math.square on complex, imaginary part

?

Percentage Accurate: 100.0% → 100.0%
Time: 788.0ms
Precision: binary64
Cost: 320

?

\[re \cdot im + im \cdot re \]
↓
\[re \cdot \left(im + im\right) \]
(FPCore im_sqr (re im) :precision binary64 (+ (* re im) (* im re)))
↓
(FPCore im_sqr (re im) :precision binary64 (* re (+ im im)))
double im_sqr(double re, double im) {
	return (re * im) + (im * re);
}
↓
double im_sqr(double re, double im) {
	return re * (im + im);
}

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

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);
}

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

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

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

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]

re \cdot im + im \cdot re
↓
re \cdot \left(im + im\right)

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 1 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 100.0%

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

  2. Simplified100.0%

    \[\leadsto \color{blue}{re \cdot \left(im + im\right)} \]
    Step-by-step derivation

    [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 simplification100.0%

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

Reproduce?

herbie shell --seed 2023178 
(FPCore im_sqr (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))