_divideComplex, imaginary part

Percentage Accurate: 61.8% → 98.1%

Time: 13.5s

Alternatives: 13

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: 61.8% 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: 98.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.re}{\frac{\mathsf{hypot}\left(y.re, y.im\right)}{y.im}} \cdot \frac{-1}{\mathsf{hypot}\left(y.re, y.im\right)}\right) \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (fma
  (/ y.re (hypot y.re y.im))
  (/ x.im (hypot y.re y.im))
  (* (/ x.re (/ (hypot y.re y.im) y.im)) (/ -1.0 (hypot y.re y.im)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return fma((y_46_re / hypot(y_46_re, y_46_im)), (x_46_im / hypot(y_46_re, y_46_im)), ((x_46_re / (hypot(y_46_re, y_46_im) / y_46_im)) * (-1.0 / hypot(y_46_re, y_46_im))));
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return fma(Float64(y_46_re / hypot(y_46_re, y_46_im)), Float64(x_46_im / hypot(y_46_re, y_46_im)), Float64(Float64(x_46_re / Float64(hypot(y_46_re, y_46_im) / y_46_im)) * Float64(-1.0 / hypot(y_46_re, y_46_im))))
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := 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] + N[(N[(x$46$re / N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 97.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{-1}{\frac{\mathsf{hypot}\left(y.re, y.im\right)}{y.im}}\right) \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (fma
  (/ y.re (hypot y.re y.im))
  (/ x.im (hypot y.re y.im))
  (* (/ x.re (hypot y.re y.im)) (/ -1.0 (/ (hypot 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 fma((y_46_re / hypot(y_46_re, y_46_im)), (x_46_im / hypot(y_46_re, y_46_im)), ((x_46_re / hypot(y_46_re, y_46_im)) * (-1.0 / (hypot(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 fma(Float64(y_46_re / hypot(y_46_re, y_46_im)), Float64(x_46_im / hypot(y_46_re, y_46_im)), Float64(Float64(x_46_re / hypot(y_46_re, y_46_im)) * Float64(-1.0 / Float64(hypot(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[(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] + N[(N[(x$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 96.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{-x.re}{\frac{\mathsf{hypot}\left(y.re, y.im\right)}{\frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)}}}\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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

Alternative 4: 89.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot x.im - y.im \cdot x.re\\ \mathbf{if}\;\frac{t_0}{y.re \cdot y.re + y.im \cdot y.im} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{t_0}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, -\frac{x.re}{y.im}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (* y.re x.im) (* y.im x.re))))
   (if (<= (/ t_0 (+ (* y.re y.re) (* y.im y.im))) 2e+305)
     (* (/ 1.0 (hypot y.re y.im)) (/ t_0 (hypot y.re y.im)))
     (fma
      (/ y.re (hypot y.re y.im))
      (/ x.im (hypot y.re y.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 t_0 = (y_46_re * x_46_im) - (y_46_im * x_46_re);
	double tmp;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 2e+305) {
		tmp = (1.0 / hypot(y_46_re, y_46_im)) * (t_0 / hypot(y_46_re, y_46_im));
	} else {
		tmp = fma((y_46_re / hypot(y_46_re, y_46_im)), (x_46_im / hypot(y_46_re, y_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)
	t_0 = Float64(Float64(y_46_re * x_46_im) - Float64(y_46_im * x_46_re))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))) <= 2e+305)
		tmp = Float64(Float64(1.0 / hypot(y_46_re, y_46_im)) * Float64(t_0 / hypot(y_46_re, y_46_im)));
	else
		tmp = fma(Float64(y_46_re / hypot(y_46_re, y_46_im)), Float64(x_46_im / hypot(y_46_re, y_46_im)), Float64(-Float64(x_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[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+305], N[(N[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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] + (-N[(x$46$re / y$46$im), $MachinePrecision])), $MachinePrecision]]]

Derivation

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

Alternative 5: 85.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot x.im - y.im \cdot x.re\\ \mathbf{if}\;\frac{t_0}{y.re \cdot y.re + y.im \cdot y.im} \leq \infty:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{t_0}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (* y.re x.im) (* y.im x.re))))
   (if (<= (/ t_0 (+ (* y.re y.re) (* y.im y.im))) INFINITY)
     (* (/ 1.0 (hypot y.re y.im)) (/ t_0 (hypot y.re y.im)))
     (- (/ x.im y.re) (/ (/ x.re (/ 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 = (y_46_re * x_46_im) - (y_46_im * x_46_re);
	double tmp;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= ((double) INFINITY)) {
		tmp = (1.0 / hypot(y_46_re, y_46_im)) * (t_0 / hypot(y_46_re, y_46_im));
	} else {
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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 = (y_46_re * x_46_im) - (y_46_im * x_46_re);
	double tmp;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / Math.hypot(y_46_re, y_46_im)) * (t_0 / Math.hypot(y_46_re, y_46_im));
	} else {
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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 = (y_46_re * x_46_im) - (y_46_im * x_46_re)
	tmp = 0
	if (t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= math.inf:
		tmp = (1.0 / math.hypot(y_46_re, y_46_im)) * (t_0 / math.hypot(y_46_re, y_46_im))
	else:
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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(y_46_re * x_46_im) - Float64(y_46_im * x_46_re))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))) <= Inf)
		tmp = Float64(Float64(1.0 / hypot(y_46_re, y_46_im)) * Float64(t_0 / hypot(y_46_re, y_46_im)));
	else
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(x_46_re / Float64(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 = (y_46_re * x_46_im) - (y_46_im * x_46_re);
	tmp = 0.0;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= Inf)
		tmp = (1.0 / hypot(y_46_re, y_46_im)) * (t_0 / hypot(y_46_re, y_46_im));
	else
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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[(y$46$re * x$46$im), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 6: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im}{y.re} - \frac{y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -1.14 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 5.3 \cdot 10^{-89}:\\ \;\;\;\;\frac{x.im}{y.im \cdot \frac{y.im}{y.re}} - \frac{x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 2.65 \cdot 10^{+129}:\\ \;\;\;\;\frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (/ x.im y.re) (/ (* y.im (/ x.re y.re)) y.re))))
   (if (<= y.re -1.14e-17)
     t_0
     (if (<= y.re 5.3e-89)
       (- (/ x.im (* y.im (/ y.im y.re))) (/ x.re y.im))
       (if (<= y.re 2.65e+129)
         (/ (- (* 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 / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re);
	double tmp;
	if (y_46_re <= -1.14e-17) {
		tmp = t_0;
	} else if (y_46_re <= 5.3e-89) {
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im);
	} else if (y_46_re <= 2.65e+129) {
		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_46re) - ((y_46im * (x_46re / y_46re)) / y_46re)
    if (y_46re <= (-1.14d-17)) then
        tmp = t_0
    else if (y_46re <= 5.3d-89) then
        tmp = (x_46im / (y_46im * (y_46im / y_46re))) - (x_46re / y_46im)
    else if (y_46re <= 2.65d+129) 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 / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re);
	double tmp;
	if (y_46_re <= -1.14e-17) {
		tmp = t_0;
	} else if (y_46_re <= 5.3e-89) {
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im);
	} else if (y_46_re <= 2.65e+129) {
		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 / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re)
	tmp = 0
	if y_46_re <= -1.14e-17:
		tmp = t_0
	elif y_46_re <= 5.3e-89:
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im)
	elif y_46_re <= 2.65e+129:
		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 / y_46_re) - Float64(Float64(y_46_im * Float64(x_46_re / y_46_re)) / y_46_re))
	tmp = 0.0
	if (y_46_re <= -1.14e-17)
		tmp = t_0;
	elseif (y_46_re <= 5.3e-89)
		tmp = Float64(Float64(x_46_im / Float64(y_46_im * Float64(y_46_im / y_46_re))) - Float64(x_46_re / y_46_im));
	elseif (y_46_re <= 2.65e+129)
		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_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re);
	tmp = 0.0;
	if (y_46_re <= -1.14e-17)
		tmp = t_0;
	elseif (y_46_re <= 5.3e-89)
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im);
	elseif (y_46_re <= 2.65e+129)
		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 / y$46$re), $MachinePrecision] - N[(N[(y$46$im * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -1.14e-17], t$95$0, If[LessEqual[y$46$re, 5.3e-89], N[(N[(x$46$im / N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.65e+129], 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 7: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\frac{x.re}{y.im}\\ t_1 := \frac{x.im}{y.re} - \frac{\frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{if}\;y.im \leq -4.5 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 6.2 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 3.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{y.im \cdot \left(-x.re\right)}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 2.5 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (/ x.re y.im)))
        (t_1 (- (/ x.im y.re) (/ (/ x.re (/ y.re y.im)) y.re))))
   (if (<= y.im -4.5e+107)
     t_0
     (if (<= y.im 6.2e-9)
       t_1
       (if (<= y.im 3.8e+69)
         (/ (* y.im (- x.re)) (+ (* y.re y.re) (* y.im y.im)))
         (if (<= y.im 2.5e+104) 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 = (x_46_im / y_46_re) - ((x_46_re / (y_46_re / y_46_im)) / y_46_re);
	double tmp;
	if (y_46_im <= -4.5e+107) {
		tmp = t_0;
	} else if (y_46_im <= 6.2e-9) {
		tmp = t_1;
	} else if (y_46_im <= 3.8e+69) {
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_im <= 2.5e+104) {
		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 = (x_46im / y_46re) - ((x_46re / (y_46re / y_46im)) / y_46re)
    if (y_46im <= (-4.5d+107)) then
        tmp = t_0
    else if (y_46im <= 6.2d-9) then
        tmp = t_1
    else if (y_46im <= 3.8d+69) then
        tmp = (y_46im * -x_46re) / ((y_46re * y_46re) + (y_46im * y_46im))
    else if (y_46im <= 2.5d+104) 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 = (x_46_im / y_46_re) - ((x_46_re / (y_46_re / y_46_im)) / y_46_re);
	double tmp;
	if (y_46_im <= -4.5e+107) {
		tmp = t_0;
	} else if (y_46_im <= 6.2e-9) {
		tmp = t_1;
	} else if (y_46_im <= 3.8e+69) {
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_im <= 2.5e+104) {
		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 = (x_46_im / y_46_re) - ((x_46_re / (y_46_re / y_46_im)) / y_46_re)
	tmp = 0
	if y_46_im <= -4.5e+107:
		tmp = t_0
	elif y_46_im <= 6.2e-9:
		tmp = t_1
	elif y_46_im <= 3.8e+69:
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	elif y_46_im <= 2.5e+104:
		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(x_46_im / y_46_re) - Float64(Float64(x_46_re / Float64(y_46_re / y_46_im)) / y_46_re))
	tmp = 0.0
	if (y_46_im <= -4.5e+107)
		tmp = t_0;
	elseif (y_46_im <= 6.2e-9)
		tmp = t_1;
	elseif (y_46_im <= 3.8e+69)
		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)));
	elseif (y_46_im <= 2.5e+104)
		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 = (x_46_im / y_46_re) - ((x_46_re / (y_46_re / y_46_im)) / y_46_re);
	tmp = 0.0;
	if (y_46_im <= -4.5e+107)
		tmp = t_0;
	elseif (y_46_im <= 6.2e-9)
		tmp = t_1;
	elseif (y_46_im <= 3.8e+69)
		tmp = (y_46_im * -x_46_re) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	elseif (y_46_im <= 2.5e+104)
		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[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -4.5e+107], t$95$0, If[LessEqual[y$46$im, 6.2e-9], t$95$1, If[LessEqual[y$46$im, 3.8e+69], 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], If[LessEqual[y$46$im, 2.5e+104], t$95$1, t$95$0]]]]]]

Derivation

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

Alternative 8: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 4.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x.im}{y.im \cdot \frac{y.im}{y.re}} - \frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} + y.im \cdot \left(\frac{x.re}{y.re} \cdot \frac{-1}{y.re}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -1.25e-13)
   (- (/ x.im y.re) (/ (* y.im (/ x.re y.re)) y.re))
   (if (<= y.re 4.2e+93)
     (- (/ x.im (* y.im (/ y.im y.re))) (/ x.re y.im))
     (+ (/ x.im y.re) (* y.im (* (/ x.re y.re) (/ -1.0 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 <= -1.25e-13) {
		tmp = (x_46_im / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re);
	} else if (y_46_re <= 4.2e+93) {
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im);
	} else {
		tmp = (x_46_im / y_46_re) + (y_46_im * ((x_46_re / y_46_re) * (-1.0 / 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 <= (-1.25d-13)) then
        tmp = (x_46im / y_46re) - ((y_46im * (x_46re / y_46re)) / y_46re)
    else if (y_46re <= 4.2d+93) then
        tmp = (x_46im / (y_46im * (y_46im / y_46re))) - (x_46re / y_46im)
    else
        tmp = (x_46im / y_46re) + (y_46im * ((x_46re / y_46re) * ((-1.0d0) / 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 <= -1.25e-13) {
		tmp = (x_46_im / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re);
	} else if (y_46_re <= 4.2e+93) {
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im);
	} else {
		tmp = (x_46_im / y_46_re) + (y_46_im * ((x_46_re / y_46_re) * (-1.0 / 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 <= -1.25e-13:
		tmp = (x_46_im / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re)
	elif y_46_re <= 4.2e+93:
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im)
	else:
		tmp = (x_46_im / y_46_re) + (y_46_im * ((x_46_re / y_46_re) * (-1.0 / 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 <= -1.25e-13)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(y_46_im * Float64(x_46_re / y_46_re)) / y_46_re));
	elseif (y_46_re <= 4.2e+93)
		tmp = Float64(Float64(x_46_im / Float64(y_46_im * Float64(y_46_im / y_46_re))) - Float64(x_46_re / y_46_im));
	else
		tmp = Float64(Float64(x_46_im / y_46_re) + Float64(y_46_im * Float64(Float64(x_46_re / y_46_re) * Float64(-1.0 / 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 <= -1.25e-13)
		tmp = (x_46_im / y_46_re) - ((y_46_im * (x_46_re / y_46_re)) / y_46_re);
	elseif (y_46_re <= 4.2e+93)
		tmp = (x_46_im / (y_46_im * (y_46_im / y_46_re))) - (x_46_re / y_46_im);
	else
		tmp = (x_46_im / y_46_re) + (y_46_im * ((x_46_re / y_46_re) * (-1.0 / 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, -1.25e-13], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 4.2e+93], N[(N[(x$46$im / N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$re), $MachinePrecision] + N[(y$46$im * N[(N[(x$46$re / y$46$re), $MachinePrecision] * N[(-1.0 / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -8.5 \cdot 10^{-17} \lor \neg \left(y.re \leq 4 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x.im}{y.re} - y.im \cdot \frac{\frac{x.re}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x.re}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -8.5e-17) (not (<= y.re 4e+23)))
   (- (/ x.im y.re) (* y.im (/ (/ x.re y.re) y.re)))
   (- (/ 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_re <= -8.5e-17) || !(y_46_re <= 4e+23)) {
		tmp = (x_46_im / y_46_re) - (y_46_im * ((x_46_re / y_46_re) / y_46_re));
	} else {
		tmp = -(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_46re <= (-8.5d-17)) .or. (.not. (y_46re <= 4d+23))) then
        tmp = (x_46im / y_46re) - (y_46im * ((x_46re / y_46re) / y_46re))
    else
        tmp = -(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_re <= -8.5e-17) || !(y_46_re <= 4e+23)) {
		tmp = (x_46_im / y_46_re) - (y_46_im * ((x_46_re / y_46_re) / y_46_re));
	} else {
		tmp = -(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_re <= -8.5e-17) or not (y_46_re <= 4e+23):
		tmp = (x_46_im / y_46_re) - (y_46_im * ((x_46_re / y_46_re) / y_46_re))
	else:
		tmp = -(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_re <= -8.5e-17) || !(y_46_re <= 4e+23))
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(y_46_im * Float64(Float64(x_46_re / y_46_re) / y_46_re)));
	else
		tmp = Float64(-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_re <= -8.5e-17) || ~((y_46_re <= 4e+23)))
		tmp = (x_46_im / y_46_re) - (y_46_im * ((x_46_re / y_46_re) / y_46_re));
	else
		tmp = -(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[Or[LessEqual[y$46$re, -8.5e-17], N[Not[LessEqual[y$46$re, 4e+23]], $MachinePrecision]], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(y$46$im * N[(N[(x$46$re / y$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(x$46$re / y$46$im), $MachinePrecision])]

Derivation

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

Alternative 10: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -9 \cdot 10^{+112} \lor \neg \left(y.im \leq 6.5 \cdot 10^{-11}\right):\\ \;\;\;\;-\frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -9e+112) (not (<= y.im 6.5e-11)))
   (- (/ 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 <= -9e+112) || !(y_46_im <= 6.5e-11)) {
		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 <= (-9d+112)) .or. (.not. (y_46im <= 6.5d-11))) 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 <= -9e+112) || !(y_46_im <= 6.5e-11)) {
		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 <= -9e+112) or not (y_46_im <= 6.5e-11):
		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 <= -9e+112) || !(y_46_im <= 6.5e-11))
		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(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 <= -9e+112) || ~((y_46_im <= 6.5e-11)))
		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, -9e+112], N[Not[LessEqual[y$46$im, 6.5e-11]], $MachinePrecision]], (-N[(x$46$re / y$46$im), $MachinePrecision]), N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(y$46$im * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.8 \cdot 10^{+105} \lor \neg \left(y.im \leq 1.05 \cdot 10^{-8}\right):\\ \;\;\;\;-\frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1.8e+105) (not (<= y.im 1.05e-8)))
   (- (/ x.re y.im))
   (- (/ x.im y.re) (/ (/ x.re (/ 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 tmp;
	if ((y_46_im <= -1.8e+105) || !(y_46_im <= 1.05e-8)) {
		tmp = -(x_46_re / y_46_im);
	} else {
		tmp = (x_46_im / y_46_re) - ((x_46_re / (y_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_46im <= (-1.8d+105)) .or. (.not. (y_46im <= 1.05d-8))) then
        tmp = -(x_46re / y_46im)
    else
        tmp = (x_46im / y_46re) - ((x_46re / (y_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_im <= -1.8e+105) || !(y_46_im <= 1.05e-8)) {
		tmp = -(x_46_re / y_46_im);
	} else {
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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):
	tmp = 0
	if (y_46_im <= -1.8e+105) or not (y_46_im <= 1.05e-8):
		tmp = -(x_46_re / y_46_im)
	else:
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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)
	tmp = 0.0
	if ((y_46_im <= -1.8e+105) || !(y_46_im <= 1.05e-8))
		tmp = Float64(-Float64(x_46_re / y_46_im));
	else
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(Float64(x_46_re / Float64(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)
	tmp = 0.0;
	if ((y_46_im <= -1.8e+105) || ~((y_46_im <= 1.05e-8)))
		tmp = -(x_46_re / y_46_im);
	else
		tmp = (x_46_im / y_46_re) - ((x_46_re / (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_] := If[Or[LessEqual[y$46$im, -1.8e+105], N[Not[LessEqual[y$46$im, 1.05e-8]], $MachinePrecision]], (-N[(x$46$re / y$46$im), $MachinePrecision]), N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 64.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -28000000 \lor \neg \left(y.re \leq 2.3 \cdot 10^{+103}\right):\\ \;\;\;\;\frac{x.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x.re}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -28000000.0) (not (<= y.re 2.3e+103)))
   (/ x.im y.re)
   (- (/ 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_re <= -28000000.0) || !(y_46_re <= 2.3e+103)) {
		tmp = x_46_im / y_46_re;
	} else {
		tmp = -(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_46re <= (-28000000.0d0)) .or. (.not. (y_46re <= 2.3d+103))) then
        tmp = x_46im / y_46re
    else
        tmp = -(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_re <= -28000000.0) || !(y_46_re <= 2.3e+103)) {
		tmp = x_46_im / y_46_re;
	} else {
		tmp = -(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_re <= -28000000.0) or not (y_46_re <= 2.3e+103):
		tmp = x_46_im / y_46_re
	else:
		tmp = -(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_re <= -28000000.0) || !(y_46_re <= 2.3e+103))
		tmp = Float64(x_46_im / y_46_re);
	else
		tmp = Float64(-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_re <= -28000000.0) || ~((y_46_re <= 2.3e+103)))
		tmp = x_46_im / y_46_re;
	else
		tmp = -(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[Or[LessEqual[y$46$re, -28000000.0], N[Not[LessEqual[y$46$re, 2.3e+103]], $MachinePrecision]], N[(x$46$im / y$46$re), $MachinePrecision], (-N[(x$46$re / y$46$im), $MachinePrecision])]

Derivation

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

Alternative 13: 42.8% 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 2023350 
(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))))