_multiplyComplex, real part

Percentage Accurate: 99.2% → 99.9%

Time: 3.1s

Alternatives: 4

Speedup: 0.4×

• 23.4% 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: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.re \cdot y.re - x.im \cdot y.im\\ \mathbf{if}\;t\_0 \leq 10^{+304}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(y.re - y.im \cdot \frac{x.im}{x.re}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (* x.re y.re) (* x.im y.im))))
   (if (<= t_0 1e+304) t_0 (* x.re (- y.re (* y.im (/ x.im x.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 (t_0 <= 1e+304) {
		tmp = t_0;
	} else {
		tmp = x_46_re * (y_46_re - (y_46_im * (x_46_im / 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) :: t_0
    real(8) :: tmp
    t_0 = (x_46re * y_46re) - (x_46im * y_46im)
    if (t_0 <= 1d+304) then
        tmp = t_0
    else
        tmp = x_46re * (y_46re - (y_46im * (x_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 t_0 = (x_46_re * y_46_re) - (x_46_im * y_46_im);
	double tmp;
	if (t_0 <= 1e+304) {
		tmp = t_0;
	} else {
		tmp = x_46_re * (y_46_re - (y_46_im * (x_46_im / x_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 t_0 <= 1e+304:
		tmp = t_0
	else:
		tmp = x_46_re * (y_46_re - (y_46_im * (x_46_im / x_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 (t_0 <= 1e+304)
		tmp = t_0;
	else
		tmp = Float64(x_46_re * Float64(y_46_re - Float64(y_46_im * Float64(x_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)
	t_0 = (x_46_re * y_46_re) - (x_46_im * y_46_im);
	tmp = 0.0;
	if (t_0 <= 1e+304)
		tmp = t_0;
	else
		tmp = x_46_re * (y_46_re - (y_46_im * (x_46_im / x_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[t$95$0, 1e+304], t$95$0, N[(x$46$re * N[(y$46$re - N[(y$46$im * N[(x$46$im / x$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) < 9.9999999999999994e303

   1. Initial program 100.0%

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

   if 9.9999999999999994e303 < (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

   1. Initial program 84.4%

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

   3. Taylor expanded in x.re around inf 96.9%

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

      1. mul-1-neg 96.9%

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

      2. unsub-neg 96.9%

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

      3. *-commutative 96.9%

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

      4. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

Alternative 2: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.re \cdot y.re \leq -2.1 \cdot 10^{+55} \lor \neg \left(x.re \cdot y.re \leq 1.65 \cdot 10^{-68}\right):\\ \;\;\;\;x.re \cdot y.re\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(-y.im\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= (* x.re y.re) -2.1e+55) (not (<= (* x.re y.re) 1.65e-68)))
   (* 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 (((x_46_re * y_46_re) <= -2.1e+55) || !((x_46_re * y_46_re) <= 1.65e-68)) {
		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 (((x_46re * y_46re) <= (-2.1d+55)) .or. (.not. ((x_46re * y_46re) <= 1.65d-68))) 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 (((x_46_re * y_46_re) <= -2.1e+55) || !((x_46_re * y_46_re) <= 1.65e-68)) {
		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 ((x_46_re * y_46_re) <= -2.1e+55) or not ((x_46_re * y_46_re) <= 1.65e-68):
		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 ((Float64(x_46_re * y_46_re) <= -2.1e+55) || !(Float64(x_46_re * y_46_re) <= 1.65e-68))
		tmp = Float64(x_46_re * y_46_re);
	else
		tmp = Float64(x_46_im * Float64(-y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (((x_46_re * y_46_re) <= -2.1e+55) || ~(((x_46_re * y_46_re) <= 1.65e-68)))
		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[N[(x$46$re * y$46$re), $MachinePrecision], -2.1e+55], N[Not[LessEqual[N[(x$46$re * y$46$re), $MachinePrecision], 1.65e-68]], $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 (*.f64 x.re y.re) < -2.1000000000000001e55 or 1.6499999999999999e-68 < (*.f64 x.re y.re)

   1. Initial program 96.2%

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

   3. Taylor expanded in x.re around inf 78.9%

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

   if -2.1000000000000001e55 < (*.f64 x.re y.re) < 1.6499999999999999e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in x.re around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. distribute-rgt-neg-out 79.3%

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

   5. Simplified 79.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \cdot y.re \leq -2.1 \cdot 10^{+55} \lor \neg \left(x.re \cdot y.re \leq 1.65 \cdot 10^{-68}\right):\\ \;\;\;\;x.re \cdot y.re\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(-y.im\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.re \cdot y.re - x.im \cdot y.im\\ \mathbf{if}\;t\_0 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(-y.im\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (- (* x.re y.re) (* x.im y.im))))
   (if (<= t_0 INFINITY) t_0 (* x.im (- y.im)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re * y_46_re) - (x_46_im * y_46_im);
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = x_46_im * -y_46_im;
	}
	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 (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = x_46_im * -y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re * y_46_re) - (x_46_im * y_46_im)
	tmp = 0
	if t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = x_46_im * -y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re * y_46_re) - Float64(x_46_im * y_46_im))
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = Float64(x_46_im * Float64(-y_46_im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re * y_46_re) - (x_46_im * y_46_im);
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = x_46_im * -y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re * y$46$re), $MachinePrecision] - N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], t$95$0, N[(x$46$im * (-y$46$im)), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

   1. Initial program 0.0%

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

   3. Taylor expanded in x.re around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-out 80.0%

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

   5. Simplified 80.0%

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

Alternative 4: 52.4% accurate, 2.3× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x.re around inf 52.5%

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))