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

Percentage Accurate: 96.5% → 99.4%

Time: 6.3s

Alternatives: 5

Speedup: 0.3×

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: 96.5% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+301} \lor \neg \left(y \cdot z \leq 10^{+132}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+301) (not (<= (* y z) 1e+132)))
   (* (* y x) (- z))
   (- x (* (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+301) || !((y * z) <= 1e+132)) {
		tmp = (y * x) * -z;
	} else {
		tmp = x - ((y * z) * 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) <= (-2d+301)) .or. (.not. ((y * z) <= 1d+132))) then
        tmp = (y * x) * -z
    else
        tmp = x - ((y * z) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+301) || !((y * z) <= 1e+132)) {
		tmp = (y * x) * -z;
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+301) or not ((y * z) <= 1e+132):
		tmp = (y * x) * -z
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2e+301) || !(Float64(y * z) <= 1e+132))
		tmp = Float64(Float64(y * x) * Float64(-z));
	else
		tmp = Float64(x - Float64(Float64(y * z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -2e+301) || ~(((y * z) <= 1e+132)))
		tmp = (y * x) * -z;
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2e+301], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+132]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.00000000000000011e301 or 9.99999999999999991e131 < (*.f64 y z)

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

   if -2.00000000000000011e301 < (*.f64 y z) < 9.99999999999999991e131

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-*r* 91.0%

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

   5. Simplified 91.0%

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

      1. unsub-neg 91.0%

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

      2. associate-*l* 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+301} \lor \neg \left(y \cdot z \leq 10^{+132}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+301} \lor \neg \left(y \cdot z \leq 10^{+132}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+301) (not (<= (* y z) 1e+132)))
   (* (* y x) (- z))
   (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+301) || !((y * z) <= 1e+132)) {
		tmp = (y * x) * -z;
	} else {
		tmp = x * (1.0 - (y * 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+301)) .or. (.not. ((y * z) <= 1d+132))) then
        tmp = (y * x) * -z
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+301) || !((y * z) <= 1e+132)) {
		tmp = (y * x) * -z;
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+301) or not ((y * z) <= 1e+132):
		tmp = (y * x) * -z
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2e+301) || !(Float64(y * z) <= 1e+132))
		tmp = Float64(Float64(y * x) * Float64(-z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -2e+301) || ~(((y * z) <= 1e+132)))
		tmp = (y * x) * -z;
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2e+301], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+132]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.00000000000000011e301 or 9.99999999999999991e131 < (*.f64 y z)

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

   if -2.00000000000000011e301 < (*.f64 y z) < 9.99999999999999991e131

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+301} \lor \neg \left(y \cdot z \leq 10^{+132}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 0.005:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+19)
   (* (* y x) (- z))
   (if (<= (* y z) 0.005) x (* y (* x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+19) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 0.005) {
		tmp = x;
	} 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) <= (-5d+19)) then
        tmp = (y * x) * -z
    else if ((y * z) <= 0.005d0) then
        tmp = x
    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) <= -5e+19) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 0.005) {
		tmp = x;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+19:
		tmp = (y * x) * -z
	elif (y * z) <= 0.005:
		tmp = x
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5e+19)
		tmp = Float64(Float64(y * x) * Float64(-z));
	elseif (Float64(y * z) <= 0.005)
		tmp = x;
	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) <= -5e+19)
		tmp = (y * x) * -z;
	elseif ((y * z) <= 0.005)
		tmp = x;
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+19], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.005], x, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5e19

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. associate-*r* 91.5%

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

   5. Simplified 91.5%

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

   if -5e19 < (*.f64 y z) < 0.0050000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

   if 0.0050000000000000001 < (*.f64 y z)

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. associate-*r* 91.2%

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

      3. distribute-rgt-neg-in 91.2%

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

      4. *-commutative 91.2%

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

      5. associate-*r* 91.3%

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

   5. Simplified 91.3%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 0.005:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{-71} \lor \neg \left(z \leq 135000000000\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.72e-71) (not (<= z 135000000000.0))) (* (* y x) (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.72e-71) || !(z <= 135000000000.0)) {
		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 <= (-1.72d-71)) .or. (.not. (z <= 135000000000.0d0))) 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 <= -1.72e-71) || !(z <= 135000000000.0)) {
		tmp = (y * x) * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.72e-71) or not (z <= 135000000000.0):
		tmp = (y * x) * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.72e-71) || !(z <= 135000000000.0))
		tmp = Float64(Float64(y * x) * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.72e-71) || ~((z <= 135000000000.0)))
		tmp = (y * x) * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.72e-71], N[Not[LessEqual[z, 135000000000.0]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.72e-71 or 1.35e11 < z

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-*r* 75.1%

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

   5. Simplified 75.1%

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

   if -1.72e-71 < z < 1.35e11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{-71} \lor \neg \left(z \leq 135000000000\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.1% 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 94.4%

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

3. Taylor expanded in y around 0 47.9%

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

4. Final simplification 47.9%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024048 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))