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

Percentage Accurate: 95.9% → 97.7%

Time: 3.7s

Alternatives: 4

Speedup: 0.6×

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: 95.9% 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: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -2e+129) (* y (* x (- z))) (* x (- 1.0 (* y z)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2e+129) {
		tmp = y * (x * -z);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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 * z) <= (-2d+129)) then
        tmp = y * (x * -z)
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2e+129) {
		tmp = y * (x * -z);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -2e+129:
		tmp = y * (x * -z)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -2e+129)
		tmp = Float64(y * Float64(x * Float64(-z)));
	else
		tmp = Float64(x * Float64(1.0 - 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 ((y * z) <= -2e+129)
		tmp = y * (x * -z);
	else
		tmp = x * (1.0 - (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[(y * z), $MachinePrecision], -2e+129], N[(y * N[(x * (-z)), $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) < -2e129

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 97.0%

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

      1. mul-1-neg 97.0%

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

      2. distribute-rgt-neg-in 97.0%

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

      3. distribute-lft-neg-out 97.0%

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

      4. *-commutative 97.0%

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

   4. Simplified 97.0%

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

   if -2e129 < (*.f64 y z)

   1. Initial program 98.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 2: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+107} \lor \neg \left(y \leq 4.8 \cdot 10^{-149}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.42e+107) (not (<= y 4.8e-149))) (* x (* z (- y))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42e+107) || !(y <= 4.8e-149)) {
		tmp = x * (z * -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 <= (-1.42d+107)) .or. (.not. (y <= 4.8d-149))) then
        tmp = x * (z * -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 <= -1.42e+107) || !(y <= 4.8e-149)) {
		tmp = x * (z * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -1.42e+107) or not (y <= 4.8e-149):
		tmp = x * (z * -y)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.42e+107) || !(y <= 4.8e-149))
		tmp = Float64(x * Float64(z * 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 <= -1.42e+107) || ~((y <= 4.8e-149)))
		tmp = x * (z * -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, -1.42e+107], N[Not[LessEqual[y, 4.8e-149]], $MachinePrecision]], N[(x * N[(z * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.42000000000000006e107 or 4.8000000000000002e-149 < y

   1. Initial program 92.6%

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

   2. Taylor expanded in y around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-*r* 67.8%

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

      3. distribute-lft-neg-in 67.8%

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

      4. distribute-rgt-neg-out 67.8%

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

      5. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -1.42000000000000006e107 < y < 4.8000000000000002e-149

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+107} \lor \neg \left(y \leq 4.8 \cdot 10^{-149}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+98} \lor \neg \left(y \leq 5.5 \cdot 10^{-175}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+98) (not (<= y 5.5e-175))) (* y (* x (- z))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+98) || !(y <= 5.5e-175)) {
		tmp = y * (x * -z);
	} 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 <= (-1.1d+98)) .or. (.not. (y <= 5.5d-175))) then
        tmp = y * (x * -z)
    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 <= -1.1e+98) || !(y <= 5.5e-175)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+98) or not (y <= 5.5e-175):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+98) || !(y <= 5.5e-175))
		tmp = Float64(y * Float64(x * Float64(-z)));
	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 <= -1.1e+98) || ~((y <= 5.5e-175)))
		tmp = y * (x * -z);
	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, -1.1e+98], N[Not[LessEqual[y, 5.5e-175]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000004e98 or 5.50000000000000054e-175 < y

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-rgt-neg-in 68.1%

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

      3. distribute-lft-neg-out 68.1%

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

      4. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   if -1.10000000000000004e98 < y < 5.50000000000000054e-175

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+98} \lor \neg \left(y \leq 5.5 \cdot 10^{-175}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 50.0% 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 95.5%

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

2. Taylor expanded in y around 0 49.0%

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

3. Final simplification 49.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))