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

Percentage Accurate: 99.7% → 99.8%

Time: 6.4s

Alternatives: 13

Speedup: 1.0×

• 20.6% 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 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-*l* 99.8%

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

   3. fma-def 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. Final simplification 99.8%

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

Alternative 2: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.165:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+147} \lor \neg \left(z \leq 5.6 \cdot 10^{+175}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -1.32e+243)
     t_0
     (if (<= z -0.165)
       t_1
       (if (<= z 8.5e-13)
         x
         (if (or (<= z 1.25e+147) (not (<= z 5.6e+175))) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.32e+243) {
		tmp = t_0;
	} else if (z <= -0.165) {
		tmp = t_1;
	} else if (z <= 8.5e-13) {
		tmp = x;
	} else if ((z <= 1.25e+147) || !(z <= 5.6e+175)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-1.32d+243)) then
        tmp = t_0
    else if (z <= (-0.165d0)) then
        tmp = t_1
    else if (z <= 8.5d-13) then
        tmp = x
    else if ((z <= 1.25d+147) .or. (.not. (z <= 5.6d+175))) then
        tmp = t_0
    else
        tmp = t_1
    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 t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.32e+243) {
		tmp = t_0;
	} else if (z <= -0.165) {
		tmp = t_1;
	} else if (z <= 8.5e-13) {
		tmp = x;
	} else if ((z <= 1.25e+147) || !(z <= 5.6e+175)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -1.32e+243:
		tmp = t_0
	elif z <= -0.165:
		tmp = t_1
	elif z <= 8.5e-13:
		tmp = x
	elif (z <= 1.25e+147) or not (z <= 5.6e+175):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.32e+243)
		tmp = t_0;
	elseif (z <= -0.165)
		tmp = t_1;
	elseif (z <= 8.5e-13)
		tmp = x;
	elseif ((z <= 1.25e+147) || !(z <= 5.6e+175))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.32e+243)
		tmp = t_0;
	elseif (z <= -0.165)
		tmp = t_1;
	elseif (z <= 8.5e-13)
		tmp = x;
	elseif ((z <= 1.25e+147) || ~((z <= 5.6e+175)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e+243], t$95$0, If[LessEqual[z, -0.165], t$95$1, If[LessEqual[z, 8.5e-13], x, If[Or[LessEqual[z, 1.25e+147], N[Not[LessEqual[z, 5.6e+175]], $MachinePrecision]], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32000000000000009e243 or 8.5000000000000001e-13 < z < 1.2500000000000001e147 or 5.6000000000000002e175 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.5%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

   6. Simplified 64.9%

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

   if -1.32000000000000009e243 < z < -0.165000000000000008 or 1.2500000000000001e147 < z < 5.6000000000000002e175

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.4%

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

   4. Taylor expanded in y around 0 68.5%

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

   if -0.165000000000000008 < z < 8.5000000000000001e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+243}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.165:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+147} \lor \neg \left(z \leq 5.6 \cdot 10^{+175}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.165:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+146} \lor \neg \left(z \leq 2.8 \cdot 10^{+177}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -5.1e+243)
     t_0
     (if (<= z -0.165)
       (* x (* z -6.0))
       (if (<= z 4.1e-14)
         x
         (if (or (<= z 9.5e+146) (not (<= z 2.8e+177)))
           t_0
           (* -6.0 (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -5.1e+243) {
		tmp = t_0;
	} else if (z <= -0.165) {
		tmp = x * (z * -6.0);
	} else if (z <= 4.1e-14) {
		tmp = x;
	} else if ((z <= 9.5e+146) || !(z <= 2.8e+177)) {
		tmp = t_0;
	} else {
		tmp = -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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-5.1d+243)) then
        tmp = t_0
    else if (z <= (-0.165d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 4.1d-14) then
        tmp = x
    else if ((z <= 9.5d+146) .or. (.not. (z <= 2.8d+177))) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (x * z)
    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 (z <= -5.1e+243) {
		tmp = t_0;
	} else if (z <= -0.165) {
		tmp = x * (z * -6.0);
	} else if (z <= 4.1e-14) {
		tmp = x;
	} else if ((z <= 9.5e+146) || !(z <= 2.8e+177)) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -5.1e+243:
		tmp = t_0
	elif z <= -0.165:
		tmp = x * (z * -6.0)
	elif z <= 4.1e-14:
		tmp = x
	elif (z <= 9.5e+146) or not (z <= 2.8e+177):
		tmp = t_0
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5.1e+243)
		tmp = t_0;
	elseif (z <= -0.165)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 4.1e-14)
		tmp = x;
	elseif ((z <= 9.5e+146) || !(z <= 2.8e+177))
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5.1e+243)
		tmp = t_0;
	elseif (z <= -0.165)
		tmp = x * (z * -6.0);
	elseif (z <= 4.1e-14)
		tmp = x;
	elseif ((z <= 9.5e+146) || ~((z <= 2.8e+177)))
		tmp = t_0;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+243], t$95$0, If[LessEqual[z, -0.165], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-14], x, If[Or[LessEqual[z, 9.5e+146], N[Not[LessEqual[z, 2.8e+177]], $MachinePrecision]], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1000000000000002e243 or 4.1000000000000002e-14 < z < 9.49999999999999926e146 or 2.80000000000000002e177 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.5%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

   6. Simplified 64.9%

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

   if -5.1000000000000002e243 < z < -0.165000000000000008

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 68.3%

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

   3. Taylor expanded in z around inf 66.6%

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

   if -0.165000000000000008 < z < 4.1000000000000002e-14

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.2%

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

   if 9.49999999999999926e146 < z < 2.80000000000000002e177

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around 0 78.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+243}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.165:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+146} \lor \neg \left(z \leq 2.8 \cdot 10^{+177}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+237}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.165:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+146} \lor \neg \left(z \leq 5.8 \cdot 10^{+175}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+237)
   (* 6.0 (* y z))
   (if (<= z -0.165)
     (* x (* z -6.0))
     (if (<= z 6.6e-11)
       x
       (if (or (<= z 5e+146) (not (<= z 5.8e+175)))
         (* z (* y 6.0))
         (* -6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+237) {
		tmp = 6.0 * (y * z);
	} else if (z <= -0.165) {
		tmp = x * (z * -6.0);
	} else if (z <= 6.6e-11) {
		tmp = x;
	} else if ((z <= 5e+146) || !(z <= 5.8e+175)) {
		tmp = z * (y * 6.0);
	} else {
		tmp = -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 <= (-5.8d+237)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= (-0.165d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 6.6d-11) then
        tmp = x
    else if ((z <= 5d+146) .or. (.not. (z <= 5.8d+175))) then
        tmp = z * (y * 6.0d0)
    else
        tmp = (-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 <= -5.8e+237) {
		tmp = 6.0 * (y * z);
	} else if (z <= -0.165) {
		tmp = x * (z * -6.0);
	} else if (z <= 6.6e-11) {
		tmp = x;
	} else if ((z <= 5e+146) || !(z <= 5.8e+175)) {
		tmp = z * (y * 6.0);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+237:
		tmp = 6.0 * (y * z)
	elif z <= -0.165:
		tmp = x * (z * -6.0)
	elif z <= 6.6e-11:
		tmp = x
	elif (z <= 5e+146) or not (z <= 5.8e+175):
		tmp = z * (y * 6.0)
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+237)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= -0.165)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 6.6e-11)
		tmp = x;
	elseif ((z <= 5e+146) || !(z <= 5.8e+175))
		tmp = Float64(z * Float64(y * 6.0));
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+237)
		tmp = 6.0 * (y * z);
	elseif (z <= -0.165)
		tmp = x * (z * -6.0);
	elseif (z <= 6.6e-11)
		tmp = x;
	elseif ((z <= 5e+146) || ~((z <= 5.8e+175)))
		tmp = z * (y * 6.0);
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+237], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.165], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-11], x, If[Or[LessEqual[z, 5e+146], N[Not[LessEqual[z, 5.8e+175]], $MachinePrecision]], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.8000000000000002e237

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   if -5.8000000000000002e237 < z < -0.165000000000000008

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 68.3%

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

   3. Taylor expanded in z around inf 66.6%

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

   if -0.165000000000000008 < z < 6.6000000000000005e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.2%

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

   if 6.6000000000000005e-11 < z < 4.9999999999999999e146 or 5.8e175 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.2%

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

   4. Taylor expanded in y around inf 63.8%

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

      1. associate-*r* 63.9%

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

   6. Simplified 63.9%

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

   if 4.9999999999999999e146 < z < 5.8e175

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around 0 78.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+237}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.165:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+146} \lor \neg \left(z \leq 5.8 \cdot 10^{+175}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-81} \lor \neg \left(z \leq 6.5 \cdot 10^{-13}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.45e-81) (not (<= z 6.5e-13))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.45e-81) || !(z <= 6.5e-13)) {
		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 <= (-3.45d-81)) .or. (.not. (z <= 6.5d-13))) 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 <= -3.45e-81) || !(z <= 6.5e-13)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.45e-81) or not (z <= 6.5e-13):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.45e-81) || !(z <= 6.5e-13))
		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 <= -3.45e-81) || ~((z <= 6.5e-13)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.45e-81], N[Not[LessEqual[z, 6.5e-13]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4500000000000001e-81 or 6.49999999999999957e-13 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 93.4%

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

   if -3.4500000000000001e-81 < z < 6.49999999999999957e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-81} \lor \neg \left(z \leq 6.5 \cdot 10^{-13}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-81}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e-81)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.55e-12) x (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e-81) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.55e-12) {
		tmp = x;
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.1d-81)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.55d-12) then
        tmp = x
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e-81) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.55e-12) {
		tmp = x;
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.1e-81:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.55e-12:
		tmp = x
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e-81)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.55e-12)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e-81)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.55e-12)
		tmp = x;
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.1e-81], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-12], x, N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e-81

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 88.0%

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

   if -2.0999999999999999e-81 < z < 1.5500000000000001e-12

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.8%

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

   if 1.5500000000000001e-12 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.3%

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

      1. associate-*r* 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-*l* 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-81}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 7: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-81}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.6e-81)
   (* 6.0 (* (- y x) z))
   (if (<= z 4e-8) (* x (+ 1.0 (* z -6.0))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e-81) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 4e-8) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.6d-81)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 4d-8) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e-81) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 4e-8) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.6e-81:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 4e-8:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.6e-81)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 4e-8)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.6e-81)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 4e-8)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.6e-81], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-8], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999982e-81

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 88.0%

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

   if -4.59999999999999982e-81 < z < 4.0000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.3%

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

   if 4.0000000000000001e-8 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. associate-*r* 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*l* 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-81}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 8: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* 6.0 (* (- y x) z))
   (if (<= z 4.8e-5) (+ x (* 6.0 (* y z))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 4.8e-5) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 4.8d-5) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 4.8e-5) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 4.8e-5:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 4.8e-5)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 4.8e-5)
		tmp = x + (6.0 * (y * z));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-5], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.6%

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

   if -0.165000000000000008 < z < 4.8000000000000001e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.2%

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

   if 4.8000000000000001e-5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. associate-*r* 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*l* 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 9: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1200000000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 1200000000.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 1200000000.0)) {
		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 <= 1200000000.0d0))) 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 <= 1200000000.0)) {
		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 <= 1200000000.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 1200000000.0))
		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 <= 1200000000.0)))
		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, 1200000000.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 1.2e9 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.1%

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

   4. Taylor expanded in y around 0 52.5%

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

   if -0.165000000000000008 < z < 1.2e9

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 72.7%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1200000000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 11: 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 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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. Final simplification 99.8%

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

Alternative 12: 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 99.8%

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

2. Taylor expanded in z around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 13: 35.8% 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 99.8%

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

2. Taylor expanded in z around 0 34.7%

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

3. Final simplification 34.7%

   \[\leadsto x \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023221 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))