Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.3% → 96.9%

Time: 3.3s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

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(Float64(x * 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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

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(Float64(x * 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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z - t}{z - y}} \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.3%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-/l* N/A

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

   6. lower-*.f64 N/A

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

   7. sub-negate-rev N/A

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

   8. sub-negate-rev N/A

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

   9. frac-2neg-rev N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lower--.f64 96.9

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

3. Applied rewrites 96.9%

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

   1. lift--.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. division-flip N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift--.f64 96.6

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

5. Applied rewrites 96.6%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-/.f64 N/A

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

   6. mult-flip-rev N/A

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

   7. lower-/.f64 N/A

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

   8. lift-/.f64 N/A

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

   9. lift--.f64 N/A

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

   10. lift--.f64 96.9

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

7. Applied rewrites 96.9%

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

Alternative 2: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((z - y) / (z - 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 = x * ((z - y) / (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.3%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-/l* N/A

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

   6. lower-*.f64 N/A

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

   7. sub-negate-rev N/A

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

   8. sub-negate-rev N/A

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

   9. frac-2neg-rev N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lower--.f64 96.9

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

3. Applied rewrites 96.9%

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

Alternative 3: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.38e+38)
   (/ x (/ z (- z y)))
   (if (<= z 5.5e+67) (/ (* x y) (- t z)) (* x (/ (- z y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.38e+38) {
		tmp = x / (z / (z - y));
	} else if (z <= 5.5e+67) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-1.38d+38)) then
        tmp = x / (z / (z - y))
    else if (z <= 5.5d+67) then
        tmp = (x * y) / (t - z)
    else
        tmp = x * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.38e+38) {
		tmp = x / (z / (z - y));
	} else if (z <= 5.5e+67) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.38e+38:
		tmp = x / (z / (z - y))
	elif z <= 5.5e+67:
		tmp = (x * y) / (t - z)
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.38e+38)
		tmp = Float64(x / Float64(z / Float64(z - y)));
	elseif (z <= 5.5e+67)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.38e+38)
		tmp = x / (z / (z - y));
	elseif (z <= 5.5e+67)
		tmp = (x * y) / (t - z);
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.38e+38], N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+67], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3799999999999999e38

   1. Initial program 74.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. sub-negate-rev N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 99.8

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

   3. Applied rewrites 99.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. division-flip N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 79.3%

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

   if -1.3799999999999999e38 < z < 5.49999999999999968e67

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 71.4%

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

   if 5.49999999999999968e67 < z

   1. Initial program 70.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. sub-negate-rev N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 78.8%

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

Alternative 4: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -1.38e+38) t_1 (if (<= z 5.5e+67) (/ (* x y) (- t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.38e+38) {
		tmp = t_1;
	} else if (z <= 5.5e+67) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 - y) / z)
    if (z <= (-1.38d+38)) then
        tmp = t_1
    else if (z <= 5.5d+67) then
        tmp = (x * y) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.38e+38) {
		tmp = t_1;
	} else if (z <= 5.5e+67) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -1.38e+38:
		tmp = t_1
	elif z <= 5.5e+67:
		tmp = (x * y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -1.38e+38)
		tmp = t_1;
	elseif (z <= 5.5e+67)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -1.38e+38)
		tmp = t_1;
	elseif (z <= 5.5e+67)
		tmp = (x * y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.38e+38], t$95$1, If[LessEqual[z, 5.5e+67], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3799999999999999e38 or 5.49999999999999968e67 < z

   1. Initial program 72.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. sub-negate-rev N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 79.1%

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

   if -1.3799999999999999e38 < z < 5.49999999999999968e67

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 71.4%

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

Alternative 5: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -1.38e+38) t_1 (if (<= z 6e+67) (* x (/ y (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.38e+38) {
		tmp = t_1;
	} else if (z <= 6e+67) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 - y) / z)
    if (z <= (-1.38d+38)) then
        tmp = t_1
    else if (z <= 6d+67) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.38e+38) {
		tmp = t_1;
	} else if (z <= 6e+67) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -1.38e+38:
		tmp = t_1
	elif z <= 6e+67:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -1.38e+38)
		tmp = t_1;
	elseif (z <= 6e+67)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -1.38e+38)
		tmp = t_1;
	elseif (z <= 6e+67)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.38e+38], t$95$1, If[LessEqual[z, 6e+67], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3799999999999999e38 or 6.0000000000000002e67 < z

   1. Initial program 72.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. sub-negate-rev N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 79.1%

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

   if -1.3799999999999999e38 < z < 6.0000000000000002e67

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 72.9

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

   4. Applied rewrites 72.9%

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

Alternative 6: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-123}:\\ \;\;\;\;\frac{z \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -6.5e-89) t_1 (if (<= y 1.38e-123) (/ (* z x) (- z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -6.5e-89) {
		tmp = t_1;
	} else if (y <= 1.38e-123) {
		tmp = (z * x) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 / (t - z))
    if (y <= (-6.5d-89)) then
        tmp = t_1
    else if (y <= 1.38d-123) then
        tmp = (z * x) / (z - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -6.5e-89) {
		tmp = t_1;
	} else if (y <= 1.38e-123) {
		tmp = (z * x) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -6.5e-89:
		tmp = t_1
	elif y <= 1.38e-123:
		tmp = (z * x) / (z - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -6.5e-89)
		tmp = t_1;
	elseif (y <= 1.38e-123)
		tmp = Float64(Float64(z * x) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -6.5e-89)
		tmp = t_1;
	elseif (y <= 1.38e-123)
		tmp = (z * x) / (z - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-89], t$95$1, If[LessEqual[y, 1.38e-123], N[(N[(z * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000034e-89 or 1.38e-123 < y

   1. Initial program 84.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -6.50000000000000034e-89 < y < 1.38e-123

   1. Initial program 84.4%

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

   2. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. sub-negate-rev N/A

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

      4. frac-2neg-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 74.8

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

   4. Applied rewrites 74.8%

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

Alternative 7: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e+154) x (if (<= z 1.05e+68) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+154) {
		tmp = x;
	} else if (z <= 1.05e+68) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-9d+154)) then
        tmp = x
    else if (z <= 1.05d+68) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+154) {
		tmp = x;
	} else if (z <= 1.05e+68) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9e+154:
		tmp = x
	elif z <= 1.05e+68:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e+154)
		tmp = x;
	elseif (z <= 1.05e+68)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9e+154)
		tmp = x;
	elseif (z <= 1.05e+68)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9e+154], x, If[LessEqual[z, 1.05e+68], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000018e154 or 1.05e68 < z

   1. Initial program 68.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 69.4%

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

   if -9.00000000000000018e154 < z < 1.05e68

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 68.2

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

   4. Applied rewrites 68.2%

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

Alternative 8: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+148)
   x
   (if (<= z -4.1e+31) (* x (/ y (- z))) (if (<= z 9.2e+67) (/ x (/ t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+148) {
		tmp = x;
	} else if (z <= -4.1e+31) {
		tmp = x * (y / -z);
	} else if (z <= 9.2e+67) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-1.2d+148)) then
        tmp = x
    else if (z <= (-4.1d+31)) then
        tmp = x * (y / -z)
    else if (z <= 9.2d+67) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+148) {
		tmp = x;
	} else if (z <= -4.1e+31) {
		tmp = x * (y / -z);
	} else if (z <= 9.2e+67) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+148:
		tmp = x
	elif z <= -4.1e+31:
		tmp = x * (y / -z)
	elif z <= 9.2e+67:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+148)
		tmp = x;
	elseif (z <= -4.1e+31)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= 9.2e+67)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+148)
		tmp = x;
	elseif (z <= -4.1e+31)
		tmp = x * (y / -z);
	elseif (z <= 9.2e+67)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+148], x, If[LessEqual[z, -4.1e+31], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+67], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999997e148 or 9.1999999999999994e67 < z

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 69.4%

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

   if -1.19999999999999997e148 < z < -4.1000000000000002e31

   1. Initial program 85.0%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 58.1

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

   4. Applied rewrites 58.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 25.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 29.2

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

   9. Applied rewrites 29.2%

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

   if -4.1000000000000002e31 < z < 9.1999999999999994e67

   1. Initial program 92.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. sub-negate-rev N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 94.7

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

   3. Applied rewrites 94.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. division-flip N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 94.3

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 60.0

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

   8. Applied rewrites 60.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 60.2

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

   10. Applied rewrites 60.2%

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

Alternative 9: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+137) x (if (<= z 9.2e+67) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+137) {
		tmp = x;
	} else if (z <= 9.2e+67) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-2.3d+137)) then
        tmp = x
    else if (z <= 9.2d+67) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+137) {
		tmp = x;
	} else if (z <= 9.2e+67) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+137:
		tmp = x
	elif z <= 9.2e+67:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+137)
		tmp = x;
	elseif (z <= 9.2e+67)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+137)
		tmp = x;
	elseif (z <= 9.2e+67)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+137], x, If[LessEqual[z, 9.2e+67], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999999e137 or 9.1999999999999994e67 < z

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 69.3%

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

   if -2.29999999999999999e137 < z < 9.1999999999999994e67

   1. Initial program 91.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. sub-negate-rev N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 95.4

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

   3. Applied rewrites 95.4%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. division-flip N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 54.7

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

   8. Applied rewrites 54.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 54.9

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

   10. Applied rewrites 54.9%

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

Alternative 10: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+137) x (if (<= z 9.2e+67) (/ (* y x) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+137) {
		tmp = x;
	} else if (z <= 9.2e+67) {
		tmp = (y * x) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-2.3d+137)) then
        tmp = x
    else if (z <= 9.2d+67) then
        tmp = (y * x) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+137) {
		tmp = x;
	} else if (z <= 9.2e+67) {
		tmp = (y * x) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+137:
		tmp = x
	elif z <= 9.2e+67:
		tmp = (y * x) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+137)
		tmp = x;
	elseif (z <= 9.2e+67)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+137)
		tmp = x;
	elseif (z <= 9.2e+67)
		tmp = (y * x) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+137], x, If[LessEqual[z, 9.2e+67], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999999e137 or 9.1999999999999994e67 < z

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 69.3%

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

   if -2.29999999999999999e137 < z < 9.1999999999999994e67

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 52.7

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

   4. Applied rewrites 52.7%

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

Alternative 11: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.48e+38) x (if (<= z 9.2e+67) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.48e+38) {
		tmp = x;
	} else if (z <= 9.2e+67) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-1.48d+38)) then
        tmp = x
    else if (z <= 9.2d+67) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.48e+38) {
		tmp = x;
	} else if (z <= 9.2e+67) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.48e+38:
		tmp = x
	elif z <= 9.2e+67:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.48e+38)
		tmp = x;
	elseif (z <= 9.2e+67)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.48e+38)
		tmp = x;
	elseif (z <= 9.2e+67)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.48e+38], x, If[LessEqual[z, 9.2e+67], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.48e38 or 9.1999999999999994e67 < z

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 63.9%

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

   if -1.48e38 < z < 9.1999999999999994e67

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.6

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

   4. Applied rewrites 57.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 57.7

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

   6. Applied rewrites 57.7%

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

Alternative 12: 35.5% accurate, 12.6× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 84.3%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 35.5%

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

Reproduce

herbie shell --seed 2025128 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))