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

Percentage Accurate: 95.9% → 99.2%

Time: 10.2s

Alternatives: 5

Speedup: 0.4×

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: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x (- z)))))
   (if (<= (* y z) -1e+174)
     t_0
     (if (<= (* y z) 2e+89) (* x (- 1.0 (* y z))) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if ((y * z) <= -1e+174) {
		tmp = t_0;
	} else if ((y * z) <= 2e+89) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (x * -z)
    if ((y * z) <= (-1d+174)) then
        tmp = t_0
    else if ((y * z) <= 2d+89) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if ((y * z) <= -1e+174) {
		tmp = t_0;
	} else if ((y * z) <= 2e+89) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = y * (x * -z)
	tmp = 0
	if (y * z) <= -1e+174:
		tmp = t_0
	elif (y * z) <= 2e+89:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(x * Float64(-z)))
	tmp = 0.0
	if (Float64(y * z) <= -1e+174)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e+89)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (x * -z);
	tmp = 0.0;
	if ((y * z) <= -1e+174)
		tmp = t_0;
	elseif ((y * z) <= 2e+89)
		tmp = x * (1.0 - (y * z));
	else
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -1e+174], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e+89], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000007e174 or 1.99999999999999999e89 < (*.f64 y z)

   1. Initial program 85.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -1.00000000000000007e174 < (*.f64 y z) < 1.99999999999999999e89

   1. Initial program 99.9%

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

Alternative 2: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4.2:\\ \;\;\;\;\left(x \cdot \left(-y\right)\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq 0.002:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

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) -4.2)
   (* (* x (- y)) z)
   (if (<= (* y z) 0.002) (* x 1.0) (* y (* x (- z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -4.2) {
		tmp = (x * -y) * z;
	} else if ((y * z) <= 0.002) {
		tmp = x * 1.0;
	} else {
		tmp = y * (x * -z);
	}
	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) <= (-4.2d0)) then
        tmp = (x * -y) * z
    else if ((y * z) <= 0.002d0) then
        tmp = x * 1.0d0
    else
        tmp = y * (x * -z)
    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) <= -4.2) {
		tmp = (x * -y) * z;
	} else if ((y * z) <= 0.002) {
		tmp = x * 1.0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -4.2:
		tmp = (x * -y) * z
	elif (y * z) <= 0.002:
		tmp = x * 1.0
	else:
		tmp = y * (x * -z)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -4.2)
		tmp = Float64(Float64(x * Float64(-y)) * z);
	elseif (Float64(y * z) <= 0.002)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	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) <= -4.2)
		tmp = (x * -y) * z;
	elseif ((y * z) <= 0.002)
		tmp = x * 1.0;
	else
		tmp = y * (x * -z);
	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], -4.2], N[(N[(x * (-y)), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.002], N[(x * 1.0), $MachinePrecision], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.20000000000000018

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 90.5

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

   5. Applied rewrites 90.5%

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

   7. Applied rewrites 90.2%

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

   if -4.20000000000000018 < (*.f64 y z) < 2e-3

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.9%

      \[\leadsto x \cdot \color{blue}{1} \]

   if 2e-3 < (*.f64 y z)

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 90.1

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

   5. Applied rewrites 90.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4.2:\\ \;\;\;\;\left(x \cdot \left(-y\right)\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq 0.002:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024229 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))