math.square on complex, imaginary part

Average Accuracy: 100.0% → 100.0%

Time: 1.3s

Precision: binary64

Cost: 320

Math

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

↓

\[re \cdot \left(im + im\right) \]

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function im_sqr(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    im_sqr = (re * im) + (im * re)
end function

↓

real(8) function im_sqr(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    im_sqr = re * (im + im)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Simplified 100.0%

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

   [Start] 100.0	\[ re \cdot im + im \cdot re \]
   *-commutative [=>] 100.0	\[ \color{blue}{im \cdot re} + im \cdot re \]
   distribute-rgt-out [=>] 100.0	\[ \color{blue}{re \cdot \left(im + im\right)} \]

3. Final simplification 100.0%

   \[\leadsto re \cdot \left(im + im\right) \]

Reproduce

herbie shell --seed 2023137 
(FPCore im_sqr (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))