_multiplyComplex, real part

Percentage Accurate: 99.2% → 99.2%

Time: 3.3s

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: 67.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.im \leq -3.35 \cdot 10^{-34} \lor \neg \left(x.im \leq -5.6 \cdot 10^{-104}\right) \land \left(x.im \leq -9 \cdot 10^{-106} \lor \neg \left(x.im \leq -8.5 \cdot 10^{-113}\right) \land \left(x.im \leq -1.4 \cdot 10^{-114} \lor \neg \left(x.im \leq -9.6 \cdot 10^{-139}\right) \land \left(x.im \leq -7 \cdot 10^{-139} \lor \neg \left(x.im \leq -2.3 \cdot 10^{-147}\right) \land \left(x.im \leq -1.22 \cdot 10^{-147} \lor \neg \left(x.im \leq -4.2 \cdot 10^{-161}\right) \land \left(x.im \leq -4.8 \cdot 10^{-172} \lor \neg \left(x.im \leq -4.8 \cdot 10^{-192}\right) \land \left(x.im \leq -4.7 \cdot 10^{-192} \lor \neg \left(x.im \leq -1.5 \cdot 10^{-259}\right) \land \left(x.im \leq -8.6 \cdot 10^{-260} \lor \neg \left(x.im \leq -7.8 \cdot 10^{-271}\right) \land \left(x.im \leq -7.6 \cdot 10^{-271} \lor \neg \left(x.im \leq 1.3 \cdot 10^{-255}\right) \land \left(x.im \leq 1.35 \cdot 10^{-255} \lor \neg \left(x.im \leq 1.05 \cdot 10^{-248}\right) \land \left(x.im \leq 5.4 \cdot 10^{-248} \lor \neg \left(x.im \leq 2.4 \cdot 10^{-196}\right) \land \left(x.im \leq 2.5 \cdot 10^{-196} \lor \neg \left(x.im \leq 5 \cdot 10^{-187}\right) \land \left(x.im \leq 5.2 \cdot 10^{-187} \lor \neg \left(x.im \leq 2.3 \cdot 10^{-178}\right) \land \left(x.im \leq 2.35 \cdot 10^{-178} \lor \neg \left(x.im \leq 9.5 \cdot 10^{-150}\right) \land \left(x.im \leq 1.2 \cdot 10^{-120} \lor \neg \left(x.im \leq 1.55 \cdot 10^{-105}\right) \land \left(x.im \leq 2.35 \cdot 10^{-102} \lor \neg \left(x.im \leq 7.5 \cdot 10^{-95}\right) \land \left(x.im \leq 1.85 \cdot 10^{-90} \lor \neg \left(x.im \leq 1.4 \cdot 10^{-83}\right) \land \left(x.im \leq 1.45 \cdot 10^{-65} \lor \neg \left(x.im \leq 1.05 \cdot 10^{-58} \lor \neg \left(x.im \leq 9.6 \cdot 10^{-57}\right) \land \left(x.im \leq 1.15 \cdot 10^{-49} \lor \neg \left(x.im \leq 7.6 \cdot 10^{-25}\right) \land \left(x.im \leq 18 \lor \neg \left(x.im \leq 1300\right) \land \left(x.im \leq 125000000 \lor \neg \left(x.im \leq 1.9 \cdot 10^{+75}\right) \land x.im \leq 5.8 \cdot 10^{+76}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x.im \cdot \left(-y.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot y.re\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= x.im -3.35e-34)
         (and (not (<= x.im -5.6e-104))
              (or (<= x.im -9e-106)
                  (and (not (<= x.im -8.5e-113))
                       (or (<= x.im -1.4e-114)
                           (and (not (<= x.im -9.6e-139))
                                (or (<= x.im -7e-139)
                                    (and (not (<= x.im -2.3e-147))
                                         (or (<= x.im -1.22e-147)
                                             (and (not (<= x.im -4.2e-161))
                                                  (or (<= x.im -4.8e-172)
                                                      (and (not
                                                            (<=
                                                             x.im
                                                             -4.8e-192))
                                                           (or (<=
                                                                x.im
                                                                -4.7e-192)
                                                               (and (not
                                                                     (<=
                                                                      x.im
                                                                      -1.5e-259))
                                                                    (or (<=
                                                                         x.im
                                                                         -8.6e-260)
                                                                        (and (not
                                                                              (<=
                                                                               x.im
                                                                               -7.8e-271))
                                                                             (or (<=
                                                                                  x.im
                                                                                  -7.6e-271)
                                                                                 (and (not
                                                                                       (<=
                                                                                        x.im
                                                                                        1.3e-255))
                                                                                      (or (<=
                                                                                           x.im
                                                                                           1.35e-255)
                                                                                          (and (not
                                                                                                (<=
                                                                                                 x.im
                                                                                                 1.05e-248))
                                                                                               (or (<=
                                                                                                    x.im
                                                                                                    5.4e-248)
                                                                                                   (and (not
                                                                                                         (<=
                                                                                                          x.im
                                                                                                          2.4e-196))
                                                                                                        (or (<=
                                                                                                             x.im
                                                                                                             2.5e-196)
                                                                                                            (and (not
                                                                                                                  (<=
                                                                                                                   x.im
                                                                                                                   5e-187))
                                                                                                                 (or (<=
                                                                                                                      x.im
                                                                                                                      5.2e-187)
                                                                                                                     (and (not
                                                                                                                           (<=
                                                                                                                            x.im
                                                                                                                            2.3e-178))
                                                                                                                          (or (<=
                                                                                                                               x.im
                                                                                                                               2.35e-178)
                                                                                                                              (and (not
                                                                                                                                    (<=
                                                                                                                                     x.im
                                                                                                                                     9.5e-150))
                                                                                                                                   (or (<=
                                                                                                                                        x.im
                                                                                                                                        1.2e-120)
                                                                                                                                       (and (not
                                                                                                                                             (<=
                                                                                                                                              x.im
                                                                                                                                              1.55e-105))
                                                                                                                                            (or (<=
                                                                                                                                                 x.im
                                                                                                                                                 2.35e-102)
                                                                                                                                                (and (not
                                                                                                                                                      (<=
                                                                                                                                                       x.im
                                                                                                                                                       7.5e-95))
                                                                                                                                                     (or (<=
                                                                                                                                                          x.im
                                                                                                                                                          1.85e-90)
                                                                                                                                                         (and (not
                                                                                                                                                               (<=
                                                                                                                                                                x.im
                                                                                                                                                                1.4e-83))
                                                                                                                                                              (or (<=
                                                                                                                                                                   x.im
                                                                                                                                                                   1.45e-65)
                                                                                                                                                                  (not
                                                                                                                                                                   (or (<=
                                                                                                                                                                        x.im
                                                                                                                                                                        1.05e-58)
                                                                                                                                                                       (and (not
                                                                                                                                                                             (<=
                                                                                                                                                                              x.im
                                                                                                                                                                              9.6e-57))
                                                                                                                                                                            (or (<=
                                                                                                                                                                                 x.im
                                                                                                                                                                                 1.15e-49)
                                                                                                                                                                                (and (not
                                                                                                                                                                                      (<=
                                                                                                                                                                                       x.im
                                                                                                                                                                                       7.6e-25))
                                                                                                                                                                                     (or (<=
                                                                                                                                                                                          x.im
                                                                                                                                                                                          18.0)
                                                                                                                                                                                         (and (not
                                                                                                                                                                                               (<=
                                                                                                                                                                                                x.im
                                                                                                                                                                                                1300.0))
                                                                                                                                                                                              (or (<=
                                                                                                                                                                                                   x.im
                                                                                                                                                                                                   125000000.0)
                                                                                                                                                                                                  (and (not
                                                                                                                                                                                                        (<=
                                                                                                                                                                                                         x.im
                                                                                                                                                                                                         1.9e+75))
                                                                                                                                                                                                       (<=
                                                                                                                                                                                                        x.im
                                                                                                                                                                                                        5.8e+76)))))))))))))))))))))))))))))))))))))))))))))
   (* x.im (- y.im))
   (* x.re 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_im <= -3.35e-34) || (!(x_46_im <= -5.6e-104) && ((x_46_im <= -9e-106) || (!(x_46_im <= -8.5e-113) && ((x_46_im <= -1.4e-114) || (!(x_46_im <= -9.6e-139) && ((x_46_im <= -7e-139) || (!(x_46_im <= -2.3e-147) && ((x_46_im <= -1.22e-147) || (!(x_46_im <= -4.2e-161) && ((x_46_im <= -4.8e-172) || (!(x_46_im <= -4.8e-192) && ((x_46_im <= -4.7e-192) || (!(x_46_im <= -1.5e-259) && ((x_46_im <= -8.6e-260) || (!(x_46_im <= -7.8e-271) && ((x_46_im <= -7.6e-271) || (!(x_46_im <= 1.3e-255) && ((x_46_im <= 1.35e-255) || (!(x_46_im <= 1.05e-248) && ((x_46_im <= 5.4e-248) || (!(x_46_im <= 2.4e-196) && ((x_46_im <= 2.5e-196) || (!(x_46_im <= 5e-187) && ((x_46_im <= 5.2e-187) || (!(x_46_im <= 2.3e-178) && ((x_46_im <= 2.35e-178) || (!(x_46_im <= 9.5e-150) && ((x_46_im <= 1.2e-120) || (!(x_46_im <= 1.55e-105) && ((x_46_im <= 2.35e-102) || (!(x_46_im <= 7.5e-95) && ((x_46_im <= 1.85e-90) || (!(x_46_im <= 1.4e-83) && ((x_46_im <= 1.45e-65) || !((x_46_im <= 1.05e-58) || (!(x_46_im <= 9.6e-57) && ((x_46_im <= 1.15e-49) || (!(x_46_im <= 7.6e-25) && ((x_46_im <= 18.0) || (!(x_46_im <= 1300.0) && ((x_46_im <= 125000000.0) || (!(x_46_im <= 1.9e+75) && (x_46_im <= 5.8e+76)))))))))))))))))))))))))))))))))))))))))))) {
		tmp = x_46_im * -y_46_im;
	} else {
		tmp = x_46_re * 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 ((x_46im <= (-3.35d-34)) .or. (.not. (x_46im <= (-5.6d-104))) .and. (x_46im <= (-9d-106)) .or. (.not. (x_46im <= (-8.5d-113))) .and. (x_46im <= (-1.4d-114)) .or. (.not. (x_46im <= (-9.6d-139))) .and. (x_46im <= (-7d-139)) .or. (.not. (x_46im <= (-2.3d-147))) .and. (x_46im <= (-1.22d-147)) .or. (.not. (x_46im <= (-4.2d-161))) .and. (x_46im <= (-4.8d-172)) .or. (.not. (x_46im <= (-4.8d-192))) .and. (x_46im <= (-4.7d-192)) .or. (.not. (x_46im <= (-1.5d-259))) .and. (x_46im <= (-8.6d-260)) .or. (.not. (x_46im <= (-7.8d-271))) .and. (x_46im <= (-7.6d-271)) .or. (.not. (x_46im <= 1.3d-255)) .and. (x_46im <= 1.35d-255) .or. (.not. (x_46im <= 1.05d-248)) .and. (x_46im <= 5.4d-248) .or. (.not. (x_46im <= 2.4d-196)) .and. (x_46im <= 2.5d-196) .or. (.not. (x_46im <= 5d-187)) .and. (x_46im <= 5.2d-187) .or. (.not. (x_46im <= 2.3d-178)) .and. (x_46im <= 2.35d-178) .or. (.not. (x_46im <= 9.5d-150)) .and. (x_46im <= 1.2d-120) .or. (.not. (x_46im <= 1.55d-105)) .and. (x_46im <= 2.35d-102) .or. (.not. (x_46im <= 7.5d-95)) .and. (x_46im <= 1.85d-90) .or. (.not. (x_46im <= 1.4d-83)) .and. (x_46im <= 1.45d-65) .or. (.not. (x_46im <= 1.05d-58) .or. (.not. (x_46im <= 9.6d-57)) .and. (x_46im <= 1.15d-49) .or. (.not. (x_46im <= 7.6d-25)) .and. (x_46im <= 18.0d0) .or. (.not. (x_46im <= 1300.0d0)) .and. (x_46im <= 125000000.0d0) .or. (.not. (x_46im <= 1.9d+75)) .and. (x_46im <= 5.8d+76))) then
        tmp = x_46im * -y_46im
    else
        tmp = x_46re * 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 ((x_46_im <= -3.35e-34) || (!(x_46_im <= -5.6e-104) && ((x_46_im <= -9e-106) || (!(x_46_im <= -8.5e-113) && ((x_46_im <= -1.4e-114) || (!(x_46_im <= -9.6e-139) && ((x_46_im <= -7e-139) || (!(x_46_im <= -2.3e-147) && ((x_46_im <= -1.22e-147) || (!(x_46_im <= -4.2e-161) && ((x_46_im <= -4.8e-172) || (!(x_46_im <= -4.8e-192) && ((x_46_im <= -4.7e-192) || (!(x_46_im <= -1.5e-259) && ((x_46_im <= -8.6e-260) || (!(x_46_im <= -7.8e-271) && ((x_46_im <= -7.6e-271) || (!(x_46_im <= 1.3e-255) && ((x_46_im <= 1.35e-255) || (!(x_46_im <= 1.05e-248) && ((x_46_im <= 5.4e-248) || (!(x_46_im <= 2.4e-196) && ((x_46_im <= 2.5e-196) || (!(x_46_im <= 5e-187) && ((x_46_im <= 5.2e-187) || (!(x_46_im <= 2.3e-178) && ((x_46_im <= 2.35e-178) || (!(x_46_im <= 9.5e-150) && ((x_46_im <= 1.2e-120) || (!(x_46_im <= 1.55e-105) && ((x_46_im <= 2.35e-102) || (!(x_46_im <= 7.5e-95) && ((x_46_im <= 1.85e-90) || (!(x_46_im <= 1.4e-83) && ((x_46_im <= 1.45e-65) || !((x_46_im <= 1.05e-58) || (!(x_46_im <= 9.6e-57) && ((x_46_im <= 1.15e-49) || (!(x_46_im <= 7.6e-25) && ((x_46_im <= 18.0) || (!(x_46_im <= 1300.0) && ((x_46_im <= 125000000.0) || (!(x_46_im <= 1.9e+75) && (x_46_im <= 5.8e+76)))))))))))))))))))))))))))))))))))))))))))) {
		tmp = x_46_im * -y_46_im;
	} else {
		tmp = x_46_re * y_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 <= -3.35e-34) or (not (x_46_im <= -5.6e-104) and ((x_46_im <= -9e-106) or (not (x_46_im <= -8.5e-113) and ((x_46_im <= -1.4e-114) or (not (x_46_im <= -9.6e-139) and ((x_46_im <= -7e-139) or (not (x_46_im <= -2.3e-147) and ((x_46_im <= -1.22e-147) or (not (x_46_im <= -4.2e-161) and ((x_46_im <= -4.8e-172) or (not (x_46_im <= -4.8e-192) and ((x_46_im <= -4.7e-192) or (not (x_46_im <= -1.5e-259) and ((x_46_im <= -8.6e-260) or (not (x_46_im <= -7.8e-271) and ((x_46_im <= -7.6e-271) or (not (x_46_im <= 1.3e-255) and ((x_46_im <= 1.35e-255) or (not (x_46_im <= 1.05e-248) and ((x_46_im <= 5.4e-248) or (not (x_46_im <= 2.4e-196) and ((x_46_im <= 2.5e-196) or (not (x_46_im <= 5e-187) and ((x_46_im <= 5.2e-187) or (not (x_46_im <= 2.3e-178) and ((x_46_im <= 2.35e-178) or (not (x_46_im <= 9.5e-150) and ((x_46_im <= 1.2e-120) or (not (x_46_im <= 1.55e-105) and ((x_46_im <= 2.35e-102) or (not (x_46_im <= 7.5e-95) and ((x_46_im <= 1.85e-90) or (not (x_46_im <= 1.4e-83) and ((x_46_im <= 1.45e-65) or not ((x_46_im <= 1.05e-58) or (not (x_46_im <= 9.6e-57) and ((x_46_im <= 1.15e-49) or (not (x_46_im <= 7.6e-25) and ((x_46_im <= 18.0) or (not (x_46_im <= 1300.0) and ((x_46_im <= 125000000.0) or (not (x_46_im <= 1.9e+75) and (x_46_im <= 5.8e+76))))))))))))))))))))))))))))))))))))))))))):
		tmp = x_46_im * -y_46_im
	else:
		tmp = x_46_re * y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((x_46_im <= -3.35e-34) || (!(x_46_im <= -5.6e-104) && ((x_46_im <= -9e-106) || (!(x_46_im <= -8.5e-113) && ((x_46_im <= -1.4e-114) || (!(x_46_im <= -9.6e-139) && ((x_46_im <= -7e-139) || (!(x_46_im <= -2.3e-147) && ((x_46_im <= -1.22e-147) || (!(x_46_im <= -4.2e-161) && ((x_46_im <= -4.8e-172) || (!(x_46_im <= -4.8e-192) && ((x_46_im <= -4.7e-192) || (!(x_46_im <= -1.5e-259) && ((x_46_im <= -8.6e-260) || (!(x_46_im <= -7.8e-271) && ((x_46_im <= -7.6e-271) || (!(x_46_im <= 1.3e-255) && ((x_46_im <= 1.35e-255) || (!(x_46_im <= 1.05e-248) && ((x_46_im <= 5.4e-248) || (!(x_46_im <= 2.4e-196) && ((x_46_im <= 2.5e-196) || (!(x_46_im <= 5e-187) && ((x_46_im <= 5.2e-187) || (!(x_46_im <= 2.3e-178) && ((x_46_im <= 2.35e-178) || (!(x_46_im <= 9.5e-150) && ((x_46_im <= 1.2e-120) || (!(x_46_im <= 1.55e-105) && ((x_46_im <= 2.35e-102) || (!(x_46_im <= 7.5e-95) && ((x_46_im <= 1.85e-90) || (!(x_46_im <= 1.4e-83) && ((x_46_im <= 1.45e-65) || !((x_46_im <= 1.05e-58) || (!(x_46_im <= 9.6e-57) && ((x_46_im <= 1.15e-49) || (!(x_46_im <= 7.6e-25) && ((x_46_im <= 18.0) || (!(x_46_im <= 1300.0) && ((x_46_im <= 125000000.0) || (!(x_46_im <= 1.9e+75) && (x_46_im <= 5.8e+76))))))))))))))))))))))))))))))))))))))))))))
		tmp = Float64(x_46_im * Float64(-y_46_im));
	else
		tmp = Float64(x_46_re * 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 ((x_46_im <= -3.35e-34) || (~((x_46_im <= -5.6e-104)) && ((x_46_im <= -9e-106) || (~((x_46_im <= -8.5e-113)) && ((x_46_im <= -1.4e-114) || (~((x_46_im <= -9.6e-139)) && ((x_46_im <= -7e-139) || (~((x_46_im <= -2.3e-147)) && ((x_46_im <= -1.22e-147) || (~((x_46_im <= -4.2e-161)) && ((x_46_im <= -4.8e-172) || (~((x_46_im <= -4.8e-192)) && ((x_46_im <= -4.7e-192) || (~((x_46_im <= -1.5e-259)) && ((x_46_im <= -8.6e-260) || (~((x_46_im <= -7.8e-271)) && ((x_46_im <= -7.6e-271) || (~((x_46_im <= 1.3e-255)) && ((x_46_im <= 1.35e-255) || (~((x_46_im <= 1.05e-248)) && ((x_46_im <= 5.4e-248) || (~((x_46_im <= 2.4e-196)) && ((x_46_im <= 2.5e-196) || (~((x_46_im <= 5e-187)) && ((x_46_im <= 5.2e-187) || (~((x_46_im <= 2.3e-178)) && ((x_46_im <= 2.35e-178) || (~((x_46_im <= 9.5e-150)) && ((x_46_im <= 1.2e-120) || (~((x_46_im <= 1.55e-105)) && ((x_46_im <= 2.35e-102) || (~((x_46_im <= 7.5e-95)) && ((x_46_im <= 1.85e-90) || (~((x_46_im <= 1.4e-83)) && ((x_46_im <= 1.45e-65) || ~(((x_46_im <= 1.05e-58) || (~((x_46_im <= 9.6e-57)) && ((x_46_im <= 1.15e-49) || (~((x_46_im <= 7.6e-25)) && ((x_46_im <= 18.0) || (~((x_46_im <= 1300.0)) && ((x_46_im <= 125000000.0) || (~((x_46_im <= 1.9e+75)) && (x_46_im <= 5.8e+76)))))))))))))))))))))))))))))))))))))))))))))
		tmp = x_46_im * -y_46_im;
	else
		tmp = x_46_re * y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[x$46$im, -3.35e-34], And[N[Not[LessEqual[x$46$im, -5.6e-104]], $MachinePrecision], Or[LessEqual[x$46$im, -9e-106], And[N[Not[LessEqual[x$46$im, -8.5e-113]], $MachinePrecision], Or[LessEqual[x$46$im, -1.4e-114], And[N[Not[LessEqual[x$46$im, -9.6e-139]], $MachinePrecision], Or[LessEqual[x$46$im, -7e-139], And[N[Not[LessEqual[x$46$im, -2.3e-147]], $MachinePrecision], Or[LessEqual[x$46$im, -1.22e-147], And[N[Not[LessEqual[x$46$im, -4.2e-161]], $MachinePrecision], Or[LessEqual[x$46$im, -4.8e-172], And[N[Not[LessEqual[x$46$im, -4.8e-192]], $MachinePrecision], Or[LessEqual[x$46$im, -4.7e-192], And[N[Not[LessEqual[x$46$im, -1.5e-259]], $MachinePrecision], Or[LessEqual[x$46$im, -8.6e-260], And[N[Not[LessEqual[x$46$im, -7.8e-271]], $MachinePrecision], Or[LessEqual[x$46$im, -7.6e-271], And[N[Not[LessEqual[x$46$im, 1.3e-255]], $MachinePrecision], Or[LessEqual[x$46$im, 1.35e-255], And[N[Not[LessEqual[x$46$im, 1.05e-248]], $MachinePrecision], Or[LessEqual[x$46$im, 5.4e-248], And[N[Not[LessEqual[x$46$im, 2.4e-196]], $MachinePrecision], Or[LessEqual[x$46$im, 2.5e-196], And[N[Not[LessEqual[x$46$im, 5e-187]], $MachinePrecision], Or[LessEqual[x$46$im, 5.2e-187], And[N[Not[LessEqual[x$46$im, 2.3e-178]], $MachinePrecision], Or[LessEqual[x$46$im, 2.35e-178], And[N[Not[LessEqual[x$46$im, 9.5e-150]], $MachinePrecision], Or[LessEqual[x$46$im, 1.2e-120], And[N[Not[LessEqual[x$46$im, 1.55e-105]], $MachinePrecision], Or[LessEqual[x$46$im, 2.35e-102], And[N[Not[LessEqual[x$46$im, 7.5e-95]], $MachinePrecision], Or[LessEqual[x$46$im, 1.85e-90], And[N[Not[LessEqual[x$46$im, 1.4e-83]], $MachinePrecision], Or[LessEqual[x$46$im, 1.45e-65], N[Not[Or[LessEqual[x$46$im, 1.05e-58], And[N[Not[LessEqual[x$46$im, 9.6e-57]], $MachinePrecision], Or[LessEqual[x$46$im, 1.15e-49], And[N[Not[LessEqual[x$46$im, 7.6e-25]], $MachinePrecision], Or[LessEqual[x$46$im, 18.0], And[N[Not[LessEqual[x$46$im, 1300.0]], $MachinePrecision], Or[LessEqual[x$46$im, 125000000.0], And[N[Not[LessEqual[x$46$im, 1.9e+75]], $MachinePrecision], LessEqual[x$46$im, 5.8e+76]]]]]]]]]], $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]], N[(x$46$im * (-y$46$im)), $MachinePrecision], N[(x$46$re * y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x.im < -3.3500000000000002e-34 or -5.6e-104 < x.im < -8.99999999999999911e-106 or -8.4999999999999995e-113 < x.im < -1.4000000000000001e-114 or -9.60000000000000059e-139 < x.im < -7.00000000000000002e-139 or -2.2999999999999999e-147 < x.im < -1.21999999999999995e-147 or -4.2000000000000001e-161 < x.im < -4.8000000000000002e-172 or -4.7999999999999998e-192 < x.im < -4.6999999999999997e-192 or -1.5000000000000001e-259 < x.im < -8.60000000000000043e-260 or -7.79999999999999995e-271 < x.im < -7.60000000000000019e-271 or 1.3000000000000001e-255 < x.im < 1.35000000000000008e-255 or 1.05e-248 < x.im < 5.4000000000000002e-248 or 2.40000000000000021e-196 < x.im < 2.5000000000000002e-196 or 4.9999999999999996e-187 < x.im < 5.1999999999999999e-187 or 2.29999999999999994e-178 < x.im < 2.35e-178 or 9.50000000000000013e-150 < x.im < 1.2e-120 or 1.55000000000000007e-105 < x.im < 2.3500000000000001e-102 or 7.5000000000000003e-95 < x.im < 1.85000000000000009e-90 or 1.4e-83 < x.im < 1.4499999999999999e-65 or 1.04999999999999994e-58 < x.im < 9.60000000000000025e-57 or 1.15e-49 < x.im < 7.5999999999999996e-25 or 18 < x.im < 1300 or 1.25e8 < x.im < 1.9000000000000001e75 or 5.8000000000000003e76 < x.im

   1. Initial program 99.4%

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

   3. Taylor expanded in x.re around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-rgt-neg-out 69.3%

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

   5. Simplified 69.3%

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

   if -3.3500000000000002e-34 < x.im < -5.6e-104 or -8.99999999999999911e-106 < x.im < -8.4999999999999995e-113 or -1.4000000000000001e-114 < x.im < -9.60000000000000059e-139 or -7.00000000000000002e-139 < x.im < -2.2999999999999999e-147 or -1.21999999999999995e-147 < x.im < -4.2000000000000001e-161 or -4.8000000000000002e-172 < x.im < -4.7999999999999998e-192 or -4.6999999999999997e-192 < x.im < -1.5000000000000001e-259 or -8.60000000000000043e-260 < x.im < -7.79999999999999995e-271 or -7.60000000000000019e-271 < x.im < 1.3000000000000001e-255 or 1.35000000000000008e-255 < x.im < 1.05e-248 or 5.4000000000000002e-248 < x.im < 2.40000000000000021e-196 or 2.5000000000000002e-196 < x.im < 4.9999999999999996e-187 or 5.1999999999999999e-187 < x.im < 2.29999999999999994e-178 or 2.35e-178 < x.im < 9.50000000000000013e-150 or 1.2e-120 < x.im < 1.55000000000000007e-105 or 2.3500000000000001e-102 < x.im < 7.5000000000000003e-95 or 1.85000000000000009e-90 < x.im < 1.4e-83 or 1.4499999999999999e-65 < x.im < 1.04999999999999994e-58 or 9.60000000000000025e-57 < x.im < 1.15e-49 or 7.5999999999999996e-25 < x.im < 18 or 1300 < x.im < 1.25e8 or 1.9000000000000001e75 < x.im < 5.8000000000000003e76

   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 inf 90.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq -3.35 \cdot 10^{-34} \lor \neg \left(x.im \leq -5.6 \cdot 10^{-104}\right) \land \left(x.im \leq -9 \cdot 10^{-106} \lor \neg \left(x.im \leq -8.5 \cdot 10^{-113}\right) \land \left(x.im \leq -1.4 \cdot 10^{-114} \lor \neg \left(x.im \leq -9.6 \cdot 10^{-139}\right) \land \left(x.im \leq -7 \cdot 10^{-139} \lor \neg \left(x.im \leq -2.3 \cdot 10^{-147}\right) \land \left(x.im \leq -1.22 \cdot 10^{-147} \lor \neg \left(x.im \leq -4.2 \cdot 10^{-161}\right) \land \left(x.im \leq -4.8 \cdot 10^{-172} \lor \neg \left(x.im \leq -4.8 \cdot 10^{-192}\right) \land \left(x.im \leq -4.7 \cdot 10^{-192} \lor \neg \left(x.im \leq -1.5 \cdot 10^{-259}\right) \land \left(x.im \leq -8.6 \cdot 10^{-260} \lor \neg \left(x.im \leq -7.8 \cdot 10^{-271}\right) \land \left(x.im \leq -7.6 \cdot 10^{-271} \lor \neg \left(x.im \leq 1.3 \cdot 10^{-255}\right) \land \left(x.im \leq 1.35 \cdot 10^{-255} \lor \neg \left(x.im \leq 1.05 \cdot 10^{-248}\right) \land \left(x.im \leq 5.4 \cdot 10^{-248} \lor \neg \left(x.im \leq 2.4 \cdot 10^{-196}\right) \land \left(x.im \leq 2.5 \cdot 10^{-196} \lor \neg \left(x.im \leq 5 \cdot 10^{-187}\right) \land \left(x.im \leq 5.2 \cdot 10^{-187} \lor \neg \left(x.im \leq 2.3 \cdot 10^{-178}\right) \land \left(x.im \leq 2.35 \cdot 10^{-178} \lor \neg \left(x.im \leq 9.5 \cdot 10^{-150}\right) \land \left(x.im \leq 1.2 \cdot 10^{-120} \lor \neg \left(x.im \leq 1.55 \cdot 10^{-105}\right) \land \left(x.im \leq 2.35 \cdot 10^{-102} \lor \neg \left(x.im \leq 7.5 \cdot 10^{-95}\right) \land \left(x.im \leq 1.85 \cdot 10^{-90} \lor \neg \left(x.im \leq 1.4 \cdot 10^{-83}\right) \land \left(x.im \leq 1.45 \cdot 10^{-65} \lor \neg \left(x.im \leq 1.05 \cdot 10^{-58} \lor \neg \left(x.im \leq 9.6 \cdot 10^{-57}\right) \land \left(x.im \leq 1.15 \cdot 10^{-49} \lor \neg \left(x.im \leq 7.6 \cdot 10^{-25}\right) \land \left(x.im \leq 18 \lor \neg \left(x.im \leq 1300\right) \land \left(x.im \leq 125000000 \lor \neg \left(x.im \leq 1.9 \cdot 10^{+75}\right) \land x.im \leq 5.8 \cdot 10^{+76}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x.im \cdot \left(-y.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot y.re\\ \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)))