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

Percentage Accurate: 99.7% → 99.8%

Time: 5.3s

Alternatives: 7

Speedup: 1.0×

• 20.9% 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 99.7%

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

2. Taylor expanded in y around 0 98.2%

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

   1. +-commutative 98.2%

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

   2. *-commutative 98.2%

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

   3. associate-*l* 98.2%

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

   4. *-commutative 98.2%

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

   5. metadata-eval 98.2%

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

   6. cancel-sign-sub-inv 98.2%

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

   7. associate-*l* 98.2%

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

   8. *-commutative 98.2%

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

   9. distribute-lft-out-- 99.8%

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

   10. associate-*r* 99.8%

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

4. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+37} \lor \neg \left(y \leq 2.95 \cdot 10^{-134}\right):\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+37) (not (<= y 2.95e-134)))
   (+ x (* 6.0 (* z y)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+37) || !(y <= 2.95e-134)) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = x * (1.0 + (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 ((y <= (-4d+37)) .or. (.not. (y <= 2.95d-134))) then
        tmp = x + (6.0d0 * (z * y))
    else
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+37) || !(y <= 2.95e-134)) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+37) or not (y <= 2.95e-134):
		tmp = x + (6.0 * (z * y))
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+37) || !(y <= 2.95e-134))
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+37) || ~((y <= 2.95e-134)))
		tmp = x + (6.0 * (z * y));
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+37], N[Not[LessEqual[y, 2.95e-134]], $MachinePrecision]], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999982e37 or 2.95e-134 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 92.4%

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

   if -3.99999999999999982e37 < y < 2.95e-134

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.0%

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

   3. Taylor expanded in x around 0 87.0%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+37} \lor \neg \left(y \leq 2.95 \cdot 10^{-134}\right):\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.95e+38)
   (+ x (* z (* 6.0 y)))
   (if (<= y 2.65e-133) (* x (+ 1.0 (* z -6.0))) (+ x (* 6.0 (* z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.95e+38) {
		tmp = x + (z * (6.0 * y));
	} else if (y <= 2.65e-133) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (6.0 * (z * y));
	}
	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 <= (-2.95d+38)) then
        tmp = x + (z * (6.0d0 * y))
    else if (y <= 2.65d-133) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = x + (6.0d0 * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.95e+38) {
		tmp = x + (z * (6.0 * y));
	} else if (y <= 2.65e-133) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (6.0 * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.95e+38:
		tmp = x + (z * (6.0 * y))
	elif y <= 2.65e-133:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = x + (6.0 * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.95e+38)
		tmp = Float64(x + Float64(z * Float64(6.0 * y)));
	elseif (y <= 2.65e-133)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.95e+38)
		tmp = x + (z * (6.0 * y));
	elseif (y <= 2.65e-133)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = x + (6.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.95e+38], N[(x + N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-133], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.94999999999999991e38

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 94.1%

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

   if -2.94999999999999991e38 < y < 2.64999999999999992e-133

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.0%

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

   3. Taylor expanded in x around 0 87.0%

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

   if 2.64999999999999992e-133 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 91.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 4: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 1.36 \cdot 10^{-8}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 1.36e-8))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 1.36e-8)) {
		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 <= (-0.17d0)) .or. (.not. (z <= 1.36d-8))) 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 <= -0.17) || !(z <= 1.36e-8)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 1.36e-8):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 1.36e-8))
		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 <= -0.17) || ~((z <= 1.36e-8)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 1.36e-8]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 1.3599999999999999e-8 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 45.2%

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

   3. Taylor expanded in x around 0 45.3%

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

   4. Taylor expanded in z around inf 43.5%

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

   if -0.170000000000000012 < z < 1.3599999999999999e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.5%

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

   3. Taylor expanded in z around 0 76.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 1.36 \cdot 10^{-8}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17) (* -6.0 (* x z)) (if (<= z 1.36e-8) x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.36e-8) {
		tmp = x;
	} else {
		tmp = x * (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 (z <= (-0.17d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 1.36d-8) then
        tmp = x
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.36e-8) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = -6.0 * (x * z)
	elif z <= 1.36e-8:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 1.36e-8)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = -6.0 * (x * z);
	elseif (z <= 1.36e-8)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e-8], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 46.4%

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

   3. Taylor expanded in x around 0 46.4%

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

   4. Taylor expanded in z around inf 43.3%

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

   if -0.170000000000000012 < z < 1.3599999999999999e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.5%

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

   3. Taylor expanded in z around 0 76.9%

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

   if 1.3599999999999999e-8 < z

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 43.8%

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

   3. Taylor expanded in x around 0 43.9%

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

   4. Taylor expanded in z around inf 43.6%

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

      1. associate-*r* 43.7%

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

   6. Simplified 43.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 6: 62.1% 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 99.7%

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

2. Taylor expanded in y around 0 61.4%

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

3. Taylor expanded in x around 0 61.4%

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

4. Final simplification 61.4%

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

Alternative 7: 36.6% 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 99.7%

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

2. Taylor expanded in y around 0 61.4%

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

3. Taylor expanded in z around 0 40.1%

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

4. Final simplification 40.1%

   \[\leadsto x \]

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 2023257 
(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)))