Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A

Percentage Accurate: 99.1% → 99.1%

Time: 3.7s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 - \frac{\frac{x}{y - z}}{y - t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- 1.0 (/ (/ x (- y z)) (- y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 - ((x / (y - z)) / (y - t));
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - ((x / (y - z)) / (y - t))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 - ((x / (y - z)) / (y - t));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - ((x / (y - z)) / (y - t))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 - Float64(Float64(x / Float64(y - z)) / Float64(y - t)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - ((x / (y - z)) / (y - t));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-/r* N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

   6. lower-/.f64 N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

   7. lower-/.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y - z}}}{y - t} \]

   8. lift--.f64 N/A

      \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y - z}}}{y - t} \]

   9. lift--.f64 98.2

      \[\leadsto 1 - \frac{\frac{x}{y - z}}{\color{blue}{y - t}} \]

3. Applied rewrites 98.2%

   \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]
4. Add Preprocessing

Alternative 2: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (y - t)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

Alternative 3: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := -\frac{x}{\left(y - t\right) \cdot \left(y - z\right)}\\ t_2 := 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x (* (- y t) (- y z)))))
        (t_2 (- 1.0 (/ x (* (- y z) (- y t))))))
   (if (<= t_2 -1e+14) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -(x / ((y - t) * (y - z)));
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -(x / ((y - t) * (y - z)))
    t_2 = 1.0d0 - (x / ((y - z) * (y - t)))
    if (t_2 <= (-1d+14)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -(x / ((y - t) * (y - z)));
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -(x / ((y - t) * (y - z)))
	t_2 = 1.0 - (x / ((y - z) * (y - t)))
	tmp = 0
	if t_2 <= -1e+14:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(-Float64(x / Float64(Float64(y - t) * Float64(y - z))))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
	tmp = 0.0
	if (t_2 <= -1e+14)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -(x / ((y - t) * (y - z)));
	t_2 = 1.0 - (x / ((y - z) * (y - t)));
	tmp = 0.0;
	if (t_2 <= -1e+14)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(x / N[(N[(y - t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+14], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -1e14 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. lower-neg.f64 N/A

         \[\leadsto -\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto -\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

      5. *-commutative N/A

         \[\leadsto -\frac{x}{\left(y - t\right) \cdot \left(y - z\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto -\frac{x}{\left(y - t\right) \cdot \left(y - z\right)} \]

      7. lift--.f64 N/A

         \[\leadsto -\frac{x}{\left(y - t\right) \cdot \left(y - z\right)} \]

      8. lift--.f64 95.0

         \[\leadsto -\frac{x}{\left(y - t\right) \cdot \left(y - z\right)} \]

   4. Applied rewrites 95.0%

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

   if -1e14 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 98.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 92.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-111)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= z 2.1e-236)
     (- 1.0 (/ (/ x y) (- y t)))
     (+ (/ (/ x t) (- y z)) 1.0))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-111) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 2.1e-236) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = ((x / t) / (y - z)) + 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-111)) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (z <= 2.1d-236) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = ((x / t) / (y - z)) + 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-111) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 2.1e-236) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = ((x / t) / (y - z)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-111:
		tmp = (x / ((y - t) * z)) + 1.0
	elif z <= 2.1e-236:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = ((x / t) / (y - z)) + 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-111)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (z <= 2.1e-236)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(Float64(Float64(x / t) / Float64(y - z)) + 1.0);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-111)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (z <= 2.1e-236)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = ((x / t) / (y - z)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-111], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[z, 2.1e-236], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-111

   1. Initial program 99.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 93.6

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

   4. Applied rewrites 93.6%

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

   if -1.5999999999999999e-111 < z < 2.09999999999999979e-236

   1. Initial program 97.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      6. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      7. lower-/.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y - z}}}{y - t} \]

      8. lift--.f64 N/A

         \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y - z}}}{y - t} \]

      9. lift--.f64 95.7

         \[\leadsto 1 - \frac{\frac{x}{y - z}}{\color{blue}{y - t}} \]

   3. Applied rewrites 95.7%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

   4. Taylor expanded in y around inf

      \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y}}}{y - t} \]
   5. Step-by-step derivation

   6. Applied rewrites 88.0%

      \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y}}}{y - t} \]

   if 2.09999999999999979e-236 < z

   1. Initial program 99.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 92.0

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

   4. Applied rewrites 92.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{t}}{y - z} + 1 \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x}{t}}{y - z} + 1 \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x}{t}}{y - z} + 1 \]

      8. lift--.f64 92.4

         \[\leadsto \frac{\frac{x}{t}}{y - z} + 1 \]

   6. Applied rewrites 92.4%

      \[\leadsto \frac{\frac{x}{t}}{y - z} + 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 92.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-111)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= z 2.1e-236)
     (- 1.0 (/ (/ x y) (- y t)))
     (- 1.0 (/ x (* (- z y) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-111) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 2.1e-236) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-111)) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (z <= 2.1d-236) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = 1.0d0 - (x / ((z - y) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-111) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 2.1e-236) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-111:
		tmp = (x / ((y - t) * z)) + 1.0
	elif z <= 2.1e-236:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-111)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (z <= 2.1e-236)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-111)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (z <= 2.1e-236)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-111], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[z, 2.1e-236], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-111

   1. Initial program 99.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 93.6

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

   4. Applied rewrites 93.6%

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

   if -1.5999999999999999e-111 < z < 2.09999999999999979e-236

   1. Initial program 97.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      6. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      7. lower-/.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y - z}}}{y - t} \]

      8. lift--.f64 N/A

         \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y - z}}}{y - t} \]

      9. lift--.f64 95.7

         \[\leadsto 1 - \frac{\frac{x}{y - z}}{\color{blue}{y - t}} \]

   3. Applied rewrites 95.7%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

   4. Taylor expanded in y around inf

      \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y}}}{y - t} \]
   5. Step-by-step derivation

   6. Applied rewrites 88.0%

      \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y}}}{y - t} \]

   if 2.09999999999999979e-236 < z

   1. Initial program 99.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lift--.f64 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 92.0

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

   7. Applied rewrites 92.0%

      \[\leadsto 1 - \frac{x}{\left(z - y\right) \cdot t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-236}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-111)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= z 2.2e-236)
     (- 1.0 (/ x (* y (- y t))))
     (- 1.0 (/ x (* (- z y) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-111) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 2.2e-236) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-111)) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (z <= 2.2d-236) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 - (x / ((z - y) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-111) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 2.2e-236) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-111:
		tmp = (x / ((y - t) * z)) + 1.0
	elif z <= 2.2e-236:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-111)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (z <= 2.2e-236)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-111)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (z <= 2.2e-236)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-111], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[z, 2.2e-236], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-111

   1. Initial program 99.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 93.6

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

   4. Applied rewrites 93.6%

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

   if -1.5999999999999999e-111 < z < 2.19999999999999992e-236

   1. Initial program 97.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 89.6%

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

   if 2.19999999999999992e-236 < z

   1. Initial program 99.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lift--.f64 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 92.0

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

   7. Applied rewrites 92.0%

      \[\leadsto 1 - \frac{x}{\left(z - y\right) \cdot t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z}\\ t_2 := 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y t) z))) (t_2 (- 1.0 (/ x (* (- y z) (- y t))))))
   (if (<= t_2 -1e+14) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - t) * z);
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - t) * z)
    t_2 = 1.0d0 - (x / ((y - z) * (y - t)))
    if (t_2 <= (-1d+14)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - t) * z);
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - t) * z)
	t_2 = 1.0 - (x / ((y - z) * (y - t)))
	tmp = 0
	if t_2 <= -1e+14:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - t) * z))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
	tmp = 0.0
	if (t_2 <= -1e+14)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - t) * z);
	t_2 = 1.0 - (x / ((y - z) * (y - t)));
	tmp = 0.0;
	if (t_2 <= -1e+14)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+14], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -1e14 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      6. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      7. lower-/.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y - z}}}{y - t} \]

      8. lift--.f64 N/A

         \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y - z}}}{y - t} \]

      9. lift--.f64 92.7

         \[\leadsto 1 - \frac{\frac{x}{y - z}}{\color{blue}{y - t}} \]

   3. Applied rewrites 92.7%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

   4. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.4

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

   6. Applied rewrites 61.4%

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

   7. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - t\right) \cdot z} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - t\right) \cdot z} \]

      4. lift-*.f64 60.6

         \[\leadsto \frac{x}{\left(y - t\right) \cdot z} \]

   9. Applied rewrites 60.6%

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

   if -1e14 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 98.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 88.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* (- y z) t))))
   (if (<= t_1 -2e+28) t_2 (if (<= t_1 2e-5) 1.0 t_2))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / ((y - z) * t);
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = t_2;
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = x / ((y - z) * t)
    if (t_1 <= (-2d+28)) then
        tmp = t_2
    else if (t_1 <= 2d-5) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / ((y - z) * t);
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = t_2;
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = x / ((y - z) * t)
	tmp = 0
	if t_1 <= -2e+28:
		tmp = t_2
	elif t_1 <= 2e-5:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t_1 <= -2e+28)
		tmp = t_2;
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / ((y - z) * t);
	tmp = 0.0;
	if (t_1 <= -2e+28)
		tmp = t_2;
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+28], t$95$2, If[LessEqual[t$95$1, 2e-5], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.99999999999999992e28 or 2.00000000000000016e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.7

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

   4. Applied rewrites 61.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      4. lift-/.f64 60.5

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

   7. Applied rewrites 60.5%

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

   if -1.99999999999999992e28 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.00000000000000016e-5

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 97.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -2e+28)
     (/ (/ x t) (- z))
     (if (<= t_1 2e-5) 1.0 (/ x (* (- z) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = (x / t) / -z;
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = x / (-z * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if (t_1 <= (-2d+28)) then
        tmp = (x / t) / -z
    else if (t_1 <= 2d-5) then
        tmp = 1.0d0
    else
        tmp = x / (-z * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = (x / t) / -z;
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = x / (-z * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -2e+28:
		tmp = (x / t) / -z
	elif t_1 <= 2e-5:
		tmp = 1.0
	else:
		tmp = x / (-z * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -2e+28)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(-z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -2e+28)
		tmp = (x / t) / -z;
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = x / (-z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+28], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[t$95$1, 2e-5], 1.0, N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.99999999999999992e28

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.7

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

   4. Applied rewrites 61.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      4. lift-/.f64 61.7

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

   7. Applied rewrites 61.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      4. *-commutative N/A

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

      5. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{t}}{y - \color{blue}{z}} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x}{t}}{y - \color{blue}{z}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{\frac{x}{t}}{y - z} \]

      8. lift--.f64 60.0

         \[\leadsto \frac{\frac{x}{t}}{y - z} \]

   9. Applied rewrites 60.0%

      \[\leadsto \frac{\frac{x}{t}}{y - \color{blue}{z}} \]

   10. Taylor expanded in y around 0

       \[\leadsto \frac{\frac{x}{t}}{-1 \cdot z} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \frac{\frac{x}{t}}{\mathsf{neg}\left(z\right)} \]

       2. lower-neg.f64 44.4

          \[\leadsto \frac{\frac{x}{t}}{-z} \]

   12. Applied rewrites 44.4%

       \[\leadsto \frac{\frac{x}{t}}{-z} \]

   if -1.99999999999999992e28 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.00000000000000016e-5

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 97.7%

      \[\leadsto \color{blue}{1} \]

   if 2.00000000000000016e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.6

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

   4. Applied rewrites 61.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      4. lift-/.f64 59.5

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

   7. Applied rewrites 59.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x}{\left(-1 \cdot z\right) \cdot t} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 42.8

         \[\leadsto \frac{x}{\left(-z\right) \cdot t} \]

   10. Applied rewrites 42.8%

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

Alternative 10: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(-z\right) \cdot t}\\ t_2 := 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- z) t))) (t_2 (- 1.0 (/ x (* (- y z) (- y t))))))
   (if (<= t_2 -1e+14) t_1 (if (<= t_2 5e+25) 1.0 t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (-z * t);
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = t_1;
	} else if (t_2 <= 5e+25) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (-z * t)
    t_2 = 1.0d0 - (x / ((y - z) * (y - t)))
    if (t_2 <= (-1d+14)) then
        tmp = t_1
    else if (t_2 <= 5d+25) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (-z * t);
	double t_2 = 1.0 - (x / ((y - z) * (y - t)));
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = t_1;
	} else if (t_2 <= 5e+25) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (-z * t)
	t_2 = 1.0 - (x / ((y - z) * (y - t)))
	tmp = 0
	if t_2 <= -1e+14:
		tmp = t_1
	elif t_2 <= 5e+25:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(-z) * t))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
	tmp = 0.0
	if (t_2 <= -1e+14)
		tmp = t_1;
	elseif (t_2 <= 5e+25)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (-z * t);
	t_2 = 1.0 - (x / ((y - z) * (y - t)));
	tmp = 0.0;
	if (t_2 <= -1e+14)
		tmp = t_1;
	elseif (t_2 <= 5e+25)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+14], t$95$1, If[LessEqual[t$95$2, 5e+25], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -1e14 or 5.00000000000000024e25 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.8

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

   4. Applied rewrites 61.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      4. lift-/.f64 61.8

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

   7. Applied rewrites 61.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x}{\left(-1 \cdot z\right) \cdot t} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 45.4

         \[\leadsto \frac{x}{\left(-z\right) \cdot t} \]

   10. Applied rewrites 45.4%

       \[\leadsto \frac{x}{\left(-z\right) \cdot t} \]

   if -1e14 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 5.00000000000000024e25

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 96.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 81.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{y \cdot z}\\ \mathbf{if}\;t\_1 \leq -2000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* y z))))
   (if (<= t_1 -2000000000000.0) t_2 (if (<= t_1 5e+51) 1.0 t_2))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / (y * z);
	double tmp;
	if (t_1 <= -2000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e+51) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = x / (y * z)
    if (t_1 <= (-2000000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d+51) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / (y * z);
	double tmp;
	if (t_1 <= -2000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e+51) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = x / (y * z)
	tmp = 0
	if t_1 <= -2000000000000.0:
		tmp = t_2
	elif t_1 <= 5e+51:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(x / Float64(y * z))
	tmp = 0.0
	if (t_1 <= -2000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e+51)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / (y * z);
	tmp = 0.0;
	if (t_1 <= -2000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e+51)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2000000000000.0], t$95$2, If[LessEqual[t$95$1, 5e+51], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e12 or 5e51 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      6. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

      7. lower-/.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y - z}}}{y - t} \]

      8. lift--.f64 N/A

         \[\leadsto 1 - \frac{\frac{x}{\color{blue}{y - z}}}{y - t} \]

      9. lift--.f64 92.4

         \[\leadsto 1 - \frac{\frac{x}{y - z}}{\color{blue}{y - t}} \]

   3. Applied rewrites 92.4%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

   4. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.7

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

   6. Applied rewrites 61.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - t\right) \cdot z} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - t\right) \cdot z} \]

      4. lift-*.f64 61.6

         \[\leadsto \frac{x}{\left(y - t\right) \cdot z} \]

   9. Applied rewrites 61.6%

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

   10. Taylor expanded in y around inf

       \[\leadsto \frac{x}{y \cdot z} \]
   11. Step-by-step derivation

       1. lower-*.f64 28.4

          \[\leadsto \frac{x}{y \cdot z} \]

   12. Applied rewrites 28.4%

       \[\leadsto \frac{x}{y \cdot z} \]

   if -2e12 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5e51

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 95.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 80.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{t \cdot y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* t y))))
   (if (<= t_1 -5e+40) t_2 (if (<= t_1 2e-5) 1.0 t_2))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / (t * y);
	double tmp;
	if (t_1 <= -5e+40) {
		tmp = t_2;
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = x / (t * y)
    if (t_1 <= (-5d+40)) then
        tmp = t_2
    else if (t_1 <= 2d-5) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / (t * y);
	double tmp;
	if (t_1 <= -5e+40) {
		tmp = t_2;
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = x / (t * y)
	tmp = 0
	if t_1 <= -5e+40:
		tmp = t_2
	elif t_1 <= 2e-5:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(x / Float64(t * y))
	tmp = 0.0
	if (t_1 <= -5e+40)
		tmp = t_2;
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / (t * y);
	tmp = 0.0;
	if (t_1 <= -5e+40)
		tmp = t_2;
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+40], t$95$2, If[LessEqual[t$95$1, 2e-5], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.00000000000000003e40 or 2.00000000000000016e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 61.9

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

   4. Applied rewrites 61.9%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x}{\left(y - z\right) \cdot t} \]

      4. lift-/.f64 60.7

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

   7. Applied rewrites 60.7%

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

   8. Taylor expanded in y around inf

      \[\leadsto \frac{x}{t \cdot y} \]
   9. Step-by-step derivation

      1. lower-*.f64 28.7

         \[\leadsto \frac{x}{t \cdot y} \]

   10. Applied rewrites 28.7%

       \[\leadsto \frac{x}{t \cdot y} \]

   if -5.00000000000000003e40 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.00000000000000016e-5

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 96.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 75.0% accurate, 15.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 1.0)

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

NOTE: x, y, z, and t 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return 1.0
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 99.1%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
3. Step-by-step derivation

4. Applied rewrites 75.0%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))