Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[re \cdot re - im \cdot im \]
↓
\[\left(re + im\right) \cdot \left(re - im\right) \]
(FPCore re_sqr (re im) :precision binary64 (- (* re re) (* im im)))
↓
(FPCore re_sqr (re im) :precision binary64 (* (+ re im) (- re im)))
double re_sqr(double re, double im) {
	return (re * re) - (im * im);
}
↓
double re_sqr(double re, double im) {
	return (re + im) * (re - im);
}

real(8) function re_sqr(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    re_sqr = (re * re) - (im * im)
end function
↓
real(8) function re_sqr(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    re_sqr = (re + im) * (re - im)
end function

public static double re_sqr(double re, double im) {
	return (re * re) - (im * im);
}
↓
public static double re_sqr(double re, double im) {
	return (re + im) * (re - im);
}

def re_sqr(re, im):
	return (re * re) - (im * im)
↓
def re_sqr(re, im):
	return (re + im) * (re - im)

function re_sqr(re, im)
	return Float64(Float64(re * re) - Float64(im * im))
end
↓
function re_sqr(re, im)
	return Float64(Float64(re + im) * Float64(re - im))
end

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

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

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

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re - im \cdot im \]

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022159 
(FPCore re_sqr (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))