_divideComplex, real part

Percentage Accurate: 62.1% → 80.3%

Time: 8.5s

Alternatives: 10

Speedup: 0.8×

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: 80.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {y.im}^{2} + {y.re}^{2}\\ \mathbf{if}\;y.im \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{elif}\;y.im \leq 6.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{x.re + \frac{1}{y.re} \cdot \left(y.im \cdot x.im\right)}{y.re}\\ \mathbf{elif}\;y.im \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;x.re \cdot \left(\frac{y.re}{t\_0} + x.im \cdot \frac{y.im}{x.re \cdot t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (pow y.im 2.0) (pow y.re 2.0))))
   (if (<= y.im -4e-8)
     (/ (+ x.im (* (/ x.re y.im) y.re)) y.im)
     (if (<= y.im 6.2e-90)
       (/ (+ x.re (* (/ 1.0 y.re) (* y.im x.im))) y.re)
       (if (<= y.im 2.4e+39)
         (* x.re (+ (/ y.re t_0) (* x.im (/ y.im (* x.re t_0)))))
         (/ (+ x.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 t_0 = pow(y_46_im, 2.0) + pow(y_46_re, 2.0);
	double tmp;
	if (y_46_im <= -4e-8) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else if (y_46_im <= 6.2e-90) {
		tmp = (x_46_re + ((1.0 / y_46_re) * (y_46_im * x_46_im))) / y_46_re;
	} else if (y_46_im <= 2.4e+39) {
		tmp = x_46_re * ((y_46_re / t_0) + (x_46_im * (y_46_im / (x_46_re * t_0))));
	} else {
		tmp = (x_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) :: t_0
    real(8) :: tmp
    t_0 = (y_46im ** 2.0d0) + (y_46re ** 2.0d0)
    if (y_46im <= (-4d-8)) then
        tmp = (x_46im + ((x_46re / y_46im) * y_46re)) / y_46im
    else if (y_46im <= 6.2d-90) then
        tmp = (x_46re + ((1.0d0 / y_46re) * (y_46im * x_46im))) / y_46re
    else if (y_46im <= 2.4d+39) then
        tmp = x_46re * ((y_46re / t_0) + (x_46im * (y_46im / (x_46re * t_0))))
    else
        tmp = (x_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 t_0 = Math.pow(y_46_im, 2.0) + Math.pow(y_46_re, 2.0);
	double tmp;
	if (y_46_im <= -4e-8) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else if (y_46_im <= 6.2e-90) {
		tmp = (x_46_re + ((1.0 / y_46_re) * (y_46_im * x_46_im))) / y_46_re;
	} else if (y_46_im <= 2.4e+39) {
		tmp = x_46_re * ((y_46_re / t_0) + (x_46_im * (y_46_im / (x_46_re * t_0))));
	} else {
		tmp = (x_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):
	t_0 = math.pow(y_46_im, 2.0) + math.pow(y_46_re, 2.0)
	tmp = 0
	if y_46_im <= -4e-8:
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im
	elif y_46_im <= 6.2e-90:
		tmp = (x_46_re + ((1.0 / y_46_re) * (y_46_im * x_46_im))) / y_46_re
	elif y_46_im <= 2.4e+39:
		tmp = x_46_re * ((y_46_re / t_0) + (x_46_im * (y_46_im / (x_46_re * t_0))))
	else:
		tmp = (x_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)
	t_0 = Float64((y_46_im ^ 2.0) + (y_46_re ^ 2.0))
	tmp = 0.0
	if (y_46_im <= -4e-8)
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re / y_46_im) * y_46_re)) / y_46_im);
	elseif (y_46_im <= 6.2e-90)
		tmp = Float64(Float64(x_46_re + Float64(Float64(1.0 / y_46_re) * Float64(y_46_im * x_46_im))) / y_46_re);
	elseif (y_46_im <= 2.4e+39)
		tmp = Float64(x_46_re * Float64(Float64(y_46_re / t_0) + Float64(x_46_im * Float64(y_46_im / Float64(x_46_re * t_0)))));
	else
		tmp = Float64(Float64(x_46_im + 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)
	t_0 = (y_46_im ^ 2.0) + (y_46_re ^ 2.0);
	tmp = 0.0;
	if (y_46_im <= -4e-8)
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	elseif (y_46_im <= 6.2e-90)
		tmp = (x_46_re + ((1.0 / y_46_re) * (y_46_im * x_46_im))) / y_46_re;
	elseif (y_46_im <= 2.4e+39)
		tmp = x_46_re * ((y_46_re / t_0) + (x_46_im * (y_46_im / (x_46_re * t_0))));
	else
		tmp = (x_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_] := Block[{t$95$0 = N[(N[Power[y$46$im, 2.0], $MachinePrecision] + N[Power[y$46$re, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -4e-8], N[(N[(x$46$im + N[(N[(x$46$re / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, 6.2e-90], N[(N[(x$46$re + N[(N[(1.0 / y$46$re), $MachinePrecision] * N[(y$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 2.4e+39], N[(x$46$re * N[(N[(y$46$re / t$95$0), $MachinePrecision] + N[(x$46$im * N[(y$46$im / N[(x$46$re * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -4.0000000000000001e-8

   1. Initial program 61.8%

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

   3. Taylor expanded in y.im around inf 84.0%

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

      1. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 82.6%

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

      2. un-div-inv 82.6%

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

   7. Applied egg-rr 82.6%

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

      1. associate-/r/ 85.7%

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

   9. Simplified 85.7%

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

   if -4.0000000000000001e-8 < y.im < 6.2000000000000003e-90

   1. Initial program 72.7%

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

   3. Taylor expanded in y.re around inf 92.7%

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

      1. associate-/l* 91.8%

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

   5. Simplified 91.8%

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

      1. associate-*r/ 92.7%

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

      2. clear-num 92.7%

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

      3. *-commutative 92.7%

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

   7. Applied egg-rr 92.7%

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

      1. associate-/r/ 92.8%

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

   9. Simplified 92.8%

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

   if 6.2000000000000003e-90 < y.im < 2.4000000000000001e39

   1. Initial program 81.7%

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

   3. Taylor expanded in x.re around inf 87.1%

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

   5. Simplified 87.0%

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

   if 2.4000000000000001e39 < y.im

   1. Initial program 47.3%

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

   3. Taylor expanded in y.im around inf 83.9%

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

      1. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{elif}\;y.im \leq 6.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{x.re + \frac{1}{y.re} \cdot \left(y.im \cdot x.im\right)}{y.re}\\ \mathbf{elif}\;y.im \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;x.re \cdot \left(\frac{y.re}{{y.im}^{2} + {y.re}^{2}} + x.im \cdot \frac{y.im}{x.re \cdot \left({y.im}^{2} + {y.re}^{2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{elif}\;y.im \leq 5.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{y.im \cdot x.im + x.re \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.im -6e-8)
   (/ (+ x.im (* (/ x.re y.im) y.re)) y.im)
   (if (<= y.im 5.8e-37)
     (/ (+ x.re (/ (* y.im x.im) y.re)) y.re)
     (if (<= y.im 2.4e+39)
       (/ (+ (* y.im x.im) (* x.re y.re)) (+ (* y.re y.re) (* y.im y.im)))
       (/ (+ x.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_im <= -6e-8) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else if (y_46_im <= 5.8e-37) {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 2.4e+39) {
		tmp = ((y_46_im * x_46_im) + (x_46_re * y_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (x_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_46im <= (-6d-8)) then
        tmp = (x_46im + ((x_46re / y_46im) * y_46re)) / y_46im
    else if (y_46im <= 5.8d-37) then
        tmp = (x_46re + ((y_46im * x_46im) / y_46re)) / y_46re
    else if (y_46im <= 2.4d+39) then
        tmp = ((y_46im * x_46im) + (x_46re * y_46re)) / ((y_46re * y_46re) + (y_46im * y_46im))
    else
        tmp = (x_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_im <= -6e-8) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else if (y_46_im <= 5.8e-37) {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 2.4e+39) {
		tmp = ((y_46_im * x_46_im) + (x_46_re * y_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (x_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_im <= -6e-8:
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im
	elif y_46_im <= 5.8e-37:
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re
	elif y_46_im <= 2.4e+39:
		tmp = ((y_46_im * x_46_im) + (x_46_re * y_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	else:
		tmp = (x_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_im <= -6e-8)
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re / y_46_im) * y_46_re)) / y_46_im);
	elseif (y_46_im <= 5.8e-37)
		tmp = Float64(Float64(x_46_re + Float64(Float64(y_46_im * x_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_im <= 2.4e+39)
		tmp = Float64(Float64(Float64(y_46_im * x_46_im) + Float64(x_46_re * y_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	else
		tmp = Float64(Float64(x_46_im + 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_im <= -6e-8)
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	elseif (y_46_im <= 5.8e-37)
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_im <= 2.4e+39)
		tmp = ((y_46_im * x_46_im) + (x_46_re * y_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	else
		tmp = (x_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[LessEqual[y$46$im, -6e-8], N[(N[(x$46$im + N[(N[(x$46$re / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, 5.8e-37], N[(N[(x$46$re + N[(N[(y$46$im * x$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 2.4e+39], N[(N[(N[(y$46$im * x$46$im), $MachinePrecision] + N[(x$46$re * y$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -5.99999999999999946e-8

   1. Initial program 61.8%

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

   3. Taylor expanded in y.im around inf 84.0%

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

      1. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 82.6%

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

      2. un-div-inv 82.6%

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

   7. Applied egg-rr 82.6%

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

      1. associate-/r/ 85.7%

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

   9. Simplified 85.7%

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

   if -5.99999999999999946e-8 < y.im < 5.80000000000000009e-37

   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. Add Preprocessing

   3. Taylor expanded in y.re around inf 91.3%

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

   if 5.80000000000000009e-37 < y.im < 2.4000000000000001e39

   1. Initial program 90.0%

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

   if 2.4000000000000001e39 < y.im

   1. Initial program 47.3%

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

   3. Taylor expanded in y.im around inf 83.9%

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

      1. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{elif}\;y.im \leq 5.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{y.im \cdot x.im + x.re \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ t_1 := \frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{if}\;y.im \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y.im \leq 6.6 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.im \leq 1600:\\ \;\;\;\;\frac{y.im \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 6.8 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (+ x.re (/ (* y.im x.im) y.re)) y.re))
        (t_1 (/ (+ x.im (* (/ x.re y.im) y.re)) y.im)))
   (if (<= y.im -3.5e-9)
     t_1
     (if (<= y.im 6.6e-37)
       t_0
       (if (<= y.im 1600.0)
         (/ (* y.im x.im) (+ (* y.re y.re) (* y.im y.im)))
         (if (<= y.im 6.8e+25) t_0 t_1))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	double t_1 = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	double tmp;
	if (y_46_im <= -3.5e-9) {
		tmp = t_1;
	} else if (y_46_im <= 6.6e-37) {
		tmp = t_0;
	} else if (y_46_im <= 1600.0) {
		tmp = (y_46_im * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_im <= 6.8e+25) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x_46re + ((y_46im * x_46im) / y_46re)) / y_46re
    t_1 = (x_46im + ((x_46re / y_46im) * y_46re)) / y_46im
    if (y_46im <= (-3.5d-9)) then
        tmp = t_1
    else if (y_46im <= 6.6d-37) then
        tmp = t_0
    else if (y_46im <= 1600.0d0) then
        tmp = (y_46im * x_46im) / ((y_46re * y_46re) + (y_46im * y_46im))
    else if (y_46im <= 6.8d+25) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	double t_1 = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	double tmp;
	if (y_46_im <= -3.5e-9) {
		tmp = t_1;
	} else if (y_46_im <= 6.6e-37) {
		tmp = t_0;
	} else if (y_46_im <= 1600.0) {
		tmp = (y_46_im * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_im <= 6.8e+25) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re
	t_1 = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im
	tmp = 0
	if y_46_im <= -3.5e-9:
		tmp = t_1
	elif y_46_im <= 6.6e-37:
		tmp = t_0
	elif y_46_im <= 1600.0:
		tmp = (y_46_im * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	elif y_46_im <= 6.8e+25:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re + Float64(Float64(y_46_im * x_46_im) / y_46_re)) / y_46_re)
	t_1 = Float64(Float64(x_46_im + Float64(Float64(x_46_re / y_46_im) * y_46_re)) / y_46_im)
	tmp = 0.0
	if (y_46_im <= -3.5e-9)
		tmp = t_1;
	elseif (y_46_im <= 6.6e-37)
		tmp = t_0;
	elseif (y_46_im <= 1600.0)
		tmp = Float64(Float64(y_46_im * x_46_im) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_im <= 6.8e+25)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	t_1 = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	tmp = 0.0;
	if (y_46_im <= -3.5e-9)
		tmp = t_1;
	elseif (y_46_im <= 6.6e-37)
		tmp = t_0;
	elseif (y_46_im <= 1600.0)
		tmp = (y_46_im * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	elseif (y_46_im <= 6.8e+25)
		tmp = t_0;
	else
		tmp = t_1;
	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 + N[(N[(y$46$im * x$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$46$im + N[(N[(x$46$re / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]}, If[LessEqual[y$46$im, -3.5e-9], t$95$1, If[LessEqual[y$46$im, 6.6e-37], t$95$0, If[LessEqual[y$46$im, 1600.0], N[(N[(y$46$im * x$46$im), $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, 6.8e+25], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y.im < -3.4999999999999999e-9 or 6.79999999999999967e25 < y.im

   1. Initial program 57.1%

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

   3. Taylor expanded in y.im around inf 83.9%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

      1. clear-num 84.9%

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

      2. un-div-inv 84.9%

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

   7. Applied egg-rr 84.9%

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

      1. associate-/r/ 86.4%

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

   9. Simplified 86.4%

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

   if -3.4999999999999999e-9 < y.im < 6.59999999999999964e-37 or 1600 < y.im < 6.79999999999999967e25

   1. Initial program 72.8%

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

   3. Taylor expanded in y.re around inf 91.7%

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

   if 6.59999999999999964e-37 < y.im < 1600

   1. Initial program 88.3%

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

   3. Taylor expanded in x.re around 0 88.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{elif}\;y.im \leq 6.6 \cdot 10^{-37}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1600:\\ \;\;\;\;\frac{y.im \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 6.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.2 \cdot 10^{+18} \lor \neg \left(y.re \leq -9.6 \cdot 10^{-58} \lor \neg \left(y.re \leq -2 \cdot 10^{-85}\right) \land y.re \leq 3.8 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -3.2e+18)
         (not
          (or (<= y.re -9.6e-58)
              (and (not (<= y.re -2e-85)) (<= y.re 3.8e+23)))))
   (/ 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_re <= -3.2e+18) || !((y_46_re <= -9.6e-58) || (!(y_46_re <= -2e-85) && (y_46_re <= 3.8e+23)))) {
		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_46re <= (-3.2d+18)) .or. (.not. (y_46re <= (-9.6d-58)) .or. (.not. (y_46re <= (-2d-85))) .and. (y_46re <= 3.8d+23))) 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_re <= -3.2e+18) || !((y_46_re <= -9.6e-58) || (!(y_46_re <= -2e-85) && (y_46_re <= 3.8e+23)))) {
		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_re <= -3.2e+18) or not ((y_46_re <= -9.6e-58) or (not (y_46_re <= -2e-85) and (y_46_re <= 3.8e+23))):
		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_re <= -3.2e+18) || !((y_46_re <= -9.6e-58) || (!(y_46_re <= -2e-85) && (y_46_re <= 3.8e+23))))
		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_re <= -3.2e+18) || ~(((y_46_re <= -9.6e-58) || (~((y_46_re <= -2e-85)) && (y_46_re <= 3.8e+23)))))
		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[Or[LessEqual[y$46$re, -3.2e+18], N[Not[Or[LessEqual[y$46$re, -9.6e-58], And[N[Not[LessEqual[y$46$re, -2e-85]], $MachinePrecision], LessEqual[y$46$re, 3.8e+23]]]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -3.2e18 or -9.6000000000000002e-58 < y.re < -2e-85 or 3.79999999999999975e23 < y.re

   1. Initial program 57.2%

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

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

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

   if -3.2e18 < y.re < -9.6000000000000002e-58 or -2e-85 < y.re < 3.79999999999999975e23

   1. Initial program 74.6%

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

   3. Taylor expanded in y.re around 0 73.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.2 \cdot 10^{+18} \lor \neg \left(y.re \leq -9.6 \cdot 10^{-58} \lor \neg \left(y.re \leq -2 \cdot 10^{-85}\right) \land y.re \leq 3.8 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -2.8 \cdot 10^{+77} \lor \neg \left(y.re \leq 3.8 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -2.8e+77) (not (<= y.re 3.8e+27)))
   (/ x.re y.re)
   (/ (+ x.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 <= -2.8e+77) || !(y_46_re <= 3.8e+27)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_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 <= (-2.8d+77)) .or. (.not. (y_46re <= 3.8d+27))) then
        tmp = x_46re / y_46re
    else
        tmp = (x_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 <= -2.8e+77) || !(y_46_re <= 3.8e+27)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_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 <= -2.8e+77) or not (y_46_re <= 3.8e+27):
		tmp = x_46_re / y_46_re
	else:
		tmp = (x_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 <= -2.8e+77) || !(y_46_re <= 3.8e+27))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + 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 <= -2.8e+77) || ~((y_46_re <= 3.8e+27)))
		tmp = x_46_re / y_46_re;
	else
		tmp = (x_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, -2.8e+77], N[Not[LessEqual[y$46$re, 3.8e+27]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -2.8e77 or 3.80000000000000022e27 < y.re

   1. Initial program 51.9%

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

   3. Taylor expanded in y.re around inf 73.9%

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

   if -2.8e77 < y.re < 3.80000000000000022e27

   1. Initial program 76.0%

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

   3. Taylor expanded in y.im around inf 80.4%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -2.8 \cdot 10^{+77} \lor \neg \left(y.re \leq 3.8 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -2.6 \cdot 10^{+77} \lor \neg \left(y.re \leq 1.6 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -2.6e+77) (not (<= y.re 1.6e+25)))
   (/ x.re y.re)
   (/ (+ x.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 <= -2.6e+77) || !(y_46_re <= 1.6e+25)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_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 <= (-2.6d+77)) .or. (.not. (y_46re <= 1.6d+25))) then
        tmp = x_46re / y_46re
    else
        tmp = (x_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 <= -2.6e+77) || !(y_46_re <= 1.6e+25)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_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 <= -2.6e+77) or not (y_46_re <= 1.6e+25):
		tmp = x_46_re / y_46_re
	else:
		tmp = (x_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 <= -2.6e+77) || !(y_46_re <= 1.6e+25))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re * 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 <= -2.6e+77) || ~((y_46_re <= 1.6e+25)))
		tmp = x_46_re / y_46_re;
	else
		tmp = (x_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, -2.6e+77], N[Not[LessEqual[y$46$re, 1.6e+25]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -2.6000000000000002e77 or 1.6e25 < y.re

   1. Initial program 51.9%

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

   3. Taylor expanded in y.re around inf 73.9%

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

   if -2.6000000000000002e77 < y.re < 1.6e25

   1. Initial program 76.0%

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

   3. Taylor expanded in y.im around inf 80.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -2.6 \cdot 10^{+77} \lor \neg \left(y.re \leq 1.6 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -2.7 \cdot 10^{-9} \lor \neg \left(y.im \leq 3.8 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -2.7e-9) (not (<= y.im 3.8e+25)))
   (/ (+ x.im (* (/ x.re y.im) y.re)) y.im)
   (/ (+ x.re (* x.im (/ y.im y.re))) y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -2.7e-9) || !(y_46_im <= 3.8e+25)) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-2.7d-9)) .or. (.not. (y_46im <= 3.8d+25))) then
        tmp = (x_46im + ((x_46re / y_46im) * y_46re)) / y_46im
    else
        tmp = (x_46re + (x_46im * (y_46im / y_46re))) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -2.7e-9) || !(y_46_im <= 3.8e+25)) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -2.7e-9) or not (y_46_im <= 3.8e+25):
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im
	else:
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -2.7e-9) || !(y_46_im <= 3.8e+25))
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re / y_46_im) * y_46_re)) / y_46_im);
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im * Float64(y_46_im / y_46_re))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -2.7e-9) || ~((y_46_im <= 3.8e+25)))
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	else
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -2.7e-9], N[Not[LessEqual[y$46$im, 3.8e+25]], $MachinePrecision]], N[(N[(x$46$im + N[(N[(x$46$re / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$re + N[(x$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -2.7000000000000002e-9 or 3.8e25 < y.im

   1. Initial program 57.1%

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

   3. Taylor expanded in y.im around inf 83.9%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

      1. clear-num 84.9%

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

      2. un-div-inv 84.9%

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

   7. Applied egg-rr 84.9%

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

      1. associate-/r/ 86.4%

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

   9. Simplified 86.4%

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

   if -2.7000000000000002e-9 < y.im < 3.8e25

   1. Initial program 73.9%

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

   3. Taylor expanded in y.re around inf 88.0%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.7 \cdot 10^{-9} \lor \neg \left(y.im \leq 3.8 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -5 \cdot 10^{-8} \lor \neg \left(y.im \leq 1.36 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -5e-8) (not (<= y.im 1.36e+26)))
   (/ (+ x.im (* (/ x.re y.im) y.re)) y.im)
   (/ (+ x.re (/ x.im (/ y.re y.im))) y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -5e-8) || !(y_46_im <= 1.36e+26)) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-5d-8)) .or. (.not. (y_46im <= 1.36d+26))) then
        tmp = (x_46im + ((x_46re / y_46im) * y_46re)) / y_46im
    else
        tmp = (x_46re + (x_46im / (y_46re / y_46im))) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -5e-8) || !(y_46_im <= 1.36e+26)) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -5e-8) or not (y_46_im <= 1.36e+26):
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im
	else:
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -5e-8) || !(y_46_im <= 1.36e+26))
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re / y_46_im) * y_46_re)) / y_46_im);
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im / Float64(y_46_re / y_46_im))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -5e-8) || ~((y_46_im <= 1.36e+26)))
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	else
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -5e-8], N[Not[LessEqual[y$46$im, 1.36e+26]], $MachinePrecision]], N[(N[(x$46$im + N[(N[(x$46$re / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$re + N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -4.9999999999999998e-8 or 1.35999999999999993e26 < y.im

   1. Initial program 57.1%

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

   3. Taylor expanded in y.im around inf 83.9%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

      1. clear-num 84.9%

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

      2. un-div-inv 84.9%

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

   7. Applied egg-rr 84.9%

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

      1. associate-/r/ 86.4%

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

   9. Simplified 86.4%

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

   if -4.9999999999999998e-8 < y.im < 1.35999999999999993e26

   1. Initial program 73.9%

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

   3. Taylor expanded in y.re around inf 88.0%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

      1. clear-num 86.9%

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

      2. un-div-inv 86.9%

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

   7. Applied egg-rr 86.9%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -5 \cdot 10^{-8} \lor \neg \left(y.im \leq 1.36 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -2.8 \cdot 10^{-8} \lor \neg \left(y.im \leq 7.5 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -2.8e-8) (not (<= y.im 7.5e+25)))
   (/ (+ x.im (* (/ x.re y.im) y.re)) y.im)
   (/ (+ x.re (/ (* y.im x.im) y.re)) y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -2.8e-8) || !(y_46_im <= 7.5e+25)) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-2.8d-8)) .or. (.not. (y_46im <= 7.5d+25))) then
        tmp = (x_46im + ((x_46re / y_46im) * y_46re)) / y_46im
    else
        tmp = (x_46re + ((y_46im * x_46im) / y_46re)) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -2.8e-8) || !(y_46_im <= 7.5e+25)) {
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	} else {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -2.8e-8) or not (y_46_im <= 7.5e+25):
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im
	else:
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -2.8e-8) || !(y_46_im <= 7.5e+25))
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re / y_46_im) * y_46_re)) / y_46_im);
	else
		tmp = Float64(Float64(x_46_re + Float64(Float64(y_46_im * x_46_im) / y_46_re)) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -2.8e-8) || ~((y_46_im <= 7.5e+25)))
		tmp = (x_46_im + ((x_46_re / y_46_im) * y_46_re)) / y_46_im;
	else
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -2.8e-8], N[Not[LessEqual[y$46$im, 7.5e+25]], $MachinePrecision]], N[(N[(x$46$im + N[(N[(x$46$re / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$re + N[(N[(y$46$im * x$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -2.7999999999999999e-8 or 7.49999999999999993e25 < y.im

   1. Initial program 57.1%

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

   3. Taylor expanded in y.im around inf 83.9%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

      1. clear-num 84.9%

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

      2. un-div-inv 84.9%

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

   7. Applied egg-rr 84.9%

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

      1. associate-/r/ 86.4%

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

   9. Simplified 86.4%

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

   if -2.7999999999999999e-8 < y.im < 7.49999999999999993e25

   1. Initial program 73.9%

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

   3. Taylor expanded in y.re around inf 88.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.8 \cdot 10^{-8} \lor \neg \left(y.im \leq 7.5 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x.im + \frac{x.re}{y.im} \cdot y.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.9% 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 66.0%

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

3. Taylor expanded in y.re around 0 44.8%

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

4. Final simplification 44.8%

   \[\leadsto \frac{x.im}{y.im} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024112 
(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))))