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

Percentage Accurate: 99.7% → 99.8%
Time: 4.0s
Alternatives: 13
Speedup: 1.1×

Specification

?
\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

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

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

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

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

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

\begin{array}{l}

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

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 13 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 99.7% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

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

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

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

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

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

\begin{array}{l}

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

Alternative 1: 99.8% accurate, 1.1× speedup?

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, z \cdot 6, x\right) \end{array} \]
(FPCore (x y z) :precision binary64 (fma (- y x) (* z 6.0) x))
double code(double x, double y, double z) {
	return fma((y - x), (z * 6.0), x);
}

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

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

\begin{array}{l}

\\
\mathsf{fma}\left(y - x, z \cdot 6, x\right)
\end{array}
Derivation

  1. Initial program 99.7%

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

    1. lift-*.f64N/A

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

    2. lift--.f64N/A

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

    3. lift-*.f64N/A

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

    4. lower-+.f64N/A

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

    5. +-commutativeN/A

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

    6. associate-*l*N/A

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

    7. lower-fma.f64N/A

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

    8. lift--.f64N/A

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

    9. *-commutativeN/A

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

    10. lower-*.f6499.8

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

  4. Applied rewrites99.8%

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

Alternative 2: 61.9% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot -6\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+82}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-40}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) -6.0)))
   (if (<= z -2.9e+82)
     t_0
     (if (<= z -8e-40)
       (* (* z y) 6.0)
       (if (<= z 1.75e-20) x (if (<= z 3.4e+226) (* (* z 6.0) y) t_0))))))
double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double tmp;
	if (z <= -2.9e+82) {
		tmp = t_0;
	} else if (z <= -8e-40) {
		tmp = (z * y) * 6.0;
	} else if (z <= 1.75e-20) {
		tmp = x;
	} else if (z <= 3.4e+226) {
		tmp = (z * 6.0) * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * x) * (-6.0d0)
    if (z <= (-2.9d+82)) then
        tmp = t_0
    else if (z <= (-8d-40)) then
        tmp = (z * y) * 6.0d0
    else if (z <= 1.75d-20) then
        tmp = x
    else if (z <= 3.4d+226) then
        tmp = (z * 6.0d0) * y
    else
        tmp = t_0
    end if
    code = tmp
end function

public static double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double tmp;
	if (z <= -2.9e+82) {
		tmp = t_0;
	} else if (z <= -8e-40) {
		tmp = (z * y) * 6.0;
	} else if (z <= 1.75e-20) {
		tmp = x;
	} else if (z <= 3.4e+226) {
		tmp = (z * 6.0) * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

def code(x, y, z):
	t_0 = (z * x) * -6.0
	tmp = 0
	if z <= -2.9e+82:
		tmp = t_0
	elif z <= -8e-40:
		tmp = (z * y) * 6.0
	elif z <= 1.75e-20:
		tmp = x
	elif z <= 3.4e+226:
		tmp = (z * 6.0) * y
	else:
		tmp = t_0
	return tmp

function code(x, y, z)
	t_0 = Float64(Float64(z * x) * -6.0)
	tmp = 0.0
	if (z <= -2.9e+82)
		tmp = t_0;
	elseif (z <= -8e-40)
		tmp = Float64(Float64(z * y) * 6.0);
	elseif (z <= 1.75e-20)
		tmp = x;
	elseif (z <= 3.4e+226)
		tmp = Float64(Float64(z * 6.0) * y);
	else
		tmp = t_0;
	end
	return tmp
end

function tmp_2 = code(x, y, z)
	t_0 = (z * x) * -6.0;
	tmp = 0.0;
	if (z <= -2.9e+82)
		tmp = t_0;
	elseif (z <= -8e-40)
		tmp = (z * y) * 6.0;
	elseif (z <= 1.75e-20)
		tmp = x;
	elseif (z <= 3.4e+226)
		tmp = (z * 6.0) * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision]}, If[LessEqual[z, -2.9e+82], t$95$0, If[LessEqual[z, -8e-40], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[z, 1.75e-20], x, If[LessEqual[z, 3.4e+226], N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision], t$95$0]]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(z \cdot x\right) \cdot -6\\
\mathbf{if}\;z \leq -2.9 \cdot 10^{+82}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;z \leq -8 \cdot 10^{-40}:\\
\;\;\;\;\left(z \cdot y\right) \cdot 6\\

\mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\
\;\;\;\;x\\

\mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\
\;\;\;\;\left(z \cdot 6\right) \cdot y\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}
Derivation
  1. Split input into 4 regimes

  2. if z < -2.9000000000000001e82 or 3.39999999999999979e226 < z

    1. Initial program 99.8%

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

    3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
    4. Step-by-step derivation

      1. *-commutativeN/A

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

      2. lower-*.f64N/A

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

      3. +-commutativeN/A

        \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

      4. lower-fma.f6464.2

        \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

    5. Applied rewrites64.2%

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

    6. Taylor expanded in z around inf

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

      1. *-commutativeN/A

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

      2. *-commutativeN/A

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

      3. lift-*.f64N/A

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

      4. lift-*.f6464.2

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

    8. Applied rewrites64.2%

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

    if -2.9000000000000001e82 < z < -7.9999999999999994e-40

    1. Initial program 99.4%

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

    3. Taylor expanded in x around 0

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

      1. *-commutativeN/A

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

      2. lower-*.f64N/A

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

      3. *-commutativeN/A

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

      4. lower-*.f6454.2

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

    5. Applied rewrites54.2%

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

    if -7.9999999999999994e-40 < z < 1.75000000000000002e-20

    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

      \[\leadsto \color{blue}{x} \]
    4. Step-by-step derivation

      1. Applied rewrites72.5%

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

      if 1.75000000000000002e-20 < z < 3.39999999999999979e226

      1. Initial program 99.7%

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

      3. Taylor expanded in x around 0

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

        1. *-commutativeN/A

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

        2. lower-*.f64N/A

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

        3. *-commutativeN/A

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

        4. lower-*.f6456.0

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

      5. Applied rewrites56.0%

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

        1. lift-*.f64N/A

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

        2. lift-*.f64N/A

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

        3. *-commutativeN/A

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

        4. *-commutativeN/A

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

        5. *-commutativeN/A

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

        6. associate-*r*N/A

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

        7. lower-*.f64N/A

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

        8. *-commutativeN/A

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

        9. lift-*.f6456.0

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

      7. Applied rewrites56.0%

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

    Alternative 3: 62.0% accurate, 0.5× speedup?

    \[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot -6\\ t_1 := \left(z \cdot 6\right) \cdot y\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]
    (FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) -6.0)) (t_1 (* (* z 6.0) y)))
   (if (<= z -4.8e+107)
     t_0
     (if (<= z -8e-40)
       t_1
       (if (<= z 1.75e-20) x (if (<= z 3.4e+226) t_1 t_0))))))
    double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double t_1 = (z * 6.0) * y;
	double tmp;
	if (z <= -4.8e+107) {
		tmp = t_0;
	} else if (z <= -8e-40) {
		tmp = t_1;
	} else if (z <= 1.75e-20) {
		tmp = x;
	} else if (z <= 3.4e+226) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

    module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    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 = (z * x) * (-6.0d0)
    t_1 = (z * 6.0d0) * y
    if (z <= (-4.8d+107)) then
        tmp = t_0
    else if (z <= (-8d-40)) then
        tmp = t_1
    else if (z <= 1.75d-20) then
        tmp = x
    else if (z <= 3.4d+226) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

    public static double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double t_1 = (z * 6.0) * y;
	double tmp;
	if (z <= -4.8e+107) {
		tmp = t_0;
	} else if (z <= -8e-40) {
		tmp = t_1;
	} else if (z <= 1.75e-20) {
		tmp = x;
	} else if (z <= 3.4e+226) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

    def code(x, y, z):
	t_0 = (z * x) * -6.0
	t_1 = (z * 6.0) * y
	tmp = 0
	if z <= -4.8e+107:
		tmp = t_0
	elif z <= -8e-40:
		tmp = t_1
	elif z <= 1.75e-20:
		tmp = x
	elif z <= 3.4e+226:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

    function code(x, y, z)
	t_0 = Float64(Float64(z * x) * -6.0)
	t_1 = Float64(Float64(z * 6.0) * y)
	tmp = 0.0
	if (z <= -4.8e+107)
		tmp = t_0;
	elseif (z <= -8e-40)
		tmp = t_1;
	elseif (z <= 1.75e-20)
		tmp = x;
	elseif (z <= 3.4e+226)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

    function tmp_2 = code(x, y, z)
	t_0 = (z * x) * -6.0;
	t_1 = (z * 6.0) * y;
	tmp = 0.0;
	if (z <= -4.8e+107)
		tmp = t_0;
	elseif (z <= -8e-40)
		tmp = t_1;
	elseif (z <= 1.75e-20)
		tmp = x;
	elseif (z <= 3.4e+226)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

    code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -4.8e+107], t$95$0, If[LessEqual[z, -8e-40], t$95$1, If[LessEqual[z, 1.75e-20], x, If[LessEqual[z, 3.4e+226], t$95$1, t$95$0]]]]]]

    \begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(z \cdot x\right) \cdot -6\\
t_1 := \left(z \cdot 6\right) \cdot y\\
\mathbf{if}\;z \leq -4.8 \cdot 10^{+107}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;z \leq -8 \cdot 10^{-40}:\\
\;\;\;\;t\_1\\

\mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\
\;\;\;\;x\\

\mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\
\;\;\;\;t\_1\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}
    Derivation
    1. Split input into 3 regimes

    2. if z < -4.8000000000000001e107 or 3.39999999999999979e226 < z

      1. Initial program 99.8%

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

      3. Taylor expanded in x around inf

        \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
      4. Step-by-step derivation

        1. *-commutativeN/A

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

        2. lower-*.f64N/A

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

        3. +-commutativeN/A

          \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

        4. lower-fma.f6465.6

          \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

      5. Applied rewrites65.6%

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

      6. Taylor expanded in z around inf

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

        1. *-commutativeN/A

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

        2. *-commutativeN/A

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

        3. lift-*.f64N/A

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

        4. lift-*.f6465.7

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

      8. Applied rewrites65.7%

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

      if -4.8000000000000001e107 < z < -7.9999999999999994e-40 or 1.75000000000000002e-20 < z < 3.39999999999999979e226

      1. Initial program 99.6%

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

      3. Taylor expanded in x around 0

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

        1. *-commutativeN/A

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

        2. lower-*.f64N/A

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

        3. *-commutativeN/A

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

        4. lower-*.f6455.0

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

      5. Applied rewrites55.0%

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

        1. lift-*.f64N/A

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

        2. lift-*.f64N/A

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

        3. *-commutativeN/A

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

        4. *-commutativeN/A

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

        5. *-commutativeN/A

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

        6. associate-*r*N/A

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

        7. lower-*.f64N/A

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

        8. *-commutativeN/A

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

        9. lift-*.f6455.1

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

      7. Applied rewrites55.1%

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

      if -7.9999999999999994e-40 < z < 1.75000000000000002e-20

      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

        \[\leadsto \color{blue}{x} \]
      4. Step-by-step derivation

        1. Applied rewrites72.5%

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

      Alternative 4: 61.6% accurate, 0.6× speedup?

      \[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot -6\\ \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]
      (FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) -6.0)))
   (if (<= z -0.165)
     t_0
     (if (<= z 1.75e-20) x (if (<= z 3.4e+226) (* (* 6.0 y) z) t_0)))))
      double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double tmp;
	if (z <= -0.165) {
		tmp = t_0;
	} else if (z <= 1.75e-20) {
		tmp = x;
	} else if (z <= 3.4e+226) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

      module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * x) * (-6.0d0)
    if (z <= (-0.165d0)) then
        tmp = t_0
    else if (z <= 1.75d-20) then
        tmp = x
    else if (z <= 3.4d+226) then
        tmp = (6.0d0 * y) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

      public static double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double tmp;
	if (z <= -0.165) {
		tmp = t_0;
	} else if (z <= 1.75e-20) {
		tmp = x;
	} else if (z <= 3.4e+226) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

      def code(x, y, z):
	t_0 = (z * x) * -6.0
	tmp = 0
	if z <= -0.165:
		tmp = t_0
	elif z <= 1.75e-20:
		tmp = x
	elif z <= 3.4e+226:
		tmp = (6.0 * y) * z
	else:
		tmp = t_0
	return tmp

      function code(x, y, z)
	t_0 = Float64(Float64(z * x) * -6.0)
	tmp = 0.0
	if (z <= -0.165)
		tmp = t_0;
	elseif (z <= 1.75e-20)
		tmp = x;
	elseif (z <= 3.4e+226)
		tmp = Float64(Float64(6.0 * y) * z);
	else
		tmp = t_0;
	end
	return tmp
end

      function tmp_2 = code(x, y, z)
	t_0 = (z * x) * -6.0;
	tmp = 0.0;
	if (z <= -0.165)
		tmp = t_0;
	elseif (z <= 1.75e-20)
		tmp = x;
	elseif (z <= 3.4e+226)
		tmp = (6.0 * y) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

      code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision]}, If[LessEqual[z, -0.165], t$95$0, If[LessEqual[z, 1.75e-20], x, If[LessEqual[z, 3.4e+226], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]]

      \begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(z \cdot x\right) \cdot -6\\
\mathbf{if}\;z \leq -0.165:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\
\;\;\;\;x\\

\mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\
\;\;\;\;\left(6 \cdot y\right) \cdot z\\

\mathbf{else}:\\
\;\;\;\;t\_0\\


\end{array}
\end{array}
      Derivation
      1. Split input into 3 regimes

      2. if z < -0.165000000000000008 or 3.39999999999999979e226 < z

        1. Initial program 99.7%

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

        3. Taylor expanded in x around inf

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
        4. Step-by-step derivation

          1. *-commutativeN/A

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

          2. lower-*.f64N/A

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

          3. +-commutativeN/A

            \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

          4. lower-fma.f6460.7

            \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

        5. Applied rewrites60.7%

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

        6. Taylor expanded in z around inf

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

          1. *-commutativeN/A

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

          2. *-commutativeN/A

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

          3. lift-*.f64N/A

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

          4. lift-*.f6459.3

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

        8. Applied rewrites59.3%

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

        if -0.165000000000000008 < z < 1.75000000000000002e-20

        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

          \[\leadsto \color{blue}{x} \]
        4. Step-by-step derivation

          1. Applied rewrites69.6%

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

          if 1.75000000000000002e-20 < z < 3.39999999999999979e226

          1. Initial program 99.7%

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

          3. Taylor expanded in x around 0

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

            1. *-commutativeN/A

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

            2. lower-*.f64N/A

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

            3. *-commutativeN/A

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

            4. lower-*.f6456.0

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

          5. Applied rewrites56.0%

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

            1. lift-*.f64N/A

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

            2. lift-*.f64N/A

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

            3. *-commutativeN/A

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

            4. *-commutativeN/A

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

            5. associate-*r*N/A

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

            6. lower-*.f64N/A

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

            7. lift-*.f6455.9

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

          7. Applied rewrites55.9%

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

        Alternative 5: 98.9% accurate, 0.7× speedup?

        \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot 6, x\right)\\ \end{array} \end{array} \]
        (FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.175) (not (<= z 0.165)))
   (* (* (- y x) 6.0) z)
   (fma y (* z 6.0) x)))
        double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.175) || !(z <= 0.165)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = fma(y, (z * 6.0), x);
	}
	return tmp;
}

        function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.175) || !(z <= 0.165))
		tmp = Float64(Float64(Float64(y - x) * 6.0) * z);
	else
		tmp = fma(y, Float64(z * 6.0), x);
	end
	return tmp
end

        code[x_, y_, z_] := If[Or[LessEqual[z, -0.175], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision], N[(y * N[(z * 6.0), $MachinePrecision] + x), $MachinePrecision]]

        \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 0.165\right):\\
\;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y, z \cdot 6, x\right)\\


\end{array}
\end{array}
        Derivation
        1. Split input into 2 regimes

        2. if z < -0.17499999999999999 or 0.165000000000000008 < z

          1. Initial program 99.7%

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

          3. Taylor expanded in z around inf

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

            1. *-commutativeN/A

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

            2. associate-*r*N/A

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

            3. *-commutativeN/A

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

            4. lift-*.f64N/A

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

            5. lift--.f64N/A

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

            6. lift-*.f6498.6

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

          5. Applied rewrites98.6%

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

          if -0.17499999999999999 < z < 0.165000000000000008

          1. Initial program 99.8%

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

            1. lift-*.f64N/A

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

            2. lift--.f64N/A

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

            3. lift-*.f64N/A

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

            4. lower-+.f64N/A

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

            5. +-commutativeN/A

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

            6. associate-*l*N/A

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

            7. lower-fma.f64N/A

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

            8. lift--.f64N/A

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

            9. *-commutativeN/A

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

            10. lower-*.f6499.9

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

          4. Applied rewrites99.9%

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

          5. Taylor expanded in x around 0

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

            1. Applied rewrites99.3%

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

          8. Final simplification98.9%

            \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot 6, x\right)\\ \end{array} \]
          9. Add Preprocessing

          Alternative 6: 85.5% accurate, 0.7× speedup?

          \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.014 \lor \neg \left(y \leq 1.6 \cdot 10^{-162}\right):\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \end{array} \end{array} \]
          (FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.014) (not (<= y 1.6e-162)))
   (fma y (* z 6.0) x)
   (fma (* -6.0 x) z x)))
          double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.014) || !(y <= 1.6e-162)) {
		tmp = fma(y, (z * 6.0), x);
	} else {
		tmp = fma((-6.0 * x), z, x);
	}
	return tmp;
}

          function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.014) || !(y <= 1.6e-162))
		tmp = fma(y, Float64(z * 6.0), x);
	else
		tmp = fma(Float64(-6.0 * x), z, x);
	end
	return tmp
end

          code[x_, y_, z_] := If[Or[LessEqual[y, -0.014], N[Not[LessEqual[y, 1.6e-162]], $MachinePrecision]], N[(y * N[(z * 6.0), $MachinePrecision] + x), $MachinePrecision], N[(N[(-6.0 * x), $MachinePrecision] * z + x), $MachinePrecision]]

          \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.014 \lor \neg \left(y \leq 1.6 \cdot 10^{-162}\right):\\
\;\;\;\;\mathsf{fma}\left(y, z \cdot 6, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\


\end{array}
\end{array}
          Derivation
          1. Split input into 2 regimes

          2. if y < -0.0140000000000000003 or 1.59999999999999988e-162 < y

            1. Initial program 99.7%

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

              1. lift-*.f64N/A

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

              2. lift--.f64N/A

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

              3. lift-*.f64N/A

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

              4. lower-+.f64N/A

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

              5. +-commutativeN/A

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

              6. associate-*l*N/A

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

              7. lower-fma.f64N/A

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

              8. lift--.f64N/A

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

              9. *-commutativeN/A

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

              10. lower-*.f6499.8

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

            4. Applied rewrites99.8%

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

            5. Taylor expanded in x around 0

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

              1. Applied rewrites88.2%

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

              if -0.0140000000000000003 < y < 1.59999999999999988e-162

              1. Initial program 99.8%

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

              3. Taylor expanded in x around inf

                \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
              4. Step-by-step derivation

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. +-commutativeN/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                4. lower-fma.f6489.8

                  \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

              5. Applied rewrites89.8%

                \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]
              6. Step-by-step derivation

                1. lift-fma.f64N/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                2. lower-*.f64N/A

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

                3. *-commutativeN/A

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

                4. distribute-rgt-inN/A

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

                5. *-lft-identityN/A

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

                6. *-commutativeN/A

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

                7. associate-*r*N/A

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

                8. *-commutativeN/A

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

                9. lower-fma.f64N/A

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

                10. lower-*.f6489.8

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

              7. Applied rewrites89.8%

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

            8. Final simplification88.8%

              \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.014 \lor \neg \left(y \leq 1.6 \cdot 10^{-162}\right):\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \end{array} \]
            9. Add Preprocessing

            Alternative 7: 73.1% accurate, 0.7× speedup?

            \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-144} \lor \neg \left(x \leq 6 \cdot 10^{+55}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \end{array} \end{array} \]
            (FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-144) (not (<= x 6e+55)))
   (* (fma -6.0 z 1.0) x)
   (* (* z y) 6.0)))
            double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-144) || !(x <= 6e+55)) {
		tmp = fma(-6.0, z, 1.0) * x;
	} else {
		tmp = (z * y) * 6.0;
	}
	return tmp;
}

            function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-144) || !(x <= 6e+55))
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	else
		tmp = Float64(Float64(z * y) * 6.0);
	end
	return tmp
end

            code[x_, y_, z_] := If[Or[LessEqual[x, -2.2e-144], N[Not[LessEqual[x, 6e+55]], $MachinePrecision]], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision]]

            \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.2 \cdot 10^{-144} \lor \neg \left(x \leq 6 \cdot 10^{+55}\right):\\
\;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\

\mathbf{else}:\\
\;\;\;\;\left(z \cdot y\right) \cdot 6\\


\end{array}
\end{array}
            Derivation
            1. Split input into 2 regimes

            2. if x < -2.20000000000000006e-144 or 6.00000000000000033e55 < x

              1. Initial program 99.8%

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

              3. Taylor expanded in x around inf

                \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
              4. Step-by-step derivation

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. +-commutativeN/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                4. lower-fma.f6479.4

                  \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

              5. Applied rewrites79.4%

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

              if -2.20000000000000006e-144 < x < 6.00000000000000033e55

              1. Initial program 99.6%

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

              3. Taylor expanded in x around 0

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

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. *-commutativeN/A

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

                4. lower-*.f6469.4

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

              5. Applied rewrites69.4%

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

            4. Final simplification75.7%

              \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-144} \lor \neg \left(x \leq 6 \cdot 10^{+55}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \end{array} \]
            5. Add Preprocessing

            Alternative 8: 73.1% accurate, 0.7× speedup?

            \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-144}:\\ \;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+55}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \end{array} \end{array} \]
            (FPCore (x y z)
 :precision binary64
 (if (<= x -2.2e-144)
   (fma (* -6.0 x) z x)
   (if (<= x 6e+55) (* (* z y) 6.0) (* (fma -6.0 z 1.0) x))))
            double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e-144) {
		tmp = fma((-6.0 * x), z, x);
	} else if (x <= 6e+55) {
		tmp = (z * y) * 6.0;
	} else {
		tmp = fma(-6.0, z, 1.0) * x;
	}
	return tmp;
}

            function code(x, y, z)
	tmp = 0.0
	if (x <= -2.2e-144)
		tmp = fma(Float64(-6.0 * x), z, x);
	elseif (x <= 6e+55)
		tmp = Float64(Float64(z * y) * 6.0);
	else
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	end
	return tmp
end

            code[x_, y_, z_] := If[LessEqual[x, -2.2e-144], N[(N[(-6.0 * x), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[x, 6e+55], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * x), $MachinePrecision]]]

            \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.2 \cdot 10^{-144}:\\
\;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\

\mathbf{elif}\;x \leq 6 \cdot 10^{+55}:\\
\;\;\;\;\left(z \cdot y\right) \cdot 6\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\


\end{array}
\end{array}
            Derivation
            1. Split input into 3 regimes

            2. if x < -2.20000000000000006e-144

              1. Initial program 99.8%

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

              3. Taylor expanded in x around inf

                \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
              4. Step-by-step derivation

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. +-commutativeN/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                4. lower-fma.f6473.4

                  \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

              5. Applied rewrites73.4%

                \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]
              6. Step-by-step derivation

                1. lift-fma.f64N/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                2. lower-*.f64N/A

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

                3. *-commutativeN/A

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

                4. distribute-rgt-inN/A

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

                5. *-lft-identityN/A

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

                6. *-commutativeN/A

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

                7. associate-*r*N/A

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

                8. *-commutativeN/A

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

                9. lower-fma.f64N/A

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

                10. lower-*.f6473.4

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

              7. Applied rewrites73.4%

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

              if -2.20000000000000006e-144 < x < 6.00000000000000033e55

              1. Initial program 99.6%

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

              3. Taylor expanded in x around 0

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

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. *-commutativeN/A

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

                4. lower-*.f6469.4

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

              5. Applied rewrites69.4%

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

              if 6.00000000000000033e55 < x

              1. Initial program 99.8%

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

              3. Taylor expanded in x around inf

                \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
              4. Step-by-step derivation

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. +-commutativeN/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                4. lower-fma.f6490.0

                  \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

              5. Applied rewrites90.0%

                \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]
            3. Recombined 3 regimes into one program.
            4. Add Preprocessing

            Alternative 9: 60.4% accurate, 0.7× speedup?

            \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]
            (FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.165))) (* (* z x) -6.0) x))
            double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.165)) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = x;
	}
	return tmp;
}

            module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    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 <= 0.165d0))) then
        tmp = (z * x) * (-6.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

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

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

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

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

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

            \begin{array}{l}

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

\mathbf{else}:\\
\;\;\;\;x\\


\end{array}
\end{array}
            Derivation
            1. Split input into 2 regimes

            2. if z < -0.165000000000000008 or 0.165000000000000008 < z

              1. Initial program 99.7%

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

              3. Taylor expanded in x around inf

                \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
              4. Step-by-step derivation

                1. *-commutativeN/A

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

                2. lower-*.f64N/A

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

                3. +-commutativeN/A

                  \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                4. lower-fma.f6454.6

                  \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

              5. Applied rewrites54.6%

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

              6. Taylor expanded in z around inf

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

                1. *-commutativeN/A

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

                2. *-commutativeN/A

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

                3. lift-*.f64N/A

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

                4. lift-*.f6453.7

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

              8. Applied rewrites53.7%

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

              if -0.165000000000000008 < z < 0.165000000000000008

              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

                \[\leadsto \color{blue}{x} \]
              4. Step-by-step derivation

                1. Applied rewrites68.1%

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

              6. Final simplification60.7%

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

              Alternative 10: 60.4% accurate, 0.7× speedup?

              \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot x\\ \end{array} \end{array} \]
              (FPCore (x y z)
 :precision binary64
 (if (<= z -0.165) (* (* z x) -6.0) (if (<= z 0.165) x (* (* -6.0 z) x))))
              double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (z * x) * -6.0;
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = (-6.0 * z) * x;
	}
	return tmp;
}

              module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

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

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

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

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

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

              \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.165:\\
\;\;\;\;\left(z \cdot x\right) \cdot -6\\

\mathbf{elif}\;z \leq 0.165:\\
\;\;\;\;x\\

\mathbf{else}:\\
\;\;\;\;\left(-6 \cdot z\right) \cdot x\\


\end{array}
\end{array}
              Derivation
              1. Split input into 3 regimes

              2. if z < -0.165000000000000008

                1. Initial program 99.6%

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

                3. Taylor expanded in x around inf

                  \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
                4. Step-by-step derivation

                  1. *-commutativeN/A

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

                  2. lower-*.f64N/A

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

                  3. +-commutativeN/A

                    \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                  4. lower-fma.f6457.1

                    \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

                5. Applied rewrites57.1%

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

                6. Taylor expanded in z around inf

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

                  1. *-commutativeN/A

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

                  2. *-commutativeN/A

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

                  3. lift-*.f64N/A

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

                  4. lift-*.f6455.3

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

                8. Applied rewrites55.3%

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

                if -0.165000000000000008 < z < 0.165000000000000008

                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

                  \[\leadsto \color{blue}{x} \]
                4. Step-by-step derivation

                  1. Applied rewrites68.1%

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

                  if 0.165000000000000008 < z

                  1. Initial program 99.8%

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

                  3. Taylor expanded in x around inf

                    \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
                  4. Step-by-step derivation

                    1. *-commutativeN/A

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

                    2. lower-*.f64N/A

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

                    3. +-commutativeN/A

                      \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                    4. lower-fma.f6452.4

                      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

                  5. Applied rewrites52.4%

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

                  6. Taylor expanded in z around inf

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

                    1. lower-*.f6452.2

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

                  8. Applied rewrites52.2%

                    \[\leadsto \left(-6 \cdot z\right) \cdot x \]
                5. Recombined 3 regimes into one program.
                6. Add Preprocessing

                Alternative 11: 60.4% accurate, 0.7× speedup?

                \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]
                (FPCore (x y z)
 :precision binary64
 (if (<= z -0.165) (* (* z x) -6.0) (if (<= z 0.165) x (* (* -6.0 x) z))))
                double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (z * x) * -6.0;
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

                module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

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

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

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

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

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

                \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.165:\\
\;\;\;\;\left(z \cdot x\right) \cdot -6\\

\mathbf{elif}\;z \leq 0.165:\\
\;\;\;\;x\\

\mathbf{else}:\\
\;\;\;\;\left(-6 \cdot x\right) \cdot z\\


\end{array}
\end{array}
                Derivation
                1. Split input into 3 regimes

                2. if z < -0.165000000000000008

                  1. Initial program 99.6%

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

                  3. Taylor expanded in x around inf

                    \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
                  4. Step-by-step derivation

                    1. *-commutativeN/A

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

                    2. lower-*.f64N/A

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

                    3. +-commutativeN/A

                      \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

                    4. lower-fma.f6457.1

                      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

                  5. Applied rewrites57.1%

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

                  6. Taylor expanded in z around inf

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

                    1. *-commutativeN/A

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

                    2. *-commutativeN/A

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

                    3. lift-*.f64N/A

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

                    4. lift-*.f6455.3

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

                  8. Applied rewrites55.3%

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

                  if -0.165000000000000008 < z < 0.165000000000000008

                  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

                    \[\leadsto \color{blue}{x} \]
                  4. Step-by-step derivation

                    1. Applied rewrites68.1%

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

                    if 0.165000000000000008 < z

                    1. Initial program 99.8%

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

                    3. Taylor expanded in z around inf

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

                      1. *-commutativeN/A

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

                      2. associate-*r*N/A

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

                      3. *-commutativeN/A

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

                      4. lift-*.f64N/A

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

                      5. lift--.f64N/A

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

                      6. lift-*.f6499.3

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

                    5. Applied rewrites99.3%

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

                    6. Taylor expanded in x around inf

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

                      1. lower-*.f6452.2

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

                    8. Applied rewrites52.2%

                      \[\leadsto \left(-6 \cdot x\right) \cdot z \]
                  5. Recombined 3 regimes into one program.
                  6. Add Preprocessing

                  Alternative 12: 99.8% accurate, 1.1× speedup?

                  \[\begin{array}{l} \\ \mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right) \end{array} \]
                  (FPCore (x y z) :precision binary64 (fma (* (- y x) z) 6.0 x))
                  double code(double x, double y, double z) {
	return fma(((y - x) * z), 6.0, x);
}

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

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

                  \begin{array}{l}

\\
\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)
\end{array}
                  Derivation

                  1. Initial program 99.7%

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

                    1. lift-+.f64N/A

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

                    2. lift-*.f64N/A

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

                    3. lift--.f64N/A

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

                    4. lift-*.f64N/A

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

                    5. *-commutativeN/A

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

                    6. associate-*r*N/A

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

                    7. *-commutativeN/A

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

                    8. +-commutativeN/A

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

                    9. *-commutativeN/A

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

                    10. lower-fma.f64N/A

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

                    11. *-commutativeN/A

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

                    12. lower-*.f64N/A

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

                    13. lift--.f6499.8

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

                  4. Applied rewrites99.8%

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

                  Alternative 13: 35.7% accurate, 17.0× speedup?

                  \[\begin{array}{l} \\ x \end{array} \]
                  (FPCore (x y z) :precision binary64 x)
                  double code(double x, double y, double z) {
	return x;
}

                  module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

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

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

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

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

                  code[x_, y_, z_] := x

                  \begin{array}{l}

\\
x
\end{array}
                  Derivation

                  1. Initial program 99.7%

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

                  3. Taylor expanded in z around 0

                    \[\leadsto \color{blue}{x} \]
                  4. Step-by-step derivation

                    1. Applied rewrites34.8%

                      \[\leadsto \color{blue}{x} \]
                    2. Add Preprocessing

                    Developer Target 1: 99.8% accurate, 1.0× speedup?

                    \[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]
                    (FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))
                    double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

                    module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

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

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

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

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

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

                    \begin{array}{l}

\\
x - \left(6 \cdot z\right) \cdot \left(x - y\right)
\end{array}

                    Reproduce

                    ?
                    herbie shell --seed 2025038 
(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)))