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

Percentage Accurate: 99.7% → 99.7%

Time: 9.6s

Alternatives: 10

Speedup: 1.0×

• 21.7% 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: 99.7% 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]

Derivation

1. Initial program 99.8%

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

Alternative 2: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+28} \lor \neg \left(x \leq 1.45 \cdot 10^{+52}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.55e+28) (not (<= x 1.45e+52)))
   (+ x (* -6.0 (* x z)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.55e+28) || !(x <= 1.45e+52)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (6.0 * (y * 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 ((x <= (-2.55d+28)) .or. (.not. (x <= 1.45d+52))) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.55e+28) || !(x <= 1.45e+52)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.55e+28) or not (x <= 1.45e+52):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.55e+28) || !(x <= 1.45e+52))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.55e+28) || ~((x <= 1.45e+52)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.55e+28], N[Not[LessEqual[x, 1.45e+52]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5500000000000002e28 or 1.45e52 < x

   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 89.8%

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

   if -2.5500000000000002e28 < x < 1.45e52

   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 86.8%

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

      1. *-commutative 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+28} \lor \neg \left(x \leq 1.45 \cdot 10^{+52}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-68} \lor \neg \left(x \leq 2 \cdot 10^{-107}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-68) (not (<= x 2e-107)))
   (+ x (* -6.0 (* x z)))
   (* 6.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-68) || !(x <= 2e-107)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * (y * 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 ((x <= (-5.5d-68)) .or. (.not. (x <= 2d-107))) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-68) || !(x <= 2e-107)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-68) or not (x <= 2e-107):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-68) || !(x <= 2e-107))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e-68) || ~((x <= 2e-107)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-68], N[Not[LessEqual[x, 2e-107]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e-68 or 2e-107 < x

   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 80.9%

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

   if -5.5000000000000003e-68 < x < 2e-107

   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 inf 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in x around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. fma-define 78.4%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(6, \frac{y \cdot z}{x}, 1\right)} \]

      3. *-commutative 78.4%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \frac{\color{blue}{z \cdot y}}{x}, 1\right) \]

      4. associate-/l* 65.1%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \color{blue}{z \cdot \frac{y}{x}}, 1\right) \]

   8. Simplified 65.1%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(6, z \cdot \frac{y}{x}, 1\right)} \]

   9. Taylor expanded in x around 0 72.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-68} \lor \neg \left(x \leq 2 \cdot 10^{-107}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+27}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e+27)
   (+ x (* x (* z -6.0)))
   (if (<= x 3.3e+52) (+ x (* z (* y 6.0))) (+ x (* -6.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e+27) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 3.3e+52) {
		tmp = x + (z * (y * 6.0));
	} 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 (x <= (-1.85d+27)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (x <= 3.3d+52) then
        tmp = x + (z * (y * 6.0d0))
    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 (x <= -1.85e+27) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 3.3e+52) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.85e+27:
		tmp = x + (x * (z * -6.0))
	elif x <= 3.3e+52:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e+27)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (x <= 3.3e+52)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	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 (x <= -1.85e+27)
		tmp = x + (x * (z * -6.0));
	elseif (x <= 3.3e+52)
		tmp = x + (z * (y * 6.0));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e+27], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+52], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85000000000000001e27

   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 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*r* 88.9%

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

      3. *-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -1.85000000000000001e27 < x < 3.3e52

   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 86.8%

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

   if 3.3e52 < x

   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 90.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+27}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+53}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+27)
   (+ x (* x (* z -6.0)))
   (if (<= x 8e+53) (+ x (* 6.0 (* y z))) (+ x (* -6.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+27) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 8e+53) {
		tmp = x + (6.0 * (y * z));
	} 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 (x <= (-1.25d+27)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (x <= 8d+53) then
        tmp = x + (6.0d0 * (y * z))
    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 (x <= -1.25e+27) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 8e+53) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+27:
		tmp = x + (x * (z * -6.0))
	elif x <= 8e+53:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+27)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (x <= 8e+53)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	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 (x <= -1.25e+27)
		tmp = x + (x * (z * -6.0));
	elseif (x <= 8e+53)
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+27], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+53], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999995e27

   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 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*r* 88.9%

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

      3. *-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -1.24999999999999995e27 < x < 7.9999999999999999e53

   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 86.8%

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

      1. *-commutative 86.8%

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

   5. Simplified 86.8%

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

   if 7.9999999999999999e53 < x

   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 90.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+53}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-13} \lor \neg \left(z \leq 3.9 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.2e-13) (not (<= z 3.9e-16))) (* z (* y 6.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.2e-13) || !(z <= 3.9e-16)) {
		tmp = z * (y * 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 <= (-7.2d-13)) .or. (.not. (z <= 3.9d-16))) then
        tmp = z * (y * 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 <= -7.2e-13) || !(z <= 3.9e-16)) {
		tmp = z * (y * 6.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.2e-13) or not (z <= 3.9e-16):
		tmp = z * (y * 6.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.2e-13) || !(z <= 3.9e-16))
		tmp = Float64(z * Float64(y * 6.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.2e-13) || ~((z <= 3.9e-16)))
		tmp = z * (y * 6.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.2e-13], N[Not[LessEqual[z, 3.9e-16]], $MachinePrecision]], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999996e-13 or 3.89999999999999977e-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 inf 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in x around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. fma-define 46.1%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(6, \frac{y \cdot z}{x}, 1\right)} \]

      3. *-commutative 46.1%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \frac{\color{blue}{z \cdot y}}{x}, 1\right) \]

      4. associate-/l* 46.2%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \color{blue}{z \cdot \frac{y}{x}}, 1\right) \]

   8. Simplified 46.2%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(6, z \cdot \frac{y}{x}, 1\right)} \]

   9. Taylor expanded in x around 0 53.1%

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

       1. associate-*r* 53.2%

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

   11. Simplified 53.2%

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

   if -7.1999999999999996e-13 < z < 3.89999999999999977e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-13} \lor \neg \left(z \leq 3.9 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-16} \lor \neg \left(z \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e-16) (not (<= z 5.5e-16))) (* 6.0 (* y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-16) || !(z <= 5.5e-16)) {
		tmp = 6.0 * (y * z);
	} 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 <= (-2.7d-16)) .or. (.not. (z <= 5.5d-16))) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-16) || !(z <= 5.5e-16)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e-16) or not (z <= 5.5e-16):
		tmp = 6.0 * (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e-16) || !(z <= 5.5e-16))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.7e-16) || ~((z <= 5.5e-16)))
		tmp = 6.0 * (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e-16], N[Not[LessEqual[z, 5.5e-16]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999999e-16 or 5.49999999999999964e-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 inf 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in x around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. fma-define 46.1%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(6, \frac{y \cdot z}{x}, 1\right)} \]

      3. *-commutative 46.1%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \frac{\color{blue}{z \cdot y}}{x}, 1\right) \]

      4. associate-/l* 46.2%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \color{blue}{z \cdot \frac{y}{x}}, 1\right) \]

   8. Simplified 46.2%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(6, z \cdot \frac{y}{x}, 1\right)} \]

   9. Taylor expanded in x around 0 53.1%

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

   if -2.69999999999999999e-16 < z < 5.49999999999999964e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-16} \lor \neg \left(z \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-14}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e-14) (* 6.0 (* y z)) (if (<= z 5e-16) x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e-14) {
		tmp = 6.0 * (y * z);
	} else if (z <= 5e-16) {
		tmp = x;
	} else {
		tmp = y * (6.0 * 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 (z <= (-4d-14)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 5d-16) then
        tmp = x
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e-14) {
		tmp = 6.0 * (y * z);
	} else if (z <= 5e-16) {
		tmp = x;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e-14:
		tmp = 6.0 * (y * z)
	elif z <= 5e-16:
		tmp = x
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e-14)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 5e-16)
		tmp = x;
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e-14)
		tmp = 6.0 * (y * z);
	elseif (z <= 5e-16)
		tmp = x;
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e-14], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-16], x, N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4e-14

   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 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in x around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. fma-define 48.9%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(6, \frac{y \cdot z}{x}, 1\right)} \]

      3. *-commutative 48.9%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \frac{\color{blue}{z \cdot y}}{x}, 1\right) \]

      4. associate-/l* 48.9%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \color{blue}{z \cdot \frac{y}{x}}, 1\right) \]

   8. Simplified 48.9%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(6, z \cdot \frac{y}{x}, 1\right)} \]

   9. Taylor expanded in x around 0 55.0%

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

   if -4e-14 < z < 5.0000000000000004e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.1%

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

   if 5.0000000000000004e-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 inf 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in x around inf 43.5%

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

      1. +-commutative 43.5%

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

      2. fma-define 43.5%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(6, \frac{y \cdot z}{x}, 1\right)} \]

      3. *-commutative 43.5%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \frac{\color{blue}{z \cdot y}}{x}, 1\right) \]

      4. associate-/l* 43.6%

         \[\leadsto x \cdot \mathsf{fma}\left(6, \color{blue}{z \cdot \frac{y}{x}}, 1\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(6, z \cdot \frac{y}{x}, 1\right)} \]

   9. Taylor expanded in x around 0 51.4%

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

       1. associate-*r* 51.4%

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

       2. *-commutative 51.4%

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

       3. associate-*r* 51.4%

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

   11. Simplified 51.4%

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

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 * N[(N[(y - x), $MachinePrecision] * 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 z around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 10: 35.9% 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 z around 0 36.2%

   \[\leadsto \color{blue}{x} \]
4. 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 2024150 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

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

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