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

Percentage Accurate: 99.5% → 99.5%

Time: 1.7s

Alternatives: 10

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := x + \left(y - x\right) \cdot t\_0\\ \mathbf{if}\;t\_0 \leq 0.17:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5.2:\\ \;\;\;\;x + \left(x + \left(x + \left(y - x\right) \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (+ x (* (- y x) t_0))))
   (if (<= t_0 0.17)
     t_1
     (if (<= t_0 5.2) (+ x (+ x (+ x (* (- y x) 6.0)))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = x + ((y - x) * t_0);
	double tmp;
	if (t_0 <= 0.17) {
		tmp = t_1;
	} else if (t_0 <= 5.2) {
		tmp = x + (x + (x + ((y - x) * 6.0)));
	} 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 = (2.0d0 / 3.0d0) - z
    t_1 = x + ((y - x) * t_0)
    if (t_0 <= 0.17d0) then
        tmp = t_1
    else if (t_0 <= 5.2d0) then
        tmp = x + (x + (x + ((y - x) * 6.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = x + ((y - x) * t_0);
	double tmp;
	if (t_0 <= 0.17) {
		tmp = t_1;
	} else if (t_0 <= 5.2) {
		tmp = x + (x + (x + ((y - x) * 6.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (2.0 / 3.0) - z
	t_1 = x + ((y - x) * t_0)
	tmp = 0
	if t_0 <= 0.17:
		tmp = t_1
	elif t_0 <= 5.2:
		tmp = x + (x + (x + ((y - x) * 6.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(x + Float64(Float64(y - x) * t_0))
	tmp = 0.0
	if (t_0 <= 0.17)
		tmp = t_1;
	elseif (t_0 <= 5.2)
		tmp = Float64(x + Float64(x + Float64(x + Float64(Float64(y - x) * 6.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (2.0 / 3.0) - z;
	t_1 = x + ((y - x) * t_0);
	tmp = 0.0;
	if (t_0 <= 0.17)
		tmp = t_1;
	elseif (t_0 <= 5.2)
		tmp = x + (x + (x + ((y - x) * 6.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.17], t$95$1, If[LessEqual[t$95$0, 5.2], N[(x + N[(x + N[(x + N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 0.170000000000000012 or 5.20000000000000018 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right)} \cdot \left(\frac{2}{3} - z\right) \]

   5. Applied rewrites 54.0%

      \[\leadsto x + \color{blue}{\left(y - x\right)} \cdot \left(\frac{2}{3} - z\right) \]

   if 0.170000000000000012 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 5.20000000000000018

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

   5. Applied rewrites 19.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.6%

      \[\leadsto x + \left(x + \left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

   9. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{x \cdot \left(-6 \cdot \left(\frac{2}{3} - z\right) + 6 \cdot \frac{y \cdot \left(\frac{2}{3} - z\right)}{x}\right)} \]

   11. Applied rewrites 56.6%

       \[\leadsto x + \color{blue}{\left(x + \left(x + \left(y - x\right) \cdot 6\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := \left(y - x\right) \cdot t\_0\\ \mathbf{if}\;t\_0 \leq 0.21:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4.8:\\ \;\;\;\;x + \left(x + \left(x + \left(y - x\right) \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (* (- y x) t_0)))
   (if (<= t_0 0.21)
     t_1
     (if (<= t_0 4.8) (+ x (+ x (+ x (* (- y x) 6.0)))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = (y - x) * t_0;
	double tmp;
	if (t_0 <= 0.21) {
		tmp = t_1;
	} else if (t_0 <= 4.8) {
		tmp = x + (x + (x + ((y - x) * 6.0)));
	} 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 = (2.0d0 / 3.0d0) - z
    t_1 = (y - x) * t_0
    if (t_0 <= 0.21d0) then
        tmp = t_1
    else if (t_0 <= 4.8d0) then
        tmp = x + (x + (x + ((y - x) * 6.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = (y - x) * t_0;
	double tmp;
	if (t_0 <= 0.21) {
		tmp = t_1;
	} else if (t_0 <= 4.8) {
		tmp = x + (x + (x + ((y - x) * 6.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (2.0 / 3.0) - z
	t_1 = (y - x) * t_0
	tmp = 0
	if t_0 <= 0.21:
		tmp = t_1
	elif t_0 <= 4.8:
		tmp = x + (x + (x + ((y - x) * 6.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(Float64(y - x) * t_0)
	tmp = 0.0
	if (t_0 <= 0.21)
		tmp = t_1;
	elseif (t_0 <= 4.8)
		tmp = Float64(x + Float64(x + Float64(x + Float64(Float64(y - x) * 6.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (2.0 / 3.0) - z;
	t_1 = (y - x) * t_0;
	tmp = 0.0;
	if (t_0 <= 0.21)
		tmp = t_1;
	elseif (t_0 <= 4.8)
		tmp = x + (x + (x + ((y - x) * 6.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * t$95$0), $MachinePrecision]}, If[LessEqual[t$95$0, 0.21], t$95$1, If[LessEqual[t$95$0, 4.8], N[(x + N[(x + N[(x + N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 0.209999999999999992 or 4.79999999999999982 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]

   5. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(6 \cdot y\right) \cdot \left(\color{blue}{\frac{2}{3}} - z\right) \]

   8. Applied rewrites 54.0%

      \[\leadsto \left(y - x\right) \cdot \left(\color{blue}{\frac{2}{3}} - z\right) \]

   if 0.209999999999999992 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 4.79999999999999982

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

   5. Applied rewrites 19.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.6%

      \[\leadsto x + \left(x + \left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

   9. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{x \cdot \left(-6 \cdot \left(\frac{2}{3} - z\right) + 6 \cdot \frac{y \cdot \left(\frac{2}{3} - z\right)}{x}\right)} \]

   11. Applied rewrites 56.6%

       \[\leadsto x + \color{blue}{\left(x + \left(x + \left(y - x\right) \cdot 6\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 78.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+237}:\\ \;\;\;\;x + \left(x + \left(x + \left(y - x\right) \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+237)
   (+ x (+ x (+ x (* (- y x) 6.0))))
   (* (* (- y x) (- (/ 2.0 3.0) z)) 6.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+237) {
		tmp = x + (x + (x + ((y - x) * 6.0)));
	} else {
		tmp = ((y - x) * ((2.0 / 3.0) - z)) * 6.0;
	}
	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) :: tmp
    if (x <= (-3.2d+237)) then
        tmp = x + (x + (x + ((y - x) * 6.0d0)))
    else
        tmp = ((y - x) * ((2.0d0 / 3.0d0) - z)) * 6.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+237) {
		tmp = x + (x + (x + ((y - x) * 6.0)));
	} else {
		tmp = ((y - x) * ((2.0 / 3.0) - z)) * 6.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e+237:
		tmp = x + (x + (x + ((y - x) * 6.0)))
	else:
		tmp = ((y - x) * ((2.0 / 3.0) - z)) * 6.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+237)
		tmp = Float64(x + Float64(x + Float64(x + Float64(Float64(y - x) * 6.0))));
	else
		tmp = Float64(Float64(Float64(y - x) * Float64(Float64(2.0 / 3.0) - z)) * 6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.2e+237)
		tmp = x + (x + (x + ((y - x) * 6.0)));
	else
		tmp = ((y - x) * ((2.0 / 3.0) - z)) * 6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+237], N[(x + N[(x + N[(x + N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.20000000000000017e237

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

   5. Applied rewrites 18.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 9.2%

      \[\leadsto x + \left(x + \left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

   9. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{x \cdot \left(-6 \cdot \left(\frac{2}{3} - z\right) + 6 \cdot \frac{y \cdot \left(\frac{2}{3} - z\right)}{x}\right)} \]

   11. Applied rewrites 82.7%

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

   if -3.20000000000000017e237 < x

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

   5. Applied rewrites 11.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.8%

      \[\leadsto x + \left(x + \left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 99.5%

       \[\leadsto x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

   12. Taylor expanded in x around 0

       \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]

   14. Applied rewrites 80.4%

       \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) (- (/ 2.0 3.0) z)) 6.0)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z)) * 6.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * ((2.0 / 3.0) - z)) * 6.0);
}

Python

def code(x, y, z):
	return x + (((y - x) * ((2.0 / 3.0) - z)) * 6.0)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(Float64(2.0 / 3.0) - z)) * 6.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * ((2.0 / 3.0) - z)) * 6.0);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

5. Applied rewrites 11.6%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 73.0%

   \[\leadsto x + \left(x + \left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

9. Taylor expanded in x around inf

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

11. Applied rewrites 99.5%

    \[\leadsto x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]
12. Add Preprocessing

Alternative 6: 30.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

5. Applied rewrites 11.6%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 73.0%

   \[\leadsto x + \left(x + \left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot 6 \]

9. Taylor expanded in x around inf

   \[\leadsto x + \color{blue}{x \cdot \left(-6 \cdot \left(\frac{2}{3} - z\right) + 6 \cdot \frac{y \cdot \left(\frac{2}{3} - z\right)}{x}\right)} \]

11. Applied rewrites 30.5%

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

Alternative 7: 12.2% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

5. Applied rewrites 11.6%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 12.0%

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

Alternative 8: 11.9% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)\right)} \]

5. Applied rewrites 11.6%

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

Alternative 9: 11.7% accurate, 3.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]

5. Applied rewrites 78.1%

   \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto -6 \cdot \left(x \cdot \left(\frac{2}{3} - z\right)\right) + \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

8. Applied rewrites 11.4%

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

Alternative 10: 10.6% accurate, 7.8× 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]

5. Applied rewrites 78.1%

   \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 + \left(-6 \cdot \left(\frac{2}{3} - z\right) + 6 \cdot \frac{y \cdot \left(\frac{2}{3} - z\right)}{x}\right)\right)} \]

8. Applied rewrites 10.5%

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  :pre (TRUE)
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))