_divideComplex, imaginary part

Percentage Accurate: 62.4% → 92.1%

Time: 12.2s

Alternatives: 15

Speedup: 1.8×

Specification

Math

\[\begin{array}{l} \\ \frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = ((x_46im * y_46re) - (x_46re * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(Float64(x_46_im * y_46_re) - Float64(x_46_re * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] - N[(x$46$re * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = ((x_46im * y_46re) - (x_46re * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(Float64(x_46_im * y_46_re) - Float64(x_46_re * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_im * y_46_re) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] - N[(x$46$re * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}\\ t_1 := t_0 - y.im \cdot \frac{\frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right)}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ t_2 := t_0 - \frac{x.re}{y.im}\\ \mathbf{if}\;y.im \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y.im \leq -8.6 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.6 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (/ y.re (hypot y.re y.im)) (/ x.im (hypot y.re y.im))))
        (t_1 (- t_0 (* y.im (/ (/ x.re (hypot y.re y.im)) (hypot y.re y.im)))))
        (t_2 (- t_0 (/ x.re y.im))))
   (if (<= y.im -4.7e+149)
     t_2
     (if (<= y.im -8.6e-189)
       t_1
       (if (<= y.im 2.4e-200)
         (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))
         (if (<= y.im 2.6e+115) t_1 t_2))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re / hypot(y_46_re, y_46_im)) * (x_46_im / hypot(y_46_re, y_46_im));
	double t_1 = t_0 - (y_46_im * ((x_46_re / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im)));
	double t_2 = t_0 - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -4.7e+149) {
		tmp = t_2;
	} else if (y_46_im <= -8.6e-189) {
		tmp = t_1;
	} else if (y_46_im <= 2.4e-200) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 2.6e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re / Math.hypot(y_46_re, y_46_im)) * (x_46_im / Math.hypot(y_46_re, y_46_im));
	double t_1 = t_0 - (y_46_im * ((x_46_re / Math.hypot(y_46_re, y_46_im)) / Math.hypot(y_46_re, y_46_im)));
	double t_2 = t_0 - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -4.7e+149) {
		tmp = t_2;
	} else if (y_46_im <= -8.6e-189) {
		tmp = t_1;
	} else if (y_46_im <= 2.4e-200) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 2.6e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (y_46_re / math.hypot(y_46_re, y_46_im)) * (x_46_im / math.hypot(y_46_re, y_46_im))
	t_1 = t_0 - (y_46_im * ((x_46_re / math.hypot(y_46_re, y_46_im)) / math.hypot(y_46_re, y_46_im)))
	t_2 = t_0 - (x_46_re / y_46_im)
	tmp = 0
	if y_46_im <= -4.7e+149:
		tmp = t_2
	elif y_46_im <= -8.6e-189:
		tmp = t_1
	elif y_46_im <= 2.4e-200:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	elif y_46_im <= 2.6e+115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(y_46_re / hypot(y_46_re, y_46_im)) * Float64(x_46_im / hypot(y_46_re, y_46_im)))
	t_1 = Float64(t_0 - Float64(y_46_im * Float64(Float64(x_46_re / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im))))
	t_2 = Float64(t_0 - Float64(x_46_re / y_46_im))
	tmp = 0.0
	if (y_46_im <= -4.7e+149)
		tmp = t_2;
	elseif (y_46_im <= -8.6e-189)
		tmp = t_1;
	elseif (y_46_im <= 2.4e-200)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	elseif (y_46_im <= 2.6e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (y_46_re / hypot(y_46_re, y_46_im)) * (x_46_im / hypot(y_46_re, y_46_im));
	t_1 = t_0 - (y_46_im * ((x_46_re / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im)));
	t_2 = t_0 - (x_46_re / y_46_im);
	tmp = 0.0;
	if (y_46_im <= -4.7e+149)
		tmp = t_2;
	elseif (y_46_im <= -8.6e-189)
		tmp = t_1;
	elseif (y_46_im <= 2.4e-200)
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	elseif (y_46_im <= 2.6e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(y$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(x$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - N[(y$46$im * N[(N[(x$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -4.7e+149], t$95$2, If[LessEqual[y$46$im, -8.6e-189], t$95$1, If[LessEqual[y$46$im, 2.4e-200], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 2.6e+115], t$95$1, t$95$2]]]]]]]

Derivation

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

Alternative 2: 89.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}\\ t_1 := t_0 - y.im \cdot \frac{x.re}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\\ t_2 := t_0 - \frac{x.re}{y.im}\\ \mathbf{if}\;y.im \leq -6.6 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y.im \leq -7.4 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 1.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 3.4 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (/ y.re (hypot y.re y.im)) (/ x.im (hypot y.re y.im))))
        (t_1 (- t_0 (* y.im (/ x.re (pow (hypot y.re y.im) 2.0)))))
        (t_2 (- t_0 (/ x.re y.im))))
   (if (<= y.im -6.6e+147)
     t_2
     (if (<= y.im -7.4e-115)
       t_1
       (if (<= y.im 1.5e-284)
         (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))
         (if (<= y.im 3.4e+115) t_1 t_2))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re / hypot(y_46_re, y_46_im)) * (x_46_im / hypot(y_46_re, y_46_im));
	double t_1 = t_0 - (y_46_im * (x_46_re / pow(hypot(y_46_re, y_46_im), 2.0)));
	double t_2 = t_0 - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -6.6e+147) {
		tmp = t_2;
	} else if (y_46_im <= -7.4e-115) {
		tmp = t_1;
	} else if (y_46_im <= 1.5e-284) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 3.4e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re / Math.hypot(y_46_re, y_46_im)) * (x_46_im / Math.hypot(y_46_re, y_46_im));
	double t_1 = t_0 - (y_46_im * (x_46_re / Math.pow(Math.hypot(y_46_re, y_46_im), 2.0)));
	double t_2 = t_0 - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -6.6e+147) {
		tmp = t_2;
	} else if (y_46_im <= -7.4e-115) {
		tmp = t_1;
	} else if (y_46_im <= 1.5e-284) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 3.4e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (y_46_re / math.hypot(y_46_re, y_46_im)) * (x_46_im / math.hypot(y_46_re, y_46_im))
	t_1 = t_0 - (y_46_im * (x_46_re / math.pow(math.hypot(y_46_re, y_46_im), 2.0)))
	t_2 = t_0 - (x_46_re / y_46_im)
	tmp = 0
	if y_46_im <= -6.6e+147:
		tmp = t_2
	elif y_46_im <= -7.4e-115:
		tmp = t_1
	elif y_46_im <= 1.5e-284:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	elif y_46_im <= 3.4e+115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(y_46_re / hypot(y_46_re, y_46_im)) * Float64(x_46_im / hypot(y_46_re, y_46_im)))
	t_1 = Float64(t_0 - Float64(y_46_im * Float64(x_46_re / (hypot(y_46_re, y_46_im) ^ 2.0))))
	t_2 = Float64(t_0 - Float64(x_46_re / y_46_im))
	tmp = 0.0
	if (y_46_im <= -6.6e+147)
		tmp = t_2;
	elseif (y_46_im <= -7.4e-115)
		tmp = t_1;
	elseif (y_46_im <= 1.5e-284)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	elseif (y_46_im <= 3.4e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (y_46_re / hypot(y_46_re, y_46_im)) * (x_46_im / hypot(y_46_re, y_46_im));
	t_1 = t_0 - (y_46_im * (x_46_re / (hypot(y_46_re, y_46_im) ^ 2.0)));
	t_2 = t_0 - (x_46_re / y_46_im);
	tmp = 0.0;
	if (y_46_im <= -6.6e+147)
		tmp = t_2;
	elseif (y_46_im <= -7.4e-115)
		tmp = t_1;
	elseif (y_46_im <= 1.5e-284)
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	elseif (y_46_im <= 3.4e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(y$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(x$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - N[(y$46$im * N[(x$46$re / N[Power[N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -6.6e+147], t$95$2, If[LessEqual[y$46$im, -7.4e-115], t$95$1, If[LessEqual[y$46$im, 1.5e-284], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 3.4e+115], t$95$1, t$95$2]]]]]]]

Derivation

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

Alternative 3: 91.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ t_1 := \frac{t_0 \cdot x.im}{\mathsf{hypot}\left(y.re, y.im\right)} - y.im \cdot \frac{x.re}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\\ t_2 := t_0 \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)} - \frac{x.re}{y.im}\\ \mathbf{if}\;y.im \leq -1.55 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y.im \leq -2.3 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 5.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.8 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ y.re (hypot y.re y.im)))
        (t_1
         (-
          (/ (* t_0 x.im) (hypot y.re y.im))
          (* y.im (/ x.re (pow (hypot y.re y.im) 2.0)))))
        (t_2 (- (* t_0 (/ x.im (hypot y.re y.im))) (/ x.re y.im))))
   (if (<= y.im -1.55e+147)
     t_2
     (if (<= y.im -2.3e-159)
       t_1
       (if (<= y.im 5.2e-199)
         (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))
         (if (<= y.im 1.8e+115) t_1 t_2))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re / hypot(y_46_re, y_46_im);
	double t_1 = ((t_0 * x_46_im) / hypot(y_46_re, y_46_im)) - (y_46_im * (x_46_re / pow(hypot(y_46_re, y_46_im), 2.0)));
	double t_2 = (t_0 * (x_46_im / hypot(y_46_re, y_46_im))) - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -1.55e+147) {
		tmp = t_2;
	} else if (y_46_im <= -2.3e-159) {
		tmp = t_1;
	} else if (y_46_im <= 5.2e-199) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 1.8e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re / Math.hypot(y_46_re, y_46_im);
	double t_1 = ((t_0 * x_46_im) / Math.hypot(y_46_re, y_46_im)) - (y_46_im * (x_46_re / Math.pow(Math.hypot(y_46_re, y_46_im), 2.0)));
	double t_2 = (t_0 * (x_46_im / Math.hypot(y_46_re, y_46_im))) - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -1.55e+147) {
		tmp = t_2;
	} else if (y_46_im <= -2.3e-159) {
		tmp = t_1;
	} else if (y_46_im <= 5.2e-199) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 1.8e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re / math.hypot(y_46_re, y_46_im)
	t_1 = ((t_0 * x_46_im) / math.hypot(y_46_re, y_46_im)) - (y_46_im * (x_46_re / math.pow(math.hypot(y_46_re, y_46_im), 2.0)))
	t_2 = (t_0 * (x_46_im / math.hypot(y_46_re, y_46_im))) - (x_46_re / y_46_im)
	tmp = 0
	if y_46_im <= -1.55e+147:
		tmp = t_2
	elif y_46_im <= -2.3e-159:
		tmp = t_1
	elif y_46_im <= 5.2e-199:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	elif y_46_im <= 1.8e+115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re / hypot(y_46_re, y_46_im))
	t_1 = Float64(Float64(Float64(t_0 * x_46_im) / hypot(y_46_re, y_46_im)) - Float64(y_46_im * Float64(x_46_re / (hypot(y_46_re, y_46_im) ^ 2.0))))
	t_2 = Float64(Float64(t_0 * Float64(x_46_im / hypot(y_46_re, y_46_im))) - Float64(x_46_re / y_46_im))
	tmp = 0.0
	if (y_46_im <= -1.55e+147)
		tmp = t_2;
	elseif (y_46_im <= -2.3e-159)
		tmp = t_1;
	elseif (y_46_im <= 5.2e-199)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	elseif (y_46_im <= 1.8e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re / hypot(y_46_re, y_46_im);
	t_1 = ((t_0 * x_46_im) / hypot(y_46_re, y_46_im)) - (y_46_im * (x_46_re / (hypot(y_46_re, y_46_im) ^ 2.0)));
	t_2 = (t_0 * (x_46_im / hypot(y_46_re, y_46_im))) - (x_46_re / y_46_im);
	tmp = 0.0;
	if (y_46_im <= -1.55e+147)
		tmp = t_2;
	elseif (y_46_im <= -2.3e-159)
		tmp = t_1;
	elseif (y_46_im <= 5.2e-199)
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	elseif (y_46_im <= 1.8e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(t$95$0 * x$46$im), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] - N[(y$46$im * N[(x$46$re / N[Power[N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$0 * N[(x$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -1.55e+147], t$95$2, If[LessEqual[y$46$im, -2.3e-159], t$95$1, If[LessEqual[y$46$im, 5.2e-199], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 1.8e+115], t$95$1, t$95$2]]]]]]]

Derivation

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

Alternative 4: 83.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}\\ t_1 := t_0 - \frac{x.re}{y.im}\\ \mathbf{if}\;y.im \leq -3.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 1.56 \cdot 10^{-94}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im \cdot x.re}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 115:\\ \;\;\;\;\frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 175000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (/ y.re (hypot y.re y.im)) (/ x.im (hypot y.re y.im))))
        (t_1 (- t_0 (/ x.re y.im))))
   (if (<= y.im -3.5e+18)
     t_1
     (if (<= y.im 1.56e-94)
       (- (/ x.im y.re) (/ (/ (* y.im x.re) y.re) y.re))
       (if (<= y.im 115.0)
         (/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))
         (if (<= y.im 175000000.0) t_0 t_1))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re / hypot(y_46_re, y_46_im)) * (x_46_im / hypot(y_46_re, y_46_im));
	double t_1 = t_0 - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -3.5e+18) {
		tmp = t_1;
	} else if (y_46_im <= 1.56e-94) {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	} else if (y_46_im <= 115.0) {
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_im <= 175000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re / Math.hypot(y_46_re, y_46_im)) * (x_46_im / Math.hypot(y_46_re, y_46_im));
	double t_1 = t_0 - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -3.5e+18) {
		tmp = t_1;
	} else if (y_46_im <= 1.56e-94) {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	} else if (y_46_im <= 115.0) {
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_im <= 175000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (y_46_re / math.hypot(y_46_re, y_46_im)) * (x_46_im / math.hypot(y_46_re, y_46_im))
	t_1 = t_0 - (x_46_re / y_46_im)
	tmp = 0
	if y_46_im <= -3.5e+18:
		tmp = t_1
	elif y_46_im <= 1.56e-94:
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re)
	elif y_46_im <= 115.0:
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	elif y_46_im <= 175000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(y_46_re / hypot(y_46_re, y_46_im)) * Float64(x_46_im / hypot(y_46_re, y_46_im)))
	t_1 = Float64(t_0 - Float64(x_46_re / y_46_im))
	tmp = 0.0
	if (y_46_im <= -3.5e+18)
		tmp = t_1;
	elseif (y_46_im <= 1.56e-94)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(Float64(y_46_im * x_46_re) / y_46_re) / y_46_re));
	elseif (y_46_im <= 115.0)
		tmp = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_im <= 175000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (y_46_re / hypot(y_46_re, y_46_im)) * (x_46_im / hypot(y_46_re, y_46_im));
	t_1 = t_0 - (x_46_re / y_46_im);
	tmp = 0.0;
	if (y_46_im <= -3.5e+18)
		tmp = t_1;
	elseif (y_46_im <= 1.56e-94)
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	elseif (y_46_im <= 115.0)
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	elseif (y_46_im <= 175000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(y$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(x$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -3.5e+18], t$95$1, If[LessEqual[y$46$im, 1.56e-94], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(N[(y$46$im * x$46$re), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 115.0], N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 175000000.0], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 5: 76.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im}{\frac{{y.im}^{2}}{y.re}} - \frac{x.re}{y.im}\\ \mathbf{if}\;y.im \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 9.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im \cdot x.re}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (/ x.im (/ (pow y.im 2.0) y.re)) (/ x.re y.im))))
   (if (<= y.im -1.55e+18)
     t_0
     (if (<= y.im 9.2e-104)
       (- (/ x.im y.re) (/ (/ (* y.im x.re) y.re) y.re))
       (if (<= y.im 9.5e+32)
         (/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))
         t_0)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_im / (pow(y_46_im, 2.0) / y_46_re)) - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -1.55e+18) {
		tmp = t_0;
	} else if (y_46_im <= 9.2e-104) {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	} else if (y_46_im <= 9.5e+32) {
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x_46im / ((y_46im ** 2.0d0) / y_46re)) - (x_46re / y_46im)
    if (y_46im <= (-1.55d+18)) then
        tmp = t_0
    else if (y_46im <= 9.2d-104) then
        tmp = (x_46im / y_46re) - (((y_46im * x_46re) / y_46re) / y_46re)
    else if (y_46im <= 9.5d+32) then
        tmp = ((y_46re * x_46im) - (y_46im * x_46re)) / ((y_46re * y_46re) + (y_46im * y_46im))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_im / (Math.pow(y_46_im, 2.0) / y_46_re)) - (x_46_re / y_46_im);
	double tmp;
	if (y_46_im <= -1.55e+18) {
		tmp = t_0;
	} else if (y_46_im <= 9.2e-104) {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	} else if (y_46_im <= 9.5e+32) {
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_im / (math.pow(y_46_im, 2.0) / y_46_re)) - (x_46_re / y_46_im)
	tmp = 0
	if y_46_im <= -1.55e+18:
		tmp = t_0
	elif y_46_im <= 9.2e-104:
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re)
	elif y_46_im <= 9.5e+32:
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_im / Float64((y_46_im ^ 2.0) / y_46_re)) - Float64(x_46_re / y_46_im))
	tmp = 0.0
	if (y_46_im <= -1.55e+18)
		tmp = t_0;
	elseif (y_46_im <= 9.2e-104)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(Float64(y_46_im * x_46_re) / y_46_re) / y_46_re));
	elseif (y_46_im <= 9.5e+32)
		tmp = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_im / ((y_46_im ^ 2.0) / y_46_re)) - (x_46_re / y_46_im);
	tmp = 0.0;
	if (y_46_im <= -1.55e+18)
		tmp = t_0;
	elseif (y_46_im <= 9.2e-104)
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	elseif (y_46_im <= 9.5e+32)
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$im / N[(N[Power[y$46$im, 2.0], $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -1.55e+18], t$95$0, If[LessEqual[y$46$im, 9.2e-104], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(N[(y$46$im * x$46$re), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 9.5e+32], N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 6: 77.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{x.im}{\frac{{y.im}^{2}}{y.re}} - \frac{x.re}{y.im}\\ \mathbf{elif}\;y.im \leq 4.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im \cdot x.re}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 9 \cdot 10^{+32}:\\ \;\;\;\;\frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{y.re}{\frac{{y.im}^{2}}{x.im}} - \frac{x.re}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.im -1.1e+19)
   (- (/ x.im (/ (pow y.im 2.0) y.re)) (/ x.re y.im))
   (if (<= y.im 4.6e-95)
     (- (/ x.im y.re) (/ (/ (* y.im x.re) y.re) y.re))
     (if (<= y.im 9e+32)
       (/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))
       (- (/ y.re (/ (pow y.im 2.0) x.im)) (/ x.re y.im))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_im <= -1.1e+19) {
		tmp = (x_46_im / (pow(y_46_im, 2.0) / y_46_re)) - (x_46_re / y_46_im);
	} else if (y_46_im <= 4.6e-95) {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	} else if (y_46_im <= 9e+32) {
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (y_46_re / (pow(y_46_im, 2.0) / x_46_im)) - (x_46_re / y_46_im);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46im <= (-1.1d+19)) then
        tmp = (x_46im / ((y_46im ** 2.0d0) / y_46re)) - (x_46re / y_46im)
    else if (y_46im <= 4.6d-95) then
        tmp = (x_46im / y_46re) - (((y_46im * x_46re) / y_46re) / y_46re)
    else if (y_46im <= 9d+32) then
        tmp = ((y_46re * x_46im) - (y_46im * x_46re)) / ((y_46re * y_46re) + (y_46im * y_46im))
    else
        tmp = (y_46re / ((y_46im ** 2.0d0) / x_46im)) - (x_46re / y_46im)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_im <= -1.1e+19) {
		tmp = (x_46_im / (Math.pow(y_46_im, 2.0) / y_46_re)) - (x_46_re / y_46_im);
	} else if (y_46_im <= 4.6e-95) {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	} else if (y_46_im <= 9e+32) {
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (y_46_re / (Math.pow(y_46_im, 2.0) / x_46_im)) - (x_46_re / y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_im <= -1.1e+19:
		tmp = (x_46_im / (math.pow(y_46_im, 2.0) / y_46_re)) - (x_46_re / y_46_im)
	elif y_46_im <= 4.6e-95:
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re)
	elif y_46_im <= 9e+32:
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	else:
		tmp = (y_46_re / (math.pow(y_46_im, 2.0) / x_46_im)) - (x_46_re / y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_im <= -1.1e+19)
		tmp = Float64(Float64(x_46_im / Float64((y_46_im ^ 2.0) / y_46_re)) - Float64(x_46_re / y_46_im));
	elseif (y_46_im <= 4.6e-95)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(Float64(y_46_im * x_46_re) / y_46_re) / y_46_re));
	elseif (y_46_im <= 9e+32)
		tmp = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	else
		tmp = Float64(Float64(y_46_re / Float64((y_46_im ^ 2.0) / x_46_im)) - Float64(x_46_re / y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_im <= -1.1e+19)
		tmp = (x_46_im / ((y_46_im ^ 2.0) / y_46_re)) - (x_46_re / y_46_im);
	elseif (y_46_im <= 4.6e-95)
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	elseif (y_46_im <= 9e+32)
		tmp = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	else
		tmp = (y_46_re / ((y_46_im ^ 2.0) / x_46_im)) - (x_46_re / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$im, -1.1e+19], N[(N[(x$46$im / N[(N[Power[y$46$im, 2.0], $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 4.6e-95], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(N[(y$46$im * x$46$re), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 9e+32], N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y$46$re / N[(N[Power[y$46$im, 2.0], $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision] - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 78.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -9.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{elif}\;y.im \leq -4.6 \cdot 10^{-110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 6.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-x.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.im -9.2e+132)
     (/ (- x.re) y.im)
     (if (<= y.im -4.6e-110)
       t_0
       (if (<= y.im 6.8e-106)
         (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))
         (if (<= y.im 3.5e+66) t_0 (/ (- x.re) (hypot y.re y.im))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -9.2e+132) {
		tmp = -x_46_re / y_46_im;
	} else if (y_46_im <= -4.6e-110) {
		tmp = t_0;
	} else if (y_46_im <= 6.8e-106) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 3.5e+66) {
		tmp = t_0;
	} else {
		tmp = -x_46_re / hypot(y_46_re, y_46_im);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -9.2e+132) {
		tmp = -x_46_re / y_46_im;
	} else if (y_46_im <= -4.6e-110) {
		tmp = t_0;
	} else if (y_46_im <= 6.8e-106) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 3.5e+66) {
		tmp = t_0;
	} else {
		tmp = -x_46_re / Math.hypot(y_46_re, y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_im <= -9.2e+132:
		tmp = -x_46_re / y_46_im
	elif y_46_im <= -4.6e-110:
		tmp = t_0
	elif y_46_im <= 6.8e-106:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	elif y_46_im <= 3.5e+66:
		tmp = t_0
	else:
		tmp = -x_46_re / math.hypot(y_46_re, y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_im <= -9.2e+132)
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	elseif (y_46_im <= -4.6e-110)
		tmp = t_0;
	elseif (y_46_im <= 6.8e-106)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	elseif (y_46_im <= 3.5e+66)
		tmp = t_0;
	else
		tmp = Float64(Float64(-x_46_re) / hypot(y_46_re, y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_im <= -9.2e+132)
		tmp = -x_46_re / y_46_im;
	elseif (y_46_im <= -4.6e-110)
		tmp = t_0;
	elseif (y_46_im <= 6.8e-106)
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	elseif (y_46_im <= 3.5e+66)
		tmp = t_0;
	else
		tmp = -x_46_re / hypot(y_46_re, y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -9.2e+132], N[((-x$46$re) / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, -4.6e-110], t$95$0, If[LessEqual[y$46$im, 6.8e-106], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 3.5e+66], t$95$0, N[((-x$46$re) / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 8: 79.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -6.9 \cdot 10^{+131}:\\ \;\;\;\;\frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.im \leq -1.2 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 7 \cdot 10^{-101}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-x.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.im -6.9e+131)
     (/ x.re (hypot y.re y.im))
     (if (<= y.im -1.2e-104)
       t_0
       (if (<= y.im 7e-101)
         (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))
         (if (<= y.im 4.5e+65) t_0 (/ (- x.re) (hypot y.re y.im))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -6.9e+131) {
		tmp = x_46_re / hypot(y_46_re, y_46_im);
	} else if (y_46_im <= -1.2e-104) {
		tmp = t_0;
	} else if (y_46_im <= 7e-101) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 4.5e+65) {
		tmp = t_0;
	} else {
		tmp = -x_46_re / hypot(y_46_re, y_46_im);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -6.9e+131) {
		tmp = x_46_re / Math.hypot(y_46_re, y_46_im);
	} else if (y_46_im <= -1.2e-104) {
		tmp = t_0;
	} else if (y_46_im <= 7e-101) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 4.5e+65) {
		tmp = t_0;
	} else {
		tmp = -x_46_re / Math.hypot(y_46_re, y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_im <= -6.9e+131:
		tmp = x_46_re / math.hypot(y_46_re, y_46_im)
	elif y_46_im <= -1.2e-104:
		tmp = t_0
	elif y_46_im <= 7e-101:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	elif y_46_im <= 4.5e+65:
		tmp = t_0
	else:
		tmp = -x_46_re / math.hypot(y_46_re, y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_im <= -6.9e+131)
		tmp = Float64(x_46_re / hypot(y_46_re, y_46_im));
	elseif (y_46_im <= -1.2e-104)
		tmp = t_0;
	elseif (y_46_im <= 7e-101)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	elseif (y_46_im <= 4.5e+65)
		tmp = t_0;
	else
		tmp = Float64(Float64(-x_46_re) / hypot(y_46_re, y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_im <= -6.9e+131)
		tmp = x_46_re / hypot(y_46_re, y_46_im);
	elseif (y_46_im <= -1.2e-104)
		tmp = t_0;
	elseif (y_46_im <= 7e-101)
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	elseif (y_46_im <= 4.5e+65)
		tmp = t_0;
	else
		tmp = -x_46_re / hypot(y_46_re, y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -6.9e+131], N[(x$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, -1.2e-104], t$95$0, If[LessEqual[y$46$im, 7e-101], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 4.5e+65], t$95$0, N[((-x$46$re) / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 9: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x.re}{y.im}\\ t_1 := \frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -1.55 \cdot 10^{+134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq -1.45 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 4.05 \cdot 10^{-88}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.8 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (- x.re) y.im))
        (t_1
         (/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.im -1.55e+134)
     t_0
     (if (<= y.im -1.45e-112)
       t_1
       (if (<= y.im 4.05e-88)
         (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))
         (if (<= y.im 2.8e+66) t_1 t_0))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = -x_46_re / y_46_im;
	double t_1 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -1.55e+134) {
		tmp = t_0;
	} else if (y_46_im <= -1.45e-112) {
		tmp = t_1;
	} else if (y_46_im <= 4.05e-88) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 2.8e+66) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = -x_46re / y_46im
    t_1 = ((y_46re * x_46im) - (y_46im * x_46re)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46im <= (-1.55d+134)) then
        tmp = t_0
    else if (y_46im <= (-1.45d-112)) then
        tmp = t_1
    else if (y_46im <= 4.05d-88) then
        tmp = (x_46im / y_46re) - ((y_46im / (y_46re / x_46re)) / y_46re)
    else if (y_46im <= 2.8d+66) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = -x_46_re / y_46_im;
	double t_1 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -1.55e+134) {
		tmp = t_0;
	} else if (y_46_im <= -1.45e-112) {
		tmp = t_1;
	} else if (y_46_im <= 4.05e-88) {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	} else if (y_46_im <= 2.8e+66) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = -x_46_re / y_46_im
	t_1 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_im <= -1.55e+134:
		tmp = t_0
	elif y_46_im <= -1.45e-112:
		tmp = t_1
	elif y_46_im <= 4.05e-88:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	elif y_46_im <= 2.8e+66:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(-x_46_re) / y_46_im)
	t_1 = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_im <= -1.55e+134)
		tmp = t_0;
	elseif (y_46_im <= -1.45e-112)
		tmp = t_1;
	elseif (y_46_im <= 4.05e-88)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	elseif (y_46_im <= 2.8e+66)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = -x_46_re / y_46_im;
	t_1 = ((y_46_re * x_46_im) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_im <= -1.55e+134)
		tmp = t_0;
	elseif (y_46_im <= -1.45e-112)
		tmp = t_1;
	elseif (y_46_im <= 4.05e-88)
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	elseif (y_46_im <= 2.8e+66)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[((-x$46$re) / y$46$im), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -1.55e+134], t$95$0, If[LessEqual[y$46$im, -1.45e-112], t$95$1, If[LessEqual[y$46$im, 4.05e-88], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 2.8e+66], t$95$1, t$95$0]]]]]]

Derivation

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

Alternative 10: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x.re}{y.im}\\ \mathbf{if}\;y.im \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 3.9 \cdot 10^{-75}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \mathbf{elif}\;y.im \leq 1.18 \cdot 10^{+23}:\\ \;\;\;\;\frac{y.im \cdot \left(-x.re\right)}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (- x.re) y.im)))
   (if (<= y.im -5e+18)
     t_0
     (if (<= y.im 3.9e-75)
       (/ x.im y.re)
       (if (<= y.im 1.18e+23)
         (/ (* y.im (- x.re)) (+ (* y.re y.re) (* y.im y.im)))
         t_0)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = -x_46_re / y_46_im;
	double tmp;
	if (y_46_im <= -5e+18) {
		tmp = t_0;
	} else if (y_46_im <= 3.9e-75) {
		tmp = x_46_im / y_46_re;
	} else if (y_46_im <= 1.18e+23) {
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x_46re / y_46im
    if (y_46im <= (-5d+18)) then
        tmp = t_0
    else if (y_46im <= 3.9d-75) then
        tmp = x_46im / y_46re
    else if (y_46im <= 1.18d+23) then
        tmp = (y_46im * -x_46re) / ((y_46re * y_46re) + (y_46im * y_46im))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = -x_46_re / y_46_im;
	double tmp;
	if (y_46_im <= -5e+18) {
		tmp = t_0;
	} else if (y_46_im <= 3.9e-75) {
		tmp = x_46_im / y_46_re;
	} else if (y_46_im <= 1.18e+23) {
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = -x_46_re / y_46_im
	tmp = 0
	if y_46_im <= -5e+18:
		tmp = t_0
	elif y_46_im <= 3.9e-75:
		tmp = x_46_im / y_46_re
	elif y_46_im <= 1.18e+23:
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(-x_46_re) / y_46_im)
	tmp = 0.0
	if (y_46_im <= -5e+18)
		tmp = t_0;
	elseif (y_46_im <= 3.9e-75)
		tmp = Float64(x_46_im / y_46_re);
	elseif (y_46_im <= 1.18e+23)
		tmp = Float64(Float64(y_46_im * Float64(-x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = -x_46_re / y_46_im;
	tmp = 0.0;
	if (y_46_im <= -5e+18)
		tmp = t_0;
	elseif (y_46_im <= 3.9e-75)
		tmp = x_46_im / y_46_re;
	elseif (y_46_im <= 1.18e+23)
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[((-x$46$re) / y$46$im), $MachinePrecision]}, If[LessEqual[y$46$im, -5e+18], t$95$0, If[LessEqual[y$46$im, 3.9e-75], N[(x$46$im / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 1.18e+23], N[(N[(y$46$im * (-x$46$re)), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 11: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -8.2 \cdot 10^{+18} \lor \neg \left(y.im \leq 6 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{y.im}{y.re} \cdot \frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -8.2e+18) (not (<= y.im 6e+51)))
   (/ (- x.re) y.im)
   (- (/ x.im y.re) (* (/ y.im y.re) (/ x.re y.re)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -8.2e+18) || !(y_46_im <= 6e+51)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im / y_46_re) - ((y_46_im / y_46_re) * (x_46_re / y_46_re));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-8.2d+18)) .or. (.not. (y_46im <= 6d+51))) then
        tmp = -x_46re / y_46im
    else
        tmp = (x_46im / y_46re) - ((y_46im / y_46re) * (x_46re / y_46re))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -8.2e+18) || !(y_46_im <= 6e+51)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im / y_46_re) - ((y_46_im / y_46_re) * (x_46_re / y_46_re));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -8.2e+18) or not (y_46_im <= 6e+51):
		tmp = -x_46_re / y_46_im
	else:
		tmp = (x_46_im / y_46_re) - ((y_46_im / y_46_re) * (x_46_re / y_46_re))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -8.2e+18) || !(y_46_im <= 6e+51))
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / y_46_re) * Float64(x_46_re / y_46_re)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -8.2e+18) || ~((y_46_im <= 6e+51)))
		tmp = -x_46_re / y_46_im;
	else
		tmp = (x_46_im / y_46_re) - ((y_46_im / y_46_re) * (x_46_re / y_46_re));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -8.2e+18], N[Not[LessEqual[y$46$im, 6e+51]], $MachinePrecision]], N[((-x$46$re) / y$46$im), $MachinePrecision], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.5 \cdot 10^{+18} \lor \neg \left(y.im \leq 9.5 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1.5e+18) (not (<= y.im 9.5e+48)))
   (/ (- x.re) y.im)
   (- (/ x.im y.re) (/ (/ y.im (/ y.re x.re)) y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.5e+18) || !(y_46_im <= 9.5e+48)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-1.5d+18)) .or. (.not. (y_46im <= 9.5d+48))) then
        tmp = -x_46re / y_46im
    else
        tmp = (x_46im / y_46re) - ((y_46im / (y_46re / x_46re)) / y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.5e+18) || !(y_46_im <= 9.5e+48)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -1.5e+18) or not (y_46_im <= 9.5e+48):
		tmp = -x_46_re / y_46_im
	else:
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -1.5e+18) || !(y_46_im <= 9.5e+48))
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im / Float64(y_46_re / x_46_re)) / y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -1.5e+18) || ~((y_46_im <= 9.5e+48)))
		tmp = -x_46_re / y_46_im;
	else
		tmp = (x_46_im / y_46_re) - ((y_46_im / (y_46_re / x_46_re)) / y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -1.5e+18], N[Not[LessEqual[y$46$im, 9.5e+48]], $MachinePrecision]], N[((-x$46$re) / y$46$im), $MachinePrecision], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.2 \cdot 10^{+19} \lor \neg \left(y.im \leq 1.6 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{y.im \cdot x.re}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1.2e+19) (not (<= y.im 1.6e+51)))
   (/ (- x.re) y.im)
   (- (/ x.im y.re) (/ (/ (* y.im x.re) y.re) y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.2e+19) || !(y_46_im <= 1.6e+51)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-1.2d+19)) .or. (.not. (y_46im <= 1.6d+51))) then
        tmp = -x_46re / y_46im
    else
        tmp = (x_46im / y_46re) - (((y_46im * x_46re) / y_46re) / y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.2e+19) || !(y_46_im <= 1.6e+51)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -1.2e+19) or not (y_46_im <= 1.6e+51):
		tmp = -x_46_re / y_46_im
	else:
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -1.2e+19) || !(y_46_im <= 1.6e+51))
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(Float64(y_46_im * x_46_re) / y_46_re) / y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -1.2e+19) || ~((y_46_im <= 1.6e+51)))
		tmp = -x_46_re / y_46_im;
	else
		tmp = (x_46_im / y_46_re) - (((y_46_im * x_46_re) / y_46_re) / y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -1.2e+19], N[Not[LessEqual[y$46$im, 1.6e+51]], $MachinePrecision]], N[((-x$46$re) / y$46$im), $MachinePrecision], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(N[(y$46$im * x$46$re), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 63.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.8 \cdot 10^{+18} \lor \neg \left(y.im \leq 8 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1.8e+18) (not (<= y.im 8e+48)))
   (/ (- x.re) y.im)
   (/ x.im y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.8e+18) || !(y_46_im <= 8e+48)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = x_46_im / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-1.8d+18)) .or. (.not. (y_46im <= 8d+48))) then
        tmp = -x_46re / y_46im
    else
        tmp = x_46im / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.8e+18) || !(y_46_im <= 8e+48)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = x_46_im / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -1.8e+18) or not (y_46_im <= 8e+48):
		tmp = -x_46_re / y_46_im
	else:
		tmp = x_46_im / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -1.8e+18) || !(y_46_im <= 8e+48))
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	else
		tmp = Float64(x_46_im / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -1.8e+18) || ~((y_46_im <= 8e+48)))
		tmp = -x_46_re / y_46_im;
	else
		tmp = x_46_im / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -1.8e+18], N[Not[LessEqual[y$46$im, 8e+48]], $MachinePrecision]], N[((-x$46$re) / y$46$im), $MachinePrecision], N[(x$46$im / y$46$re), $MachinePrecision]]

Derivation

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

Alternative 15: 42.7% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (x.re x.im y.re y.im) :precision binary64 (/ x.im y.re))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return x_46_im / y_46_re;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = x_46im / y_46re
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return x_46_im / y_46_re;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return x_46_im / y_46_re

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(x_46_im / y_46_re)
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = x_46_im / y_46_re;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(x$46$im / y$46$re), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  :precision binary64
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))