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

Percentage Accurate: 99.7% → 99.8%

Time: 7.5s

Alternatives: 14

Speedup: 1.0×

• 20.7% 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: 61.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+220}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -3.8e-32)
     t_0
     (if (<= z 6e-75) x (if (<= z 1.15e+220) 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 <= -3.8e-32) {
		tmp = t_0;
	} else if (z <= 6e-75) {
		tmp = x;
	} else if (z <= 1.15e+220) {
		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 <= (-3.8d-32)) then
        tmp = t_0
    else if (z <= 6d-75) then
        tmp = x
    else if (z <= 1.15d+220) 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 <= -3.8e-32) {
		tmp = t_0;
	} else if (z <= 6e-75) {
		tmp = x;
	} else if (z <= 1.15e+220) {
		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 <= -3.8e-32:
		tmp = t_0
	elif z <= 6e-75:
		tmp = x
	elif z <= 1.15e+220:
		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 <= -3.8e-32)
		tmp = t_0;
	elseif (z <= 6e-75)
		tmp = x;
	elseif (z <= 1.15e+220)
		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 <= -3.8e-32)
		tmp = t_0;
	elseif (z <= 6e-75)
		tmp = x;
	elseif (z <= 1.15e+220)
		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, -3.8e-32], t$95$0, If[LessEqual[z, 6e-75], x, If[LessEqual[z, 1.15e+220], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000008e-32 or 5.9999999999999997e-75 < z < 1.14999999999999998e220

   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 92.5%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. *-commutative 58.0%

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

   6. Simplified 58.0%

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

   if -3.80000000000000008e-32 < z < 5.9999999999999997e-75

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

   if 1.14999999999999998e220 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. *-commutative 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in z around 0 65.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+220}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.45e-31)
   (* 6.0 (* y z))
   (if (<= z 1.5e-70)
     x
     (if (<= z 1.3e+217) (* z (* y 6.0)) (* -6.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e-31) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.5e-70) {
		tmp = x;
	} else if (z <= 1.3e+217) {
		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 <= (-1.45d-31)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 1.5d-70) then
        tmp = x
    else if (z <= 1.3d+217) 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 <= -1.45e-31) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.5e-70) {
		tmp = x;
	} else if (z <= 1.3e+217) {
		tmp = z * (y * 6.0);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.45e-31:
		tmp = 6.0 * (y * z)
	elif z <= 1.5e-70:
		tmp = x
	elif z <= 1.3e+217:
		tmp = z * (y * 6.0)
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.45e-31)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 1.5e-70)
		tmp = x;
	elseif (z <= 1.3e+217)
		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 <= -1.45e-31)
		tmp = 6.0 * (y * z);
	elseif (z <= 1.5e-70)
		tmp = x;
	elseif (z <= 1.3e+217)
		tmp = z * (y * 6.0);
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.45e-31], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-70], x, If[LessEqual[z, 1.3e+217], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e-31

   1. Initial program 99.6%

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

   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 98.1%

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

   4. Taylor expanded in y around inf 57.3%

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

      1. *-commutative 57.3%

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

   6. Simplified 57.3%

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

   if -1.45e-31 < z < 1.5000000000000001e-70

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

   if 1.5000000000000001e-70 < z < 1.30000000000000006e217

   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 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l* 86.9%

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

      3. *-commutative 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   if 1.30000000000000006e217 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. *-commutative 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in z around 0 65.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e-31)
   (* 6.0 (* y z))
   (if (<= z 2.4e-69)
     x
     (if (<= z 2.5e+219) (* z (* y 6.0)) (* x (* z -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e-31) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.4e-69) {
		tmp = x;
	} else if (z <= 2.5e+219) {
		tmp = z * (y * 6.0);
	} 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) :: tmp
    if (z <= (-1.5d-31)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 2.4d-69) then
        tmp = x
    else if (z <= 2.5d+219) then
        tmp = z * (y * 6.0d0)
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e-31) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.4e-69) {
		tmp = x;
	} else if (z <= 2.5e+219) {
		tmp = z * (y * 6.0);
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e-31:
		tmp = 6.0 * (y * z)
	elif z <= 2.4e-69:
		tmp = x
	elif z <= 2.5e+219:
		tmp = z * (y * 6.0)
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e-31)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 2.4e-69)
		tmp = x;
	elseif (z <= 2.5e+219)
		tmp = Float64(z * Float64(y * 6.0));
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e-31)
		tmp = 6.0 * (y * z);
	elseif (z <= 2.4e-69)
		tmp = x;
	elseif (z <= 2.5e+219)
		tmp = z * (y * 6.0);
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e-31], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-69], x, If[LessEqual[z, 2.5e+219], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.49999999999999991e-31

   1. Initial program 99.6%

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

   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 98.1%

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

   4. Taylor expanded in y around inf 57.3%

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

      1. *-commutative 57.3%

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

   6. Simplified 57.3%

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

   if -1.49999999999999991e-31 < z < 2.4000000000000001e-69

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

   if 2.4000000000000001e-69 < z < 2.5e219

   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 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l* 86.9%

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

      3. *-commutative 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   if 2.5e219 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 65.2%

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

   3. Taylor expanded in z around inf 65.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-32} \lor \neg \left(z \leq 3.15 \cdot 10^{-21}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e-32) (not (<= z 3.15e-21))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e-32) || !(z <= 3.15e-21)) {
		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 <= (-3.6d-32)) .or. (.not. (z <= 3.15d-21))) 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 <= -3.6e-32) || !(z <= 3.15e-21)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.6e-32) or not (z <= 3.15e-21):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.6e-32) || !(z <= 3.15e-21))
		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 <= -3.6e-32) || ~((z <= 3.15e-21)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.6e-32], N[Not[LessEqual[z, 3.15e-21]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999993e-32 or 3.15e-21 < 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 98.6%

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

   if -3.59999999999999993e-32 < z < 3.15e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 70.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-32} \lor \neg \left(z \leq 3.15 \cdot 10^{-21}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-30}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.45e-30)
   (* 6.0 (* (- y x) z))
   (if (<= z 5.1e-21) x (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e-30) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.1e-21) {
		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 <= (-1.45d-30)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 5.1d-21) 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 <= -1.45e-30) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.1e-21) {
		tmp = x;
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.45e-30:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 5.1e-21:
		tmp = x
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.45e-30)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 5.1e-21)
		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 <= -1.45e-30)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 5.1e-21)
		tmp = x;
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.45e-30], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-21], x, N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999995e-30

   1. Initial program 99.6%

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

   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 98.1%

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

   if -1.44999999999999995e-30 < z < 5.10000000000000004e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 70.2%

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

   if 5.10000000000000004e-21 < 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. Step-by-step derivation

      1. *-commutative 99.1%

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

      2. associate-*l* 99.2%

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

      3. *-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-30}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 7: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-32}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6e-32)
   (* 6.0 (* (- y x) z))
   (if (<= z 3.6e-21) (* x (+ 1.0 (* z -6.0))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e-32) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 3.6e-21) {
		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 <= (-6d-32)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 3.6d-21) 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 <= -6e-32) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 3.6e-21) {
		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 <= -6e-32:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 3.6e-21:
		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 <= -6e-32)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 3.6e-21)
		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 <= -6e-32)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 3.6e-21)
		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, -6e-32], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-21], 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 < -6.0000000000000001e-32

   1. Initial program 99.6%

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

   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 98.1%

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

   if -6.0000000000000001e-32 < z < 3.59999999999999989e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 70.2%

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

   if 3.59999999999999989e-21 < 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. Step-by-step derivation

      1. *-commutative 99.1%

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

      2. associate-*l* 99.2%

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

      3. *-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-32}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 8: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.02e-20) (+ x (* 6.0 (* y z))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.02e-20) {
		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 <= (-0.17d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.02d-20) 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 <= -0.17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.02e-20) {
		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 <= -0.17:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.02e-20:
		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 <= -0.17)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.02e-20)
		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 <= -0.17)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.02e-20)
		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, -0.17], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-20], 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 < -0.170000000000000012

   1. Initial program 99.6%

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

   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 97.9%

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

   if -0.170000000000000012 < z < 1.02000000000000001e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.8%

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

   if 1.02000000000000001e-20 < 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. Step-by-step derivation

      1. *-commutative 99.1%

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

      2. associate-*l* 99.2%

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

      3. *-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 9: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.02e-20) (+ x (* y (* 6.0 z))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.02e-20) {
		tmp = x + (y * (6.0 * 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 <= (-0.17d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.02d-20) then
        tmp = x + (y * (6.0d0 * 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 <= -0.17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.02e-20) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.02e-20:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.02e-20)
		tmp = Float64(x + Float64(y * Float64(6.0 * 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 <= -0.17)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.02e-20)
		tmp = x + (y * (6.0 * z));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-20], N[(x + N[(y * N[(6.0 * 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 < -0.170000000000000012

   1. Initial program 99.6%

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

   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 97.9%

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

   if -0.170000000000000012 < z < 1.02000000000000001e-20

   1. Initial program 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. flip-- 55.9%

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

      4. associate-*r/ 55.3%

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

   3. Applied egg-rr 55.3%

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

      1. associate-/l* 55.8%

         \[\leadsto x + \color{blue}{\frac{6 \cdot z}{\frac{y + x}{y \cdot y - x \cdot x}}} \]

      2. *-commutative 55.8%

         \[\leadsto x + \frac{\color{blue}{z \cdot 6}}{\frac{y + x}{y \cdot y - x \cdot x}} \]

      3. associate-/l* 55.8%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{\frac{y + x}{y \cdot y - x \cdot x}}{6}}} \]

      4. difference-of-squares 56.1%

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

      5. associate-/r* 99.7%

         \[\leadsto x + \frac{z}{\frac{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}{6}} \]

      6. *-inverses 99.7%

         \[\leadsto x + \frac{z}{\frac{\frac{\color{blue}{1}}{y - x}}{6}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{z}{\frac{\frac{1}{y - x}}{6}}} \]

   6. Taylor expanded in y around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

   8. Simplified 99.9%

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

   if 1.02000000000000001e-20 < 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. Step-by-step derivation

      1. *-commutative 99.1%

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

      2. associate-*l* 99.2%

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

      3. *-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 10: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-5)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.02e-20) (+ x (* z (* y 6.0))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-5) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.02e-20) {
		tmp = x + (z * (y * 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 <= (-8.5d-5)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.02d-20) then
        tmp = x + (z * (y * 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 <= -8.5e-5) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.02e-20) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e-5:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.02e-20:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-5)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.02e-20)
		tmp = Float64(x + Float64(z * Float64(y * 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 <= -8.5e-5)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.02e-20)
		tmp = x + (z * (y * 6.0));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-5], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-20], N[(x + N[(z * N[(y * 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 < -8.500000000000001e-5

   1. Initial program 99.6%

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

   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 97.9%

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

   if -8.500000000000001e-5 < z < 1.02000000000000001e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

   if 1.02000000000000001e-20 < 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. Step-by-step derivation

      1. *-commutative 99.1%

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

      2. associate-*l* 99.2%

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

      3. *-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 11: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5} \lor \neg \left(z \leq 0.21\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-5) (not (<= z 0.21))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-5) || !(z <= 0.21)) {
		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 <= (-8.5d-5)) .or. (.not. (z <= 0.21d0))) 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 <= -8.5e-5) || !(z <= 0.21)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-5) or not (z <= 0.21):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-5) || !(z <= 0.21))
		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 <= -8.5e-5) || ~((z <= 0.21)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-5], N[Not[LessEqual[z, 0.21]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.500000000000001e-5 or 0.209999999999999992 < 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 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l* 98.6%

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

      3. *-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in z around 0 48.7%

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

   if -8.500000000000001e-5 < z < 0.209999999999999992

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 65.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5} \lor \neg \left(z \leq 0.21\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 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 13: 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 14: 36.9% 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 34.2%

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

3. Final simplification 34.2%

   \[\leadsto x \]

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 2023196 
(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)))