_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 3.1s

Precision: binary64

Cost: 832

Math

\[x.re \cdot y.re - x.im \cdot y.im \]

↓

\[x.im \cdot y.im + \left(x.re \cdot y.re - x.im \cdot \left(y.im + y.im\right)\right) \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (- (* x.re y.re) (* x.im y.im)))

↓

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (+ (* x.im y.im) (- (* x.re y.re) (* x.im (+ y.im y.im)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return (x_46_re * y_46_re) - (x_46_im * y_46_im);
}

↓

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return (x_46_im * y_46_im) + ((x_46_re * y_46_re) - (x_46_im * (y_46_im + y_46_im)));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = (x_46re * y_46re) - (x_46im * y_46im)
end function

↓

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = (x_46im * y_46im) + ((x_46re * y_46re) - (x_46im * (y_46im + y_46im)))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return (x_46_re * y_46_re) - (x_46_im * y_46_im);
}

↓

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return (x_46_im * y_46_im) + ((x_46_re * y_46_re) - (x_46_im * (y_46_im + y_46_im)));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return (x_46_re * y_46_re) - (x_46_im * y_46_im)

↓

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return (x_46_im * y_46_im) + ((x_46_re * y_46_re) - (x_46_im * (y_46_im + y_46_im)))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(x_46_re * y_46_re) - Float64(x_46_im * y_46_im))
end

↓

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(x_46_im * y_46_im) + Float64(Float64(x_46_re * y_46_re) - Float64(x_46_im * Float64(y_46_im + y_46_im))))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = (x_46_re * y_46_re) - (x_46_im * y_46_im);
end

↓

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = (x_46_im * y_46_im) + ((x_46_re * y_46_re) - (x_46_im * (y_46_im + y_46_im)));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(N[(x$46$re * y$46$re), $MachinePrecision] - N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]

↓

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(N[(x$46$im * y$46$im), $MachinePrecision] + N[(N[(x$46$re * y$46$re), $MachinePrecision] - N[(x$46$im * N[(y$46$im + y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x.re \cdot y.re - x.im \cdot y.im \]

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.3
Cost	1296

\[\begin{array}{l} t_0 := -y.im \cdot x.im\\ \mathbf{if}\;x.re \cdot y.re \leq -3000000:\\ \;\;\;\;x.re \cdot y.re\\ \mathbf{elif}\;x.re \cdot y.re \leq 1.34 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x.re \cdot y.re \leq 3.65 \cdot 10^{-17}:\\ \;\;\;\;x.re \cdot y.re\\ \mathbf{elif}\;x.re \cdot y.re \leq 5.5 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot y.re\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

\[x.re \cdot y.re - x.im \cdot y.im \]

Alternative 3
Error	30.8
Cost	192

\[x.re \cdot y.re \]

Reproduce

herbie shell --seed 2023066 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))