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

Percentage Accurate: 99.7% → 99.7%

Time: 7.4s

Alternatives: 11

Speedup: 1.1×

• 21.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   5. lift-fma.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 99.8

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 99.8

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

6. Applied rewrites 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(y - x\right) \cdot z\right) \cdot 6\\ \mathbf{if}\;z \leq -1900000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 6, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* (- y x) z) 6.0)))
   (if (<= z -1900000000.0) t_0 (if (<= z 1.45e-25) (fma (* y 6.0) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y - x) * z) * 6.0;
	double tmp;
	if (z <= -1900000000.0) {
		tmp = t_0;
	} else if (z <= 1.45e-25) {
		tmp = fma((y * 6.0), z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y - x) * z) * 6.0)
	tmp = 0.0
	if (z <= -1900000000.0)
		tmp = t_0;
	elseif (z <= 1.45e-25)
		tmp = fma(Float64(y * 6.0), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[z, -1900000000.0], t$95$0, If[LessEqual[z, 1.45e-25], N[(N[(y * 6.0), $MachinePrecision] * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e9 or 1.45e-25 < 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 98.8

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

   5. Applied rewrites 98.8%

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

   if -1.9e9 < z < 1.45e-25

   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 98.9

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

   5. Applied rewrites 98.9%

      \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]
   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 98.9

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

   7. Applied rewrites 98.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1900000000:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot 6\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 6, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{if}\;z \leq -1900000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 6, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* (- y x) 6.0) z)))
   (if (<= z -1900000000.0) t_0 (if (<= z 1.45e-25) (fma (* y 6.0) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y - x) * 6.0) * z;
	double tmp;
	if (z <= -1900000000.0) {
		tmp = t_0;
	} else if (z <= 1.45e-25) {
		tmp = fma((y * 6.0), z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y - x) * 6.0) * z)
	tmp = 0.0
	if (z <= -1900000000.0)
		tmp = t_0;
	elseif (z <= 1.45e-25)
		tmp = fma(Float64(y * 6.0), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1900000000.0], t$95$0, If[LessEqual[z, 1.45e-25], N[(N[(y * 6.0), $MachinePrecision] * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e9 or 1.45e-25 < 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 98.8

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

   5. Applied rewrites 98.8%

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

   7. Applied rewrites 98.7%

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

   if -1.9e9 < z < 1.45e-25

   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 98.9

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

   5. Applied rewrites 98.9%

      \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]
   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 98.9

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

   7. Applied rewrites 98.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1900000000:\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 6, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y \cdot 6, z, x\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-127}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* y 6.0) z x)))
   (if (<= y -3.6e-17) t_0 (if (<= y 6.2e-127) (fma (* z x) -6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((y * 6.0), z, x);
	double tmp;
	if (y <= -3.6e-17) {
		tmp = t_0;
	} else if (y <= 6.2e-127) {
		tmp = fma((z * x), -6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(y * 6.0), z, x)
	tmp = 0.0
	if (y <= -3.6e-17)
		tmp = t_0;
	elseif (y <= 6.2e-127)
		tmp = fma(Float64(z * x), -6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 6.0), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -3.6e-17], t$95$0, If[LessEqual[y, 6.2e-127], N[(N[(z * x), $MachinePrecision] * -6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999995e-17 or 6.2e-127 < 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 90.8

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

   5. Applied rewrites 90.8%

      \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]
   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 90.8

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

   7. Applied rewrites 90.8%

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

   if -3.59999999999999995e-17 < y < 6.2e-127

   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 86.9

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

   5. Applied rewrites 86.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 6, z, x\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-127}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 6, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -59:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 6\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -59.0)
   (* (* z y) 6.0)
   (if (<= y 4.6e+79) (fma (* z x) -6.0 x) (* (* y 6.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -59.0) {
		tmp = (z * y) * 6.0;
	} else if (y <= 4.6e+79) {
		tmp = fma((z * x), -6.0, x);
	} else {
		tmp = (y * 6.0) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -59.0)
		tmp = Float64(Float64(z * y) * 6.0);
	elseif (y <= 4.6e+79)
		tmp = fma(Float64(z * x), -6.0, x);
	else
		tmp = Float64(Float64(y * 6.0) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -59.0], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[y, 4.6e+79], N[(N[(z * x), $MachinePrecision] * -6.0 + x), $MachinePrecision], N[(N[(y * 6.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -59

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   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 85.6

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

   5. Applied rewrites 85.6%

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

   if -59 < y < 4.6000000000000001e79

   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 77.3

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

   5. Applied rewrites 77.3%

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

   if 4.6000000000000001e79 < y

   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

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   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 75.0

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 75.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -59:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 6\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-125}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 6\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.2e-29)
   (* (* z y) 6.0)
   (if (<= y 1.7e-125) (* (* z x) -6.0) (* (* y 6.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e-29) {
		tmp = (z * y) * 6.0;
	} else if (y <= 1.7e-125) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = (y * 6.0) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.2d-29)) then
        tmp = (z * y) * 6.0d0
    else if (y <= 1.7d-125) then
        tmp = (z * x) * (-6.0d0)
    else
        tmp = (y * 6.0d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e-29) {
		tmp = (z * y) * 6.0;
	} else if (y <= 1.7e-125) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = (y * 6.0) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.2e-29:
		tmp = (z * y) * 6.0
	elif y <= 1.7e-125:
		tmp = (z * x) * -6.0
	else:
		tmp = (y * 6.0) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.2e-29)
		tmp = Float64(Float64(z * y) * 6.0);
	elseif (y <= 1.7e-125)
		tmp = Float64(Float64(z * x) * -6.0);
	else
		tmp = Float64(Float64(y * 6.0) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.2e-29)
		tmp = (z * y) * 6.0;
	elseif (y <= 1.7e-125)
		tmp = (z * x) * -6.0;
	else
		tmp = (y * 6.0) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.2e-29], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[y, 1.7e-125], N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision], N[(N[(y * 6.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999965e-29

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   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 81.3

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

   5. Applied rewrites 81.3%

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

   if -9.19999999999999965e-29 < y < 1.69999999999999988e-125

   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 56.3

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

   5. Applied rewrites 56.3%

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

   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 43.6%

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

   if 1.69999999999999988e-125 < y

   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

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   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 59.1

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

   5. Applied rewrites 59.1%

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

   7. Applied rewrites 59.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-125}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 6\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot 6\right) \cdot z\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-125}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y 6.0) z)))
   (if (<= y -9.2e-29) t_0 (if (<= y 1.7e-125) (* (* z x) -6.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 6.0) * z;
	double tmp;
	if (y <= -9.2e-29) {
		tmp = t_0;
	} else if (y <= 1.7e-125) {
		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 = (y * 6.0d0) * z
    if (y <= (-9.2d-29)) then
        tmp = t_0
    else if (y <= 1.7d-125) 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 = (y * 6.0) * z;
	double tmp;
	if (y <= -9.2e-29) {
		tmp = t_0;
	} else if (y <= 1.7e-125) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 6.0) * z
	tmp = 0
	if y <= -9.2e-29:
		tmp = t_0
	elif y <= 1.7e-125:
		tmp = (z * x) * -6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 6.0) * z)
	tmp = 0.0
	if (y <= -9.2e-29)
		tmp = t_0;
	elseif (y <= 1.7e-125)
		tmp = Float64(Float64(z * x) * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 6.0) * z;
	tmp = 0.0;
	if (y <= -9.2e-29)
		tmp = t_0;
	elseif (y <= 1.7e-125)
		tmp = (z * x) * -6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 6.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -9.2e-29], t$95$0, If[LessEqual[y, 1.7e-125], N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.19999999999999965e-29 or 1.69999999999999988e-125 < 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 68.5

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

   5. Applied rewrites 68.5%

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

   7. Applied rewrites 68.4%

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

   if -9.19999999999999965e-29 < y < 1.69999999999999988e-125

   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 56.3

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

   5. Applied rewrites 56.3%

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

   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 43.6%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;\left(y \cdot 6\right) \cdot z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-125}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 6\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(z * 6.0), $MachinePrecision] + 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. lower-fma.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 9: 99.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. lower-fma.f64 99.8

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 10: 27.9% accurate, 1.5× speedup

Math

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

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(z * x), $MachinePrecision] * -6.0), $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 70.0

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

5. Applied rewrites 70.0%

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

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 22.5%

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

Alternative 11: 27.9% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z * N[(-6.0 * x), $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. *-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 70.0

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

5. Applied rewrites 70.0%

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

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 22.5%

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

10. Applied rewrites 22.5%

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

11. Final simplification 22.5%

    \[\leadsto z \cdot \left(-6 \cdot x\right) \]
12. 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 2024266 
(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)))