Average Error: 26.1 → 6.0
Time: 14.6s
Precision: binary64
Cost: 33680
\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
↓
\[\begin{array}{l} t_0 := \mathsf{fma}\left(\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}, y.re \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.re}{\frac{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}{-y.im}}\right)\\ t_1 := \frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{if}\;y.im \leq -4 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq -3.6 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 2.6 \cdot 10^{-148}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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
         (fma
          (/ 1.0 (hypot y.re y.im))
          (* y.re (/ x.im (hypot y.re y.im)))
          (/ x.re (/ (pow (hypot y.re y.im) 2.0) (- y.im)))))
        (t_1 (/ (- (* (/ y.re y.im) x.im) x.re) y.im)))
   (if (<= y.im -4e+163)
     t_1
     (if (<= y.im -3.6e-116)
       t_0
       (if (<= y.im 2.6e-148)
         (/ (- x.im (/ y.im (/ y.re x.re))) y.re)
         (if (<= y.im 5.2e+159) t_0 t_1))))))
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 = fma((1.0 / hypot(y_46_re, y_46_im)), (y_46_re * (x_46_im / hypot(y_46_re, y_46_im))), (x_46_re / (pow(hypot(y_46_re, y_46_im), 2.0) / -y_46_im)));
	double t_1 = (((y_46_re / y_46_im) * x_46_im) - x_46_re) / y_46_im;
	double tmp;
	if (y_46_im <= -4e+163) {
		tmp = t_1;
	} else if (y_46_im <= -3.6e-116) {
		tmp = t_0;
	} else if (y_46_im <= 2.6e-148) {
		tmp = (x_46_im - (y_46_im / (y_46_re / x_46_re))) / y_46_re;
	} else if (y_46_im <= 5.2e+159) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 = fma(Float64(1.0 / hypot(y_46_re, y_46_im)), Float64(y_46_re * Float64(x_46_im / hypot(y_46_re, y_46_im))), Float64(x_46_re / Float64((hypot(y_46_re, y_46_im) ^ 2.0) / Float64(-y_46_im))))
	t_1 = Float64(Float64(Float64(Float64(y_46_re / y_46_im) * x_46_im) - x_46_re) / y_46_im)
	tmp = 0.0
	if (y_46_im <= -4e+163)
		tmp = t_1;
	elseif (y_46_im <= -3.6e-116)
		tmp = t_0;
	elseif (y_46_im <= 2.6e-148)
		tmp = Float64(Float64(x_46_im - Float64(y_46_im / Float64(y_46_re / x_46_re))) / y_46_re);
	elseif (y_46_im <= 5.2e+159)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

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[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(y$46$re * N[(x$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x$46$re / N[(N[Power[N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision], 2.0], $MachinePrecision] / (-y$46$im)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(y$46$re / y$46$im), $MachinePrecision] * x$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]}, If[LessEqual[y$46$im, -4e+163], t$95$1, If[LessEqual[y$46$im, -3.6e-116], t$95$0, If[LessEqual[y$46$im, 2.6e-148], N[(N[(x$46$im - N[(y$46$im / N[(y$46$re / x$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 5.2e+159], t$95$0, t$95$1]]]]]]

\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 := \mathsf{fma}\left(\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}, y.re \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.re}{\frac{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}{-y.im}}\right)\\
t_1 := \frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\
\mathbf{if}\;y.im \leq -4 \cdot 10^{+163}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;y.im \leq -3.6 \cdot 10^{-116}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;y.im \leq 2.6 \cdot 10^{-148}:\\
\;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\

\mathbf{elif}\;y.im \leq 5.2 \cdot 10^{+159}:\\
\;\;\;\;t_0\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Error

Derivation

  1. Split input into 3 regimes

  2. if y.im < -3.9999999999999998e163 or 5.2000000000000001e159 < y.im

    1. Initial program 44.6

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

    2. Simplified44.6

      \[\leadsto \color{blue}{\frac{x.im \cdot y.re - x.re \cdot y.im}{\mathsf{fma}\left(y.re, y.re, y.im \cdot y.im\right)}} \]
      Proof
      (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))): 1 points increase in error, 1 points decrease in error

    3. Taylor expanded in y.re around 0 15.4

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

    4. Simplified14.1

      \[\leadsto \color{blue}{\frac{y.re}{y.im \cdot y.im} \cdot x.im - \frac{x.re}{y.im}} \]
      Proof
      (-.f64 (*.f64 (/.f64 y.re (*.f64 y.im y.im)) x.im) (/.f64 x.re y.im)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y.re (/.f64 (*.f64 y.im y.im) x.im))) (/.f64 x.re y.im)): 9 points increase in error, 12 points decrease in error
      (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y.re x.im) (*.f64 y.im y.im))) (/.f64 x.re y.im)): 25 points increase in error, 9 points decrease in error
      (-.f64 (/.f64 (*.f64 y.re x.im) (Rewrite<= unpow2_binary64 (pow.f64 y.im 2))) (/.f64 x.re y.im)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 y.re x.im) (pow.f64 y.im 2)) (neg.f64 (/.f64 x.re y.im)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 y.re x.im) (pow.f64 y.im 2)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x.re y.im)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 x.re y.im)) (/.f64 (*.f64 y.re x.im) (pow.f64 y.im 2)))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr12.3

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

    6. Applied egg-rr7.5

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

    if -3.9999999999999998e163 < y.im < -3.59999999999999975e-116 or 2.60000000000000008e-148 < y.im < 5.2000000000000001e159

    1. Initial program 18.6

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

    2. Applied egg-rr15.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im \cdot y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, -\frac{x.re \cdot y.im}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\right)} \]

    3. Simplified4.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot y.re, \frac{x.re}{\frac{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}{-y.im}}\right)} \]
      Proof
      (fma.f64 (/.f64 1 (hypot.f64 y.re y.im)) (*.f64 (/.f64 x.im (hypot.f64 y.re y.im)) y.re) (/.f64 x.re (/.f64 (pow.f64 (hypot.f64 y.re y.im) 2) (neg.f64 y.im)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 1 (hypot.f64 y.re y.im)) (Rewrite<= associate-/r/_binary64 (/.f64 x.im (/.f64 (hypot.f64 y.re y.im) y.re))) (/.f64 x.re (/.f64 (pow.f64 (hypot.f64 y.re y.im) 2) (neg.f64 y.im)))): 13 points increase in error, 10 points decrease in error
      (fma.f64 (/.f64 1 (hypot.f64 y.re y.im)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x.im y.re) (hypot.f64 y.re y.im))) (/.f64 x.re (/.f64 (pow.f64 (hypot.f64 y.re y.im) 2) (neg.f64 y.im)))): 51 points increase in error, 8 points decrease in error
      (fma.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (*.f64 x.im y.re) (hypot.f64 y.re y.im)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x.re (neg.f64 y.im)) (pow.f64 (hypot.f64 y.re y.im) 2)))): 45 points increase in error, 10 points decrease in error
      (fma.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (*.f64 x.im y.re) (hypot.f64 y.re y.im)) (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x.re y.im))) (pow.f64 (hypot.f64 y.re y.im) 2))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (*.f64 x.im y.re) (hypot.f64 y.re y.im)) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (*.f64 x.re y.im) (pow.f64 (hypot.f64 y.re y.im) 2))))): 0 points increase in error, 0 points decrease in error

    if -3.59999999999999975e-116 < y.im < 2.60000000000000008e-148

    1. Initial program 22.5

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

    2. Taylor expanded in y.re around inf 9.4

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

    3. Simplified9.4

      \[\leadsto \color{blue}{\frac{x.im}{y.re} + \frac{x.re \cdot \left(-y.im\right)}{y.re \cdot y.re}} \]
      Proof
      (+.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re (neg.f64 y.im)) (*.f64 y.re y.re))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 x.im y.re) (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x.re y.im))) (*.f64 y.re y.re))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 x.im y.re) (/.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (*.f64 x.re y.im))) (*.f64 y.re y.re))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 x.im y.re) (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 x.im y.re) (*.f64 -1 (/.f64 (*.f64 x.re y.im) (Rewrite<= unpow2_binary64 (pow.f64 y.re 2))))): 0 points increase in error, 0 points decrease in error

    4. Applied egg-rr7.0

      \[\leadsto \color{blue}{\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification6.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -4 \cdot 10^{+163}:\\ \;\;\;\;\frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{elif}\;y.im \leq -3.6 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}, y.re \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.re}{\frac{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}{-y.im}}\right)\\ \mathbf{elif}\;y.im \leq 2.6 \cdot 10^{-148}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.im \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)}, y.re \cdot \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.re}{\frac{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}{-y.im}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \end{array} \]

Alternatives

Alternative 1
Error9.4
Cost14288
\[\begin{array}{l} t_0 := \frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.re \cdot x.im - y.im \cdot x.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ t_1 := \frac{x.im}{y.re} - \frac{y.im}{y.re} \cdot \frac{x.re}{y.re}\\ \mathbf{if}\;y.re \leq -5.2 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.re \leq -7.5 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 1.6 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 6.5 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error14.6
Cost13904
\[\begin{array}{l} t_0 := \frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{if}\;y.im \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 3.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 8 \cdot 10^{+56}:\\ \;\;\;\;\frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 2.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.im \leq 2.2 \cdot 10^{+140}:\\ \;\;\;\;\frac{y.im \cdot \left(-x.re\right)}{\mathsf{fma}\left(y.re, y.re, y.im \cdot y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error12.1
Cost1488
\[\begin{array}{l} t_0 := \frac{y.re \cdot x.im - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ t_1 := \frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{if}\;y.re \leq -6 \cdot 10^{+101}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{elif}\;y.re \leq -2.05 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 7.2 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.re \leq 11600:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 2.1 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re} - \frac{y.im}{y.re} \cdot \frac{x.re}{y.re}\\ \end{array} \]
Alternative 4
Error19.3
Cost1104
\[\begin{array}{l} t_0 := \frac{-x.re}{y.im}\\ t_1 := \frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{if}\;y.im \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 4.8 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error19.3
Cost1104
\[\begin{array}{l} t_0 := \frac{-x.re}{y.im}\\ \mathbf{if}\;y.im \leq -2 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.5 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 1.25 \cdot 10^{+113}:\\ \;\;\;\;\frac{x.im - \frac{y.im}{\frac{y.re}{x.re}}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error15.1
Cost968
\[\begin{array}{l} \mathbf{if}\;y.im \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{elif}\;y.im \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{y.re}{y.im} \cdot \frac{x.im}{y.im} - \frac{x.re}{y.im}\\ \end{array} \]
Alternative 7
Error15.2
Cost840
\[\begin{array}{l} t_0 := \frac{\frac{y.re}{y.im} \cdot x.im - x.re}{y.im}\\ \mathbf{if}\;y.im \leq -2.3 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error22.8
Cost520
\[\begin{array}{l} \mathbf{if}\;y.re \leq -5.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \mathbf{elif}\;y.re \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \]
Alternative 9
Error35.6
Cost324
\[\begin{array}{l} \mathbf{if}\;y.im \leq 7.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
Alternative 10
Error51.8
Cost64
\[0 \]

Error

Reproduce

herbie shell --seed 2022332 
(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))))