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

Percentage Accurate: 99.6% → 99.6%

Time: 6.9s

Alternatives: 10

Speedup: 1.1×

• 20.7% 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: 99.6% 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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;\left(z \cdot 6\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 0.000225:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y - x\right)\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1000000000.0)
   (* (* z 6.0) (- y x))
   (if (<= z 0.000225) (fma (* 6.0 y) z x) (* (* z (- y x)) 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1000000000.0) {
		tmp = (z * 6.0) * (y - x);
	} else if (z <= 0.000225) {
		tmp = fma((6.0 * y), z, x);
	} else {
		tmp = (z * (y - x)) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1000000000.0)
		tmp = Float64(Float64(z * 6.0) * Float64(y - x));
	elseif (z <= 0.000225)
		tmp = fma(Float64(6.0 * y), z, x);
	else
		tmp = Float64(Float64(z * Float64(y - x)) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1000000000.0], N[(N[(z * 6.0), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000225], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e9

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

   7. Applied rewrites 99.8%

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

   if -1e9 < z < 2.2499999999999999e-4

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.6

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

   5. Applied rewrites 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 98.6

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

   7. Applied rewrites 98.6%

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

   if 2.2499999999999999e-4 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 98.9

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

   5. Applied rewrites 98.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;\left(z \cdot 6\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 0.000225:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y - x\right)\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.000225:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y - x\right)\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1000000000.0)
   (* z (* 6.0 (- y x)))
   (if (<= z 0.000225) (fma (* 6.0 y) z x) (* (* z (- y x)) 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1000000000.0) {
		tmp = z * (6.0 * (y - x));
	} else if (z <= 0.000225) {
		tmp = fma((6.0 * y), z, x);
	} else {
		tmp = (z * (y - x)) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1000000000.0)
		tmp = Float64(z * Float64(6.0 * Float64(y - x)));
	elseif (z <= 0.000225)
		tmp = fma(Float64(6.0 * y), z, x);
	else
		tmp = Float64(Float64(z * Float64(y - x)) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1000000000.0], N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000225], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e9

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

   7. Applied rewrites 99.7%

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

   if -1e9 < z < 2.2499999999999999e-4

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.6

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

   5. Applied rewrites 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 98.6

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

   7. Applied rewrites 98.6%

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

   if 2.2499999999999999e-4 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 98.9

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

   5. Applied rewrites 98.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.000225:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y - x\right)\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.000225:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* 6.0 (- y x)))))
   (if (<= z -1000000000.0) t_0 (if (<= z 0.000225) (fma (* 6.0 y) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * (y - x));
	double tmp;
	if (z <= -1000000000.0) {
		tmp = t_0;
	} else if (z <= 0.000225) {
		tmp = fma((6.0 * y), z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * Float64(y - x)))
	tmp = 0.0
	if (z <= -1000000000.0)
		tmp = t_0;
	elseif (z <= 0.000225)
		tmp = fma(Float64(6.0 * y), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1000000000.0], t$95$0, If[LessEqual[z, 0.000225], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e9 or 2.2499999999999999e-4 < z

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   7. Applied rewrites 99.3%

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

   if -1e9 < z < 2.2499999999999999e-4

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.6

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

   5. Applied rewrites 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 98.6

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

   7. Applied rewrites 98.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.000225:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* 6.0 y) z x)))
   (if (<= y -6.5e-53) t_0 (if (<= y 3.2e-55) (fma (* -6.0 x) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((6.0 * y), z, x);
	double tmp;
	if (y <= -6.5e-53) {
		tmp = t_0;
	} else if (y <= 3.2e-55) {
		tmp = fma((-6.0 * x), z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(6.0 * y), z, x)
	tmp = 0.0
	if (y <= -6.5e-53)
		tmp = t_0;
	elseif (y <= 3.2e-55)
		tmp = fma(Float64(-6.0 * x), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -6.5e-53], t$95$0, If[LessEqual[y, 3.2e-55], N[(N[(-6.0 * x), $MachinePrecision] * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999997e-53 or 3.2000000000000001e-55 < 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

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.8

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

   5. Applied rewrites 88.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 88.8

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

   7. Applied rewrites 88.8%

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

   if -6.4999999999999997e-53 < y < 3.2000000000000001e-55

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.7

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

   5. Applied rewrites 55.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 55.7

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

   7. Applied rewrites 55.7%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 92.6

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

   10. Applied rewrites 92.6%

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

Alternative 6: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{-126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-155}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* -6.0 x) z x)))
   (if (<= x -1.32e-126) t_0 (if (<= x 5.4e-155) (* (* 6.0 y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((-6.0 * x), z, x);
	double tmp;
	if (x <= -1.32e-126) {
		tmp = t_0;
	} else if (x <= 5.4e-155) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(-6.0 * x), z, x)
	tmp = 0.0
	if (x <= -1.32e-126)
		tmp = t_0;
	elseif (x <= 5.4e-155)
		tmp = Float64(Float64(6.0 * y) * z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[x, -1.32e-126], t$95$0, If[LessEqual[x, 5.4e-155], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.31999999999999992e-126 or 5.39999999999999962e-155 < 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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 69.1

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 79.8

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

   10. Applied rewrites 79.8%

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

   if -1.31999999999999992e-126 < x < 5.39999999999999962e-155

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.6%

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

Alternative 7: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{-126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-155}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* z x) -6.0 x)))
   (if (<= x -1.32e-126) t_0 (if (<= x 5.4e-155) (* (* 6.0 y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((z * x), -6.0, x);
	double tmp;
	if (x <= -1.32e-126) {
		tmp = t_0;
	} else if (x <= 5.4e-155) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(z * x), -6.0, x)
	tmp = 0.0
	if (x <= -1.32e-126)
		tmp = t_0;
	elseif (x <= 5.4e-155)
		tmp = Float64(Float64(6.0 * y) * z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * -6.0 + x), $MachinePrecision]}, If[LessEqual[x, -1.32e-126], t$95$0, If[LessEqual[x, 5.4e-155], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.31999999999999992e-126 or 5.39999999999999962e-155 < 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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 79.8

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

   5. Applied rewrites 79.8%

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

   if -1.31999999999999992e-126 < x < 5.39999999999999962e-155

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.6%

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

Alternative 8: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot y\right) \cdot z\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-44}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 y) z)))
   (if (<= y -6.5e-53) t_0 (if (<= y 1.3e-44) (* (* -6.0 x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (y <= -6.5e-53) {
		tmp = t_0;
	} else if (y <= 1.3e-44) {
		tmp = (-6.0 * x) * z;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (6.0d0 * y) * z
    if (y <= (-6.5d-53)) then
        tmp = t_0
    else if (y <= 1.3d-44) then
        tmp = ((-6.0d0) * x) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (y <= -6.5e-53) {
		tmp = t_0;
	} else if (y <= 1.3e-44) {
		tmp = (-6.0 * x) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (6.0 * y) * z
	tmp = 0
	if y <= -6.5e-53:
		tmp = t_0
	elif y <= 1.3e-44:
		tmp = (-6.0 * x) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * y) * z)
	tmp = 0.0
	if (y <= -6.5e-53)
		tmp = t_0;
	elseif (y <= 1.3e-44)
		tmp = Float64(Float64(-6.0 * x) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (6.0 * y) * z;
	tmp = 0.0;
	if (y <= -6.5e-53)
		tmp = t_0;
	elseif (y <= 1.3e-44)
		tmp = (-6.0 * x) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -6.5e-53], t$95$0, If[LessEqual[y, 1.3e-44], N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999997e-53 or 1.2999999999999999e-44 < 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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

   7. Applied rewrites 61.4%

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

   if -6.4999999999999997e-53 < y < 1.2999999999999999e-44

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 52.2

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

   5. Applied rewrites 52.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 46.2%

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

   10. Applied rewrites 46.3%

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

Alternative 9: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. associate-*r* N/A

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

   8. lower-fma.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]
5. Add Preprocessing

Alternative 10: 27.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. lower--.f64 63.7

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

5. Applied rewrites 63.7%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 28.9%

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

10. Applied rewrites 28.9%

    \[\leadsto \color{blue}{\left(-6 \cdot x\right) \cdot z} \]
11. 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 2024244 
(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)))