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

Percentage Accurate: 89.6% → 96.9%

Time: 4.2s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (x / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. *-commutative N/A

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

   6. associate-/r* N/A

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

   7. lower-/.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lift--.f64 N/A

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

   10. lift--.f64 96.9

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

3. Applied rewrites 96.9%

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

Alternative 2: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{-z}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{t\_1}{t - z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{y - z}\\ \end{array} \end{array} \]

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))))
   (if (<= z -3.9e+69)
     (/ t_1 (- t z))
     (if (<= z 5.6e+168) (/ x (* (- y z) (- t z))) (/ t_1 (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double tmp;
	if (z <= -3.9e+69) {
		tmp = t_1 / (t - z);
	} else if (z <= 5.6e+168) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = t_1 / (y - z);
	}
	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 / -z
    if (z <= (-3.9d+69)) then
        tmp = t_1 / (t - z)
    else if (z <= 5.6d+168) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = t_1 / (y - z)
    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;
	double tmp;
	if (z <= -3.9e+69) {
		tmp = t_1 / (t - z);
	} else if (z <= 5.6e+168) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = t_1 / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / -z
	tmp = 0
	if z <= -3.9e+69:
		tmp = t_1 / (t - z)
	elif z <= 5.6e+168:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = t_1 / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(-z))
	tmp = 0.0
	if (z <= -3.9e+69)
		tmp = Float64(t_1 / Float64(t - z));
	elseif (z <= 5.6e+168)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(t_1 / Float64(y - z));
	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;
	tmp = 0.0;
	if (z <= -3.9e+69)
		tmp = t_1 / (t - z);
	elseif (z <= 5.6e+168)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = t_1 / (y - z);
	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 / (-z)), $MachinePrecision]}, If[LessEqual[z, -3.9e+69], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+168], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999999e69

   1. Initial program 82.0%

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

   2. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 77.8

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

   4. Applied rewrites 77.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 90.7

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

   6. Applied rewrites 90.7%

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

   if -3.8999999999999999e69 < z < 5.5999999999999998e168

   1. Initial program 93.1%

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

   if 5.5999999999999998e168 < z

   1. Initial program 81.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 96.4

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

   6. Applied rewrites 96.4%

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

Alternative 3: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= t -5.2e-179)
   (/ (/ x y) (- t z))
   (if (<= t 8.1e-50) (/ (/ x (- z)) (- y z)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e-179) {
		tmp = (x / y) / (t - z);
	} else if (t <= 8.1e-50) {
		tmp = (x / -z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	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 (t <= (-5.2d-179)) then
        tmp = (x / y) / (t - z)
    else if (t <= 8.1d-50) then
        tmp = (x / -z) / (y - z)
    else
        tmp = (x / t) / (y - z)
    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 (t <= -5.2e-179) {
		tmp = (x / y) / (t - z);
	} else if (t <= 8.1e-50) {
		tmp = (x / -z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -5.2e-179:
		tmp = (x / y) / (t - z)
	elif t <= 8.1e-50:
		tmp = (x / -z) / (y - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.2e-179)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 8.1e-50)
		tmp = Float64(Float64(x / Float64(-z)) / Float64(y - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	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 (t <= -5.2e-179)
		tmp = (x / y) / (t - z);
	elseif (t <= 8.1e-50)
		tmp = (x / -z) / (y - z);
	else
		tmp = (x / t) / (y - z);
	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[t, -5.2e-179], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.1e-50], N[(N[(x / (-z)), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000011e-179

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 78.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 82.4

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

   6. Applied rewrites 82.4%

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

   if -5.20000000000000011e-179 < t < 8.0999999999999999e-50

   1. Initial program 91.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 96.7

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

   3. Applied rewrites 96.7%

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

   4. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 82.3

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

   6. Applied rewrites 82.3%

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

   if 8.0999999999999999e-50 < t

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 97.0

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 82.3%

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

Alternative 4: 78.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

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 (<= y -1.12e-42)
   (/ x (* y (- t z)))
   (if (<= y 1.35e-16) (/ x (* (- z) (- t z))) (/ (/ x (- y z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e-42) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.35e-16) {
		tmp = x / (-z * (t - z));
	} else {
		tmp = (x / (y - 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) :: tmp
    if (y <= (-1.12d-42)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.35d-16) then
        tmp = x / (-z * (t - z))
    else
        tmp = (x / (y - 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 tmp;
	if (y <= -1.12e-42) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.35e-16) {
		tmp = x / (-z * (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e-42:
		tmp = x / (y * (t - z))
	elif y <= 1.35e-16:
		tmp = x / (-z * (t - z))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e-42)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.35e-16)
		tmp = Float64(x / Float64(Float64(-z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(y - 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)
	tmp = 0.0;
	if (y <= -1.12e-42)
		tmp = x / (y * (t - z));
	elseif (y <= 1.35e-16)
		tmp = x / (-z * (t - z));
	else
		tmp = (x / (y - 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_] := If[LessEqual[y, -1.12e-42], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-16], N[(x / N[((-z) * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1199999999999999e-42

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 80.7%

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

   if -1.1199999999999999e-42 < y < 1.35e-16

   1. Initial program 91.1%

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

   2. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 74.3

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

   4. Applied rewrites 74.3%

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

   if 1.35e-16 < y

   1. Initial program 85.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 93.9%

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

Alternative 5: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.4 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= t 3.4e-183)
   (/ (/ x y) (- t z))
   (if (<= t 3.4e-57) (/ x (* z z)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.4e-183) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.4e-57) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	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 (t <= 3.4d-183) then
        tmp = (x / y) / (t - z)
    else if (t <= 3.4d-57) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / (y - z)
    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 (t <= 3.4e-183) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.4e-57) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 3.4e-183:
		tmp = (x / y) / (t - z)
	elif t <= 3.4e-57:
		tmp = x / (z * z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.4e-183)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 3.4e-57)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	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 (t <= 3.4e-183)
		tmp = (x / y) / (t - z);
	elseif (t <= 3.4e-57)
		tmp = x / (z * z);
	else
		tmp = (x / t) / (y - z);
	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[t, 3.4e-183], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-57], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.40000000000000014e-183

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 67.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 68.1

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

   6. Applied rewrites 68.1%

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

   if 3.40000000000000014e-183 < t < 3.40000000000000016e-57

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

      2. lower-*.f64 52.2

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

   4. Applied rewrites 52.2%

      \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   if 3.40000000000000016e-57 < t

   1. Initial program 89.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 97.0

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 81.8%

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

Alternative 6: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.4 \cdot 10^{-183}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= t 3.4e-183)
   (/ x (* y (- t z)))
   (if (<= t 3.4e-57) (/ x (* z z)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.4e-183) {
		tmp = x / (y * (t - z));
	} else if (t <= 3.4e-57) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	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 (t <= 3.4d-183) then
        tmp = x / (y * (t - z))
    else if (t <= 3.4d-57) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / (y - z)
    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 (t <= 3.4e-183) {
		tmp = x / (y * (t - z));
	} else if (t <= 3.4e-57) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 3.4e-183:
		tmp = x / (y * (t - z))
	elif t <= 3.4e-57:
		tmp = x / (z * z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.4e-183)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 3.4e-57)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	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 (t <= 3.4e-183)
		tmp = x / (y * (t - z));
	elseif (t <= 3.4e-57)
		tmp = x / (z * z);
	else
		tmp = (x / t) / (y - z);
	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[t, 3.4e-183], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-57], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.40000000000000014e-183

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 67.0%

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

   if 3.40000000000000014e-183 < t < 3.40000000000000016e-57

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

      2. lower-*.f64 52.2

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

   4. Applied rewrites 52.2%

      \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   if 3.40000000000000016e-57 < t

   1. Initial program 89.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 97.0

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 81.8%

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

Alternative 7: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-256}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-66)
   (/ x (* y (- t z)))
   (if (<= y 4e-256) (/ x (* z z)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-66) {
		tmp = x / (y * (t - z));
	} else if (y <= 4e-256) {
		tmp = x / (z * z);
	} else {
		tmp = x / ((y - 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) :: tmp
    if (y <= (-1.05d-66)) then
        tmp = x / (y * (t - z))
    else if (y <= 4d-256) then
        tmp = x / (z * z)
    else
        tmp = x / ((y - 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 tmp;
	if (y <= -1.05e-66) {
		tmp = x / (y * (t - z));
	} else if (y <= 4e-256) {
		tmp = x / (z * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-66:
		tmp = x / (y * (t - z))
	elif y <= 4e-256:
		tmp = x / (z * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-66)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 4e-256)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(Float64(y - 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)
	tmp = 0.0;
	if (y <= -1.05e-66)
		tmp = x / (y * (t - z));
	elseif (y <= 4e-256)
		tmp = x / (z * z);
	else
		tmp = x / ((y - 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_] := If[LessEqual[y, -1.05e-66], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-256], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-66

   1. Initial program 89.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 79.2%

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

   if -1.05e-66 < y < 3.99999999999999991e-256

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

      2. lower-*.f64 54.8

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

   4. Applied rewrites 54.8%

      \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   if 3.99999999999999991e-256 < y

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 76.7%

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

Alternative 8: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z))))
   (if (<= z -2.5e+56) t_1 (if (<= z 5.4e+19) (/ x (* y (- t z))) 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 * z);
	double tmp;
	if (z <= -2.5e+56) {
		tmp = t_1;
	} else if (z <= 5.4e+19) {
		tmp = x / (y * (t - z));
	} 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) :: tmp
    t_1 = x / (z * z)
    if (z <= (-2.5d+56)) then
        tmp = t_1
    else if (z <= 5.4d+19) then
        tmp = x / (y * (t - z))
    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 * z);
	double tmp;
	if (z <= -2.5e+56) {
		tmp = t_1;
	} else if (z <= 5.4e+19) {
		tmp = x / (y * (t - z));
	} 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 * z)
	tmp = 0
	if z <= -2.5e+56:
		tmp = t_1
	elif z <= 5.4e+19:
		tmp = x / (y * (t - z))
	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(z * z))
	tmp = 0.0
	if (z <= -2.5e+56)
		tmp = t_1;
	elseif (z <= 5.4e+19)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	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 * z);
	tmp = 0.0;
	if (z <= -2.5e+56)
		tmp = t_1;
	elseif (z <= 5.4e+19)
		tmp = x / (y * (t - z));
	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 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+56], t$95$1, If[LessEqual[z, 5.4e+19], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000012e56 or 5.4e19 < z

   1. Initial program 83.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

      2. lower-*.f64 71.4

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

   4. Applied rewrites 71.4%

      \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   if -2.50000000000000012e56 < z < 5.4e19

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 70.1%

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

Alternative 9: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z))))
   (if (<= z -3.7e+42) t_1 (if (<= z 2.15e+19) (/ (/ x y) t) 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 * z);
	double tmp;
	if (z <= -3.7e+42) {
		tmp = t_1;
	} else if (z <= 2.15e+19) {
		tmp = (x / y) / t;
	} 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) :: tmp
    t_1 = x / (z * z)
    if (z <= (-3.7d+42)) then
        tmp = t_1
    else if (z <= 2.15d+19) then
        tmp = (x / y) / t
    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 * z);
	double tmp;
	if (z <= -3.7e+42) {
		tmp = t_1;
	} else if (z <= 2.15e+19) {
		tmp = (x / y) / t;
	} 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 * z)
	tmp = 0
	if z <= -3.7e+42:
		tmp = t_1
	elif z <= 2.15e+19:
		tmp = (x / y) / t
	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(z * z))
	tmp = 0.0
	if (z <= -3.7e+42)
		tmp = t_1;
	elseif (z <= 2.15e+19)
		tmp = Float64(Float64(x / y) / t);
	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 * z);
	tmp = 0.0;
	if (z <= -3.7e+42)
		tmp = t_1;
	elseif (z <= 2.15e+19)
		tmp = (x / y) / t;
	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 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+42], t$95$1, If[LessEqual[z, 2.15e+19], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999996e42 or 2.15e19 < z

   1. Initial program 83.7%

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

   2. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

      2. lower-*.f64 70.9

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

   4. Applied rewrites 70.9%

      \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   if -3.69999999999999996e42 < z < 2.15e19

   1. Initial program 94.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 93.8

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

   3. Applied rewrites 93.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 71.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 57.6

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

   9. Applied rewrites 57.6%

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

Alternative 10: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z))))
   (if (<= z -3.1e+42) t_1 (if (<= z 2.2e+18) (/ x (* t y)) 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 * z);
	double tmp;
	if (z <= -3.1e+42) {
		tmp = t_1;
	} else if (z <= 2.2e+18) {
		tmp = x / (t * y);
	} 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) :: tmp
    t_1 = x / (z * z)
    if (z <= (-3.1d+42)) then
        tmp = t_1
    else if (z <= 2.2d+18) then
        tmp = x / (t * y)
    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 * z);
	double tmp;
	if (z <= -3.1e+42) {
		tmp = t_1;
	} else if (z <= 2.2e+18) {
		tmp = x / (t * y);
	} 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 * z)
	tmp = 0
	if z <= -3.1e+42:
		tmp = t_1
	elif z <= 2.2e+18:
		tmp = x / (t * y)
	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(z * z))
	tmp = 0.0
	if (z <= -3.1e+42)
		tmp = t_1;
	elseif (z <= 2.2e+18)
		tmp = Float64(x / Float64(t * y));
	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 * z);
	tmp = 0.0;
	if (z <= -3.1e+42)
		tmp = t_1;
	elseif (z <= 2.2e+18)
		tmp = x / (t * y);
	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 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+42], t$95$1, If[LessEqual[z, 2.2e+18], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000002e42 or 2.2e18 < z

   1. Initial program 83.7%

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

   2. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

      2. lower-*.f64 70.8

         \[\leadsto \frac{x}{z \cdot \color{blue}{z}} \]

   4. Applied rewrites 70.8%

      \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   if -3.1000000000000002e42 < z < 2.2e18

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 55.1

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

   4. Applied rewrites 55.1%

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

Alternative 11: 39.8% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

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 = x / (t * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

2. Taylor expanded in z around 0

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

   1. lower-*.f64 39.8

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

4. Applied rewrites 39.8%

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64
  (/ x (* (- y z) (- t z))))