_multiplyComplex, imaginary part

Percentage Accurate: 99.0% → 99.5%

Time: 3.6s

Alternatives: 4

Speedup: 1.2×

• 23.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (+ (* 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) {
	return (x_46_re * y_46_im) + (x_46_im * y_46_re);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x_46re, x_46im, y_46re, y_46im)
use fmin_fmax_functions
    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_46im) + (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_re * y_46_im) + (x_46_im * y_46_re);
}

Python

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

Julia

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

Wolfram

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

Initial Program: 99.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (+ (* 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) {
	return (x_46_re * y_46_im) + (x_46_im * y_46_re);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x_46re, x_46im, y_46re, y_46im)
use fmin_fmax_functions
    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_46im) + (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_re * y_46_im) + (x_46_im * y_46_re);
}

Python

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

Julia

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y.im, x.re, y.re \cdot x.im\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. fp-cancel-sub-sign-inv N/A

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

   5. unpow1 N/A

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

   6. metadata-eval N/A

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

   7. sqrt-pow1 N/A

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

   8. pow2 N/A

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

   9. rem-sqrt-square-rev N/A

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

   10. remove-double-neg N/A

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

   11. lift-*.f64 N/A

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

   12. unpow1 N/A

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

   13. metadata-eval N/A

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

   14. sqrt-pow1 N/A

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

   15. pow2 N/A

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

   16. rem-sqrt-square-rev N/A

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

   17. rem-sqrt-square-rev N/A

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

   18. pow2 N/A

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

   19. sqrt-pow1 N/A

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

   20. metadata-eval N/A

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

   21. unpow1 N/A

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

4. Applied rewrites 99.6%

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

Alternative 2: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.im \cdot y.re \leq -4 \cdot 10^{+94}:\\ \;\;\;\;y.re \cdot x.im\\ \mathbf{elif}\;x.im \cdot y.re \leq 2 \cdot 10^{+36}:\\ \;\;\;\;y.im \cdot x.re\\ \mathbf{else}:\\ \;\;\;\;\left|y.re \cdot x.im\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= (* x.im y.re) -4e+94)
   (* y.re x.im)
   (if (<= (* x.im y.re) 2e+36) (* y.im x.re) (fabs (* y.re x.im)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((x_46_im * y_46_re) <= -4e+94) {
		tmp = y_46_re * x_46_im;
	} else if ((x_46_im * y_46_re) <= 2e+36) {
		tmp = y_46_im * x_46_re;
	} else {
		tmp = fabs((y_46_re * x_46_im));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x_46re, x_46im, y_46re, y_46im)
use fmin_fmax_functions
    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 ((x_46im * y_46re) <= (-4d+94)) then
        tmp = y_46re * x_46im
    else if ((x_46im * y_46re) <= 2d+36) then
        tmp = y_46im * x_46re
    else
        tmp = abs((y_46re * x_46im))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((x_46_im * y_46_re) <= -4e+94) {
		tmp = y_46_re * x_46_im;
	} else if ((x_46_im * y_46_re) <= 2e+36) {
		tmp = y_46_im * x_46_re;
	} else {
		tmp = Math.abs((y_46_re * x_46_im));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (x_46_im * y_46_re) <= -4e+94:
		tmp = y_46_re * x_46_im
	elif (x_46_im * y_46_re) <= 2e+36:
		tmp = y_46_im * x_46_re
	else:
		tmp = math.fabs((y_46_re * x_46_im))
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (Float64(x_46_im * y_46_re) <= -4e+94)
		tmp = Float64(y_46_re * x_46_im);
	elseif (Float64(x_46_im * y_46_re) <= 2e+36)
		tmp = Float64(y_46_im * x_46_re);
	else
		tmp = abs(Float64(y_46_re * x_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if ((x_46_im * y_46_re) <= -4e+94)
		tmp = y_46_re * x_46_im;
	elseif ((x_46_im * y_46_re) <= 2e+36)
		tmp = y_46_im * x_46_re;
	else
		tmp = abs((y_46_re * x_46_im));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[N[(x$46$im * y$46$re), $MachinePrecision], -4e+94], N[(y$46$re * x$46$im), $MachinePrecision], If[LessEqual[N[(x$46$im * y$46$re), $MachinePrecision], 2e+36], N[(y$46$im * x$46$re), $MachinePrecision], N[Abs[N[(y$46$re * x$46$im), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x.im y.re) < -4.0000000000000001e94

   1. Initial program 98.2%

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

   3. Taylor expanded in x.re around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.7

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

   5. Applied rewrites 84.7%

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

   if -4.0000000000000001e94 < (*.f64 x.im y.re) < 2.00000000000000008e36

   1. Initial program 100.0%

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

   3. Taylor expanded in x.re around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 27.9

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

   5. Applied rewrites 27.9%

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

   7. Applied rewrites 12.0%

      \[\leadsto \left|y.re \cdot x.im\right| \]

   8. Taylor expanded in x.re around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.8

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

   10. Applied rewrites 75.8%

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

   if 2.00000000000000008e36 < (*.f64 x.im y.re)

   1. Initial program 98.0%

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

   3. Taylor expanded in x.re around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.2

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

   5. Applied rewrites 81.2%

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

   7. Applied rewrites 81.2%

      \[\leadsto \left|y.re \cdot x.im\right| \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.im \cdot y.re \leq -4 \cdot 10^{+94} \lor \neg \left(x.im \cdot y.re \leq 2 \cdot 10^{+36}\right):\\ \;\;\;\;y.re \cdot x.im\\ \mathbf{else}:\\ \;\;\;\;y.im \cdot x.re\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= (* x.im y.re) -4e+94) (not (<= (* x.im y.re) 2e+36)))
   (* y.re x.im)
   (* y.im x.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (((x_46_im * y_46_re) <= -4e+94) || !((x_46_im * y_46_re) <= 2e+36)) {
		tmp = y_46_re * x_46_im;
	} else {
		tmp = y_46_im * x_46_re;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x_46re, x_46im, y_46re, y_46im)
use fmin_fmax_functions
    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 (((x_46im * y_46re) <= (-4d+94)) .or. (.not. ((x_46im * y_46re) <= 2d+36))) then
        tmp = y_46re * x_46im
    else
        tmp = y_46im * x_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 (((x_46_im * y_46_re) <= -4e+94) || !((x_46_im * y_46_re) <= 2e+36)) {
		tmp = y_46_re * x_46_im;
	} else {
		tmp = y_46_im * x_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if ((x_46_im * y_46_re) <= -4e+94) or not ((x_46_im * y_46_re) <= 2e+36):
		tmp = y_46_re * x_46_im
	else:
		tmp = y_46_im * x_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((Float64(x_46_im * y_46_re) <= -4e+94) || !(Float64(x_46_im * y_46_re) <= 2e+36))
		tmp = Float64(y_46_re * x_46_im);
	else
		tmp = Float64(y_46_im * x_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 (((x_46_im * y_46_re) <= -4e+94) || ~(((x_46_im * y_46_re) <= 2e+36)))
		tmp = y_46_re * x_46_im;
	else
		tmp = y_46_im * x_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[N[(x$46$im * y$46$re), $MachinePrecision], -4e+94], N[Not[LessEqual[N[(x$46$im * y$46$re), $MachinePrecision], 2e+36]], $MachinePrecision]], N[(y$46$re * x$46$im), $MachinePrecision], N[(y$46$im * x$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x.im y.re) < -4.0000000000000001e94 or 2.00000000000000008e36 < (*.f64 x.im y.re)

   1. Initial program 98.1%

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

   3. Taylor expanded in x.re around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 83.1

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

   5. Applied rewrites 83.1%

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

   if -4.0000000000000001e94 < (*.f64 x.im y.re) < 2.00000000000000008e36

   1. Initial program 100.0%

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

   3. Taylor expanded in x.re around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 27.9

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

   5. Applied rewrites 27.9%

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

   7. Applied rewrites 12.0%

      \[\leadsto \left|y.re \cdot x.im\right| \]

   8. Taylor expanded in x.re around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.8

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

   10. Applied rewrites 75.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \cdot y.re \leq -4 \cdot 10^{+94} \lor \neg \left(x.im \cdot y.re \leq 2 \cdot 10^{+36}\right):\\ \;\;\;\;y.re \cdot x.im\\ \mathbf{else}:\\ \;\;\;\;y.im \cdot x.re\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x_46re, x_46im, y_46re, y_46im)
use fmin_fmax_functions
    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 = y_46im * x_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 y_46_im * x_46_re;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x.re around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 51.0

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

5. Applied rewrites 51.0%

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

7. Applied rewrites 23.7%

   \[\leadsto \left|y.re \cdot x.im\right| \]

8. Taylor expanded in x.re around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 53.6

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

10. Applied rewrites 53.6%

    \[\leadsto \color{blue}{y.im \cdot x.re} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025015 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))