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

Percentage Accurate: 99.7% → 99.7%

Time: 10.0s

Alternatives: 12

Speedup: 1.0×

• 20.9% 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, 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]

Derivation

1. Initial program 99.8%

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

Alternative 2: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -23.5:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -3.9e+200)
     t_0
     (if (<= z -23.5)
       (* -6.0 (* x z))
       (if (<= z -1.1e-88) t_0 (if (<= z 0.17) x (* z (* x -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.9e+200) {
		tmp = t_0;
	} else if (z <= -23.5) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.1e-88) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = z * (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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-3.9d+200)) then
        tmp = t_0
    else if (z <= (-23.5d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-1.1d-88)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = z * (x * (-6.0d0))
    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 <= -3.9e+200) {
		tmp = t_0;
	} else if (z <= -23.5) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.1e-88) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -3.9e+200:
		tmp = t_0
	elif z <= -23.5:
		tmp = -6.0 * (x * z)
	elif z <= -1.1e-88:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	else:
		tmp = z * (x * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.9e+200)
		tmp = t_0;
	elseif (z <= -23.5)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -1.1e-88)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.9e+200)
		tmp = t_0;
	elseif (z <= -23.5)
		tmp = -6.0 * (x * z);
	elseif (z <= -1.1e-88)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = z * (x * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+200], t$95$0, If[LessEqual[z, -23.5], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-88], t$95$0, If[LessEqual[z, 0.17], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.90000000000000019e200 or -23.5 < z < -1.10000000000000002e-88

   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 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

      1. +-commutative 82.7%

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

      2. *-commutative 82.7%

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

      3. fma-define 82.8%

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

   7. Applied egg-rr 82.8%

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

   8. Taylor expanded in z around inf 66.2%

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

   if -3.90000000000000019e200 < z < -23.5

   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 67.1%

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

   4. Taylor expanded in z around inf 65.0%

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

   if -1.10000000000000002e-88 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 76.0%

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

   if 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 y around 0 59.9%

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

   4. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r* 59.4%

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

   6. Simplified 59.4%

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

Alternative 3: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+199}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -23.5:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-89}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -5.2e+199)
     t_0
     (if (<= z -23.5)
       (* -6.0 (* x z))
       (if (<= z -9e-89) t_0 (if (<= z 0.17) x (* x (* z -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -5.2e+199) {
		tmp = t_0;
	} else if (z <= -23.5) {
		tmp = -6.0 * (x * z);
	} else if (z <= -9e-89) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-5.2d+199)) then
        tmp = t_0
    else if (z <= (-23.5d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-9d-89)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = x * (z * (-6.0d0))
    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 <= -5.2e+199) {
		tmp = t_0;
	} else if (z <= -23.5) {
		tmp = -6.0 * (x * z);
	} else if (z <= -9e-89) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -5.2e+199:
		tmp = t_0
	elif z <= -23.5:
		tmp = -6.0 * (x * z)
	elif z <= -9e-89:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5.2e+199)
		tmp = t_0;
	elseif (z <= -23.5)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -9e-89)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5.2e+199)
		tmp = t_0;
	elseif (z <= -23.5)
		tmp = -6.0 * (x * z);
	elseif (z <= -9e-89)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+199], t$95$0, If[LessEqual[z, -23.5], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-89], t$95$0, If[LessEqual[z, 0.17], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2000000000000003e199 or -23.5 < z < -8.9999999999999998e-89

   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 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

      1. +-commutative 82.7%

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

      2. *-commutative 82.7%

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

      3. fma-define 82.8%

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

   7. Applied egg-rr 82.8%

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

   8. Taylor expanded in z around inf 66.2%

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

   if -5.2000000000000003e199 < z < -23.5

   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 67.1%

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

   4. Taylor expanded in z around inf 65.0%

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

   if -8.9999999999999998e-89 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 76.0%

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

   if 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 y around 0 59.9%

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

   4. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. *-commutative 59.3%

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

      3. *-commutative 59.3%

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

      4. associate-*r* 59.4%

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

   6. Simplified 59.4%

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

Alternative 4: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -23.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -1.5e+202)
     t_0
     (if (<= z -23.5) t_1 (if (<= z -1.1e-88) t_0 (if (<= z 0.17) x 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 <= -1.5e+202) {
		tmp = t_0;
	} else if (z <= -23.5) {
		tmp = t_1;
	} else if (z <= -1.1e-88) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} 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 <= (-1.5d+202)) then
        tmp = t_0
    else if (z <= (-23.5d0)) then
        tmp = t_1
    else if (z <= (-1.1d-88)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    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 <= -1.5e+202) {
		tmp = t_0;
	} else if (z <= -23.5) {
		tmp = t_1;
	} else if (z <= -1.1e-88) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} 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 <= -1.5e+202:
		tmp = t_0
	elif z <= -23.5:
		tmp = t_1
	elif z <= -1.1e-88:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	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 <= -1.5e+202)
		tmp = t_0;
	elseif (z <= -23.5)
		tmp = t_1;
	elseif (z <= -1.1e-88)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	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 <= -1.5e+202)
		tmp = t_0;
	elseif (z <= -23.5)
		tmp = t_1;
	elseif (z <= -1.1e-88)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	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, -1.5e+202], t$95$0, If[LessEqual[z, -23.5], t$95$1, If[LessEqual[z, -1.1e-88], t$95$0, If[LessEqual[z, 0.17], x, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e202 or -23.5 < z < -1.10000000000000002e-88

   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 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

      1. +-commutative 82.7%

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

      2. *-commutative 82.7%

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

      3. fma-define 82.8%

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

   7. Applied egg-rr 82.8%

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

   8. Taylor expanded in z around inf 66.2%

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

   if -1.5000000000000001e202 < z < -23.5 or 0.170000000000000012 < z

   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 63.2%

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

   4. Taylor expanded in z around inf 61.9%

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

   if -1.10000000000000002e-88 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 76.0%

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

Alternative 5: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-68} \lor \neg \left(x \leq 0.00017\right):\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e-68) (not (<= x 0.00017)))
   (+ x (* x (* z -6.0)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e-68) || !(x <= 0.00017)) {
		tmp = x + (x * (z * -6.0));
	} 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 ((x <= (-4.2d-68)) .or. (.not. (x <= 0.00017d0))) then
        tmp = x + (x * (z * (-6.0d0)))
    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 ((x <= -4.2e-68) || !(x <= 0.00017)) {
		tmp = x + (x * (z * -6.0));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.2e-68) or not (x <= 0.00017):
		tmp = x + (x * (z * -6.0))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e-68) || !(x <= 0.00017))
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	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 ((x <= -4.2e-68) || ~((x <= 0.00017)))
		tmp = x + (x * (z * -6.0));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e-68], N[Not[LessEqual[x, 0.00017]], $MachinePrecision]], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000016e-68 or 1.7e-4 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-*r* 89.1%

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

      3. *-commutative 89.1%

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

   5. Simplified 89.1%

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

   if -4.20000000000000016e-68 < x < 1.7e-4

   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 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-68} \lor \neg \left(x \leq 0.00017\right):\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-68} \lor \neg \left(x \leq 1.2 \cdot 10^{-5}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-68) (not (<= x 1.2e-5)))
   (+ x (* -6.0 (* x z)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-68) || !(x <= 1.2e-5)) {
		tmp = x + (-6.0 * (x * 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 ((x <= (-4.8d-68)) .or. (.not. (x <= 1.2d-5))) then
        tmp = x + ((-6.0d0) * (x * 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 ((x <= -4.8e-68) || !(x <= 1.2e-5)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-68) or not (x <= 1.2e-5):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-68) || !(x <= 1.2e-5))
		tmp = Float64(x + Float64(-6.0 * Float64(x * 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 ((x <= -4.8e-68) || ~((x <= 1.2e-5)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-68], N[Not[LessEqual[x, 1.2e-5]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999982e-68 or 1.2e-5 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.0%

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

   if -4.79999999999999982e-68 < x < 1.2e-5

   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 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-68} \lor \neg \left(x \leq 1.2 \cdot 10^{-5}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.76 \cdot 10^{-68} \lor \neg \left(x \leq 1.8 \cdot 10^{-32}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.76e-68) (not (<= x 1.8e-32)))
   (+ x (* -6.0 (* x z)))
   (* z (* y 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.76e-68) || !(x <= 1.8e-32)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = z * (y * 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 ((x <= (-1.76d-68)) .or. (.not. (x <= 1.8d-32))) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.76e-68) || !(x <= 1.8e-32)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.76e-68) or not (x <= 1.8e-32):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.76e-68) || !(x <= 1.8e-32))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.76e-68) || ~((x <= 1.8e-32)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.76e-68], N[Not[LessEqual[x, 1.8e-32]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.76e-68 or 1.79999999999999996e-32 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.7%

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

   if -1.76e-68 < x < 1.79999999999999996e-32

   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 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

      1. +-commutative 91.4%

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

      2. *-commutative 91.4%

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

      3. fma-define 91.4%

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

   7. Applied egg-rr 91.4%

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

   8. Taylor expanded in z around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*r* 72.7%

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

      4. *-commutative 72.7%

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

   10. Simplified 72.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.76 \cdot 10^{-68} \lor \neg \left(x \leq 1.8 \cdot 10^{-32}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-68}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 0.0023:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.5e-68)
   (+ x (* x (* z -6.0)))
   (if (<= x 0.0023) (+ x (* z (* y 6.0))) (+ x (* z (* x -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-68) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 0.0023) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (z * (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 (x <= (-4.5d-68)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (x <= 0.0023d0) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = x + (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-68) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 0.0023) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.5e-68:
		tmp = x + (x * (z * -6.0))
	elif x <= 0.0023:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.5e-68)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (x <= 0.0023)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.5e-68)
		tmp = x + (x * (z * -6.0));
	elseif (x <= 0.0023)
		tmp = x + (z * (y * 6.0));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.5e-68], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0023], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.49999999999999999e-68

   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 0 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*r* 88.6%

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

      3. *-commutative 88.6%

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

   5. Simplified 88.6%

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

   if -4.49999999999999999e-68 < x < 0.0023

   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 90.9%

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

   if 0.0023 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. associate-*r* 89.7%

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

   5. Simplified 89.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-68}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 0.0023:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-68}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 0.000125:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e-68)
   (+ x (* x (* z -6.0)))
   (if (<= x 0.000125) (+ x (* 6.0 (* y z))) (+ x (* z (* x -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e-68) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 0.000125) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (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 (x <= (-4.8d-68)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (x <= 0.000125d0) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e-68) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= 0.000125) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e-68:
		tmp = x + (x * (z * -6.0))
	elif x <= 0.000125:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e-68)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (x <= 0.000125)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e-68)
		tmp = x + (x * (z * -6.0));
	elseif (x <= 0.000125)
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e-68], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.000125], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999982e-68

   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 0 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*r* 88.6%

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

      3. *-commutative 88.6%

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

   5. Simplified 88.6%

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

   if -4.79999999999999982e-68 < x < 1.25e-4

   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 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   if 1.25e-4 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. associate-*r* 89.7%

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

   5. Simplified 89.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-68}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 0.000125:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.17)) {
		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 <= 0.17d0))) 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 <= 0.17)) {
		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 <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.17))
		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 <= 0.17)))
		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, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.170000000000000012 < z

   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 58.7%

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

   4. Taylor expanded in z around inf 57.7%

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

   if -0.165000000000000008 < z < 0.170000000000000012

   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 0 72.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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: 36.6% 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. Add Preprocessing

3. Taylor expanded in z around 0 39.3%

   \[\leadsto \color{blue}{x} \]
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 2024144 
(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)))