_divideComplex, real part

Percentage Accurate: 60.6% → 79.7%

Time: 6.3s

Alternatives: 9

Speedup: 2.1×

Specification

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Python

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

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
end

Wolfram

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

Initial Program: 60.6% 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: 79.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 3.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 2.85 \cdot 10^{+20}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re \cdot \frac{y.re}{x.im}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -8e-20)
   (+ (/ x.re y.re) (/ (* y.im (/ x.im y.re)) y.re))
   (if (<= y.re 3.8e-126)
     (+ (/ x.im y.im) (/ (* x.re (/ y.re y.im)) y.im))
     (if (<= y.re 2.85e+20)
       (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
       (+ (/ x.re y.re) (/ y.im (* y.re (/ y.re x.im))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -8e-20) {
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re);
	} else if (y_46_re <= 3.8e-126) {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	} else if (y_46_re <= 2.85e+20) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-8d-20)) then
        tmp = (x_46re / y_46re) + ((y_46im * (x_46im / y_46re)) / y_46re)
    else if (y_46re <= 3.8d-126) then
        tmp = (x_46im / y_46im) + ((x_46re * (y_46re / y_46im)) / y_46im)
    else if (y_46re <= 2.85d+20) then
        tmp = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    else
        tmp = (x_46re / y_46re) + (y_46im / (y_46re * (y_46re / x_46im)))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -8e-20) {
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re);
	} else if (y_46_re <= 3.8e-126) {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	} else if (y_46_re <= 2.85e+20) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -8e-20:
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re)
	elif y_46_re <= 3.8e-126:
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im)
	elif y_46_re <= 2.85e+20:
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	else:
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -8e-20)
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im * Float64(x_46_im / y_46_re)) / y_46_re));
	elseif (y_46_re <= 3.8e-126)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re * Float64(y_46_re / y_46_im)) / y_46_im));
	elseif (y_46_re <= 2.85e+20)
		tmp = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	else
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im / Float64(y_46_re * Float64(y_46_re / x_46_im))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -8e-20)
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re);
	elseif (y_46_re <= 3.8e-126)
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	elseif (y_46_re <= 2.85e+20)
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	else
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -8e-20], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 3.8e-126], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.85e+20], 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], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im / N[(y$46$re * N[(y$46$re / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -7.99999999999999956e-20

   1. Initial program 52.3%

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

   2. Taylor expanded in y.re around inf 74.6%

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

      1. unpow2 74.6%

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

      2. times-frac 79.4%

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

   4. Simplified 79.4%

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

      1. associate-*r/ 80.8%

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

   6. Applied egg-rr 80.8%

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

   if -7.99999999999999956e-20 < y.re < 3.7999999999999999e-126

   1. Initial program 68.8%

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

   2. Taylor expanded in y.re around 0 86.4%

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

      1. *-commutative 86.4%

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

      2. unpow2 86.4%

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

      3. times-frac 87.4%

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

   4. Simplified 87.4%

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

      1. associate-*r/ 88.3%

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

   6. Applied egg-rr 88.3%

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

   if 3.7999999999999999e-126 < y.re < 2.85e20

   1. Initial program 86.1%

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

   if 2.85e20 < y.re

   1. Initial program 44.7%

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

   2. Taylor expanded in y.re around inf 81.2%

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

      1. unpow2 81.2%

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

      2. times-frac 86.4%

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

   4. Simplified 86.4%

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

      1. clear-num 86.4%

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

      2. frac-times 86.4%

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

      3. *-un-lft-identity 86.4%

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

   6. Applied egg-rr 86.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 3.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 2.85 \cdot 10^{+20}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re \cdot \frac{y.re}{x.im}}\\ \end{array} \]

Alternative 2: 84.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \end{array} \end{array} \]

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)))
      5e+286)
   (*
    (/ 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))) <= 5e+286) {
		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))) <= 5e+286)
		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], 5e+286], 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))) < 5.0000000000000004e286

   1. Initial program 77.9%

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

      1. *-un-lft-identity 77.9%

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

      2. add-sqr-sqrt 77.9%

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

      3. times-frac 77.8%

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

      4. hypot-def 77.8%

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

      5. fma-def 77.8%

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

      6. hypot-def 93.3%

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

   3. Applied egg-rr 93.3%

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

   if 5.0000000000000004e286 < (/.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 5.8%

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

   2. Taylor expanded in y.re around 0 47.6%

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

      1. *-commutative 47.6%

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

      2. unpow2 47.6%

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

      3. times-frac 55.2%

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

   4. Simplified 55.2%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \end{array} \]

Alternative 3: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.1 \cdot 10^{-15} \lor \neg \left(y.re \leq 8.8 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -1.1e-15) (not (<= y.re 8.8e+49)))
   (/ x.re y.re)
   (+ (/ 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 ((y_46_re <= -1.1e-15) || !(y_46_re <= 8.8e+49)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-1.1d-15)) .or. (.not. (y_46re <= 8.8d+49))) then
        tmp = x_46re / y_46re
    else
        tmp = (x_46im / y_46im) + ((y_46re / y_46im) * (x_46re / y_46im))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -1.1e-15) || !(y_46_re <= 8.8e+49)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im / y_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):
	tmp = 0
	if (y_46_re <= -1.1e-15) or not (y_46_re <= 8.8e+49):
		tmp = x_46_re / y_46_re
	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 ((y_46_re <= -1.1e-15) || !(y_46_re <= 8.8e+49))
		tmp = Float64(x_46_re / y_46_re);
	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

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -1.1e-15) || ~((y_46_re <= 8.8e+49)))
		tmp = x_46_re / y_46_re;
	else
		tmp = (x_46_im / y_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_] := If[Or[LessEqual[y$46$re, -1.1e-15], N[Not[LessEqual[y$46$re, 8.8e+49]], $MachinePrecision]], N[(x$46$re / y$46$re), $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 y.re < -1.09999999999999993e-15 or 8.8000000000000003e49 < y.re

   1. Initial program 48.1%

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

   2. Taylor expanded in y.re around inf 71.1%

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

   if -1.09999999999999993e-15 < y.re < 8.8000000000000003e49

   1. Initial program 72.2%

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

   2. Taylor expanded in y.re around 0 79.3%

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

      1. *-commutative 79.3%

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

      2. unpow2 79.3%

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

      3. times-frac 81.2%

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

   4. Simplified 81.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.1 \cdot 10^{-15} \lor \neg \left(y.re \leq 8.8 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \end{array} \]

Alternative 4: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.9 \cdot 10^{-21} \lor \neg \left(y.re \leq 1.75 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{x.im}{y.re} \cdot \frac{y.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -1.9e-21) (not (<= y.re 1.75e+47)))
   (+ (/ x.re y.re) (* (/ x.im y.re) (/ y.im y.re)))
   (+ (/ x.im y.im) (/ (* x.re (/ y.re y.im)) y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -1.9e-21) || !(y_46_re <= 1.75e+47)) {
		tmp = (x_46_re / y_46_re) + ((x_46_im / y_46_re) * (y_46_im / y_46_re));
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-1.9d-21)) .or. (.not. (y_46re <= 1.75d+47))) then
        tmp = (x_46re / y_46re) + ((x_46im / y_46re) * (y_46im / y_46re))
    else
        tmp = (x_46im / y_46im) + ((x_46re * (y_46re / y_46im)) / y_46im)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -1.9e-21) || !(y_46_re <= 1.75e+47)) {
		tmp = (x_46_re / y_46_re) + ((x_46_im / y_46_re) * (y_46_im / y_46_re));
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -1.9e-21) or not (y_46_re <= 1.75e+47):
		tmp = (x_46_re / y_46_re) + ((x_46_im / y_46_re) * (y_46_im / y_46_re))
	else:
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -1.9e-21) || !(y_46_re <= 1.75e+47))
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(x_46_im / y_46_re) * Float64(y_46_im / y_46_re)));
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re * Float64(y_46_re / y_46_im)) / y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -1.9e-21) || ~((y_46_re <= 1.75e+47)))
		tmp = (x_46_re / y_46_re) + ((x_46_im / y_46_re) * (y_46_im / y_46_re));
	else
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -1.9e-21], N[Not[LessEqual[y$46$re, 1.75e+47]], $MachinePrecision]], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(x$46$im / y$46$re), $MachinePrecision] * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -1.8999999999999999e-21 or 1.75000000000000008e47 < y.re

   1. Initial program 48.6%

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

   2. Taylor expanded in y.re around inf 78.7%

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

      1. unpow2 78.7%

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

      2. times-frac 83.8%

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

   4. Simplified 83.8%

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

   if -1.8999999999999999e-21 < y.re < 1.75000000000000008e47

   1. Initial program 72.0%

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

   2. Taylor expanded in y.re around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. unpow2 79.8%

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

      3. times-frac 81.7%

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

   4. Simplified 81.7%

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

      1. associate-*r/ 82.4%

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

   6. Applied egg-rr 82.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.9 \cdot 10^{-21} \lor \neg \left(y.re \leq 1.75 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{x.im}{y.re} \cdot \frac{y.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]

Alternative 5: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -5.5 \cdot 10^{-19} \lor \neg \left(y.re \leq 4.6 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re \cdot \frac{y.re}{x.im}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -5.5e-19) (not (<= y.re 4.6e+46)))
   (+ (/ x.re y.re) (/ y.im (* y.re (/ y.re x.im))))
   (+ (/ x.im y.im) (/ (* x.re (/ y.re y.im)) y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -5.5e-19) || !(y_46_re <= 4.6e+46)) {
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-5.5d-19)) .or. (.not. (y_46re <= 4.6d+46))) then
        tmp = (x_46re / y_46re) + (y_46im / (y_46re * (y_46re / x_46im)))
    else
        tmp = (x_46im / y_46im) + ((x_46re * (y_46re / y_46im)) / y_46im)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -5.5e-19) || !(y_46_re <= 4.6e+46)) {
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	} else {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -5.5e-19) or not (y_46_re <= 4.6e+46):
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)))
	else:
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -5.5e-19) || !(y_46_re <= 4.6e+46))
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im / Float64(y_46_re * Float64(y_46_re / x_46_im))));
	else
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re * Float64(y_46_re / y_46_im)) / y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -5.5e-19) || ~((y_46_re <= 4.6e+46)))
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	else
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -5.5e-19], N[Not[LessEqual[y$46$re, 4.6e+46]], $MachinePrecision]], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im / N[(y$46$re * N[(y$46$re / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -5.4999999999999996e-19 or 4.6000000000000001e46 < y.re

   1. Initial program 48.6%

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

   2. Taylor expanded in y.re around inf 78.7%

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

      1. unpow2 78.7%

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

      2. times-frac 83.8%

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

   4. Simplified 83.8%

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

      1. clear-num 83.8%

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

      2. frac-times 83.8%

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

      3. *-un-lft-identity 83.8%

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

   6. Applied egg-rr 83.8%

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

   if -5.4999999999999996e-19 < y.re < 4.6000000000000001e46

   1. Initial program 72.0%

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

   2. Taylor expanded in y.re around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. unpow2 79.8%

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

      3. times-frac 81.7%

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

   4. Simplified 81.7%

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

      1. associate-*r/ 82.4%

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

   6. Applied egg-rr 82.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -5.5 \cdot 10^{-19} \lor \neg \left(y.re \leq 4.6 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re \cdot \frac{y.re}{x.im}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]

Alternative 6: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -4.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 4.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -4.8e-16)
   (/ x.re y.re)
   (if (<= y.re 4.5e+48)
     (+ (/ x.im y.im) (/ (* x.re (/ y.re y.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_re <= -4.8e-16) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 4.5e+48) {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_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_46re <= (-4.8d-16)) then
        tmp = x_46re / y_46re
    else if (y_46re <= 4.5d+48) then
        tmp = (x_46im / y_46im) + ((x_46re * (y_46re / y_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_re <= -4.8e-16) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 4.5e+48) {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_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_re <= -4.8e-16:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 4.5e+48:
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_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_re <= -4.8e-16)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 4.5e+48)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re * Float64(y_46_re / y_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_re <= -4.8e-16)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 4.5e+48)
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_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[LessEqual[y$46$re, -4.8e-16], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 4.5e+48], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision], N[(x$46$re / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y.re < -4.8000000000000001e-16 or 4.49999999999999995e48 < y.re

   1. Initial program 48.1%

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

   2. Taylor expanded in y.re around inf 71.1%

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

   if -4.8000000000000001e-16 < y.re < 4.49999999999999995e48

   1. Initial program 72.2%

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

   2. Taylor expanded in y.re around 0 79.3%

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

      1. *-commutative 79.3%

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

      2. unpow2 79.3%

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

      3. times-frac 81.2%

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

   4. Simplified 81.2%

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

      1. associate-*r/ 81.9%

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

   6. Applied egg-rr 81.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -4.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 4.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \]

Alternative 7: 78.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.65 \cdot 10^{-18}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 8.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re \cdot \frac{y.re}{x.im}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -1.65e-18)
   (+ (/ x.re y.re) (/ (* y.im (/ x.im y.re)) y.re))
   (if (<= y.re 8.6e+51)
     (+ (/ x.im y.im) (/ (* x.re (/ y.re y.im)) y.im))
     (+ (/ x.re y.re) (/ y.im (* y.re (/ y.re x.im)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -1.65e-18) {
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re);
	} else if (y_46_re <= 8.6e+51) {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	} else {
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-1.65d-18)) then
        tmp = (x_46re / y_46re) + ((y_46im * (x_46im / y_46re)) / y_46re)
    else if (y_46re <= 8.6d+51) then
        tmp = (x_46im / y_46im) + ((x_46re * (y_46re / y_46im)) / y_46im)
    else
        tmp = (x_46re / y_46re) + (y_46im / (y_46re * (y_46re / x_46im)))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -1.65e-18) {
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re);
	} else if (y_46_re <= 8.6e+51) {
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	} else {
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -1.65e-18:
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re)
	elif y_46_re <= 8.6e+51:
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im)
	else:
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -1.65e-18)
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im * Float64(x_46_im / y_46_re)) / y_46_re));
	elseif (y_46_re <= 8.6e+51)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(x_46_re * Float64(y_46_re / y_46_im)) / y_46_im));
	else
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im / Float64(y_46_re * Float64(y_46_re / x_46_im))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -1.65e-18)
		tmp = (x_46_re / y_46_re) + ((y_46_im * (x_46_im / y_46_re)) / y_46_re);
	elseif (y_46_re <= 8.6e+51)
		tmp = (x_46_im / y_46_im) + ((x_46_re * (y_46_re / y_46_im)) / y_46_im);
	else
		tmp = (x_46_re / y_46_re) + (y_46_im / (y_46_re * (y_46_re / x_46_im)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -1.65e-18], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 8.6e+51], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im / N[(y$46$re * N[(y$46$re / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -1.6500000000000001e-18

   1. Initial program 52.3%

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

   2. Taylor expanded in y.re around inf 74.6%

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

      1. unpow2 74.6%

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

      2. times-frac 79.4%

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

   4. Simplified 79.4%

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

      1. associate-*r/ 80.8%

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

   6. Applied egg-rr 80.8%

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

   if -1.6500000000000001e-18 < y.re < 8.5999999999999994e51

   1. Initial program 72.0%

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

   2. Taylor expanded in y.re around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. unpow2 79.8%

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

      3. times-frac 81.7%

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

   4. Simplified 81.7%

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

      1. associate-*r/ 82.4%

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

   6. Applied egg-rr 82.4%

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

   if 8.5999999999999994e51 < y.re

   1. Initial program 44.2%

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

   2. Taylor expanded in y.re around inf 83.4%

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

      1. unpow2 83.4%

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

      2. times-frac 89.1%

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

   4. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. frac-times 89.1%

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

      3. *-un-lft-identity 89.1%

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

   6. Applied egg-rr 89.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.65 \cdot 10^{-18}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 8.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re \cdot \frac{y.re}{x.im}}\\ \end{array} \]

Alternative 8: 64.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -9 \cdot 10^{-16}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -9e-16)
   (/ x.re y.re)
   (if (<= y.re 3e-7) (/ 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_re <= -9e-16) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3e-7) {
		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_46re <= (-9d-16)) then
        tmp = x_46re / y_46re
    else if (y_46re <= 3d-7) 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_re <= -9e-16) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3e-7) {
		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_re <= -9e-16:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 3e-7:
		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_re <= -9e-16)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 3e-7)
		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_re <= -9e-16)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 3e-7)
		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[LessEqual[y$46$re, -9e-16], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 3e-7], 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.re < -9.0000000000000003e-16 or 2.9999999999999999e-7 < y.re

   1. Initial program 49.3%

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

   2. Taylor expanded in y.re around inf 69.8%

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

   if -9.0000000000000003e-16 < y.re < 2.9999999999999999e-7

   1. Initial program 72.5%

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

   2. Taylor expanded in y.re around 0 74.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -9 \cdot 10^{-16}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \]

Alternative 9: 42.4% 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 61.6%

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

2. Taylor expanded in y.re around 0 47.0%

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

3. Final simplification 47.0%

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

Reproduce

herbie shell --seed 2023271 
(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))))