_multiplyComplex, real part

Percentage Accurate: 99.2% → 99.2%

Time: 3.1s

Alternatives: 3

Speedup: 1.0×

• 24.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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);
}

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)
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);
}

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)

Julia

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

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);
}

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)
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);
}

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)

Julia

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return (y_46_re * x_46_re) - (y_46_im * x_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 = (y_46re * x_46re) - (y_46im * x_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 (y_46_re * x_46_re) - (y_46_im * x_46_im);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

   \[\leadsto y.re \cdot x.re - y.im \cdot x.im \]
4. Add Preprocessing

Alternative 2: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \cdot x.re \leq -4 \cdot 10^{-26}:\\ \;\;\;\;y.re \cdot x.re\\ \mathbf{elif}\;y.re \cdot x.re \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\left(-y.im\right) \cdot x.im\\ \mathbf{else}:\\ \;\;\;\;y.re \cdot x.re\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= (* y.re x.re) -4e-26)
   (* y.re x.re)
   (if (<= (* y.re x.re) 5e-55) (* (- y.im) x.im) (* y.re x.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 * x_46_re) <= -4e-26) {
		tmp = y_46_re * x_46_re;
	} else if ((y_46_re * x_46_re) <= 5e-55) {
		tmp = -y_46_im * x_46_im;
	} else {
		tmp = y_46_re * x_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 * x_46re) <= (-4d-26)) then
        tmp = y_46re * x_46re
    else if ((y_46re * x_46re) <= 5d-55) then
        tmp = -y_46im * x_46im
    else
        tmp = y_46re * 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 ((y_46_re * x_46_re) <= -4e-26) {
		tmp = y_46_re * x_46_re;
	} else if ((y_46_re * x_46_re) <= 5e-55) {
		tmp = -y_46_im * x_46_im;
	} else {
		tmp = y_46_re * x_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 * x_46_re) <= -4e-26:
		tmp = y_46_re * x_46_re
	elif (y_46_re * x_46_re) <= 5e-55:
		tmp = -y_46_im * x_46_im
	else:
		tmp = y_46_re * 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(y_46_re * x_46_re) <= -4e-26)
		tmp = Float64(y_46_re * x_46_re);
	elseif (Float64(y_46_re * x_46_re) <= 5e-55)
		tmp = Float64(Float64(-y_46_im) * x_46_im);
	else
		tmp = Float64(y_46_re * 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 ((y_46_re * x_46_re) <= -4e-26)
		tmp = y_46_re * x_46_re;
	elseif ((y_46_re * x_46_re) <= 5e-55)
		tmp = -y_46_im * x_46_im;
	else
		tmp = y_46_re * x_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[N[(y$46$re * x$46$re), $MachinePrecision], -4e-26], N[(y$46$re * x$46$re), $MachinePrecision], If[LessEqual[N[(y$46$re * x$46$re), $MachinePrecision], 5e-55], N[((-y$46$im) * x$46$im), $MachinePrecision], N[(y$46$re * x$46$re), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x.re y.re) < -4.0000000000000002e-26 or 5.0000000000000002e-55 < (*.f64 x.re y.re)

   1. Initial program 97.7%

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

   3. Taylor expanded in y.im around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -4.0000000000000002e-26 < (*.f64 x.re y.re) < 5.0000000000000002e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in y.im around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 85.4

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

   5. Applied rewrites 85.4%

      \[\leadsto \color{blue}{\left(-y.im\right) \cdot x.im} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \cdot x.re \leq -4 \cdot 10^{-26}:\\ \;\;\;\;y.re \cdot x.re\\ \mathbf{elif}\;y.re \cdot x.re \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\left(-y.im\right) \cdot x.im\\ \mathbf{else}:\\ \;\;\;\;y.re \cdot x.re\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.2% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = y_46re * 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_re * x_46_re;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in y.im around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 49.6

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

5. Applied rewrites 49.6%

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

Reproduce

herbie shell --seed 2024266 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))