Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.7% → 99.8%

Time: 1.1s

Alternatives: 6

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot z\right) \cdot 6 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) z) 6.0)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * z) * 6.0);
}

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 + (((y - x) * z) * 6.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * z) * 6.0);
}

Python

def code(x, y, z):
	return x + (((y - x) * z) * 6.0)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * z) * 6.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * z) * 6.0);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right)\right)} \]

5. Applied rewrites 3.3%

   \[\leadsto x + \color{blue}{\left(y - x\right) \cdot 6} \]

6. Taylor expanded in x around 0

   \[\leadsto x + \left(y + -1 \cdot x\right) \cdot 6 \]

8. Applied rewrites 68.5%

   \[\leadsto x + \left(x + \left(y - x\right) \cdot z\right) \cdot 6 \]

9. Taylor expanded in x around inf

   \[\leadsto x + \left(-1 \cdot x\right) \cdot 6 \]

11. Applied rewrites 99.8%

    \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot 6 \]
12. Add Preprocessing

Alternative 2: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ t_1 := t\_0 \cdot 6\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.000115:\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)) (t_1 (* t_0 6.0)))
   (if (<= z -6.6e-34) t_1 (if (<= z 0.000115) (+ x t_0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double t_1 = t_0 * 6.0;
	double tmp;
	if (z <= -6.6e-34) {
		tmp = t_1;
	} else if (z <= 0.000115) {
		tmp = x + t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - x) * z
    t_1 = t_0 * 6.0d0
    if (z <= (-6.6d-34)) then
        tmp = t_1
    else if (z <= 0.000115d0) then
        tmp = x + t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double t_1 = t_0 * 6.0;
	double tmp;
	if (z <= -6.6e-34) {
		tmp = t_1;
	} else if (z <= 0.000115) {
		tmp = x + t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	t_1 = t_0 * 6.0
	tmp = 0
	if z <= -6.6e-34:
		tmp = t_1
	elif z <= 0.000115:
		tmp = x + t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	t_1 = Float64(t_0 * 6.0)
	tmp = 0.0
	if (z <= -6.6e-34)
		tmp = t_1;
	elseif (z <= 0.000115)
		tmp = Float64(x + t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * z;
	t_1 = t_0 * 6.0;
	tmp = 0.0;
	if (z <= -6.6e-34)
		tmp = t_1;
	elseif (z <= 0.000115)
		tmp = x + t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * 6.0), $MachinePrecision]}, If[LessEqual[z, -6.6e-34], t$95$1, If[LessEqual[z, 0.000115], N[(x + t$95$0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.59999999999999965e-34 or 1.15e-4 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right)\right)} \]

   5. Applied rewrites 4.0%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot 6} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + \left(y + -1 \cdot x\right) \cdot 6 \]

   8. Applied rewrites 97.3%

      \[\leadsto x + \left(x + \left(y - x\right) \cdot z\right) \cdot 6 \]

   9. Taylor expanded in x around inf

      \[\leadsto x + \left(-1 \cdot x\right) \cdot 6 \]

   11. Applied rewrites 99.8%

       \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot 6 \]

   12. Taylor expanded in x around 0

       \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   14. Applied rewrites 97.4%

       \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} \]

   if -6.59999999999999965e-34 < z < 1.15e-4

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right)} \cdot z \]

   5. Applied rewrites 77.0%

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

Alternative 3: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) * 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 + ((y - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Python

def code(x, y, z):
	return x + ((y - x) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(6 \cdot y\right)} \cdot z \]

5. Applied rewrites 64.4%

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

Alternative 4: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(y - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (- y x) z))

C

double code(double x, double y, double z) {
	return (y - x) * 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 = (y - x) * z
end function

Java

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

Python

def code(x, y, z):
	return (y - x) * z

Julia

function code(x, y, z)
	return Float64(Float64(y - x) * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y - x) * z;
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

5. Applied rewrites 63.9%

   \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(6 \cdot y\right) \cdot z \]

8. Applied rewrites 30.1%

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

Alternative 5: 3.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (- y x)))

C

double code(double x, double y, double z) {
	return x + (y - x);
}

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 + (y - x)
end function

Java

public static double code(double x, double y, double z) {
	return x + (y - x);
}

Python

def code(x, y, z):
	return x + (y - x)

Julia

function code(x, y, z)
	return Float64(x + Float64(y - x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y - x);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right)\right)} \]

5. Applied rewrites 3.3%

   \[\leadsto x + \color{blue}{\left(y - x\right) \cdot 6} \]

6. Taylor expanded in x around 0

   \[\leadsto x + 6 \cdot \color{blue}{y} \]

8. Applied rewrites 3.3%

   \[\leadsto x + \left(y - \color{blue}{x}\right) \]
9. Add Preprocessing

Alternative 6: 3.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y - x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- y x))

C

double code(double x, double y, double z) {
	return y - x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y - x
end function

Java

public static double code(double x, double y, double z) {
	return y - x;
}

Python

def code(x, y, z):
	return y - x

Julia

function code(x, y, z)
	return Float64(y - x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y - x;
end

Wolfram

code[x_, y_, z_] := N[(y - x), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

5. Applied rewrites 63.9%

   \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 + \left(-6 \cdot z + 6 \cdot \frac{y \cdot z}{x}\right)\right)} \]

8. Applied rewrites 3.3%

   \[\leadsto \color{blue}{y - x} \]
9. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

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 - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

  (+ x (* (* (- y x) 6.0) z)))