math.square on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 787.0ms

Precision: binary64

Cost: 320

Math

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

↓

\[\left(re \cdot 2\right) \cdot im \]

FPCore

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

↓

(FPCore im_sqr (re im) :precision binary64 (* (* re 2.0) im))

C

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

↓

double im_sqr(double re, double im) {
	return (re * 2.0) * 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 * 2.0d0) * 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 * 2.0) * im;
}

Python

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

↓

def im_sqr(re, im):
	return (re * 2.0) * im

Julia

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

↓

function im_sqr(re, im)
	return Float64(Float64(re * 2.0) * im)
end

MATLAB

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

↓

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

Wolfram

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

↓

im$95$sqr[re_, im_] := N[(N[(re * 2.0), $MachinePrecision] * im), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{re \cdot im + re \cdot im} \]
   Proof

   [Start] 0.0	\[ re \cdot im + im \cdot re \]
   rational.json-simplify-2 [<=] 0.0	\[ re \cdot im + \color{blue}{re \cdot im} \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

   \[\leadsto \left(re \cdot 2\right) \cdot im \]

Reproduce

herbie shell --seed 2023053 
(FPCore im_sqr (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))