_divideComplex, imaginary part

Percentage Accurate: 61.3% → 91.1%

Time: 13.0s

Alternatives: 11

Speedup: 1.1×

Specification

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (- (* x.im y.re) (* x.re 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_im * y_46_re) - (x_46_re * 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_46im * y_46re) - (x_46re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - Float64(x_46_re * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_im * y_46_re) - (x_46_re * 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$46$im * y$46$re), $MachinePrecision] - N[(x$46$re * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (- (* x.im y.re) (* x.re 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_im * y_46_re) - (x_46_re * 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_46im * y_46re) - (x_46re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - Float64(x_46_re * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_im * y_46_re) - (x_46_re * 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$46$im * y$46$re), $MachinePrecision] - N[(x$46$re * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, x.re \cdot \frac{-y.im}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\right)\\ \mathbf{if}\;y.im \leq -2.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\frac{x.im}{y.im} \cdot y.re - x.re}{y.im}\\ \mathbf{elif}\;y.im \leq -4.2 \cdot 10^{-115}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.im \leq 2.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.75 \cdot 10^{+145}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y.re}{\frac{y.im}{x.im}} - x.re\right) \cdot \frac{1}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (fma
          (/ y.re (hypot y.re y.im))
          (/ x.im (hypot y.re y.im))
          (* x.re (/ (- y.im) (pow (hypot y.re y.im) 2.0))))))
   (if (<= y.im -2.2e+125)
     (/ (- (* (/ x.im y.im) y.re) x.re) y.im)
     (if (<= y.im -4.2e-115)
       t_0
       (if (<= y.im 2.7e-136)
         (/ (- x.im (* x.re (/ y.im y.re))) y.re)
         (if (<= y.im 1.75e+145)
           t_0
           (* (- (/ y.re (/ y.im x.im)) x.re) (/ 1.0 y.im))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = fma((y_46_re / hypot(y_46_re, y_46_im)), (x_46_im / hypot(y_46_re, y_46_im)), (x_46_re * (-y_46_im / pow(hypot(y_46_re, y_46_im), 2.0))));
	double tmp;
	if (y_46_im <= -2.2e+125) {
		tmp = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	} else if (y_46_im <= -4.2e-115) {
		tmp = t_0;
	} else if (y_46_im <= 2.7e-136) {
		tmp = (x_46_im - (x_46_re * (y_46_im / y_46_re))) / y_46_re;
	} else if (y_46_im <= 1.75e+145) {
		tmp = t_0;
	} else {
		tmp = ((y_46_re / (y_46_im / x_46_im)) - x_46_re) * (1.0 / y_46_im);
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = fma(Float64(y_46_re / hypot(y_46_re, y_46_im)), Float64(x_46_im / hypot(y_46_re, y_46_im)), Float64(x_46_re * Float64(Float64(-y_46_im) / (hypot(y_46_re, y_46_im) ^ 2.0))))
	tmp = 0.0
	if (y_46_im <= -2.2e+125)
		tmp = Float64(Float64(Float64(Float64(x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im);
	elseif (y_46_im <= -4.2e-115)
		tmp = t_0;
	elseif (y_46_im <= 2.7e-136)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re * Float64(y_46_im / y_46_re))) / y_46_re);
	elseif (y_46_im <= 1.75e+145)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(y_46_re / Float64(y_46_im / x_46_im)) - x_46_re) * Float64(1.0 / y_46_im));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(y$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(x$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] + N[(x$46$re * N[((-y$46$im) / N[Power[N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -2.2e+125], N[(N[(N[(N[(x$46$im / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, -4.2e-115], t$95$0, If[LessEqual[y$46$im, 2.7e-136], N[(N[(x$46$im - N[(x$46$re * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 1.75e+145], t$95$0, N[(N[(N[(y$46$re / N[(y$46$im / x$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -2.19999999999999991e125

   1. Initial program 39.2%

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

   3. Taylor expanded in y.re around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

      4. unpow2 75.9%

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

      5. associate-/r* 85.5%

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

      6. div-sub 85.5%

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

      7. associate-/l* 95.2%

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

   5. Simplified 95.2%

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

      1. clear-num 95.2%

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

      2. un-div-inv 95.2%

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

   7. Applied egg-rr 95.2%

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

      1. associate-/r/ 95.2%

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

   9. Simplified 95.2%

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

   if -2.19999999999999991e125 < y.im < -4.20000000000000003e-115 or 2.6999999999999998e-136 < y.im < 1.7500000000000001e145

   1. Initial program 70.2%

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

      1. div-sub 70.2%

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

      2. *-commutative 70.2%

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

      3. fma-define 70.2%

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

      4. add-sqr-sqrt 70.2%

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

      5. times-frac 72.2%

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

      6. fma-neg 72.2%

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

      7. fma-define 72.1%

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

      8. hypot-define 72.2%

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

      9. fma-define 72.2%

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

      10. hypot-define 90.8%

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

      11. associate-/l* 95.1%

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

      12. fma-define 95.1%

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

      13. add-sqr-sqrt 95.0%

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

      14. pow2 95.0%

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

   4. Applied egg-rr 95.0%

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

   if -4.20000000000000003e-115 < y.im < 2.6999999999999998e-136

   1. Initial program 75.1%

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

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

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

      1. remove-double-neg 92.7%

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

      2. mul-1-neg 92.7%

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

      3. neg-mul-1 92.7%

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

      4. distribute-lft-in 92.7%

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

      5. mul-1-neg 92.7%

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

      6. distribute-neg-in 92.7%

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

      7. mul-1-neg 92.7%

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

      8. remove-double-neg 92.7%

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

      9. unsub-neg 92.7%

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

      10. associate-/l* 93.2%

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

   5. Simplified 93.2%

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

   if 1.7500000000000001e145 < y.im

   1. Initial program 37.8%

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

   3. Taylor expanded in y.re around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. mul-1-neg 79.1%

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

      3. unsub-neg 79.1%

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

      4. unpow2 79.1%

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

      5. associate-/r* 81.7%

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

      6. div-sub 81.7%

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

      7. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

      1. div-inv 86.5%

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

      2. fma-neg 86.5%

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

   7. Applied egg-rr 86.5%

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

   8. Taylor expanded in x.im around 0 81.7%

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

      1. associate-*r/ 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-/r/ 88.7%

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

   10. Simplified 88.7%

       \[\leadsto \color{blue}{\left(\frac{y.re}{\frac{y.im}{x.im}} - x.re\right)} \cdot \frac{1}{y.im} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\frac{x.im}{y.im} \cdot y.re - x.re}{y.im}\\ \mathbf{elif}\;y.im \leq -4.2 \cdot 10^{-115}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, x.re \cdot \frac{-y.im}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\right)\\ \mathbf{elif}\;y.im \leq 2.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.75 \cdot 10^{+145}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y.re}{\mathsf{hypot}\left(y.re, y.im\right)}, \frac{x.im}{\mathsf{hypot}\left(y.re, y.im\right)}, x.re \cdot \frac{-y.im}{{\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y.re}{\frac{y.im}{x.im}} - x.re\right) \cdot \frac{1}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -7.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x.im, y.re, y.im \cdot \left(-x.re\right)\right)}{\mathsf{fma}\left(y.im, y.im, y.re \cdot y.re\right)}\\ \mathbf{elif}\;y.re \leq 8.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 5.5 \cdot 10^{+131}:\\ \;\;\;\;\frac{x.im \cdot y.re - y.im \cdot x.re}{\mathsf{fma}\left(y.re, y.re, y.im \cdot y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -1.1e+58)
   (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
   (if (<= y.re -7.2e-151)
     (/ (fma x.im y.re (* y.im (- x.re))) (fma y.im y.im (* y.re y.re)))
     (if (<= y.re 8.2e-55)
       (/ (- (/ (* x.im y.re) y.im) x.re) y.im)
       (if (<= y.re 5.5e+131)
         (/ (- (* x.im y.re) (* y.im x.re)) (fma y.re y.re (* y.im y.im)))
         (/ (- x.im (* y.im (/ x.re 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_re <= -1.1e+58) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -7.2e-151) {
		tmp = fma(x_46_im, y_46_re, (y_46_im * -x_46_re)) / fma(y_46_im, y_46_im, (y_46_re * y_46_re));
	} else if (y_46_re <= 8.2e-55) {
		tmp = (((x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 5.5e+131) {
		tmp = ((x_46_im * y_46_re) - (y_46_im * x_46_re)) / fma(y_46_re, y_46_re, (y_46_im * y_46_im));
	} else {
		tmp = (x_46_im - (y_46_im * (x_46_re / 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_re <= -1.1e+58)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= -7.2e-151)
		tmp = Float64(fma(x_46_im, y_46_re, Float64(y_46_im * Float64(-x_46_re))) / fma(y_46_im, y_46_im, Float64(y_46_re * y_46_re)));
	elseif (y_46_re <= 8.2e-55)
		tmp = Float64(Float64(Float64(Float64(x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im);
	elseif (y_46_re <= 5.5e+131)
		tmp = Float64(Float64(Float64(x_46_im * y_46_re) - Float64(y_46_im * x_46_re)) / fma(y_46_re, y_46_re, Float64(y_46_im * y_46_im)));
	else
		tmp = Float64(Float64(x_46_im - Float64(y_46_im * Float64(x_46_re / y_46_re))) / y_46_re);
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -1.1e+58], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -7.2e-151], N[(N[(x$46$im * y$46$re + N[(y$46$im * (-x$46$re)), $MachinePrecision]), $MachinePrecision] / N[(y$46$im * y$46$im + N[(y$46$re * y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 8.2e-55], N[(N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 5.5e+131], N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(y$46$re * y$46$re + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im - N[(y$46$im * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y.re < -1.1e58

   1. Initial program 34.4%

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

   3. Taylor expanded in y.re around inf 78.4%

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

      1. remove-double-neg 78.4%

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

      2. mul-1-neg 78.4%

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

      3. neg-mul-1 78.4%

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

      4. distribute-lft-in 78.4%

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

      5. mul-1-neg 78.4%

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

      6. distribute-neg-in 78.4%

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

      7. mul-1-neg 78.4%

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

      8. remove-double-neg 78.4%

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

      9. unsub-neg 78.4%

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

      10. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

   if -1.1e58 < y.re < -7.20000000000000064e-151

   1. Initial program 84.5%

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

      1. fma-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

      3. +-commutative 84.5%

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

      4. fma-define 84.5%

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

   3. Simplified 84.5%

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

   if -7.20000000000000064e-151 < y.re < 8.1999999999999996e-55

   1. Initial program 66.3%

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

      1. div-sub 62.2%

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

      2. *-commutative 62.2%

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

      3. fma-define 62.2%

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

      4. add-sqr-sqrt 62.2%

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

      5. times-frac 60.8%

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

      6. fma-neg 60.8%

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

      7. fma-define 60.8%

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

      8. hypot-define 60.8%

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

      9. fma-define 60.8%

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

      10. hypot-define 62.1%

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

      11. associate-/l* 68.6%

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

      12. fma-define 68.6%

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

      13. add-sqr-sqrt 68.6%

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

      14. pow2 68.6%

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

   4. Applied egg-rr 68.6%

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

   5. Taylor expanded in y.im around inf 96.0%

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

   if 8.1999999999999996e-55 < y.re < 5.49999999999999971e131

   1. Initial program 80.9%

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

      1. fma-define 80.9%

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

   3. Simplified 80.9%

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

   if 5.49999999999999971e131 < y.re

   1. Initial program 29.3%

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

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

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

      1. remove-double-neg 79.5%

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

      2. mul-1-neg 79.5%

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

      3. neg-mul-1 79.5%

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

      4. distribute-lft-in 79.5%

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

      5. mul-1-neg 79.5%

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

      6. distribute-neg-in 79.5%

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

      7. mul-1-neg 79.5%

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

      8. remove-double-neg 79.5%

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

      9. unsub-neg 79.5%

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

      10. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

      1. clear-num 82.6%

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

      2. un-div-inv 82.5%

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

   7. Applied egg-rr 82.5%

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

      1. associate-/r/ 85.5%

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

   9. Simplified 85.5%

      \[\leadsto \frac{x.im - \color{blue}{\frac{x.re}{y.re} \cdot y.im}}{y.re} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -7.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x.im, y.re, y.im \cdot \left(-x.re\right)\right)}{\mathsf{fma}\left(y.im, y.im, y.re \cdot y.re\right)}\\ \mathbf{elif}\;y.re \leq 8.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 5.5 \cdot 10^{+131}:\\ \;\;\;\;\frac{x.im \cdot y.re - y.im \cdot x.re}{\mathsf{fma}\left(y.re, y.re, y.im \cdot y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.im \cdot y.re - y.im \cdot x.re\\ \mathbf{if}\;y.re \leq -2.3 \cdot 10^{+58}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -8.8 \cdot 10^{-147}:\\ \;\;\;\;\frac{t\_0}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 3.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 2.3 \cdot 10^{+131}:\\ \;\;\;\;\frac{t\_0}{\mathsf{fma}\left(y.re, y.re, y.im \cdot y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (* x.im y.re) (* y.im x.re))))
   (if (<= y.re -2.3e+58)
     (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
     (if (<= y.re -8.8e-147)
       (/ t_0 (+ (* y.re y.re) (* y.im y.im)))
       (if (<= y.re 3.8e-55)
         (/ (- (/ (* x.im y.re) y.im) x.re) y.im)
         (if (<= y.re 2.3e+131)
           (/ t_0 (fma y.re y.re (* y.im y.im)))
           (/ (- x.im (* y.im (/ x.re y.re))) y.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_im * y_46_re) - (y_46_im * x_46_re);
	double tmp;
	if (y_46_re <= -2.3e+58) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -8.8e-147) {
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 3.8e-55) {
		tmp = (((x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 2.3e+131) {
		tmp = t_0 / fma(y_46_re, y_46_re, (y_46_im * y_46_im));
	} else {
		tmp = (x_46_im - (y_46_im * (x_46_re / y_46_re))) / y_46_re;
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_im * y_46_re) - Float64(y_46_im * x_46_re))
	tmp = 0.0
	if (y_46_re <= -2.3e+58)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= -8.8e-147)
		tmp = Float64(t_0 / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_re <= 3.8e-55)
		tmp = Float64(Float64(Float64(Float64(x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im);
	elseif (y_46_re <= 2.3e+131)
		tmp = Float64(t_0 / fma(y_46_re, y_46_re, Float64(y_46_im * y_46_im)));
	else
		tmp = Float64(Float64(x_46_im - Float64(y_46_im * Float64(x_46_re / y_46_re))) / y_46_re);
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$im * y$46$re), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -2.3e+58], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -8.8e-147], N[(t$95$0 / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 3.8e-55], N[(N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 2.3e+131], N[(t$95$0 / N[(y$46$re * y$46$re + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im - N[(y$46$im * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y.re < -2.30000000000000002e58

   1. Initial program 34.4%

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

   3. Taylor expanded in y.re around inf 78.4%

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

      1. remove-double-neg 78.4%

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

      2. mul-1-neg 78.4%

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

      3. neg-mul-1 78.4%

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

      4. distribute-lft-in 78.4%

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

      5. mul-1-neg 78.4%

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

      6. distribute-neg-in 78.4%

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

      7. mul-1-neg 78.4%

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

      8. remove-double-neg 78.4%

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

      9. unsub-neg 78.4%

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

      10. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

   if -2.30000000000000002e58 < y.re < -8.8000000000000004e-147

   1. Initial program 84.5%

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

   if -8.8000000000000004e-147 < y.re < 3.7999999999999997e-55

   1. Initial program 66.3%

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

      1. div-sub 62.2%

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

      2. *-commutative 62.2%

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

      3. fma-define 62.2%

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

      4. add-sqr-sqrt 62.2%

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

      5. times-frac 60.8%

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

      6. fma-neg 60.8%

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

      7. fma-define 60.8%

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

      8. hypot-define 60.8%

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

      9. fma-define 60.8%

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

      10. hypot-define 62.1%

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

      11. associate-/l* 68.6%

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

      12. fma-define 68.6%

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

      13. add-sqr-sqrt 68.6%

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

      14. pow2 68.6%

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

   4. Applied egg-rr 68.6%

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

   5. Taylor expanded in y.im around inf 96.0%

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

   if 3.7999999999999997e-55 < y.re < 2.29999999999999992e131

   1. Initial program 80.9%

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

      1. fma-define 80.9%

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

   3. Simplified 80.9%

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

   if 2.29999999999999992e131 < y.re

   1. Initial program 29.3%

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

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

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

      1. remove-double-neg 79.5%

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

      2. mul-1-neg 79.5%

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

      3. neg-mul-1 79.5%

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

      4. distribute-lft-in 79.5%

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

      5. mul-1-neg 79.5%

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

      6. distribute-neg-in 79.5%

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

      7. mul-1-neg 79.5%

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

      8. remove-double-neg 79.5%

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

      9. unsub-neg 79.5%

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

      10. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

      1. clear-num 82.6%

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

      2. un-div-inv 82.5%

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

   7. Applied egg-rr 82.5%

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

      1. associate-/r/ 85.5%

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

   9. Simplified 85.5%

      \[\leadsto \frac{x.im - \color{blue}{\frac{x.re}{y.re} \cdot y.im}}{y.re} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -2.3 \cdot 10^{+58}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -8.8 \cdot 10^{-147}:\\ \;\;\;\;\frac{x.im \cdot y.re - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 3.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 2.3 \cdot 10^{+131}:\\ \;\;\;\;\frac{x.im \cdot y.re - y.im \cdot x.re}{\mathsf{fma}\left(y.re, y.re, y.im \cdot y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im \cdot y.re - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.re \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq 2.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (- (* x.im y.re) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.re -4.2e+57)
     (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
     (if (<= y.re -3.1e-145)
       t_0
       (if (<= y.re 2.15e-55)
         (/ (- (/ (* x.im y.re) y.im) x.re) y.im)
         (if (<= y.re 9.2e+131)
           t_0
           (/ (- x.im (* y.im (/ x.re y.re))) y.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((x_46_im * y_46_re) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -4.2e+57) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -3.1e-145) {
		tmp = t_0;
	} else if (y_46_re <= 2.15e-55) {
		tmp = (((x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 9.2e+131) {
		tmp = t_0;
	} else {
		tmp = (x_46_im - (y_46_im * (x_46_re / 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) :: t_0
    real(8) :: tmp
    t_0 = ((x_46im * y_46re) - (y_46im * x_46re)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46re <= (-4.2d+57)) then
        tmp = (x_46im - (x_46re / (y_46re / y_46im))) / y_46re
    else if (y_46re <= (-3.1d-145)) then
        tmp = t_0
    else if (y_46re <= 2.15d-55) then
        tmp = (((x_46im * y_46re) / y_46im) - x_46re) / y_46im
    else if (y_46re <= 9.2d+131) then
        tmp = t_0
    else
        tmp = (x_46im - (y_46im * (x_46re / 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 t_0 = ((x_46_im * y_46_re) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -4.2e+57) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -3.1e-145) {
		tmp = t_0;
	} else if (y_46_re <= 2.15e-55) {
		tmp = (((x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 9.2e+131) {
		tmp = t_0;
	} else {
		tmp = (x_46_im - (y_46_im * (x_46_re / y_46_re))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((x_46_im * y_46_re) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_re <= -4.2e+57:
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	elif y_46_re <= -3.1e-145:
		tmp = t_0
	elif y_46_re <= 2.15e-55:
		tmp = (((x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im
	elif y_46_re <= 9.2e+131:
		tmp = t_0
	else:
		tmp = (x_46_im - (y_46_im * (x_46_re / y_46_re))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(x_46_im * y_46_re) - Float64(y_46_im * x_46_re)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_re <= -4.2e+57)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= -3.1e-145)
		tmp = t_0;
	elseif (y_46_re <= 2.15e-55)
		tmp = Float64(Float64(Float64(Float64(x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im);
	elseif (y_46_re <= 9.2e+131)
		tmp = t_0;
	else
		tmp = Float64(Float64(x_46_im - Float64(y_46_im * Float64(x_46_re / 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)
	t_0 = ((x_46_im * y_46_re) - (y_46_im * x_46_re)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_re <= -4.2e+57)
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	elseif (y_46_re <= -3.1e-145)
		tmp = t_0;
	elseif (y_46_re <= 2.15e-55)
		tmp = (((x_46_im * y_46_re) / y_46_im) - x_46_re) / y_46_im;
	elseif (y_46_re <= 9.2e+131)
		tmp = t_0;
	else
		tmp = (x_46_im - (y_46_im * (x_46_re / 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_] := Block[{t$95$0 = N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] - N[(y$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -4.2e+57], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -3.1e-145], t$95$0, If[LessEqual[y$46$re, 2.15e-55], N[(N[(N[(N[(x$46$im * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 9.2e+131], t$95$0, N[(N[(x$46$im - N[(y$46$im * N[(x$46$re / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -4.19999999999999982e57

   1. Initial program 34.4%

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

   3. Taylor expanded in y.re around inf 78.4%

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

      1. remove-double-neg 78.4%

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

      2. mul-1-neg 78.4%

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

      3. neg-mul-1 78.4%

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

      4. distribute-lft-in 78.4%

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

      5. mul-1-neg 78.4%

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

      6. distribute-neg-in 78.4%

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

      7. mul-1-neg 78.4%

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

      8. remove-double-neg 78.4%

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

      9. unsub-neg 78.4%

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

      10. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

   if -4.19999999999999982e57 < y.re < -3.1e-145 or 2.15000000000000005e-55 < y.re < 9.19999999999999966e131

   1. Initial program 82.9%

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

   if -3.1e-145 < y.re < 2.15000000000000005e-55

   1. Initial program 66.3%

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

      1. div-sub 62.2%

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

      2. *-commutative 62.2%

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

      3. fma-define 62.2%

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

      4. add-sqr-sqrt 62.2%

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

      5. times-frac 60.8%

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

      6. fma-neg 60.8%

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

      7. fma-define 60.8%

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

      8. hypot-define 60.8%

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

      9. fma-define 60.8%

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

      10. hypot-define 62.1%

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

      11. associate-/l* 68.6%

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

      12. fma-define 68.6%

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

      13. add-sqr-sqrt 68.6%

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

      14. pow2 68.6%

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

   4. Applied egg-rr 68.6%

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

   5. Taylor expanded in y.im around inf 96.0%

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

   if 9.19999999999999966e131 < y.re

   1. Initial program 29.3%

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

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

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

      1. remove-double-neg 79.5%

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

      2. mul-1-neg 79.5%

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

      3. neg-mul-1 79.5%

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

      4. distribute-lft-in 79.5%

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

      5. mul-1-neg 79.5%

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

      6. distribute-neg-in 79.5%

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

      7. mul-1-neg 79.5%

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

      8. remove-double-neg 79.5%

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

      9. unsub-neg 79.5%

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

      10. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

      1. clear-num 82.6%

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

      2. un-div-inv 82.5%

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

   7. Applied egg-rr 82.5%

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

      1. associate-/r/ 85.5%

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

   9. Simplified 85.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;\frac{x.im \cdot y.re - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 2.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x.im \cdot y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{x.im \cdot y.re - y.im \cdot x.re}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - y.im \cdot \frac{x.re}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ t_1 := \frac{\frac{x.im}{y.im} \cdot y.re - x.re}{y.im}\\ \mathbf{if}\;y.im \leq -7.8 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y.im \leq -1.36 \cdot 10^{+100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.im \leq -3 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y.im \leq 2.8 \cdot 10^{+55}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y.re}{\frac{y.im}{x.im}} - x.re\right) \cdot \frac{1}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (- x.im (* x.re (/ y.im y.re))) y.re))
        (t_1 (/ (- (* (/ x.im y.im) y.re) x.re) y.im)))
   (if (<= y.im -7.8e+121)
     t_1
     (if (<= y.im -1.36e+100)
       t_0
       (if (<= y.im -3e-55)
         t_1
         (if (<= y.im 2.8e+55)
           t_0
           (* (- (/ y.re (/ y.im x.im)) x.re) (/ 1.0 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_im - (x_46_re * (y_46_im / y_46_re))) / y_46_re;
	double t_1 = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	double tmp;
	if (y_46_im <= -7.8e+121) {
		tmp = t_1;
	} else if (y_46_im <= -1.36e+100) {
		tmp = t_0;
	} else if (y_46_im <= -3e-55) {
		tmp = t_1;
	} else if (y_46_im <= 2.8e+55) {
		tmp = t_0;
	} else {
		tmp = ((y_46_re / (y_46_im / x_46_im)) - x_46_re) * (1.0 / y_46_im);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x_46im - (x_46re * (y_46im / y_46re))) / y_46re
    t_1 = (((x_46im / y_46im) * y_46re) - x_46re) / y_46im
    if (y_46im <= (-7.8d+121)) then
        tmp = t_1
    else if (y_46im <= (-1.36d+100)) then
        tmp = t_0
    else if (y_46im <= (-3d-55)) then
        tmp = t_1
    else if (y_46im <= 2.8d+55) then
        tmp = t_0
    else
        tmp = ((y_46re / (y_46im / x_46im)) - x_46re) * (1.0d0 / 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_im - (x_46_re * (y_46_im / y_46_re))) / y_46_re;
	double t_1 = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	double tmp;
	if (y_46_im <= -7.8e+121) {
		tmp = t_1;
	} else if (y_46_im <= -1.36e+100) {
		tmp = t_0;
	} else if (y_46_im <= -3e-55) {
		tmp = t_1;
	} else if (y_46_im <= 2.8e+55) {
		tmp = t_0;
	} else {
		tmp = ((y_46_re / (y_46_im / x_46_im)) - x_46_re) * (1.0 / y_46_im);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_im - (x_46_re * (y_46_im / y_46_re))) / y_46_re
	t_1 = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im
	tmp = 0
	if y_46_im <= -7.8e+121:
		tmp = t_1
	elif y_46_im <= -1.36e+100:
		tmp = t_0
	elif y_46_im <= -3e-55:
		tmp = t_1
	elif y_46_im <= 2.8e+55:
		tmp = t_0
	else:
		tmp = ((y_46_re / (y_46_im / x_46_im)) - x_46_re) * (1.0 / 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_im - Float64(x_46_re * Float64(y_46_im / y_46_re))) / y_46_re)
	t_1 = Float64(Float64(Float64(Float64(x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im)
	tmp = 0.0
	if (y_46_im <= -7.8e+121)
		tmp = t_1;
	elseif (y_46_im <= -1.36e+100)
		tmp = t_0;
	elseif (y_46_im <= -3e-55)
		tmp = t_1;
	elseif (y_46_im <= 2.8e+55)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(y_46_re / Float64(y_46_im / x_46_im)) - x_46_re) * Float64(1.0 / 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_im - (x_46_re * (y_46_im / y_46_re))) / y_46_re;
	t_1 = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	tmp = 0.0;
	if (y_46_im <= -7.8e+121)
		tmp = t_1;
	elseif (y_46_im <= -1.36e+100)
		tmp = t_0;
	elseif (y_46_im <= -3e-55)
		tmp = t_1;
	elseif (y_46_im <= 2.8e+55)
		tmp = t_0;
	else
		tmp = ((y_46_re / (y_46_im / x_46_im)) - x_46_re) * (1.0 / 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$46$im - N[(x$46$re * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(x$46$im / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]}, If[LessEqual[y$46$im, -7.8e+121], t$95$1, If[LessEqual[y$46$im, -1.36e+100], t$95$0, If[LessEqual[y$46$im, -3e-55], t$95$1, If[LessEqual[y$46$im, 2.8e+55], t$95$0, N[(N[(N[(y$46$re / N[(y$46$im / x$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y.im < -7.79999999999999967e121 or -1.35999999999999994e100 < y.im < -3.00000000000000016e-55

   1. Initial program 57.3%

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

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

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. unsub-neg 69.7%

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

      4. unpow2 69.7%

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

      5. associate-/r* 74.8%

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

      6. div-sub 74.9%

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

      7. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

      1. clear-num 79.9%

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

      2. un-div-inv 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. associate-/r/ 80.0%

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

   9. Simplified 80.0%

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

   if -7.79999999999999967e121 < y.im < -1.35999999999999994e100 or -3.00000000000000016e-55 < y.im < 2.8000000000000001e55

   1. Initial program 73.2%

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

   3. Taylor expanded in y.re around inf 86.4%

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

      1. remove-double-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. neg-mul-1 86.4%

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

      4. distribute-lft-in 86.4%

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

      5. mul-1-neg 86.4%

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

      6. distribute-neg-in 86.4%

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

      7. mul-1-neg 86.4%

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

      8. remove-double-neg 86.4%

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

      9. unsub-neg 86.4%

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

      10. associate-/l* 86.7%

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

   5. Simplified 86.7%

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

   if 2.8000000000000001e55 < y.im

   1. Initial program 44.4%

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

   3. Taylor expanded in y.re around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. unpow2 73.1%

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

      5. associate-/r* 74.7%

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

      6. div-sub 74.7%

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

      7. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

      1. div-inv 76.4%

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

      2. fma-neg 76.4%

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

   7. Applied egg-rr 76.4%

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

   8. Taylor expanded in x.im around 0 74.7%

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

      1. associate-*r/ 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-/r/ 79.4%

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

   10. Simplified 79.4%

       \[\leadsto \color{blue}{\left(\frac{y.re}{\frac{y.im}{x.im}} - x.re\right)} \cdot \frac{1}{y.im} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -2.15 \cdot 10^{+122} \lor \neg \left(y.im \leq -1.4 \cdot 10^{+100}\right) \land \left(y.im \leq -4 \cdot 10^{-55} \lor \neg \left(y.im \leq 3 \cdot 10^{+55}\right)\right):\\ \;\;\;\;\frac{\frac{x.im}{y.im} \cdot y.re - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -2.15e+122)
         (and (not (<= y.im -1.4e+100))
              (or (<= y.im -4e-55) (not (<= y.im 3e+55)))))
   (/ (- (* (/ x.im y.im) y.re) x.re) y.im)
   (/ (- x.im (* x.re (/ 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 <= -2.15e+122) || (!(y_46_im <= -1.4e+100) && ((y_46_im <= -4e-55) || !(y_46_im <= 3e+55)))) {
		tmp = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (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 <= (-2.15d+122)) .or. (.not. (y_46im <= (-1.4d+100))) .and. (y_46im <= (-4d-55)) .or. (.not. (y_46im <= 3d+55))) then
        tmp = (((x_46im / y_46im) * y_46re) - x_46re) / y_46im
    else
        tmp = (x_46im - (x_46re * (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 <= -2.15e+122) || (!(y_46_im <= -1.4e+100) && ((y_46_im <= -4e-55) || !(y_46_im <= 3e+55)))) {
		tmp = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (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 <= -2.15e+122) or (not (y_46_im <= -1.4e+100) and ((y_46_im <= -4e-55) or not (y_46_im <= 3e+55))):
		tmp = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im
	else:
		tmp = (x_46_im - (x_46_re * (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 <= -2.15e+122) || (!(y_46_im <= -1.4e+100) && ((y_46_im <= -4e-55) || !(y_46_im <= 3e+55))))
		tmp = Float64(Float64(Float64(Float64(x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re * 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 <= -2.15e+122) || (~((y_46_im <= -1.4e+100)) && ((y_46_im <= -4e-55) || ~((y_46_im <= 3e+55)))))
		tmp = (((x_46_im / y_46_im) * y_46_re) - x_46_re) / y_46_im;
	else
		tmp = (x_46_im - (x_46_re * (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, -2.15e+122], And[N[Not[LessEqual[y$46$im, -1.4e+100]], $MachinePrecision], Or[LessEqual[y$46$im, -4e-55], N[Not[LessEqual[y$46$im, 3e+55]], $MachinePrecision]]]], N[(N[(N[(N[(x$46$im / y$46$im), $MachinePrecision] * y$46$re), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re * 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 < -2.14999999999999986e122 or -1.3999999999999999e100 < y.im < -3.99999999999999998e-55 or 3.00000000000000017e55 < y.im

   1. Initial program 51.5%

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

   3. Taylor expanded in y.re around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. unpow2 71.3%

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

      5. associate-/r* 74.8%

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

      6. div-sub 74.8%

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

      7. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

      1. clear-num 78.3%

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

      2. un-div-inv 78.3%

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

   7. Applied egg-rr 78.3%

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

      1. associate-/r/ 79.7%

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

   9. Simplified 79.7%

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

   if -2.14999999999999986e122 < y.im < -1.3999999999999999e100 or -3.99999999999999998e-55 < y.im < 3.00000000000000017e55

   1. Initial program 73.2%

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

   3. Taylor expanded in y.re around inf 86.4%

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

      1. remove-double-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. neg-mul-1 86.4%

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

      4. distribute-lft-in 86.4%

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

      5. mul-1-neg 86.4%

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

      6. distribute-neg-in 86.4%

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

      7. mul-1-neg 86.4%

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

      8. remove-double-neg 86.4%

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

      9. unsub-neg 86.4%

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

      10. associate-/l* 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.15 \cdot 10^{+122} \lor \neg \left(y.im \leq -1.4 \cdot 10^{+100}\right) \land \left(y.im \leq -4 \cdot 10^{-55} \lor \neg \left(y.im \leq 3 \cdot 10^{+55}\right)\right):\\ \;\;\;\;\frac{\frac{x.im}{y.im} \cdot y.re - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -7.8 \cdot 10^{+121} \lor \neg \left(y.im \leq -1.32 \cdot 10^{+100}\right) \land \left(y.im \leq -4.5 \cdot 10^{-55} \lor \neg \left(y.im \leq 4.6 \cdot 10^{+55}\right)\right):\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -7.8e+121)
         (and (not (<= y.im -1.32e+100))
              (or (<= y.im -4.5e-55) (not (<= y.im 4.6e+55)))))
   (/ (- (* x.im (/ y.re y.im)) x.re) y.im)
   (/ (- x.im (* x.re (/ 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 <= -7.8e+121) || (!(y_46_im <= -1.32e+100) && ((y_46_im <= -4.5e-55) || !(y_46_im <= 4.6e+55)))) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (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 <= (-7.8d+121)) .or. (.not. (y_46im <= (-1.32d+100))) .and. (y_46im <= (-4.5d-55)) .or. (.not. (y_46im <= 4.6d+55))) then
        tmp = ((x_46im * (y_46re / y_46im)) - x_46re) / y_46im
    else
        tmp = (x_46im - (x_46re * (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 <= -7.8e+121) || (!(y_46_im <= -1.32e+100) && ((y_46_im <= -4.5e-55) || !(y_46_im <= 4.6e+55)))) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (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 <= -7.8e+121) or (not (y_46_im <= -1.32e+100) and ((y_46_im <= -4.5e-55) or not (y_46_im <= 4.6e+55))):
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im
	else:
		tmp = (x_46_im - (x_46_re * (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 <= -7.8e+121) || (!(y_46_im <= -1.32e+100) && ((y_46_im <= -4.5e-55) || !(y_46_im <= 4.6e+55))))
		tmp = Float64(Float64(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re * 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 <= -7.8e+121) || (~((y_46_im <= -1.32e+100)) && ((y_46_im <= -4.5e-55) || ~((y_46_im <= 4.6e+55)))))
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	else
		tmp = (x_46_im - (x_46_re * (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, -7.8e+121], And[N[Not[LessEqual[y$46$im, -1.32e+100]], $MachinePrecision], Or[LessEqual[y$46$im, -4.5e-55], N[Not[LessEqual[y$46$im, 4.6e+55]], $MachinePrecision]]]], N[(N[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re * 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 < -7.79999999999999967e121 or -1.32e100 < y.im < -4.4999999999999997e-55 or 4.59999999999999975e55 < y.im

   1. Initial program 51.5%

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

   3. Taylor expanded in y.re around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. unpow2 71.3%

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

      5. associate-/r* 74.8%

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

      6. div-sub 74.8%

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

      7. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

   if -7.79999999999999967e121 < y.im < -1.32e100 or -4.4999999999999997e-55 < y.im < 4.59999999999999975e55

   1. Initial program 73.2%

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

   3. Taylor expanded in y.re around inf 86.4%

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

      1. remove-double-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. neg-mul-1 86.4%

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

      4. distribute-lft-in 86.4%

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

      5. mul-1-neg 86.4%

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

      6. distribute-neg-in 86.4%

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

      7. mul-1-neg 86.4%

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

      8. remove-double-neg 86.4%

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

      9. unsub-neg 86.4%

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

      10. associate-/l* 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -7.8 \cdot 10^{+121} \lor \neg \left(y.im \leq -1.32 \cdot 10^{+100}\right) \land \left(y.im \leq -4.5 \cdot 10^{-55} \lor \neg \left(y.im \leq 4.6 \cdot 10^{+55}\right)\right):\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -8.1 \cdot 10^{+121} \lor \neg \left(y.im \leq -1.42 \cdot 10^{+100} \lor \neg \left(y.im \leq -1.2 \cdot 10^{+45}\right) \land y.im \leq 6.2 \cdot 10^{+118}\right):\\ \;\;\;\;\frac{x.re}{-y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -8.1e+121)
         (not
          (or (<= y.im -1.42e+100)
              (and (not (<= y.im -1.2e+45)) (<= y.im 6.2e+118)))))
   (/ x.re (- y.im))
   (/ (- x.im (* x.re (/ 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 <= -8.1e+121) || !((y_46_im <= -1.42e+100) || (!(y_46_im <= -1.2e+45) && (y_46_im <= 6.2e+118)))) {
		tmp = x_46_re / -y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (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 <= (-8.1d+121)) .or. (.not. (y_46im <= (-1.42d+100)) .or. (.not. (y_46im <= (-1.2d+45))) .and. (y_46im <= 6.2d+118))) then
        tmp = x_46re / -y_46im
    else
        tmp = (x_46im - (x_46re * (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 <= -8.1e+121) || !((y_46_im <= -1.42e+100) || (!(y_46_im <= -1.2e+45) && (y_46_im <= 6.2e+118)))) {
		tmp = x_46_re / -y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (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 <= -8.1e+121) or not ((y_46_im <= -1.42e+100) or (not (y_46_im <= -1.2e+45) and (y_46_im <= 6.2e+118))):
		tmp = x_46_re / -y_46_im
	else:
		tmp = (x_46_im - (x_46_re * (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 <= -8.1e+121) || !((y_46_im <= -1.42e+100) || (!(y_46_im <= -1.2e+45) && (y_46_im <= 6.2e+118))))
		tmp = Float64(x_46_re / Float64(-y_46_im));
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re * 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 <= -8.1e+121) || ~(((y_46_im <= -1.42e+100) || (~((y_46_im <= -1.2e+45)) && (y_46_im <= 6.2e+118)))))
		tmp = x_46_re / -y_46_im;
	else
		tmp = (x_46_im - (x_46_re * (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, -8.1e+121], N[Not[Or[LessEqual[y$46$im, -1.42e+100], And[N[Not[LessEqual[y$46$im, -1.2e+45]], $MachinePrecision], LessEqual[y$46$im, 6.2e+118]]]], $MachinePrecision]], N[(x$46$re / (-y$46$im)), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re * 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 < -8.09999999999999969e121 or -1.41999999999999999e100 < y.im < -1.19999999999999995e45 or 6.19999999999999973e118 < y.im

   1. Initial program 45.9%

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

   3. Taylor expanded in y.re around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

   5. Simplified 77.9%

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

   if -8.09999999999999969e121 < y.im < -1.41999999999999999e100 or -1.19999999999999995e45 < y.im < 6.19999999999999973e118

   1. Initial program 70.8%

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

   3. Taylor expanded in y.re around inf 75.0%

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

      1. remove-double-neg 75.0%

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

      2. mul-1-neg 75.0%

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

      3. neg-mul-1 75.0%

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

      4. distribute-lft-in 75.0%

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

      5. mul-1-neg 75.0%

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

      6. distribute-neg-in 75.0%

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

      7. mul-1-neg 75.0%

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

      8. remove-double-neg 75.0%

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

      9. unsub-neg 75.0%

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

      10. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -8.1 \cdot 10^{+121} \lor \neg \left(y.im \leq -1.42 \cdot 10^{+100} \lor \neg \left(y.im \leq -1.2 \cdot 10^{+45}\right) \land y.im \leq 6.2 \cdot 10^{+118}\right):\\ \;\;\;\;\frac{x.re}{-y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.2 \cdot 10^{+46} \lor \neg \left(y.re \leq 3.9 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{-y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -1.2e+46) (not (<= y.re 3.9e-54)))
   (/ x.im y.re)
   (/ x.re (- y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -1.2e+46) || !(y_46_re <= 3.9e-54)) {
		tmp = x_46_im / y_46_re;
	} else {
		tmp = x_46_re / -y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-1.2d+46)) .or. (.not. (y_46re <= 3.9d-54))) then
        tmp = x_46im / y_46re
    else
        tmp = x_46re / -y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -1.2e+46) || !(y_46_re <= 3.9e-54)) {
		tmp = x_46_im / y_46_re;
	} else {
		tmp = x_46_re / -y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -1.2e+46) or not (y_46_re <= 3.9e-54):
		tmp = x_46_im / y_46_re
	else:
		tmp = x_46_re / -y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -1.2e+46) || !(y_46_re <= 3.9e-54))
		tmp = Float64(x_46_im / y_46_re);
	else
		tmp = Float64(x_46_re / Float64(-y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -1.2e+46) || ~((y_46_re <= 3.9e-54)))
		tmp = x_46_im / y_46_re;
	else
		tmp = x_46_re / -y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -1.2e+46], N[Not[LessEqual[y$46$re, 3.9e-54]], $MachinePrecision]], N[(x$46$im / y$46$re), $MachinePrecision], N[(x$46$re / (-y$46$im)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -1.20000000000000004e46 or 3.9e-54 < y.re

   1. Initial program 48.9%

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

   3. Taylor expanded in y.re around inf 63.9%

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

   if -1.20000000000000004e46 < y.re < 3.9e-54

   1. Initial program 73.1%

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

   3. Taylor expanded in y.re around 0 67.0%

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

      1. associate-*r/ 67.0%

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

      2. neg-mul-1 67.0%

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

   5. Simplified 67.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.2 \cdot 10^{+46} \lor \neg \left(y.re \leq 3.9 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x.im}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{-y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.05 \cdot 10^{+124} \lor \neg \left(y.im \leq 6.4 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1.05e+124) (not (<= y.im 6.4e+121)))
   (/ x.re y.im)
   (/ x.im y.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.05e+124) || !(y_46_im <= 6.4e+121)) {
		tmp = x_46_re / y_46_im;
	} else {
		tmp = x_46_im / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46im <= (-1.05d+124)) .or. (.not. (y_46im <= 6.4d+121))) then
        tmp = x_46re / y_46im
    else
        tmp = x_46im / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_im <= -1.05e+124) || !(y_46_im <= 6.4e+121)) {
		tmp = x_46_re / y_46_im;
	} else {
		tmp = x_46_im / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_im <= -1.05e+124) or not (y_46_im <= 6.4e+121):
		tmp = x_46_re / y_46_im
	else:
		tmp = x_46_im / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_im <= -1.05e+124) || !(y_46_im <= 6.4e+121))
		tmp = Float64(x_46_re / y_46_im);
	else
		tmp = Float64(x_46_im / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_im <= -1.05e+124) || ~((y_46_im <= 6.4e+121)))
		tmp = x_46_re / y_46_im;
	else
		tmp = x_46_im / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$im, -1.05e+124], N[Not[LessEqual[y$46$im, 6.4e+121]], $MachinePrecision]], N[(x$46$re / y$46$im), $MachinePrecision], N[(x$46$im / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -1.05000000000000006e124 or 6.3999999999999999e121 < y.im

   1. Initial program 41.3%

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

   3. Taylor expanded in x.im around inf 35.0%

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

      1. mul-1-neg 35.0%

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

      2. unsub-neg 35.0%

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

      3. associate-/l* 25.6%

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

   5. Simplified 25.6%

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

      1. *-commutative 25.6%

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

      2. add-sqr-sqrt 25.6%

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

      3. hypot-undefine 25.6%

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

      4. hypot-undefine 25.6%

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

      5. times-frac 58.2%

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

      6. cancel-sign-sub-inv 58.2%

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

      7. clear-num 58.3%

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

      8. un-div-inv 58.2%

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

      9. add-sqr-sqrt 37.1%

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

      10. sqrt-unprod 44.8%

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

      11. sqr-neg 44.8%

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

      12. sqrt-unprod 13.2%

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

      13. add-sqr-sqrt 35.8%

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

   7. Applied egg-rr 35.8%

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

   8. Taylor expanded in y.re around 0 34.1%

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

   if -1.05000000000000006e124 < y.im < 6.3999999999999999e121

   1. Initial program 71.5%

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

   3. Taylor expanded in y.re around inf 51.5%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -1.05 \cdot 10^{+124} \lor \neg \left(y.im \leq 6.4 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.2% accurate, 5.0× speedup

Math

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

FPCore

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

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_re;
}

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_46re
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_re;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.4%

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

3. Taylor expanded in y.re around inf 38.0%

   \[\leadsto \color{blue}{\frac{x.im}{y.re}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  :precision binary64
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))