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

Percentage Accurate: 83.9% → 96.9%

Time: 15.6s

Alternatives: 11

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: 83.9% 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, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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. div-sub N/A

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

   7. distribute-lft-out-- N/A

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

   8. associate-/l* N/A

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

   9. associate-/l* N/A

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

   10. div-sub N/A

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

   11. fp-cancel-sub-sign N/A

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

   12. mul-1-neg N/A

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

   13. associate-*r* N/A

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

   14. +-commutative N/A

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

   15. *-commutative N/A

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

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

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

   17. distribute-lft-neg-in N/A

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

   18. *-commutative N/A

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

   19. div-sub N/A

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

3. Applied rewrites 96.9%

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

Alternative 2: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lift--.f64 N/A

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

   10. lift--.f64 96.9

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

3. Applied rewrites 96.9%

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

Alternative 3: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+162}:\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.35e+162)
   (* (/ z (- t z)) (- x))
   (if (<= z 5.6e+149) (* (/ x (- t z)) (- y z)) (- x (* (/ y z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+162) {
		tmp = (z / (t - z)) * -x;
	} else if (z <= 5.6e+149) {
		tmp = (x / (t - z)) * (y - z);
	} else {
		tmp = x - ((y / z) * 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 <= (-1.35d+162)) then
        tmp = (z / (t - z)) * -x
    else if (z <= 5.6d+149) then
        tmp = (x / (t - z)) * (y - z)
    else
        tmp = x - ((y / z) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+162) {
		tmp = (z / (t - z)) * -x;
	} else if (z <= 5.6e+149) {
		tmp = (x / (t - z)) * (y - z);
	} else {
		tmp = x - ((y / z) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.35e+162:
		tmp = (z / (t - z)) * -x
	elif z <= 5.6e+149:
		tmp = (x / (t - z)) * (y - z)
	else:
		tmp = x - ((y / z) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.35e+162)
		tmp = Float64(Float64(z / Float64(t - z)) * Float64(-x));
	elseif (z <= 5.6e+149)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(y - z));
	else
		tmp = Float64(x - Float64(Float64(y / z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.35e+162)
		tmp = (z / (t - z)) * -x;
	elseif (z <= 5.6e+149)
		tmp = (x / (t - z)) * (y - z);
	else
		tmp = x - ((y / z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.35e+162], N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 5.6e+149], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e162

   1. Initial program 61.2%

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

   2. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 88.4

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

   4. Applied rewrites 88.4%

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

   if -1.3500000000000001e162 < z < 5.5999999999999998e149

   1. Initial program 90.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. div-sub N/A

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

      7. distribute-lft-out-- N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

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

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. lift--.f64 91.0

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

   3. Applied rewrites 91.0%

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

   if 5.5999999999999998e149 < z

   1. Initial program 64.5%

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

   2. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

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

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. mul-1-neg N/A

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

      19. metadata-eval N/A

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

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

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

      21. *-lft-identity N/A

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

      22. lower--.f64 88.4

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

   4. Applied rewrites 88.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. div-sub N/A

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

      6. *-inverses N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

      12. fp-cancel-sub-sign N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 88.4

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

   6. Applied rewrites 88.4%

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

Alternative 4: 75.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t - z} \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 560000:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- t z)) (- x))))
   (if (<= z -5.4e-34) t_1 (if (<= z 560000.0) (* (/ x (- t z)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (t - z)) * -x;
	double tmp;
	if (z <= -5.4e-34) {
		tmp = t_1;
	} else if (z <= 560000.0) {
		tmp = (x / (t - z)) * y;
	} 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 = (z / (t - z)) * -x
    if (z <= (-5.4d-34)) then
        tmp = t_1
    else if (z <= 560000.0d0) then
        tmp = (x / (t - z)) * y
    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 = (z / (t - z)) * -x;
	double tmp;
	if (z <= -5.4e-34) {
		tmp = t_1;
	} else if (z <= 560000.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / (t - z)) * -x
	tmp = 0
	if z <= -5.4e-34:
		tmp = t_1
	elif z <= 560000.0:
		tmp = (x / (t - z)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / Float64(t - z)) * Float64(-x))
	tmp = 0.0
	if (z <= -5.4e-34)
		tmp = t_1;
	elseif (z <= 560000.0)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / (t - z)) * -x;
	tmp = 0.0;
	if (z <= -5.4e-34)
		tmp = t_1;
	elseif (z <= 560000.0)
		tmp = (x / (t - z)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[z, -5.4e-34], t$95$1, If[LessEqual[z, 560000.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.40000000000000034e-34 or 5.6e5 < z

   1. Initial program 75.3%

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

   2. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 74.8

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

   4. Applied rewrites 74.8%

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

   if -5.40000000000000034e-34 < z < 5.6e5

   1. Initial program 93.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. div-sub N/A

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

      7. distribute-lft-out-- N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

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

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. lift--.f64 93.4

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

   3. Applied rewrites 93.4%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 77.1%

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

Alternative 5: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{-6}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 11000:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.65e-6)
   (* (/ (- z y) z) x)
   (if (<= z 11000.0) (* (/ x (- t z)) y) (- x (* (/ y z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.65e-6) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 11000.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = x - ((y / z) * 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 <= (-3.65d-6)) then
        tmp = ((z - y) / z) * x
    else if (z <= 11000.0d0) then
        tmp = (x / (t - z)) * y
    else
        tmp = x - ((y / z) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.65e-6) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 11000.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = x - ((y / z) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.65e-6:
		tmp = ((z - y) / z) * x
	elif z <= 11000.0:
		tmp = (x / (t - z)) * y
	else:
		tmp = x - ((y / z) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.65e-6)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= 11000.0)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = Float64(x - Float64(Float64(y / z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.65e-6)
		tmp = ((z - y) / z) * x;
	elseif (z <= 11000.0)
		tmp = (x / (t - z)) * y;
	else
		tmp = x - ((y / z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.65e-6], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 11000.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.65000000000000021e-6

   1. Initial program 74.4%

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

   2. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

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

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. mul-1-neg N/A

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

      19. metadata-eval N/A

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

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

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

      21. *-lft-identity N/A

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

      22. lower--.f64 74.4

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

   4. Applied rewrites 74.4%

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

   if -3.65000000000000021e-6 < z < 11000

   1. Initial program 93.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. div-sub N/A

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

      7. distribute-lft-out-- N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

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

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 N/A

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

      18. lift--.f64 93.4

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

   3. Applied rewrites 93.4%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 75.8%

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

   if 11000 < z

   1. Initial program 74.6%

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

   2. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

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

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. mul-1-neg N/A

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

      19. metadata-eval N/A

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

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

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

      21. *-lft-identity N/A

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

      22. lower--.f64 75.0

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

   4. Applied rewrites 75.0%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. div-sub N/A

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

      6. *-inverses N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

      12. fp-cancel-sub-sign N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 75.0

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

   6. Applied rewrites 75.0%

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

Alternative 6: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{t} \cdot x\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+47}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- y z) t) x)))
   (if (<= t -2.2e-28) t_1 (if (<= t 1.25e+47) (- x (* (/ y z) x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y - z) / t) * x;
	double tmp;
	if (t <= -2.2e-28) {
		tmp = t_1;
	} else if (t <= 1.25e+47) {
		tmp = x - ((y / z) * x);
	} 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 = ((y - z) / t) * x
    if (t <= (-2.2d-28)) then
        tmp = t_1
    else if (t <= 1.25d+47) then
        tmp = x - ((y / z) * x)
    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 = ((y - z) / t) * x;
	double tmp;
	if (t <= -2.2e-28) {
		tmp = t_1;
	} else if (t <= 1.25e+47) {
		tmp = x - ((y / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y - z) / t) * x
	tmp = 0
	if t <= -2.2e-28:
		tmp = t_1
	elif t <= 1.25e+47:
		tmp = x - ((y / z) * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y - z) / t) * x)
	tmp = 0.0
	if (t <= -2.2e-28)
		tmp = t_1;
	elseif (t <= 1.25e+47)
		tmp = Float64(x - Float64(Float64(y / z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y - z) / t) * x;
	tmp = 0.0;
	if (t <= -2.2e-28)
		tmp = t_1;
	elseif (t <= 1.25e+47)
		tmp = x - ((y / z) * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -2.2e-28], t$95$1, If[LessEqual[t, 1.25e+47], N[(x - N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.19999999999999996e-28 or 1.25000000000000005e47 < t

   1. Initial program 82.9%

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

   2. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 73.8

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

   4. Applied rewrites 73.8%

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

   if -2.19999999999999996e-28 < t < 1.25000000000000005e47

   1. Initial program 84.9%

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

   2. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

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

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. mul-1-neg N/A

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

      19. metadata-eval N/A

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

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

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

      21. *-lft-identity N/A

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

      22. lower--.f64 74.6

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

   4. Applied rewrites 74.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. div-sub N/A

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

      6. *-inverses N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

      12. fp-cancel-sub-sign N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 74.6

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

   6. Applied rewrites 74.6%

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

Alternative 7: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{t} \cdot x\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+47}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- y z) t) x)))
   (if (<= t -2.2e-28) t_1 (if (<= t 1.25e+47) (* (/ (- z y) z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y - z) / t) * x;
	double tmp;
	if (t <= -2.2e-28) {
		tmp = t_1;
	} else if (t <= 1.25e+47) {
		tmp = ((z - y) / z) * x;
	} 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 = ((y - z) / t) * x
    if (t <= (-2.2d-28)) then
        tmp = t_1
    else if (t <= 1.25d+47) then
        tmp = ((z - y) / z) * x
    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 = ((y - z) / t) * x;
	double tmp;
	if (t <= -2.2e-28) {
		tmp = t_1;
	} else if (t <= 1.25e+47) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y - z) / t) * x
	tmp = 0
	if t <= -2.2e-28:
		tmp = t_1
	elif t <= 1.25e+47:
		tmp = ((z - y) / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y - z) / t) * x)
	tmp = 0.0
	if (t <= -2.2e-28)
		tmp = t_1;
	elseif (t <= 1.25e+47)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y - z) / t) * x;
	tmp = 0.0;
	if (t <= -2.2e-28)
		tmp = t_1;
	elseif (t <= 1.25e+47)
		tmp = ((z - y) / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -2.2e-28], t$95$1, If[LessEqual[t, 1.25e+47], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.19999999999999996e-28 or 1.25000000000000005e47 < t

   1. Initial program 82.9%

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

   2. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 73.8

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

   4. Applied rewrites 73.8%

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

   if -2.19999999999999996e-28 < t < 1.25000000000000005e47

   1. Initial program 84.9%

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

   2. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

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

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. mul-1-neg N/A

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

      19. metadata-eval N/A

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

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

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

      21. *-lft-identity N/A

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

      22. lower--.f64 74.6

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

   4. Applied rewrites 74.6%

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

Alternative 8: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 29500000:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+88) x (if (<= z 29500000.0) (* (/ (- y z) t) x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+88) {
		tmp = x;
	} else if (z <= 29500000.0) {
		tmp = ((y - z) / t) * x;
	} 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 <= (-6.6d+88)) then
        tmp = x
    else if (z <= 29500000.0d0) then
        tmp = ((y - z) / t) * x
    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 <= -6.6e+88) {
		tmp = x;
	} else if (z <= 29500000.0) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+88:
		tmp = x
	elif z <= 29500000.0:
		tmp = ((y - z) / t) * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+88)
		tmp = x;
	elseif (z <= 29500000.0)
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.6e+88)
		tmp = x;
	elseif (z <= 29500000.0)
		tmp = ((y - z) / t) * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+88], x, If[LessEqual[z, 29500000.0], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000006e88 or 2.95e7 < z

   1. Initial program 71.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 63.5%

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

   if -6.6000000000000006e88 < z < 2.95e7

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 70.9

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

   4. Applied rewrites 70.9%

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

Alternative 9: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 44000:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+19) x (if (<= z 44000.0) (* (/ y t) x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+19) {
		tmp = x;
	} else if (z <= 44000.0) {
		tmp = (y / t) * x;
	} 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 <= (-1.7d+19)) then
        tmp = x
    else if (z <= 44000.0d0) then
        tmp = (y / t) * x
    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 <= -1.7e+19) {
		tmp = x;
	} else if (z <= 44000.0) {
		tmp = (y / t) * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+19:
		tmp = x
	elif z <= 44000.0:
		tmp = (y / t) * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+19)
		tmp = x;
	elseif (z <= 44000.0)
		tmp = Float64(Float64(y / t) * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e+19)
		tmp = x;
	elseif (z <= 44000.0)
		tmp = (y / t) * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+19], x, If[LessEqual[z, 44000.0], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e19 or 44000 < z

   1. Initial program 73.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.0%

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

   if -1.7e19 < z < 44000

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 63.9

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

   4. Applied rewrites 63.9%

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

Alternative 10: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -125:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 40000:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -125.0) x (if (<= z 40000.0) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -125.0) {
		tmp = x;
	} else if (z <= 40000.0) {
		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 <= (-125.0d0)) then
        tmp = x
    else if (z <= 40000.0d0) 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 <= -125.0) {
		tmp = x;
	} else if (z <= 40000.0) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -125.0:
		tmp = x
	elif z <= 40000.0:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -125.0)
		tmp = x;
	elseif (z <= 40000.0)
		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 <= -125.0)
		tmp = x;
	elseif (z <= 40000.0)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -125.0], x, If[LessEqual[z, 40000.0], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -125 or 4e4 < z

   1. Initial program 74.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.0%

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

   if -125 < z < 4e4

   1. Initial program 93.1%

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

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

      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. div-sub N/A

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

      7. distribute-lft-out-- N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

      10. div-sub N/A

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

      11. fp-cancel-sub-sign N/A

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

      12. mul-1-neg N/A

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

      13. associate-*r* N/A

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

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

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

      17. distribute-lft-neg-in N/A

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

      18. *-commutative N/A

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

      19. div-sub N/A

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

   3. Applied rewrites 94.1%

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

   4. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   5. 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 62.5

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

   6. Applied rewrites 62.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]
   7. 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 62.8

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

   8. Applied rewrites 62.8%

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

Alternative 11: 34.8% 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 83.9%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 34.8%

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

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))