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

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:

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: 99.7% 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}

Derivation

Initial program 99.8%
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
Add Preprocessing
Add Preprocessing

Alternative 2: 60.6% accurate, 0.6× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-112}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+154}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.15e-112)
   (* (* z 6.0) y)
   (if (<= z 6.6e-44)
     x
     (if (<= z 1.16e+154) (* (* 6.0 y) z) (* (* -6.0 x) z)))))

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e-112) {
		tmp = (z * 6.0) * y;
	} else if (z <= 6.6e-44) {
		tmp = x;
	} else if (z <= 1.16e+154) {
		tmp = (6.0 * y) * z;
	} 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 <= (-3.15d-112)) then
        tmp = (z * 6.0d0) * y
    else if (z <= 6.6d-44) then
        tmp = x
    else if (z <= 1.16d+154) then
        tmp = (6.0d0 * y) * z
    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 <= -3.15e-112) {
		tmp = (z * 6.0) * y;
	} else if (z <= 6.6e-44) {
		tmp = x;
	} else if (z <= 1.16e+154) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

def code(x, y, z):
	tmp = 0
	if z <= -3.15e-112:
		tmp = (z * 6.0) * y
	elif z <= 6.6e-44:
		tmp = x
	elif z <= 1.16e+154:
		tmp = (6.0 * y) * z
	else:
		tmp = (-6.0 * x) * z
	return tmp

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.15e-112)
		tmp = Float64(Float64(z * 6.0) * y);
	elseif (z <= 6.6e-44)
		tmp = x;
	elseif (z <= 1.16e+154)
		tmp = Float64(Float64(6.0 * y) * z);
	else
		tmp = Float64(Float64(-6.0 * x) * z);
	end
	return tmp
end

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.15e-112)
		tmp = (z * 6.0) * y;
	elseif (z <= 6.6e-44)
		tmp = x;
	elseif (z <= 1.16e+154)
		tmp = (6.0 * y) * z;
	else
		tmp = (-6.0 * x) * z;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := If[LessEqual[z, -3.15e-112], N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 6.6e-44], x, If[LessEqual[z, 1.16e+154], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision]]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -3.15 \cdot 10^{-112}:\\
\;\;\;\;\left(z \cdot 6\right) \cdot y\\

\mathbf{elif}\;z \leq 6.6 \cdot 10^{-44}:\\
\;\;\;\;x\\

\mathbf{elif}\;z \leq 1.16 \cdot 10^{+154}:\\
\;\;\;\;\left(6 \cdot y\right) \cdot z\\

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


\end{array}
\end{array}

Derivation

Split input into 4 regimes
if z < -3.15000000000000008e-112
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 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-*.f6459.2
    \[\leadsto \left(z \cdot y\right) \cdot 6 \]
5. Applied rewrites59.2%
  \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
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. lower-*.f6459.3
    \[\leadsto \left(z \cdot 6\right) \cdot y \]
7. Applied rewrites59.3%
  \[\leadsto \left(z \cdot 6\right) \cdot \color{blue}{y} \]
if -3.15000000000000008e-112 < z < 6.60000000000000011e-44
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in z around 0
  \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation
5. Applied rewrites76.0%
  \[\leadsto \color{blue}{x} \]
if 6.60000000000000011e-44 < z < 1.16000000000000001e154
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-*.f6491.8
    \[\leadsto \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{z} \]
5. Applied rewrites91.8%
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]
6. Taylor expanded in x around 0
  \[\leadsto \left(6 \cdot y\right) \cdot z \]
7. Step-by-step derivation
  1. lower-*.f6465.0
    \[\leadsto \left(6 \cdot y\right) \cdot z \]
8. Applied rewrites65.0%
  \[\leadsto \left(6 \cdot y\right) \cdot z \]
if 1.16000000000000001e154 < z
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in z around 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-*.f6499.9
    \[\leadsto \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{z} \]
5. Applied rewrites99.9%
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]
6. Taylor expanded in x around inf
  \[\leadsto \left(-6 \cdot x\right) \cdot z \]
7. Step-by-step derivation
  1. lower-*.f6480.5
    \[\leadsto \left(-6 \cdot x\right) \cdot z \]
8. Applied rewrites80.5%
  \[\leadsto \left(-6 \cdot x\right) \cdot z \]
Recombined 4 regimes into one program.
Add Preprocessing

Alternative 3: 60.5% accurate, 0.6× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot y\right) \cdot z\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{-112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+154}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 y) z)))
   (if (<= z -3.15e-112)
     t_0
     (if (<= z 6.6e-44) x (if (<= z 1.16e+154) t_0 (* (* -6.0 x) z))))))

double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (z <= -3.15e-112) {
		tmp = t_0;
	} else if (z <= 6.6e-44) {
		tmp = x;
	} else if (z <= 1.16e+154) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (6.0d0 * y) * z
    if (z <= (-3.15d-112)) then
        tmp = t_0
    else if (z <= 6.6d-44) then
        tmp = x
    else if (z <= 1.16d+154) then
        tmp = t_0
    else
        tmp = ((-6.0d0) * x) * z
    end if
    code = tmp
end function

public static double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (z <= -3.15e-112) {
		tmp = t_0;
	} else if (z <= 6.6e-44) {
		tmp = x;
	} else if (z <= 1.16e+154) {
		tmp = t_0;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

def code(x, y, z):
	t_0 = (6.0 * y) * z
	tmp = 0
	if z <= -3.15e-112:
		tmp = t_0
	elif z <= 6.6e-44:
		tmp = x
	elif z <= 1.16e+154:
		tmp = t_0
	else:
		tmp = (-6.0 * x) * z
	return tmp

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * y) * z)
	tmp = 0.0
	if (z <= -3.15e-112)
		tmp = t_0;
	elseif (z <= 6.6e-44)
		tmp = x;
	elseif (z <= 1.16e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(-6.0 * x) * z);
	end
	return tmp
end

function tmp_2 = code(x, y, z)
	t_0 = (6.0 * y) * z;
	tmp = 0.0;
	if (z <= -3.15e-112)
		tmp = t_0;
	elseif (z <= 6.6e-44)
		tmp = x;
	elseif (z <= 1.16e+154)
		tmp = t_0;
	else
		tmp = (-6.0 * x) * z;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -3.15e-112], t$95$0, If[LessEqual[z, 6.6e-44], x, If[LessEqual[z, 1.16e+154], t$95$0, N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision]]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left(6 \cdot y\right) \cdot z\\
\mathbf{if}\;z \leq -3.15 \cdot 10^{-112}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;z \leq 6.6 \cdot 10^{-44}:\\
\;\;\;\;x\\

\mathbf{elif}\;z \leq 1.16 \cdot 10^{+154}:\\
\;\;\;\;t\_0\\

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


\end{array}
\end{array}

Derivation

Split input into 3 regimes
if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z < 1.16000000000000001e154
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-*.f6487.1
    \[\leadsto \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{z} \]
5. Applied rewrites87.1%
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]
6. Taylor expanded in x around 0
  \[\leadsto \left(6 \cdot y\right) \cdot z \]
7. Step-by-step derivation
  1. lower-*.f6461.2
    \[\leadsto \left(6 \cdot y\right) \cdot z \]
8. Applied rewrites61.2%
  \[\leadsto \left(6 \cdot y\right) \cdot z \]
if -3.15000000000000008e-112 < z < 6.60000000000000011e-44
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in z around 0
  \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation
5. Applied rewrites76.0%
  \[\leadsto \color{blue}{x} \]
if 1.16000000000000001e154 < z
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in z around 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-*.f6499.9
    \[\leadsto \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{z} \]
5. Applied rewrites99.9%
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]
6. Taylor expanded in x around inf
  \[\leadsto \left(-6 \cdot x\right) \cdot z \]
7. Step-by-step derivation
  1. lower-*.f6480.5
    \[\leadsto \left(-6 \cdot x\right) \cdot z \]
8. Applied rewrites80.5%
  \[\leadsto \left(-6 \cdot x\right) \cdot z \]
Recombined 3 regimes into one program.
Add Preprocessing

Alternative 4: 98.9% accurate, 0.7× speedup?

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

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

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.165)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = x + ((y * 6.0) * 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)) .or. (.not. (z <= 0.165d0))) then
        tmp = ((y - x) * 6.0d0) * z
    else
        tmp = x + ((y * 6.0d0) * z)
    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 = ((y - x) * 6.0) * z;
	} else {
		tmp = x + ((y * 6.0) * z);
	}
	return tmp;
}

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

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

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

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

\begin{array}{l}

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

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if z < -0.165000000000000008 or 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-*.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 -0.165000000000000008 < z < 0.165000000000000008
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in x around 0
  \[\leadsto x + \left(\color{blue}{y} \cdot 6\right) \cdot z \]
4. Step-by-step derivation
5. Applied rewrites97.2%
  \[\leadsto x + \left(\color{blue}{y} \cdot 6\right) \cdot z \]
Recombined 2 regimes into one program.
Final simplification97.9%
\[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 6\right) \cdot z\\ \end{array} \]
Add Preprocessing

Alternative 5: 98.9% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(6 \cdot z\right) \cdot y\\ \end{array} \end{array} \]

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.15) (not (<= z 0.165)))
   (* (* (- y x) 6.0) z)
   (+ x (* (* 6.0 z) y))))

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.15) || !(z <= 0.165)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = x + ((6.0 * z) * y);
	}
	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 <= (-0.15d0)) .or. (.not. (z <= 0.165d0))) then
        tmp = ((y - x) * 6.0d0) * z
    else
        tmp = x + ((6.0d0 * z) * y)
    end if
    code = tmp
end function

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.15) || !(z <= 0.165)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = x + ((6.0 * z) * y);
	}
	return tmp;
}

def code(x, y, z):
	tmp = 0
	if (z <= -0.15) or not (z <= 0.165):
		tmp = ((y - x) * 6.0) * z
	else:
		tmp = x + ((6.0 * z) * y)
	return tmp

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.15) || !(z <= 0.165))
		tmp = Float64(Float64(Float64(y - x) * 6.0) * z);
	else
		tmp = Float64(x + Float64(Float64(6.0 * z) * y));
	end
	return tmp
end

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.15) || ~((z <= 0.165)))
		tmp = ((y - x) * 6.0) * z;
	else
		tmp = x + ((6.0 * z) * y);
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := If[Or[LessEqual[z, -0.15], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision], N[(x + N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 0.165\right):\\
\;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if z < -0.149999999999999994 or 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-*.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 -0.149999999999999994 < z < 0.165000000000000008
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in x around 0
  \[\leadsto x + \left(\color{blue}{y} \cdot 6\right) \cdot z \]
4. Step-by-step derivation
5. Applied rewrites97.2%
  \[\leadsto x + \left(\color{blue}{y} \cdot 6\right) \cdot z \]
6. Step-by-step derivation
  1. lift-*.f64N/A
    \[\leadsto x + \color{blue}{\left(y \cdot 6\right) \cdot z} \]
  2. lift-*.f64N/A
    \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]
  3. associate-*l*N/A
    \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]
  4. *-commutativeN/A
    \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot y} \]
  5. lower-*.f64N/A
    \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot y} \]
  6. lower-*.f6497.2
    \[\leadsto x + \color{blue}{\left(6 \cdot z\right)} \cdot y \]
7. Applied rewrites97.2%
  \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot y} \]
Recombined 2 regimes into one program.
Final simplification97.9%
\[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(6 \cdot z\right) \cdot y\\ \end{array} \]
Add Preprocessing

Alternative 6: 98.8% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 2600000\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot y\right) \cdot 6\\ \end{array} \end{array} \]

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.175) (not (<= z 2600000.0)))
   (* (* (- y x) 6.0) z)
   (+ x (* (* z y) 6.0))))

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.175) || !(z <= 2600000.0)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = x + ((z * y) * 6.0);
	}
	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) :: tmp
    if ((z <= (-0.175d0)) .or. (.not. (z <= 2600000.0d0))) then
        tmp = ((y - x) * 6.0d0) * z
    else
        tmp = x + ((z * y) * 6.0d0)
    end if
    code = tmp
end function

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.175) || !(z <= 2600000.0)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = x + ((z * y) * 6.0);
	}
	return tmp;
}

def code(x, y, z):
	tmp = 0
	if (z <= -0.175) or not (z <= 2600000.0):
		tmp = ((y - x) * 6.0) * z
	else:
		tmp = x + ((z * y) * 6.0)
	return tmp

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.175) || !(z <= 2600000.0))
		tmp = Float64(Float64(Float64(y - x) * 6.0) * z);
	else
		tmp = Float64(x + Float64(Float64(z * y) * 6.0));
	end
	return tmp
end

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.175) || ~((z <= 2600000.0)))
		tmp = ((y - x) * 6.0) * z;
	else
		tmp = x + ((z * y) * 6.0);
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := If[Or[LessEqual[z, -0.175], N[Not[LessEqual[z, 2600000.0]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 2600000\right):\\
\;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if z < -0.17499999999999999 or 2.6e6 < 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-*.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 < 2.6e6
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in x around inf
  \[\leadsto x + \color{blue}{x \cdot \left(-6 \cdot z + 6 \cdot \frac{y \cdot z}{x}\right)} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto x + \left(-6 \cdot z + 6 \cdot \frac{y \cdot z}{x}\right) \cdot \color{blue}{x} \]
  2. lower-*.f64N/A
    \[\leadsto x + \left(-6 \cdot z + 6 \cdot \frac{y \cdot z}{x}\right) \cdot \color{blue}{x} \]
  3. fp-cancel-sign-sub-invN/A
    \[\leadsto x + \left(-6 \cdot z - \left(\mathsf{neg}\left(6\right)\right) \cdot \frac{y \cdot z}{x}\right) \cdot x \]
  4. metadata-evalN/A
    \[\leadsto x + \left(-6 \cdot z - -6 \cdot \frac{y \cdot z}{x}\right) \cdot x \]
  5. distribute-lft-out--N/A
    \[\leadsto x + \left(-6 \cdot \left(z - \frac{y \cdot z}{x}\right)\right) \cdot x \]
  6. lower-*.f64N/A
    \[\leadsto x + \left(-6 \cdot \left(z - \frac{y \cdot z}{x}\right)\right) \cdot x \]
  7. lower--.f64N/A
    \[\leadsto x + \left(-6 \cdot \left(z - \frac{y \cdot z}{x}\right)\right) \cdot x \]
  8. lower-/.f64N/A
    \[\leadsto x + \left(-6 \cdot \left(z - \frac{y \cdot z}{x}\right)\right) \cdot x \]
  9. *-commutativeN/A
    \[\leadsto x + \left(-6 \cdot \left(z - \frac{z \cdot y}{x}\right)\right) \cdot x \]
  10. lower-*.f6496.0
    \[\leadsto x + \left(-6 \cdot \left(z - \frac{z \cdot y}{x}\right)\right) \cdot x \]
5. Applied rewrites96.0%
  \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z - \frac{z \cdot y}{x}\right)\right) \cdot x} \]
6. Taylor expanded in x around 0
  \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot z\right)} \]
7. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{6} \]
  2. *-commutativeN/A
    \[\leadsto x + \left(z \cdot y\right) \cdot 6 \]
  3. lift-*.f64N/A
    \[\leadsto x + \left(z \cdot y\right) \cdot \color{blue}{6} \]
  4. lift-*.f6497.3
    \[\leadsto x + \left(z \cdot y\right) \cdot 6 \]
8. Applied rewrites97.3%
  \[\leadsto x + \color{blue}{\left(z \cdot y\right) \cdot 6} \]
Recombined 2 regimes into one program.
Final simplification97.9%
\[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 2600000\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot y\right) \cdot 6\\ \end{array} \]
Add Preprocessing

Alternative 7: 83.5% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-112} \lor \neg \left(z \leq 6.6 \cdot 10^{-44}\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.15e-112) (not (<= z 6.6e-44))) (* (* (- y x) 6.0) z) x))

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.15e-112) || !(z <= 6.6e-44)) {
		tmp = ((y - x) * 6.0) * z;
	} 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 <= (-3.15d-112)) .or. (.not. (z <= 6.6d-44))) then
        tmp = ((y - x) * 6.0d0) * z
    else
        tmp = x
    end if
    code = tmp
end function

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.15e-112) || !(z <= 6.6e-44)) {
		tmp = ((y - x) * 6.0) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

def code(x, y, z):
	tmp = 0
	if (z <= -3.15e-112) or not (z <= 6.6e-44):
		tmp = ((y - x) * 6.0) * z
	else:
		tmp = x
	return tmp

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.15e-112) || !(z <= 6.6e-44))
		tmp = Float64(Float64(Float64(y - x) * 6.0) * z);
	else
		tmp = x;
	end
	return tmp
end

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.15e-112) || ~((z <= 6.6e-44)))
		tmp = ((y - x) * 6.0) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := If[Or[LessEqual[z, -3.15e-112], N[Not[LessEqual[z, 6.6e-44]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision], x]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -3.15 \cdot 10^{-112} \lor \neg \left(z \leq 6.6 \cdot 10^{-44}\right):\\
\;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < 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-*.f6489.3
    \[\leadsto \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{z} \]
5. Applied rewrites89.3%
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]
if -3.15000000000000008e-112 < z < 6.60000000000000011e-44
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in z around 0
  \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation
5. Applied rewrites76.0%
  \[\leadsto \color{blue}{x} \]
Recombined 2 regimes into one program.
Final simplification85.0%
\[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-112} \lor \neg \left(z \leq 6.6 \cdot 10^{-44}\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot 6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Add Preprocessing

Alternative 8: 61.3% accurate, 0.7× speedup?

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

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

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

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

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.165))
		tmp = Float64(Float64(-6.0 * x) * z);
	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 = (-6.0 * x) * z;
	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[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision], x]

\begin{array}{l}

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

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


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if z < -0.165000000000000008 or 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-*.f6498.6
    \[\leadsto \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{z} \]
5. Applied rewrites98.6%
  \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} \]
6. Taylor expanded in x around inf
  \[\leadsto \left(-6 \cdot x\right) \cdot z \]
7. Step-by-step derivation
  1. lower-*.f6451.4
    \[\leadsto \left(-6 \cdot x\right) \cdot z \]
8. Applied rewrites51.4%
  \[\leadsto \left(-6 \cdot x\right) \cdot z \]
if -0.165000000000000008 < z < 0.165000000000000008
1. Initial program 99.9%
  \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Taylor expanded in z around 0
  \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation
5. Applied rewrites62.5%
  \[\leadsto \color{blue}{x} \]
Recombined 2 regimes into one program.
Final simplification56.7%
\[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Add Preprocessing

Alternative 9: 36.6% 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

Initial program 99.8%
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
Add Preprocessing
Taylor expanded in z around 0
\[\leadsto \color{blue}{x} \]
Step-by-step derivation
Applied rewrites31.3%
\[\leadsto \color{blue}{x} \]
Add Preprocessing

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

20.8% of points produce a very large (infinite) output. You may want to add a precondition. (more)

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 99.7% accurate, 1.0× speedup?

Alternative 1: 99.7% accurate, 1.0× speedup?

Alternative 2: 60.6% accurate, 0.6× speedup?

`if z < -3.15000000000000008e-112`

`if -3.15000000000000008e-112 < z < 6.60000000000000011e-44`

`if 6.60000000000000011e-44 < z < 1.16000000000000001e154`

`if 1.16000000000000001e154 < z`

Alternative 3: 60.5% accurate, 0.6× speedup?

`if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z < 1.16000000000000001e154`

`if -3.15000000000000008e-112 < z < 6.60000000000000011e-44`

`if 1.16000000000000001e154 < z`

Alternative 4: 98.9% accurate, 0.7× speedup?

`if z < -0.165000000000000008 or 0.165000000000000008 < z`

`if -0.165000000000000008 < z < 0.165000000000000008`

Alternative 5: 98.9% accurate, 0.7× speedup?

`if z < -0.149999999999999994 or 0.165000000000000008 < z`

`if -0.149999999999999994 < z < 0.165000000000000008`

Alternative 6: 98.8% accurate, 0.7× speedup?

`if z < -0.17499999999999999 or 2.6e6 < z`

`if -0.17499999999999999 < z < 2.6e6`

Alternative 7: 83.5% accurate, 0.7× speedup?

`if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z`

`if -3.15000000000000008e-112 < z < 6.60000000000000011e-44`

Alternative 8: 61.3% accurate, 0.7× speedup?

`if z < -0.165000000000000008 or 0.165000000000000008 < z`

`if -0.165000000000000008 < z < 0.165000000000000008`

Alternative 9: 36.6% accurate, 17.0× speedup?

Reproduce

20.8% of points produce a very large (infinite) output. You may want to add a precondition. (more)

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 99.7% accurate, 1.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Alternative 1: 99.7% accurate, 1.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Alternative 2: 60.6% accurate, 0.6× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -3.15000000000000008e-112

if -3.15000000000000008e-112 < z < 6.60000000000000011e-44

if 6.60000000000000011e-44 < z < 1.16000000000000001e154

if 1.16000000000000001e154 < z

Alternative 3: 60.5% accurate, 0.6× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z < 1.16000000000000001e154

if -3.15000000000000008e-112 < z < 6.60000000000000011e-44

if 1.16000000000000001e154 < z

Alternative 4: 98.9% accurate, 0.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -0.165000000000000008 or 0.165000000000000008 < z

if -0.165000000000000008 < z < 0.165000000000000008

Alternative 5: 98.9% accurate, 0.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -0.149999999999999994 or 0.165000000000000008 < z

if -0.149999999999999994 < z < 0.165000000000000008

Alternative 6: 98.8% accurate, 0.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -0.17499999999999999 or 2.6e6 < z

if -0.17499999999999999 < z < 2.6e6

Alternative 7: 83.5% accurate, 0.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z

if -3.15000000000000008e-112 < z < 6.60000000000000011e-44

Alternative 8: 61.3% accurate, 0.7× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if z < -0.165000000000000008 or 0.165000000000000008 < z

if -0.165000000000000008 < z < 0.165000000000000008

Alternative 9: 36.6% accurate, 17.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Reproduce

Initial Program: 99.7% accurate, 1.0× speedup?

Alternative 1: 99.7% accurate, 1.0× speedup?

Alternative 2: 60.6% accurate, 0.6× speedup?

`if z < -3.15000000000000008e-112`

`if -3.15000000000000008e-112 < z < 6.60000000000000011e-44`

`if 6.60000000000000011e-44 < z < 1.16000000000000001e154`

`if 1.16000000000000001e154 < z`

Alternative 3: 60.5% accurate, 0.6× speedup?

`if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z < 1.16000000000000001e154`

`if -3.15000000000000008e-112 < z < 6.60000000000000011e-44`

`if 1.16000000000000001e154 < z`

Alternative 4: 98.9% accurate, 0.7× speedup?

`if z < -0.165000000000000008 or 0.165000000000000008 < z`

`if -0.165000000000000008 < z < 0.165000000000000008`

Alternative 5: 98.9% accurate, 0.7× speedup?

`if z < -0.149999999999999994 or 0.165000000000000008 < z`

`if -0.149999999999999994 < z < 0.165000000000000008`

Alternative 6: 98.8% accurate, 0.7× speedup?

`if z < -0.17499999999999999 or 2.6e6 < z`

`if -0.17499999999999999 < z < 2.6e6`

Alternative 7: 83.5% accurate, 0.7× speedup?

`if z < -3.15000000000000008e-112 or 6.60000000000000011e-44 < z`

`if -3.15000000000000008e-112 < z < 6.60000000000000011e-44`

Alternative 8: 61.3% accurate, 0.7× speedup?

`if z < -0.165000000000000008 or 0.165000000000000008 < z`

`if -0.165000000000000008 < z < 0.165000000000000008`

Alternative 9: 36.6% accurate, 17.0× speedup?