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

Percentage Accurate: 96.0% → 99.8%

Time: 4.3s

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: 96.0% 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: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+252} \lor \neg \left(y \cdot z \leq 10^{+191}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+252) (not (<= (* y z) 1e+191)))
   (- (* z (* y x)))
   (- x (* (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+252) || !((y * z) <= 1e+191)) {
		tmp = -(z * (y * x));
	} 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+252)) .or. (.not. ((y * z) <= 1d+191))) then
        tmp = -(z * (y * x))
    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+252) || !((y * z) <= 1e+191)) {
		tmp = -(z * (y * x));
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+252) or not ((y * z) <= 1e+191):
		tmp = -(z * (y * x))
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2e+252) || !(Float64(y * z) <= 1e+191))
		tmp = Float64(-Float64(z * Float64(y * x)));
	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+252) || ~(((y * z) <= 1e+191)))
		tmp = -(z * (y * x));
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2e+252], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+191]], $MachinePrecision]], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.0000000000000002e252 or 1.00000000000000007e191 < (*.f64 y z)

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. associate-*r* 100.0%

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

   4. Simplified 100.0%

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

   if -2.0000000000000002e252 < (*.f64 y z) < 1.00000000000000007e191

   1. Initial program 99.9%

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

      1. flip-- 94.9%

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

      2. associate-*r/ 92.7%

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

      3. metadata-eval 92.7%

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

      4. pow2 92.7%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

      5. +-commutative 92.7%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{y \cdot z + 1}} \]

      6. fma-def 92.7%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{\mathsf{fma}\left(y, z, 1\right)}} \]

   3. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\mathsf{fma}\left(y, z, 1\right)}} \]
   4. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{\mathsf{fma}\left(y, z, 1\right)}{1 - {\left(y \cdot z\right)}^{2}}}} \]

   5. Simplified 94.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{\mathsf{fma}\left(y, z, 1\right)}{1 - {\left(y \cdot z\right)}^{2}}}} \]

   6. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 94.6%

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

   8. Simplified 94.6%

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

   9. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+252} \lor \neg \left(y \cdot z \leq 10^{+191}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]

Alternative 2: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+252} \lor \neg \left(y \cdot z \leq 10^{+191}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+252) (not (<= (* y z) 1e+191)))
   (- (* z (* y x)))
   (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+252) || !((y * z) <= 1e+191)) {
		tmp = -(z * (y * x));
	} 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+252)) .or. (.not. ((y * z) <= 1d+191))) then
        tmp = -(z * (y * x))
    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+252) || !((y * z) <= 1e+191)) {
		tmp = -(z * (y * x));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+252) or not ((y * z) <= 1e+191):
		tmp = -(z * (y * x))
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2e+252) || !(Float64(y * z) <= 1e+191))
		tmp = Float64(-Float64(z * Float64(y * x)));
	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+252) || ~(((y * z) <= 1e+191)))
		tmp = -(z * (y * x));
	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+252], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+191]], $MachinePrecision]], (-N[(z * N[(y * x), $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) < -2.0000000000000002e252 or 1.00000000000000007e191 < (*.f64 y z)

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. associate-*r* 100.0%

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

   4. Simplified 100.0%

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

   if -2.0000000000000002e252 < (*.f64 y z) < 1.00000000000000007e191

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+252} \lor \neg \left(y \cdot z \leq 10^{+191}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 3: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-80} \lor \neg \left(z \leq 1.55 \cdot 10^{+77}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-80) (not (<= z 1.55e+77))) (- (* z (* y x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-80) || !(z <= 1.55e+77)) {
		tmp = -(z * (y * 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 ((z <= (-5.3d-80)) .or. (.not. (z <= 1.55d+77))) then
        tmp = -(z * (y * x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-80) || !(z <= 1.55e+77)) {
		tmp = -(z * (y * x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.3e-80) or not (z <= 1.55e+77):
		tmp = -(z * (y * x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.3e-80) || !(z <= 1.55e+77))
		tmp = Float64(-Float64(z * Float64(y * x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.3e-80) || ~((z <= 1.55e+77)))
		tmp = -(z * (y * x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.3e-80], N[Not[LessEqual[z, 1.55e+77]], $MachinePrecision]], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if z < -5.30000000000000026e-80 or 1.54999999999999999e77 < z

   1. Initial program 91.0%

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

   2. Taylor expanded in y around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. associate-*r* 68.1%

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

   4. Simplified 68.1%

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

   if -5.30000000000000026e-80 < z < 1.54999999999999999e77

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-80} \lor \neg \left(z \leq 1.55 \cdot 10^{+77}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-80} \lor \neg \left(z \leq 2.1 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-80) (not (<= z 2.1e+78))) (* y (* z (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-80) || !(z <= 2.1e+78)) {
		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 ((z <= (-5.3d-80)) .or. (.not. (z <= 2.1d+78))) 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 ((z <= -5.3e-80) || !(z <= 2.1e+78)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.3e-80) or not (z <= 2.1e+78):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.3e-80) || !(z <= 2.1e+78))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.3e-80) || ~((z <= 2.1e+78)))
		tmp = y * (z * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.3e-80], N[Not[LessEqual[z, 2.1e+78]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.30000000000000026e-80 or 2.1000000000000001e78 < z

   1. Initial program 91.0%

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

   2. Taylor expanded in y around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. associate-*r* 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

      4. *-commutative 68.1%

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

      5. associate-*r* 67.6%

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

      6. distribute-rgt-neg-out 67.6%

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

   4. Simplified 67.6%

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

   if -5.30000000000000026e-80 < z < 2.1000000000000001e78

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-80} \lor \neg \left(z \leq 2.1 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 51.2% 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 54.5%

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

3. Final simplification 54.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))