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

Percentage Accurate: 96.0% → 96.9%

Time: 4.1s

Alternatives: 4

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: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 2e+40) (- x (* (* y z) x)) (* z (- (* y x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+40) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = z * -(y * x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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+40) then
        tmp = x - ((y * z) * x)
    else
        tmp = z * -(y * x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+40) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = z * -(y * x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 2e+40:
		tmp = x - ((y * z) * x)
	else:
		tmp = z * -(y * x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 2e+40)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(z * Float64(-Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 2e+40)
		tmp = x - ((y * z) * x);
	else
		tmp = z * -(y * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 2e+40], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(z * (-N[(y * x), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 2.00000000000000006e40

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-rgt-in 98.1%

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

      3. *-un-lft-identity 98.1%

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

      4. distribute-rgt-neg-in 98.1%

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

   4. Applied egg-rr 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l* 90.2%

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

      3. add-sqr-sqrt 49.7%

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

      4. sqrt-unprod 67.1%

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

      5. sqr-neg 67.1%

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

      6. sqrt-unprod 26.7%

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

      7. add-sqr-sqrt 56.2%

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

      8. associate-*r* 59.7%

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

      9. *-commutative 59.7%

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

      10. cancel-sign-sub 59.7%

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

      11. distribute-rgt-neg-out 59.7%

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

      12. *-commutative 59.7%

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

      13. associate-*r* 56.2%

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

      14. add-sqr-sqrt 29.5%

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

      15. sqrt-unprod 62.0%

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

      16. sqr-neg 62.0%

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

      17. sqrt-unprod 40.3%

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

      18. add-sqr-sqrt 90.2%

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

      19. associate-*l* 98.1%

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

   6. Applied egg-rr 98.1%

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

   if 2.00000000000000006e40 < (*.f64 y z)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. associate-*r* 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+83} \lor \neg \left(y \leq 4.2 \cdot 10^{-103}\right):\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+83) (not (<= y 4.2e-103))) (* z (- (* y x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+83) || !(y <= 4.2e-103)) {
		tmp = z * -(y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-1.8d+83)) .or. (.not. (y <= 4.2d-103))) then
        tmp = z * -(y * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+83) || !(y <= 4.2e-103)) {
		tmp = z * -(y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+83) or not (y <= 4.2e-103):
		tmp = z * -(y * x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+83) || !(y <= 4.2e-103))
		tmp = Float64(z * Float64(-Float64(y * x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+83) || ~((y <= 4.2e-103)))
		tmp = z * -(y * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+83], N[Not[LessEqual[y, 4.2e-103]], $MachinePrecision]], N[(z * (-N[(y * x), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e83 or 4.20000000000000009e-103 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. associate-*r* 70.5%

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

   5. Simplified 70.5%

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

   if -1.7999999999999999e83 < y < 4.20000000000000009e-103

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+83} \lor \neg \left(y \leq 4.2 \cdot 10^{-103}\right):\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 2e+40) (* x (- 1.0 (* y z))) (* z (- (* y x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+40) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * -(y * x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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+40) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = z * -(y * x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+40) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * -(y * x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 2e+40:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = z * -(y * x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 2e+40)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(z * Float64(-Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 2e+40)
		tmp = x * (1.0 - (y * z));
	else
		tmp = z * -(y * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 2e+40], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * (-N[(y * x), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 2.00000000000000006e40

   1. Initial program 98.1%

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

   if 2.00000000000000006e40 < (*.f64 y z)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. associate-*r* 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in y around 0 50.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))