_divideComplex, real part

Percentage Accurate: 62.1% → 77.5%

Time: 8.2s

Alternatives: 9

Speedup: 1.3×

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: 62.1% 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: 77.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ t_1 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -7 \cdot 10^{-55}:\\ \;\;\;\;\left(x.im + x.re \cdot \frac{y.re}{y.im}\right) \cdot \frac{-1}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.im \leq 2 \cdot 10^{-144}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 7.6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 4.2 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 1.05 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{\frac{x.re}{\frac{y.im}{y.re}}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re))))
        (t_1
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.im -7e-55)
     (* (+ x.im (* x.re (/ y.re y.im))) (/ -1.0 (hypot y.re y.im)))
     (if (<= y.im 2e-144)
       t_0
       (if (<= y.im 7.6e-15)
         t_1
         (if (<= y.im 4.2e+26)
           t_0
           (if (<= y.im 1.05e+120)
             t_1
             (+ (/ x.im y.im) (/ (/ x.re (/ y.im 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_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double t_1 = ((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_im <= -7e-55) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) * (-1.0 / hypot(y_46_re, y_46_im));
	} else if (y_46_im <= 2e-144) {
		tmp = t_0;
	} else if (y_46_im <= 7.6e-15) {
		tmp = t_1;
	} else if (y_46_im <= 4.2e+26) {
		tmp = t_0;
	} else if (y_46_im <= 1.05e+120) {
		tmp = t_1;
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double t_1 = ((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_im <= -7e-55) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) * (-1.0 / Math.hypot(y_46_re, y_46_im));
	} else if (y_46_im <= 2e-144) {
		tmp = t_0;
	} else if (y_46_im <= 7.6e-15) {
		tmp = t_1;
	} else if (y_46_im <= 4.2e+26) {
		tmp = t_0;
	} else if (y_46_im <= 1.05e+120) {
		tmp = t_1;
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	t_1 = ((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_im <= -7e-55:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) * (-1.0 / math.hypot(y_46_re, y_46_im))
	elif y_46_im <= 2e-144:
		tmp = t_0
	elif y_46_im <= 7.6e-15:
		tmp = t_1
	elif y_46_im <= 4.2e+26:
		tmp = t_0
	elif y_46_im <= 1.05e+120:
		tmp = t_1
	else:
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)))
	t_1 = 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_im <= -7e-55)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) * Float64(-1.0 / hypot(y_46_re, y_46_im)));
	elseif (y_46_im <= 2e-144)
		tmp = t_0;
	elseif (y_46_im <= 7.6e-15)
		tmp = t_1;
	elseif (y_46_im <= 4.2e+26)
		tmp = t_0;
	elseif (y_46_im <= 1.05e+120)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re / Float64(y_46_im / y_46_re)) / y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	t_1 = ((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_im <= -7e-55)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) * (-1.0 / hypot(y_46_re, y_46_im));
	elseif (y_46_im <= 2e-144)
		tmp = t_0;
	elseif (y_46_im <= 7.6e-15)
		tmp = t_1;
	elseif (y_46_im <= 4.2e+26)
		tmp = t_0;
	elseif (y_46_im <= 1.05e+120)
		tmp = t_1;
	else
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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$46$im, -7e-55], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 2e-144], t$95$0, If[LessEqual[y$46$im, 7.6e-15], t$95$1, If[LessEqual[y$46$im, 4.2e+26], t$95$0, If[LessEqual[y$46$im, 1.05e+120], t$95$1, N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -7.00000000000000051e-55

   1. Initial program 49.1%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 49.1%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x.re \cdot y.re + x.im \cdot y.im\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]

      2. add-sqr-sqrt 49.1%

         \[\leadsto \frac{1 \cdot \left(x.re \cdot y.re + x.im \cdot y.im\right)}{\color{blue}{\sqrt{y.re \cdot y.re + y.im \cdot y.im} \cdot \sqrt{y.re \cdot y.re + y.im \cdot y.im}}} \]

      3. times-frac 49.1%

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

      4. hypot-def 49.1%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{hypot}\left(y.re, y.im\right)}} \cdot \frac{x.re \cdot y.re + x.im \cdot y.im}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}} \]

      5. fma-def 49.1%

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

      6. hypot-def 62.0%

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

   3. Applied egg-rr 62.0%

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

   4. Taylor expanded in y.im around -inf 74.4%

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

      1. neg-mul-1 74.4%

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

      2. +-commutative 74.4%

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

      3. mul-1-neg 74.4%

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

      4. unsub-neg 74.4%

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

      5. *-lft-identity 74.4%

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

      6. times-frac 81.1%

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

      7. /-rgt-identity 81.1%

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

   6. Simplified 81.1%

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

   if -7.00000000000000051e-55 < y.im < 1.9999999999999999e-144 or 7.6000000000000004e-15 < y.im < 4.2000000000000002e26

   1. Initial program 61.7%

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

   2. Taylor expanded in y.re around inf 86.7%

      \[\leadsto \color{blue}{\frac{x.re}{y.re} + \frac{y.im \cdot x.im}{{y.re}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 86.7%

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

      2. times-frac 89.5%

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

   4. Simplified 89.5%

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

   if 1.9999999999999999e-144 < y.im < 7.6000000000000004e-15 or 4.2000000000000002e26 < y.im < 1.05e120

   1. Initial program 81.0%

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

   if 1.05e120 < y.im

   1. Initial program 32.3%

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

   2. Taylor expanded in y.re around 0 80.6%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 80.6%

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

      2. unpow2 80.6%

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

      3. associate-/l* 80.7%

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

   4. Simplified 80.7%

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

      1. clear-num 80.7%

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

      2. inv-pow 80.7%

         \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im \cdot y.im}{y.re}}{x.re}\right)}^{-1}} \]

      3. associate-/l* 82.7%

         \[\leadsto \frac{x.im}{y.im} + {\left(\frac{\color{blue}{\frac{y.im}{\frac{y.re}{y.im}}}}{x.re}\right)}^{-1} \]

   6. Applied egg-rr 82.7%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im}{\frac{y.re}{y.im}}}{x.re}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 82.7%

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

      2. associate-/l/ 90.3%

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

   8. Simplified 90.3%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}} \]
   9. Step-by-step derivation

      1. frac-2neg 90.3%

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

      2. metadata-eval 90.3%

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

      3. div-inv 90.3%

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

      4. distribute-neg-frac 90.3%

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

   10. Applied egg-rr 90.3%

       \[\leadsto \frac{x.im}{y.im} + \color{blue}{-1 \cdot \frac{1}{\frac{-y.im}{x.re \cdot \frac{y.re}{y.im}}}} \]
   11. Step-by-step derivation

       1. mul-1-neg 90.3%

          \[\leadsto \frac{x.im}{y.im} + \color{blue}{\left(-\frac{1}{\frac{-y.im}{x.re \cdot \frac{y.re}{y.im}}}\right)} \]

       2. associate-/r/ 90.4%

          \[\leadsto \frac{x.im}{y.im} + \left(-\color{blue}{\frac{1}{-y.im} \cdot \left(x.re \cdot \frac{y.re}{y.im}\right)}\right) \]

       3. associate-*r* 90.3%

          \[\leadsto \frac{x.im}{y.im} + \left(-\color{blue}{\left(\frac{1}{-y.im} \cdot x.re\right) \cdot \frac{y.re}{y.im}}\right) \]

       4. distribute-rgt-neg-out 90.3%

          \[\leadsto \frac{x.im}{y.im} + \color{blue}{\left(\frac{1}{-y.im} \cdot x.re\right) \cdot \left(-\frac{y.re}{y.im}\right)} \]

       5. distribute-neg-frac 90.3%

          \[\leadsto \frac{x.im}{y.im} + \left(\frac{1}{-y.im} \cdot x.re\right) \cdot \color{blue}{\frac{-y.re}{y.im}} \]

       6. associate-*r/ 90.3%

          \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{\left(\frac{1}{-y.im} \cdot x.re\right) \cdot \left(-y.re\right)}{y.im}} \]

       7. associate-*l/ 90.4%

          \[\leadsto \frac{x.im}{y.im} + \frac{\color{blue}{\frac{1 \cdot x.re}{-y.im}} \cdot \left(-y.re\right)}{y.im} \]

       8. *-lft-identity 90.4%

          \[\leadsto \frac{x.im}{y.im} + \frac{\frac{\color{blue}{x.re}}{-y.im} \cdot \left(-y.re\right)}{y.im} \]

       9. /-rgt-identity 90.4%

          \[\leadsto \frac{x.im}{y.im} + \frac{\frac{x.re}{-y.im} \cdot \left(-\color{blue}{\frac{y.re}{1}}\right)}{y.im} \]

       10. distribute-neg-frac 90.4%

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

       11. times-frac 86.4%

           \[\leadsto \frac{x.im}{y.im} + \frac{\color{blue}{\frac{x.re \cdot \left(-y.re\right)}{\left(-y.im\right) \cdot 1}}}{y.im} \]

       12. *-rgt-identity 86.4%

           \[\leadsto \frac{x.im}{y.im} + \frac{\frac{x.re \cdot \left(-y.re\right)}{\color{blue}{-y.im}}}{y.im} \]

       13. associate-/l* 90.4%

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

       14. neg-mul-1 90.4%

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

       15. neg-mul-1 90.4%

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

       16. times-frac 90.4%

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

       17. metadata-eval 90.4%

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

   12. Simplified 90.4%

       \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{\frac{x.re}{1 \cdot \frac{y.im}{y.re}}}{y.im}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -7 \cdot 10^{-55}:\\ \;\;\;\;\left(x.im + x.re \cdot \frac{y.re}{y.im}\right) \cdot \frac{-1}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.im \leq 2 \cdot 10^{-144}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.im \leq 7.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 4.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.im \leq 1.05 \cdot 10^{+120}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{\frac{x.re}{\frac{y.im}{y.re}}}{y.im}\\ \end{array} \]

Alternative 2: 85.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \end{array} \end{array} \]

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)))
      2e+302)
   (*
    (/ 1.0 (hypot y.re y.im))
    (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
   (+ (/ x.im y.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) {
	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))) <= 2e+302) {
		tmp = (1.0 / hypot(y_46_re, y_46_im)) * (fma(x_46_re, y_46_re, (x_46_im * y_46_im)) / hypot(y_46_re, y_46_im));
	} else {
		tmp = (x_46_im / y_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)
	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))) <= 2e+302)
		tmp = Float64(Float64(1.0 / hypot(y_46_re, y_46_im)) * Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)));
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(y_46_re / y_46_im) * 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_] := 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], 2e+302], N[(N[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * 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]), $MachinePrecision], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(y$46$re / y$46$im), $MachinePrecision] * N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) < 2.0000000000000002e302

   1. Initial program 75.1%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 75.1%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x.re \cdot y.re + x.im \cdot y.im\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]

      2. add-sqr-sqrt 75.1%

         \[\leadsto \frac{1 \cdot \left(x.re \cdot y.re + x.im \cdot y.im\right)}{\color{blue}{\sqrt{y.re \cdot y.re + y.im \cdot y.im} \cdot \sqrt{y.re \cdot y.re + y.im \cdot y.im}}} \]

      3. times-frac 75.1%

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

      4. hypot-def 75.1%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{hypot}\left(y.re, y.im\right)}} \cdot \frac{x.re \cdot y.re + x.im \cdot y.im}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}} \]

      5. fma-def 75.1%

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

      6. hypot-def 94.9%

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

   3. Applied egg-rr 94.9%

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

   if 2.0000000000000002e302 < (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

   1. Initial program 8.6%

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

   2. Taylor expanded in y.re around 0 46.9%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 46.9%

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

      2. *-commutative 46.9%

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

      3. unpow2 46.9%

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

      4. times-frac 59.8%

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

   4. Simplified 59.8%

      \[\leadsto \color{blue}{\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \end{array} \]

Alternative 3: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ t_1 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{y.im \cdot \frac{\frac{y.im}{x.re}}{y.re}}\\ \mathbf{elif}\;y.im \leq 1.95 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.im \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.im \leq 4.6 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{\frac{x.re}{\frac{y.im}{y.re}}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re))))
        (t_1
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.im -2.9e-55)
     (+ (/ x.im y.im) (/ 1.0 (* y.im (/ (/ y.im x.re) y.re))))
     (if (<= y.im 1.95e-143)
       t_0
       (if (<= y.im 3.4e-15)
         t_1
         (if (<= y.im 8.8e+27)
           t_0
           (if (<= y.im 4.6e+118)
             t_1
             (+ (/ x.im y.im) (/ (/ x.re (/ y.im 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_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double t_1 = ((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_im <= -2.9e-55) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)));
	} else if (y_46_im <= 1.95e-143) {
		tmp = t_0;
	} else if (y_46_im <= 3.4e-15) {
		tmp = t_1;
	} else if (y_46_im <= 8.8e+27) {
		tmp = t_0;
	} else if (y_46_im <= 4.6e+118) {
		tmp = t_1;
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    t_1 = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46im <= (-2.9d-55)) then
        tmp = (x_46im / y_46im) + (1.0d0 / (y_46im * ((y_46im / x_46re) / y_46re)))
    else if (y_46im <= 1.95d-143) then
        tmp = t_0
    else if (y_46im <= 3.4d-15) then
        tmp = t_1
    else if (y_46im <= 8.8d+27) then
        tmp = t_0
    else if (y_46im <= 4.6d+118) then
        tmp = t_1
    else
        tmp = (x_46im / y_46im) + ((x_46re / (y_46im / y_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 t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double t_1 = ((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_im <= -2.9e-55) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)));
	} else if (y_46_im <= 1.95e-143) {
		tmp = t_0;
	} else if (y_46_im <= 3.4e-15) {
		tmp = t_1;
	} else if (y_46_im <= 8.8e+27) {
		tmp = t_0;
	} else if (y_46_im <= 4.6e+118) {
		tmp = t_1;
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	t_1 = ((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_im <= -2.9e-55:
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)))
	elif y_46_im <= 1.95e-143:
		tmp = t_0
	elif y_46_im <= 3.4e-15:
		tmp = t_1
	elif y_46_im <= 8.8e+27:
		tmp = t_0
	elif y_46_im <= 4.6e+118:
		tmp = t_1
	else:
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)))
	t_1 = 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_im <= -2.9e-55)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(1.0 / Float64(y_46_im * Float64(Float64(y_46_im / x_46_re) / y_46_re))));
	elseif (y_46_im <= 1.95e-143)
		tmp = t_0;
	elseif (y_46_im <= 3.4e-15)
		tmp = t_1;
	elseif (y_46_im <= 8.8e+27)
		tmp = t_0;
	elseif (y_46_im <= 4.6e+118)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re / Float64(y_46_im / y_46_re)) / y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	t_1 = ((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_im <= -2.9e-55)
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)));
	elseif (y_46_im <= 1.95e-143)
		tmp = t_0;
	elseif (y_46_im <= 3.4e-15)
		tmp = t_1;
	elseif (y_46_im <= 8.8e+27)
		tmp = t_0;
	elseif (y_46_im <= 4.6e+118)
		tmp = t_1;
	else
		tmp = (x_46_im / y_46_im) + ((x_46_re / (y_46_im / y_46_re)) / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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$46$im, -2.9e-55], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(1.0 / N[(y$46$im * N[(N[(y$46$im / x$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, 1.95e-143], t$95$0, If[LessEqual[y$46$im, 3.4e-15], t$95$1, If[LessEqual[y$46$im, 8.8e+27], t$95$0, If[LessEqual[y$46$im, 4.6e+118], t$95$1, N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -2.9e-55

   1. Initial program 49.1%

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

   2. Taylor expanded in y.re around 0 67.7%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 67.7%

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

      2. unpow2 67.7%

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

      3. associate-/l* 69.5%

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

   4. Simplified 69.5%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

         \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im \cdot y.im}{y.re}}{x.re}\right)}^{-1}} \]

      3. associate-/l* 74.0%

         \[\leadsto \frac{x.im}{y.im} + {\left(\frac{\color{blue}{\frac{y.im}{\frac{y.re}{y.im}}}}{x.re}\right)}^{-1} \]

   6. Applied egg-rr 74.0%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im}{\frac{y.re}{y.im}}}{x.re}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 74.0%

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

      2. associate-/l/ 77.9%

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

   8. Simplified 77.9%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}} \]
   9. Step-by-step derivation

      1. associate-/r* 79.3%

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

      2. associate-/r/ 79.3%

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

   10. Applied egg-rr 79.3%

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

   if -2.9e-55 < y.im < 1.95000000000000002e-143 or 3.4e-15 < y.im < 8.7999999999999995e27

   1. Initial program 61.7%

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

   2. Taylor expanded in y.re around inf 86.7%

      \[\leadsto \color{blue}{\frac{x.re}{y.re} + \frac{y.im \cdot x.im}{{y.re}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 86.7%

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

      2. times-frac 89.5%

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

   4. Simplified 89.5%

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

   if 1.95000000000000002e-143 < y.im < 3.4e-15 or 8.7999999999999995e27 < y.im < 4.60000000000000032e118

   1. Initial program 81.0%

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

   if 4.60000000000000032e118 < y.im

   1. Initial program 32.3%

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

   2. Taylor expanded in y.re around 0 80.6%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 80.6%

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

      2. unpow2 80.6%

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

      3. associate-/l* 80.7%

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

   4. Simplified 80.7%

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

      1. clear-num 80.7%

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

      2. inv-pow 80.7%

         \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im \cdot y.im}{y.re}}{x.re}\right)}^{-1}} \]

      3. associate-/l* 82.7%

         \[\leadsto \frac{x.im}{y.im} + {\left(\frac{\color{blue}{\frac{y.im}{\frac{y.re}{y.im}}}}{x.re}\right)}^{-1} \]

   6. Applied egg-rr 82.7%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im}{\frac{y.re}{y.im}}}{x.re}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 82.7%

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

      2. associate-/l/ 90.3%

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

   8. Simplified 90.3%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}} \]
   9. Step-by-step derivation

      1. frac-2neg 90.3%

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

      2. metadata-eval 90.3%

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

      3. div-inv 90.3%

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

      4. distribute-neg-frac 90.3%

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

   10. Applied egg-rr 90.3%

       \[\leadsto \frac{x.im}{y.im} + \color{blue}{-1 \cdot \frac{1}{\frac{-y.im}{x.re \cdot \frac{y.re}{y.im}}}} \]
   11. Step-by-step derivation

       1. mul-1-neg 90.3%

          \[\leadsto \frac{x.im}{y.im} + \color{blue}{\left(-\frac{1}{\frac{-y.im}{x.re \cdot \frac{y.re}{y.im}}}\right)} \]

       2. associate-/r/ 90.4%

          \[\leadsto \frac{x.im}{y.im} + \left(-\color{blue}{\frac{1}{-y.im} \cdot \left(x.re \cdot \frac{y.re}{y.im}\right)}\right) \]

       3. associate-*r* 90.3%

          \[\leadsto \frac{x.im}{y.im} + \left(-\color{blue}{\left(\frac{1}{-y.im} \cdot x.re\right) \cdot \frac{y.re}{y.im}}\right) \]

       4. distribute-rgt-neg-out 90.3%

          \[\leadsto \frac{x.im}{y.im} + \color{blue}{\left(\frac{1}{-y.im} \cdot x.re\right) \cdot \left(-\frac{y.re}{y.im}\right)} \]

       5. distribute-neg-frac 90.3%

          \[\leadsto \frac{x.im}{y.im} + \left(\frac{1}{-y.im} \cdot x.re\right) \cdot \color{blue}{\frac{-y.re}{y.im}} \]

       6. associate-*r/ 90.3%

          \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{\left(\frac{1}{-y.im} \cdot x.re\right) \cdot \left(-y.re\right)}{y.im}} \]

       7. associate-*l/ 90.4%

          \[\leadsto \frac{x.im}{y.im} + \frac{\color{blue}{\frac{1 \cdot x.re}{-y.im}} \cdot \left(-y.re\right)}{y.im} \]

       8. *-lft-identity 90.4%

          \[\leadsto \frac{x.im}{y.im} + \frac{\frac{\color{blue}{x.re}}{-y.im} \cdot \left(-y.re\right)}{y.im} \]

       9. /-rgt-identity 90.4%

          \[\leadsto \frac{x.im}{y.im} + \frac{\frac{x.re}{-y.im} \cdot \left(-\color{blue}{\frac{y.re}{1}}\right)}{y.im} \]

       10. distribute-neg-frac 90.4%

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

       11. times-frac 86.4%

           \[\leadsto \frac{x.im}{y.im} + \frac{\color{blue}{\frac{x.re \cdot \left(-y.re\right)}{\left(-y.im\right) \cdot 1}}}{y.im} \]

       12. *-rgt-identity 86.4%

           \[\leadsto \frac{x.im}{y.im} + \frac{\frac{x.re \cdot \left(-y.re\right)}{\color{blue}{-y.im}}}{y.im} \]

       13. associate-/l* 90.4%

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

       14. neg-mul-1 90.4%

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

       15. neg-mul-1 90.4%

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

       16. times-frac 90.4%

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

       17. metadata-eval 90.4%

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

   12. Simplified 90.4%

       \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{\frac{x.re}{1 \cdot \frac{y.im}{y.re}}}{y.im}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{y.im \cdot \frac{\frac{y.im}{x.re}}{y.re}}\\ \mathbf{elif}\;y.im \leq 1.95 \cdot 10^{-143}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.im \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.im \leq 4.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{\frac{x.re}{\frac{y.im}{y.re}}}{y.im}\\ \end{array} \]

Alternative 4: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -3.8 \cdot 10^{-57} \lor \neg \left(y.im \leq 6.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{y.im \cdot \frac{\frac{y.im}{x.re}}{y.re}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -3.8e-57) (not (<= y.im 6.5e+30)))
   (+ (/ x.im y.im) (/ 1.0 (* y.im (/ (/ y.im x.re) y.re))))
   (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -3.8e-57) || !(y_46_im <= 6.5e+30)) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)));
	} else {
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-3.8d-57)) .or. (.not. (y_46im <= 6.5d+30))) then
        tmp = (x_46im / y_46im) + (1.0d0 / (y_46im * ((y_46im / x_46re) / y_46re)))
    else
        tmp = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -3.8e-57) || !(y_46_im <= 6.5e+30)) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)));
	} else {
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -3.8e-57) or not (y_46_im <= 6.5e+30):
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)))
	else:
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -3.8e-57) || !(y_46_im <= 6.5e+30))
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(1.0 / Float64(y_46_im * Float64(Float64(y_46_im / x_46_re) / y_46_re))));
	else
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -3.8e-57) || ~((y_46_im <= 6.5e+30)))
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im * ((y_46_im / x_46_re) / y_46_re)));
	else
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -3.8e-57], N[Not[LessEqual[y$46$im, 6.5e+30]], $MachinePrecision]], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(1.0 / N[(y$46$im * N[(N[(y$46$im / x$46$re), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -3.7999999999999997e-57 or 6.5e30 < y.im

   1. Initial program 47.4%

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

   2. Taylor expanded in y.re around 0 71.8%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 71.8%

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

      2. unpow2 71.8%

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

      3. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

      1. clear-num 72.1%

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

      2. inv-pow 72.1%

         \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im \cdot y.im}{y.re}}{x.re}\right)}^{-1}} \]

      3. associate-/l* 75.2%

         \[\leadsto \frac{x.im}{y.im} + {\left(\frac{\color{blue}{\frac{y.im}{\frac{y.re}{y.im}}}}{x.re}\right)}^{-1} \]

   6. Applied egg-rr 75.2%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{{\left(\frac{\frac{y.im}{\frac{y.re}{y.im}}}{x.re}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 75.2%

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

      2. associate-/l/ 79.9%

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

   8. Simplified 79.9%

      \[\leadsto \frac{x.im}{y.im} + \color{blue}{\frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}} \]
   9. Step-by-step derivation

      1. associate-/r* 80.6%

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

      2. associate-/r/ 81.3%

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

   10. Applied egg-rr 81.3%

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

   if -3.7999999999999997e-57 < y.im < 6.5e30

   1. Initial program 67.3%

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

   2. Taylor expanded in y.re around inf 79.5%

      \[\leadsto \color{blue}{\frac{x.re}{y.re} + \frac{y.im \cdot x.im}{{y.re}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 79.5%

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

      2. times-frac 81.8%

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

   4. Simplified 81.8%

      \[\leadsto \color{blue}{\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3.8 \cdot 10^{-57} \lor \neg \left(y.im \leq 6.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{y.im \cdot \frac{\frac{y.im}{x.re}}{y.re}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \]

Alternative 5: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -3 \cdot 10^{-55} \lor \neg \left(y.im \leq 5.3 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -3e-55) (not (<= y.im 5.3e+26)))
   (+ (/ x.im y.im) (* (/ y.re y.im) (/ x.re y.im)))
   (/ x.re y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -3e-55) || !(y_46_im <= 5.3e+26)) {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-3d-55)) .or. (.not. (y_46im <= 5.3d+26))) then
        tmp = (x_46im / y_46im) + ((y_46re / y_46im) * (x_46re / y_46im))
    else
        tmp = x_46re / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -3e-55) || !(y_46_im <= 5.3e+26)) {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -3e-55) or not (y_46_im <= 5.3e+26):
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im))
	else:
		tmp = x_46_re / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -3e-55) || !(y_46_im <= 5.3e+26))
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(y_46_re / y_46_im) * Float64(x_46_re / y_46_im)));
	else
		tmp = Float64(x_46_re / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -3e-55) || ~((y_46_im <= 5.3e+26)))
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	else
		tmp = x_46_re / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -3e-55], N[Not[LessEqual[y$46$im, 5.3e+26]], $MachinePrecision]], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(y$46$re / y$46$im), $MachinePrecision] * N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$46$re / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -3.00000000000000016e-55 or 5.29999999999999969e26 < y.im

   1. Initial program 47.4%

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

   2. Taylor expanded in y.re around 0 71.8%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. unpow2 71.8%

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

      4. times-frac 80.6%

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

   4. Simplified 80.6%

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

   if -3.00000000000000016e-55 < y.im < 5.29999999999999969e26

   1. Initial program 67.3%

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

   2. Taylor expanded in y.re around inf 68.4%

      \[\leadsto \color{blue}{\frac{x.re}{y.re}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3 \cdot 10^{-55} \lor \neg \left(y.im \leq 5.3 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \]

Alternative 6: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1 \cdot 10^{-54} \lor \neg \left(y.im \leq 1.9 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1e-54) (not (<= y.im 1.9e+30)))
   (+ (/ x.im y.im) (* (/ y.re y.im) (/ x.re y.im)))
   (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1e-54) || !(y_46_im <= 1.9e+30)) {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	} else {
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-1d-54)) .or. (.not. (y_46im <= 1.9d+30))) then
        tmp = (x_46im / y_46im) + ((y_46re / y_46im) * (x_46re / y_46im))
    else
        tmp = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1e-54) || !(y_46_im <= 1.9e+30)) {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	} else {
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -1e-54) or not (y_46_im <= 1.9e+30):
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im))
	else:
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -1e-54) || !(y_46_im <= 1.9e+30))
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(y_46_re / y_46_im) * Float64(x_46_re / y_46_im)));
	else
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -1e-54) || ~((y_46_im <= 1.9e+30)))
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	else
		tmp = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -1e-54], N[Not[LessEqual[y$46$im, 1.9e+30]], $MachinePrecision]], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(y$46$re / y$46$im), $MachinePrecision] * N[(x$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -1e-54 or 1.9000000000000001e30 < y.im

   1. Initial program 47.4%

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

   2. Taylor expanded in y.re around 0 71.8%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.im}^{2}} + \frac{x.im}{y.im}} \]
   3. Step-by-step derivation

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. unpow2 71.8%

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

      4. times-frac 80.6%

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

   4. Simplified 80.6%

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

   if -1e-54 < y.im < 1.9000000000000001e30

   1. Initial program 67.3%

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

   2. Taylor expanded in y.re around inf 79.5%

      \[\leadsto \color{blue}{\frac{x.re}{y.re} + \frac{y.im \cdot x.im}{{y.re}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 79.5%

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

      2. times-frac 81.8%

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

   4. Simplified 81.8%

      \[\leadsto \color{blue}{\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -1 \cdot 10^{-54} \lor \neg \left(y.im \leq 1.9 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \]

Alternative 7: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{elif}\;y.im \leq -1.35 \cdot 10^{-30}:\\ \;\;\;\;y.re \cdot \frac{x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq -5.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{elif}\;y.im \leq 1.3 \cdot 10^{+30}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.im -3.5e+69)
   (/ x.im y.im)
   (if (<= y.im -1.35e-30)
     (* y.re (/ x.re (+ (* y.re y.re) (* y.im y.im))))
     (if (<= y.im -5.8e-55)
       (/ x.im y.im)
       (if (<= y.im 1.3e+30) (/ 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_im <= -3.5e+69) {
		tmp = x_46_im / y_46_im;
	} else if (y_46_im <= -1.35e-30) {
		tmp = y_46_re * (x_46_re / ((y_46_re * y_46_re) + (y_46_im * y_46_im)));
	} else if (y_46_im <= -5.8e-55) {
		tmp = x_46_im / y_46_im;
	} else if (y_46_im <= 1.3e+30) {
		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_46im <= (-3.5d+69)) then
        tmp = x_46im / y_46im
    else if (y_46im <= (-1.35d-30)) then
        tmp = y_46re * (x_46re / ((y_46re * y_46re) + (y_46im * y_46im)))
    else if (y_46im <= (-5.8d-55)) then
        tmp = x_46im / y_46im
    else if (y_46im <= 1.3d+30) 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_im <= -3.5e+69) {
		tmp = x_46_im / y_46_im;
	} else if (y_46_im <= -1.35e-30) {
		tmp = y_46_re * (x_46_re / ((y_46_re * y_46_re) + (y_46_im * y_46_im)));
	} else if (y_46_im <= -5.8e-55) {
		tmp = x_46_im / y_46_im;
	} else if (y_46_im <= 1.3e+30) {
		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_im <= -3.5e+69:
		tmp = x_46_im / y_46_im
	elif y_46_im <= -1.35e-30:
		tmp = y_46_re * (x_46_re / ((y_46_re * y_46_re) + (y_46_im * y_46_im)))
	elif y_46_im <= -5.8e-55:
		tmp = x_46_im / y_46_im
	elif y_46_im <= 1.3e+30:
		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_im <= -3.5e+69)
		tmp = Float64(x_46_im / y_46_im);
	elseif (y_46_im <= -1.35e-30)
		tmp = Float64(y_46_re * Float64(x_46_re / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))));
	elseif (y_46_im <= -5.8e-55)
		tmp = Float64(x_46_im / y_46_im);
	elseif (y_46_im <= 1.3e+30)
		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_im <= -3.5e+69)
		tmp = x_46_im / y_46_im;
	elseif (y_46_im <= -1.35e-30)
		tmp = y_46_re * (x_46_re / ((y_46_re * y_46_re) + (y_46_im * y_46_im)));
	elseif (y_46_im <= -5.8e-55)
		tmp = x_46_im / y_46_im;
	elseif (y_46_im <= 1.3e+30)
		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[LessEqual[y$46$im, -3.5e+69], N[(x$46$im / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, -1.35e-30], N[(y$46$re * N[(x$46$re / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, -5.8e-55], N[(x$46$im / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, 1.3e+30], N[(x$46$re / y$46$re), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y.im < -3.49999999999999987e69 or -1.34999999999999994e-30 < y.im < -5.8e-55 or 1.29999999999999994e30 < y.im

   1. Initial program 44.3%

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

   2. Taylor expanded in y.re around 0 73.0%

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

   if -3.49999999999999987e69 < y.im < -1.34999999999999994e-30

   1. Initial program 65.7%

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

   2. Taylor expanded in x.re around inf 46.2%

      \[\leadsto \color{blue}{\frac{x.re \cdot y.re}{{y.re}^{2} + {y.im}^{2}}} \]
   3. Step-by-step derivation

      1. associate-/l* 47.1%

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

      2. associate-/r/ 46.8%

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

      3. unpow2 46.8%

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

      4. unpow2 46.8%

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

      5. +-commutative 46.8%

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

      6. fma-udef 46.8%

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

   4. Simplified 46.8%

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

      1. fma-udef 46.8%

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

      2. +-commutative 46.8%

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

   6. Applied egg-rr 46.8%

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

   if -5.8e-55 < y.im < 1.29999999999999994e30

   1. Initial program 67.3%

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

   2. Taylor expanded in y.re around inf 68.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{elif}\;y.im \leq -1.35 \cdot 10^{-30}:\\ \;\;\;\;y.re \cdot \frac{x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq -5.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{elif}\;y.im \leq 1.3 \cdot 10^{+30}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \]

Alternative 8: 63.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -3.1 \cdot 10^{+24} \lor \neg \left(y.im \leq -1.6 \cdot 10^{-30}\right) \land \left(y.im \leq -1.05 \cdot 10^{-54} \lor \neg \left(y.im \leq 1.05 \cdot 10^{+30}\right)\right):\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -3.1e+24)
         (and (not (<= y.im -1.6e-30))
              (or (<= y.im -1.05e-54) (not (<= y.im 1.05e+30)))))
   (/ x.im y.im)
   (/ x.re y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -3.1e+24) || (!(y_46_im <= -1.6e-30) && ((y_46_im <= -1.05e-54) || !(y_46_im <= 1.05e+30)))) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-3.1d+24)) .or. (.not. (y_46im <= (-1.6d-30))) .and. (y_46im <= (-1.05d-54)) .or. (.not. (y_46im <= 1.05d+30))) then
        tmp = x_46im / y_46im
    else
        tmp = x_46re / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -3.1e+24) || (!(y_46_im <= -1.6e-30) && ((y_46_im <= -1.05e-54) || !(y_46_im <= 1.05e+30)))) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -3.1e+24) or (not (y_46_im <= -1.6e-30) and ((y_46_im <= -1.05e-54) or not (y_46_im <= 1.05e+30))):
		tmp = x_46_im / y_46_im
	else:
		tmp = x_46_re / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -3.1e+24) || (!(y_46_im <= -1.6e-30) && ((y_46_im <= -1.05e-54) || !(y_46_im <= 1.05e+30))))
		tmp = Float64(x_46_im / y_46_im);
	else
		tmp = Float64(x_46_re / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -3.1e+24) || (~((y_46_im <= -1.6e-30)) && ((y_46_im <= -1.05e-54) || ~((y_46_im <= 1.05e+30)))))
		tmp = x_46_im / y_46_im;
	else
		tmp = x_46_re / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -3.1e+24], And[N[Not[LessEqual[y$46$im, -1.6e-30]], $MachinePrecision], Or[LessEqual[y$46$im, -1.05e-54], N[Not[LessEqual[y$46$im, 1.05e+30]], $MachinePrecision]]]], N[(x$46$im / y$46$im), $MachinePrecision], N[(x$46$re / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -3.10000000000000011e24 or -1.6e-30 < y.im < -1.05e-54 or 1.05e30 < y.im

   1. Initial program 46.7%

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

   2. Taylor expanded in y.re around 0 69.7%

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

   if -3.10000000000000011e24 < y.im < -1.6e-30 or -1.05e-54 < y.im < 1.05e30

   1. Initial program 66.2%

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

   2. Taylor expanded in y.re around inf 68.1%

      \[\leadsto \color{blue}{\frac{x.re}{y.re}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3.1 \cdot 10^{+24} \lor \neg \left(y.im \leq -1.6 \cdot 10^{-30}\right) \land \left(y.im \leq -1.05 \cdot 10^{-54} \lor \neg \left(y.im \leq 1.05 \cdot 10^{+30}\right)\right):\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \]

Alternative 9: 42.3% 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

1. Initial program 56.4%

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

2. Taylor expanded in y.re around 0 43.5%

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

3. Final simplification 43.5%

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

Reproduce

herbie shell --seed 2023188 
(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))))