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

Percentage Accurate: 96.3% → 99.7%

Time: 8.0s

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: 96.3% 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: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(-z\right) \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+277}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \cdot y \leq 10^{+197}:\\ \;\;\;\;\left(1 - z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (<= (* z y) -5e+277)
     t_0
     (if (<= (* z y) 1e+197) (* (- 1.0 (* z y)) x) 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 ((z * y) <= -5e+277) {
		tmp = t_0;
	} else if ((z * y) <= 1e+197) {
		tmp = (1.0 - (z * y)) * x;
	} 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 ((z * y) <= (-5d+277)) then
        tmp = t_0
    else if ((z * y) <= 1d+197) then
        tmp = (1.0d0 - (z * y)) * x
    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 ((z * y) <= -5e+277) {
		tmp = t_0;
	} else if ((z * y) <= 1e+197) {
		tmp = (1.0 - (z * y)) * x;
	} 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 (z * y) <= -5e+277:
		tmp = t_0
	elif (z * y) <= 1e+197:
		tmp = (1.0 - (z * y)) * x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(-z) * Float64(x * y))
	tmp = 0.0
	if (Float64(z * y) <= -5e+277)
		tmp = t_0;
	elseif (Float64(z * y) <= 1e+197)
		tmp = Float64(Float64(1.0 - Float64(z * y)) * x);
	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 ((z * y) <= -5e+277)
		tmp = t_0;
	elseif ((z * y) <= 1e+197)
		tmp = (1.0 - (z * y)) * x;
	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[(z * y), $MachinePrecision], -5e+277], t$95$0, If[LessEqual[N[(z * y), $MachinePrecision], 1e+197], N[(N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.99999999999999982e277 or 9.9999999999999995e196 < (*.f64 y z)

   1. Initial program 65.3%

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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -4.99999999999999982e277 < (*.f64 y z) < 9.9999999999999995e196

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+277}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{+197}:\\ \;\;\;\;\left(1 - z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+277}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot y \leq -40000:\\ \;\;\;\;\left(\left(-z\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{-9}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* z y) -5e+277)
   (* (- z) (* x y))
   (if (<= (* z y) -40000.0)
     (* (* (- z) y) x)
     (if (<= (* z y) 5e-9) (* 1.0 x) (* (* x z) (- y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z * y) <= -5e+277) {
		tmp = -z * (x * y);
	} else if ((z * y) <= -40000.0) {
		tmp = (-z * y) * x;
	} else if ((z * y) <= 5e-9) {
		tmp = 1.0 * x;
	} else {
		tmp = (x * z) * -y;
	}
	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 ((z * y) <= (-5d+277)) then
        tmp = -z * (x * y)
    else if ((z * y) <= (-40000.0d0)) then
        tmp = (-z * y) * x
    else if ((z * y) <= 5d-9) then
        tmp = 1.0d0 * x
    else
        tmp = (x * z) * -y
    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 ((z * y) <= -5e+277) {
		tmp = -z * (x * y);
	} else if ((z * y) <= -40000.0) {
		tmp = (-z * y) * x;
	} else if ((z * y) <= 5e-9) {
		tmp = 1.0 * x;
	} else {
		tmp = (x * z) * -y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z * y) <= -5e+277:
		tmp = -z * (x * y)
	elif (z * y) <= -40000.0:
		tmp = (-z * y) * x
	elif (z * y) <= 5e-9:
		tmp = 1.0 * x
	else:
		tmp = (x * z) * -y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(z * y) <= -5e+277)
		tmp = Float64(Float64(-z) * Float64(x * y));
	elseif (Float64(z * y) <= -40000.0)
		tmp = Float64(Float64(Float64(-z) * y) * x);
	elseif (Float64(z * y) <= 5e-9)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(x * z) * Float64(-y));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * y) <= -5e+277)
		tmp = -z * (x * y);
	elseif ((z * y) <= -40000.0)
		tmp = (-z * y) * x;
	elseif ((z * y) <= 5e-9)
		tmp = 1.0 * x;
	else
		tmp = (x * z) * -y;
	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[(z * y), $MachinePrecision], -5e+277], N[((-z) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], -40000.0], N[(N[((-z) * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 5e-9], N[(1.0 * x), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 75.5%

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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -4.99999999999999982e277 < (*.f64 y z) < -4e4

   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. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -4e4 < (*.f64 y z) < 5.0000000000000001e-9

   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. Applied rewrites 98.1%

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

   if 5.0000000000000001e-9 < (*.f64 y z)

   1. Initial program 93.2%

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

   4. Applied rewrites 36.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 88.0

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

   7. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\left(\left(-x\right) \cdot z\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+277}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot y \leq -40000:\\ \;\;\;\;\left(\left(-z\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{-9}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))