_divideComplex, imaginary part

Percentage Accurate: 61.8% → 85.0%

Time: 16.1s

Precision: binary64

Cost: 14788

Math

\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]

↓

\[\begin{array}{l} t_0 := x.im \cdot y.re - x.re \cdot y.im\\ \mathbf{if}\;\frac{t_0}{y.re \cdot y.re + y.im \cdot y.im} \leq 2 \cdot 10^{+267}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{t_0}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

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))))

↓

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (* x.im y.re) (* x.re y.im))))
   (if (<= (/ t_0 (+ (* y.re y.re) (* y.im y.im))) 2e+267)
     (* (/ 1.0 (hypot y.re y.im)) (/ t_0 (hypot y.re y.im)))
     (/ (- (* x.im (/ 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) {
	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));
}

↓

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) - (x_46_re * y_46_im);
	double tmp;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 2e+267) {
		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 / y_46_im)) - x_46_re) / y_46_im;
	}
	return tmp;
}

Java

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

↓

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) - (x_46_re * y_46_im);
	double tmp;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 2e+267) {
		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 / y_46_im)) - x_46_re) / y_46_im;
	}
	return tmp;
}

Python

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

↓

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_im * y_46_re) - (x_46_re * y_46_im)
	tmp = 0
	if (t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 2e+267:
		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 / 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)
	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

↓

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(x_46_re * y_46_im))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))) <= 2e+267)
		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(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	end
	return tmp
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

↓

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_im * y_46_re) - (x_46_re * y_46_im);
	tmp = 0.0;
	if ((t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 2e+267)
		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 / y_46_im)) - x_46_re) / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := 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]

↓

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[(x$46$re * y$46$im), $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+267], 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[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) < 1.9999999999999999e267

   1. Initial program 77.9%

      \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]

   2. Applied egg-rr 95.9%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im \cdot y.re - x.re \cdot y.im}{\mathsf{hypot}\left(y.re, y.im\right)}} \]
      Step-by-step derivation

      [Start] 77.9	\[ \frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
      *-un-lft-identity [=>] 77.9	\[ \frac{\color{blue}{1 \cdot \left(x.im \cdot y.re - x.re \cdot y.im\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
      add-sqr-sqrt [=>] 77.9	\[ \frac{1 \cdot \left(x.im \cdot y.re - x.re \cdot y.im\right)}{\color{blue}{\sqrt{y.re \cdot y.re + y.im \cdot y.im} \cdot \sqrt{y.re \cdot y.re + y.im \cdot y.im}}} \]
      times-frac [=>] 77.9	\[ \color{blue}{\frac{1}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}} \cdot \frac{x.im \cdot y.re - x.re \cdot y.im}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}} \]
      hypot-def [=>] 77.9	\[ \frac{1}{\color{blue}{\mathsf{hypot}\left(y.re, y.im\right)}} \cdot \frac{x.im \cdot y.re - x.re \cdot y.im}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}} \]
      hypot-def [=>] 95.9	\[ \frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im \cdot y.re - x.re \cdot y.im}{\color{blue}{\mathsf{hypot}\left(y.re, y.im\right)}} \]

   if 1.9999999999999999e267 < (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

   1. Initial program 14.7%

      \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]

   2. Taylor expanded in y.re around 0 46.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{y.re \cdot x.im}{{y.im}^{2}}} \]

   3. Simplified 61.7%

      \[\leadsto \color{blue}{\frac{y.re}{y.im} \cdot \frac{x.im}{y.im} - \frac{x.re}{y.im}} \]
      Step-by-step derivation

      [Start] 46.0	\[ -1 \cdot \frac{x.re}{y.im} + \frac{y.re \cdot x.im}{{y.im}^{2}} \]
      +-commutative [=>] 46.0	\[ \color{blue}{\frac{y.re \cdot x.im}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]
      mul-1-neg [=>] 46.0	\[ \frac{y.re \cdot x.im}{{y.im}^{2}} + \color{blue}{\left(-\frac{x.re}{y.im}\right)} \]
      unsub-neg [=>] 46.0	\[ \color{blue}{\frac{y.re \cdot x.im}{{y.im}^{2}} - \frac{x.re}{y.im}} \]
      unpow2 [=>] 46.0	\[ \frac{y.re \cdot x.im}{\color{blue}{y.im \cdot y.im}} - \frac{x.re}{y.im} \]
      times-frac [=>] 61.7	\[ \color{blue}{\frac{y.re}{y.im} \cdot \frac{x.im}{y.im}} - \frac{x.re}{y.im} \]

   4. Taylor expanded in y.re around 0 46.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{y.re \cdot x.im}{{y.im}^{2}}} \]

   5. Simplified 64.6%

      \[\leadsto \color{blue}{\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}} \]
      Step-by-step derivation

      [Start] 46.0	\[ -1 \cdot \frac{x.re}{y.im} + \frac{y.re \cdot x.im}{{y.im}^{2}} \]
      mul-1-neg [=>] 46.0	\[ \color{blue}{\left(-\frac{x.re}{y.im}\right)} + \frac{y.re \cdot x.im}{{y.im}^{2}} \]
      distribute-frac-neg [<=] 46.0	\[ \color{blue}{\frac{-x.re}{y.im}} + \frac{y.re \cdot x.im}{{y.im}^{2}} \]
      +-commutative [=>] 46.0	\[ \color{blue}{\frac{y.re \cdot x.im}{{y.im}^{2}} + \frac{-x.re}{y.im}} \]
      unpow2 [=>] 46.0	\[ \frac{y.re \cdot x.im}{\color{blue}{y.im \cdot y.im}} + \frac{-x.re}{y.im} \]
      times-frac [=>] 61.7	\[ \color{blue}{\frac{y.re}{y.im} \cdot \frac{x.im}{y.im}} + \frac{-x.re}{y.im} \]
      distribute-frac-neg [=>] 61.7	\[ \frac{y.re}{y.im} \cdot \frac{x.im}{y.im} + \color{blue}{\left(-\frac{x.re}{y.im}\right)} \]
      sub-neg [<=] 61.7	\[ \color{blue}{\frac{y.re}{y.im} \cdot \frac{x.im}{y.im} - \frac{x.re}{y.im}} \]
      associate-*l/ [=>] 61.6	\[ \color{blue}{\frac{y.re \cdot \frac{x.im}{y.im}}{y.im}} - \frac{x.re}{y.im} \]
      div-sub [<=] 63.2	\[ \color{blue}{\frac{y.re \cdot \frac{x.im}{y.im} - x.re}{y.im}} \]
      associate-*r/ [=>] 52.3	\[ \frac{\color{blue}{\frac{y.re \cdot x.im}{y.im}} - x.re}{y.im} \]
      *-commutative [=>] 52.3	\[ \frac{\frac{\color{blue}{x.im \cdot y.re}}{y.im} - x.re}{y.im} \]
      associate-*r/ [<=] 64.6	\[ \frac{\color{blue}{x.im \cdot \frac{y.re}{y.im}} - x.re}{y.im} \]

3. Recombined 2 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 2 \cdot 10^{+267}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im \cdot y.re - x.re \cdot y.im}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	81.7%
Cost	13896

\[\begin{array}{l} t_0 := x.im \cdot y.re - x.re \cdot y.im\\ \mathbf{if}\;y.im \leq -2.9 \cdot 10^{+90}:\\ \;\;\;\;\frac{y.re \cdot \frac{x.im}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.im \leq -5 \cdot 10^{-82}:\\ \;\;\;\;t_0 \cdot \frac{1}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\\ \mathbf{elif}\;y.im \leq 1.46 \cdot 10^{-127}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 7.5 \cdot 10^{+148}:\\ \;\;\;\;\frac{t_0}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y.re, \frac{x.im}{y.im} \cdot \frac{1}{y.im}, \frac{-x.re}{y.im}\right)\\ \end{array} \]

Alternative 2
Accuracy	81.8%
Cost	7696

\[\begin{array}{l} t_0 := \frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -1.25 \cdot 10^{+90}:\\ \;\;\;\;\frac{y.re \cdot \frac{x.im}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.im \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 1.85 \cdot 10^{-127}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.05 \cdot 10^{+148}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y.re, \frac{x.im}{y.im} \cdot \frac{1}{y.im}, \frac{-x.re}{y.im}\right)\\ \end{array} \]

Alternative 3
Accuracy	82.1%
Cost	1488

\[\begin{array}{l} t_0 := \frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ t_1 := \frac{y.re \cdot \frac{x.im}{y.im} - x.re}{y.im}\\ \mathbf{if}\;y.im \leq -9.5 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq -7.5 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 1.12 \cdot 10^{-127}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 6.8 \cdot 10^{+146}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	77.1%
Cost	1371

\[\begin{array}{l} \mathbf{if}\;y.re \leq -6 \cdot 10^{+79} \lor \neg \left(y.re \leq -8.5 \cdot 10^{+47} \lor \neg \left(y.re \leq -9600000\right) \land \left(y.re \leq 360000000 \lor \neg \left(y.re \leq 9 \cdot 10^{+61}\right) \land y.re \leq 7.5 \cdot 10^{+102}\right)\right):\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

Alternative 5
Accuracy	76.8%
Cost	1370

\[\begin{array}{l} t_0 := \frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -8 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{x.im}{\frac{y.im}{y.re}} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -14 \lor \neg \left(y.re \leq 1250000 \lor \neg \left(y.re \leq 7.4 \cdot 10^{+58}\right) \land y.re \leq 6.8 \cdot 10^{+102}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

Alternative 6
Accuracy	77.4%
Cost	1369

\[\begin{array}{l} t_0 := \frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -4.2 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq -1.45 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x.im}{\frac{y.im}{y.re}} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -185000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 165000:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 1.1 \cdot 10^{+62} \lor \neg \left(y.re \leq 6.8 \cdot 10^{+102}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

Alternative 7
Accuracy	77.1%
Cost	1369

\[\begin{array}{l} t_0 := \frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -8 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x.im}{\frac{y.im}{y.re}} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -220:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{x.re}{y.re} \cdot \frac{y.im}{y.re}\\ \mathbf{elif}\;y.re \leq 260000000:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 8.2 \cdot 10^{+56} \lor \neg \left(y.re \leq 7.5 \cdot 10^{+102}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

Alternative 8
Accuracy	77.2%
Cost	1369

\[\begin{array}{l} \mathbf{if}\;y.re \leq -6.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{\frac{x.re}{y.re}}{\frac{y.re}{y.im}}\\ \mathbf{elif}\;y.re \leq -9 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x.im}{\frac{y.im}{y.re}} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -36000000:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{x.re}{y.re} \cdot \frac{y.im}{y.re}\\ \mathbf{elif}\;y.re \leq 360:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 10^{+62} \lor \neg \left(y.re \leq 6.8 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \end{array} \]

Alternative 9
Accuracy	69.8%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;y.im \leq -6 \cdot 10^{+103} \lor \neg \left(y.im \leq -3 \cdot 10^{+60}\right) \land \left(y.im \leq -100000000 \lor \neg \left(y.im \leq 6.8 \cdot 10^{+146}\right)\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \]

Alternative 10
Accuracy	70.0%
Cost	1105

\[\begin{array}{l} t_0 := \frac{-x.re}{y.im}\\ \mathbf{if}\;y.im \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq -1.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq -155000000 \lor \neg \left(y.im \leq 6.8 \cdot 10^{+146}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \end{array} \]

Alternative 11
Accuracy	62.0%
Cost	786

\[\begin{array}{l} \mathbf{if}\;y.im \leq -8 \cdot 10^{+103} \lor \neg \left(y.im \leq -1.65 \cdot 10^{+60}\right) \land \left(y.im \leq -8 \cdot 10^{-7} \lor \neg \left(y.im \leq 1.05 \cdot 10^{+101}\right)\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \]

Alternative 12
Accuracy	43.1%
Cost	192

\[\frac{x.im}{y.re} \]

Reproduce

herbie shell --seed 2023163 
(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))))