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

Percentage Accurate: 99.9% → 99.9%

Time: 2.6s

Alternatives: 7

Speedup: 1.0×

• 26.0% 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 99.9%

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

Alternative 2: 46.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{elif}\;x + y \leq 10^{-29}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -2e-112)
   (/ x (+ t t))
   (if (<= (+ x y) 1e-29) (* -0.5 (/ z t)) (/ y (+ t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -2e-112) {
		tmp = x / (t + t);
	} else if ((x + y) <= 1e-29) {
		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-112)) then
        tmp = x / (t + t)
    else if ((x + y) <= 1d-29) 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-112) {
		tmp = x / (t + t);
	} else if ((x + y) <= 1e-29) {
		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-112:
		tmp = x / (t + t)
	elif (x + y) <= 1e-29:
		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-112)
		tmp = Float64(x / Float64(t + t));
	elseif (Float64(x + y) <= 1e-29)
		tmp = Float64(-0.5 * Float64(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-112)
		tmp = x / (t + t);
	elseif ((x + y) <= 1e-29)
		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-112], N[(x / N[(t + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e-29], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(y / N[(t + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.9999999999999999e-112

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x \cdot \left(\left(1 + \frac{y}{x}\right) - \frac{z}{x}\right)}}{t \cdot 2} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(1 + \frac{y}{x}\right) - \frac{z}{x}\right) \cdot \color{blue}{x}}{t \cdot 2} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(1 + \frac{y}{x}\right) - \frac{z}{x}\right) \cdot \color{blue}{x}}{t \cdot 2} \]

      3. associate--l+ N/A

         \[\leadsto \frac{\left(1 + \left(\frac{y}{x} - \frac{z}{x}\right)\right) \cdot x}{t \cdot 2} \]

      4. div-sub N/A

         \[\leadsto \frac{\left(1 + \frac{y - z}{x}\right) \cdot x}{t \cdot 2} \]

      5. +-commutative N/A

         \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      7. *-lft-identity N/A

         \[\leadsto \frac{\left(\frac{y - 1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

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

         \[\leadsto \frac{\left(\frac{y + \left(\mathsf{neg}\left(1\right)\right) \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{y + -1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{y + -1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

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

          \[\leadsto \frac{\left(\frac{y - \left(\mathsf{neg}\left(-1\right)\right) \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      12. metadata-eval N/A

          \[\leadsto \frac{\left(\frac{y - 1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      13. *-lft-identity N/A

          \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      14. lower--.f64 87.9

          \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

   4. Applied rewrites 87.9%

      \[\leadsto \frac{\color{blue}{\left(\frac{y - z}{x} + 1\right) \cdot x}}{t \cdot 2} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 39.3%

      \[\leadsto \frac{x}{t \cdot 2} \]
   8. 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. lift-+.f64 39.3

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

   9. Applied rewrites 39.3%

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

   if -1.9999999999999999e-112 < (+.f64 x y) < 9.99999999999999943e-30

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\frac{z}{t}} \]

      2. lower-/.f64 77.1

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

   4. Applied rewrites 77.1%

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

   if 9.99999999999999943e-30 < (+.f64 x y)

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 40.5%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
   5. 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

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

   6. Applied rewrites 40.5%

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

Alternative 3: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (/ z t))))
   (if (<= z -9.5e+181) t_1 (if (<= z 1.3e+180) (/ (+ y x) (+ t t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double tmp;
	if (z <= -9.5e+181) {
		tmp = t_1;
	} else if (z <= 1.3e+180) {
		tmp = (y + x) / (t + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-0.5d0) * (z / t)
    if (z <= (-9.5d+181)) then
        tmp = t_1
    else if (z <= 1.3d+180) then
        tmp = (y + x) / (t + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double tmp;
	if (z <= -9.5e+181) {
		tmp = t_1;
	} else if (z <= 1.3e+180) {
		tmp = (y + x) / (t + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (z / t)
	tmp = 0
	if z <= -9.5e+181:
		tmp = t_1
	elif z <= 1.3e+180:
		tmp = (y + x) / (t + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(z / t))
	tmp = 0.0
	if (z <= -9.5e+181)
		tmp = t_1;
	elseif (z <= 1.3e+180)
		tmp = Float64(Float64(y + x) / Float64(t + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (z / t);
	tmp = 0.0;
	if (z <= -9.5e+181)
		tmp = t_1;
	elseif (z <= 1.3e+180)
		tmp = (y + x) / (t + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+181], t$95$1, If[LessEqual[z, 1.3e+180], N[(N[(y + x), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000032e181 or 1.3000000000000001e180 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\frac{z}{t}} \]

      2. lower-/.f64 82.6

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

   4. Applied rewrites 82.6%

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

   if -9.50000000000000032e181 < z < 1.3000000000000001e180

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.6

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

   4. Applied rewrites 79.6%

      \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]
   5. 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. lift-+.f64 79.6

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

   6. Applied rewrites 79.6%

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

Alternative 4: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - z \leq -1 \cdot 10^{-135}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (+ x y) z) -1e-135) (/ (- x z) (+ t t)) (/ (+ y x) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + y) - z) <= -1e-135) {
		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) - z) <= (-1d-135)) 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) - z) <= -1e-135) {
		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) - z) <= -1e-135:
		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(Float64(x + y) - z) <= -1e-135)
		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) - z) <= -1e-135)
		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[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], -1e-135], 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 (+.f64 x y) z) < -1e-135

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 69.1%

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   5. 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 69.1

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

   6. Applied rewrites 69.1%

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

   if -1e-135 < (-.f64 (+.f64 x y) z)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 68.8

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

   4. Applied rewrites 68.8%

      \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]
   5. 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. lift-+.f64 68.8

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

   6. Applied rewrites 68.8%

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

Alternative 5: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-145}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-145) (/ (- 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-145) {
		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-145)) 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-145) {
		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-145:
		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-145)
		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-145)
		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-145], 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) < -4.9999999999999998e-145

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 67.2%

      \[\leadsto \frac{\color{blue}{x} - z}{t \cdot 2} \]
   5. 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 67.2

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

   6. Applied rewrites 67.2%

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

   if -4.9999999999999998e-145 < (+.f64 x y)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x \cdot \left(1 + \frac{y}{x}\right)} - z}{t \cdot 2} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{x \cdot \left(\frac{y}{x} + \color{blue}{1}\right) - z}{t \cdot 2} \]

      2. distribute-rgt-in N/A

         \[\leadsto \frac{\left(\frac{y}{x} \cdot x + \color{blue}{1 \cdot x}\right) - z}{t \cdot 2} \]

      3. *-lft-identity N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y}{x}, \color{blue}{x}, x\right) - z}{t \cdot 2} \]

      5. lower-/.f64 92.5

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y}{x}, x, x\right) - z}{t \cdot 2} \]

   4. Applied rewrites 92.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{y}{x}, x, x\right)} - z}{t \cdot 2} \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 70.7%

      \[\leadsto \frac{y - z}{t \cdot 2} \]
   8. 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. lift-+.f64 70.7

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

   9. Applied rewrites 70.7%

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

Alternative 6: 37.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - z \leq -5 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (+ x y) z) -5e-145) (/ x (+ t t)) (/ y (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + y) - z) <= -5e-145) {
		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) <= (-5d-145)) 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) <= -5e-145) {
		tmp = x / (t + t);
	} else {
		tmp = y / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + y) - z) <= -5e-145:
		tmp = x / (t + t)
	else:
		tmp = y / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x + y) - z) <= -5e-145)
		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) <= -5e-145)
		tmp = x / (t + t);
	else
		tmp = y / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], -5e-145], 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 x y) z) < -4.9999999999999998e-145

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x \cdot \left(\left(1 + \frac{y}{x}\right) - \frac{z}{x}\right)}}{t \cdot 2} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(1 + \frac{y}{x}\right) - \frac{z}{x}\right) \cdot \color{blue}{x}}{t \cdot 2} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(1 + \frac{y}{x}\right) - \frac{z}{x}\right) \cdot \color{blue}{x}}{t \cdot 2} \]

      3. associate--l+ N/A

         \[\leadsto \frac{\left(1 + \left(\frac{y}{x} - \frac{z}{x}\right)\right) \cdot x}{t \cdot 2} \]

      4. div-sub N/A

         \[\leadsto \frac{\left(1 + \frac{y - z}{x}\right) \cdot x}{t \cdot 2} \]

      5. +-commutative N/A

         \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      7. *-lft-identity N/A

         \[\leadsto \frac{\left(\frac{y - 1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

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

         \[\leadsto \frac{\left(\frac{y + \left(\mathsf{neg}\left(1\right)\right) \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{y + -1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{y + -1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

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

          \[\leadsto \frac{\left(\frac{y - \left(\mathsf{neg}\left(-1\right)\right) \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      12. metadata-eval N/A

          \[\leadsto \frac{\left(\frac{y - 1 \cdot z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      13. *-lft-identity N/A

          \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

      14. lower--.f64 86.4

          \[\leadsto \frac{\left(\frac{y - z}{x} + 1\right) \cdot x}{t \cdot 2} \]

   4. Applied rewrites 86.4%

      \[\leadsto \frac{\color{blue}{\left(\frac{y - z}{x} + 1\right) \cdot x}}{t \cdot 2} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 37.0%

      \[\leadsto \frac{x}{t \cdot 2} \]
   8. 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. lift-+.f64 37.0

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

   9. Applied rewrites 37.0%

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

   if -4.9999999999999998e-145 < (-.f64 (+.f64 x y) z)

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 37.3%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
   5. 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 37.3

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

   6. Applied rewrites 37.3%

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

Alternative 7: 37.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around inf

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

4. Applied rewrites 37.0%

   \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
5. 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 37.0

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

6. Applied rewrites 37.0%

   \[\leadsto \frac{y}{\color{blue}{t + t}} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025093 
(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)))