_divideComplex, real part

Percentage Accurate: 61.5% → 89.0%

Time: 8.8s

Alternatives: 10

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 10^{+295}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x.re, \frac{y.re}{x.im}, y.im\right)}{\mathsf{hypot}\left(y.im, y.re\right)} \cdot \frac{x.im}{\mathsf{hypot}\left(y.im, y.re\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<=
      (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
      1e+295)
   (*
    (/ 1.0 (hypot y.re y.im))
    (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
   (*
    (/ (fma x.re (/ y.re x.im) y.im) (hypot y.im y.re))
    (/ x.im (hypot y.im y.re)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 1e+295) {
		tmp = (1.0 / hypot(y_46_re, y_46_im)) * (fma(x_46_re, y_46_re, (x_46_im * y_46_im)) / hypot(y_46_re, y_46_im));
	} else {
		tmp = (fma(x_46_re, (y_46_re / x_46_im), y_46_im) / hypot(y_46_im, y_46_re)) * (x_46_im / hypot(y_46_im, y_46_re));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))) <= 1e+295)
		tmp = Float64(Float64(1.0 / hypot(y_46_re, y_46_im)) * Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)));
	else
		tmp = Float64(Float64(fma(x_46_re, Float64(y_46_re / x_46_im), y_46_im) / hypot(y_46_im, y_46_re)) * Float64(x_46_im / hypot(y_46_im, y_46_re)));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+295], N[(N[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(x$46$re * y$46$re + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x$46$re * N[(y$46$re / x$46$im), $MachinePrecision] + y$46$im), $MachinePrecision] / N[Sqrt[y$46$im ^ 2 + y$46$re ^ 2], $MachinePrecision]), $MachinePrecision] * N[(x$46$im / N[Sqrt[y$46$im ^ 2 + y$46$re ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) < 9.9999999999999998e294

   1. Initial program 83.1%

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

      1. *-un-lft-identity 83.1%

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

      2. add-sqr-sqrt 83.1%

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

      3. times-frac 83.1%

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

      4. hypot-define 83.1%

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

      5. fma-define 83.1%

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

      6. hypot-define 96.4%

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

   4. Applied egg-rr 96.4%

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

   if 9.9999999999999998e294 < (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

   1. Initial program 7.4%

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

   3. Taylor expanded in x.im around inf 7.4%

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

      1. *-commutative 7.4%

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

      2. add-sqr-sqrt 7.4%

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

      3. hypot-undefine 7.4%

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

      4. hypot-undefine 7.4%

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

      5. times-frac 55.1%

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

      6. +-commutative 55.1%

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

      7. associate-/l* 69.9%

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

      8. fma-define 69.9%

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

      9. hypot-undefine 15.5%

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

      10. +-commutative 15.5%

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

      11. hypot-define 69.9%

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

      12. hypot-undefine 15.5%

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

      13. +-commutative 15.5%

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

      14. hypot-define 69.9%

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

   5. Applied egg-rr 69.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x.re, \frac{y.re}{x.im}, y.im\right)}{\mathsf{hypot}\left(y.im, y.re\right)} \cdot \frac{x.im}{\mathsf{hypot}\left(y.im, y.re\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 10^{+307}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<=
      (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
      1e+307)
   (*
    (/ 1.0 (hypot y.re y.im))
    (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
   (/ (+ x.im (* x.re (/ y.re y.im))) y.im)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 1e+307) {
		tmp = (1.0 / hypot(y_46_re, y_46_im)) * (fma(x_46_re, y_46_re, (x_46_im * y_46_im)) / hypot(y_46_re, y_46_im));
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))) <= 1e+307)
		tmp = Float64(Float64(1.0 / hypot(y_46_re, y_46_im)) * Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)));
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+307], N[(N[(1.0 / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(x$46$re * y$46$re + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) < 9.99999999999999986e306

   1. Initial program 83.2%

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

      1. *-un-lft-identity 83.2%

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

      2. add-sqr-sqrt 83.2%

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

      3. times-frac 83.1%

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

      4. hypot-define 83.2%

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

      5. fma-define 83.2%

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

      6. hypot-define 96.4%

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

   4. Applied egg-rr 96.4%

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

   if 9.99999999999999986e306 < (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

   1. Initial program 5.9%

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

   3. Taylor expanded in y.im around inf 48.9%

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

      1. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

Alternative 3: 82.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.re \cdot y.re + x.im \cdot y.im\\ \mathbf{if}\;y.re \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -3 \cdot 10^{-73}:\\ \;\;\;\;t\_0 \cdot {\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{-2}\\ \mathbf{elif}\;y.re \leq 1.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;\frac{t\_0}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (* x.re y.re) (* x.im y.im))))
   (if (<= y.re -1.5e+101)
     (/ (+ x.re (* y.im (/ x.im y.re))) y.re)
     (if (<= y.re -3e-73)
       (* t_0 (pow (hypot y.re y.im) -2.0))
       (if (<= y.re 1.7e-78)
         (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
         (if (<= y.re 4.7e+45)
           (/ t_0 (+ (* y.re y.re) (* y.im y.im)))
           (/ (+ x.re (/ x.im (/ y.re y.im))) y.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re * y_46_re) + (x_46_im * y_46_im);
	double tmp;
	if (y_46_re <= -1.5e+101) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= -3e-73) {
		tmp = t_0 * pow(hypot(y_46_re, y_46_im), -2.0);
	} else if (y_46_re <= 1.7e-78) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_re <= 4.7e+45) {
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re * y_46_re) + (x_46_im * y_46_im);
	double tmp;
	if (y_46_re <= -1.5e+101) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= -3e-73) {
		tmp = t_0 * Math.pow(Math.hypot(y_46_re, y_46_im), -2.0);
	} else if (y_46_re <= 1.7e-78) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_re <= 4.7e+45) {
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re * y_46_re) + (x_46_im * y_46_im)
	tmp = 0
	if y_46_re <= -1.5e+101:
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	elif y_46_re <= -3e-73:
		tmp = t_0 * math.pow(math.hypot(y_46_re, y_46_im), -2.0)
	elif y_46_re <= 1.7e-78:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif y_46_re <= 4.7e+45:
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	else:
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im))
	tmp = 0.0
	if (y_46_re <= -1.5e+101)
		tmp = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re);
	elseif (y_46_re <= -3e-73)
		tmp = Float64(t_0 * (hypot(y_46_re, y_46_im) ^ -2.0));
	elseif (y_46_re <= 1.7e-78)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif (y_46_re <= 4.7e+45)
		tmp = Float64(t_0 / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im / Float64(y_46_re / y_46_im))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re * y_46_re) + (x_46_im * y_46_im);
	tmp = 0.0;
	if (y_46_re <= -1.5e+101)
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	elseif (y_46_re <= -3e-73)
		tmp = t_0 * (hypot(y_46_re, y_46_im) ^ -2.0);
	elseif (y_46_re <= 1.7e-78)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif (y_46_re <= 4.7e+45)
		tmp = t_0 / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	else
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -1.5e+101], N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -3e-73], N[(t$95$0 * N[Power[N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.7e-78], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 4.7e+45], N[(t$95$0 / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re + N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y.re < -1.49999999999999997e101

   1. Initial program 30.7%

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

   3. Taylor expanded in y.re around inf 75.5%

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

      1. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

      1. clear-num 82.9%

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

      2. un-div-inv 82.9%

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

   7. Applied egg-rr 82.9%

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

      1. associate-/r/ 85.2%

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

   9. Simplified 85.2%

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

   if -1.49999999999999997e101 < y.re < -3e-73

   1. Initial program 86.9%

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

      1. *-un-lft-identity 86.9%

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

      2. add-sqr-sqrt 86.9%

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

      3. times-frac 86.9%

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

      4. hypot-define 86.9%

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

      5. fma-define 86.9%

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

      6. hypot-define 87.0%

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

   4. Applied egg-rr 87.0%

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

      1. pow1 87.0%

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

      2. *-commutative 87.0%

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

      3. div-inv 86.7%

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

      4. associate-*l* 86.5%

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

      5. inv-pow 86.5%

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

      6. inv-pow 86.5%

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

      7. pow-prod-up 87.1%

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

      8. metadata-eval 87.1%

         \[\leadsto {\left(\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right) \cdot {\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{\color{blue}{-2}}\right)}^{1} \]

   6. Applied egg-rr 87.1%

      \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right) \cdot {\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{-2}\right)}^{1}} \]
   7. Step-by-step derivation

      1. unpow1 87.1%

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

      2. fma-undefine 87.1%

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

      3. +-commutative 87.1%

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

      4. fma-define 87.1%

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

      5. *-commutative 87.1%

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

   8. Simplified 87.1%

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

      1. fma-undefine 87.1%

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

   10. Applied egg-rr 87.1%

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

   if -3e-73 < y.re < 1.70000000000000006e-78

   1. Initial program 71.1%

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

   3. Taylor expanded in y.im around inf 91.6%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

   if 1.70000000000000006e-78 < y.re < 4.70000000000000002e45

   1. Initial program 95.4%

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

   if 4.70000000000000002e45 < y.re

   1. Initial program 48.4%

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

   3. Taylor expanded in y.re around inf 81.9%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.5%

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

   7. Applied egg-rr 85.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -3 \cdot 10^{-73}:\\ \;\;\;\;\left(x.re \cdot y.re + x.im \cdot y.im\right) \cdot {\left(\mathsf{hypot}\left(y.re, y.im\right)\right)}^{-2}\\ \mathbf{elif}\;y.re \leq 1.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.re \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -4.8 \cdot 10^{-73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.re -1.6e+100)
     (/ (+ x.re (* y.im (/ x.im y.re))) y.re)
     (if (<= y.re -4.8e-73)
       t_0
       (if (<= y.re 3.2e-81)
         (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
         (if (<= y.re 4.7e+45)
           t_0
           (/ (+ x.re (/ x.im (/ y.re y.im))) y.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -1.6e+100) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= -4.8e-73) {
		tmp = t_0;
	} else if (y_46_re <= 3.2e-81) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_re <= 4.7e+45) {
		tmp = t_0;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46re <= (-1.6d+100)) then
        tmp = (x_46re + (y_46im * (x_46im / y_46re))) / y_46re
    else if (y_46re <= (-4.8d-73)) then
        tmp = t_0
    else if (y_46re <= 3.2d-81) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else if (y_46re <= 4.7d+45) then
        tmp = t_0
    else
        tmp = (x_46re + (x_46im / (y_46re / y_46im))) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -1.6e+100) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= -4.8e-73) {
		tmp = t_0;
	} else if (y_46_re <= 3.2e-81) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_re <= 4.7e+45) {
		tmp = t_0;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_re <= -1.6e+100:
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	elif y_46_re <= -4.8e-73:
		tmp = t_0
	elif y_46_re <= 3.2e-81:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif y_46_re <= 4.7e+45:
		tmp = t_0
	else:
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_re <= -1.6e+100)
		tmp = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re);
	elseif (y_46_re <= -4.8e-73)
		tmp = t_0;
	elseif (y_46_re <= 3.2e-81)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif (y_46_re <= 4.7e+45)
		tmp = t_0;
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im / Float64(y_46_re / y_46_im))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_re <= -1.6e+100)
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	elseif (y_46_re <= -4.8e-73)
		tmp = t_0;
	elseif (y_46_re <= 3.2e-81)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif (y_46_re <= 4.7e+45)
		tmp = t_0;
	else
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -1.6e+100], N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -4.8e-73], t$95$0, If[LessEqual[y$46$re, 3.2e-81], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 4.7e+45], t$95$0, N[(N[(x$46$re + N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -1.5999999999999999e100

   1. Initial program 32.4%

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

   3. Taylor expanded in y.re around inf 76.1%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. associate-/r/ 85.6%

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

   9. Simplified 85.6%

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

   if -1.5999999999999999e100 < y.re < -4.80000000000000011e-73 or 3.2e-81 < y.re < 4.70000000000000002e45

   1. Initial program 89.9%

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

   if -4.80000000000000011e-73 < y.re < 3.2e-81

   1. Initial program 71.1%

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

   3. Taylor expanded in y.im around inf 91.6%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

   if 4.70000000000000002e45 < y.re

   1. Initial program 48.4%

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

   3. Taylor expanded in y.re around inf 81.9%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.5%

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

   7. Applied egg-rr 85.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -4.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.5 \cdot 10^{-49} \lor \neg \left(y.re \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -3.5e-49) (not (<= y.re 1.9e+35)))
   (/ (+ x.re (* y.im (/ x.im y.re))) y.re)
   (/ (+ x.im (* x.re (/ y.re y.im))) y.im)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -3.5e-49) || !(y_46_re <= 1.9e+35)) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-3.5d-49)) .or. (.not. (y_46re <= 1.9d+35))) then
        tmp = (x_46re + (y_46im * (x_46im / y_46re))) / y_46re
    else
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -3.5e-49) || !(y_46_re <= 1.9e+35)) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -3.5e-49) or not (y_46_re <= 1.9e+35):
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	else:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -3.5e-49) || !(y_46_re <= 1.9e+35))
		tmp = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -3.5e-49) || ~((y_46_re <= 1.9e+35)))
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	else
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -3.5e-49], N[Not[LessEqual[y$46$re, 1.9e+35]], $MachinePrecision]], N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -3.50000000000000006e-49 or 1.9e35 < y.re

   1. Initial program 51.7%

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

   3. Taylor expanded in y.re around inf 77.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.7%

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

   7. Applied egg-rr 80.7%

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

      1. associate-/r/ 82.2%

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

   9. Simplified 82.2%

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

   if -3.50000000000000006e-49 < y.re < 1.9e35

   1. Initial program 76.1%

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

   3. Taylor expanded in y.im around inf 85.3%

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

      1. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.5 \cdot 10^{-49} \lor \neg \left(y.re \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -9.5 \cdot 10^{-49} \lor \neg \left(y.re \leq 5.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -9.5e-49) (not (<= y.re 5.8e+34)))
   (/ (+ x.re (* x.im (/ y.im y.re))) y.re)
   (/ (+ x.im (* x.re (/ y.re y.im))) y.im)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -9.5e-49) || !(y_46_re <= 5.8e+34)) {
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-9.5d-49)) .or. (.not. (y_46re <= 5.8d+34))) then
        tmp = (x_46re + (x_46im * (y_46im / y_46re))) / y_46re
    else
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -9.5e-49) || !(y_46_re <= 5.8e+34)) {
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -9.5e-49) or not (y_46_re <= 5.8e+34):
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re
	else:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -9.5e-49) || !(y_46_re <= 5.8e+34))
		tmp = Float64(Float64(x_46_re + Float64(x_46_im * Float64(y_46_im / y_46_re))) / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -9.5e-49) || ~((y_46_re <= 5.8e+34)))
		tmp = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	else
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -9.5e-49], N[Not[LessEqual[y$46$re, 5.8e+34]], $MachinePrecision]], N[(N[(x$46$re + N[(x$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -9.50000000000000006e-49 or 5.8000000000000003e34 < y.re

   1. Initial program 51.7%

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

   3. Taylor expanded in y.re around inf 77.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -9.50000000000000006e-49 < y.re < 5.8000000000000003e34

   1. Initial program 76.1%

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

   3. Taylor expanded in y.im around inf 85.3%

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

      1. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -9.5 \cdot 10^{-49} \lor \neg \left(y.re \leq 5.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -0.222 \lor \neg \left(y.re \leq 1.04 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -0.222) (not (<= y.re 1.04e+108)))
   (/ x.re y.re)
   (/ (+ x.im (* x.re (/ y.re y.im))) y.im)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -0.222) || !(y_46_re <= 1.04e+108)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-0.222d0)) .or. (.not. (y_46re <= 1.04d+108))) then
        tmp = x_46re / y_46re
    else
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -0.222) || !(y_46_re <= 1.04e+108)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -0.222) or not (y_46_re <= 1.04e+108):
		tmp = x_46_re / y_46_re
	else:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -0.222) || !(y_46_re <= 1.04e+108))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -0.222) || ~((y_46_re <= 1.04e+108)))
		tmp = x_46_re / y_46_re;
	else
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -0.222], N[Not[LessEqual[y$46$re, 1.04e+108]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -0.222000000000000003 or 1.04e108 < y.re

   1. Initial program 49.6%

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

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

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

   if -0.222000000000000003 < y.re < 1.04e108

   1. Initial program 75.2%

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

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

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -0.222 \lor \neg \left(y.re \leq 1.04 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 1.75 \cdot 10^{+42}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -1.3e-48)
   (/ (+ x.re (* y.im (/ x.im y.re))) y.re)
   (if (<= y.re 1.75e+42)
     (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
     (/ (+ x.re (/ x.im (/ y.re y.im))) y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -1.3e-48) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= 1.75e+42) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-1.3d-48)) then
        tmp = (x_46re + (y_46im * (x_46im / y_46re))) / y_46re
    else if (y_46re <= 1.75d+42) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else
        tmp = (x_46re + (x_46im / (y_46re / y_46im))) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -1.3e-48) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= 1.75e+42) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -1.3e-48:
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	elif y_46_re <= 1.75e+42:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	else:
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -1.3e-48)
		tmp = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re);
	elseif (y_46_re <= 1.75e+42)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im / Float64(y_46_re / y_46_im))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -1.3e-48)
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	elseif (y_46_re <= 1.75e+42)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	else
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -1.3e-48], N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 1.75e+42], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$re + N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -1.29999999999999994e-48

   1. Initial program 54.4%

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

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

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

      1. associate-/l* 76.8%

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

   5. Simplified 76.8%

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

      1. clear-num 76.8%

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

      2. un-div-inv 76.8%

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

   7. Applied egg-rr 76.8%

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

      1. associate-/r/ 79.7%

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

   9. Simplified 79.7%

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

   if -1.29999999999999994e-48 < y.re < 1.75000000000000012e42

   1. Initial program 76.1%

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

   3. Taylor expanded in y.im around inf 85.3%

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

      1. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

   if 1.75000000000000012e42 < y.re

   1. Initial program 48.4%

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

   3. Taylor expanded in y.re around inf 81.9%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.5%

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

   7. Applied egg-rr 85.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 1.75 \cdot 10^{+42}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.4 \cdot 10^{-54} \lor \neg \left(y.re \leq 10^{+105}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -3.4e-54) (not (<= y.re 1e+105)))
   (/ x.re y.re)
   (/ x.im y.im)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -3.4e-54) || !(y_46_re <= 1e+105)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = x_46_im / y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if ((y_46re <= (-3.4d-54)) .or. (.not. (y_46re <= 1d+105))) then
        tmp = x_46re / y_46re
    else
        tmp = x_46im / y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((y_46_re <= -3.4e-54) || !(y_46_re <= 1e+105)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = x_46_im / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -3.4e-54) or not (y_46_re <= 1e+105):
		tmp = x_46_re / y_46_re
	else:
		tmp = x_46_im / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -3.4e-54) || !(y_46_re <= 1e+105))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(x_46_im / y_46_im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((y_46_re <= -3.4e-54) || ~((y_46_re <= 1e+105)))
		tmp = x_46_re / y_46_re;
	else
		tmp = x_46_im / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -3.4e-54], N[Not[LessEqual[y$46$re, 1e+105]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -3.39999999999999987e-54 or 9.9999999999999994e104 < y.re

   1. Initial program 52.3%

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

   3. Taylor expanded in y.re around inf 71.8%

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

   if -3.39999999999999987e-54 < y.re < 9.9999999999999994e104

   1. Initial program 74.8%

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

   3. Taylor expanded in y.re around 0 66.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.4 \cdot 10^{-54} \lor \neg \left(y.re \leq 10^{+105}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.4% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.8%

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

3. Taylor expanded in y.re around 0 44.1%

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

Reproduce

herbie shell --seed 2024106 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  :precision binary64
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))