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

Percentage Accurate: 84.4% → 97.0%

Time: 2.5s

Alternatives: 9

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: 84.4% 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: 97.0% 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 84.4%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-/l* N/A

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

   6. lower-*.f64 N/A

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

   7. 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 97.0

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

3. Applied rewrites 97.0%

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

Alternative 2: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{t - z}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) (- t z)))))
   (if (<= z -2.55e-36) t_1 (if (<= z 8.8e-20) (/ (* x y) (- t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / (t - z));
	double tmp;
	if (z <= -2.55e-36) {
		tmp = t_1;
	} else if (z <= 8.8e-20) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (-z / (t - z))
    if (z <= (-2.55d-36)) then
        tmp = t_1
    else if (z <= 8.8d-20) then
        tmp = (x * y) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / (t - z));
	double tmp;
	if (z <= -2.55e-36) {
		tmp = t_1;
	} else if (z <= 8.8e-20) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-z / (t - z))
	tmp = 0
	if z <= -2.55e-36:
		tmp = t_1
	elif z <= 8.8e-20:
		tmp = (x * y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-z) / Float64(t - z)))
	tmp = 0.0
	if (z <= -2.55e-36)
		tmp = t_1;
	elseif (z <= 8.8e-20)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-z / (t - z));
	tmp = 0.0;
	if (z <= -2.55e-36)
		tmp = t_1;
	elseif (z <= 8.8e-20)
		tmp = (x * y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-z) / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e-36], t$95$1, If[LessEqual[z, 8.8e-20], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.54999999999999987e-36 or 8.79999999999999964e-20 < z

   1. Initial program 77.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. 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 99.7

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

   3. Applied rewrites 99.7%

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

   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 73.3

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

   6. Applied rewrites 73.3%

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

   if -2.54999999999999987e-36 < z < 8.79999999999999964e-20

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 77.1%

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

Alternative 3: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y - z\right)\\ t_2 := \frac{t\_1}{t - z}\\ \mathbf{if}\;t\_2 \leq -0.0001:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-310}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y z))) (t_2 (/ t_1 (- t z))))
   (if (<= t_2 -0.0001)
     (* x (/ y (- t z)))
     (if (<= t_2 2e-310) (/ t_1 t) (* x (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y - z);
	double t_2 = t_1 / (t - z);
	double tmp;
	if (t_2 <= -0.0001) {
		tmp = x * (y / (t - z));
	} else if (t_2 <= 2e-310) {
		tmp = t_1 / t;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y - z)
    t_2 = t_1 / (t - z)
    if (t_2 <= (-0.0001d0)) then
        tmp = x * (y / (t - z))
    else if (t_2 <= 2d-310) then
        tmp = t_1 / t
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y - z);
	double t_2 = t_1 / (t - z);
	double tmp;
	if (t_2 <= -0.0001) {
		tmp = x * (y / (t - z));
	} else if (t_2 <= 2e-310) {
		tmp = t_1 / t;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y - z)
	t_2 = t_1 / (t - z)
	tmp = 0
	if t_2 <= -0.0001:
		tmp = x * (y / (t - z))
	elif t_2 <= 2e-310:
		tmp = t_1 / t
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y - z))
	t_2 = Float64(t_1 / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -0.0001)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t_2 <= 2e-310)
		tmp = Float64(t_1 / t);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y - z);
	t_2 = t_1 / (t - z);
	tmp = 0.0;
	if (t_2 <= -0.0001)
		tmp = x * (y / (t - z));
	elseif (t_2 <= 2e-310)
		tmp = t_1 / t;
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -0.0001], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-310], N[(t$95$1 / t), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -1.00000000000000005e-4

   1. Initial program 72.3%

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

   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 56.0

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

   4. Applied rewrites 56.0%

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

   if -1.00000000000000005e-4 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.999999999999994e-310

   1. Initial program 95.5%

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

   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 58.9%

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

   if 1.999999999999994e-310 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 83.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. 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 96.3

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

   3. Applied rewrites 96.3%

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

   4. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r/ N/A

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

      5. mul-1-neg N/A

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

      6. sub-div N/A

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

      7. mul-1-neg N/A

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

      8. mul-1-neg N/A

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

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

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 56.4

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

   6. Applied rewrites 56.4%

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

   7. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 56.5

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

   9. Applied rewrites 56.5%

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

Alternative 4: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.55e-45) t_1 (if (<= z 1.4e-19) (/ (* x y) (- t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.55e-45) {
		tmp = t_1;
	} else if (z <= 1.4e-19) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-2.55d-45)) then
        tmp = t_1
    else if (z <= 1.4d-19) then
        tmp = (x * y) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.55e-45) {
		tmp = t_1;
	} else if (z <= 1.4e-19) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.55e-45:
		tmp = t_1
	elif z <= 1.4e-19:
		tmp = (x * y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.55e-45)
		tmp = t_1;
	elseif (z <= 1.4e-19)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.55e-45)
		tmp = t_1;
	elseif (z <= 1.4e-19)
		tmp = (x * y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e-45], t$95$1, If[LessEqual[z, 1.4e-19], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e-45 or 1.40000000000000001e-19 < z

   1. Initial program 77.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. 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 99.7

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r/ N/A

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

      5. mul-1-neg N/A

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

      6. sub-div N/A

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

      7. mul-1-neg N/A

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

      8. mul-1-neg N/A

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

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

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 73.8

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

   6. Applied rewrites 73.8%

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

   7. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 73.9

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

   9. Applied rewrites 73.9%

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

   if -2.5499999999999999e-45 < z < 1.40000000000000001e-19

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 77.5%

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

Alternative 5: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 650000000000:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.55e-45)
     t_1
     (if (<= z 650000000000.0) (* x (/ y (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.55e-45) {
		tmp = t_1;
	} else if (z <= 650000000000.0) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-2.55d-45)) then
        tmp = t_1
    else if (z <= 650000000000.0d0) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.55e-45) {
		tmp = t_1;
	} else if (z <= 650000000000.0) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.55e-45:
		tmp = t_1
	elif z <= 650000000000.0:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.55e-45)
		tmp = t_1;
	elseif (z <= 650000000000.0)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.55e-45)
		tmp = t_1;
	elseif (z <= 650000000000.0)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e-45], t$95$1, If[LessEqual[z, 650000000000.0], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e-45 or 6.5e11 < z

   1. Initial program 76.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. 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 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r/ N/A

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

      5. mul-1-neg N/A

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

      6. sub-div N/A

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

      7. mul-1-neg N/A

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

      8. mul-1-neg N/A

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

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

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 74.7

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

   6. Applied rewrites 74.7%

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

   7. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 74.8

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

   9. Applied rewrites 74.8%

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

   if -2.5499999999999999e-45 < z < 6.5e11

   1. Initial program 93.3%

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

   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 77.0

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

   4. Applied rewrites 77.0%

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

Alternative 6: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+74}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e+172) x (if (<= z 1e+74) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+172) {
		tmp = x;
	} else if (z <= 1e+74) {
		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 <= (-2.4d+172)) then
        tmp = x
    else if (z <= 1d+74) 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 <= -2.4e+172) {
		tmp = x;
	} else if (z <= 1e+74) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e+172:
		tmp = x
	elif z <= 1e+74:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e+172)
		tmp = x;
	elseif (z <= 1e+74)
		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 <= -2.4e+172)
		tmp = x;
	elseif (z <= 1e+74)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e+172], x, If[LessEqual[z, 1e+74], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e172 or 9.99999999999999952e73 < z

   1. Initial program 68.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 71.7%

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

   if -2.4000000000000001e172 < z < 9.99999999999999952e73

   1. Initial program 91.3%

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

   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 66.7

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

   4. Applied rewrites 66.7%

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

Alternative 7: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -780000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1800000000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -780000000000.0) x (if (<= z 1800000000000.0) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -780000000000.0) {
		tmp = x;
	} else if (z <= 1800000000000.0) {
		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 <= (-780000000000.0d0)) then
        tmp = x
    else if (z <= 1800000000000.0d0) 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 <= -780000000000.0) {
		tmp = x;
	} else if (z <= 1800000000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -780000000000.0:
		tmp = x
	elif z <= 1800000000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -780000000000.0)
		tmp = x;
	elseif (z <= 1800000000000.0)
		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 <= -780000000000.0)
		tmp = x;
	elseif (z <= 1800000000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -780000000000.0], x, If[LessEqual[z, 1800000000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e11 or 1.8e12 < z

   1. Initial program 74.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 59.8%

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

   if -7.8e11 < z < 1.8e12

   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

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. 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 94.3

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

   3. Applied rewrites 94.3%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 62.7

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

   6. Applied rewrites 62.7%

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

Alternative 8: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -650000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -650000000000.0) x (if (<= z 1.4e-19) (/ (* y x) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -650000000000.0) {
		tmp = x;
	} else if (z <= 1.4e-19) {
		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 <= (-650000000000.0d0)) then
        tmp = x
    else if (z <= 1.4d-19) 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 <= -650000000000.0) {
		tmp = x;
	} else if (z <= 1.4e-19) {
		tmp = (y * x) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -650000000000.0:
		tmp = x
	elif z <= 1.4e-19:
		tmp = (y * x) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -650000000000.0)
		tmp = x;
	elseif (z <= 1.4e-19)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -650000000000.0)
		tmp = x;
	elseif (z <= 1.4e-19)
		tmp = (y * x) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -650000000000.0], x, If[LessEqual[z, 1.4e-19], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e11 or 1.40000000000000001e-19 < z

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 58.5%

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

   if -6.5e11 < z < 1.40000000000000001e-19

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.3

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

   4. Applied rewrites 62.3%

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

Alternative 9: 35.5% accurate, 12.6× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 35.5%

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

Reproduce

herbie shell --seed 2025118 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))