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

Average Error: 3.1 → 0.1

Time: 3.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ t_1 := -y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 1.0463474943731297 \cdot 10^{+308}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))) (t_1 (- (* y (* x z)))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 1.0463474943731297e+308) t_0 t_1))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double t_1 = -(y * (x * z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= 1.0463474943731297e+308) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 t_0 = x * (1.0 - (y * z));
	double t_1 = -(y * (x * z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= 1.0463474943731297e+308) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	t_1 = -(y * (x * z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= 1.0463474943731297e+308:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	t_1 = Float64(-Float64(y * Float64(x * z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= 1.0463474943731297e+308)
		tmp = t_0;
	else
		tmp = t_1;
	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)
	t_0 = x * (1.0 - (y * z));
	t_1 = -(y * (x * z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= 1.0463474943731297e+308)
		tmp = t_0;
	else
		tmp = t_1;
	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_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, 1.0463474943731297e+308], t$95$0, t$95$1]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < -inf.0 or 1.04634749437312969e308 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 63.7

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

   2. Taylor expanded in y around inf 0.6

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

   3. Simplified 0.6

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 y z))) < 1.04634749437312969e308

   1. Initial program 0.1

      \[x \cdot \left(1 - y \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq -\infty:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \cdot \left(1 - y \cdot z\right) \leq 1.0463474943731297 \cdot 10^{+308}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))