Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 8

Speedup: 1.0×

• 26.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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 * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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 * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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 * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

Alternative 2: 37.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x + y\right) - z}{t \cdot 2} \leq -2 \cdot 10^{-219}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- (+ x y) z) (* t 2.0)) -2e-219) (/ x (+ t t)) (/ y (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x + y) - z) / (t * 2.0)) <= -2e-219) {
		tmp = x / (t + t);
	} else {
		tmp = y / (t + 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) - z) / (t * 2.0d0)) <= (-2d-219)) then
        tmp = x / (t + t)
    else
        tmp = y / (t + 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) - z) / (t * 2.0)) <= -2e-219) {
		tmp = x / (t + t);
	} else {
		tmp = y / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x + y) - z) / (t * 2.0)) <= -2e-219:
		tmp = x / (t + t)
	else:
		tmp = y / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0)) <= -2e-219)
		tmp = Float64(x / Float64(t + t));
	else
		tmp = Float64(y / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((x + y) - z) / (t * 2.0)) <= -2e-219)
		tmp = x / (t + t);
	else
		tmp = y / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], -2e-219], N[(x / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(y / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64))) < -2.0000000000000001e-219

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 38.2%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 38.2

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

   7. Applied rewrites 38.2%

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

   if -2.0000000000000001e-219 < (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64)))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 45.3%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 45.3

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

   7. Applied rewrites 45.3%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 39.3%

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

Alternative 3: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{elif}\;x + y \leq 2000:\\ \;\;\;\;\frac{-z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e+20)
   (/ x (+ t t))
   (if (<= (+ x y) 2000.0) (/ (- z) (+ t t)) (/ y (+ t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e+20) {
		tmp = x / (t + t);
	} else if ((x + y) <= 2000.0) {
		tmp = -z / (t + t);
	} else {
		tmp = y / (t + 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) <= (-5d+20)) then
        tmp = x / (t + t)
    else if ((x + y) <= 2000.0d0) then
        tmp = -z / (t + t)
    else
        tmp = y / (t + 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) <= -5e+20) {
		tmp = x / (t + t);
	} else if ((x + y) <= 2000.0) {
		tmp = -z / (t + t);
	} else {
		tmp = y / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e+20:
		tmp = x / (t + t)
	elif (x + y) <= 2000.0:
		tmp = -z / (t + t)
	else:
		tmp = y / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e+20)
		tmp = Float64(x / Float64(t + t));
	elseif (Float64(x + y) <= 2000.0)
		tmp = Float64(Float64(-z) / Float64(t + t));
	else
		tmp = Float64(y / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e+20)
		tmp = x / (t + t);
	elseif ((x + y) <= 2000.0)
		tmp = -z / (t + t);
	else
		tmp = y / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+20], N[(x / N[(t + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2000.0], N[((-z) / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(y / N[(t + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5e20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 43.0%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 43.0

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

   7. Applied rewrites 43.0%

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

   if -5e20 < (+.f64 x y) < 2e3

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{\color{blue}{-1 \cdot z}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 75.8%

      \[\leadsto \frac{\color{blue}{-z}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-z}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{-z}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 75.8

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

   7. Applied rewrites 75.8%

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

   if 2e3 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.7%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 52.7

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

   7. Applied rewrites 52.7%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 40.3%

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

Alternative 4: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{elif}\;x + y \leq 2000:\\ \;\;\;\;\frac{-0.5}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e+20)
   (/ x (+ t t))
   (if (<= (+ x y) 2000.0) (* (/ -0.5 t) z) (/ y (+ t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e+20) {
		tmp = x / (t + t);
	} else if ((x + y) <= 2000.0) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = y / (t + 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) <= (-5d+20)) then
        tmp = x / (t + t)
    else if ((x + y) <= 2000.0d0) then
        tmp = ((-0.5d0) / t) * z
    else
        tmp = y / (t + 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) <= -5e+20) {
		tmp = x / (t + t);
	} else if ((x + y) <= 2000.0) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = y / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e+20:
		tmp = x / (t + t)
	elif (x + y) <= 2000.0:
		tmp = (-0.5 / t) * z
	else:
		tmp = y / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e+20)
		tmp = Float64(x / Float64(t + t));
	elseif (Float64(x + y) <= 2000.0)
		tmp = Float64(Float64(-0.5 / t) * z);
	else
		tmp = Float64(y / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e+20)
		tmp = x / (t + t);
	elseif ((x + y) <= 2000.0)
		tmp = (-0.5 / t) * z;
	else
		tmp = y / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+20], N[(x / N[(t + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2000.0], N[(N[(-0.5 / t), $MachinePrecision] * z), $MachinePrecision], N[(y / N[(t + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5e20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 43.0%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 43.0

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

   7. Applied rewrites 43.0%

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

   if -5e20 < (+.f64 x y) < 2e3

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

   5. Applied rewrites 75.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 2e3 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.7%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 52.7

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

   7. Applied rewrites 52.7%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 40.3%

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

Alternative 5: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+145} \lor \neg \left(z \leq 4.5 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{-z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.6e+145) (not (<= z 4.5e+100)))
   (/ (- z) (+ t t))
   (/ (+ y x) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+145) || !(z <= 4.5e+100)) {
		tmp = -z / (t + t);
	} else {
		tmp = (y + x) / (t + 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 ((z <= (-8.6d+145)) .or. (.not. (z <= 4.5d+100))) then
        tmp = -z / (t + t)
    else
        tmp = (y + x) / (t + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+145) || !(z <= 4.5e+100)) {
		tmp = -z / (t + t);
	} else {
		tmp = (y + x) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.6e+145) or not (z <= 4.5e+100):
		tmp = -z / (t + t)
	else:
		tmp = (y + x) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.6e+145) || !(z <= 4.5e+100))
		tmp = Float64(Float64(-z) / Float64(t + t));
	else
		tmp = Float64(Float64(y + x) / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.6e+145) || ~((z <= 4.5e+100)))
		tmp = -z / (t + t);
	else
		tmp = (y + x) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.6e+145], N[Not[LessEqual[z, 4.5e+100]], $MachinePrecision]], N[((-z) / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999996e145 or 4.50000000000000036e100 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{\color{blue}{-1 \cdot z}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 74.5%

      \[\leadsto \frac{\color{blue}{-z}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{-z}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{-z}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 74.5

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

   7. Applied rewrites 74.5%

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

   if -8.59999999999999996e145 < z < 4.50000000000000036e100

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 53.4%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 53.4

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

   7. Applied rewrites 53.4%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 86.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+145} \lor \neg \left(z \leq 4.5 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{-z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-215}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-215) (/ (- x z) (+ t t)) (/ (- y z) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-215) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y - z) / (t + 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) <= (-5d-215)) then
        tmp = (x - z) / (t + t)
    else
        tmp = (y - z) / (t + 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) <= -5e-215) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y - z) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e-215:
		tmp = (x - z) / (t + t)
	else:
		tmp = (y - z) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e-215)
		tmp = Float64(Float64(x - z) / Float64(t + t));
	else
		tmp = Float64(Float64(y - z) / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e-215)
		tmp = (x - z) / (t + t);
	else
		tmp = (y - z) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-215], N[(N[(x - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.99999999999999956e-215

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x - z}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x - z}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 71.9

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

   7. Applied rewrites 71.9%

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

   if -4.99999999999999956e-215 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 74.2%

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x - z}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x - z}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 74.2

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

   7. Applied rewrites 74.2%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 61.2%

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

Alternative 7: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2000:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2000.0) (/ (- x z) (+ t t)) (/ (+ y x) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2000.0) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y + x) / (t + 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) <= 2000.0d0) then
        tmp = (x - z) / (t + t)
    else
        tmp = (y + x) / (t + 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) <= 2000.0) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y + x) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2000.0:
		tmp = (x - z) / (t + t)
	else:
		tmp = (y + x) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2000.0)
		tmp = Float64(Float64(x - z) / Float64(t + t));
	else
		tmp = Float64(Float64(y + x) / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2000.0)
		tmp = (x - z) / (t + t);
	else
		tmp = (y + x) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2000.0], N[(N[(x - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 2e3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 76.8%

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x - z}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x - z}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 76.8

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

   7. Applied rewrites 76.8%

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

   if 2e3 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.7%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 52.7

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

   7. Applied rewrites 52.7%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 87.5%

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

Alternative 8: 36.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t + t} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

   \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
4. Step-by-step derivation

5. Applied rewrites 41.8%

   \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{x}{\color{blue}{t \cdot 2}} \]

   2. *-commutative N/A

      \[\leadsto \frac{x}{\color{blue}{2 \cdot t}} \]

   3. count-2-rev N/A

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

   4. lower-+.f64 41.8

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

7. Applied rewrites 41.8%

   \[\leadsto \frac{x}{\color{blue}{t + t}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025018 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))