math.square on complex, imaginary part

Percentage Accurate: 56.4% → 56.4%

Time: 1.3s

Alternatives: 3

Speedup: 1.4×

Specification

Math

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

FPCore

(FPCore im_sqr (re im) :precision binary64 (+ (* re im) (* im re)))

C

double im_sqr(double re, double im) {
	return (re * im) + (im * 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 im_sqr(re, im)
use fmin_fmax_functions
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    im_sqr = (re * im) + (im * re)
end function

Java

public static double im_sqr(double re, double im) {
	return (re * im) + (im * re);
}

Python

def im_sqr(re, im):
	return (re * im) + (im * re)

Julia

function im_sqr(re, im)
	return Float64(Float64(re * im) + Float64(im * re))
end

MATLAB

function tmp = im_sqr(re, im)
	tmp = (re * im) + (im * re);
end

Wolfram

im$95$sqr[re_, im_] := N[(N[(re * im), $MachinePrecision] + N[(im * re), $MachinePrecision]), $MachinePrecision]

Initial Program: 56.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore im_sqr (re im) :precision binary64 (+ (* re im) (* im re)))

C

double im_sqr(double re, double im) {
	return (re * im) + (im * 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 im_sqr(re, im)
use fmin_fmax_functions
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    im_sqr = (re * im) + (im * re)
end function

Java

public static double im_sqr(double re, double im) {
	return (re * im) + (im * re);
}

Python

def im_sqr(re, im):
	return (re * im) + (im * re)

Julia

function im_sqr(re, im)
	return Float64(Float64(re * im) + Float64(im * re))
end

MATLAB

function tmp = im_sqr(re, im)
	tmp = (re * im) + (im * re);
end

Wolfram

im$95$sqr[re_, im_] := N[(N[(re * im), $MachinePrecision] + N[(im * re), $MachinePrecision]), $MachinePrecision]

Alternative 1: 56.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} re_m = \left|re\right| \\ im_m = \left|im\right| \\ 2 \cdot \left(im\_m \cdot re\_m\right) \end{array} \]

FPCore

re_m = (fabs.f64 re)
im_m = (fabs.f64 im)
(FPCore im_sqr (re_m im_m) :precision binary64 (* 2.0 (* im_m re_m)))

C

re_m = fabs(re);
im_m = fabs(im);
double im_sqr(double re_m, double im_m) {
	return 2.0 * (im_m * re_m);
}

Fortran

re_m =     private
im_m =     private
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 im_sqr(re_m, im_m)
use fmin_fmax_functions
    real(8), intent (in) :: re_m
    real(8), intent (in) :: im_m
    im_sqr = 2.0d0 * (im_m * re_m)
end function

Java

re_m = Math.abs(re);
im_m = Math.abs(im);
public static double im_sqr(double re_m, double im_m) {
	return 2.0 * (im_m * re_m);
}

Python

re_m = math.fabs(re)
im_m = math.fabs(im)
def im_sqr(re_m, im_m):
	return 2.0 * (im_m * re_m)

Julia

re_m = abs(re)
im_m = abs(im)
function im_sqr(re_m, im_m)
	return Float64(2.0 * Float64(im_m * re_m))
end

MATLAB

re_m = abs(re);
im_m = abs(im);
function tmp = im_sqr(re_m, im_m)
	tmp = 2.0 * (im_m * re_m);
end

Wolfram

re_m = N[Abs[re], $MachinePrecision]
im_m = N[Abs[im], $MachinePrecision]
im$95$sqr[re$95$m_, im$95$m_] := N[(2.0 * N[(im$95$m * re$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 56.4%

   \[re \cdot im + im \cdot re \]

2. Taylor expanded in re around 0

   \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)} \]

4. Applied rewrites 56.4%

   \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)} \]
5. Add Preprocessing

Alternative 2: 26.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} re_m = \left|re\right| \\ im_m = \left|im\right| \\ im\_m \cdot re\_m \end{array} \]

FPCore

re_m = (fabs.f64 re)
im_m = (fabs.f64 im)
(FPCore im_sqr (re_m im_m) :precision binary64 (* im_m re_m))

C

re_m = fabs(re);
im_m = fabs(im);
double im_sqr(double re_m, double im_m) {
	return im_m * re_m;
}

Fortran

re_m =     private
im_m =     private
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 im_sqr(re_m, im_m)
use fmin_fmax_functions
    real(8), intent (in) :: re_m
    real(8), intent (in) :: im_m
    im_sqr = im_m * re_m
end function

Java

re_m = Math.abs(re);
im_m = Math.abs(im);
public static double im_sqr(double re_m, double im_m) {
	return im_m * re_m;
}

Python

re_m = math.fabs(re)
im_m = math.fabs(im)
def im_sqr(re_m, im_m):
	return im_m * re_m

Julia

re_m = abs(re)
im_m = abs(im)
function im_sqr(re_m, im_m)
	return Float64(im_m * re_m)
end

MATLAB

re_m = abs(re);
im_m = abs(im);
function tmp = im_sqr(re_m, im_m)
	tmp = im_m * re_m;
end

Wolfram

re_m = N[Abs[re], $MachinePrecision]
im_m = N[Abs[im], $MachinePrecision]
im$95$sqr[re$95$m_, im$95$m_] := N[(im$95$m * re$95$m), $MachinePrecision]

Derivation

1. Initial program 56.4%

   \[re \cdot im + im \cdot re \]

2. Taylor expanded in re around 0

   \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)} \]

4. Applied rewrites 56.4%

   \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)} \]

6. Applied rewrites 26.1%

   \[\leadsto im \cdot \color{blue}{re} \]
7. Add Preprocessing

Alternative 3: 14.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} re_m = \left|re\right| \\ im_m = \left|im\right| \\ 0 \end{array} \]

FPCore

re_m = (fabs.f64 re)
im_m = (fabs.f64 im)
(FPCore im_sqr (re_m im_m) :precision binary64 0.0)

C

re_m = fabs(re);
im_m = fabs(im);
double im_sqr(double re_m, double im_m) {
	return 0.0;
}

Fortran

re_m =     private
im_m =     private
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 im_sqr(re_m, im_m)
use fmin_fmax_functions
    real(8), intent (in) :: re_m
    real(8), intent (in) :: im_m
    im_sqr = 0.0d0
end function

Java

re_m = Math.abs(re);
im_m = Math.abs(im);
public static double im_sqr(double re_m, double im_m) {
	return 0.0;
}

Python

re_m = math.fabs(re)
im_m = math.fabs(im)
def im_sqr(re_m, im_m):
	return 0.0

Julia

re_m = abs(re)
im_m = abs(im)
function im_sqr(re_m, im_m)
	return 0.0
end

MATLAB

re_m = abs(re);
im_m = abs(im);
function tmp = im_sqr(re_m, im_m)
	tmp = 0.0;
end

Wolfram

re_m = N[Abs[re], $MachinePrecision]
im_m = N[Abs[im], $MachinePrecision]
im$95$sqr[re$95$m_, im$95$m_] := 0.0

Derivation

1. Initial program 56.4%

   \[re \cdot im + im \cdot re \]

3. Applied rewrites 14.9%

   \[\leadsto \color{blue}{0} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2025159 
(FPCore im_sqr (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))