Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Percentage Accurate: 95.6% → 95.6%

Time: 3.6s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -5000000000 \lor \neg \left(t\_0 \leq 200000000\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (or (<= t_0 -5000000000.0) (not (<= t_0 200000000.0)))
     (* (* x z) (- y))
     x)))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -5000000000.0) || !(t_0 <= 200000000.0)) {
		tmp = (x * z) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

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 = 1.0d0 - (y * z)
    if ((t_0 <= (-5000000000.0d0)) .or. (.not. (t_0 <= 200000000.0d0))) then
        tmp = (x * z) * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -5000000000.0) || !(t_0 <= 200000000.0)) {
		tmp = (x * z) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if (t_0 <= -5000000000.0) or not (t_0 <= 200000000.0):
		tmp = (x * z) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -5000000000.0) || !(t_0 <= 200000000.0))
		tmp = Float64(Float64(x * z) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if ((t_0 <= -5000000000.0) || ~((t_0 <= 200000000.0)))
		tmp = (x * z) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5000000000.0], N[Not[LessEqual[t$95$0, 200000000.0]], $MachinePrecision]], N[(N[(x * z), $MachinePrecision] * (-y)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5e9 or 2e8 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 96.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. flip-- N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 55.7%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   5. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \color{blue}{{\left(z \cdot y\right)}^{2}}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)} \]

      2. unpow2 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 50.4

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

   6. Applied rewrites 50.4%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 93.7%

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

   11. Applied rewrites 90.0%

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

   if -5e9 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2e8

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 95.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -5000000000 \lor \neg \left(1 - y \cdot z \leq 200000000\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -5000000000:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{elif}\;t\_0 \leq 200000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= t_0 -5000000000.0)
     (* (* (- y) x) z)
     (if (<= t_0 200000000.0) x (* (* x z) (- y))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -5000000000.0) {
		tmp = (-y * x) * z;
	} else if (t_0 <= 200000000.0) {
		tmp = x;
	} else {
		tmp = (x * z) * -y;
	}
	return tmp;
}

Fortran

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 = 1.0d0 - (y * z)
    if (t_0 <= (-5000000000.0d0)) then
        tmp = (-y * x) * z
    else if (t_0 <= 200000000.0d0) then
        tmp = x
    else
        tmp = (x * z) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -5000000000.0) {
		tmp = (-y * x) * z;
	} else if (t_0 <= 200000000.0) {
		tmp = x;
	} else {
		tmp = (x * z) * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if t_0 <= -5000000000.0:
		tmp = (-y * x) * z
	elif t_0 <= 200000000.0:
		tmp = x
	else:
		tmp = (x * z) * -y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= -5000000000.0)
		tmp = Float64(Float64(Float64(-y) * x) * z);
	elseif (t_0 <= 200000000.0)
		tmp = x;
	else
		tmp = Float64(Float64(x * z) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= -5000000000.0)
		tmp = (-y * x) * z;
	elseif (t_0 <= 200000000.0)
		tmp = x;
	else
		tmp = (x * z) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5000000000.0], N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$0, 200000000.0], x, N[(N[(x * z), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5e9

   1. Initial program 93.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. flip-- N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 58.7%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   5. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \color{blue}{{\left(z \cdot y\right)}^{2}}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)} \]

      2. unpow2 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 52.4

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

   6. Applied rewrites 52.4%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 96.1%

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

   if -5e9 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2e8

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 95.9%

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

   if 2e8 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 98.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. flip-- N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 52.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   5. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \color{blue}{{\left(z \cdot y\right)}^{2}}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)} \]

      2. unpow2 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 48.7

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

   6. Applied rewrites 48.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 91.6%

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

   11. Applied rewrites 89.9%

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

Alternative 4: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -100000000:\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 0.001:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -100000000.0)
   (* x (* (- y) z))
   (if (<= (* y z) 0.001) x (* (* (- y) x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -100000000.0) {
		tmp = x * (-y * z);
	} else if ((y * z) <= 0.001) {
		tmp = x;
	} else {
		tmp = (-y * x) * z;
	}
	return tmp;
}

Fortran

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 ((y * z) <= (-100000000.0d0)) then
        tmp = x * (-y * z)
    else if ((y * z) <= 0.001d0) then
        tmp = x
    else
        tmp = (-y * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -100000000.0) {
		tmp = x * (-y * z);
	} else if ((y * z) <= 0.001) {
		tmp = x;
	} else {
		tmp = (-y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -100000000.0:
		tmp = x * (-y * z)
	elif (y * z) <= 0.001:
		tmp = x
	else:
		tmp = (-y * x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -100000000.0)
		tmp = Float64(x * Float64(Float64(-y) * z));
	elseif (Float64(y * z) <= 0.001)
		tmp = x;
	else
		tmp = Float64(Float64(Float64(-y) * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -100000000.0)
		tmp = x * (-y * z);
	elseif ((y * z) <= 0.001)
		tmp = x;
	else
		tmp = (-y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -100000000.0], N[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.001], x, N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1e8

   1. Initial program 98.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 97.8%

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

   if -1e8 < (*.f64 y z) < 1e-3

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.6%

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

   if 1e-3 < (*.f64 y z)

   1. Initial program 93.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. flip-- N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 58.7%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   5. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{\left(1 - \color{blue}{{\left(z \cdot y\right)}^{2}}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)} \]

      2. unpow2 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 52.4

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

   6. Applied rewrites 52.4%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 96.1%

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

Alternative 5: 51.2% accurate, 14.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 98.0%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

5. Applied rewrites 50.4%

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

Reproduce

herbie shell --seed 2025018 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))