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

Percentage Accurate: 96.2% → 98.0%

Time: 3.4s

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: 96.2% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= t_0 5e+296) (* x t_0) (* y (* x (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= 5e+296) {
		tmp = x * t_0;
	} else {
		tmp = y * (x * -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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if (t_0 <= 5d+296) then
        tmp = x * t_0
    else
        tmp = y * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= 5e+296) {
		tmp = x * t_0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if t_0 <= 5e+296:
		tmp = x * t_0
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= 5e+296)
		tmp = Float64(x * t_0);
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= 5e+296)
		tmp = x * t_0;
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+296], N[(x * t$95$0), $MachinePrecision], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 (*.f64 y z)) < 5.0000000000000001e296

   1. Initial program 98.2%

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

   if 5.0000000000000001e296 < (-.f64 1 (*.f64 y z))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-in 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. *-commutative 99.9%

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

   4. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 2: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-79} \lor \neg \left(z \leq 4.2 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e-79) (not (<= z 4.2e+55))) (* x (* y (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e-79) || !(z <= 4.2e+55)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if ((z <= (-6d-79)) .or. (.not. (z <= 4.2d+55))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e-79) || !(z <= 4.2e+55)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e-79) or not (z <= 4.2e+55):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e-79) || !(z <= 4.2e+55))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e-79) || ~((z <= 4.2e+55)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e-79], N[Not[LessEqual[z, 4.2e+55]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999999e-79 or 4.2000000000000001e55 < z

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate-*r* 69.4%

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

      3. distribute-lft-neg-in 69.4%

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

      4. distribute-rgt-neg-out 69.4%

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

      5. *-commutative 69.4%

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

   4. Simplified 69.4%

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

   if -5.99999999999999999e-79 < z < 4.2000000000000001e55

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-79} \lor \neg \left(z \leq 4.2 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-79} \lor \neg \left(z \leq 4.2 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-79) (not (<= z 4.2e+55))) (* y (* x (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-79) || !(z <= 4.2e+55)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if ((z <= (-4.8d-79)) .or. (.not. (z <= 4.2d+55))) then
        tmp = y * (x * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-79) || !(z <= 4.2e+55)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-79) or not (z <= 4.2e+55):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-79) || !(z <= 4.2e+55))
		tmp = Float64(y * Float64(x * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-79) || ~((z <= 4.2e+55)))
		tmp = y * (x * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-79], N[Not[LessEqual[z, 4.2e+55]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000011e-79 or 4.2000000000000001e55 < z

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-rgt-neg-in 75.0%

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

      3. distribute-lft-neg-out 75.0%

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

      4. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   if -4.80000000000000011e-79 < z < 4.2000000000000001e55

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-79} \lor \neg \left(z \leq 4.2 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - (y * (x * 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 - (y * (x * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

2. Taylor expanded in x around 0 95.8%

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

   1. *-commutative 95.8%

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

   2. distribute-rgt-out-- 95.9%

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

   3. associate-*r* 94.3%

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

   4. *-lft-identity 94.3%

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

4. Simplified 94.3%

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

5. Final simplification 94.3%

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

Alternative 5: 51.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.8%

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

2. Taylor expanded in y around 0 52.4%

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

3. Final simplification 52.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))