_divideComplex, real part

Percentage Accurate: 62.0% → 85.9%

Time: 12.6s

Alternatives: 9

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.0% 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: 85.9% accurate, 0.0× speedup

Math

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

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)))
      INFINITY)
   (*
    (/ 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) (/ y.im x.re)))))

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))) <= ((double) INFINITY)) {
		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) / (y_46_im / x_46_re));
	}
	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))) <= Inf)
		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(y_46_im / x_46_re)));
	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], Infinity], 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[(y$46$im / x$46$re), $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))) < +inf.0

   1. Initial program 78.7%

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

      1. *-un-lft-identity 78.7%

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

      2. add-sqr-sqrt 78.7%

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

      3. times-frac 78.6%

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

      4. hypot-def 78.6%

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

      5. fma-def 78.6%

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

      6. hypot-def 95.8%

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

   3. Applied egg-rr 95.8%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in y.re around 0 49.7%

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

      1. +-commutative 49.7%

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

      2. unpow2 49.7%

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

      3. associate-/l* 50.2%

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

   4. Simplified 50.2%

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

      1. clear-num 50.2%

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

      2. inv-pow 50.2%

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

      3. associate-/l* 52.3%

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

   6. Applied egg-rr 52.3%

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

      1. unpow-1 52.3%

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

      2. associate-/l/ 57.8%

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

   8. Simplified 57.8%

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

      1. associate-/r/ 57.8%

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

      2. clear-num 57.8%

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

      3. un-div-inv 57.8%

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

      4. times-frac 52.3%

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

      5. *-un-lft-identity 52.3%

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

      6. associate-/r* 57.9%

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

      7. div-inv 57.8%

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

      8. clear-num 57.8%

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

   10. Applied egg-rr 57.8%

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

       1. *-commutative 57.8%

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

       2. clear-num 57.9%

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

       3. clear-num 57.9%

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

       4. frac-times 57.8%

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

       5. metadata-eval 57.8%

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

       6. associate-/r* 57.9%

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

       7. clear-num 57.9%

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

   12. Applied egg-rr 57.9%

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

4. Final simplification 89.0%

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

Alternative 2: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ t_1 := \frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{if}\;y.re \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.re \leq -3.25 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}\\ \mathbf{elif}\;y.re \leq 1.02 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
        (t_1 (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re)))))
   (if (<= y.re -5.5e+84)
     t_1
     (if (<= y.re -3.25e-201)
       t_0
       (if (<= y.re 2.3e-25)
         (+ (/ x.im y.im) (/ 1.0 (/ y.im (* x.re (/ y.re y.im)))))
         (if (<= y.re 1.02e+95) 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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double t_1 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -5.5e+84) {
		tmp = t_1;
	} else if (y_46_re <= -3.25e-201) {
		tmp = t_0;
	} else if (y_46_re <= 2.3e-25) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))));
	} else if (y_46_re <= 1.02e+95) {
		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_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    t_1 = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    if (y_46re <= (-5.5d+84)) then
        tmp = t_1
    else if (y_46re <= (-3.25d-201)) then
        tmp = t_0
    else if (y_46re <= 2.3d-25) then
        tmp = (x_46im / y_46im) + (1.0d0 / (y_46im / (x_46re * (y_46re / y_46im))))
    else if (y_46re <= 1.02d+95) 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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double t_1 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -5.5e+84) {
		tmp = t_1;
	} else if (y_46_re <= -3.25e-201) {
		tmp = t_0;
	} else if (y_46_re <= 2.3e-25) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))));
	} else if (y_46_re <= 1.02e+95) {
		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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	t_1 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	tmp = 0
	if y_46_re <= -5.5e+84:
		tmp = t_1
	elif y_46_re <= -3.25e-201:
		tmp = t_0
	elif y_46_re <= 2.3e-25:
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))))
	elif y_46_re <= 1.02e+95:
		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(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)))
	t_1 = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)))
	tmp = 0.0
	if (y_46_re <= -5.5e+84)
		tmp = t_1;
	elseif (y_46_re <= -3.25e-201)
		tmp = t_0;
	elseif (y_46_re <= 2.3e-25)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(1.0 / Float64(y_46_im / Float64(x_46_re * Float64(y_46_re / y_46_im)))));
	elseif (y_46_re <= 1.02e+95)
		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_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	t_1 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	tmp = 0.0;
	if (y_46_re <= -5.5e+84)
		tmp = t_1;
	elseif (y_46_re <= -3.25e-201)
		tmp = t_0;
	elseif (y_46_re <= 2.3e-25)
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))));
	elseif (y_46_re <= 1.02e+95)
		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[(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]}, Block[{t$95$1 = N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -5.5e+84], t$95$1, If[LessEqual[y$46$re, -3.25e-201], t$95$0, If[LessEqual[y$46$re, 2.3e-25], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(1.0 / N[(y$46$im / N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.02e+95], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -5.5000000000000004e84 or 1.0200000000000001e95 < y.re

   1. Initial program 41.7%

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

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

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

      1. unpow2 79.5%

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

      2. times-frac 89.6%

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

   4. Simplified 89.6%

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

   if -5.5000000000000004e84 < y.re < -3.24999999999999987e-201 or 2.2999999999999999e-25 < y.re < 1.0200000000000001e95

   1. Initial program 80.8%

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

   if -3.24999999999999987e-201 < y.re < 2.2999999999999999e-25

   1. Initial program 70.0%

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

   2. Taylor expanded in y.re around 0 85.5%

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

      1. +-commutative 85.5%

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

      2. unpow2 85.5%

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

      3. associate-/l* 87.0%

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

   4. Simplified 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

      3. associate-/l* 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

      2. associate-/l/ 93.1%

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

   8. Simplified 93.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.re \leq -3.25 \cdot 10^{-201}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}\\ \mathbf{elif}\;y.re \leq 1.02 \cdot 10^{+95}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \]

Alternative 3: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{if}\;y.re \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 1.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re}{y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 3 \cdot 10^{+24} \lor \neg \left(y.re \leq 2.6 \cdot 10^{+53}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re)))))
   (if (<= y.re -2.8e-5)
     t_0
     (if (<= y.re 1.8e-23)
       (+ (/ x.im y.im) (/ x.re (* y.im (/ y.im y.re))))
       (if (or (<= y.re 3e+24) (not (<= y.re 2.6e+53))) t_0 (/ x.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 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -2.8e-5) {
		tmp = t_0;
	} else if (y_46_re <= 1.8e-23) {
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	} else if ((y_46_re <= 3e+24) || !(y_46_re <= 2.6e+53)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    if (y_46re <= (-2.8d-5)) then
        tmp = t_0
    else if (y_46re <= 1.8d-23) then
        tmp = (x_46im / y_46im) + (x_46re / (y_46im * (y_46im / y_46re)))
    else if ((y_46re <= 3d+24) .or. (.not. (y_46re <= 2.6d+53))) then
        tmp = t_0
    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 t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -2.8e-5) {
		tmp = t_0;
	} else if (y_46_re <= 1.8e-23) {
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	} else if ((y_46_re <= 3e+24) || !(y_46_re <= 2.6e+53)) {
		tmp = t_0;
	} 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):
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	tmp = 0
	if y_46_re <= -2.8e-5:
		tmp = t_0
	elif y_46_re <= 1.8e-23:
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)))
	elif (y_46_re <= 3e+24) or not (y_46_re <= 2.6e+53):
		tmp = t_0
	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)
	t_0 = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)))
	tmp = 0.0
	if (y_46_re <= -2.8e-5)
		tmp = t_0;
	elseif (y_46_re <= 1.8e-23)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(x_46_re / Float64(y_46_im * Float64(y_46_im / y_46_re))));
	elseif ((y_46_re <= 3e+24) || !(y_46_re <= 2.6e+53))
		tmp = t_0;
	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)
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	tmp = 0.0;
	if (y_46_re <= -2.8e-5)
		tmp = t_0;
	elseif (y_46_re <= 1.8e-23)
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	elseif ((y_46_re <= 3e+24) || ~((y_46_re <= 2.6e+53)))
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -2.8e-5], t$95$0, If[LessEqual[y$46$re, 1.8e-23], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(x$46$re / N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y$46$re, 3e+24], N[Not[LessEqual[y$46$re, 2.6e+53]], $MachinePrecision]], t$95$0, N[(x$46$im / y$46$im), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -2.79999999999999996e-5 or 1.7999999999999999e-23 < y.re < 2.99999999999999995e24 or 2.59999999999999998e53 < y.re

   1. Initial program 55.1%

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

   2. Taylor expanded in y.re around inf 74.9%

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

      1. unpow2 74.9%

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

      2. times-frac 81.8%

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

   4. Simplified 81.8%

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

   if -2.79999999999999996e-5 < y.re < 1.7999999999999999e-23

   1. Initial program 73.4%

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

   2. Taylor expanded in y.re around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. unpow2 81.9%

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

      3. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in y.im around 0 82.1%

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

      1. unpow2 82.1%

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

      2. associate-*r/ 86.0%

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

   7. Simplified 86.0%

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

   if 2.99999999999999995e24 < y.re < 2.59999999999999998e53

   1. Initial program 77.6%

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

   2. Taylor expanded in y.re around 0 78.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.re \leq 1.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re}{y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 3 \cdot 10^{+24} \lor \neg \left(y.re \leq 2.6 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \]

Alternative 4: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{if}\;y.re \leq -0.35:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re}{y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{\frac{y.re \cdot y.re}{x.im}}\\ \mathbf{elif}\;y.re \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re)))))
   (if (<= y.re -0.35)
     t_0
     (if (<= y.re 1.2e-24)
       (+ (/ x.im y.im) (/ x.re (* y.im (/ y.im y.re))))
       (if (<= y.re 3.4e+24)
         (+ (/ x.re y.re) (/ y.im (/ (* y.re y.re) x.im)))
         (if (<= y.re 2.25e+52) (/ x.im y.im) t_0))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -0.35) {
		tmp = t_0;
	} else if (y_46_re <= 1.2e-24) {
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	} else if (y_46_re <= 3.4e+24) {
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im));
	} else if (y_46_re <= 2.25e+52) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = t_0;
	}
	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 = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    if (y_46re <= (-0.35d0)) then
        tmp = t_0
    else if (y_46re <= 1.2d-24) then
        tmp = (x_46im / y_46im) + (x_46re / (y_46im * (y_46im / y_46re)))
    else if (y_46re <= 3.4d+24) then
        tmp = (x_46re / y_46re) + (y_46im / ((y_46re * y_46re) / x_46im))
    else if (y_46re <= 2.25d+52) then
        tmp = x_46im / y_46im
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -0.35) {
		tmp = t_0;
	} else if (y_46_re <= 1.2e-24) {
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	} else if (y_46_re <= 3.4e+24) {
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im));
	} else if (y_46_re <= 2.25e+52) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	tmp = 0
	if y_46_re <= -0.35:
		tmp = t_0
	elif y_46_re <= 1.2e-24:
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)))
	elif y_46_re <= 3.4e+24:
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im))
	elif y_46_re <= 2.25e+52:
		tmp = x_46_im / y_46_im
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)))
	tmp = 0.0
	if (y_46_re <= -0.35)
		tmp = t_0;
	elseif (y_46_re <= 1.2e-24)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(x_46_re / Float64(y_46_im * Float64(y_46_im / y_46_re))));
	elseif (y_46_re <= 3.4e+24)
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im / Float64(Float64(y_46_re * y_46_re) / x_46_im)));
	elseif (y_46_re <= 2.25e+52)
		tmp = Float64(x_46_im / y_46_im);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	tmp = 0.0;
	if (y_46_re <= -0.35)
		tmp = t_0;
	elseif (y_46_re <= 1.2e-24)
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	elseif (y_46_re <= 3.4e+24)
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im));
	elseif (y_46_re <= 2.25e+52)
		tmp = x_46_im / y_46_im;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -0.35], t$95$0, If[LessEqual[y$46$re, 1.2e-24], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(x$46$re / N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 3.4e+24], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im / N[(N[(y$46$re * y$46$re), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.25e+52], N[(x$46$im / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -0.34999999999999998 or 2.25e52 < y.re

   1. Initial program 52.1%

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

   2. Taylor expanded in y.re around inf 74.0%

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

      1. unpow2 74.0%

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

      2. times-frac 81.4%

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

   4. Simplified 81.4%

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

   if -0.34999999999999998 < y.re < 1.1999999999999999e-24

   1. Initial program 73.4%

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

   2. Taylor expanded in y.re around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. unpow2 81.9%

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

      3. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in y.im around 0 82.1%

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

      1. unpow2 82.1%

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

      2. associate-*r/ 86.0%

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

   7. Simplified 86.0%

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

   if 1.1999999999999999e-24 < y.re < 3.4000000000000001e24

   1. Initial program 99.8%

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

   2. Taylor expanded in y.re around inf 80.8%

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

      1. unpow2 80.8%

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

      2. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

   if 3.4000000000000001e24 < y.re < 2.25e52

   1. Initial program 71.2%

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

   2. Taylor expanded in y.re around 0 86.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -0.35:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re}{y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{\frac{y.re \cdot y.re}{x.im}}\\ \mathbf{elif}\;y.re \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \]

Alternative 5: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{if}\;y.re \leq -6.6 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y.re \leq 1.9 \cdot 10^{-23}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}\\ \mathbf{elif}\;y.re \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{\frac{y.re \cdot y.re}{x.im}}\\ \mathbf{elif}\;y.re \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (/ x.re y.re) (* (/ y.im y.re) (/ x.im y.re)))))
   (if (<= y.re -6.6e-8)
     t_0
     (if (<= y.re 1.9e-23)
       (+ (/ x.im y.im) (/ 1.0 (/ y.im (* x.re (/ y.re y.im)))))
       (if (<= y.re 2.2e+24)
         (+ (/ x.re y.re) (/ y.im (/ (* y.re y.re) x.im)))
         (if (<= y.re 2.2e+52) (/ x.im y.im) t_0))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -6.6e-8) {
		tmp = t_0;
	} else if (y_46_re <= 1.9e-23) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))));
	} else if (y_46_re <= 2.2e+24) {
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im));
	} else if (y_46_re <= 2.2e+52) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = t_0;
	}
	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 = (x_46re / y_46re) + ((y_46im / y_46re) * (x_46im / y_46re))
    if (y_46re <= (-6.6d-8)) then
        tmp = t_0
    else if (y_46re <= 1.9d-23) then
        tmp = (x_46im / y_46im) + (1.0d0 / (y_46im / (x_46re * (y_46re / y_46im))))
    else if (y_46re <= 2.2d+24) then
        tmp = (x_46re / y_46re) + (y_46im / ((y_46re * y_46re) / x_46im))
    else if (y_46re <= 2.2d+52) then
        tmp = x_46im / y_46im
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	double tmp;
	if (y_46_re <= -6.6e-8) {
		tmp = t_0;
	} else if (y_46_re <= 1.9e-23) {
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))));
	} else if (y_46_re <= 2.2e+24) {
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im));
	} else if (y_46_re <= 2.2e+52) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re))
	tmp = 0
	if y_46_re <= -6.6e-8:
		tmp = t_0
	elif y_46_re <= 1.9e-23:
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))))
	elif y_46_re <= 2.2e+24:
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im))
	elif y_46_re <= 2.2e+52:
		tmp = x_46_im / y_46_im
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re / y_46_re) + Float64(Float64(y_46_im / y_46_re) * Float64(x_46_im / y_46_re)))
	tmp = 0.0
	if (y_46_re <= -6.6e-8)
		tmp = t_0;
	elseif (y_46_re <= 1.9e-23)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(1.0 / Float64(y_46_im / Float64(x_46_re * Float64(y_46_re / y_46_im)))));
	elseif (y_46_re <= 2.2e+24)
		tmp = Float64(Float64(x_46_re / y_46_re) + Float64(y_46_im / Float64(Float64(y_46_re * y_46_re) / x_46_im)));
	elseif (y_46_re <= 2.2e+52)
		tmp = Float64(x_46_im / y_46_im);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re / y_46_re) + ((y_46_im / y_46_re) * (x_46_im / y_46_re));
	tmp = 0.0;
	if (y_46_re <= -6.6e-8)
		tmp = t_0;
	elseif (y_46_re <= 1.9e-23)
		tmp = (x_46_im / y_46_im) + (1.0 / (y_46_im / (x_46_re * (y_46_re / y_46_im))));
	elseif (y_46_re <= 2.2e+24)
		tmp = (x_46_re / y_46_re) + (y_46_im / ((y_46_re * y_46_re) / x_46_im));
	elseif (y_46_re <= 2.2e+52)
		tmp = x_46_im / y_46_im;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(N[(y$46$im / y$46$re), $MachinePrecision] * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -6.6e-8], t$95$0, If[LessEqual[y$46$re, 1.9e-23], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(1.0 / N[(y$46$im / N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.2e+24], N[(N[(x$46$re / y$46$re), $MachinePrecision] + N[(y$46$im / N[(N[(y$46$re * y$46$re), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.2e+52], N[(x$46$im / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -6.59999999999999954e-8 or 2.2e52 < y.re

   1. Initial program 52.1%

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

   2. Taylor expanded in y.re around inf 74.0%

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

      1. unpow2 74.0%

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

      2. times-frac 81.4%

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

   4. Simplified 81.4%

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

   if -6.59999999999999954e-8 < y.re < 1.90000000000000006e-23

   1. Initial program 73.4%

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

   2. Taylor expanded in y.re around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. unpow2 81.9%

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

      3. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

      1. clear-num 82.1%

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

      2. inv-pow 82.1%

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

      3. associate-/l* 86.0%

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

   6. Applied egg-rr 86.0%

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

      1. unpow-1 86.0%

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

      2. associate-/l/ 86.6%

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

   8. Simplified 86.6%

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

   if 1.90000000000000006e-23 < y.re < 2.20000000000000002e24

   1. Initial program 99.8%

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

   2. Taylor expanded in y.re around inf 80.8%

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

      1. unpow2 80.8%

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

      2. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

   if 2.20000000000000002e24 < y.re < 2.2e52

   1. Initial program 71.2%

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

   2. Taylor expanded in y.re around 0 86.3%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -6.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \mathbf{elif}\;y.re \leq 1.9 \cdot 10^{-23}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{1}{\frac{y.im}{x.re \cdot \frac{y.re}{y.im}}}\\ \mathbf{elif}\;y.re \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{\frac{y.re \cdot y.re}{x.im}}\\ \mathbf{elif}\;y.re \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re} + \frac{y.im}{y.re} \cdot \frac{x.im}{y.re}\\ \end{array} \]

Alternative 6: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 6 \cdot 10^{+53}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -3.4e+80)
   (/ x.re y.re)
   (if (<= y.re 3.5e-24)
     (+ (/ x.im y.im) (* (/ y.re y.im) (/ x.re y.im)))
     (if (<= y.re 1.3e+24)
       (/ x.re y.re)
       (if (<= y.re 6e+53) (/ 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 <= -3.4e+80) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3.5e-24) {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	} else if (y_46_re <= 1.3e+24) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 6e+53) {
		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 <= (-3.4d+80)) then
        tmp = x_46re / y_46re
    else if (y_46re <= 3.5d-24) then
        tmp = (x_46im / y_46im) + ((y_46re / y_46im) * (x_46re / y_46im))
    else if (y_46re <= 1.3d+24) then
        tmp = x_46re / y_46re
    else if (y_46re <= 6d+53) 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 <= -3.4e+80) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3.5e-24) {
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	} else if (y_46_re <= 1.3e+24) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 6e+53) {
		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 <= -3.4e+80:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 3.5e-24:
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im))
	elif y_46_re <= 1.3e+24:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 6e+53:
		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 <= -3.4e+80)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 3.5e-24)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(Float64(y_46_re / y_46_im) * Float64(x_46_re / y_46_im)));
	elseif (y_46_re <= 1.3e+24)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 6e+53)
		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 <= -3.4e+80)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 3.5e-24)
		tmp = (x_46_im / y_46_im) + ((y_46_re / y_46_im) * (x_46_re / y_46_im));
	elseif (y_46_re <= 1.3e+24)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 6e+53)
		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, -3.4e+80], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 3.5e-24], 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], If[LessEqual[y$46$re, 1.3e+24], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 6e+53], N[(x$46$im / y$46$im), $MachinePrecision], N[(x$46$re / y$46$re), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -3.39999999999999992e80 or 3.4999999999999996e-24 < y.re < 1.2999999999999999e24 or 5.99999999999999996e53 < y.re

   1. Initial program 51.8%

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

   2. Taylor expanded in y.re around inf 72.6%

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

   if -3.39999999999999992e80 < y.re < 3.4999999999999996e-24

   1. Initial program 73.5%

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

   2. Taylor expanded in y.re around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. unpow2 76.8%

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

      3. associate-/l* 77.7%

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

   4. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

      3. associate-/l* 81.0%

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

   6. Applied egg-rr 81.0%

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

      1. unpow-1 81.0%

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

      2. associate-/l/ 81.6%

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

   8. Simplified 81.6%

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

      1. associate-/r/ 81.6%

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

      2. clear-num 81.1%

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

      3. un-div-inv 81.1%

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

      4. times-frac 81.1%

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

      5. *-un-lft-identity 81.1%

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

      6. associate-/r* 80.5%

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

      7. div-inv 80.5%

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

      8. clear-num 81.0%

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

   10. Applied egg-rr 81.0%

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

   if 1.2999999999999999e24 < y.re < 5.99999999999999996e53

   1. Initial program 77.6%

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

   2. Taylor expanded in y.re around 0 78.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{y.re}{y.im} \cdot \frac{x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 6 \cdot 10^{+53}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \]

Alternative 7: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -4.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re}{y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 1.25 \cdot 10^{+24} \lor \neg \left(y.re \leq 2.35 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -4.4e+80)
   (/ x.re y.re)
   (if (<= y.re 1.1e-23)
     (+ (/ x.im y.im) (/ x.re (* y.im (/ y.im y.re))))
     (if (or (<= y.re 1.25e+24) (not (<= y.re 2.35e+53)))
       (/ 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 <= -4.4e+80) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 1.1e-23) {
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	} else if ((y_46_re <= 1.25e+24) || !(y_46_re <= 2.35e+53)) {
		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 <= (-4.4d+80)) then
        tmp = x_46re / y_46re
    else if (y_46re <= 1.1d-23) then
        tmp = (x_46im / y_46im) + (x_46re / (y_46im * (y_46im / y_46re)))
    else if ((y_46re <= 1.25d+24) .or. (.not. (y_46re <= 2.35d+53))) 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 <= -4.4e+80) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 1.1e-23) {
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	} else if ((y_46_re <= 1.25e+24) || !(y_46_re <= 2.35e+53)) {
		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 <= -4.4e+80:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 1.1e-23:
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)))
	elif (y_46_re <= 1.25e+24) or not (y_46_re <= 2.35e+53):
		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 <= -4.4e+80)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 1.1e-23)
		tmp = Float64(Float64(x_46_im / y_46_im) + Float64(x_46_re / Float64(y_46_im * Float64(y_46_im / y_46_re))));
	elseif ((y_46_re <= 1.25e+24) || !(y_46_re <= 2.35e+53))
		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 <= -4.4e+80)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 1.1e-23)
		tmp = (x_46_im / y_46_im) + (x_46_re / (y_46_im * (y_46_im / y_46_re)));
	elseif ((y_46_re <= 1.25e+24) || ~((y_46_re <= 2.35e+53)))
		tmp = x_46_re / y_46_re;
	else
		tmp = x_46_im / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -4.4e+80], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 1.1e-23], N[(N[(x$46$im / y$46$im), $MachinePrecision] + N[(x$46$re / N[(y$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y$46$re, 1.25e+24], N[Not[LessEqual[y$46$re, 2.35e+53]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -4.40000000000000005e80 or 1.1e-23 < y.re < 1.25000000000000011e24 or 2.34999999999999988e53 < y.re

   1. Initial program 51.8%

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

   2. Taylor expanded in y.re around inf 72.6%

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

   if -4.40000000000000005e80 < y.re < 1.1e-23

   1. Initial program 73.5%

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

   2. Taylor expanded in y.re around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. unpow2 76.8%

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

      3. associate-/l* 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in y.im around 0 77.7%

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

      1. unpow2 77.7%

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

      2. associate-*r/ 81.1%

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

   7. Simplified 81.1%

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

   if 1.25000000000000011e24 < y.re < 2.34999999999999988e53

   1. Initial program 77.6%

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

   2. Taylor expanded in y.re around 0 78.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -4.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{x.im}{y.im} + \frac{x.re}{y.im \cdot \frac{y.im}{y.re}}\\ \mathbf{elif}\;y.re \leq 1.25 \cdot 10^{+24} \lor \neg \left(y.re \leq 2.35 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \]

Alternative 8: 63.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.3 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 2.6 \cdot 10^{-24} \lor \neg \left(y.re \leq 1.5 \cdot 10^{+24}\right) \land y.re \leq 3.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -3.3e+80)
   (/ x.re y.re)
   (if (or (<= y.re 2.6e-24) (and (not (<= y.re 1.5e+24)) (<= y.re 3.3e+53)))
     (/ 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 <= -3.3e+80) {
		tmp = x_46_re / y_46_re;
	} else if ((y_46_re <= 2.6e-24) || (!(y_46_re <= 1.5e+24) && (y_46_re <= 3.3e+53))) {
		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 <= (-3.3d+80)) then
        tmp = x_46re / y_46re
    else if ((y_46re <= 2.6d-24) .or. (.not. (y_46re <= 1.5d+24)) .and. (y_46re <= 3.3d+53)) 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 <= -3.3e+80) {
		tmp = x_46_re / y_46_re;
	} else if ((y_46_re <= 2.6e-24) || (!(y_46_re <= 1.5e+24) && (y_46_re <= 3.3e+53))) {
		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 <= -3.3e+80:
		tmp = x_46_re / y_46_re
	elif (y_46_re <= 2.6e-24) or (not (y_46_re <= 1.5e+24) and (y_46_re <= 3.3e+53)):
		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 <= -3.3e+80)
		tmp = Float64(x_46_re / y_46_re);
	elseif ((y_46_re <= 2.6e-24) || (!(y_46_re <= 1.5e+24) && (y_46_re <= 3.3e+53)))
		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 <= -3.3e+80)
		tmp = x_46_re / y_46_re;
	elseif ((y_46_re <= 2.6e-24) || (~((y_46_re <= 1.5e+24)) && (y_46_re <= 3.3e+53)))
		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, -3.3e+80], N[(x$46$re / y$46$re), $MachinePrecision], If[Or[LessEqual[y$46$re, 2.6e-24], And[N[Not[LessEqual[y$46$re, 1.5e+24]], $MachinePrecision], LessEqual[y$46$re, 3.3e+53]]], 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 < -3.29999999999999991e80 or 2.6e-24 < y.re < 1.49999999999999997e24 or 3.3000000000000002e53 < y.re

   1. Initial program 51.8%

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

   2. Taylor expanded in y.re around inf 72.6%

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

   if -3.29999999999999991e80 < y.re < 2.6e-24 or 1.49999999999999997e24 < y.re < 3.3000000000000002e53

   1. Initial program 73.7%

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

   2. Taylor expanded in y.re around 0 69.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.3 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 2.6 \cdot 10^{-24} \lor \neg \left(y.re \leq 1.5 \cdot 10^{+24}\right) \land y.re \leq 3.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \]

Alternative 9: 43.2% 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 64.5%

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

2. Taylor expanded in y.re around 0 47.2%

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

3. Final simplification 47.2%

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

Reproduce

herbie shell --seed 2023274 
(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))))