Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A

Percentage Accurate: 68.7% → 99.8%

Time: 14.0s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))

C

double code(double x, double y) {
	return (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0));
}

Python

def code(x, y):
	return (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0))

Julia

function code(x, y)
	return Float64(Float64(x * y) / Float64(Float64(Float64(x + y) * Float64(x + y)) * Float64(Float64(x + y) + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0));
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] / N[(N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))

C

double code(double x, double y) {
	return (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0));
}

Python

def code(x, y):
	return (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0))

Julia

function code(x, y)
	return Float64(Float64(x * y) / Float64(Float64(Float64(x + y) * Float64(x + y)) * Float64(Float64(x + y) + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) / (((x + y) * (x + y)) * ((x + y) + 1.0));
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] / N[(N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (* (/ x (+ y (+ x 1.0))) (/ (/ y (+ x y)) (+ x y))))

C

double code(double x, double y) {
	return (x / (y + (x + 1.0))) * ((y / (x + y)) / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (y + (x + 1.0d0))) * ((y / (x + y)) / (x + y))
end function

Java

public static double code(double x, double y) {
	return (x / (y + (x + 1.0))) * ((y / (x + y)) / (x + y));
}

Python

def code(x, y):
	return (x / (y + (x + 1.0))) * ((y / (x + y)) / (x + y))

Julia

function code(x, y)
	return Float64(Float64(x / Float64(y + Float64(x + 1.0))) * Float64(Float64(y / Float64(x + y)) / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / (y + (x + 1.0))) * ((y / (x + y)) / (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x / N[(y + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{x + y}}{x + \left(y + \left(y + 1\right)\right)}\\ \mathbf{if}\;x \leq -1.66 \cdot 10^{-49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{x + \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (/ y (+ x y)) (+ x (+ y (+ y 1.0))))))
   (if (<= x -1.66e-49)
     t_0
     (if (<= x -3.7e-91)
       (* (/ y (* (+ x y) (+ x y))) (/ x y))
       (if (<= x -1.7e-143) t_0 (/ (/ x y) (+ x (+ y 1.0))))))))

C

double code(double x, double y) {
	double t_0 = (y / (x + y)) / (x + (y + (y + 1.0)));
	double tmp;
	if (x <= -1.66e-49) {
		tmp = t_0;
	} else if (x <= -3.7e-91) {
		tmp = (y / ((x + y) * (x + y))) * (x / y);
	} else if (x <= -1.7e-143) {
		tmp = t_0;
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / (x + y)) / (x + (y + (y + 1.0d0)))
    if (x <= (-1.66d-49)) then
        tmp = t_0
    else if (x <= (-3.7d-91)) then
        tmp = (y / ((x + y) * (x + y))) * (x / y)
    else if (x <= (-1.7d-143)) then
        tmp = t_0
    else
        tmp = (x / y) / (x + (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / (x + y)) / (x + (y + (y + 1.0)));
	double tmp;
	if (x <= -1.66e-49) {
		tmp = t_0;
	} else if (x <= -3.7e-91) {
		tmp = (y / ((x + y) * (x + y))) * (x / y);
	} else if (x <= -1.7e-143) {
		tmp = t_0;
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / (x + y)) / (x + (y + (y + 1.0)))
	tmp = 0
	if x <= -1.66e-49:
		tmp = t_0
	elif x <= -3.7e-91:
		tmp = (y / ((x + y) * (x + y))) * (x / y)
	elif x <= -1.7e-143:
		tmp = t_0
	else:
		tmp = (x / y) / (x + (y + 1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / Float64(x + y)) / Float64(x + Float64(y + Float64(y + 1.0))))
	tmp = 0.0
	if (x <= -1.66e-49)
		tmp = t_0;
	elseif (x <= -3.7e-91)
		tmp = Float64(Float64(y / Float64(Float64(x + y) * Float64(x + y))) * Float64(x / y));
	elseif (x <= -1.7e-143)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / y) / Float64(x + Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / (x + y)) / (x + (y + (y + 1.0)));
	tmp = 0.0;
	if (x <= -1.66e-49)
		tmp = t_0;
	elseif (x <= -3.7e-91)
		tmp = (y / ((x + y) * (x + y))) * (x / y);
	elseif (x <= -1.7e-143)
		tmp = t_0;
	else
		tmp = (x / y) / (x + (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.66e-49], t$95$0, If[LessEqual[x, -3.7e-91], N[(N[(y / N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-143], t$95$0, N[(N[(x / y), $MachinePrecision] / N[(x + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{y}{x + y}}{x + \left(y + \left(y + 1\right)\right)}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{x + \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.15e+104)
   (/ (/ y (+ x y)) (+ x (+ y (+ y 1.0))))
   (if (<= x -1.55e-143)
     (* (/ y (* (+ x y) (+ x y))) (/ x (+ x 1.0)))
     (/ (/ x y) (+ x (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.15e+104) {
		tmp = (y / (x + y)) / (x + (y + (y + 1.0)));
	} else if (x <= -1.55e-143) {
		tmp = (y / ((x + y) * (x + y))) * (x / (x + 1.0));
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.15d+104)) then
        tmp = (y / (x + y)) / (x + (y + (y + 1.0d0)))
    else if (x <= (-1.55d-143)) then
        tmp = (y / ((x + y) * (x + y))) * (x / (x + 1.0d0))
    else
        tmp = (x / y) / (x + (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.15e+104) {
		tmp = (y / (x + y)) / (x + (y + (y + 1.0)));
	} else if (x <= -1.55e-143) {
		tmp = (y / ((x + y) * (x + y))) * (x / (x + 1.0));
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.15e+104:
		tmp = (y / (x + y)) / (x + (y + (y + 1.0)))
	elif x <= -1.55e-143:
		tmp = (y / ((x + y) * (x + y))) * (x / (x + 1.0))
	else:
		tmp = (x / y) / (x + (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.15e+104)
		tmp = Float64(Float64(y / Float64(x + y)) / Float64(x + Float64(y + Float64(y + 1.0))));
	elseif (x <= -1.55e-143)
		tmp = Float64(Float64(y / Float64(Float64(x + y) * Float64(x + y))) * Float64(x / Float64(x + 1.0)));
	else
		tmp = Float64(Float64(x / y) / Float64(x + Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.15e+104)
		tmp = (y / (x + y)) / (x + (y + (y + 1.0)));
	elseif (x <= -1.55e-143)
		tmp = (y / ((x + y) * (x + y))) * (x / (x + 1.0));
	else
		tmp = (x / y) / (x + (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.15e+104], N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e-143], N[(N[(y / N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(x + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot \left(y + 1\right)}\\ t_1 := \frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y (+ y 1.0)))) (t_1 (/ y (* x (+ x 1.0)))))
   (if (<= x -1e+67)
     (/ (/ y x) x)
     (if (<= x -2.1e-47)
       t_1
       (if (<= x -3.2e-91)
         t_0
         (if (<= x -1.7e-143)
           t_1
           (if (<= x 2.15e-39) t_0 (* (/ x y) (/ 1.0 y)))))))))

C

double code(double x, double y) {
	double t_0 = x / (y * (y + 1.0));
	double t_1 = y / (x * (x + 1.0));
	double tmp;
	if (x <= -1e+67) {
		tmp = (y / x) / x;
	} else if (x <= -2.1e-47) {
		tmp = t_1;
	} else if (x <= -3.2e-91) {
		tmp = t_0;
	} else if (x <= -1.7e-143) {
		tmp = t_1;
	} else if (x <= 2.15e-39) {
		tmp = t_0;
	} else {
		tmp = (x / y) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (y * (y + 1.0d0))
    t_1 = y / (x * (x + 1.0d0))
    if (x <= (-1d+67)) then
        tmp = (y / x) / x
    else if (x <= (-2.1d-47)) then
        tmp = t_1
    else if (x <= (-3.2d-91)) then
        tmp = t_0
    else if (x <= (-1.7d-143)) then
        tmp = t_1
    else if (x <= 2.15d-39) then
        tmp = t_0
    else
        tmp = (x / y) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * (y + 1.0));
	double t_1 = y / (x * (x + 1.0));
	double tmp;
	if (x <= -1e+67) {
		tmp = (y / x) / x;
	} else if (x <= -2.1e-47) {
		tmp = t_1;
	} else if (x <= -3.2e-91) {
		tmp = t_0;
	} else if (x <= -1.7e-143) {
		tmp = t_1;
	} else if (x <= 2.15e-39) {
		tmp = t_0;
	} else {
		tmp = (x / y) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * (y + 1.0))
	t_1 = y / (x * (x + 1.0))
	tmp = 0
	if x <= -1e+67:
		tmp = (y / x) / x
	elif x <= -2.1e-47:
		tmp = t_1
	elif x <= -3.2e-91:
		tmp = t_0
	elif x <= -1.7e-143:
		tmp = t_1
	elif x <= 2.15e-39:
		tmp = t_0
	else:
		tmp = (x / y) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * Float64(y + 1.0)))
	t_1 = Float64(y / Float64(x * Float64(x + 1.0)))
	tmp = 0.0
	if (x <= -1e+67)
		tmp = Float64(Float64(y / x) / x);
	elseif (x <= -2.1e-47)
		tmp = t_1;
	elseif (x <= -3.2e-91)
		tmp = t_0;
	elseif (x <= -1.7e-143)
		tmp = t_1;
	elseif (x <= 2.15e-39)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * (y + 1.0));
	t_1 = y / (x * (x + 1.0));
	tmp = 0.0;
	if (x <= -1e+67)
		tmp = (y / x) / x;
	elseif (x <= -2.1e-47)
		tmp = t_1;
	elseif (x <= -3.2e-91)
		tmp = t_0;
	elseif (x <= -1.7e-143)
		tmp = t_1;
	elseif (x <= 2.15e-39)
		tmp = t_0;
	else
		tmp = (x / y) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+67], N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, -2.1e-47], t$95$1, If[LessEqual[x, -3.2e-91], t$95$0, If[LessEqual[x, -1.7e-143], t$95$1, If[LessEqual[x, 2.15e-39], t$95$0, N[(N[(x / y), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 5: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{x + y}}{x + 1}\\ \mathbf{if}\;x \leq -1 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{x + \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (/ y (+ x y)) (+ x 1.0))))
   (if (<= x -1e-47)
     t_0
     (if (<= x -4.1e-91)
       (* (/ y (* (+ x y) (+ x y))) (/ x y))
       (if (<= x -1.7e-143) t_0 (/ (/ x y) (+ x (+ y 1.0))))))))

C

double code(double x, double y) {
	double t_0 = (y / (x + y)) / (x + 1.0);
	double tmp;
	if (x <= -1e-47) {
		tmp = t_0;
	} else if (x <= -4.1e-91) {
		tmp = (y / ((x + y) * (x + y))) * (x / y);
	} else if (x <= -1.7e-143) {
		tmp = t_0;
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / (x + y)) / (x + 1.0d0)
    if (x <= (-1d-47)) then
        tmp = t_0
    else if (x <= (-4.1d-91)) then
        tmp = (y / ((x + y) * (x + y))) * (x / y)
    else if (x <= (-1.7d-143)) then
        tmp = t_0
    else
        tmp = (x / y) / (x + (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / (x + y)) / (x + 1.0);
	double tmp;
	if (x <= -1e-47) {
		tmp = t_0;
	} else if (x <= -4.1e-91) {
		tmp = (y / ((x + y) * (x + y))) * (x / y);
	} else if (x <= -1.7e-143) {
		tmp = t_0;
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / (x + y)) / (x + 1.0)
	tmp = 0
	if x <= -1e-47:
		tmp = t_0
	elif x <= -4.1e-91:
		tmp = (y / ((x + y) * (x + y))) * (x / y)
	elif x <= -1.7e-143:
		tmp = t_0
	else:
		tmp = (x / y) / (x + (y + 1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / Float64(x + y)) / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -1e-47)
		tmp = t_0;
	elseif (x <= -4.1e-91)
		tmp = Float64(Float64(y / Float64(Float64(x + y) * Float64(x + y))) * Float64(x / y));
	elseif (x <= -1.7e-143)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / y) / Float64(x + Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / (x + y)) / (x + 1.0);
	tmp = 0.0;
	if (x <= -1e-47)
		tmp = t_0;
	elseif (x <= -4.1e-91)
		tmp = (y / ((x + y) * (x + y))) * (x / y);
	elseif (x <= -1.7e-143)
		tmp = t_0;
	else
		tmp = (x / y) / (x + (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-47], t$95$0, If[LessEqual[x, -4.1e-91], N[(N[(y / N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-143], t$95$0, N[(N[(x / y), $MachinePrecision] / N[(x + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x + y}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{t_0}{x + \left(y + \left(y + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{\left(x + y\right) \cdot \frac{y + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ x y))))
   (if (<= x -2.1e-10)
     (/ t_0 (+ x (+ y (+ y 1.0))))
     (/ t_0 (* (+ x y) (/ (+ y 1.0) x))))))

C

double code(double x, double y) {
	double t_0 = y / (x + y);
	double tmp;
	if (x <= -2.1e-10) {
		tmp = t_0 / (x + (y + (y + 1.0)));
	} else {
		tmp = t_0 / ((x + y) * ((y + 1.0) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (x + y)
    if (x <= (-2.1d-10)) then
        tmp = t_0 / (x + (y + (y + 1.0d0)))
    else
        tmp = t_0 / ((x + y) * ((y + 1.0d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (x + y);
	double tmp;
	if (x <= -2.1e-10) {
		tmp = t_0 / (x + (y + (y + 1.0)));
	} else {
		tmp = t_0 / ((x + y) * ((y + 1.0) / x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (x + y)
	tmp = 0
	if x <= -2.1e-10:
		tmp = t_0 / (x + (y + (y + 1.0)))
	else:
		tmp = t_0 / ((x + y) * ((y + 1.0) / x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(x + y))
	tmp = 0.0
	if (x <= -2.1e-10)
		tmp = Float64(t_0 / Float64(x + Float64(y + Float64(y + 1.0))));
	else
		tmp = Float64(t_0 / Float64(Float64(x + y) * Float64(Float64(y + 1.0) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (x + y);
	tmp = 0.0;
	if (x <= -2.1e-10)
		tmp = t_0 / (x + (y + (y + 1.0)));
	else
		tmp = t_0 / ((x + y) * ((y + 1.0) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e-10], N[(t$95$0 / N[(x + N[(y + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 / N[(N[(x + y), $MachinePrecision] * N[(N[(y + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 7: 59.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + 1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (* x (+ x 1.0)))))
   (if (<= x -1e+67)
     (/ (/ y x) x)
     (if (<= x -2.9e-48)
       t_0
       (if (<= x -3.2e-91)
         (/ x (* y (+ y 1.0)))
         (if (<= x -1.7e-143) t_0 (/ (/ x (+ y 1.0)) y)))))))

C

double code(double x, double y) {
	double t_0 = y / (x * (x + 1.0));
	double tmp;
	if (x <= -1e+67) {
		tmp = (y / x) / x;
	} else if (x <= -2.9e-48) {
		tmp = t_0;
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.7e-143) {
		tmp = t_0;
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (x * (x + 1.0d0))
    if (x <= (-1d+67)) then
        tmp = (y / x) / x
    else if (x <= (-2.9d-48)) then
        tmp = t_0
    else if (x <= (-3.2d-91)) then
        tmp = x / (y * (y + 1.0d0))
    else if (x <= (-1.7d-143)) then
        tmp = t_0
    else
        tmp = (x / (y + 1.0d0)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (x * (x + 1.0));
	double tmp;
	if (x <= -1e+67) {
		tmp = (y / x) / x;
	} else if (x <= -2.9e-48) {
		tmp = t_0;
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.7e-143) {
		tmp = t_0;
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (x * (x + 1.0))
	tmp = 0
	if x <= -1e+67:
		tmp = (y / x) / x
	elif x <= -2.9e-48:
		tmp = t_0
	elif x <= -3.2e-91:
		tmp = x / (y * (y + 1.0))
	elif x <= -1.7e-143:
		tmp = t_0
	else:
		tmp = (x / (y + 1.0)) / y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(x * Float64(x + 1.0)))
	tmp = 0.0
	if (x <= -1e+67)
		tmp = Float64(Float64(y / x) / x);
	elseif (x <= -2.9e-48)
		tmp = t_0;
	elseif (x <= -3.2e-91)
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	elseif (x <= -1.7e-143)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / Float64(y + 1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (x * (x + 1.0));
	tmp = 0.0;
	if (x <= -1e+67)
		tmp = (y / x) / x;
	elseif (x <= -2.9e-48)
		tmp = t_0;
	elseif (x <= -3.2e-91)
		tmp = x / (y * (y + 1.0));
	elseif (x <= -1.7e-143)
		tmp = t_0;
	else
		tmp = (x / (y + 1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+67], N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, -2.9e-48], t$95$0, If[LessEqual[x, -3.2e-91], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-143], t$95$0, N[(N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

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

Alternative 8: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-48}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{x + \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.75e-48)
   (/ (/ y x) (+ x 1.0))
   (if (<= x -3.2e-91)
     (/ x (* y (+ y 1.0)))
     (if (<= x -1.4e-143) (/ y (* x (+ x 1.0))) (/ (/ x y) (+ x (+ y 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.75e-48) {
		tmp = (y / x) / (x + 1.0);
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.4e-143) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.75d-48)) then
        tmp = (y / x) / (x + 1.0d0)
    else if (x <= (-3.2d-91)) then
        tmp = x / (y * (y + 1.0d0))
    else if (x <= (-1.4d-143)) then
        tmp = y / (x * (x + 1.0d0))
    else
        tmp = (x / y) / (x + (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.75e-48) {
		tmp = (y / x) / (x + 1.0);
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.4e-143) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.75e-48:
		tmp = (y / x) / (x + 1.0)
	elif x <= -3.2e-91:
		tmp = x / (y * (y + 1.0))
	elif x <= -1.4e-143:
		tmp = y / (x * (x + 1.0))
	else:
		tmp = (x / y) / (x + (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.75e-48)
		tmp = Float64(Float64(y / x) / Float64(x + 1.0));
	elseif (x <= -3.2e-91)
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	elseif (x <= -1.4e-143)
		tmp = Float64(y / Float64(x * Float64(x + 1.0)));
	else
		tmp = Float64(Float64(x / y) / Float64(x + Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.75e-48)
		tmp = (y / x) / (x + 1.0);
	elseif (x <= -3.2e-91)
		tmp = x / (y * (y + 1.0));
	elseif (x <= -1.4e-143)
		tmp = y / (x * (x + 1.0));
	else
		tmp = (x / y) / (x + (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.75e-48], N[(N[(y / x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-91], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e-143], N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(x + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 9: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{x + y}}{x + 1}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{x + \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (/ y (+ x y)) (+ x 1.0))))
   (if (<= x -4.5e-48)
     t_0
     (if (<= x -3.2e-91)
       (/ x (* y (+ y 1.0)))
       (if (<= x -1.2e-143) t_0 (/ (/ x y) (+ x (+ y 1.0))))))))

C

double code(double x, double y) {
	double t_0 = (y / (x + y)) / (x + 1.0);
	double tmp;
	if (x <= -4.5e-48) {
		tmp = t_0;
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.2e-143) {
		tmp = t_0;
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / (x + y)) / (x + 1.0d0)
    if (x <= (-4.5d-48)) then
        tmp = t_0
    else if (x <= (-3.2d-91)) then
        tmp = x / (y * (y + 1.0d0))
    else if (x <= (-1.2d-143)) then
        tmp = t_0
    else
        tmp = (x / y) / (x + (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / (x + y)) / (x + 1.0);
	double tmp;
	if (x <= -4.5e-48) {
		tmp = t_0;
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.2e-143) {
		tmp = t_0;
	} else {
		tmp = (x / y) / (x + (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / (x + y)) / (x + 1.0)
	tmp = 0
	if x <= -4.5e-48:
		tmp = t_0
	elif x <= -3.2e-91:
		tmp = x / (y * (y + 1.0))
	elif x <= -1.2e-143:
		tmp = t_0
	else:
		tmp = (x / y) / (x + (y + 1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / Float64(x + y)) / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -4.5e-48)
		tmp = t_0;
	elseif (x <= -3.2e-91)
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	elseif (x <= -1.2e-143)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / y) / Float64(x + Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / (x + y)) / (x + 1.0);
	tmp = 0.0;
	if (x <= -4.5e-48)
		tmp = t_0;
	elseif (x <= -3.2e-91)
		tmp = x / (y * (y + 1.0));
	elseif (x <= -1.2e-143)
		tmp = t_0;
	else
		tmp = (x / y) / (x + (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e-48], t$95$0, If[LessEqual[x, -3.2e-91], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e-143], t$95$0, N[(N[(x / y), $MachinePrecision] / N[(x + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 10: 54.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-180} \lor \neg \left(x \leq 9.2 \cdot 10^{-163}\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e-10)
   (/ (/ y x) x)
   (if (or (<= x -2.8e-180) (not (<= x 9.2e-163)))
     (* (/ x y) (/ 1.0 y))
     (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-10) {
		tmp = (y / x) / x;
	} else if ((x <= -2.8e-180) || !(x <= 9.2e-163)) {
		tmp = (x / y) * (1.0 / y);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.1d-10)) then
        tmp = (y / x) / x
    else if ((x <= (-2.8d-180)) .or. (.not. (x <= 9.2d-163))) then
        tmp = (x / y) * (1.0d0 / y)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-10) {
		tmp = (y / x) / x;
	} else if ((x <= -2.8e-180) || !(x <= 9.2e-163)) {
		tmp = (x / y) * (1.0 / y);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e-10:
		tmp = (y / x) / x
	elif (x <= -2.8e-180) or not (x <= 9.2e-163):
		tmp = (x / y) * (1.0 / y)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e-10)
		tmp = Float64(Float64(y / x) / x);
	elseif ((x <= -2.8e-180) || !(x <= 9.2e-163))
		tmp = Float64(Float64(x / y) * Float64(1.0 / y));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e-10)
		tmp = (y / x) / x;
	elseif ((x <= -2.8e-180) || ~((x <= 9.2e-163)))
		tmp = (x / y) * (1.0 / y);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e-10], N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision], If[Or[LessEqual[x, -2.8e-180], N[Not[LessEqual[x, 9.2e-163]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

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

Alternative 11: 59.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + 1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e-47)
   (/ (/ y x) (+ x 1.0))
   (if (<= x -3.2e-91)
     (/ x (* y (+ y 1.0)))
     (if (<= x -1.7e-143) (/ y (* x (+ x 1.0))) (/ (/ x (+ y 1.0)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e-47) {
		tmp = (y / x) / (x + 1.0);
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.7e-143) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2d-47)) then
        tmp = (y / x) / (x + 1.0d0)
    else if (x <= (-3.2d-91)) then
        tmp = x / (y * (y + 1.0d0))
    else if (x <= (-1.7d-143)) then
        tmp = y / (x * (x + 1.0d0))
    else
        tmp = (x / (y + 1.0d0)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2e-47) {
		tmp = (y / x) / (x + 1.0);
	} else if (x <= -3.2e-91) {
		tmp = x / (y * (y + 1.0));
	} else if (x <= -1.7e-143) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e-47:
		tmp = (y / x) / (x + 1.0)
	elif x <= -3.2e-91:
		tmp = x / (y * (y + 1.0))
	elif x <= -1.7e-143:
		tmp = y / (x * (x + 1.0))
	else:
		tmp = (x / (y + 1.0)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e-47)
		tmp = Float64(Float64(y / x) / Float64(x + 1.0));
	elseif (x <= -3.2e-91)
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	elseif (x <= -1.7e-143)
		tmp = Float64(y / Float64(x * Float64(x + 1.0)));
	else
		tmp = Float64(Float64(x / Float64(y + 1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e-47)
		tmp = (y / x) / (x + 1.0);
	elseif (x <= -3.2e-91)
		tmp = x / (y * (y + 1.0));
	elseif (x <= -1.7e-143)
		tmp = y / (x * (x + 1.0));
	else
		tmp = (x / (y + 1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e-47], N[(N[(y / x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-91], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-143], N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

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

Alternative 12: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e-10)
   (/ (/ y x) x)
   (if (<= x 2.15e-39) (/ x (* y (+ y 1.0))) (* (/ x y) (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-10) {
		tmp = (y / x) / x;
	} else if (x <= 2.15e-39) {
		tmp = x / (y * (y + 1.0));
	} else {
		tmp = (x / y) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.1d-10)) then
        tmp = (y / x) / x
    else if (x <= 2.15d-39) then
        tmp = x / (y * (y + 1.0d0))
    else
        tmp = (x / y) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-10) {
		tmp = (y / x) / x;
	} else if (x <= 2.15e-39) {
		tmp = x / (y * (y + 1.0));
	} else {
		tmp = (x / y) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e-10:
		tmp = (y / x) / x
	elif x <= 2.15e-39:
		tmp = x / (y * (y + 1.0))
	else:
		tmp = (x / y) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e-10)
		tmp = Float64(Float64(y / x) / x);
	elseif (x <= 2.15e-39)
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e-10)
		tmp = (y / x) / x;
	elseif (x <= 2.15e-39)
		tmp = x / (y * (y + 1.0));
	else
		tmp = (x / y) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e-10], N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 2.15e-39], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 13: 43.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.1e-10) (/ (/ y x) x) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-10) {
		tmp = (y / x) / x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.1d-10)) then
        tmp = (y / x) / x
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-10) {
		tmp = (y / x) / x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e-10:
		tmp = (y / x) / x
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e-10)
		tmp = Float64(Float64(y / x) / x);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e-10)
		tmp = (y / x) / x;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e-10], N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

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

Alternative 14: 4.2% accurate, 5.7× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 x))

C

double code(double x, double y) {
	return 1.0 / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / x
end function

Java

public static double code(double x, double y) {
	return 1.0 / x;
}

Python

def code(x, y):
	return 1.0 / x

Julia

function code(x, y)
	return Float64(1.0 / x)
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / x;
end

Wolfram

code[x_, y_] := N[(1.0 / x), $MachinePrecision]

Derivation

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

Alternative 15: 26.1% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x y))

C

double code(double x, double y) {
	return x / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / y
end function

Java

public static double code(double x, double y) {
	return x / y;
}

Python

def code(x, y):
	return x / y

Julia

function code(x, y)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y)
	tmp = x / y;
end

Wolfram

code[x_, y_] := N[(x / y), $MachinePrecision]

Derivation

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

Developer target: 99.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ (/ (/ x (+ (+ y 1.0) x)) (+ y x)) (/ 1.0 (/ y (+ y x)))))

C

double code(double x, double y) {
	return ((x / ((y + 1.0) + x)) / (y + x)) / (1.0 / (y / (y + x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x / ((y + 1.0d0) + x)) / (y + x)) / (1.0d0 / (y / (y + x)))
end function

Java

public static double code(double x, double y) {
	return ((x / ((y + 1.0) + x)) / (y + x)) / (1.0 / (y / (y + x)));
}

Python

def code(x, y):
	return ((x / ((y + 1.0) + x)) / (y + x)) / (1.0 / (y / (y + x)))

Julia

function code(x, y)
	return Float64(Float64(Float64(x / Float64(Float64(y + 1.0) + x)) / Float64(y + x)) / Float64(1.0 / Float64(y / Float64(y + x))))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x / ((y + 1.0) + x)) / (y + x)) / (1.0 / (y / (y + x)));
end

Wolfram

code[x_, y_] := N[(N[(N[(x / N[(N[(y + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024008 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ (/ x (+ (+ y 1.0) x)) (+ y x)) (/ 1.0 (/ y (+ y x))))

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))