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

Percentage Accurate: 95.7% → 99.8%

Time: 4.4s

Alternatives: 6

Speedup: 0.7×

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: 95.7% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{elif}\;t\_0 \leq 10^{+237}:\\ \;\;\;\;x \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= t_0 (- INFINITY))
     (* (* (- y) x) z)
     (if (<= t_0 1e+237) (* x t_0) (* (* (- x) z) y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = (-y * x) * z;
	} else if (t_0 <= 1e+237) {
		tmp = x * t_0;
	} else {
		tmp = (-x * z) * y;
	}
	return tmp;
}

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = (-y * x) * z;
	} else if (t_0 <= 1e+237) {
		tmp = x * t_0;
	} else {
		tmp = (-x * z) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (-y * x) * z
	elif t_0 <= 1e+237:
		tmp = x * t_0
	else:
		tmp = (-x * z) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-y) * x) * z);
	elseif (t_0 <= 1e+237)
		tmp = Float64(x * t_0);
	else
		tmp = Float64(Float64(Float64(-x) * z) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = (-y * x) * z;
	elseif (t_0 <= 1e+237)
		tmp = x * t_0;
	else
		tmp = (-x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$0, 1e+237], N[(x * t$95$0), $MachinePrecision], N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -inf.0

   1. Initial program 78.3%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 0.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   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 0.0

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

   6. Applied rewrites 0.0%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 99.9%

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

   11. Applied rewrites 99.9%

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

   if -inf.0 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 9.9999999999999994e236

   1. Initial program 99.8%

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

   if 9.9999999999999994e236 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 75.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 10.7%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   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 10.7

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

   6. Applied rewrites 10.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -\infty:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{elif}\;1 - y \cdot z \leq 10^{+237}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ t_1 := \left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_0 \leq 10^{+237}:\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))) (t_1 (* (* (- x) z) y)))
   (if (<= t_0 -4e+18)
     t_1
     (if (<= t_0 2.0) x (if (<= t_0 1e+237) (* x (* (- y) z)) t_1)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = (-x * z) * y;
	double tmp;
	if (t_0 <= -4e+18) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = x;
	} else if (t_0 <= 1e+237) {
		tmp = x * (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    t_1 = (-x * z) * y
    if (t_0 <= (-4d+18)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = x
    else if (t_0 <= 1d+237) then
        tmp = x * (-y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = (-x * z) * y;
	double tmp;
	if (t_0 <= -4e+18) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = x;
	} else if (t_0 <= 1e+237) {
		tmp = x * (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	t_1 = (-x * z) * y
	tmp = 0
	if t_0 <= -4e+18:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = x
	elif t_0 <= 1e+237:
		tmp = x * (-y * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	t_1 = Float64(Float64(Float64(-x) * z) * y)
	tmp = 0.0
	if (t_0 <= -4e+18)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = x;
	elseif (t_0 <= 1e+237)
		tmp = Float64(x * Float64(Float64(-y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	t_1 = (-x * z) * y;
	tmp = 0.0;
	if (t_0 <= -4e+18)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = x;
	elseif (t_0 <= 1e+237)
		tmp = x * (-y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+18], t$95$1, If[LessEqual[t$95$0, 2.0], x, If[LessEqual[t$95$0, 1e+237], N[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -4e18 or 9.9999999999999994e236 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 86.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 27.5%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   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 27.5

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

   6. Applied rewrites 27.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 96.8%

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

   if -4e18 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   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 97.6%

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

   if 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 9.9999999999999994e236

   1. Initial program 99.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 95.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -4 \cdot 10^{+18}:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \cdot z \leq 2:\\ \;\;\;\;x\\ \mathbf{elif}\;1 - y \cdot z \leq 10^{+237}:\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+18} \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (or (<= t_0 -4e+18) (not (<= t_0 2.0))) (* (* (- x) z) y) x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -4e+18) || !(t_0 <= 2.0)) {
		tmp = (-x * z) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-4d+18)) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = (-x * z) * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -4e+18) || !(t_0 <= 2.0)) {
		tmp = (-x * z) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if (t_0 <= -4e+18) or not (t_0 <= 2.0):
		tmp = (-x * z) * y
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -4e+18) || !(t_0 <= 2.0))
		tmp = Float64(Float64(Float64(-x) * z) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if ((t_0 <= -4e+18) || ~((t_0 <= 2.0)))
		tmp = (-x * z) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -4e+18], N[Not[LessEqual[t$95$0, 2.0]], $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)) < -4e18 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 91.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 44.4%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(z \cdot y\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(z, y, 1\right)}} \]
   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 42.2

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

   6. Applied rewrites 42.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 90.2%

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

   if -4e18 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   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 97.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -4 \cdot 10^{+18} \lor \neg \left(1 - y \cdot z \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, -y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 1, x \cdot \left(\left(-y\right) \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 1e-81) (fma (* x z) (- y) x) (fma x 1.0 (* x (* (- y) z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-81) {
		tmp = fma((x * z), -y, x);
	} else {
		tmp = fma(x, 1.0, (x * (-y * z)));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 1e-81)
		tmp = fma(Float64(x * z), Float64(-y), x);
	else
		tmp = fma(x, 1.0, Float64(x * Float64(Float64(-y) * z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, 1e-81], N[(N[(x * z), $MachinePrecision] * (-y) + x), $MachinePrecision], N[(x * 1.0 + N[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999996e-82

   1. Initial program 93.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 93.9

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

   4. Applied rewrites 93.9%

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

      1. lift-fma.f64 N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 94.7

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

   6. Applied rewrites 94.7%

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

   if 9.9999999999999996e-82 < x

   1. Initial program 99.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1, x \cdot \left(\left(-y\right) \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, -y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 1e-81) (fma (* x z) (- y) x) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-81) {
		tmp = fma((x * z), -y, x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 1e-81)
		tmp = fma(Float64(x * z), Float64(-y), x);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, 1e-81], N[(N[(x * z), $MachinePrecision] * (-y) + x), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999996e-82

   1. Initial program 93.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 93.9

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

   4. Applied rewrites 93.9%

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

      1. lift-fma.f64 N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 94.7

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

   6. Applied rewrites 94.7%

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

   if 9.9999999999999996e-82 < x

   1. Initial program 99.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 50.2% accurate, 14.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 95.8%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 51.0%

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

Reproduce

herbie shell --seed 2025019 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))