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

Average Error: 3.3 → 0.1

Time: 6.0s

Precision: binary64

Cost: 969

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+297} \lor \neg \left(y \cdot z \leq 10^{+259}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -5e+297) (not (<= (* y z) 1e+259)))
   (* z (* y (- x)))
   (* x (- 1.0 (* y z)))))

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+297) || !((y * z) <= 1e+259)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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+297)) .or. (.not. ((y * z) <= 1d+259))) then
        tmp = z * (y * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    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+297) || !((y * z) <= 1e+259)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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+297) or not ((y * z) <= 1e+259):
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	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+297) || !(Float64(y * z) <= 1e+259))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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+297) || ~(((y * z) <= 1e+259)))
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	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[Or[LessEqual[N[(y * z), $MachinePrecision], -5e+297], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+259]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.9999999999999998e297 or 9.999999999999999e258 < (*.f64 y z)

   1. Initial program 48.0

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

   2. Taylor expanded in y around inf 0.4

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

   3. Simplified 0.4

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

      [Start] 0.4	\[ -1 \cdot \left(y \cdot \left(z \cdot x\right)\right) \]
      mul-1-neg [=>] 0.4	\[ \color{blue}{-y \cdot \left(z \cdot x\right)} \]
      associate-*r* [=>] 48.0	\[ -\color{blue}{\left(y \cdot z\right) \cdot x} \]
      distribute-rgt-neg-in [=>] 48.0	\[ \color{blue}{\left(y \cdot z\right) \cdot \left(-x\right)} \]
      *-commutative [=>] 48.0	\[ \color{blue}{\left(z \cdot y\right)} \cdot \left(-x\right) \]
      associate-*l* [=>] 0.4	\[ \color{blue}{z \cdot \left(y \cdot \left(-x\right)\right)} \]

   if -4.9999999999999998e297 < (*.f64 y z) < 9.999999999999999e258

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+297} \lor \neg \left(y \cdot z \leq 10^{+259}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	17.9
Cost	1177

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+200}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+92}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+59} \lor \neg \left(y \leq 2.1 \cdot 10^{-102}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	17.7
Cost	1177

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+200}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+59} \lor \neg \left(y \leq 2.3 \cdot 10^{-102}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	18.6
Cost	914

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+225} \lor \neg \left(y \leq -3.1 \cdot 10^{+200}\right) \land \left(y \leq -7 \cdot 10^{+92} \lor \neg \left(y \leq 2.3 \cdot 10^{-102}\right)\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	25.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022356 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))