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

Percentage Accurate: 96.0% → 99.4%

Time: 2.3s

Alternatives: 5

Speedup: 0.3×

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: 96.0% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ t_1 := \left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+199}:\\ \;\;\;\;x \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e+137) t_1 (if (<= t_0 5e+199) (* x t_0) 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 <= -5e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+199) {
		tmp = x * t_0;
	} 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 <= (-5d+137)) then
        tmp = t_1
    else if (t_0 <= 5d+199) then
        tmp = x * t_0
    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 <= -5e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+199) {
		tmp = x * t_0;
	} 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 <= -5e+137:
		tmp = t_1
	elif t_0 <= 5e+199:
		tmp = x * t_0
	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 <= -5e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+199)
		tmp = Float64(x * t_0);
	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 <= -5e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+199)
		tmp = x * t_0;
	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, -5e+137], t$95$1, If[LessEqual[t$95$0, 5e+199], N[(x * t$95$0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5.0000000000000002e137 or 4.9999999999999998e199 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 85.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 85.0

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

   4. Applied rewrites 85.0%

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

   5. Taylor expanded in y around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-neg-out N/A

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

      14. lift-*.f64 N/A

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

      15. lift-neg.f64 98.2

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

   7. Applied rewrites 98.2%

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

   if -5.0000000000000002e137 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 4.9999999999999998e199

   1. Initial program 99.9%

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

Alternative 2: 97.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(\left(-y\right) \cdot z\right)\\ t_1 := 1 - y \cdot z\\ t_2 := \left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+199}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* x (* (- y) z))) (t_1 (- 1.0 (* y z))) (t_2 (* (* (- x) z) y)))
   (if (<= t_1 -5e+137)
     t_2
     (if (<= t_1 -500.0)
       t_0
       (if (<= t_1 2.0) x (if (<= t_1 5e+199) t_0 t_2))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = x * (-y * z);
	double t_1 = 1.0 - (y * z);
	double t_2 = (-x * z) * y;
	double tmp;
	if (t_1 <= -5e+137) {
		tmp = t_2;
	} else if (t_1 <= -500.0) {
		tmp = t_0;
	} else if (t_1 <= 2.0) {
		tmp = x;
	} else if (t_1 <= 5e+199) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = x * (-y * z)
    t_1 = 1.0d0 - (y * z)
    t_2 = (-x * z) * y
    if (t_1 <= (-5d+137)) then
        tmp = t_2
    else if (t_1 <= (-500.0d0)) then
        tmp = t_0
    else if (t_1 <= 2.0d0) then
        tmp = x
    else if (t_1 <= 5d+199) then
        tmp = t_0
    else
        tmp = t_2
    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 = x * (-y * z);
	double t_1 = 1.0 - (y * z);
	double t_2 = (-x * z) * y;
	double tmp;
	if (t_1 <= -5e+137) {
		tmp = t_2;
	} else if (t_1 <= -500.0) {
		tmp = t_0;
	} else if (t_1 <= 2.0) {
		tmp = x;
	} else if (t_1 <= 5e+199) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = x * (-y * z)
	t_1 = 1.0 - (y * z)
	t_2 = (-x * z) * y
	tmp = 0
	if t_1 <= -5e+137:
		tmp = t_2
	elif t_1 <= -500.0:
		tmp = t_0
	elif t_1 <= 2.0:
		tmp = x
	elif t_1 <= 5e+199:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-y) * z))
	t_1 = Float64(1.0 - Float64(y * z))
	t_2 = Float64(Float64(Float64(-x) * z) * y)
	tmp = 0.0
	if (t_1 <= -5e+137)
		tmp = t_2;
	elseif (t_1 <= -500.0)
		tmp = t_0;
	elseif (t_1 <= 2.0)
		tmp = x;
	elseif (t_1 <= 5e+199)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (-y * z);
	t_1 = 1.0 - (y * z);
	t_2 = (-x * z) * y;
	tmp = 0.0;
	if (t_1 <= -5e+137)
		tmp = t_2;
	elseif (t_1 <= -500.0)
		tmp = t_0;
	elseif (t_1 <= 2.0)
		tmp = x;
	elseif (t_1 <= 5e+199)
		tmp = t_0;
	else
		tmp = t_2;
	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[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+137], t$95$2, If[LessEqual[t$95$1, -500.0], t$95$0, If[LessEqual[t$95$1, 2.0], x, If[LessEqual[t$95$1, 5e+199], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5.0000000000000002e137 or 4.9999999999999998e199 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 85.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 85.0

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

   4. Applied rewrites 85.0%

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

   5. Taylor expanded in y around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-neg-out N/A

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

      14. lift-*.f64 N/A

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

      15. lift-neg.f64 98.2

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

   7. Applied rewrites 98.2%

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

   if -5.0000000000000002e137 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -500 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 4.9999999999999998e199

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 96.0

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

   4. Applied rewrites 96.0%

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

   if -500 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 96.9%

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

Alternative 3: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ t_1 := \left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+199}:\\ \;\;\;\;x - \left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e+137) t_1 (if (<= t_0 5e+199) (- x (* (* z y) x)) 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 <= -5e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+199) {
		tmp = x - ((z * y) * x);
	} 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 <= (-5d+137)) then
        tmp = t_1
    else if (t_0 <= 5d+199) then
        tmp = x - ((z * y) * x)
    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 <= -5e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+199) {
		tmp = x - ((z * y) * x);
	} 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 <= -5e+137:
		tmp = t_1
	elif t_0 <= 5e+199:
		tmp = x - ((z * y) * x)
	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 <= -5e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+199)
		tmp = Float64(x - Float64(Float64(z * y) * x));
	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 <= -5e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+199)
		tmp = x - ((z * y) * x);
	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, -5e+137], t$95$1, If[LessEqual[t$95$0, 5e+199], N[(x - N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5.0000000000000002e137 or 4.9999999999999998e199 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 85.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 85.0

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

   4. Applied rewrites 85.0%

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

   5. Taylor expanded in y around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-neg-out N/A

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

      14. lift-*.f64 N/A

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

      15. lift-neg.f64 98.2

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

   7. Applied rewrites 98.2%

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

   if -5.0000000000000002e137 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 4.9999999999999998e199

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 4: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ t_1 := \left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -500.0) t_1 (if (<= t_0 500000.0) x 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 <= -500.0) {
		tmp = t_1;
	} else if (t_0 <= 500000.0) {
		tmp = x;
	} 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 <= (-500.0d0)) then
        tmp = t_1
    else if (t_0 <= 500000.0d0) then
        tmp = x
    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 <= -500.0) {
		tmp = t_1;
	} else if (t_0 <= 500000.0) {
		tmp = x;
	} 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 <= -500.0:
		tmp = t_1
	elif t_0 <= 500000.0:
		tmp = x
	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 <= -500.0)
		tmp = t_1;
	elseif (t_0 <= 500000.0)
		tmp = x;
	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 <= -500.0)
		tmp = t_1;
	elseif (t_0 <= 500000.0)
		tmp = x;
	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, -500.0], t$95$1, If[LessEqual[t$95$0, 500000.0], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -500 or 5e5 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 92.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 92.0

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in y around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-neg-out N/A

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

      14. lift-*.f64 N/A

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

      15. lift-neg.f64 90.7

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

   7. Applied rewrites 90.7%

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

   if -500 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 5e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 96.2%

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

Alternative 5: 50.6% 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 96.0%

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

2. Taylor expanded in y around 0

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

4. Applied rewrites 50.6%

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

Reproduce

herbie shell --seed 2025106 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))