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

Percentage Accurate: 96.4% → 98.1%

Time: 3.8s

Alternatives: 5

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: 96.4% 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: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((x * (1.0 - (y * z))) <= -((double) INFINITY)) {
		tmp = y * (z * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((x * (1.0 - (y * z))) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (x * (1.0 - (y * z))) <= -math.inf:
		tmp = y * (z * -x)
	else:
		tmp = x - (x * (y * z))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 66.4%

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

   2. Taylor expanded in y around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      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-*r* 99.9%

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

      6. distribute-rgt-neg-out 99.9%

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

   4. Simplified 99.9%

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

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

   1. Initial program 98.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 98.6%

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

      2. distribute-rgt-in 98.7%

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

      3. *-un-lft-identity 98.7%

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

      4. distribute-rgt-neg-in 98.7%

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

   3. Applied egg-rr 98.7%

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

4. Final simplification 98.8%

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

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 (- INFINITY)) (* y (* z (- x))) t_0)))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y * (z * -x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z * -x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y * (z * -x)
	else:
		tmp = t_0
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = y * (z * -x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 66.4%

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

   2. Taylor expanded in y around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      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-*r* 99.9%

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

      6. distribute-rgt-neg-out 99.9%

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

   4. Simplified 99.9%

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

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

   1. Initial program 98.6%

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

4. Final simplification 98.8%

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

Alternative 3: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+84} \lor \neg \left(y \leq 6.4 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+84) (not (<= y 6.4e-24))) (* z (* x (- y))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+84) || !(y <= 6.4e-24)) {
		tmp = z * (x * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-4d+84)) .or. (.not. (y <= 6.4d-24))) then
        tmp = z * (x * -y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+84) || !(y <= 6.4e-24)) {
		tmp = z * (x * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -4e+84) or not (y <= 6.4e-24):
		tmp = z * (x * -y)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+84) || !(y <= 6.4e-24))
		tmp = Float64(z * Float64(x * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+84) || ~((y <= 6.4e-24)))
		tmp = z * (x * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -4e+84], N[Not[LessEqual[y, 6.4e-24]], $MachinePrecision]], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000023e84 or 6.40000000000000025e-24 < y

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. associate-*r* 64.6%

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

   4. Simplified 64.6%

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

   if -4.00000000000000023e84 < y < 6.40000000000000025e-24

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+84} \lor \neg \left(y \leq 6.4 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+84) (* y (* z (- x))) (if (<= y 4.5e-25) x (* z (* x (- y))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+84) {
		tmp = y * (z * -x);
	} else if (y <= 4.5e-25) {
		tmp = x;
	} else {
		tmp = z * (x * -y);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-7d+84)) then
        tmp = y * (z * -x)
    else if (y <= 4.5d-25) then
        tmp = x
    else
        tmp = z * (x * -y)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+84) {
		tmp = y * (z * -x);
	} else if (y <= 4.5e-25) {
		tmp = x;
	} else {
		tmp = z * (x * -y);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if y <= -7e+84:
		tmp = y * (z * -x)
	elif y <= 4.5e-25:
		tmp = x
	else:
		tmp = z * (x * -y)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+84)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (y <= 4.5e-25)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+84)
		tmp = y * (z * -x);
	elseif (y <= 4.5e-25)
		tmp = x;
	else
		tmp = z * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -7e+84], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-25], x, N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999998e84

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. associate-*r* 71.3%

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

      3. distribute-rgt-neg-in 71.3%

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

      4. *-commutative 71.3%

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

      5. associate-*r* 72.7%

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

      6. distribute-rgt-neg-out 72.7%

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

   4. Simplified 72.7%

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

   if -6.9999999999999998e84 < y < 4.5000000000000001e-25

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.0%

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

   if 4.5000000000000001e-25 < y

   1. Initial program 89.1%

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

   2. Taylor expanded in y around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-*r* 59.1%

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

   4. Simplified 59.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 5: 50.9% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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 y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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. Taylor expanded in y around 0 55.9%

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

3. Final simplification 55.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))