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

Percentage Accurate: 84.0% → 96.8%

Time: 2.9s

Alternatives: 10

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: 84.0% 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: 96.8% accurate, 1.0× speedup

Math

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

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(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]

Derivation

1. Initial program 84.0%

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

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

   4. lift-*.f64 N/A

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

   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. lower-/.f64 N/A

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

   8. lift--.f64 N/A

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

   9. lift--.f64 96.8

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

3. Applied rewrites 96.8%

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

Alternative 2: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e-14)
   (* x (/ y (- t z)))
   (if (<= y 1.28e+36) (* x (/ (- z) (- t z))) (* (/ x (- t z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-14) {
		tmp = x * (y / (t - z));
	} else if (y <= 1.28e+36) {
		tmp = x * (-z / (t - z));
	} else {
		tmp = (x / (t - z)) * y;
	}
	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 (y <= (-4.6d-14)) then
        tmp = x * (y / (t - z))
    else if (y <= 1.28d+36) then
        tmp = x * (-z / (t - z))
    else
        tmp = (x / (t - z)) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-14) {
		tmp = x * (y / (t - z));
	} else if (y <= 1.28e+36) {
		tmp = x * (-z / (t - z));
	} else {
		tmp = (x / (t - z)) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e-14:
		tmp = x * (y / (t - z))
	elif y <= 1.28e+36:
		tmp = x * (-z / (t - z))
	else:
		tmp = (x / (t - z)) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e-14)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (y <= 1.28e+36)
		tmp = Float64(x * Float64(Float64(-z) / Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e-14)
		tmp = x * (y / (t - z));
	elseif (y <= 1.28e+36)
		tmp = x * (-z / (t - z));
	else
		tmp = (x / (t - z)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e-14], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e+36], N[(x * N[((-z) / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999996e-14

   1. Initial program 83.8%

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

   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 71.6

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

   4. Applied rewrites 71.6%

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

   if -4.59999999999999996e-14 < y < 1.27999999999999993e36

   1. Initial program 85.1%

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

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

      4. lift-*.f64 N/A

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

      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. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 96.7

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

   3. Applied rewrites 96.7%

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

   4. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 77.2

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

   6. Applied rewrites 77.2%

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

   if 1.27999999999999993e36 < y

   1. Initial program 81.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 87.0

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

   4. Applied rewrites 87.0%

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

   5. Taylor expanded in y around inf

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 68.8

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

   7. Applied rewrites 68.8%

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

Alternative 3: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+101) x (if (<= z 4.3e+140) (* (/ x (- t z)) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+101) {
		tmp = x;
	} else if (z <= 4.3e+140) {
		tmp = (x / (t - z)) * 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 <= (-4d+101)) then
        tmp = x
    else if (z <= 4.3d+140) then
        tmp = (x / (t - z)) * 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 <= -4e+101) {
		tmp = x;
	} else if (z <= 4.3e+140) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+101:
		tmp = x
	elif z <= 4.3e+140:
		tmp = (x / (t - z)) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+101)
		tmp = x;
	elseif (z <= 4.3e+140)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e+101)
		tmp = x;
	elseif (z <= 4.3e+140)
		tmp = (x / (t - z)) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+101], x, If[LessEqual[z, 4.3e+140], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e101 or 4.30000000000000002e140 < z

   1. Initial program 66.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 71.1%

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

   if -3.9999999999999999e101 < z < 4.30000000000000002e140

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 82.6

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

   4. Applied rewrites 82.6%

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

   5. Taylor expanded in y around inf

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 65.7

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

   7. Applied rewrites 65.7%

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

Alternative 4: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+101) x (if (<= z 4.3e+140) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+101) {
		tmp = x;
	} else if (z <= 4.3e+140) {
		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 <= (-4d+101)) then
        tmp = x
    else if (z <= 4.3d+140) 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 <= -4e+101) {
		tmp = x;
	} else if (z <= 4.3e+140) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+101:
		tmp = x
	elif z <= 4.3e+140:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+101)
		tmp = x;
	elseif (z <= 4.3e+140)
		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 <= -4e+101)
		tmp = x;
	elseif (z <= 4.3e+140)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+101], x, If[LessEqual[z, 4.3e+140], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e101 or 4.30000000000000002e140 < z

   1. Initial program 66.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 71.1%

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

   if -3.9999999999999999e101 < z < 4.30000000000000002e140

   1. Initial program 91.6%

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

   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 67.6

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

   4. Applied rewrites 67.6%

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

Alternative 5: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+85)
   x
   (if (<= z -2.35e+29)
     (* x (/ (- y) z))
     (if (<= z 4.8e+25)
       (* x (/ y t))
       (if (<= z 2.15e+110) (/ (* x (- z)) t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+85) {
		tmp = x;
	} else if (z <= -2.35e+29) {
		tmp = x * (-y / z);
	} else if (z <= 4.8e+25) {
		tmp = x * (y / t);
	} else if (z <= 2.15e+110) {
		tmp = (x * -z) / 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 <= (-2.8d+85)) then
        tmp = x
    else if (z <= (-2.35d+29)) then
        tmp = x * (-y / z)
    else if (z <= 4.8d+25) then
        tmp = x * (y / t)
    else if (z <= 2.15d+110) then
        tmp = (x * -z) / 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 <= -2.8e+85) {
		tmp = x;
	} else if (z <= -2.35e+29) {
		tmp = x * (-y / z);
	} else if (z <= 4.8e+25) {
		tmp = x * (y / t);
	} else if (z <= 2.15e+110) {
		tmp = (x * -z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+85:
		tmp = x
	elif z <= -2.35e+29:
		tmp = x * (-y / z)
	elif z <= 4.8e+25:
		tmp = x * (y / t)
	elif z <= 2.15e+110:
		tmp = (x * -z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+85)
		tmp = x;
	elseif (z <= -2.35e+29)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 4.8e+25)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 2.15e+110)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+85)
		tmp = x;
	elseif (z <= -2.35e+29)
		tmp = x * (-y / z);
	elseif (z <= 4.8e+25)
		tmp = x * (y / t);
	elseif (z <= 2.15e+110)
		tmp = (x * -z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+85], x, If[LessEqual[z, -2.35e+29], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+25], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+110], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999999e85 or 2.15000000000000003e110 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 68.0%

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

   if -2.7999999999999999e85 < z < -2.3500000000000001e29

   1. Initial program 87.8%

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

   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 48.6

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

   4. Applied rewrites 48.6%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 30.8

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

   7. Applied rewrites 30.8%

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

   if -2.3500000000000001e29 < z < 4.79999999999999992e25

   1. Initial program 93.5%

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

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

      4. lift-*.f64 N/A

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

      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. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 94.1

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

   3. Applied rewrites 94.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 62.1

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

   6. Applied rewrites 62.1%

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

   if 4.79999999999999992e25 < z < 2.15000000000000003e110

   1. Initial program 86.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 35.3%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 28.1

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

   7. Applied rewrites 28.1%

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

Alternative 6: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+85)
   x
   (if (<= z -2.35e+29)
     (* x (/ (- y) z))
     (if (<= z 1.12e+27)
       (* x (/ y t))
       (if (<= z 2.15e+110) (* x (/ (- z) t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+85) {
		tmp = x;
	} else if (z <= -2.35e+29) {
		tmp = x * (-y / z);
	} else if (z <= 1.12e+27) {
		tmp = x * (y / t);
	} else if (z <= 2.15e+110) {
		tmp = x * (-z / 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 <= (-2.8d+85)) then
        tmp = x
    else if (z <= (-2.35d+29)) then
        tmp = x * (-y / z)
    else if (z <= 1.12d+27) then
        tmp = x * (y / t)
    else if (z <= 2.15d+110) then
        tmp = x * (-z / 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 <= -2.8e+85) {
		tmp = x;
	} else if (z <= -2.35e+29) {
		tmp = x * (-y / z);
	} else if (z <= 1.12e+27) {
		tmp = x * (y / t);
	} else if (z <= 2.15e+110) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+85:
		tmp = x
	elif z <= -2.35e+29:
		tmp = x * (-y / z)
	elif z <= 1.12e+27:
		tmp = x * (y / t)
	elif z <= 2.15e+110:
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+85)
		tmp = x;
	elseif (z <= -2.35e+29)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 1.12e+27)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 2.15e+110)
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+85)
		tmp = x;
	elseif (z <= -2.35e+29)
		tmp = x * (-y / z);
	elseif (z <= 1.12e+27)
		tmp = x * (y / t);
	elseif (z <= 2.15e+110)
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+85], x, If[LessEqual[z, -2.35e+29], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+27], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+110], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999999e85 or 2.15000000000000003e110 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 68.0%

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

   if -2.7999999999999999e85 < z < -2.3500000000000001e29

   1. Initial program 87.8%

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

   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 48.6

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

   4. Applied rewrites 48.6%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 30.8

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

   7. Applied rewrites 30.8%

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

   if -2.3500000000000001e29 < z < 1.12e27

   1. Initial program 93.5%

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

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

      4. lift-*.f64 N/A

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

      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. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 94.1

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

   3. Applied rewrites 94.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 62.0

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

   6. Applied rewrites 62.0%

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

   if 1.12e27 < z < 2.15000000000000003e110

   1. Initial program 86.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 35.5%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 28.0

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

   7. Applied rewrites 28.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 30.1

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

   9. Applied rewrites 30.1%

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

Alternative 7: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+85)
   x
   (if (<= z -2.35e+29)
     (* x (/ (- y) z))
     (if (<= z 7.8e+99) (* x (/ y t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+85) {
		tmp = x;
	} else if (z <= -2.35e+29) {
		tmp = x * (-y / z);
	} else if (z <= 7.8e+99) {
		tmp = x * (y / 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 <= (-2.8d+85)) then
        tmp = x
    else if (z <= (-2.35d+29)) then
        tmp = x * (-y / z)
    else if (z <= 7.8d+99) then
        tmp = x * (y / 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 <= -2.8e+85) {
		tmp = x;
	} else if (z <= -2.35e+29) {
		tmp = x * (-y / z);
	} else if (z <= 7.8e+99) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+85:
		tmp = x
	elif z <= -2.35e+29:
		tmp = x * (-y / z)
	elif z <= 7.8e+99:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+85)
		tmp = x;
	elseif (z <= -2.35e+29)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 7.8e+99)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+85)
		tmp = x;
	elseif (z <= -2.35e+29)
		tmp = x * (-y / z);
	elseif (z <= 7.8e+99)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+85], x, If[LessEqual[z, -2.35e+29], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+99], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e85 or 7.79999999999999989e99 < z

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 67.5%

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

   if -2.7999999999999999e85 < z < -2.3500000000000001e29

   1. Initial program 87.8%

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

   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 48.6

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

   4. Applied rewrites 48.6%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 30.8

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

   7. Applied rewrites 30.8%

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

   if -2.3500000000000001e29 < z < 7.79999999999999989e99

   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

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

      4. lift-*.f64 N/A

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

      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. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 94.7

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 57.8

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

   6. Applied rewrites 57.8%

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

Alternative 8: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+47) x (if (<= z 7.8e+99) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+47) {
		tmp = x;
	} else if (z <= 7.8e+99) {
		tmp = x * (y / 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 <= (-5d+47)) then
        tmp = x
    else if (z <= 7.8d+99) then
        tmp = x * (y / 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 <= -5e+47) {
		tmp = x;
	} else if (z <= 7.8e+99) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e+47:
		tmp = x
	elif z <= 7.8e+99:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+47)
		tmp = x;
	elseif (z <= 7.8e+99)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+47)
		tmp = x;
	elseif (z <= 7.8e+99)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+47], x, If[LessEqual[z, 7.8e+99], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000022e47 or 7.79999999999999989e99 < z

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 64.9%

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

   if -5.00000000000000022e47 < z < 7.79999999999999989e99

   1. Initial program 92.6%

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

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

      4. lift-*.f64 N/A

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

      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. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 94.9

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

   3. Applied rewrites 94.9%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 57.3

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

   6. Applied rewrites 57.3%

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

Alternative 9: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+47) x (if (<= z 7.8e+99) (* (/ x t) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+47) {
		tmp = x;
	} else if (z <= 7.8e+99) {
		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 <= (-5d+47)) then
        tmp = x
    else if (z <= 7.8d+99) 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 <= -5e+47) {
		tmp = x;
	} else if (z <= 7.8e+99) {
		tmp = (x / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e+47:
		tmp = x
	elif z <= 7.8e+99:
		tmp = (x / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+47)
		tmp = x;
	elseif (z <= 7.8e+99)
		tmp = Float64(Float64(x / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+47)
		tmp = x;
	elseif (z <= 7.8e+99)
		tmp = (x / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+47], x, If[LessEqual[z, 7.8e+99], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000022e47 or 7.79999999999999989e99 < z

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 64.9%

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

   if -5.00000000000000022e47 < z < 7.79999999999999989e99

   1. Initial program 92.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 82.8

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

   4. Applied rewrites 82.8%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 55.2

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

   7. Applied rewrites 55.2%

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

Alternative 10: 34.5% accurate, 9.0× 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 84.0%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 34.5%

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

Reproduce

herbie shell --seed 2025101 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))