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

Percentage Accurate: 96.1% → 97.4%

Time: 6.3s

Alternatives: 4

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: 96.1% 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: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq 4 \cdot 10^{+107}:\\ \;\;\;\;\left(1 - z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y\right) \cdot x, z, x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* z y) 4e+107) (* (- 1.0 (* z y)) x) (fma (* (- y) x) z x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z * y) <= 4e+107) {
		tmp = (1.0 - (z * y)) * x;
	} else {
		tmp = fma((-y * x), z, x);
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(z * y) <= 4e+107)
		tmp = Float64(Float64(1.0 - Float64(z * y)) * x);
	else
		tmp = fma(Float64(Float64(-y) * x), z, x);
	end
	return 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], 4e+107], N[(N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-y) * x), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 3.9999999999999999e107

   1. Initial program 98.5%

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

   if 3.9999999999999999e107 < (*.f64 y z)

   1. Initial program 81.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq 4 \cdot 10^{+107}:\\ \;\;\;\;\left(1 - z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y\right) \cdot x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - z \cdot y\\ t_1 := \left(\left(-y\right) \cdot z\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -5000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- 1.0 (* z y))) (t_1 (* (* (- y) z) x)))
   (if (<= t_0 -5000.0) t_1 (if (<= t_0 2.0) (* 1.0 x) t_1))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * y);
	double t_1 = (-y * z) * x;
	double tmp;
	if (t_0 <= -5000.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0 * x;
	} 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 = 1.0d0 - (z * y)
    t_1 = (-y * z) * x
    if (t_0 <= (-5000.0d0)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0 * x
    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 = 1.0 - (z * y);
	double t_1 = (-y * z) * x;
	double tmp;
	if (t_0 <= -5000.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (z * y)
	t_1 = (-y * z) * x
	tmp = 0
	if t_0 <= -5000.0:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(z * y))
	t_1 = Float64(Float64(Float64(-y) * z) * x)
	tmp = 0.0
	if (t_0 <= -5000.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = Float64(1.0 * x);
	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 = 1.0 - (z * y);
	t_1 = (-y * z) * x;
	tmp = 0.0;
	if (t_0 <= -5000.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0 * x;
	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[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[((-y) * z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$0, -5000.0], t$95$1, If[LessEqual[t$95$0, 2.0], N[(1.0 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5e3 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 90.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 88.2

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

   5. Applied rewrites 88.2%

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

   if -5e3 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   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 97.7%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \cdot y \leq -5000:\\ \;\;\;\;\left(\left(-y\right) \cdot z\right) \cdot x\\ \mathbf{elif}\;1 - z \cdot y \leq 2:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-y\right) \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \left(1 - z \cdot y\right) \cdot x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* (- 1.0 (* z y)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (1.0 - (z * y)) * 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 = (1.0d0 - (z * y)) * x
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return (1.0 - (z * y)) * x;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (1.0 - (z * y)) * x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(1.0 - Float64(z * y)) * x)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (1.0 - (z * y)) * x;
end

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Final simplification 95.1%

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

Alternative 4: 51.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 1 \cdot x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* 1.0 x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return 1.0 * x;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 1.0 * x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(1.0 * x)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 1.0 * x;
end

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 46.8%

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

6. Final simplification 46.8%

   \[\leadsto 1 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024294 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))