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

Percentage Accurate: 99.7% → 99.8%

Time: 15.8s

Alternatives: 12

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -1.4e+57)
     t_0
     (if (<= z -1.16e-12) (* z (* y 6.0)) (if (<= z 9.6e-7) x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.4e+57) {
		tmp = t_0;
	} else if (z <= -1.16e-12) {
		tmp = z * (y * 6.0);
	} else if (z <= 9.6e-7) {
		tmp = x;
	} 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) * (x * z)
    if (z <= (-1.4d+57)) then
        tmp = t_0
    else if (z <= (-1.16d-12)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 9.6d-7) then
        tmp = x
    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 * (x * z);
	double tmp;
	if (z <= -1.4e+57) {
		tmp = t_0;
	} else if (z <= -1.16e-12) {
		tmp = z * (y * 6.0);
	} else if (z <= 9.6e-7) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -1.4e+57:
		tmp = t_0
	elif z <= -1.16e-12:
		tmp = z * (y * 6.0)
	elif z <= 9.6e-7:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.4e+57)
		tmp = t_0;
	elseif (z <= -1.16e-12)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 9.6e-7)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.4e+57)
		tmp = t_0;
	elseif (z <= -1.16e-12)
		tmp = z * (y * 6.0);
	elseif (z <= 9.6e-7)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+57], t$95$0, If[LessEqual[z, -1.16e-12], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-7], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e57 or 9.59999999999999914e-7 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.6%

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

   5. Taylor expanded in y around 0 54.9%

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

   if -1.4e57 < z < -1.1599999999999999e-12

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 99.3%

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

   5. Taylor expanded in y around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

   7. Simplified 83.6%

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

   if -1.1599999999999999e-12 < z < 9.59999999999999914e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+57}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -1.26e+57)
     t_0
     (if (<= z -1.7e-9) (* 6.0 (* y z)) (if (<= z 9.6e-7) x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.26e+57) {
		tmp = t_0;
	} else if (z <= -1.7e-9) {
		tmp = 6.0 * (y * z);
	} else if (z <= 9.6e-7) {
		tmp = x;
	} 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) * (x * z)
    if (z <= (-1.26d+57)) then
        tmp = t_0
    else if (z <= (-1.7d-9)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 9.6d-7) then
        tmp = x
    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 * (x * z);
	double tmp;
	if (z <= -1.26e+57) {
		tmp = t_0;
	} else if (z <= -1.7e-9) {
		tmp = 6.0 * (y * z);
	} else if (z <= 9.6e-7) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -1.26e+57:
		tmp = t_0
	elif z <= -1.7e-9:
		tmp = 6.0 * (y * z)
	elif z <= 9.6e-7:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.26e+57)
		tmp = t_0;
	elseif (z <= -1.7e-9)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 9.6e-7)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.26e+57)
		tmp = t_0;
	elseif (z <= -1.7e-9)
		tmp = 6.0 * (y * z);
	elseif (z <= 9.6e-7)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+57], t$95$0, If[LessEqual[z, -1.7e-9], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-7], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.26e57 or 9.59999999999999914e-7 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.6%

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

   5. Taylor expanded in y around 0 54.9%

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

   if -1.26e57 < z < -1.6999999999999999e-9

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 99.3%

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

   5. Taylor expanded in y around inf 83.5%

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

      1. *-commutative 83.5%

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

   7. Simplified 83.5%

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

   if -1.6999999999999999e-9 < z < 9.59999999999999914e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+57}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15600000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -15600000000.0) (not (<= z 0.17)))
   (* (- y x) (* 6.0 z))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -15600000000.0) || !(z <= 0.17)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (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 ((z <= (-15600000000.0d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -15600000000.0) || !(z <= 0.17)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -15600000000.0) or not (z <= 0.17):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -15600000000.0) || !(z <= 0.17))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -15600000000.0) || ~((z <= 0.17)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -15600000000.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.56e10 or 0.170000000000000012 < 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 0 99.7%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in y around 0 91.4%

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

      1. associate-*r* 91.4%

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

      2. associate-*r* 91.4%

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

      3. distribute-rgt-in 98.7%

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

      4. metadata-eval 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

      7. +-commutative 98.7%

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

      8. distribute-lft-out 98.7%

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

      9. sub-neg 98.7%

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

      10. associate-*r* 98.8%

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

   7. Simplified 98.8%

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

   if -1.56e10 < z < 0.170000000000000012

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*r* 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15600000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.0) (not (<= z 0.17)))
   (* (- y x) (* 6.0 z))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.0) || !(z <= 0.17)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.0d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.0) || !(z <= 0.17)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.0) or not (z <= 0.17):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.0) || !(z <= 0.17))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.0) || ~((z <= 0.17)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5 or 0.170000000000000012 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in y around 0 91.6%

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

      1. associate-*r* 91.6%

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

      2. associate-*r* 91.6%

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

      3. distribute-rgt-in 98.8%

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

      4. metadata-eval 98.8%

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

      5. distribute-lft-neg-in 98.8%

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

      6. distribute-rgt-neg-out 98.8%

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

      7. +-commutative 98.8%

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

      8. distribute-lft-out 98.8%

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

      9. sub-neg 98.8%

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

      10. associate-*r* 98.8%

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

   7. Simplified 98.8%

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

   if -5 < z < 0.170000000000000012

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 99.1%

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

      1. *-commutative 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-12} \lor \neg \left(z \leq 3.2 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e-12) (not (<= z 3.2e-8)))
   (* (- y x) (* 6.0 z))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-12) || !(z <= 3.2e-8)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7d-12)) .or. (.not. (z <= 3.2d-8))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-12) || !(z <= 3.2e-8)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e-12) or not (z <= 3.2e-8):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7e-12) || !(z <= 3.2e-8))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7e-12) || ~((z <= 3.2e-8)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e-12], N[Not[LessEqual[z, 3.2e-8]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000001e-12 or 3.2000000000000002e-8 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.6%

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

   5. Taylor expanded in y around 0 91.7%

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

      1. associate-*r* 91.8%

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

      2. associate-*r* 91.8%

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

      3. distribute-rgt-in 98.7%

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

      4. metadata-eval 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

      7. +-commutative 98.7%

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

      8. distribute-lft-out 98.7%

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

      9. sub-neg 98.7%

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

      10. associate-*r* 98.7%

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

   7. Simplified 98.7%

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

   if -7.0000000000000001e-12 < z < 3.2000000000000002e-8

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 77.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-12} \lor \neg \left(z \leq 3.2 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-12} \lor \neg \left(z \leq 1.8 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e-12) (not (<= z 1.8e-9))) (* (- y x) (* 6.0 z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e-12) || !(z <= 1.8e-9)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.7d-12)) .or. (.not. (z <= 1.8d-9))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e-12) || !(z <= 1.8e-9)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7e-12) or not (z <= 1.8e-9):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e-12) || !(z <= 1.8e-9))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e-12) || ~((z <= 1.8e-9)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e-12], N[Not[LessEqual[z, 1.8e-9]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999999e-12 or 1.8e-9 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.6%

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

   5. Taylor expanded in y around 0 91.7%

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

      1. associate-*r* 91.8%

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

      2. associate-*r* 91.8%

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

      3. distribute-rgt-in 98.7%

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

      4. metadata-eval 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

      7. +-commutative 98.7%

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

      8. distribute-lft-out 98.7%

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

      9. sub-neg 98.7%

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

      10. associate-*r* 98.7%

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

   7. Simplified 98.7%

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

   if -3.69999999999999999e-12 < z < 1.8e-9

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-12} \lor \neg \left(z \leq 1.8 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-12} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e-12) (not (<= z 4e-8))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e-12) || !(z <= 4e-8)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.05d-12)) .or. (.not. (z <= 4d-8))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e-12) || !(z <= 4e-8)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e-12) or not (z <= 4e-8):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e-12) || !(z <= 4e-8))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05e-12) || ~((z <= 4e-8)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e-12], N[Not[LessEqual[z, 4e-8]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999997e-12 or 4.0000000000000001e-8 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.6%

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

   if -1.04999999999999997e-12 < z < 4.0000000000000001e-8

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-12} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 9.6 \cdot 10^{-7}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 9.6e-7))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 9.6e-7)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 9.6d-7))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 9.6e-7)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 9.6e-7):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 9.6e-7))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 9.6e-7)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 9.6e-7]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 9.59999999999999914e-7 < 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 0 99.6%

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

   4. Taylor expanded in z around inf 98.6%

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

   5. Taylor expanded in y around 0 51.5%

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

   if -0.165000000000000008 < z < 9.59999999999999914e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 9.6 \cdot 10^{-7}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. associate-*l* 99.8%

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

3. Simplified 99.8%

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

Alternative 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in z around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 12: 37.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in z around 0 39.2%

   \[\leadsto \color{blue}{x} \]
4. 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 2024186 
(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)))