Octave 3.8, jcobi/4

Percentage Accurate: 15.6% → 84.9%

Time: 24.9s

Alternatives: 12

Speedup: 53.0×

Specification

\[\left(\alpha > -1 \land \beta > -1\right) \land i > 1\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := i \cdot \left(\left(\alpha + \beta\right) + i\right)\\ t_1 := \left(\alpha + \beta\right) + 2 \cdot i\\ t_2 := t_1 \cdot t_1\\ \frac{\frac{t_0 \cdot \left(\beta \cdot \alpha + t_0\right)}{t_2}}{t_2 - 1} \end{array} \end{array} \]

FPCore

(FPCore (alpha beta i)
 :precision binary64
 (let* ((t_0 (* i (+ (+ alpha beta) i)))
        (t_1 (+ (+ alpha beta) (* 2.0 i)))
        (t_2 (* t_1 t_1)))
   (/ (/ (* t_0 (+ (* beta alpha) t_0)) t_2) (- t_2 1.0))))

C

double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Fortran

real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = i * ((alpha + beta) + i)
    t_1 = (alpha + beta) + (2.0d0 * i)
    t_2 = t_1 * t_1
    code = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0d0)
end function

Java

public static double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Python

def code(alpha, beta, i):
	t_0 = i * ((alpha + beta) + i)
	t_1 = (alpha + beta) + (2.0 * i)
	t_2 = t_1 * t_1
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0)

Julia

function code(alpha, beta, i)
	t_0 = Float64(i * Float64(Float64(alpha + beta) + i))
	t_1 = Float64(Float64(alpha + beta) + Float64(2.0 * i))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(Float64(t_0 * Float64(Float64(beta * alpha) + t_0)) / t_2) / Float64(t_2 - 1.0))
end

MATLAB

function tmp = code(alpha, beta, i)
	t_0 = i * ((alpha + beta) + i);
	t_1 = (alpha + beta) + (2.0 * i);
	t_2 = t_1 * t_1;
	tmp = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
end

Wolfram

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

Initial Program: 15.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := i \cdot \left(\left(\alpha + \beta\right) + i\right)\\ t_1 := \left(\alpha + \beta\right) + 2 \cdot i\\ t_2 := t_1 \cdot t_1\\ \frac{\frac{t_0 \cdot \left(\beta \cdot \alpha + t_0\right)}{t_2}}{t_2 - 1} \end{array} \end{array} \]

FPCore

(FPCore (alpha beta i)
 :precision binary64
 (let* ((t_0 (* i (+ (+ alpha beta) i)))
        (t_1 (+ (+ alpha beta) (* 2.0 i)))
        (t_2 (* t_1 t_1)))
   (/ (/ (* t_0 (+ (* beta alpha) t_0)) t_2) (- t_2 1.0))))

C

double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Fortran

real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = i * ((alpha + beta) + i)
    t_1 = (alpha + beta) + (2.0d0 * i)
    t_2 = t_1 * t_1
    code = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0d0)
end function

Java

public static double code(double alpha, double beta, double i) {
	double t_0 = i * ((alpha + beta) + i);
	double t_1 = (alpha + beta) + (2.0 * i);
	double t_2 = t_1 * t_1;
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
}

Python

def code(alpha, beta, i):
	t_0 = i * ((alpha + beta) + i)
	t_1 = (alpha + beta) + (2.0 * i)
	t_2 = t_1 * t_1
	return ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0)

Julia

function code(alpha, beta, i)
	t_0 = Float64(i * Float64(Float64(alpha + beta) + i))
	t_1 = Float64(Float64(alpha + beta) + Float64(2.0 * i))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(Float64(t_0 * Float64(Float64(beta * alpha) + t_0)) / t_2) / Float64(t_2 - 1.0))
end

MATLAB

function tmp = code(alpha, beta, i)
	t_0 = i * ((alpha + beta) + i);
	t_1 = (alpha + beta) + (2.0 * i);
	t_2 = t_1 * t_1;
	tmp = ((t_0 * ((beta * alpha) + t_0)) / t_2) / (t_2 - 1.0);
end

Wolfram

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

Alternative 1: 84.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} t_0 := \mathsf{fma}\left(i, 2, \beta + \alpha\right)\\ t_1 := \frac{i}{t_0}\\ t_2 := \left(\beta + \alpha\right) + i \cdot 2\\ t_3 := \alpha + \left(\beta + i\right)\\ \mathbf{if}\;\beta \leq 6 \cdot 10^{+31}:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;\beta \leq 4.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{t_3}{t_0} \cdot \left(t_1 \cdot \mathsf{fma}\left(i, t_3, \beta \cdot \alpha\right)\right)}{t_2 \cdot t_2 + -1}\\ \mathbf{elif}\;\beta \leq 1.34 \cdot 10^{+178}:\\ \;\;\;\;\left(t_1 \cdot \frac{\beta + i}{\beta + i \cdot 2}\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(i, 2, \beta + 1\right)} \cdot \frac{i}{\frac{\mathsf{fma}\left(i, 2, \beta + -1\right)}{\alpha + i}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (let* ((t_0 (fma i 2.0 (+ beta alpha)))
        (t_1 (/ i t_0))
        (t_2 (+ (+ beta alpha) (* i 2.0)))
        (t_3 (+ alpha (+ beta i))))
   (if (<= beta 6e+31)
     0.0625
     (if (<= beta 4.4e+43)
       (/
        (* (/ t_3 t_0) (* t_1 (fma i t_3 (* beta alpha))))
        (+ (* t_2 t_2) -1.0))
       (if (<= beta 1.34e+178)
         (* (* t_1 (/ (+ beta i) (+ beta (* i 2.0)))) 0.25)
         (*
          (/ 1.0 (fma i 2.0 (+ beta 1.0)))
          (/ i (/ (fma i 2.0 (+ beta -1.0)) (+ alpha i)))))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double t_0 = fma(i, 2.0, (beta + alpha));
	double t_1 = i / t_0;
	double t_2 = (beta + alpha) + (i * 2.0);
	double t_3 = alpha + (beta + i);
	double tmp;
	if (beta <= 6e+31) {
		tmp = 0.0625;
	} else if (beta <= 4.4e+43) {
		tmp = ((t_3 / t_0) * (t_1 * fma(i, t_3, (beta * alpha)))) / ((t_2 * t_2) + -1.0);
	} else if (beta <= 1.34e+178) {
		tmp = (t_1 * ((beta + i) / (beta + (i * 2.0)))) * 0.25;
	} else {
		tmp = (1.0 / fma(i, 2.0, (beta + 1.0))) * (i / (fma(i, 2.0, (beta + -1.0)) / (alpha + i)));
	}
	return tmp;
}

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	t_0 = fma(i, 2.0, Float64(beta + alpha))
	t_1 = Float64(i / t_0)
	t_2 = Float64(Float64(beta + alpha) + Float64(i * 2.0))
	t_3 = Float64(alpha + Float64(beta + i))
	tmp = 0.0
	if (beta <= 6e+31)
		tmp = 0.0625;
	elseif (beta <= 4.4e+43)
		tmp = Float64(Float64(Float64(t_3 / t_0) * Float64(t_1 * fma(i, t_3, Float64(beta * alpha)))) / Float64(Float64(t_2 * t_2) + -1.0));
	elseif (beta <= 1.34e+178)
		tmp = Float64(Float64(t_1 * Float64(Float64(beta + i) / Float64(beta + Float64(i * 2.0)))) * 0.25);
	else
		tmp = Float64(Float64(1.0 / fma(i, 2.0, Float64(beta + 1.0))) * Float64(i / Float64(fma(i, 2.0, Float64(beta + -1.0)) / Float64(alpha + i))));
	end
	return tmp
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := Block[{t$95$0 = N[(i * 2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(i / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(beta + alpha), $MachinePrecision] + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(alpha + N[(beta + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 6e+31], 0.0625, If[LessEqual[beta, 4.4e+43], N[(N[(N[(t$95$3 / t$95$0), $MachinePrecision] * N[(t$95$1 * N[(i * t$95$3 + N[(beta * alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$2 * t$95$2), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[beta, 1.34e+178], N[(N[(t$95$1 * N[(N[(beta + i), $MachinePrecision] / N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision], N[(N[(1.0 / N[(i * 2.0 + N[(beta + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0 + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 2: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} t_0 := \beta + i \cdot 2\\ t_1 := \mathsf{fma}\left(i, 2, \beta + \alpha\right)\\ t_2 := \frac{i}{t_1}\\ \mathbf{if}\;\beta \leq 6 \cdot 10^{+31}:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;\beta \leq 4.4 \cdot 10^{+43}:\\ \;\;\;\;\left(t_2 \cdot \frac{i + \left(\beta + \alpha\right)}{t_1}\right) \cdot \frac{i \cdot \left(\beta + i\right)}{\left(t_0 \cdot \left(i \cdot 2\right) + \beta \cdot t_0\right) + -1}\\ \mathbf{elif}\;\beta \leq 1.08 \cdot 10^{+178}:\\ \;\;\;\;\left(t_2 \cdot \frac{\beta + i}{t_0}\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(i, 2, \beta + 1\right)} \cdot \frac{i}{\frac{\mathsf{fma}\left(i, 2, \beta + -1\right)}{\alpha + i}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (let* ((t_0 (+ beta (* i 2.0)))
        (t_1 (fma i 2.0 (+ beta alpha)))
        (t_2 (/ i t_1)))
   (if (<= beta 6e+31)
     0.0625
     (if (<= beta 4.4e+43)
       (*
        (* t_2 (/ (+ i (+ beta alpha)) t_1))
        (/ (* i (+ beta i)) (+ (+ (* t_0 (* i 2.0)) (* beta t_0)) -1.0)))
       (if (<= beta 1.08e+178)
         (* (* t_2 (/ (+ beta i) t_0)) 0.25)
         (*
          (/ 1.0 (fma i 2.0 (+ beta 1.0)))
          (/ i (/ (fma i 2.0 (+ beta -1.0)) (+ alpha i)))))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double t_0 = beta + (i * 2.0);
	double t_1 = fma(i, 2.0, (beta + alpha));
	double t_2 = i / t_1;
	double tmp;
	if (beta <= 6e+31) {
		tmp = 0.0625;
	} else if (beta <= 4.4e+43) {
		tmp = (t_2 * ((i + (beta + alpha)) / t_1)) * ((i * (beta + i)) / (((t_0 * (i * 2.0)) + (beta * t_0)) + -1.0));
	} else if (beta <= 1.08e+178) {
		tmp = (t_2 * ((beta + i) / t_0)) * 0.25;
	} else {
		tmp = (1.0 / fma(i, 2.0, (beta + 1.0))) * (i / (fma(i, 2.0, (beta + -1.0)) / (alpha + i)));
	}
	return tmp;
}

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	t_0 = Float64(beta + Float64(i * 2.0))
	t_1 = fma(i, 2.0, Float64(beta + alpha))
	t_2 = Float64(i / t_1)
	tmp = 0.0
	if (beta <= 6e+31)
		tmp = 0.0625;
	elseif (beta <= 4.4e+43)
		tmp = Float64(Float64(t_2 * Float64(Float64(i + Float64(beta + alpha)) / t_1)) * Float64(Float64(i * Float64(beta + i)) / Float64(Float64(Float64(t_0 * Float64(i * 2.0)) + Float64(beta * t_0)) + -1.0)));
	elseif (beta <= 1.08e+178)
		tmp = Float64(Float64(t_2 * Float64(Float64(beta + i) / t_0)) * 0.25);
	else
		tmp = Float64(Float64(1.0 / fma(i, 2.0, Float64(beta + 1.0))) * Float64(i / Float64(fma(i, 2.0, Float64(beta + -1.0)) / Float64(alpha + i))));
	end
	return tmp
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := Block[{t$95$0 = N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(i * 2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i / t$95$1), $MachinePrecision]}, If[LessEqual[beta, 6e+31], 0.0625, If[LessEqual[beta, 4.4e+43], N[(N[(t$95$2 * N[(N[(i + N[(beta + alpha), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * N[(N[(i * N[(beta + i), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t$95$0 * N[(i * 2.0), $MachinePrecision]), $MachinePrecision] + N[(beta * t$95$0), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[beta, 1.08e+178], N[(N[(t$95$2 * N[(N[(beta + i), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision], N[(N[(1.0 / N[(i * 2.0 + N[(beta + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0 + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 3: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} t_0 := \beta + i \cdot 2\\ t_1 := \frac{i}{\mathsf{fma}\left(i, 2, \beta + \alpha\right)} \cdot \frac{\beta + i}{t_0}\\ \mathbf{if}\;\beta \leq 6 \cdot 10^{+31}:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;\beta \leq 4.4 \cdot 10^{+43}:\\ \;\;\;\;t_1 \cdot \frac{i \cdot \left(\beta + i\right)}{{t_0}^{2} + -1}\\ \mathbf{elif}\;\beta \leq 1.08 \cdot 10^{+178}:\\ \;\;\;\;t_1 \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(i, 2, \beta + 1\right)} \cdot \frac{i}{\frac{\mathsf{fma}\left(i, 2, \beta + -1\right)}{\alpha + i}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (let* ((t_0 (+ beta (* i 2.0)))
        (t_1 (* (/ i (fma i 2.0 (+ beta alpha))) (/ (+ beta i) t_0))))
   (if (<= beta 6e+31)
     0.0625
     (if (<= beta 4.4e+43)
       (* t_1 (/ (* i (+ beta i)) (+ (pow t_0 2.0) -1.0)))
       (if (<= beta 1.08e+178)
         (* t_1 0.25)
         (*
          (/ 1.0 (fma i 2.0 (+ beta 1.0)))
          (/ i (/ (fma i 2.0 (+ beta -1.0)) (+ alpha i)))))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double t_0 = beta + (i * 2.0);
	double t_1 = (i / fma(i, 2.0, (beta + alpha))) * ((beta + i) / t_0);
	double tmp;
	if (beta <= 6e+31) {
		tmp = 0.0625;
	} else if (beta <= 4.4e+43) {
		tmp = t_1 * ((i * (beta + i)) / (pow(t_0, 2.0) + -1.0));
	} else if (beta <= 1.08e+178) {
		tmp = t_1 * 0.25;
	} else {
		tmp = (1.0 / fma(i, 2.0, (beta + 1.0))) * (i / (fma(i, 2.0, (beta + -1.0)) / (alpha + i)));
	}
	return tmp;
}

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	t_0 = Float64(beta + Float64(i * 2.0))
	t_1 = Float64(Float64(i / fma(i, 2.0, Float64(beta + alpha))) * Float64(Float64(beta + i) / t_0))
	tmp = 0.0
	if (beta <= 6e+31)
		tmp = 0.0625;
	elseif (beta <= 4.4e+43)
		tmp = Float64(t_1 * Float64(Float64(i * Float64(beta + i)) / Float64((t_0 ^ 2.0) + -1.0)));
	elseif (beta <= 1.08e+178)
		tmp = Float64(t_1 * 0.25);
	else
		tmp = Float64(Float64(1.0 / fma(i, 2.0, Float64(beta + 1.0))) * Float64(i / Float64(fma(i, 2.0, Float64(beta + -1.0)) / Float64(alpha + i))));
	end
	return tmp
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := Block[{t$95$0 = N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(i / N[(i * 2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(beta + i), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 6e+31], 0.0625, If[LessEqual[beta, 4.4e+43], N[(t$95$1 * N[(N[(i * N[(beta + i), $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$0, 2.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[beta, 1.08e+178], N[(t$95$1 * 0.25), $MachinePrecision], N[(N[(1.0 / N[(i * 2.0 + N[(beta + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0 + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} t_0 := \beta + i \cdot 2\\ t_1 := {t_0}^{2}\\ t_2 := i \cdot \left(\beta + i\right)\\ \mathbf{if}\;\beta \leq 6 \cdot 10^{+31}:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;\beta \leq 4.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{t_2}{t_1 + -1} \cdot \frac{t_2}{t_1}\\ \mathbf{elif}\;\beta \leq 7.9 \cdot 10^{+177}:\\ \;\;\;\;\left(\frac{i}{\mathsf{fma}\left(i, 2, \beta + \alpha\right)} \cdot \frac{\beta + i}{t_0}\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(i, 2, \beta + 1\right)} \cdot \frac{i}{\frac{\mathsf{fma}\left(i, 2, \beta + -1\right)}{\alpha + i}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (let* ((t_0 (+ beta (* i 2.0))) (t_1 (pow t_0 2.0)) (t_2 (* i (+ beta i))))
   (if (<= beta 6e+31)
     0.0625
     (if (<= beta 4.4e+43)
       (* (/ t_2 (+ t_1 -1.0)) (/ t_2 t_1))
       (if (<= beta 7.9e+177)
         (* (* (/ i (fma i 2.0 (+ beta alpha))) (/ (+ beta i) t_0)) 0.25)
         (*
          (/ 1.0 (fma i 2.0 (+ beta 1.0)))
          (/ i (/ (fma i 2.0 (+ beta -1.0)) (+ alpha i)))))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double t_0 = beta + (i * 2.0);
	double t_1 = pow(t_0, 2.0);
	double t_2 = i * (beta + i);
	double tmp;
	if (beta <= 6e+31) {
		tmp = 0.0625;
	} else if (beta <= 4.4e+43) {
		tmp = (t_2 / (t_1 + -1.0)) * (t_2 / t_1);
	} else if (beta <= 7.9e+177) {
		tmp = ((i / fma(i, 2.0, (beta + alpha))) * ((beta + i) / t_0)) * 0.25;
	} else {
		tmp = (1.0 / fma(i, 2.0, (beta + 1.0))) * (i / (fma(i, 2.0, (beta + -1.0)) / (alpha + i)));
	}
	return tmp;
}

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	t_0 = Float64(beta + Float64(i * 2.0))
	t_1 = t_0 ^ 2.0
	t_2 = Float64(i * Float64(beta + i))
	tmp = 0.0
	if (beta <= 6e+31)
		tmp = 0.0625;
	elseif (beta <= 4.4e+43)
		tmp = Float64(Float64(t_2 / Float64(t_1 + -1.0)) * Float64(t_2 / t_1));
	elseif (beta <= 7.9e+177)
		tmp = Float64(Float64(Float64(i / fma(i, 2.0, Float64(beta + alpha))) * Float64(Float64(beta + i) / t_0)) * 0.25);
	else
		tmp = Float64(Float64(1.0 / fma(i, 2.0, Float64(beta + 1.0))) * Float64(i / Float64(fma(i, 2.0, Float64(beta + -1.0)) / Float64(alpha + i))));
	end
	return tmp
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := Block[{t$95$0 = N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[t$95$0, 2.0], $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(beta + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 6e+31], 0.0625, If[LessEqual[beta, 4.4e+43], N[(N[(t$95$2 / N[(t$95$1 + -1.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[beta, 7.9e+177], N[(N[(N[(i / N[(i * 2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(beta + i), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision], N[(N[(1.0 / N[(i * 2.0 + N[(beta + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0 + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 5: 85.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 6.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\frac{i}{\mathsf{fma}\left(i, 2, \beta + \alpha\right)} \cdot \frac{\beta + i}{\beta + i \cdot 2}\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(i, 2, \beta + 1\right)} \cdot \frac{i}{\frac{\mathsf{fma}\left(i, 2, \beta + -1\right)}{\alpha + i}}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 6.6e+177)
   (*
    (* (/ i (fma i 2.0 (+ beta alpha))) (/ (+ beta i) (+ beta (* i 2.0))))
    0.25)
   (*
    (/ 1.0 (fma i 2.0 (+ beta 1.0)))
    (/ i (/ (fma i 2.0 (+ beta -1.0)) (+ alpha i))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 6.6e+177) {
		tmp = ((i / fma(i, 2.0, (beta + alpha))) * ((beta + i) / (beta + (i * 2.0)))) * 0.25;
	} else {
		tmp = (1.0 / fma(i, 2.0, (beta + 1.0))) * (i / (fma(i, 2.0, (beta + -1.0)) / (alpha + i)));
	}
	return tmp;
}

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 6.6e+177)
		tmp = Float64(Float64(Float64(i / fma(i, 2.0, Float64(beta + alpha))) * Float64(Float64(beta + i) / Float64(beta + Float64(i * 2.0)))) * 0.25);
	else
		tmp = Float64(Float64(1.0 / fma(i, 2.0, Float64(beta + 1.0))) * Float64(i / Float64(fma(i, 2.0, Float64(beta + -1.0)) / Float64(alpha + i))));
	end
	return tmp
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 6.6e+177], N[(N[(N[(i / N[(i * 2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(beta + i), $MachinePrecision] / N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision], N[(N[(1.0 / N[(i * 2.0 + N[(beta + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0 + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision] / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 1.4 \cdot 10^{+178}:\\ \;\;\;\;\left(\frac{i}{\mathsf{fma}\left(i, 2, \beta + \alpha\right)} \cdot \frac{\beta + i}{\beta + i \cdot 2}\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha + i}{\left(\beta + 1\right) + i \cdot 2} \cdot \frac{i}{i \cdot 2 + \left(\beta + -1\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 1.4e+178)
   (*
    (* (/ i (fma i 2.0 (+ beta alpha))) (/ (+ beta i) (+ beta (* i 2.0))))
    0.25)
   (*
    (/ (+ alpha i) (+ (+ beta 1.0) (* i 2.0)))
    (/ i (+ (* i 2.0) (+ beta -1.0))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 1.4e+178) {
		tmp = ((i / fma(i, 2.0, (beta + alpha))) * ((beta + i) / (beta + (i * 2.0)))) * 0.25;
	} else {
		tmp = ((alpha + i) / ((beta + 1.0) + (i * 2.0))) * (i / ((i * 2.0) + (beta + -1.0)));
	}
	return tmp;
}

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 1.4e+178)
		tmp = Float64(Float64(Float64(i / fma(i, 2.0, Float64(beta + alpha))) * Float64(Float64(beta + i) / Float64(beta + Float64(i * 2.0)))) * 0.25);
	else
		tmp = Float64(Float64(Float64(alpha + i) / Float64(Float64(beta + 1.0) + Float64(i * 2.0))) * Float64(i / Float64(Float64(i * 2.0) + Float64(beta + -1.0))));
	end
	return tmp
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 1.4e+178], N[(N[(N[(i / N[(i * 2.0 + N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(beta + i), $MachinePrecision] / N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision], N[(N[(N[(alpha + i), $MachinePrecision] / N[(N[(beta + 1.0), $MachinePrecision] + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0), $MachinePrecision] + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 85.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 5.5 \cdot 10^{+177}:\\ \;\;\;\;0.0625\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha + i}{\left(\beta + 1\right) + i \cdot 2} \cdot \frac{i}{i \cdot 2 + \left(\beta + -1\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 5.5e+177)
   0.0625
   (*
    (/ (+ alpha i) (+ (+ beta 1.0) (* i 2.0)))
    (/ i (+ (* i 2.0) (+ beta -1.0))))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 5.5e+177) {
		tmp = 0.0625;
	} else {
		tmp = ((alpha + i) / ((beta + 1.0) + (i * 2.0))) * (i / ((i * 2.0) + (beta + -1.0)));
	}
	return tmp;
}

Fortran

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (beta <= 5.5d+177) then
        tmp = 0.0625d0
    else
        tmp = ((alpha + i) / ((beta + 1.0d0) + (i * 2.0d0))) * (i / ((i * 2.0d0) + (beta + (-1.0d0))))
    end if
    code = tmp
end function

Java

assert alpha < beta && beta < i;
public static double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 5.5e+177) {
		tmp = 0.0625;
	} else {
		tmp = ((alpha + i) / ((beta + 1.0) + (i * 2.0))) * (i / ((i * 2.0) + (beta + -1.0)));
	}
	return tmp;
}

Python

[alpha, beta, i] = sort([alpha, beta, i])
def code(alpha, beta, i):
	tmp = 0
	if beta <= 5.5e+177:
		tmp = 0.0625
	else:
		tmp = ((alpha + i) / ((beta + 1.0) + (i * 2.0))) * (i / ((i * 2.0) + (beta + -1.0)))
	return tmp

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 5.5e+177)
		tmp = 0.0625;
	else
		tmp = Float64(Float64(Float64(alpha + i) / Float64(Float64(beta + 1.0) + Float64(i * 2.0))) * Float64(i / Float64(Float64(i * 2.0) + Float64(beta + -1.0))));
	end
	return tmp
end

MATLAB

alpha, beta, i = num2cell(sort([alpha, beta, i])){:}
function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (beta <= 5.5e+177)
		tmp = 0.0625;
	else
		tmp = ((alpha + i) / ((beta + 1.0) + (i * 2.0))) * (i / ((i * 2.0) + (beta + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 5.5e+177], 0.0625, N[(N[(N[(alpha + i), $MachinePrecision] / N[(N[(beta + 1.0), $MachinePrecision] + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(i / N[(N[(i * 2.0), $MachinePrecision] + N[(beta + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 84.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 1.05 \cdot 10^{+178}:\\ \;\;\;\;0.0625\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{i}{\frac{\beta}{\alpha + i}}}{\beta + i \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 1.05e+178)
   0.0625
   (/ (/ i (/ beta (+ alpha i))) (+ beta (* i 2.0)))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 1.05e+178) {
		tmp = 0.0625;
	} else {
		tmp = (i / (beta / (alpha + i))) / (beta + (i * 2.0));
	}
	return tmp;
}

Fortran

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (beta <= 1.05d+178) then
        tmp = 0.0625d0
    else
        tmp = (i / (beta / (alpha + i))) / (beta + (i * 2.0d0))
    end if
    code = tmp
end function

Java

assert alpha < beta && beta < i;
public static double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 1.05e+178) {
		tmp = 0.0625;
	} else {
		tmp = (i / (beta / (alpha + i))) / (beta + (i * 2.0));
	}
	return tmp;
}

Python

[alpha, beta, i] = sort([alpha, beta, i])
def code(alpha, beta, i):
	tmp = 0
	if beta <= 1.05e+178:
		tmp = 0.0625
	else:
		tmp = (i / (beta / (alpha + i))) / (beta + (i * 2.0))
	return tmp

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 1.05e+178)
		tmp = 0.0625;
	else
		tmp = Float64(Float64(i / Float64(beta / Float64(alpha + i))) / Float64(beta + Float64(i * 2.0)));
	end
	return tmp
end

MATLAB

alpha, beta, i = num2cell(sort([alpha, beta, i])){:}
function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (beta <= 1.05e+178)
		tmp = 0.0625;
	else
		tmp = (i / (beta / (alpha + i))) / (beta + (i * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 1.05e+178], 0.0625, N[(N[(i / N[(beta / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(beta + N[(i * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 75.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 7.6 \cdot 10^{+207}:\\ \;\;\;\;0.0625\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha}{\beta} \cdot \frac{i}{\beta + \alpha}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 7.6e+207) 0.0625 (* (/ alpha beta) (/ i (+ beta alpha)))))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 7.6e+207) {
		tmp = 0.0625;
	} else {
		tmp = (alpha / beta) * (i / (beta + alpha));
	}
	return tmp;
}

Fortran

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (beta <= 7.6d+207) then
        tmp = 0.0625d0
    else
        tmp = (alpha / beta) * (i / (beta + alpha))
    end if
    code = tmp
end function

Java

assert alpha < beta && beta < i;
public static double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 7.6e+207) {
		tmp = 0.0625;
	} else {
		tmp = (alpha / beta) * (i / (beta + alpha));
	}
	return tmp;
}

Python

[alpha, beta, i] = sort([alpha, beta, i])
def code(alpha, beta, i):
	tmp = 0
	if beta <= 7.6e+207:
		tmp = 0.0625
	else:
		tmp = (alpha / beta) * (i / (beta + alpha))
	return tmp

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 7.6e+207)
		tmp = 0.0625;
	else
		tmp = Float64(Float64(alpha / beta) * Float64(i / Float64(beta + alpha)));
	end
	return tmp
end

MATLAB

alpha, beta, i = num2cell(sort([alpha, beta, i])){:}
function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (beta <= 7.6e+207)
		tmp = 0.0625;
	else
		tmp = (alpha / beta) * (i / (beta + alpha));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 7.6e+207], 0.0625, N[(N[(alpha / beta), $MachinePrecision] * N[(i / N[(beta + alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 84.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 1.2 \cdot 10^{+178}:\\ \;\;\;\;0.0625\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{i}{\frac{\beta}{\alpha + i}}}{\beta}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 1.2e+178) 0.0625 (/ (/ i (/ beta (+ alpha i))) beta)))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 1.2e+178) {
		tmp = 0.0625;
	} else {
		tmp = (i / (beta / (alpha + i))) / beta;
	}
	return tmp;
}

Fortran

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (beta <= 1.2d+178) then
        tmp = 0.0625d0
    else
        tmp = (i / (beta / (alpha + i))) / beta
    end if
    code = tmp
end function

Java

assert alpha < beta && beta < i;
public static double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 1.2e+178) {
		tmp = 0.0625;
	} else {
		tmp = (i / (beta / (alpha + i))) / beta;
	}
	return tmp;
}

Python

[alpha, beta, i] = sort([alpha, beta, i])
def code(alpha, beta, i):
	tmp = 0
	if beta <= 1.2e+178:
		tmp = 0.0625
	else:
		tmp = (i / (beta / (alpha + i))) / beta
	return tmp

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 1.2e+178)
		tmp = 0.0625;
	else
		tmp = Float64(Float64(i / Float64(beta / Float64(alpha + i))) / beta);
	end
	return tmp
end

MATLAB

alpha, beta, i = num2cell(sort([alpha, beta, i])){:}
function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (beta <= 1.2e+178)
		tmp = 0.0625;
	else
		tmp = (i / (beta / (alpha + i))) / beta;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 1.2e+178], 0.0625, N[(N[(i / N[(beta / N[(alpha + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / beta), $MachinePrecision]]

Derivation

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

Alternative 11: 74.1% accurate, 5.3× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ \begin{array}{l} \mathbf{if}\;\beta \leq 5 \cdot 10^{+258}:\\ \;\;\;\;0.0625\\ \mathbf{else}:\\ \;\;\;\;\frac{\beta \cdot 0}{i}\\ \end{array} \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i)
 :precision binary64
 (if (<= beta 5e+258) 0.0625 (/ (* beta 0.0) i)))

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 5e+258) {
		tmp = 0.0625;
	} else {
		tmp = (beta * 0.0) / i;
	}
	return tmp;
}

Fortran

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    real(8) :: tmp
    if (beta <= 5d+258) then
        tmp = 0.0625d0
    else
        tmp = (beta * 0.0d0) / i
    end if
    code = tmp
end function

Java

assert alpha < beta && beta < i;
public static double code(double alpha, double beta, double i) {
	double tmp;
	if (beta <= 5e+258) {
		tmp = 0.0625;
	} else {
		tmp = (beta * 0.0) / i;
	}
	return tmp;
}

Python

[alpha, beta, i] = sort([alpha, beta, i])
def code(alpha, beta, i):
	tmp = 0
	if beta <= 5e+258:
		tmp = 0.0625
	else:
		tmp = (beta * 0.0) / i
	return tmp

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	tmp = 0.0
	if (beta <= 5e+258)
		tmp = 0.0625;
	else
		tmp = Float64(Float64(beta * 0.0) / i);
	end
	return tmp
end

MATLAB

alpha, beta, i = num2cell(sort([alpha, beta, i])){:}
function tmp_2 = code(alpha, beta, i)
	tmp = 0.0;
	if (beta <= 5e+258)
		tmp = 0.0625;
	else
		tmp = (beta * 0.0) / i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := If[LessEqual[beta, 5e+258], 0.0625, N[(N[(beta * 0.0), $MachinePrecision] / i), $MachinePrecision]]

Derivation

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

Alternative 12: 71.1% accurate, 53.0× speedup

Math

\[\begin{array}{l} [alpha, beta, i] = \mathsf{sort}([alpha, beta, i])\\ \\ 0.0625 \end{array} \]

FPCore

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
(FPCore (alpha beta i) :precision binary64 0.0625)

C

assert(alpha < beta && beta < i);
double code(double alpha, double beta, double i) {
	return 0.0625;
}

Fortran

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
real(8) function code(alpha, beta, i)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8), intent (in) :: i
    code = 0.0625d0
end function

Java

assert alpha < beta && beta < i;
public static double code(double alpha, double beta, double i) {
	return 0.0625;
}

Python

[alpha, beta, i] = sort([alpha, beta, i])
def code(alpha, beta, i):
	return 0.0625

Julia

alpha, beta, i = sort([alpha, beta, i])
function code(alpha, beta, i)
	return 0.0625
end

MATLAB

alpha, beta, i = num2cell(sort([alpha, beta, i])){:}
function tmp = code(alpha, beta, i)
	tmp = 0.0625;
end

Wolfram

NOTE: alpha, beta, and i should be sorted in increasing order before calling this function.
code[alpha_, beta_, i_] := 0.0625

Derivation

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

Reproduce

herbie shell --seed 2024006 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :precision binary64
  :pre (and (and (> alpha -1.0) (> beta -1.0)) (> i 1.0))
  (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)))