5e+219) || !(alpha <= 1.85e+252)) {
		tmp = (2.0 / alpha) / 2.0;
	} else {
		tmp = (2.0 * (beta / alpha)) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if alpha <= 31500000000000.0:
		tmp = 1.0
	elif (alpha <= 3.5e+219) or not (alpha <= 1.85e+252):
		tmp = (2.0 / alpha) / 2.0
	else:
		tmp = (2.0 * (beta / alpha)) / 2.0
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 31500000000000.0)
		tmp = 1.0;
	elseif ((alpha <= 3.5e+219) || !(alpha <= 1.85e+252))
		tmp = Float64(Float64(2.0 / alpha) / 2.0);
	else
		tmp = Float64(Float64(2.0 * Float64(beta / alpha)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 31500000000000.0)
		tmp = 1.0;
	elseif ((alpha <= 3.5e+219) || ~((alpha <= 1.85e+252)))
		tmp = (2.0 / alpha) / 2.0;
	else
		tmp = (2.0 * (beta / alpha)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[alpha, 31500000000000.0], 1.0, If[Or[LessEqual[alpha, 3.5e+219], N[Not[LessEqual[alpha, 1.85e+252]], $MachinePrecision]], N[(N[(2.0 / alpha), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(2.0 * N[(beta / alpha), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

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

Alternative 8: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 31500000000000:\\ \;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\ \mathbf{elif}\;\alpha \leq 3.5 \cdot 10^{+219} \lor \neg \left(\alpha \leq 1.7 \cdot 10^{+252}\right):\\ \;\;\;\;\frac{\frac{\beta + 2}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{\beta}{\alpha}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 31500000000000.0)
   (/ (+ 1.0 (/ beta (+ beta 2.0))) 2.0)
   (if (or (<= alpha 3.5e+219) (not (<= alpha 1.7e+252)))
     (/ (/ (+ beta 2.0) alpha) 2.0)
     (/ (* 2.0 (/ beta alpha)) 2.0))))

C

double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 31500000000000.0) {
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0;
	} else if ((alpha <= 3.5e+219) || !(alpha <= 1.7e+252)) {
		tmp = ((beta + 2.0) / alpha) / 2.0;
	} else {
		tmp = (2.0 * (beta / alpha)) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 31500000000000.0d0) then
        tmp = (1.0d0 + (beta / (beta + 2.0d0))) / 2.0d0
    else if ((alpha <= 3.5d+219) .or. (.not. (alpha <= 1.7d+252))) then
        tmp = ((beta + 2.0d0) / alpha) / 2.0d0
    else
        tmp = (2.0d0 * (beta / alpha)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 31500000000000.0) {
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0;
	} else if ((alpha <= 3.5e+219) || !(alpha <= 1.7e+252)) {
		tmp = ((beta + 2.0) / alpha) / 2.0;
	} else {
		tmp = (2.0 * (beta / alpha)) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if alpha <= 31500000000000.0:
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0
	elif (alpha <= 3.5e+219) or not (alpha <= 1.7e+252):
		tmp = ((beta + 2.0) / alpha) / 2.0
	else:
		tmp = (2.0 * (beta / alpha)) / 2.0
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 31500000000000.0)
		tmp = Float64(Float64(1.0 + Float64(beta / Float64(beta + 2.0))) / 2.0);
	elseif ((alpha <= 3.5e+219) || !(alpha <= 1.7e+252))
		tmp = Float64(Float64(Float64(beta + 2.0) / alpha) / 2.0);
	else
		tmp = Float64(Float64(2.0 * Float64(beta / alpha)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 31500000000000.0)
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0;
	elseif ((alpha <= 3.5e+219) || ~((alpha <= 1.7e+252)))
		tmp = ((beta + 2.0) / alpha) / 2.0;
	else
		tmp = (2.0 * (beta / alpha)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[alpha, 31500000000000.0], N[(N[(1.0 + N[(beta / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[Or[LessEqual[alpha, 3.5e+219], N[Not[LessEqual[alpha, 1.7e+252]], $MachinePrecision]], N[(N[(N[(beta + 2.0), $MachinePrecision] / alpha), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(2.0 * N[(beta / alpha), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

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

Alternative 9: 93.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 31500000000000:\\ \;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2 + \beta \cdot 2}{\alpha}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 31500000000000.0)
   (/ (+ 1.0 (/ beta (+ beta 2.0))) 2.0)
   (/ (/ (+ 2.0 (* beta 2.0)) alpha) 2.0)))

C

double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 31500000000000.0) {
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0;
	} else {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 31500000000000.0d0) then
        tmp = (1.0d0 + (beta / (beta + 2.0d0))) / 2.0d0
    else
        tmp = ((2.0d0 + (beta * 2.0d0)) / alpha) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 31500000000000.0) {
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0;
	} else {
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if alpha <= 31500000000000.0:
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0
	else:
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 31500000000000.0)
		tmp = Float64(Float64(1.0 + Float64(beta / Float64(beta + 2.0))) / 2.0);
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(beta * 2.0)) / alpha) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 31500000000000.0)
		tmp = (1.0 + (beta / (beta + 2.0))) / 2.0;
	else
		tmp = ((2.0 + (beta * 2.0)) / alpha) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[alpha, 31500000000000.0], N[(N[(1.0 + N[(beta / N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(2.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

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

Alternative 10: 71.6% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 2.0], N[(N[(1.0 + N[(beta * 0.5), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], 1.0]

Derivation

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

Alternative 11: 71.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[alpha_, beta_] := If[LessEqual[beta, 2.0], N[(N[(1.0 + N[(beta * 0.5), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(2.0 - N[(2.0 / beta), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

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

Alternative 12: 51.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\alpha \leq 1.5 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{\alpha}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (if (<= alpha 1.5e+15) 1.0 (/ (/ 2.0 alpha) 2.0)))

C

double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 1.5e+15) {
		tmp = 1.0;
	} else {
		tmp = (2.0 / alpha) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: tmp
    if (alpha <= 1.5d+15) then
        tmp = 1.0d0
    else
        tmp = (2.0d0 / alpha) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 1.5e+15) {
		tmp = 1.0;
	} else {
		tmp = (2.0 / alpha) / 2.0;
	}
	return tmp;
}

Python

def code(alpha, beta):
	tmp = 0
	if alpha <= 1.5e+15:
		tmp = 1.0
	else:
		tmp = (2.0 / alpha) / 2.0
	return tmp

Julia

function code(alpha, beta)
	tmp = 0.0
	if (alpha <= 1.5e+15)
		tmp = 1.0;
	else
		tmp = Float64(Float64(2.0 / alpha) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(alpha, beta)
	tmp = 0.0;
	if (alpha <= 1.5e+15)
		tmp = 1.0;
	else
		tmp = (2.0 / alpha) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[alpha_, beta_] := If[LessEqual[alpha, 1.5e+15], 1.0, N[(N[(2.0 / alpha), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

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

Alternative 13: 37.2% accurate, 13.0× speedup

Math

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

FPCore

(FPCore (alpha beta) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(alpha, beta):
	return 1.0

Julia

function code(alpha, beta)
	return 1.0
end

MATLAB

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

Wolfram

code[alpha_, beta_] := 1.0

Derivation

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

Reproduce

herbie shell --seed 2023340 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/1"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0))