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

Percentage Accurate: 96.1% → 98.8%

Time: 9.7s

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: 96.1% 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: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (* z (* x (- y)))))
   (if (<= (* y z) -5e+153)
     t_0
     (if (<= (* y z) 5e+67) (* x (- 1.0 (* y z))) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if ((y * z) <= -5e+153) {
		tmp = t_0;
	} else if ((y * z) <= 5e+67) {
		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 = z * (x * -y)
    if ((y * z) <= (-5d+153)) then
        tmp = t_0
    else if ((y * z) <= 5d+67) 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 = z * (x * -y);
	double tmp;
	if ((y * z) <= -5e+153) {
		tmp = t_0;
	} else if ((y * z) <= 5e+67) {
		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 = z * (x * -y)
	tmp = 0
	if (y * z) <= -5e+153:
		tmp = t_0
	elif (y * z) <= 5e+67:
		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(z * Float64(x * Float64(-y)))
	tmp = 0.0
	if (Float64(y * z) <= -5e+153)
		tmp = t_0;
	elseif (Float64(y * z) <= 5e+67)
		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 = z * (x * -y);
	tmp = 0.0;
	if ((y * z) <= -5e+153)
		tmp = t_0;
	elseif ((y * z) <= 5e+67)
		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[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5e+153], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 5e+67], 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) < -5.00000000000000018e153 or 4.99999999999999976e67 < (*.f64 y z)

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 85.6

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

   5. Simplified 85.6%

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

      1. distribute-rgt-neg-out N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lift-neg.f64 N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-*.f64 99.8

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-neg.f64 N/A

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

      10. distribute-lft-neg-out N/A

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

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

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

      12. lift-neg.f64 N/A

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

      13. lower-*.f64 99.8

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

   7. Applied egg-rr 99.8%

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

   if -5.00000000000000018e153 < (*.f64 y z) < 4.99999999999999976e67

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+153}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(y \cdot z\right) \cdot \left(-x\right)\\ t_1 := \left(-y\right) \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -4000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z) (- x))) (t_1 (* (- y) (* z x))))
   (if (<= (* y z) -5e+210)
     t_1
     (if (<= (* y z) -4000.0)
       t_0
       (if (<= (* y z) 5e-5) x (if (<= (* y z) 5e+277) t_0 t_1))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (y * z) * -x;
	double t_1 = -y * (z * x);
	double tmp;
	if ((y * z) <= -5e+210) {
		tmp = t_1;
	} else if ((y * z) <= -4000.0) {
		tmp = t_0;
	} else if ((y * z) <= 5e-5) {
		tmp = x;
	} else if ((y * z) <= 5e+277) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (y * z) * -x
    t_1 = -y * (z * x)
    if ((y * z) <= (-5d+210)) then
        tmp = t_1
    else if ((y * z) <= (-4000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 5d-5) then
        tmp = x
    else if ((y * z) <= 5d+277) then
        tmp = t_0
    else
        tmp = t_1
    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 * z) * -x;
	double t_1 = -y * (z * x);
	double tmp;
	if ((y * z) <= -5e+210) {
		tmp = t_1;
	} else if ((y * z) <= -4000.0) {
		tmp = t_0;
	} else if ((y * z) <= 5e-5) {
		tmp = x;
	} else if ((y * z) <= 5e+277) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (y * z) * -x
	t_1 = -y * (z * x)
	tmp = 0
	if (y * z) <= -5e+210:
		tmp = t_1
	elif (y * z) <= -4000.0:
		tmp = t_0
	elif (y * z) <= 5e-5:
		tmp = x
	elif (y * z) <= 5e+277:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(y * z) * Float64(-x))
	t_1 = Float64(Float64(-y) * Float64(z * x))
	tmp = 0.0
	if (Float64(y * z) <= -5e+210)
		tmp = t_1;
	elseif (Float64(y * z) <= -4000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 5e-5)
		tmp = x;
	elseif (Float64(y * z) <= 5e+277)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (y * z) * -x;
	t_1 = -y * (z * x);
	tmp = 0.0;
	if ((y * z) <= -5e+210)
		tmp = t_1;
	elseif ((y * z) <= -4000.0)
		tmp = t_0;
	elseif ((y * z) <= 5e-5)
		tmp = x;
	elseif ((y * z) <= 5e+277)
		tmp = t_0;
	else
		tmp = t_1;
	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[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[((-y) * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5e+210], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -4000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 5e-5], x, If[LessEqual[N[(y * z), $MachinePrecision], 5e+277], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.9999999999999998e210 or 4.99999999999999982e277 < (*.f64 y z)

   1. Initial program 79.4%

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

   3. Taylor expanded in y 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. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.4

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

   5. Simplified 99.4%

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

   if -4.9999999999999998e210 < (*.f64 y z) < -4e3 or 5.00000000000000024e-5 < (*.f64 y z) < 4.99999999999999982e277

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 96.1

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

   5. Simplified 96.1%

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

   if -4e3 < (*.f64 y z) < 5.00000000000000024e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 97.7%

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

      1. *-rgt-identity 97.7

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

   7. Applied egg-rr 97.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+210}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -4000:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024218 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))