_divideComplex, real part

Percentage Accurate: 61.2% → 83.8%

Time: 17.2s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (+ (* x.re y.re) (* x.im 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_re * y_46_re) + (x_46_im * 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_46re * y_46re) + (x_46im * 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_re * y_46_re) + (x_46_im * 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_re * y_46_re) + (x_46_im * 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_re * y_46_re) + Float64(x_46_im * 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_re * y_46_re) + (x_46_im * 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$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * 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: 61.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (+ (* x.re y.re) (* x.im 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_re * y_46_re) + (x_46_im * 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_46re * y_46re) + (x_46im * 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_re * y_46_re) + (x_46_im * 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_re * y_46_re) + (x_46_im * 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_re * y_46_re) + Float64(x_46_im * 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_re * y_46_re) + (x_46_im * 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$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * 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: 83.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<=
      (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
      INFINITY)
   (/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
   (/ x.re (+ y.re (* y.im (/ y.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 ((((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= ((double) INFINITY)) {
		tmp = (fma(x_46_re, y_46_re, (x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im);
	} else {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_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 (Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))) <= Inf)
		tmp = Float64(Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im));
	else
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_46_im / y_46_re))));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x$46$re * y$46$re + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], N[(x$46$re / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 82.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im}{\frac{y.re}{y.im}}\\ \mathbf{if}\;y.re \leq -4.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{\left(-x.re\right) - t_0}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.re \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \mathbf{elif}\;y.re \leq 5 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right) \cdot {\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{-2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + t_0}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ x.im (/ y.re y.im))))
   (if (<= y.re -4.5e+88)
     (/ (- (- x.re) t_0) (hypot y.re y.im))
     (if (<= y.re -1.05e-134)
       (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
       (if (<= y.re 7.2e-163)
         (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.im y.re))))
         (if (<= y.re 5e+103)
           (* (fma x.re y.re (* x.im y.im)) (pow (hypot y.re y.im) -2.0))
           (/ (+ x.re t_0) (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 = x_46_im / (y_46_re / y_46_im);
	double tmp;
	if (y_46_re <= -4.5e+88) {
		tmp = (-x_46_re - t_0) / hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -1.05e-134) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 5e+103) {
		tmp = fma(x_46_re, y_46_re, (x_46_im * y_46_im)) * pow(hypot(y_46_re, y_46_im), -2.0);
	} else {
		tmp = (x_46_re + t_0) / 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(x_46_im / Float64(y_46_re / y_46_im))
	tmp = 0.0
	if (y_46_re <= -4.5e+88)
		tmp = Float64(Float64(Float64(-x_46_re) - t_0) / hypot(y_46_re, y_46_im));
	elseif (y_46_re <= -1.05e-134)
		tmp = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_re <= 7.2e-163)
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_46_im / y_46_re))));
	elseif (y_46_re <= 5e+103)
		tmp = Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) * (hypot(y_46_re, y_46_im) ^ -2.0));
	else
		tmp = Float64(Float64(x_46_re + t_0) / hypot(y_46_re, y_46_im));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -4.5e+88], N[(N[((-x$46$re) - t$95$0), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -1.05e-134], N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 7.2e-163], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 5e+103], N[(N[(x$46$re * y$46$re + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] * N[Power[N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re + t$95$0), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 81.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.re \cdot y.re + x.im \cdot y.im\\ \mathbf{if}\;y.re \leq -1.15 \cdot 10^{+87}:\\ \;\;\;\;\frac{\left(-x.re\right) - \frac{x.im}{\frac{y.re}{y.im}}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.re \leq -1.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{t_0}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \mathbf{elif}\;y.re \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;\frac{t_0}{\frac{\mathsf{hypot}\left(y.re, y.im\right)}{\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right) \cdot \frac{\mathsf{hypot}\left(y.re, y.im\right)}{y.re}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (* x.re y.re) (* x.im y.im))))
   (if (<= y.re -1.15e+87)
     (/ (- (- x.re) (/ x.im (/ y.re y.im))) (hypot y.re y.im))
     (if (<= y.re -1.6e-134)
       (/ t_0 (+ (* y.re y.re) (* y.im y.im)))
       (if (<= y.re 7.2e-163)
         (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.im y.re))))
         (if (<= y.re 3.3e+68)
           (/ t_0 (/ (hypot y.re y.im) (/ 1.0 (hypot y.re y.im))))
           (/ x.re (* (hypot y.re y.im) (/ (hypot y.re y.im) y.re)))))))))

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_re) + (x_46_im * y_46_im);
	double tmp;
	if (y_46_re <= -1.15e+87) {
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -1.6e-134) {
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 3.3e+68) {
		tmp = t_0 / (hypot(y_46_re, y_46_im) / (1.0 / hypot(y_46_re, y_46_im)));
	} else {
		tmp = x_46_re / (hypot(y_46_re, y_46_im) * (hypot(y_46_re, y_46_im) / y_46_re));
	}
	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 = (x_46_re * y_46_re) + (x_46_im * y_46_im);
	double tmp;
	if (y_46_re <= -1.15e+87) {
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / Math.hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -1.6e-134) {
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 3.3e+68) {
		tmp = t_0 / (Math.hypot(y_46_re, y_46_im) / (1.0 / Math.hypot(y_46_re, y_46_im)));
	} else {
		tmp = x_46_re / (Math.hypot(y_46_re, y_46_im) * (Math.hypot(y_46_re, y_46_im) / y_46_re));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re * y_46_re) + (x_46_im * y_46_im)
	tmp = 0
	if y_46_re <= -1.15e+87:
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / math.hypot(y_46_re, y_46_im)
	elif y_46_re <= -1.6e-134:
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	elif y_46_re <= 7.2e-163:
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)))
	elif y_46_re <= 3.3e+68:
		tmp = t_0 / (math.hypot(y_46_re, y_46_im) / (1.0 / math.hypot(y_46_re, y_46_im)))
	else:
		tmp = x_46_re / (math.hypot(y_46_re, y_46_im) * (math.hypot(y_46_re, y_46_im) / y_46_re))
	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_re) + Float64(x_46_im * y_46_im))
	tmp = 0.0
	if (y_46_re <= -1.15e+87)
		tmp = Float64(Float64(Float64(-x_46_re) - Float64(x_46_im / Float64(y_46_re / y_46_im))) / hypot(y_46_re, y_46_im));
	elseif (y_46_re <= -1.6e-134)
		tmp = Float64(t_0 / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_re <= 7.2e-163)
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_46_im / y_46_re))));
	elseif (y_46_re <= 3.3e+68)
		tmp = Float64(t_0 / Float64(hypot(y_46_re, y_46_im) / Float64(1.0 / hypot(y_46_re, y_46_im))));
	else
		tmp = Float64(x_46_re / Float64(hypot(y_46_re, y_46_im) * Float64(hypot(y_46_re, y_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)
	t_0 = (x_46_re * y_46_re) + (x_46_im * y_46_im);
	tmp = 0.0;
	if (y_46_re <= -1.15e+87)
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / hypot(y_46_re, y_46_im);
	elseif (y_46_re <= -1.6e-134)
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	elseif (y_46_re <= 7.2e-163)
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	elseif (y_46_re <= 3.3e+68)
		tmp = t_0 / (hypot(y_46_re, y_46_im) / (1.0 / hypot(y_46_re, y_46_im)));
	else
		tmp = x_46_re / (hypot(y_46_re, y_46_im) * (hypot(y_46_re, y_46_im) / y_46_re));
	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$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -1.15e+87], N[(N[((-x$46$re) - N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -1.6e-134], N[(t$95$0 / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 7.2e-163], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 3.3e+68], N[(t$95$0 / N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] / N[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$46$re / N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] * N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 81.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.re \leq -2.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{\left(-x.re\right) - \frac{x.im}{\frac{y.re}{y.im}}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.re \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \mathbf{elif}\;y.re \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right) \cdot \frac{\mathsf{hypot}\left(y.re, y.im\right)}{y.re}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.re -2.25e+86)
     (/ (- (- x.re) (/ x.im (/ y.re y.im))) (hypot y.re y.im))
     (if (<= y.re -6e-135)
       t_0
       (if (<= y.re 7.2e-163)
         (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.im y.re))))
         (if (<= y.re 1.8e+68)
           t_0
           (/ x.re (* (hypot y.re y.im) (/ (hypot y.re y.im) y.re)))))))))

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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -2.25e+86) {
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -6e-135) {
		tmp = t_0;
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 1.8e+68) {
		tmp = t_0;
	} else {
		tmp = x_46_re / (hypot(y_46_re, y_46_im) * (hypot(y_46_re, y_46_im) / y_46_re));
	}
	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 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -2.25e+86) {
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / Math.hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -6e-135) {
		tmp = t_0;
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 1.8e+68) {
		tmp = t_0;
	} else {
		tmp = x_46_re / (Math.hypot(y_46_re, y_46_im) * (Math.hypot(y_46_re, y_46_im) / y_46_re));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_re <= -2.25e+86:
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / math.hypot(y_46_re, y_46_im)
	elif y_46_re <= -6e-135:
		tmp = t_0
	elif y_46_re <= 7.2e-163:
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)))
	elif y_46_re <= 1.8e+68:
		tmp = t_0
	else:
		tmp = x_46_re / (math.hypot(y_46_re, y_46_im) * (math.hypot(y_46_re, y_46_im) / y_46_re))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_re <= -2.25e+86)
		tmp = Float64(Float64(Float64(-x_46_re) - Float64(x_46_im / Float64(y_46_re / y_46_im))) / hypot(y_46_re, y_46_im));
	elseif (y_46_re <= -6e-135)
		tmp = t_0;
	elseif (y_46_re <= 7.2e-163)
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_46_im / y_46_re))));
	elseif (y_46_re <= 1.8e+68)
		tmp = t_0;
	else
		tmp = Float64(x_46_re / Float64(hypot(y_46_re, y_46_im) * Float64(hypot(y_46_re, y_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)
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_re <= -2.25e+86)
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / hypot(y_46_re, y_46_im);
	elseif (y_46_re <= -6e-135)
		tmp = t_0;
	elseif (y_46_re <= 7.2e-163)
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	elseif (y_46_re <= 1.8e+68)
		tmp = t_0;
	else
		tmp = x_46_re / (hypot(y_46_re, y_46_im) * (hypot(y_46_re, y_46_im) / y_46_re));
	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[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -2.25e+86], N[(N[((-x$46$re) - N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -6e-135], t$95$0, If[LessEqual[y$46$re, 7.2e-163], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.8e+68], t$95$0, N[(x$46$re / N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] * N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 81.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.re \leq -9 \cdot 10^{+87}:\\ \;\;\;\;\frac{\left(-x.re\right) - \frac{x.im}{\frac{y.re}{y.im}}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.re \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \mathbf{elif}\;y.re \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.re -9e+87)
     (/ (- (- x.re) (/ x.im (/ y.re y.im))) (hypot y.re y.im))
     (if (<= y.re -6e-135)
       t_0
       (if (<= y.re 7.2e-163)
         (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.im y.re))))
         (if (<= y.re 3.3e+68)
           t_0
           (/ x.re (+ y.re (* y.im (/ y.im y.re))))))))))

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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -9e+87) {
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -6e-135) {
		tmp = t_0;
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 3.3e+68) {
		tmp = t_0;
	} else {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	}
	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 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -9e+87) {
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / Math.hypot(y_46_re, y_46_im);
	} else if (y_46_re <= -6e-135) {
		tmp = t_0;
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 3.3e+68) {
		tmp = t_0;
	} else {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_re <= -9e+87:
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / math.hypot(y_46_re, y_46_im)
	elif y_46_re <= -6e-135:
		tmp = t_0
	elif y_46_re <= 7.2e-163:
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)))
	elif y_46_re <= 3.3e+68:
		tmp = t_0
	else:
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_re <= -9e+87)
		tmp = Float64(Float64(Float64(-x_46_re) - Float64(x_46_im / Float64(y_46_re / y_46_im))) / hypot(y_46_re, y_46_im));
	elseif (y_46_re <= -6e-135)
		tmp = t_0;
	elseif (y_46_re <= 7.2e-163)
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_46_im / y_46_re))));
	elseif (y_46_re <= 3.3e+68)
		tmp = t_0;
	else
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_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)
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_re <= -9e+87)
		tmp = (-x_46_re - (x_46_im / (y_46_re / y_46_im))) / hypot(y_46_re, y_46_im);
	elseif (y_46_re <= -6e-135)
		tmp = t_0;
	elseif (y_46_re <= 7.2e-163)
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	elseif (y_46_re <= 3.3e+68)
		tmp = t_0;
	else
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	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[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -9e+87], N[(N[((-x$46$re) - N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -6e-135], t$95$0, If[LessEqual[y$46$re, 7.2e-163], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 3.3e+68], t$95$0, N[(x$46$re / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.re \leq -2.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x.re}{y.re} + y.im \cdot \left(\frac{1}{y.re} \cdot \frac{x.im}{y.re}\right)\\ \mathbf{elif}\;y.re \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \mathbf{elif}\;y.re \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.re -2.5e+89)
     (+ (/ x.re y.re) (* y.im (* (/ 1.0 y.re) (/ x.im y.re))))
     (if (<= y.re -6e-135)
       t_0
       (if (<= y.re 7.2e-163)
         (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.im y.re))))
         (if (<= y.re 2.8e+68)
           t_0
           (/ x.re (+ y.re (* y.im (/ y.im y.re))))))))))

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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -2.5e+89) {
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)));
	} else if (y_46_re <= -6e-135) {
		tmp = t_0;
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 2.8e+68) {
		tmp = t_0;
	} else {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_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) :: t_0
    real(8) :: tmp
    t_0 = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46re <= (-2.5d+89)) then
        tmp = (x_46re / y_46re) + (y_46im * ((1.0d0 / y_46re) * (x_46im / y_46re)))
    else if (y_46re <= (-6d-135)) then
        tmp = t_0
    else if (y_46re <= 7.2d-163) then
        tmp = ((-1.0d0) / y_46im) * (-x_46im - (x_46re / (y_46im / y_46re)))
    else if (y_46re <= 2.8d+68) then
        tmp = t_0
    else
        tmp = x_46re / (y_46re + (y_46im * (y_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 t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -2.5e+89) {
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)));
	} else if (y_46_re <= -6e-135) {
		tmp = t_0;
	} else if (y_46_re <= 7.2e-163) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else if (y_46_re <= 2.8e+68) {
		tmp = t_0;
	} else {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_re <= -2.5e+89:
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)))
	elif y_46_re <= -6e-135:
		tmp = t_0
	elif y_46_re <= 7.2e-163:
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)))
	elif y_46_re <= 2.8e+68:
		tmp = t_0
	else:
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_re <= -2.5e+89)
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im * Float64(Float64(1.0 / y_46_re) * Float64(x_46_im / y_46_re))));
	elseif (y_46_re <= -6e-135)
		tmp = t_0;
	elseif (y_46_re <= 7.2e-163)
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_46_im / y_46_re))));
	elseif (y_46_re <= 2.8e+68)
		tmp = t_0;
	else
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_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)
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_re <= -2.5e+89)
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)));
	elseif (y_46_re <= -6e-135)
		tmp = t_0;
	elseif (y_46_re <= 7.2e-163)
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	elseif (y_46_re <= 2.8e+68)
		tmp = t_0;
	else
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	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[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -2.5e+89], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im * N[(N[(1.0 / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -6e-135], t$95$0, If[LessEqual[y$46$re, 7.2e-163], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.8e+68], t$95$0, N[(x$46$re / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 7: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.5 \cdot 10^{-15} \lor \neg \left(y.re \leq -1.75 \cdot 10^{-47} \lor \neg \left(y.re \leq -2.65 \cdot 10^{-128}\right) \land y.re \leq 8.2 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -3.5e-15)
         (not
          (or (<= y.re -1.75e-47)
              (and (not (<= y.re -2.65e-128)) (<= y.re 8.2e-80)))))
   (/ x.re (+ y.re (* y.im (/ y.im y.re))))
   (/ x.im 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_re <= -3.5e-15) || !((y_46_re <= -1.75e-47) || (!(y_46_re <= -2.65e-128) && (y_46_re <= 8.2e-80)))) {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	} else {
		tmp = x_46_im / 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_46re <= (-3.5d-15)) .or. (.not. (y_46re <= (-1.75d-47)) .or. (.not. (y_46re <= (-2.65d-128))) .and. (y_46re <= 8.2d-80))) then
        tmp = x_46re / (y_46re + (y_46im * (y_46im / y_46re)))
    else
        tmp = x_46im / 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_re <= -3.5e-15) || !((y_46_re <= -1.75e-47) || (!(y_46_re <= -2.65e-128) && (y_46_re <= 8.2e-80)))) {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	} else {
		tmp = x_46_im / 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_re <= -3.5e-15) or not ((y_46_re <= -1.75e-47) or (not (y_46_re <= -2.65e-128) and (y_46_re <= 8.2e-80))):
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)))
	else:
		tmp = x_46_im / 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_re <= -3.5e-15) || !((y_46_re <= -1.75e-47) || (!(y_46_re <= -2.65e-128) && (y_46_re <= 8.2e-80))))
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_46_im / y_46_re))));
	else
		tmp = Float64(x_46_im / 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_re <= -3.5e-15) || ~(((y_46_re <= -1.75e-47) || (~((y_46_re <= -2.65e-128)) && (y_46_re <= 8.2e-80)))))
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	else
		tmp = x_46_im / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -3.5e-15], N[Not[Or[LessEqual[y$46$re, -1.75e-47], And[N[Not[LessEqual[y$46$re, -2.65e-128]], $MachinePrecision], LessEqual[y$46$re, 8.2e-80]]]], $MachinePrecision]], N[(x$46$re / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]

Derivation

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

Alternative 8: 68.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{if}\;y.re \leq -1.65 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{elif}\;y.re \leq -3.9 \cdot 10^{-129}:\\ \;\;\;\;\frac{x.re}{y.re + \frac{y.im \cdot y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 7 \cdot 10^{-81}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ x.re (+ y.re (* y.im (/ y.im y.re))))))
   (if (<= y.re -1.65e-13)
     t_0
     (if (<= y.re -1.5e-46)
       (/ x.im y.im)
       (if (<= y.re -3.9e-129)
         (/ x.re (+ y.re (/ (* y.im y.im) y.re)))
         (if (<= y.re 7e-81) (/ x.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_re + (y_46_im * (y_46_im / y_46_re)));
	double tmp;
	if (y_46_re <= -1.65e-13) {
		tmp = t_0;
	} else if (y_46_re <= -1.5e-46) {
		tmp = x_46_im / y_46_im;
	} else if (y_46_re <= -3.9e-129) {
		tmp = x_46_re / (y_46_re + ((y_46_im * y_46_im) / y_46_re));
	} else if (y_46_re <= 7e-81) {
		tmp = x_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_46re + (y_46im * (y_46im / y_46re)))
    if (y_46re <= (-1.65d-13)) then
        tmp = t_0
    else if (y_46re <= (-1.5d-46)) then
        tmp = x_46im / y_46im
    else if (y_46re <= (-3.9d-129)) then
        tmp = x_46re / (y_46re + ((y_46im * y_46im) / y_46re))
    else if (y_46re <= 7d-81) then
        tmp = x_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_re + (y_46_im * (y_46_im / y_46_re)));
	double tmp;
	if (y_46_re <= -1.65e-13) {
		tmp = t_0;
	} else if (y_46_re <= -1.5e-46) {
		tmp = x_46_im / y_46_im;
	} else if (y_46_re <= -3.9e-129) {
		tmp = x_46_re / (y_46_re + ((y_46_im * y_46_im) / y_46_re));
	} else if (y_46_re <= 7e-81) {
		tmp = x_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_re + (y_46_im * (y_46_im / y_46_re)))
	tmp = 0
	if y_46_re <= -1.65e-13:
		tmp = t_0
	elif y_46_re <= -1.5e-46:
		tmp = x_46_im / y_46_im
	elif y_46_re <= -3.9e-129:
		tmp = x_46_re / (y_46_re + ((y_46_im * y_46_im) / y_46_re))
	elif y_46_re <= 7e-81:
		tmp = x_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(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_46_im / y_46_re))))
	tmp = 0.0
	if (y_46_re <= -1.65e-13)
		tmp = t_0;
	elseif (y_46_re <= -1.5e-46)
		tmp = Float64(x_46_im / y_46_im);
	elseif (y_46_re <= -3.9e-129)
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(Float64(y_46_im * y_46_im) / y_46_re)));
	elseif (y_46_re <= 7e-81)
		tmp = Float64(x_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_re + (y_46_im * (y_46_im / y_46_re)));
	tmp = 0.0;
	if (y_46_re <= -1.65e-13)
		tmp = t_0;
	elseif (y_46_re <= -1.5e-46)
		tmp = x_46_im / y_46_im;
	elseif (y_46_re <= -3.9e-129)
		tmp = x_46_re / (y_46_re + ((y_46_im * y_46_im) / y_46_re));
	elseif (y_46_re <= 7e-81)
		tmp = x_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 / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -1.65e-13], t$95$0, If[LessEqual[y$46$re, -1.5e-46], N[(x$46$im / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, -3.9e-129], N[(x$46$re / N[(y$46$re + N[(N[(y$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 7e-81], N[(x$46$im / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

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

Alternative 9: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -2.3 \cdot 10^{+22} \lor \neg \left(y.re \leq 1.35 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{\frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -2.3e+22) (not (<= y.re 1.35e-87)))
   (+ (/ x.re y.re) (/ (/ (* x.im y.im) y.re) y.re))
   (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.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_re <= -2.3e+22) || !(y_46_re <= 1.35e-87)) {
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re);
	} else {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_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_46re <= (-2.3d+22)) .or. (.not. (y_46re <= 1.35d-87))) then
        tmp = (x_46re / y_46re) + (((x_46im * y_46im) / y_46re) / y_46re)
    else
        tmp = ((-1.0d0) / y_46im) * (-x_46im - (x_46re / (y_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_re <= -2.3e+22) || !(y_46_re <= 1.35e-87)) {
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re);
	} else {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_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_re <= -2.3e+22) or not (y_46_re <= 1.35e-87):
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re)
	else:
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_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_re <= -2.3e+22) || !(y_46_re <= 1.35e-87))
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(Float64(x_46_im * y_46_im) / y_46_re) / y_46_re));
	else
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_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_re <= -2.3e+22) || ~((y_46_re <= 1.35e-87)))
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re);
	else
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_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$46$re, -2.3e+22], N[Not[LessEqual[y$46$re, 1.35e-87]], $MachinePrecision]], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x.re}{y.re} + y.im \cdot \left(\frac{1}{y.re} \cdot \frac{x.im}{y.re}\right)\\ \mathbf{elif}\;y.re \leq 2.9 \cdot 10^{-90}:\\ \;\;\;\;\frac{-1}{y.im} \cdot \left(\left(-x.im\right) - \frac{x.re}{\frac{y.im}{y.re}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{\frac{x.im \cdot y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -5e-5)
   (+ (/ x.re y.re) (* y.im (* (/ 1.0 y.re) (/ x.im y.re))))
   (if (<= y.re 2.9e-90)
     (* (/ -1.0 y.im) (- (- x.im) (/ x.re (/ y.im y.re))))
     (+ (/ x.re y.re) (/ (/ (* x.im y.im) 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_re <= -5e-5) {
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)));
	} else if (y_46_re <= 2.9e-90) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else {
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / 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_46re <= (-5d-5)) then
        tmp = (x_46re / y_46re) + (y_46im * ((1.0d0 / y_46re) * (x_46im / y_46re)))
    else if (y_46re <= 2.9d-90) then
        tmp = ((-1.0d0) / y_46im) * (-x_46im - (x_46re / (y_46im / y_46re)))
    else
        tmp = (x_46re / y_46re) + (((x_46im * y_46im) / 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_re <= -5e-5) {
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)));
	} else if (y_46_re <= 2.9e-90) {
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	} else {
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / 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_re <= -5e-5:
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)))
	elif y_46_re <= 2.9e-90:
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)))
	else:
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / 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_re <= -5e-5)
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im * Float64(Float64(1.0 / y_46_re) * Float64(x_46_im / y_46_re))));
	elseif (y_46_re <= 2.9e-90)
		tmp = Float64(Float64(-1.0 / y_46_im) * Float64(Float64(-x_46_im) - Float64(x_46_re / Float64(y_46_im / y_46_re))));
	else
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(Float64(x_46_im * y_46_im) / 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_re <= -5e-5)
		tmp = (x_46_re / y_46_re) + (y_46_im * ((1.0 / y_46_re) * (x_46_im / y_46_re)));
	elseif (y_46_re <= 2.9e-90)
		tmp = (-1.0 / y_46_im) * (-x_46_im - (x_46_re / (y_46_im / y_46_re)));
	else
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / 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[LessEqual[y$46$re, -5e-5], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im * N[(N[(1.0 / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.9e-90], N[(N[(-1.0 / y$46$im), $MachinePrecision] * N[((-x$46$im) - N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -2.7 \cdot 10^{-13} \lor \neg \left(y.re \leq 1.75 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + y.re \cdot \frac{x.re}{y.im \cdot y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -2.7e-13) (not (<= y.re 1.75e-79)))
   (/ x.re (+ y.re (* y.im (/ y.im y.re))))
   (+ (/ x.im y.im) (* y.re (/ x.re (* y.im 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_re <= -2.7e-13) || !(y_46_re <= 1.75e-79)) {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	} else {
		tmp = (x_46_im / y_46_im) + (y_46_re * (x_46_re / (y_46_im * 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_46re <= (-2.7d-13)) .or. (.not. (y_46re <= 1.75d-79))) then
        tmp = x_46re / (y_46re + (y_46im * (y_46im / y_46re)))
    else
        tmp = (x_46im / y_46im) + (y_46re * (x_46re / (y_46im * 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_re <= -2.7e-13) || !(y_46_re <= 1.75e-79)) {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	} else {
		tmp = (x_46_im / y_46_im) + (y_46_re * (x_46_re / (y_46_im * 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_re <= -2.7e-13) or not (y_46_re <= 1.75e-79):
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)))
	else:
		tmp = (x_46_im / y_46_im) + (y_46_re * (x_46_re / (y_46_im * 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_re <= -2.7e-13) || !(y_46_re <= 1.75e-79))
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_46_im / y_46_re))));
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(y_46_re * Float64(x_46_re / Float64(y_46_im * 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_re <= -2.7e-13) || ~((y_46_re <= 1.75e-79)))
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	else
		tmp = (x_46_im / y_46_im) + (y_46_re * (x_46_re / (y_46_im * y_46_im)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -2.7e-13], N[Not[LessEqual[y$46$re, 1.75e-79]], $MachinePrecision]], N[(x$46$re / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(y$46$re * N[(x$46$re / N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.45 \cdot 10^{-12} \lor \neg \left(y.re \leq 3.9 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{x.re}{y.re + y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{\frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -1.45e-12) (not (<= y.re 3.9e-79)))
   (/ x.re (+ y.re (* y.im (/ y.im y.re))))
   (+ (/ x.im y.im) (/ (/ (* x.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) {
	double tmp;
	if ((y_46_re <= -1.45e-12) || !(y_46_re <= 3.9e-79)) {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	} else {
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / 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_46re <= (-1.45d-12)) .or. (.not. (y_46re <= 3.9d-79))) then
        tmp = x_46re / (y_46re + (y_46im * (y_46im / y_46re)))
    else
        tmp = (x_46im / y_46im) + (((x_46re * y_46re) / y_46im) / 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_re <= -1.45e-12) || !(y_46_re <= 3.9e-79)) {
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	} else {
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / 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_re <= -1.45e-12) or not (y_46_re <= 3.9e-79):
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)))
	else:
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / 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_re <= -1.45e-12) || !(y_46_re <= 3.9e-79))
		tmp = Float64(x_46_re / Float64(y_46_re + Float64(y_46_im * Float64(y_46_im / y_46_re))));
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(Float64(x_46_re * y_46_re) / y_46_im) / 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_re <= -1.45e-12) || ~((y_46_re <= 3.9e-79)))
		tmp = x_46_re / (y_46_re + (y_46_im * (y_46_im / y_46_re)));
	else
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -1.45e-12], N[Not[LessEqual[y$46$re, 3.9e-79]], $MachinePrecision]], N[(x$46$re / N[(y$46$re + N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -2.3 \cdot 10^{+22} \lor \neg \left(y.re \leq 1.1 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{\frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{\frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -2.3e+22) (not (<= y.re 1.1e-87)))
   (+ (/ x.re y.re) (/ (/ (* x.im y.im) y.re) y.re))
   (+ (/ x.im y.im) (/ (/ (* x.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) {
	double tmp;
	if ((y_46_re <= -2.3e+22) || !(y_46_re <= 1.1e-87)) {
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re);
	} else {
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / 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_46re <= (-2.3d+22)) .or. (.not. (y_46re <= 1.1d-87))) then
        tmp = (x_46re / y_46re) + (((x_46im * y_46im) / y_46re) / y_46re)
    else
        tmp = (x_46im / y_46im) + (((x_46re * y_46re) / y_46im) / 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_re <= -2.3e+22) || !(y_46_re <= 1.1e-87)) {
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re);
	} else {
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / 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_re <= -2.3e+22) or not (y_46_re <= 1.1e-87):
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re)
	else:
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / 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_re <= -2.3e+22) || !(y_46_re <= 1.1e-87))
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(Float64(x_46_im * y_46_im) / y_46_re) / y_46_re));
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(Float64(x_46_re * y_46_re) / y_46_im) / 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_re <= -2.3e+22) || ~((y_46_re <= 1.1e-87)))
		tmp = (x_46_re / y_46_re) + (((x_46_im * y_46_im) / y_46_re) / y_46_re);
	else
		tmp = (x_46_im / y_46_im) + (((x_46_re * y_46_re) / y_46_im) / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -2.3e+22], N[Not[LessEqual[y$46$re, 1.1e-87]], $MachinePrecision]], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 63.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -8.5 \cdot 10^{-12} \lor \neg \left(y.re \leq 2.9 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -8.5e-12) (not (<= y.re 2.9e-35)))
   (/ x.re y.re)
   (/ x.im 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_re <= -8.5e-12) || !(y_46_re <= 2.9e-35)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = x_46_im / 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_46re <= (-8.5d-12)) .or. (.not. (y_46re <= 2.9d-35))) then
        tmp = x_46re / y_46re
    else
        tmp = x_46im / 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_re <= -8.5e-12) || !(y_46_re <= 2.9e-35)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = x_46_im / 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_re <= -8.5e-12) or not (y_46_re <= 2.9e-35):
		tmp = x_46_re / y_46_re
	else:
		tmp = x_46_im / 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_re <= -8.5e-12) || !(y_46_re <= 2.9e-35))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(x_46_im / 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_re <= -8.5e-12) || ~((y_46_re <= 2.9e-35)))
		tmp = x_46_re / y_46_re;
	else
		tmp = x_46_im / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -8.5e-12], N[Not[LessEqual[y$46$re, 2.9e-35]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]

Derivation

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

Alternative 15: 42.9% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (x.re x.im y.re y.im) :precision binary64 (/ x.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_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_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_im;
}

Python

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

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(x_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_im;
end

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2024006 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  :precision binary64
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))