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

Percentage Accurate: 96.4% → 96.4%

Time: 4.1s

Alternatives: 5

Speedup: 1.0×

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: 96.4% 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: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. sub-neg 97.3%

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

   2. distribute-rgt-in 97.3%

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

   3. *-un-lft-identity 97.3%

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

   4. distribute-rgt-neg-in 97.3%

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

3. Applied egg-rr 97.3%

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

   1. associate-*l* 92.5%

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

   2. distribute-lft-neg-in 92.5%

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

   3. *-commutative 92.5%

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

   4. distribute-rgt-neg-out 92.5%

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

   5. distribute-lft-neg-in 92.5%

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

   6. add-sqr-sqrt 50.7%

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

   7. sqrt-unprod 62.8%

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

   8. sqr-neg 62.8%

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

   9. sqrt-unprod 29.6%

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

   10. add-sqr-sqrt 50.1%

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

   11. *-commutative 50.1%

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

   12. distribute-lft-neg-in 50.1%

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

   13. cancel-sign-sub-inv 50.1%

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

   14. associate-*l* 53.2%

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

   15. *-commutative 53.2%

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

   16. associate-*r* 52.2%

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

   17. *-commutative 52.2%

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

   18. associate-*r* 50.1%

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

   19. distribute-rgt-neg-in 50.1%

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

   20. add-sqr-sqrt 29.6%

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

   21. sqrt-unprod 62.8%

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

5. Applied egg-rr 92.5%

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

6. Taylor expanded in y around 0 97.3%

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

7. Final simplification 97.3%

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

Alternative 2: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-91} \lor \neg \left(z \leq 5.1 \cdot 10^{+106}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e-91) (not (<= z 5.1e+106))) (* z (* y (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-91) || !(z <= 5.1e+106)) {
		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 <= (-1.8d-91)) .or. (.not. (z <= 5.1d+106))) 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 <= -1.8e-91) || !(z <= 5.1e+106)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e-91) or not (z <= 5.1e+106):
		tmp = z * (y * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e-91) || !(z <= 5.1e+106))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e-91) || ~((z <= 5.1e+106)))
		tmp = z * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e-91], N[Not[LessEqual[z, 5.1e+106]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-91 or 5.09999999999999971e106 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*r* 65.2%

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

   4. Simplified 65.2%

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

   if -1.8e-91 < z < 5.09999999999999971e106

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-91} \lor \neg \left(z \leq 5.1 \cdot 10^{+106}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.16e-67)
   (* y (* z (- x)))
   (if (<= z 5.1e+106) x (* z (* y (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e-67) {
		tmp = y * (z * -x);
	} else if (z <= 5.1e+106) {
		tmp = x;
	} else {
		tmp = z * (y * -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 <= (-1.16d-67)) then
        tmp = y * (z * -x)
    else if (z <= 5.1d+106) then
        tmp = x
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e-67) {
		tmp = y * (z * -x);
	} else if (z <= 5.1e+106) {
		tmp = x;
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.16e-67:
		tmp = y * (z * -x)
	elif z <= 5.1e+106:
		tmp = x
	else:
		tmp = z * (y * -x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e-67)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (z <= 5.1e+106)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.16e-67)
		tmp = y * (z * -x);
	elseif (z <= 5.1e+106)
		tmp = x;
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e-67], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+106], x, N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16e-67

   1. Initial program 96.4%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. associate-*r* 61.4%

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

      3. distribute-rgt-neg-in 61.4%

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

      4. *-commutative 61.4%

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

      5. associate-*r* 61.4%

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

      6. distribute-rgt-neg-out 61.4%

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

   4. Simplified 61.4%

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

   if -1.16e-67 < z < 5.09999999999999971e106

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.5%

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

   if 5.09999999999999971e106 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. associate-*r* 80.7%

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

   4. Simplified 80.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 96.4% 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]

Derivation

1. Initial program 97.3%

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

2. Final simplification 97.3%

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

Alternative 5: 50.6% 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 97.3%

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

2. Taylor expanded in y around 0 54.3%

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

3. Final simplification 54.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023326 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))