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

Percentage Accurate: 99.7% → 99.8%

Time: 7.2s

Alternatives: 6

Speedup: 1.0×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $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 y around 0 97.1%

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

   1. +-commutative 97.1%

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

   2. associate-*r* 97.1%

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

   3. *-commutative 97.1%

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

   4. associate-*r* 97.1%

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

   5. metadata-eval 97.1%

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

   6. cancel-sign-sub-inv 97.1%

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

   7. *-commutative 97.1%

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

   8. associate-*r* 97.0%

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

   9. *-commutative 97.0%

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

   10. distribute-lft-out-- 99.8%

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

   11. associate-*r* 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-71} \lor \neg \left(y \leq 2.7 \cdot 10^{-94}\right):\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.95e-71) (not (<= y 2.7e-94)))
   (+ x (* 6.0 (* z y)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.95e-71) || !(y <= 2.7e-94)) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	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 ((y <= (-1.95d-71)) .or. (.not. (y <= 2.7d-94))) then
        tmp = x + (6.0d0 * (z * y))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.95e-71) || !(y <= 2.7e-94)) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.95e-71) or not (y <= 2.7e-94):
		tmp = x + (6.0 * (z * y))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.95e-71) || !(y <= 2.7e-94))
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.95e-71) || ~((y <= 2.7e-94)))
		tmp = x + (6.0 * (z * y));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.95e-71], N[Not[LessEqual[y, 2.7e-94]], $MachinePrecision]], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9500000000000001e-71 or 2.7000000000000001e-94 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 86.5%

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

      1. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   if -1.9500000000000001e-71 < y < 2.7000000000000001e-94

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 94.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-71} \lor \neg \left(y \leq 2.7 \cdot 10^{-94}\right):\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1.8 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 1.8e-16))) (* x (* z -6.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 1.8e-16)) {
		tmp = x * (z * -6.0);
	} else {
		tmp = x;
	}
	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 ((z <= (-0.165d0)) .or. (.not. (z <= 1.8d-16))) then
        tmp = x * (z * (-6.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 1.8e-16)) {
		tmp = x * (z * -6.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 1.8e-16):
		tmp = x * (z * -6.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 1.8e-16))
		tmp = Float64(x * Float64(z * -6.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 1.8e-16)))
		tmp = x * (z * -6.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 1.8e-16]], $MachinePrecision]], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 1.79999999999999991e-16 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.6%

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

   4. Taylor expanded in x around 0 49.6%

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

      1. +-commutative 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in z around inf 47.3%

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

   if -0.165000000000000008 < z < 1.79999999999999991e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.7%

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

   4. Taylor expanded in z around 0 69.9%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1.8 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(z \cdot -6 + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (+ (* z -6.0) 1.0)))

C

double code(double x, double y, double z) {
	return x * ((z * -6.0) + 1.0);
}

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 * ((z * (-6.0d0)) + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * ((z * -6.0) + 1.0);
}

Python

def code(x, y, z):
	return x * ((z * -6.0) + 1.0)

Julia

function code(x, y, z)
	return Float64(x * Float64(Float64(z * -6.0) + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * ((z * -6.0) + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $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 y around 0 60.0%

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

4. Taylor expanded in x around 0 60.0%

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

   1. +-commutative 60.0%

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

6. Simplified 60.0%

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

7. Final simplification 60.0%

   \[\leadsto x \cdot \left(z \cdot -6 + 1\right) \]
8. Add Preprocessing

Alternative 5: 61.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $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 y around 0 60.0%

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

4. Final simplification 60.0%

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

Alternative 6: 36.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 60.0%

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

4. Taylor expanded in z around 0 35.9%

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

5. Final simplification 35.9%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 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 2024078 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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