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

Percentage Accurate: 95.9% → 97.8%

Time: 5.4s

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: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 2e+177) (* x (- 1.0 (* y z))) (* y (* x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+177) {
		tmp = x * (1.0 - (y * z));
	} 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) :: tmp
    if ((y * z) <= 2d+177) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+177) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= 2e+177:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 2e+177)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 2e+177)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 2e+177], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 2e177

   1. Initial program 98.2%

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

   if 2e177 < (*.f64 y z)

   1. Initial program 71.6%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 2: 95.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{if}\;y \cdot z \leq -2000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot z \leq 0.005:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x (- z)))))
   (if (<= (* y z) -2000000000.0)
     t_0
     (if (<= (* y z) 0.005)
       x
       (if (<= (* y z) 2e+177) (* (* y z) (- x)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if ((y * z) <= -2000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.005) {
		tmp = x;
	} else if ((y * z) <= 2e+177) {
		tmp = (y * z) * -x;
	} else {
		tmp = t_0;
	}
	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 = y * (x * -z)
    if ((y * z) <= (-2000000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.005d0) then
        tmp = x
    else if ((y * z) <= 2d+177) then
        tmp = (y * z) * -x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if ((y * z) <= -2000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.005) {
		tmp = x;
	} else if ((y * z) <= 2e+177) {
		tmp = (y * z) * -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * -z)
	tmp = 0
	if (y * z) <= -2000000000.0:
		tmp = t_0
	elif (y * z) <= 0.005:
		tmp = x
	elif (y * z) <= 2e+177:
		tmp = (y * z) * -x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * Float64(-z)))
	tmp = 0.0
	if (Float64(y * z) <= -2000000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.005)
		tmp = x;
	elseif (Float64(y * z) <= 2e+177)
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * -z);
	tmp = 0.0;
	if ((y * z) <= -2000000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.005)
		tmp = x;
	elseif ((y * z) <= 2e+177)
		tmp = (y * z) * -x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -2000000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.005], x, If[LessEqual[N[(y * z), $MachinePrecision], 2e+177], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2e9 or 2e177 < (*.f64 y z)

   1. Initial program 86.9%

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

   2. Taylor expanded in y around inf 95.9%

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

      1. mul-1-neg 95.9%

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

      2. distribute-rgt-neg-in 95.9%

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

      3. distribute-lft-neg-out 95.9%

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

      4. *-commutative 95.9%

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

   4. Simplified 95.9%

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

   if -2e9 < (*.f64 y z) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

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

   if 0.0050000000000000001 < (*.f64 y z) < 2e177

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. associate-*r* 93.3%

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

      3. distribute-lft-neg-in 93.3%

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

      4. distribute-rgt-neg-out 93.3%

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

      5. *-commutative 93.3%

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

   4. Simplified 93.3%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000000:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.005:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 3: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000000 \lor \neg \left(y \cdot z \leq 0.005\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2000000000.0) (not (<= (* y z) 0.005)))
   (* (* y z) (- x))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2000000000.0) || !((y * z) <= 0.005)) {
		tmp = (y * z) * -x;
	} 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 (((y * z) <= (-2000000000.0d0)) .or. (.not. ((y * z) <= 0.005d0))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2000000000.0) || !((y * z) <= 0.005)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2000000000.0) or not ((y * z) <= 0.005):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2000000000.0) || !(Float64(y * z) <= 0.005))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -2000000000.0) || ~(((y * z) <= 0.005)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.005]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e9 or 0.0050000000000000001 < (*.f64 y z)

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. mul-1-neg 90.7%

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

      2. associate-*r* 88.1%

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

      3. distribute-lft-neg-in 88.1%

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

      4. distribute-rgt-neg-out 88.1%

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

      5. *-commutative 88.1%

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

   4. Simplified 88.1%

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

   if -2e9 < (*.f64 y z) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000000 \lor \neg \left(y \cdot z \leq 0.005\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 50.4% 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 95.4%

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

2. Taylor expanded in y around 0 54.4%

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

3. Final simplification 54.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))