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

Percentage Accurate: 99.7% → 99.7%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• 21.6% 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. Final simplification 99.8%

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

Alternative 2: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+45} \lor \neg \left(x \leq 7500000\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.85e+45) (not (<= x 7500000.0)))
   (* x (+ 1.0 (* z -6.0)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.85e+45) || !(x <= 7500000.0)) {
		tmp = x * (1.0 + (z * -6.0));
	} 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 <= (-2.85d+45)) .or. (.not. (x <= 7500000.0d0))) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    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 <= -2.85e+45) || !(x <= 7500000.0)) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.85e+45) or not (x <= 7500000.0):
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.85e+45) || !(x <= 7500000.0))
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	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 <= -2.85e+45) || ~((x <= 7500000.0)))
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.85e+45], N[Not[LessEqual[x, 7500000.0]], $MachinePrecision]], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.85000000000000013e45 or 7.5e6 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 89.4%

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

   if -2.85000000000000013e45 < x < 7.5e6

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 89.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+45} \lor \neg \left(x \leq 7500000\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 3: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+40} \lor \neg \left(x \leq 32000000\right):\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+40) (not (<= x 32000000.0)))
   (+ x (* z (* x -6.0)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+40) || !(x <= 32000000.0)) {
		tmp = x + (z * (x * -6.0));
	} 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 <= (-5.2d+40)) .or. (.not. (x <= 32000000.0d0))) then
        tmp = x + (z * (x * (-6.0d0)))
    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 <= -5.2e+40) || !(x <= 32000000.0)) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+40) or not (x <= 32000000.0):
		tmp = x + (z * (x * -6.0))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e+40) || !(x <= 32000000.0))
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	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 <= -5.2e+40) || ~((x <= 32000000.0)))
		tmp = x + (z * (x * -6.0));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+40], N[Not[LessEqual[x, 32000000.0]], $MachinePrecision]], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000001e40 or 3.2e7 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.5%

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

   if -5.2000000000000001e40 < x < 3.2e7

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 89.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+40} \lor \neg \left(x \leq 32000000\right):\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6500000000.0) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6500000000.0) || !(z <= 0.17)) {
		tmp = -6.0 * (x * 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 <= (-6500000000.0d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (-6.0d0) * (x * 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 <= -6500000000.0) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6500000000.0) or not (z <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6500000000.0) || !(z <= 0.17))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6500000000.0) || ~((z <= 0.17)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6500000000.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e9 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 54.2%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in z around 0 53.6%

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

   if -6.5e9 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 69.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500000000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6500000000.0)
   (* z (* x -6.0))
   (if (<= z 0.17) x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6500000000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = -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 (z <= (-6500000000.0d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6500000000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6500000000.0:
		tmp = z * (x * -6.0)
	elif z <= 0.17:
		tmp = x
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6500000000.0)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6500000000.0)
		tmp = z * (x * -6.0);
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6500000000.0], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 57.0%

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

   3. Taylor expanded in z around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in z around 0 56.9%

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

      1. *-commutative 56.9%

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

      2. associate-*r* 57.1%

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

   8. Simplified 57.1%

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

   if -6.5e9 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 69.6%

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

   if 0.170000000000000012 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 51.0%

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

   3. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in z around 0 49.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500000000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500000000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-0.16666666666666666}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6500000000.0)
   (* z (* x -6.0))
   (if (<= z 0.17) x (/ z (/ -0.16666666666666666 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6500000000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = z / (-0.16666666666666666 / 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 <= (-6500000000.0d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = z / ((-0.16666666666666666d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6500000000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = z / (-0.16666666666666666 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6500000000.0:
		tmp = z * (x * -6.0)
	elif z <= 0.17:
		tmp = x
	else:
		tmp = z / (-0.16666666666666666 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6500000000.0)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(z / Float64(-0.16666666666666666 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6500000000.0)
		tmp = z * (x * -6.0);
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = z / (-0.16666666666666666 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6500000000.0], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, N[(z / N[(-0.16666666666666666 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 57.0%

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

   3. Taylor expanded in z around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in z around 0 56.9%

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

      1. *-commutative 56.9%

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

      2. associate-*r* 57.1%

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

   8. Simplified 57.1%

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

   if -6.5e9 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 69.6%

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

   if 0.170000000000000012 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 51.0%

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

   3. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   5. Simplified 49.7%

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

      1. metadata-eval 49.7%

         \[\leadsto \left(z \cdot \color{blue}{\frac{1}{-0.16666666666666666}}\right) \cdot x \]

      2. div-inv 49.8%

         \[\leadsto \color{blue}{\frac{z}{-0.16666666666666666}} \cdot x \]

      3. associate-/r/ 49.9%

         \[\leadsto \color{blue}{\frac{z}{\frac{-0.16666666666666666}{x}}} \]

   7. Applied egg-rr 49.9%

      \[\leadsto \color{blue}{\frac{z}{\frac{-0.16666666666666666}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500000000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-0.16666666666666666}{x}}\\ \end{array} \]

Alternative 7: 62.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 + (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 * (1.0d0 + (z * (-6.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around inf 61.5%

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

3. Final simplification 61.5%

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

Alternative 8: 35.7% 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. Taylor expanded in z around 0 33.7%

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

3. Final simplification 33.7%

   \[\leadsto x \]

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 2023199 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

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