_multiplyComplex, real part

Percentage Accurate: 99.2% → 99.2%

Time: 2.6s

Alternatives: 3

Speedup: 1.0×

• 23.9% 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

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

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]

Derivation

1. Initial program 99.6%

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

Alternative 2: 75.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.re \cdot y.re \leq -1.7 \cdot 10^{+101} \lor \neg \left(x.re \cdot y.re \leq -1.5 \cdot 10^{+59} \lor \neg \left(x.re \cdot y.re \leq -3.3 \cdot 10^{-52}\right) \land x.re \cdot y.re \leq 1.4 \cdot 10^{-24}\right):\\ \;\;\;\;x.re \cdot y.re\\ \mathbf{else}:\\ \;\;\;\;y.im \cdot \left(-x.im\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= (* x.re y.re) -1.7e+101)
         (not
          (or (<= (* x.re y.re) -1.5e+59)
              (and (not (<= (* x.re y.re) -3.3e-52))
                   (<= (* x.re y.re) 1.4e-24)))))
   (* x.re y.re)
   (* y.im (- 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_re * y_46_re) <= -1.7e+101) || !(((x_46_re * y_46_re) <= -1.5e+59) || (!((x_46_re * y_46_re) <= -3.3e-52) && ((x_46_re * y_46_re) <= 1.4e-24)))) {
		tmp = x_46_re * y_46_re;
	} else {
		tmp = y_46_im * -x_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) <= (-1.7d+101)) .or. (.not. ((x_46re * y_46re) <= (-1.5d+59)) .or. (.not. ((x_46re * y_46re) <= (-3.3d-52))) .and. ((x_46re * y_46re) <= 1.4d-24))) then
        tmp = x_46re * y_46re
    else
        tmp = y_46im * -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_re * y_46_re) <= -1.7e+101) || !(((x_46_re * y_46_re) <= -1.5e+59) || (!((x_46_re * y_46_re) <= -3.3e-52) && ((x_46_re * y_46_re) <= 1.4e-24)))) {
		tmp = x_46_re * y_46_re;
	} else {
		tmp = y_46_im * -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_re * y_46_re) <= -1.7e+101) or not (((x_46_re * y_46_re) <= -1.5e+59) or (not ((x_46_re * y_46_re) <= -3.3e-52) and ((x_46_re * y_46_re) <= 1.4e-24))):
		tmp = x_46_re * y_46_re
	else:
		tmp = y_46_im * -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_re * y_46_re) <= -1.7e+101) || !((Float64(x_46_re * y_46_re) <= -1.5e+59) || (!(Float64(x_46_re * y_46_re) <= -3.3e-52) && (Float64(x_46_re * y_46_re) <= 1.4e-24))))
		tmp = Float64(x_46_re * y_46_re);
	else
		tmp = Float64(y_46_im * Float64(-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_re * y_46_re) <= -1.7e+101) || ~((((x_46_re * y_46_re) <= -1.5e+59) || (~(((x_46_re * y_46_re) <= -3.3e-52)) && ((x_46_re * y_46_re) <= 1.4e-24)))))
		tmp = x_46_re * y_46_re;
	else
		tmp = y_46_im * -x_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], -1.7e+101], N[Not[Or[LessEqual[N[(x$46$re * y$46$re), $MachinePrecision], -1.5e+59], And[N[Not[LessEqual[N[(x$46$re * y$46$re), $MachinePrecision], -3.3e-52]], $MachinePrecision], LessEqual[N[(x$46$re * y$46$re), $MachinePrecision], 1.4e-24]]]], $MachinePrecision]], N[(x$46$re * y$46$re), $MachinePrecision], N[(y$46$im * (-x$46$im)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x.re y.re) < -1.70000000000000009e101 or -1.5e59 < (*.f64 x.re y.re) < -3.29999999999999995e-52 or 1.4000000000000001e-24 < (*.f64 x.re y.re)

   1. Initial program 99.3%

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

   3. Taylor expanded in x.re around inf 77.0%

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

   if -1.70000000000000009e101 < (*.f64 x.re y.re) < -1.5e59 or -3.29999999999999995e-52 < (*.f64 x.re y.re) < 1.4000000000000001e-24

   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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-in 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \cdot y.re \leq -1.7 \cdot 10^{+101} \lor \neg \left(x.re \cdot y.re \leq -1.5 \cdot 10^{+59} \lor \neg \left(x.re \cdot y.re \leq -3.3 \cdot 10^{-52}\right) \land x.re \cdot y.re \leq 1.4 \cdot 10^{-24}\right):\\ \;\;\;\;x.re \cdot y.re\\ \mathbf{else}:\\ \;\;\;\;y.im \cdot \left(-x.im\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.7% 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 99.6%

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

3. Taylor expanded in x.re around inf 54.1%

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))