Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Average Error: 3.2 → 1.6

Time: 4.5s

Precision: binary64

Cost: 708

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ \end{array} \]

Math

\[x \cdot \left(1 - y \cdot z\right) \]

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

↓

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+291) (- x (* (* y z) x)) (* y (* z (- x)))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

↓

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+291) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= 5d+291) then
        tmp = x - ((y * z) * x)
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

↓

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+291) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

↓

def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+291:
		tmp = x - ((y * z) * x)
	else:
		tmp = y * (z * -x)
	return tmp

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

↓

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+291)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+291)
		tmp = x - ((y * z) * x);
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+291], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.0000000000000001e291

   1. Initial program 1.6

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Applied egg-rr 1.6

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

   3. Applied egg-rr 1.6

      \[\leadsto \color{blue}{x - x \cdot \left(y \cdot z\right)} \]

   if 5.0000000000000001e291 < (*.f64 y z)

   1. Initial program 51.9

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 0.3

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]

   3. Simplified 0.3

      \[\leadsto \color{blue}{y \cdot \left(x \cdot \left(-z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	17.5
Cost	648

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{if}\;z \leq -6.896432240800852 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	25.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))