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

Percentage Accurate: 96.2% → 98.0%

Time: 3.8s

Alternatives: 4

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 6 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 6e+226) (* x (- 1.0 (* y z))) (* y (* z (- x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 6e+226) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this 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) <= 6d+226) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 6e+226) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 6e+226:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 6e+226)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 6e+226)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 6e+226], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.9999999999999995e226

   1. Initial program 98.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   if 5.9999999999999995e226 < (*.f64 y z)

   1. Initial program 69.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 69.8%

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

      2. associate-*r* 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 6 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+60} \lor \neg \left(y \leq 6.2 \cdot 10^{-156}\right):\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+60) (not (<= y 6.2e-156))) (* z (- (* y x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+60) || !(y <= 6.2e-156)) {
		tmp = z * -(y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this 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 <= (-5.8d+60)) .or. (.not. (y <= 6.2d-156))) then
        tmp = z * -(y * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+60) || !(y <= 6.2e-156)) {
		tmp = z * -(y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+60) or not (y <= 6.2e-156):
		tmp = z * -(y * x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+60) || !(y <= 6.2e-156))
		tmp = Float64(z * Float64(-Float64(y * x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e+60) || ~((y <= 6.2e-156)))
		tmp = z * -(y * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+60], N[Not[LessEqual[y, 6.2e-156]], $MachinePrecision]], N[(z * (-N[(y * x), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999999e60 or 6.1999999999999996e-156 < y

   1. Initial program 92.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 58.6%

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

      2. associate-*r* 61.3%

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

   5. Simplified 61.3%

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

   if -5.79999999999999999e60 < y < 6.1999999999999996e-156

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+60} \lor \neg \left(y \leq 6.2 \cdot 10^{-156}\right):\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -3e-198)
   (* y (* z (- x)))
   (if (<= z 8.8e+119) x (* z (- (* y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-198) {
		tmp = y * (z * -x);
	} else if (z <= 8.8e+119) {
		tmp = x;
	} else {
		tmp = z * -(y * x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this 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 (z <= (-3d-198)) then
        tmp = y * (z * -x)
    else if (z <= 8.8d+119) then
        tmp = x
    else
        tmp = z * -(y * x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-198) {
		tmp = y * (z * -x);
	} else if (z <= 8.8e+119) {
		tmp = x;
	} else {
		tmp = z * -(y * x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -3e-198:
		tmp = y * (z * -x)
	elif z <= 8.8e+119:
		tmp = x
	else:
		tmp = z * -(y * x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -3e-198)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (z <= 8.8e+119)
		tmp = x;
	else
		tmp = Float64(z * Float64(-Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e-198)
		tmp = y * (z * -x);
	elseif (z <= 8.8e+119)
		tmp = x;
	else
		tmp = z * -(y * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -3e-198], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+119], x, N[(z * (-N[(y * x), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e-198

   1. Initial program 94.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 65.0%

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

      2. associate-*r* 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. *-commutative 61.9%

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

      5. associate-*l* 65.1%

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

   5. Simplified 65.1%

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

   if -3.0000000000000001e-198 < z < 8.8000000000000005e119

   1. Initial program 99.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{x} \]

   if 8.8000000000000005e119 < z

   1. Initial program 86.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.5%

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

      2. associate-*r* 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.4% accurate, 7.0× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 95.1%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 46.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))