Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Percentage Accurate: 97.6% → 97.9%

Time: 3.5s

Alternatives: 13

Speedup: 0.6×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 1e+91) (fma (/ x y) (- z t) t) (* (/ (- z t) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 1e+91) {
		tmp = fma((x / y), (z - t), t);
	} else {
		tmp = ((z - t) / y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 1e+91)
		tmp = fma(Float64(x / y), Float64(z - t), t);
	else
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 1e+91], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 1.00000000000000008e91

   1. Initial program 97.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

   if 1.00000000000000008e91 < (/.f64 x y)

   1. Initial program 86.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 99.9

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

   5. Applied rewrites 99.9%

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

Alternative 2: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+29) (not (<= (/ x y) 1.0)))
   (* (/ (- z t) y) x)
   (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+29) || !((x / y) <= 1.0)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+29) || !(Float64(x / y) <= 1.0))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+29], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999983e29 or 1 < (/.f64 x y)

   1. Initial program 92.6%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 92.4

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

   5. Applied rewrites 92.4%

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

   if -1.99999999999999983e29 < (/.f64 x y) < 1

   1. Initial program 97.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 97.9

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

   4. Applied rewrites 97.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 92.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\frac{x}{y} \cdot z + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+38)
   (/ (* (- z t) x) y)
   (if (<= (/ x y) 1.0) (+ (* (/ x y) z) t) (* (/ (- z t) y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+38) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 1.0) {
		tmp = ((x / y) * z) + t;
	} else {
		tmp = ((z - t) / y) * 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 ((x / y) <= (-5d+38)) then
        tmp = ((z - t) * x) / y
    else if ((x / y) <= 1.0d0) then
        tmp = ((x / y) * z) + t
    else
        tmp = ((z - t) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+38) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 1.0) {
		tmp = ((x / y) * z) + t;
	} else {
		tmp = ((z - t) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+38:
		tmp = ((z - t) * x) / y
	elif (x / y) <= 1.0:
		tmp = ((x / y) * z) + t
	else:
		tmp = ((z - t) / y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+38)
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	elseif (Float64(x / y) <= 1.0)
		tmp = Float64(Float64(Float64(x / y) * z) + t);
	else
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+38)
		tmp = ((z - t) * x) / y;
	elseif ((x / y) <= 1.0)
		tmp = ((x / y) * z) + t;
	else
		tmp = ((z - t) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+38], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.0], N[(N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999997e38

   1. Initial program 96.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 86.2

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

   5. Applied rewrites 86.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 96.4

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

   7. Applied rewrites 96.4%

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

   if -4.9999999999999997e38 < (/.f64 x y) < 1

   1. Initial program 97.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 91.1%

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

   if 1 < (/.f64 x y)

   1. Initial program 89.6%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 96.7

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

   5. Applied rewrites 96.7%

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

Alternative 4: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+38)
   (/ (* (- z t) x) y)
   (if (<= (/ x y) 1.0) (fma (/ x y) z t) (* (/ (- z t) y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+38) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 1.0) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = ((z - t) / y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+38)
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	elseif (Float64(x / y) <= 1.0)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+38], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.0], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999997e38

   1. Initial program 96.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 86.2

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

   5. Applied rewrites 86.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 96.4

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

   7. Applied rewrites 96.4%

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

   if -4.9999999999999997e38 < (/.f64 x y) < 1

   1. Initial program 97.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 97.9

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

   4. Applied rewrites 97.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 91.1%

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

   if 1 < (/.f64 x y)

   1. Initial program 89.6%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 96.7

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

   5. Applied rewrites 96.7%

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

Alternative 5: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+173} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+173) (not (<= (/ x y) 5e+33)))
   (* (/ (- t) y) x)
   (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+173) || !((x / y) <= 5e+33)) {
		tmp = (-t / y) * x;
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+173) || !(Float64(x / y) <= 5e+33))
		tmp = Float64(Float64(Float64(-t) / y) * x);
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+173], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+33]], $MachinePrecision]], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000034e173 or 4.99999999999999973e33 < (/.f64 x y)

   1. Initial program 90.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 96.1

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 61.9

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

   8. Applied rewrites 61.9%

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

   if -5.00000000000000034e173 < (/.f64 x y) < 4.99999999999999973e33

   1. Initial program 98.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 86.8%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+173} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+173} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+33}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+173) (not (<= (/ x y) 5e+33)))
   (* (- t) (/ x y))
   (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+173) || !((x / y) <= 5e+33)) {
		tmp = -t * (x / y);
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+173) || !(Float64(x / y) <= 5e+33))
		tmp = Float64(Float64(-t) * Float64(x / y));
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+173], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+33]], $MachinePrecision]], N[((-t) * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000034e173 or 4.99999999999999973e33 < (/.f64 x y)

   1. Initial program 90.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 96.1

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lift-/.f64 60.2

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

   8. Applied rewrites 60.2%

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

   if -5.00000000000000034e173 < (/.f64 x y) < 4.99999999999999973e33

   1. Initial program 98.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 86.8%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+173} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+33}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+173}:\\ \;\;\;\;\frac{\left(-t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+173)
   (/ (* (- t) x) y)
   (if (<= (/ x y) 5e+33) (fma (/ x y) z t) (* (/ (- t) y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+173) {
		tmp = (-t * x) / y;
	} else if ((x / y) <= 5e+33) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = (-t / y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+173)
		tmp = Float64(Float64(Float64(-t) * x) / y);
	elseif (Float64(x / y) <= 5e+33)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = Float64(Float64(Float64(-t) / y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+173], N[(N[((-t) * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+33], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000034e173

   1. Initial program 93.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 70.4

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

   8. Applied rewrites 70.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 70.7

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

   10. Applied rewrites 70.7%

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

   if -5.00000000000000034e173 < (/.f64 x y) < 4.99999999999999973e33

   1. Initial program 98.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 86.8%

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

   if 4.99999999999999973e33 < (/.f64 x y)

   1. Initial program 89.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 97.1

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

   5. Applied rewrites 97.1%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 58.2

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

   8. Applied rewrites 58.2%

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

Alternative 8: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-78} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-78) (not (<= (/ x y) 2e-5))) (* z (/ x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-78) || !((x / y) <= 2e-5)) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	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 (((x / y) <= (-1d-78)) .or. (.not. ((x / y) <= 2d-5))) then
        tmp = z * (x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-78) || !((x / y) <= 2e-5)) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-78) or not ((x / y) <= 2e-5):
		tmp = z * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-78) || !(Float64(x / y) <= 2e-5))
		tmp = Float64(z * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-78) || ~(((x / y) <= 2e-5)))
		tmp = z * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-78], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-5]], $MachinePrecision]], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999999e-79 or 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 93.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. sub-div N/A

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

      7. *-commutative N/A

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

      8. frac-sub N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lower-*.f64 61.8

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

   4. Applied rewrites 61.8%

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

   5. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 43.1

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

   7. Applied rewrites 43.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 45.4

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

   9. Applied rewrites 45.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lift-/.f64 50.2

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

   11. Applied rewrites 50.2%

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

   if -9.99999999999999999e-79 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 97.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 79.9%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-78} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-78} \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-78) (not (<= (/ x y) 1.0))) (* (/ z y) x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-78) || !((x / y) <= 1.0)) {
		tmp = (z / y) * x;
	} else {
		tmp = t;
	}
	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 (((x / y) <= (-1d-78)) .or. (.not. ((x / y) <= 1.0d0))) then
        tmp = (z / y) * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-78) || !((x / y) <= 1.0)) {
		tmp = (z / y) * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-78) or not ((x / y) <= 1.0):
		tmp = (z / y) * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-78) || !(Float64(x / y) <= 1.0))
		tmp = Float64(Float64(z / y) * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-78) || ~(((x / y) <= 1.0)))
		tmp = (z / y) * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-78], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999999e-79 or 1 < (/.f64 x y)

   1. Initial program 93.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 43.6

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

   5. Applied rewrites 43.6%

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

   if -9.99999999999999999e-79 < (/.f64 x y) < 1

   1. Initial program 97.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 78.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-78} \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e-78) (* z (/ x y)) (if (<= (/ x y) 2e-5) t (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-78) {
		tmp = z * (x / y);
	} else if ((x / y) <= 2e-5) {
		tmp = t;
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1d-78)) then
        tmp = z * (x / y)
    else if ((x / y) <= 2d-5) then
        tmp = t
    else
        tmp = (z * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-78) {
		tmp = z * (x / y);
	} else if ((x / y) <= 2e-5) {
		tmp = t;
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e-78:
		tmp = z * (x / y)
	elif (x / y) <= 2e-5:
		tmp = t
	else:
		tmp = (z * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e-78)
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= 2e-5)
		tmp = t;
	else
		tmp = Float64(Float64(z * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e-78)
		tmp = z * (x / y);
	elseif ((x / y) <= 2e-5)
		tmp = t;
	else
		tmp = (z * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e-78], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-5], t, N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.99999999999999999e-79

   1. Initial program 97.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. sub-div N/A

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

      7. *-commutative N/A

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

      8. frac-sub N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lower-*.f64 53.1

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 45.2

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

   7. Applied rewrites 45.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 47.4

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

   9. Applied rewrites 47.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lift-/.f64 56.7

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

   11. Applied rewrites 56.7%

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

   if -9.99999999999999999e-79 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 97.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 79.9%

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

   if 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 89.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. sub-div N/A

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

      7. *-commutative N/A

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

      8. frac-sub N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lower-*.f64 71.3

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 40.7

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

   7. Applied rewrites 40.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 43.1

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

   9. Applied rewrites 43.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+25} \lor \neg \left(t \leq 8.8 \cdot 10^{-84}\right):\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.2e+25) (not (<= t 8.8e-84)))
   (* (- 1.0 (/ x y)) t)
   (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+25) || !(t <= 8.8e-84)) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.2e+25) || !(t <= 8.8e-84))
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.2e+25], N[Not[LessEqual[t, 8.8e-84]], $MachinePrecision]], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1999999999999998e25 or 8.7999999999999996e-84 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-lft-identity N/A

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

      5. distribute-rgt-in N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

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

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. lower--.f64 N/A

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

      12. lift-/.f64 85.7

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

   5. Applied rewrites 85.7%

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

   if -4.1999999999999998e25 < t < 8.7999999999999996e-84

   1. Initial program 89.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 89.8

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

   4. Applied rewrites 89.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 84.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+25} \lor \neg \left(t \leq 8.8 \cdot 10^{-84}\right):\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.2%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lower-fma.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. lift--.f64 95.2

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

4. Applied rewrites 95.2%

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

5. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
6. Step-by-step derivation

7. Applied rewrites 70.7%

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{z}, t\right) \]
8. Add Preprocessing

Alternative 13: 38.0% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.2%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Applied rewrites 34.6%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 97.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025051 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

  (+ (* (/ x y) (- z t)) t))