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

Percentage Accurate: 99.9% → 99.9%

Time: 4.9s

Alternatives: 8

Speedup: 1.0×

• 26.5% 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: 99.9% 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: 99.9% 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: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x + y\right) - z}{t \cdot 2} \leq -5 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- (+ x y) z) (* t 2.0)) -5e-238) (/ 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)) <= -5e-238) {
		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)) <= (-5d-238)) 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)) <= -5e-238) {
		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)) <= -5e-238:
		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)) <= -5e-238)
		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)) <= -5e-238)
		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], -5e-238], 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))) < -5e-238

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 37.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 37.7

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

   7. Applied rewrites 37.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 37.6%

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

   if -5e-238 < (/.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 y around inf

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

   5. Applied rewrites 39.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 39.1

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

   7. Applied rewrites 39.1%

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

Alternative 3: 46.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{elif}\;x + y \leq 10^{-63}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -2e-76)
   (/ x (+ t t))
   (if (<= (+ x y) 1e-63) (/ (* -0.5 z) t) (/ y (+ t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -2e-76) {
		tmp = x / (t + t);
	} else if ((x + y) <= 1e-63) {
		tmp = (-0.5 * z) / 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) <= (-2d-76)) then
        tmp = x / (t + t)
    else if ((x + y) <= 1d-63) then
        tmp = ((-0.5d0) * z) / 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) <= -2e-76) {
		tmp = x / (t + t);
	} else if ((x + y) <= 1e-63) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = y / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -2e-76:
		tmp = x / (t + t)
	elif (x + y) <= 1e-63:
		tmp = (-0.5 * z) / t
	else:
		tmp = y / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -2e-76)
		tmp = Float64(x / Float64(t + t));
	elseif (Float64(x + y) <= 1e-63)
		tmp = Float64(Float64(-0.5 * z) / 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) <= -2e-76)
		tmp = x / (t + t);
	elseif ((x + y) <= 1e-63)
		tmp = (-0.5 * z) / t;
	else
		tmp = y / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e-76], N[(x / N[(t + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e-63], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(y / N[(t + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.99999999999999985e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 44.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 44.4

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

   7. Applied rewrites 44.4%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 41.6%

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

   if -1.99999999999999985e-76 < (+.f64 x y) < 1.00000000000000007e-63

   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 78.9%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 79.1%

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

   if 1.00000000000000007e-63 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 41.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 41.8

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

   7. Applied rewrites 41.8%

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

Alternative 4: 46.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{elif}\;x + y \leq 10^{-63}:\\ \;\;\;\;\frac{-0.5}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -2e-76)
   (/ x (+ t t))
   (if (<= (+ x y) 1e-63) (* (/ -0.5 t) z) (/ y (+ t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -2e-76) {
		tmp = x / (t + t);
	} else if ((x + y) <= 1e-63) {
		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) <= (-2d-76)) then
        tmp = x / (t + t)
    else if ((x + y) <= 1d-63) 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) <= -2e-76) {
		tmp = x / (t + t);
	} else if ((x + y) <= 1e-63) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = y / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -2e-76:
		tmp = x / (t + t)
	elif (x + y) <= 1e-63:
		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) <= -2e-76)
		tmp = Float64(x / Float64(t + t));
	elseif (Float64(x + y) <= 1e-63)
		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) <= -2e-76)
		tmp = x / (t + t);
	elseif ((x + y) <= 1e-63)
		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], -2e-76], N[(x / N[(t + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e-63], 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) < -1.99999999999999985e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 44.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 44.4

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

   7. Applied rewrites 44.4%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 41.6%

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

   if -1.99999999999999985e-76 < (+.f64 x y) < 1.00000000000000007e-63

   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 78.9%

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

   if 1.00000000000000007e-63 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 41.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 41.8

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

   7. Applied rewrites 41.8%

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

Alternative 5: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+84} \lor \neg \left(z \leq 1.05 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+84) (not (<= z 1.05e+53)))
   (/ (- x z) (+ t t))
   (/ (+ y x) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+84) || !(z <= 1.05e+53)) {
		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 ((z <= (-2.2d+84)) .or. (.not. (z <= 1.05d+53))) 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 ((z <= -2.2e+84) || !(z <= 1.05e+53)) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y + x) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+84) or not (z <= 1.05e+53):
		tmp = (x - z) / (t + t)
	else:
		tmp = (y + x) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+84) || !(z <= 1.05e+53))
		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 ((z <= -2.2e+84) || ~((z <= 1.05e+53)))
		tmp = (x - z) / (t + t);
	else
		tmp = (y + x) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+84], N[Not[LessEqual[z, 1.05e+53]], $MachinePrecision]], 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 z < -2.1999999999999998e84 or 1.0500000000000001e53 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 19.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 19.0

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

   7. Applied rewrites 19.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 86.9%

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

   if -2.1999999999999998e84 < z < 1.0500000000000001e53

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 94.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 94.1

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

   7. Applied rewrites 94.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+84} \lor \neg \left(z \leq 1.05 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+86} \lor \neg \left(z \leq 1.65 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e+86) (not (<= z 1.65e+59)))
   (/ (* -0.5 z) t)
   (/ (+ y x) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+86) || !(z <= 1.65e+59)) {
		tmp = (-0.5 * z) / 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 <= (-5.2d+86)) .or. (.not. (z <= 1.65d+59))) then
        tmp = ((-0.5d0) * z) / 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 <= -5.2e+86) || !(z <= 1.65e+59)) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = (y + x) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e+86) or not (z <= 1.65e+59):
		tmp = (-0.5 * z) / t
	else:
		tmp = (y + x) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e+86) || !(z <= 1.65e+59))
		tmp = Float64(Float64(-0.5 * z) / 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 <= -5.2e+86) || ~((z <= 1.65e+59)))
		tmp = (-0.5 * z) / t;
	else
		tmp = (y + x) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e+86], N[Not[LessEqual[z, 1.65e+59]], $MachinePrecision]], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999995e86 or 1.65e59 < 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

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

   5. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.7%

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

   if -5.1999999999999995e86 < z < 1.65e59

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 94.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 94.1

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

   7. Applied rewrites 94.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+86} \lor \neg \left(z \leq 1.65 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-170) (/ (- 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-170) {
		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-170)) 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-170) {
		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-170:
		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-170)
		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-170)
		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-170], 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) < -5.0000000000000001e-170

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 40.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 40.5

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

   7. Applied rewrites 40.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 62.5%

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

   if -5.0000000000000001e-170 < (+.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 0

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

   5. Applied rewrites 70.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 70.9

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

   7. Applied rewrites 70.9%

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

Alternative 8: 37.5% 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 y around inf

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

5. Applied rewrites 38.4%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. count-2-rev N/A

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

   4. lower-+.f64 38.4

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

7. Applied rewrites 38.4%

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

8. Taylor expanded in x around inf

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

10. Applied rewrites 37.2%

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

Reproduce

herbie shell --seed 2025019 
(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)))