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

Percentage Accurate: 99.7% → 99.7%

Time: 9.8s

Alternatives: 11

Speedup: 1.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-neg N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. *-commutative N/A

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

   8. neg-mul-1 N/A

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

   9. associate-*r* N/A

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

   10. metadata-eval N/A

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

   11. metadata-eval N/A

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

   12. lower-*.f64 N/A

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

   13. metadata-eval 99.8

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

4. Applied rewrites 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

6. Applied rewrites 99.8%

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

   1. lift-fma.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-*.f64 99.8

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

8. Applied rewrites 99.8%

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

Alternative 2: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z (- y x)))))
   (if (<= z -11500000000.0) t_0 (if (<= z 0.165) (+ x (* z (* y 6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * (y - x));
	double tmp;
	if (z <= -11500000000.0) {
		tmp = t_0;
	} else if (z <= 0.165) {
		tmp = x + (z * (y * 6.0));
	} 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 * (z * (y - x))
    if (z <= (-11500000000.0d0)) then
        tmp = t_0
    else if (z <= 0.165d0) then
        tmp = x + (z * (y * 6.0d0))
    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 * (z * (y - x));
	double tmp;
	if (z <= -11500000000.0) {
		tmp = t_0;
	} else if (z <= 0.165) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * (y - x))
	tmp = 0
	if z <= -11500000000.0:
		tmp = t_0
	elif z <= 0.165:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -11500000000.0)
		tmp = t_0;
	elseif (z <= 0.165)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -11500000000.0)
		tmp = t_0;
	elseif (z <= 0.165)
		tmp = x + (z * (y * 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -11500000000.0], t$95$0, If[LessEqual[z, 0.165], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e10 or 0.165000000000000008 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. lower-*.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 98.6

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

   7. Applied rewrites 98.6%

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

   if -1.15e10 < z < 0.165000000000000008

   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. lower-*.f64 98.2

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

   5. Applied rewrites 98.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z (- y x)))))
   (if (<= z -11500000000.0) t_0 (if (<= z 0.165) (fma (* y z) 6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * (y - x));
	double tmp;
	if (z <= -11500000000.0) {
		tmp = t_0;
	} else if (z <= 0.165) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -11500000000.0)
		tmp = t_0;
	elseif (z <= 0.165)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -11500000000.0], t$95$0, If[LessEqual[z, 0.165], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e10 or 0.165000000000000008 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. lower-*.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 98.6

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

   7. Applied rewrites 98.6%

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

   if -1.15e10 < z < 0.165000000000000008

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 98.2

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

   7. Applied rewrites 98.2%

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

Alternative 4: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-6 \cdot z\right) \cdot \left(x - y\right)\\ \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* -6.0 z) (- x y))))
   (if (<= z -11500000000.0) t_0 (if (<= z 0.165) (fma (* y z) 6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (-6.0 * z) * (x - y);
	double tmp;
	if (z <= -11500000000.0) {
		tmp = t_0;
	} else if (z <= 0.165) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-6.0 * z) * Float64(x - y))
	tmp = 0.0
	if (z <= -11500000000.0)
		tmp = t_0;
	elseif (z <= 0.165)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -11500000000.0], t$95$0, If[LessEqual[z, 0.165], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e10 or 0.165000000000000008 < 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. associate-*r* N/A

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. metadata-eval N/A

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

      13. distribute-lft-neg-in N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. distribute-lft-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. distribute-rgt-out-- N/A

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

      18. distribute-lft-out-- N/A

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

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

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

      24. *-lft-identity N/A

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

      25. *-inverses N/A

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

      26. associate-*l/ N/A

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

      27. associate-*r/ N/A

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

      28. associate-*r/ N/A

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

      29. *-rgt-identity N/A

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

   5. Applied rewrites 97.7%

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

   if -1.15e10 < z < 0.165000000000000008

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 98.2

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

   7. Applied rewrites 98.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 120000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* y z) 6.0 x)))
   (if (<= y -1.35e-37)
     t_0
     (if (<= y 120000000000.0) (fma z (* x -6.0) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((y * z), 6.0, x);
	double tmp;
	if (y <= -1.35e-37) {
		tmp = t_0;
	} else if (y <= 120000000000.0) {
		tmp = fma(z, (x * -6.0), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(y * z), 6.0, x)
	tmp = 0.0
	if (y <= -1.35e-37)
		tmp = t_0;
	elseif (y <= 120000000000.0)
		tmp = fma(z, Float64(x * -6.0), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision]}, If[LessEqual[y, -1.35e-37], t$95$0, If[LessEqual[y, 120000000000.0], N[(z * N[(x * -6.0), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000008e-37 or 1.2e11 < y

   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. lower-*.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 93.9

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

   7. Applied rewrites 93.9%

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

   if -1.35000000000000008e-37 < y < 1.2e11

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 93.5

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

   5. Applied rewrites 93.5%

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

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -66000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= y -66000.0) t_0 (if (<= y 1.05e+14) (fma z (* x -6.0) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (y <= -66000.0) {
		tmp = t_0;
	} else if (y <= 1.05e+14) {
		tmp = fma(z, (x * -6.0), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (y <= -66000.0)
		tmp = t_0;
	elseif (y <= 1.05e+14)
		tmp = fma(z, Float64(x * -6.0), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -66000.0], t$95$0, If[LessEqual[y, 1.05e+14], N[(z * N[(x * -6.0), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -66000 or 1.05e14 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 67.7

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

   5. Applied rewrites 67.7%

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

   if -66000 < y < 1.05e14

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 93.1

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

   5. Applied rewrites 93.1%

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

Alternative 7: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -0.34:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= y -0.34) t_0 (if (<= y 1.05e+14) (* z (* x -6.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (y <= -0.34) {
		tmp = t_0;
	} else if (y <= 1.05e+14) {
		tmp = z * (x * -6.0);
	} 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 <= (-0.34d0)) then
        tmp = t_0
    else if (y <= 1.05d+14) then
        tmp = z * (x * (-6.0d0))
    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 <= -0.34) {
		tmp = t_0;
	} else if (y <= 1.05e+14) {
		tmp = z * (x * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if y <= -0.34:
		tmp = t_0
	elif y <= 1.05e+14:
		tmp = z * (x * -6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (y <= -0.34)
		tmp = t_0;
	elseif (y <= 1.05e+14)
		tmp = Float64(z * Float64(x * -6.0));
	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 <= -0.34)
		tmp = t_0;
	elseif (y <= 1.05e+14)
		tmp = z * (x * -6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.34], t$95$0, If[LessEqual[y, 1.05e+14], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.340000000000000024 or 1.05e14 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -0.340000000000000024 < y < 1.05e14

   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. associate-*r* N/A

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. metadata-eval N/A

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

      13. distribute-lft-neg-in N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. distribute-lft-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. distribute-rgt-out-- N/A

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

      18. distribute-lft-out-- N/A

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

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

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

      24. *-lft-identity N/A

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

      25. *-inverses N/A

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

      26. associate-*l/ N/A

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

      27. associate-*r/ N/A

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

      28. associate-*r/ N/A

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

      29. *-rgt-identity N/A

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

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 36.3%

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

   10. Applied rewrites 36.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.34:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

   \[\leadsto x + z \cdot \left(6 \cdot \left(y - x\right)\right) \]
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. lower-*.f64 99.7

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

4. Applied rewrites 99.7%

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

5. Final simplification 99.7%

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

Alternative 10: 27.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

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

   1. associate-*r* N/A

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

   2. distribute-lft-out-- N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. metadata-eval N/A

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

   6. associate-*r* N/A

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

   7. *-commutative N/A

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

   8. associate-*r* N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. *-commutative N/A

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

   12. metadata-eval N/A

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

   13. distribute-lft-neg-in N/A

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

   14. distribute-rgt-neg-in N/A

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

   15. distribute-lft-neg-in N/A

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

   16. mul-1-neg N/A

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

   17. distribute-rgt-out-- N/A

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

   18. distribute-lft-out-- N/A

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

   19. neg-mul-1 N/A

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

   20. neg-sub0 N/A

       \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

   21. associate-+l- N/A

       \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

   22. neg-sub0 N/A

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

   23. mul-1-neg N/A

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

   24. *-lft-identity N/A

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

   25. *-inverses N/A

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

   26. associate-*l/ N/A

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

   27. associate-*r/ N/A

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

   28. associate-*r/ N/A

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

   29. *-rgt-identity N/A

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

5. Applied rewrites 60.4%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 21.0%

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

10. Applied rewrites 21.0%

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

11. Final simplification 21.0%

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

Alternative 11: 27.3% accurate, 1.5× speedup

Math

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

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(-6.0 * Float64(x * z))
end

MATLAB

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

Wolfram

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

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

   1. associate-*r* N/A

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

   2. distribute-lft-out-- N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. metadata-eval N/A

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

   6. associate-*r* N/A

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

   7. *-commutative N/A

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

   8. associate-*r* N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. *-commutative N/A

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

   12. metadata-eval N/A

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

   13. distribute-lft-neg-in N/A

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

   14. distribute-rgt-neg-in N/A

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

   15. distribute-lft-neg-in N/A

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

   16. mul-1-neg N/A

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

   17. distribute-rgt-out-- N/A

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

   18. distribute-lft-out-- N/A

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

   19. neg-mul-1 N/A

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

   20. neg-sub0 N/A

       \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

   21. associate-+l- N/A

       \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

   22. neg-sub0 N/A

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

   23. mul-1-neg N/A

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

   24. *-lft-identity N/A

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

   25. *-inverses N/A

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

   26. associate-*l/ N/A

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

   27. associate-*r/ N/A

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

   28. associate-*r/ N/A

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

   29. *-rgt-identity N/A

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

5. Applied rewrites 60.4%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 21.0%

   \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]
9. 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 2024233 
(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)))