math.square on complex, real part

Percentage Accurate: 94.0% → 94.0%
Time: 2.1s
Alternatives: 1
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ re \cdot re - im \cdot im \end{array} \]
(FPCore re_sqr (re im) :precision binary64 (- (* re re) (* im im)))
double re_sqr(double re, double im) {
	return (re * re) - (im * 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

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

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

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

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

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

\begin{array}{l}

\\
re \cdot re - im \cdot im
\end{array}

Sampling outcomes in binary64 precision:

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.

Accuracy vs Speed?

Herbie found 1 alternatives:

AlternativeAccuracySpeedup
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.

Initial Program: 94.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ re \cdot re - im \cdot im \end{array} \]
(FPCore re_sqr (re im) :precision binary64 (- (* re re) (* im im)))
double re_sqr(double re, double im) {
	return (re * re) - (im * 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

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

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

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

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

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

\begin{array}{l}

\\
re \cdot re - im \cdot im
\end{array}

Alternative 1: 94.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ re \cdot re - im \cdot im \end{array} \]
(FPCore re_sqr (re im) :precision binary64 (- (* re re) (* im im)))
double re_sqr(double re, double im) {
	return (re * re) - (im * 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

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

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

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

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

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

\begin{array}{l}

\\
re \cdot re - im \cdot im
\end{array}
Derivation

  1. Initial program 95.7%

    \[re \cdot re - im \cdot im \]
  2. Add Preprocessing

Reproduce

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herbie shell --seed 2024180 -o setup:simplify
(FPCore re_sqr (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))